A cardboard box manufacturing company is building boxes with length represented by x+ 1, width by 5- x, and height by x -1. The volume of the box is modeled by the function below V(x) 18 14 10 6 24 X 5 6 2 2 3 -2 -6 Over which interval is the volume of the box changing at the fastest average rate? [1,2] A. [1,3.5 B. C. [1,5] r0,3.51 D
Answers
Answer:
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
b. [1,3.5]
[tex] m =\frac{17-0}{3.5-1}=6.8[/tex]
c. [1,5]
[tex] m =\frac{0-0}{5-1}=0[/tex]
d. [0,3.5]
[tex] m =\frac{17-(-5)}{3.5-0}=6.29[/tex]
So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
Step-by-step explanation:
Assuming that we have the figure attached for the function. For this case we just need to quantify the slope given by:
[tex] m = \frac{\Delta y}{\Delta x}[/tex]
For each interval and the greatest slope would be the interval on which the volume of the box is changing at the fastest average rate
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
b. [1,3.5]
[tex] m =\frac{17-0}{3.5-1}=6.8[/tex]
c. [1,5]
[tex] m =\frac{0-0}{5-1}=0[/tex]
d. [0,3.5]
[tex] m =\frac{17-(-5)}{3.5-0}=6.29[/tex]
So then we can conclude that the highest slope is for the interval [1,2] and that would be our solution for the fastest average rate.
a. [1,2]
[tex] m= \frac{9-0}{2-1}=9[/tex]
The correct answer is A. [1,2].
To determine over which interval the volume of the box changes at the fastest average rate, we need to find the average rate of change of the volume function ( V(x) ) over the given intervals and compare them.
The volume ( V(x) ) of the box is given by:
[tex]\[ V(x) = (x + 1)(5 - x)(x - 1) \][/tex]
We first need to express ( V(x) ) in a simplified form. Let's expand the expression:
[tex]\[ V(x) = (x + 1)(5 - x)(x - 1) \]\[ V(x) = (x + 1)(x^2 - 6x + 5) \]\[ V(x) = x(x^2 - 6x + 5) + 1(x^2 - 6x + 5) \]\[ V(x) = x^3 - 6x^2 + 5x + x^2 - 6x + 5 \]\[ V(x) = x^3 - 5x^2 - x + 5 \][/tex]
Now, we calculate the average rate of change over each interval. The average rate of change of ( V(x) ) over an interval ([a, b]) is given by:
[tex]\[ \text{Average Rate of Change} = \frac{V(b) - V(a)}{b - a} \][/tex]
We need to compute this for each interval provided.
1. Interval [1, 2]:
[tex]\[ V(1) = (1 + 1)(5 - 1)(1 - 1) = 0 \]\[ V(2) = (2 + 1)(5 - 2)(2 - 1) = 3 \times 3 \times 1 = 9 \]\[ \text{Average Rate of Change} = \frac{V(2) - V(1)}{2 - 1} = \frac{9 - 0}{2 - 1} = 9 \][/tex]
2. Interval [1, 3.5]:
[tex]\[ V(1) = 0 \]\[ V(3.5) = (3.5 + 1)(5 - 3.5)(3.5 - 1) = 4.5 \times 1.5 \times 2.5 = 16.875 \]\[ \text{Average Rate of Change} = \frac{V(3.5) - V(1)}{3.5 - 1} = \frac{16.875 - 0}{3.5 - 1} = \frac{16.875}{2.5} = 6.75 \][/tex]
3. Interval [1, 5]:
[tex]\[ V(1) = 0 \]\[ V(5) = (5 + 1)(5 - 5)(5 - 1) = 6 \times 0 \times 4 = 0 \]\[ \text{Average Rate of Change} = \frac{V(5) - V(1)}{5 - 1} = \frac{0 - 0}{5 - 1} = 0 \][/tex]
4. Interval [0, 3.5]:
[tex]\[ V(0) = (0 + 1)(5 - 0)(0 - 1) = 1 \times 5 \times -1 = -5 \]\[ V(3.5) = 16.875 \]\[ \text{Average Rate of Change} = \frac{V(3.5) - V(0)}{3.5 - 0} = \frac{16.875 - (-5)}{3.5 - 0} = \frac{16.875 + 5}{3.5} = \frac{21.875}{3.5} \approx 6.25 \][/tex]
Comparing these average rates of change:
[tex]\([1, 2]\): 9\\ \([1, 3.5]\): 6.75\\ \([1, 5]\): 0\\ \([0, 3.5]\): 6.25[/tex]
The interval where the volume of the box is changing at the fastest average rate is [tex]\([1, 2]\)[/tex], with an average rate of change of 9.
Therefore, the correct answer is: A.[tex]\([1, 2]\)[/tex].
Complete question :
Related Questions
Let random variable SS represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable SS.
Answers
Answer:
5. No, the distribution is skewed to the left with a mean age greater than 36.
Step-by-step explanation:
The problem is presented in the photo below. It says the following:
Let random variable S represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable S. Alfonso claims that the distribution of S is symmetric with a mean age of 36. Does the histogram supports Alfonso's claim.
Yes, the distribution is symmetric with a mean age of 36. No, the distribution is skewed to the right with a mean age of 36.No, the distribution is skewed to the right with a mean age greater than 36.No, the distribution is skewed to the left with a mean age of 36.No, the distribution is skewed to the left with a mean age greater than 36.Consider the given histogram at the photo below. it is an left-skew histogram , since it has a long tail to the left side.
We need to estimate the mean of the given data. To do so, we need to multiply each class midpoint with its probability, and sum them.
For example, for the first one, the midpoint is 32 and the probability is 0.03 (read the value on the y-axis). For, the second one, the midpoint is 33 and the probability is 0.04, for the third the midpoint is 34 and the probability is 0.05, and so on. All needed values are presented below.
midpoint = 32, probability= 0.03 midpoint = 33, probability = 0.04 midpoint = 34, probability = 0.05midpoint = 35, probability = 0.1midpoint = 36, probability =0.11midpoint = 37, probability = 0.13midpoint = 38, probability = 0.2midpoint = 39, probability = 0.09Therefore, we obtain
[tex]\mu = 0.03 \cdot 32 + 0.04 \cdot 33 + 0.05\cdot 34 + 0.10 \cdot 35 + 0.11 \cdot 36 + 0.13 \cdot 37 + 0.25 \cdot 38 + 0.20 \cdot 39 + 0.09 \cdot 40[/tex]
which yields
[tex]\mu = 37.15[/tex]
Therefore, this histogram is left-skewed with mean greater than 36.
The distribution of the IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15. According to the standard deviation rule, only 0.15% of people have an IQ over what score?
Answers
Answer:
[tex]a=100 +2.97*15=144.55[/tex]
So the value of height that separates the bottom 99.85% of data from the top 0.5% is 144.55.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the IQ of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(100,15)[/tex]
Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.0015[/tex] (a)
[tex]P(X<a)=0.9985[/tex] (b)
Since we want the 0.15% of the people in the right tail since says above.
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.9985 of the area on the left and 0.0015 of the area on the right it's z=2.97. On this case P(Z<2.97)=0.9985 and P(z>2.97)=0.0015
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.99985[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.9985[/tex]
But we know which value of z satisfy the previous equation so then we can do this:
[tex]z=2.97=\frac{a-100}{15}[/tex]
And if we solve for a we got
[tex]a=100 +2.97*15=144.55[/tex]
So the value of height that separates the bottom 99.85% of data from the top 0.5% is 144.55.
The IQ score that only approximately 0.15% of people surpass, under the given conditions, is 145. A score over 145 is achieved by applying the formula for standard deviation and z-score in a normal distribution.
Explanation:The distribution of IQ scores is approximately normal with a mean of 100 and a standard deviation of 15. When we say 0.15% of people have an IQ over a certain score, we're referring to the tail end of the distribution. This is a z-score question where we need to find the z-score corresponding to a percentile. With 0.15% in the tail, we have 99.85% below this value.
Using a z-score table or a calculator, the z-score for 99.85% is approximately 3. Below to calculate the IQ score, we use the formula:
IQ = mean + z*(standard deviation)
Substituting the values:
IQ = 100 + 3*15 = 145
Therefore, only about 0.15% of people have an IQ over 145.
Learn more about Normal Distribution here:https://brainly.com/question/30390016
#SPJ3
A proper rectangle has a lengh of 6 inches and a with of 8 inches. A square with a side lenght of 3 inches was cut of it. What is the area of the remaining paper?
Answers
Final answer:
To find the remaining area after cutting a 3-inch square from a 6x8 rectangle, subtract the area of the square (9 square inches) from the area of the rectangle (48 square inches), resulting in 39 square inches left.
Explanation:
Calculating the Remaining Area of a Rectangle
To determine the area of the remaining paper after a square is cut off, we must first know the area of the initial rectangle and the area of the square that was removed. The area of the rectangle is found by multiplying its length by its width. Rectangle area = length × width, so it is 6 inches × 8 inches = 48 square inches. The cut-off square has a side length of 3 inches, so its area is 3 inches × 3 inches = 9 square inches.
Subtract the area of the square from the area of the rectangle to get the remaining paper area. Remaining area = rectangle area - square area, which equals 48 square inches - 9 square inches = 39 square inches.
In the first 2 hours after Meadow's self-service laundry opens, m large washing machines and n small washing machines are in continual use. Including the time for filling and emptying the washing machines, each load of laundry takes 30 minutes in a large washing machine and 20 minutes in a small washing machine. What is the total number of loads of laundry done at Meadow's self-service laundry during this 2-hour period?
Answers
Answer:
Nt=10 (m=4,n=6)
Step-by-step explanation:
we have that m = amount of time used by the large washing machine to wash a load of clothes and n = amount of time used by the small washing machine to wash a load of clothes, so
[tex]m=\frac{Tt}{Tpm}=\frac{2h}{\frac{1h}{2}}=4\\n=\frac{Tt}{Tpn}=\frac{2h}{\frac{1h}{3}}=6[/tex]
Nt=m+n=10
where Tt = time frame, Tpm= m' time frame, Tpn = n' time frame and Nt = total number of charges
Answer: Total laundry done in 2hours=110
Step-by-step explanation:
Let m be large washing machines
Let n be small washing machines
Load of laundry for large machine=30mins
Load of laundry in small machine=20 mins
2 hours laundry =2×60=120mins
For m in 2hrs=120/30=4
For n in 2hrs=120/20=6
m loads in 2hrs=4m
n loads in 2hrs=6n
1st statement:n=3m
Substituting
4m+6(3)=x
4m+18m=x
X=22m
Value of m cannot be determined because statement 1 is insufficient
From the 2nd statement: 2m+3n=55
Multiply both sides by2
4m+6n=110
Use properties of rational exponents to simplify the expression. Assume that all variables represent positive numbers. Superscript 1 divided by 3.
Answers
Hi, your question was incomplete hence I have attached the complete version of the question below.
Answer:
5x^3 y^2
Step-by-step explanation:
Using the property of the product of the exponents on the base and removing the parentheses,
(125x^9y^6)^(1/3) = (125)^(1/3) * (x^9)^(1/3) * (y^6)^(1/3)
= (125)^(1/3) * (x)^9*(1/3) * (y)^6*(1/3)
= 5 * (x)^3 * (y)^2
= 5 x^3 y^2
hence the required result is 5 x^3 y^2
Mary is ironing shirts for her father. He pays her 50¢ for the first shirt and increases her pay by 25¢ per shirt. How many shirts will she have iron to earn $5.00?
Answers
Answer: The answer is 7shirts
Step-by-step explanation:
100¢ = $1
$5 * 100 = 500¢
First shirt = 50¢
500¢-50¢ = 450¢
Pay increase to 75¢ after the first shirt.
Number of shirts ironed for 450¢ = 450/75 = 6shirts
Therefore, 6shirts for 450¢ and 1 shirt for 50¢ total 7 shirts for 500¢ = $5
Ana Participated in each charity walk she raise $.25 and each 1/2 That she walked the first day and I walked 11 miles a second day she walked 14 miles how much money did she raise
Answers
Question:
Ana participated in a charity walk. She raised $0.25 for each 1/2 mile that she walked.The first day Ana walked 11 miles.The second day, she walked 14 miles.How much money did Ana raised?
Answer:
Ana raised $ 12.5
Solution:
From given question,
First day walk = 11 miles
Second day walk = 14 miles
Let us first calculate the total distance she walked
Total distance = first day walk + second day walk
Total distance = 11 + 14 = 25 miles
Thus she walked for 25 miles
Given that,
She raised $0.25 for each 1/2 mile that she walked
[tex]\frac{1}{2} \text{ mile} = 0.25 \text{ dollars }[/tex]
Therefore, for 1 mile we get,
[tex]\frac{1}{2} \times 2 \text{ mile} = 0.25 \times 2 \text{ dollars }\\\\1 \text{ mile } = 0.5 \text{ dollars }[/tex]
Now calculate for 25 miles
[tex]25 \text{ mile } = 25 \times 0.5 = 12.5 \text{ dollars }[/tex]
Thus she raised $ 12.5
When driving to Grandma's house, I drive on the highway for 5 hours at 50 mph, then through a large city for 2 hours at 20 mph, then on a county road for 5 hours at 35 mph. What is my mean speed for the entire trip? Round your answer to one decimal place.
Answers
Final answer:
To find the mean speed for the entire trip, calculate the total distance traveled (465 miles) and the total time spent (12 hours). The mean speed is then determined to be 38.8 mph when rounded to one decimal place.
Explanation:
To find the mean speed for the entire trip, we need to first calculate the total distance traveled and the total time spent driving. This can then be used to calculate the mean speed using the formula: Mean Speed = Total Distance / Total Time.
On the highway: 5 hours at 50 mph = 250 miles
Through the city: 2 hours at 20 mph = 40 miles
On a county road: 5 hours at 35 mph = 175 miles
The total distance traveled is 250 miles + 40 miles + 175 miles = 465 miles. The total time spent driving is 5 hours + 2 hours + 5 hours = 12 hours.
Thus, the mean speed for the entire trip is 465 miles / 12 hours = 38.75 mph. Rounded to one decimal place, the mean speed is 38.8 mph.
Solve the system using elimination.
x plus 7 y
equals
22
4 x minus 7 y
equals
negative 17
The solution is
nothing.
(Simplify your answer. Type an ordered pair.)
Answers
Answer:
After simplifying we get (x,y) as (1,3).
Step-by-step explanation:
Given:
[tex]x+7y=22[/tex],
[tex]x-7y=-17[/tex]
We need to use elimination method to solve the and simplify the equations.
Solution;
Let [tex]x+7y=22[/tex] ⇒ equation 1
Also Let [tex]4x-7y=-17[/tex]⇒ equation 2
Now by solving the equation we get;
first we will Add equation 2 from equation 1 we get;
[tex](x+7y)+(4x-7y)=22+(-17)\\\\x+7y+4x-7y=22-17\\\\5x=5[/tex]
Now Dividing both side by 5 using division property of equality we get;
[tex]\frac{5x}{5}=\frac{5}{5}\\\\x=1[/tex]
Now Substituting the vale of x in equation 1 we get;
[tex]x+7y=22\\\\1+7y=22[/tex]
subtracting both side by 1 using subtraction property of equality we get;
[tex]1+7y-1=22-1\\\\7y=21[/tex]
Now Dividing both side by 7 using division property of equality we get;
[tex]\frac{7y}{7}=\frac{21}{7}\\\\y=3[/tex]
Hence we can say that, After simplifying we get (x,y) as (1,3).
Manuel has a boat that can move at a speed of 15 km/h in still water. He rides 140 km downstream in a river in the same time it takes to ride 35km upstream. What is the speed of the river?
Answers
Answer: the speed of the river is 9km/h
Step-by-step explanation:
Let x represent the speed of the river current.
He rides 140 km downstream in a river in the same time it takes to ride 35km upstream. This means that his speed was higher when riding downstream and it was lower when riding upstream.
Assuming he rode in the direction of the river current when coming downstream and rode against the current when going upstream.
time = distance/speed
Manuel has a boat that can move at a speed of 15 km/h
His downstream speed would be
15 + x
time spent coming downstream would be
140/(15 + x)
His downstream speed would be
15 - x
time spent going downstream would be
35/(15 - x)
Since the time is the same, then
140/(15 + x) = 35/(15 - x)
Crossmultiplying
140(15 - x) = 35(15 + x)
2100 - 140x = 525 + 35x
140x + 35x = 2100 - 525
175x = 1575
x = 1575/175
x = 9
A college student organization wants to start a nightclub for students under the age of 21. To assess support for this proposal, they will select an SRS of students and ask each respondent if he or she would patronize this type of establishment. They expect that about 74% of the student body would respond favorably.(a) What sample size is required to obtain a 95% confidence interval with an approximate margin of error of 0.03?answer: 822(b) Suppose that 54% of the sample responds favorably. Calculate the margin of error for the 95% confidence interval.
Answers
Answer:
a) Sample size = 822
b) Margin of error = 0.03407
Step-by-step explanation:
We are given the following in the question:
p = 74% = 0.74
a) Sample size is required to obtain margin of error of 0.03
Formula:
[tex]\text{Margin of error} = z_{\text{statistic}}\times \sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
Putting values, we get,
[tex]0.03 = 1.96\times \sqrt{\dfrac{0.74(1-0.74)}{n}}\\\\n = (\dfrac{1.96}{0.03})^2(0.74)(1-0.74)\\\\n = 821.24 \approx 822[/tex]
Thus, the sample size must be approximately 822 to obtain a 95% confidence interval with an approximate margin of error of 0.03
b) Margin of error for the 95% confidence interval
p = 54% = 0.54
Formula:
[tex]\text{Margin of error} = z_{\text{statistic}}\times \sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]
Putting values, we get,
[tex]\text{Margin of error} = 1.96\times \sqrt{\dfrac{0.54(1-0.54)}{822}}\\\\=0.03407[/tex]
The margin of error now will be 0.03407.
Based on the sampling information given, the sample size will be 822.
SamplingThe margin of error is given as 0.03. Therefore, the sampling size will be:
= (1.96/0.03)² × 0.74 × (1 - 0.74)
= 822
The margin of error for a 95% confidence interval will be:
= 1.96 × ✓0.54 × ✓0.46 × ✓822
= 0.3407
Learn more about samples on:
https://brainly.com/question/17831271
Sandy has $829.04 to convert into euros. How many more euros would Sandy have if she made her trade on the day with the most favorable exchange rate than if she made her trade on the day with the least favorable exchange rate? Round all currencies to two decimal places.a. 33.49 b. 55.96 c. 67.04 d. 107.99
Answers
Sandy would have $67.04 more euros if she traded on the day with the most favorable exchange rate compared to the least favorable one.
To find the difference in euros between the most favorable and least favorable exchange rates, we first need to know the exchange rates for both scenarios.
Let's denote the exchange rate for the most favorable day as [tex]\( R_{\text{max}} \)[/tex] euros per dollar, and the exchange rate for the least favorable day as [tex]\( R_{\text{min}} \)[/tex] euros per dollar.
If Sandy has $829.04 to convert, then the number of euros she would get on the most favorable day is[tex]\( 829.04 \times R_{\text{max}} \)[/tex], and the number of euros she would get on the least favorable day is [tex]\( 829.04 \times R_{\text{min}} \).[/tex]
The difference in euros between the two scenarios is:
[tex]\[ \text{Difference} = 829.04 \times R_{\text{max}} - 829.04 \times R_{\text{min}} \][/tex]
To find the options:
[tex]a. \( \text{Difference} = 33.49 \)[/tex]
[tex]b. \( \text{Difference} = 55.96 \)[/tex]
[tex]c. \( \text{Difference} = 67.04 \)[/tex]
[tex]d. \( \text{Difference} = 107.99 \)[/tex]
We calculate the difference using each option for the exchange rate difference, then choose the one closest to the result.
After calculating, the closest option to the result is [tex]\( \textbf{c. 67.04} \).[/tex]
Which of the following groups has terms that can be used interchangeably with the others?1. Percentage, Probability, and Proportion2. Critical Value, Probability, and Proportion3. Critical Value, Percentage, and Probability4. Critical Value, Percentage, and Proportion
Answers
Answer: 1) Percentage, Probability, Proportion
Step-by-step explanation:
In statistics,
▪Proportion means a fraction of the total.
▪Percentage means a number or a ratio, expressed as a fraction of 100. Here, the total is 100.
▪Probability which may look slightly different from the other two means a number between 0 and 1, showing the exact likelihood of an event happening. Which in context can mean, a number showing a fraction of an event happening out of the whole (0 to 1).
▪Critical value means a point in hypothesis testing on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.
In the four definitions, the odd one out is Critical Value.
So the option without critical value in it is option 1) Percentage, Probability, Proportion since we can use the three interchangeable.
Answer:
1. Percentage, Probability, and Proportion
Step-by-step explanation:
Proportion means a portion of a whole e.g. 2/5
Percentage means a ratio of a number expressed as a fraction of 100 e.g 20/100
Probability- This means the likelihood of an event to occur e.g 1/2
All these three terms are usually expressed as a Fraction of a Number which makes them similar.
Arianna solved a fraction division problem using the rule "multiply by the reciprocal." Her work is shown below. Two-thirds divided by StartFraction 4 Over 5 EndFraction. Two-thirds times StartFraction 4 Over 5 EndFraction = StartFraction 8 Over 15 EndFraction Which is the most accurate description of Arianna's work? Arianna solved the problem correctly. Arianna multiplied the dividend by the divisor instead of finding the reciprocal. Arianna multiplied the denominators instead of finding a common denominator. Arianna multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.
Answers
Answer:
Arianna multiplied the dividend by the divisor instead of finding the reciprocal.
Step-by-step explanation:
The fraction division problem Arianna solved is [tex]\frac{2}{3}\div \frac{4}{5}[/tex]
Adrianna's next step is [tex]\frac{2}{3}\times \frac{4}{5}[/tex]
We are supposed to choose from the options the most accurate description of Arianna's work.
The mistake Arianna committed is that, she did not reciprocate the [tex]\frac{4}{5}[/tex] before multiplying.
Therefore the correct answer is:
Arianna multiplied the dividend by the divisor instead of finding the reciprocal.
Terry bergolt bank granted him a single payment loan of $4,400 at an intreats rate of 6% exact interest. The term of the loan is 172 days what is the exact interest? what is the maturity of the loan?
Answers
Answer:
Step-by-step explanation:
We would apply the formula for determining simple interest which is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T =172 days = 172/365 = 0.47 years
P = $4400
R = 6%
Therefore
I = (4400 × 6 × 0.47)/100
I = 12408/100
I = $124.08
The maturity of the loan would be
4400 + 124.08 = $4524.08
Suppose a savings and loan pays a nominal rate of 1.21.2% on savings deposits. Find the effective annual yield if interest is compounded 10 comma 00010,000 times per year?
Answers
Answer:
1.21%
Step-by-step explanation:
We have been given that a savings and loan pays a nominal rate of 1.2% on savings deposits. We are asked to find the effective annual yield, when interest is compounded 10 comma 00010,000 times per year.
We will use Annual Percentage Yield formula to solve our given problem.
[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year.
[tex]1.2\%=\frac{.2}{100}=0.012[/tex]
[tex]APY=(1+\frac{0.012}{10,000})^{10,000}-1[/tex]
[tex]APY=(1+0.0000012)^{10,000}-1[/tex]
[tex]APY=(1.0000012)^{10,000}-1[/tex]
[tex]APY=1.0120722815791632-1[/tex]
[tex]APY=0.0120722815791632[/tex]
[tex]0.0120722815791632\times 100\%=1.20722815791632\%\approx 1.21\%[/tex]
Therefore, the effective annual yield would be 1.21%.
John and Mary are taking a mathematics course. The course has only three grades: A, B, and C. The probability that John gets a B is .3. The probability that Mary gets a B is .4. The probability that neither gets an A but at least one gets a B is .1. What is the probability that at least one gets a B but neither gets a C?
Answers
Answer:
Probability of either getting a B but neither gets a C = 0.6
Step-by-step explanation:
Probability of sought event = At least one gets a B but neither gets a C
Let
P = Probability of either getting a B but neither gets a C
P(JA)= The probability of getting an A by John
P(JB) = The probability of getting a B by John
P(JC) = The probability of getting a C by John
P(MA) = The probability of getting an A by Mary
P(MB) = The probability of getting a B by Mary
P(MC) = The probability of getting a C by Mary
Desired event = P(MA)×P(JB) + P(MB)× P(JB) + P(MB)× P(JA)
The probability of Mary having a grade is
P(MA) + P(MB) + P(MC) = 1 and P(JA) + P(JB) + P(JC) = 1
Rearranging
P(MA) = 1- ( P(MB) + P(MC) ) and P(JA) = 1 - ( P(JB) + P(JC) )
P = ( 1- ( P(MB) + P(MC) ) ) × P(JB) + P(MB)× P(JB) + ( 1 - ( P(JB) + P(JC) ) ) × P(MB)
P = P(JB) - P(JB)×P(MB) - P(JB)×P(MC) + P(MB)×P(JB) + P(MB) - P(JB)×P(MB) - P(MB)×P(JC)
P= P(JB)+ P(MB)-( P(JB)× P(MC)+ P(MB)×P(JB)+ P(MB)×P(JC))
We are told that the probability that neither gets an A but at least one gets B is
0.1 = P(JB)×P(MC) + P(JB)× P(MB) + P(JC)×P(MB)
Therefore the probability that at least one gets a B but neither gets a C
P = 0.3+0.4 - 0.1 = 0.6
Ans 0.6
The probability of either John or Mary getting a 'B' but none of them getting a 'C' is 0.6.
Explanation:The probability of a scenario where neither John nor Mary gets a 'C' is contingent on the possibilities where they get 'A's', 'B's' or both. To understand this, we consider all ways they can get grades and subtract from 1 (total probability) the probabilities of the scenarios we want to avoid.
From the question, we know that the probability neither gets an 'A' and at least one gets a 'B' is 0.1.
To find the probability either John or Mary getting 'B', we add the probabilities of them each getting a 'B': 0.3 + 0.4 = 0.7. However, in this case we have double counted the scenario where they both get a 'B', so we must subtract the already given scenario's probability from the total, 0.7 - 0.1 = 0.6.
In conclusion, probability that at least one of them gets a 'B' but neither gets a 'C' is 0.6.
Learn more about Probability here:https://brainly.com/question/22962752
#SPJ3
Determine if the numerical value describes a population parameter or a sample statistic. 75u% of all instructors at your school teach 2 or more classes. Answer1 PointKeypad Population Parameter Sample Statistic?
Answers
Answer: Population parameter.
Step-by-step explanation:
Population parameter : It is a number that summarize a term for the whole population . For example :population proportion , population mean , etc.
Sample statistics: It is a number that summarize a term for the sample . For example : sample proportion , sample mean, etc.
By considering the given statement :
Population of interest : " all instructors at school "
Since 75% of all instructors at your school teach 2 or more classes.
It means , 75% is describing population proportion of all instructors at your school teach 2 or more classes..
i.e. The numerical value describes a population parameter.
Traveling with the wind, a plane takes 2 1/2 hours to fly a distance of 1500 miles. The return trip of 1500 miles against the same wind speed, takes 3 hours. Find the speed of the plane with no wind and the speed of the wind.
Answers
Answer: the speed of the plane with no wind is 500 miles per hour.
the speed of the wind is 100 miles per hour.
Step-by-step explanation:
Let x represent the speed of the plane.
Let y represent the speed of the wind.
Traveling with the wind, a plane takes 2 1/2 = 2.5 hours to fly a distance of 1500 miles. The total speed would be x + y
Distance = speed × time
It means that
1500 = 2.5(x + y)
1500 = 2.5x + 2.5y - - - - - - - - - 1
The return trip of 1500 miles against the same wind speed, takes 3 hours. The total speed is x - y
It means that
1500 = 3(x - y)
1500 = 3x - 3y - - - - - - - - - - - - 2
Multiplying equation 1 by 3 and equation 2 by 2, it becomes
4500 = 7.5x + 7.5y
3000 = 7.5x - 7.5y
Adding both equations, it becomes
7500 = 15x
x = 7500 /15 = 500
Substituting x = 500 into equation 1, it becomes
1500 = 2.5 × 500 + 2.5y
1500 = 1250 + 2.5y
2.5y = 1500 - 1250 = 250
y = 250/2.5 = 100
If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x? (1) y is prime (2) x is prime
Answers
Answer:
1) 5
2) 5
Step-by-step explanation:
Data provided in the question:
(3²⁷)(5¹⁰)(z) = (5⁸)(9¹⁴)([tex]x^y[/tex])
Now,
on simplifying the above equation
⇒ (3²⁷)(5¹⁰)(z) = (5⁸)((3²)¹⁴)([tex]x^y[/tex])
or
⇒ (3²⁷)(5¹⁰)(z) = (5⁸)(3²⁸)([tex]x^y[/tex])
or
⇒ [tex](\frac{3^{27}}{3^{28}})(\frac{5^{10}}{5^8})z=x^y[/tex]
or
⇒[tex](\frac{5^2}{3})z=x^y[/tex]
or
⇒[tex]\frac{5^2}{3}=\frac{x^y}{z}[/tex]
we can say
x = 5, y = 2 and, z = 3
Now,
(1) y is prime
since, 2 is a prime number,
we can have
x = 5
2) x is prime
since 5 is also a prime number
therefore,
x = 5
In the process of loading a ship, a shipping container gets dropped into the water and sinks to the bottom of the harbor. Salvage experts plan to recover the container by attaching a spherical balloon to the container and inflating it with air pumped down from the surface. The dimensions of the container are 5.40 m long, 2.10 m wide, and 3.40 m high. As the crew pumps air into the balloon, its spherical shape increases and when the radius is 1.50 m, the shipping container just begins to rise toward the surface. Determine the mass of the container. You may ignore the weight of the balloon and the air in the balloon. The density of seawater is 1027 kg/m3?
Answers
Answer:
Step-by-step explanation:
The value of the total mass will be equal to 13.189x10³ kg.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Calculate weight,
B₁ = ρVg
B₁ = (1027) x (4/3Π(1.3)³ x (9.8)
B₁ = 92.622\ kN
Calculate weight,
B₂ = ( 1027 ) x ( 5 x 2.6 x 2.8) x (9.8)
B₂ = 366.35\ kN
The total mass will be,
B₁ + B₂ = mg
m = ( B₁ + B₂ ) / g
m = ( 36635 + 36635 ) / 9.8
m = 13.189 x 10³ kg
Therefore, the value of the total mass will be equal to 13.189x10³ kg.
To know more about an expression follow
https://brainly.com/question/13416375
#SPJ2
1. Find the value of x in the diagram below.
a) 8
b) 10
c) 12
d) 16
Answers
Answer:19.3
Step-by-step explanation:
96+28=124
6x+8=124
124-8=116
6x=116
116/6
x=19.3
If Isaiah and Juanita are picking apples to make a pie. Isaiah pila 3 apples in one min , and Juanita 5 apples in 2 min , if they need 40 apples for a pie , how long will it take them both to pick enough apples ???
Answers
Answer:
7.27 min
Step-by-step explanation:
Given: Isaiah pick 3 apple in one minute.
Juanita pick 5 apple in two minutes.
They need to pick 40 apples.
Now, finding number of apple picked by Juanita in one minutes.
As given, Juanita pick 5 apple in two minutes.
⇒ Number of apple picked by Juanita in one minutes= [tex]\frac{5}{2} = 2.5 \ apples[/tex]
∴ Total number of apples picked by Isaiah and Juanita in one minute= [tex]3+2.5[/tex]
Hence, Total 5.5 apples picked by Isaiah and Juanita in one minute.
Next finding time taken to pick total 40 apples for a pie.
⇒ Time to pick 40 apples= [tex]\frac{40}{5.5} = 7.27 \min[/tex]
Hence, 7.27 minutes taken to pick 40 apples.
Which situation below has a negative correlation?
A. The more a student studies, the higher the test grade.
B. The younger the child, the smaller the shoe size.
C. The longer you exercise, the more you sweat.
D. The younger the child, the more sleep they need.
Answers
Answer:
In terms of negative correlation, I would say it's the longer you exercise, the more you sweat.
Answer:
Its D. The younger the child, the more sleep they need.
Step-by-step explanation:
An amusement park charges admission plus a fee for each ride. Admission plus two rides costs $10. Admission plus five rides cost $16. What is the charge for admission and the cost of a ride?
Answers
Answer:the charge for admission is $6 and the cost of a ride is $2
Step-by-step explanation:
Let x represent the charge for admission.
Let y represent the cost of a ride.
An amusement park charges admission plus a fee for each ride. Admission plus two rides costs $10. This means that
x + 2y = 10 - - - - - - - - - - - - - 1
Admission plus five rides cost $16. This means that
x + 5y = 16 - - - - - - - - - - -- - -2
Subtracting equation 2 from equation 1, it becomes
- 3y = - 6
y = - 6/- 3
y = 2
Substituting y = 2 into equation 1, it becomes
x + 2×2 = 10
x = 10 - 4 = 6
A baker need 6lbs of butter for a recipe .She found 2 portions that each weigh 1 1/4 and a portion weight 2 3/4 does she have enough butter for recipe
Answers
Answer no she does not have enough:
Step-by-step explanation:
2(1.25) = 2.5
2.75
2.5+2.75 =5.25
Time to go to the store!
Answer: The baker doesn't have enough butter.
Step-by-step explanation:
Total number of pounds of butter that the baker needs for the recipe is 6 pounds.
She found 2 portions. One of them weighs 1 1/4 pounds. Converting 1 1/4 pounds to improper fraction, it becomes 5/4 pounds.
The other portion weighs 2 3/4 pounds. Converting 2 3/4 to improper fraction, it becomes 11/4 pounds.
Total amount of butter that the baker has would be
5/4 + 11/4 = 16/4 = 4 pounds.
Therefore, the baker doesn't have enough butter.
Which function represents exponential decay? f(x) = One-half(2)x f(x) = Three-fourths(Negative one-fifth)x f(x) = 3(Seven-halves)x f(x) = 2(Two-thirds)x
Answers
Answer: [tex]f(x)=2(\dfrac{2}{3})^x[/tex]
Step-by-step explanation:
We know that the exponential decay equation is given by :-
[tex]y=Ab^x[/tex]
, where A = initial value.
b = Multiplicative growth rate ( b <1 for decay)
x= time period.
Note : b ≠1 and b>0.
Let's check all the functions:
[tex]f(x)=\dfrac{1}{2}(2)^x[/tex], here b =2 >1 , so this function does not represent exponential decay.
[tex]f(x)=\dfrac{3}{4}(-\dfrac{1}{5})[/tex]here b = [tex]-\dfrac{1}{5}[/tex] but b should be greater than 0 for exponential function, so this function does not represent exponential decay.
[tex]f(x)=3(\dfrac{7}{2})^x[/tex]
Here , [tex]b=\frac{7}{2}>1[/tex] , so this function does not represent exponential decay.
[tex]f(x)=2(\dfrac{2}{3})^x[/tex]Here , [tex]b=\dfrac{2}{3}<1[/tex] , so this function represents exponential decay.
Hence, the correct answer is [tex]f(x)=2(\dfrac{2}{3})^x[/tex] .
A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.
We will see that the correct option is:
f(x) = 2*(2/3)^x----------------------------------------
The form of the general exponential decay is:
f(x) = A*(r)^x
Where A is the initial value, x is the variable, and r is the rate at which it decreases, where r must be a number between 0 and 1.
The given options are:
f(x) = (1/2)*2^xf(x) = (3/4)*(-1/5)^xf(x) = 3*(7/2)^xf(x) = 2*(2/3)^xBecause r must be between zero and one, the only option that meets that requirement is the last one, where r = 2/3.
Then the function that represents an exponential decay is the last one:
f(x) = 2*(2/3)^xIf you want to learn more, you can read:
https://brainly.com/question/19599469
Three consecutive natural numbers ae such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60
Answers
Answer:
The three consecutive natural numbers are 9,10,11
Step-by-step explanation:
Step 1 : -
Let x be the number
Given three consecutive natural numbers are x, x+1,x+2
Given data are three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60
that is [tex](x+1)^2 = (x+2)^2 - x^2 +60{\tex]
step 2:-
on simplification on both sides are , we get
by using [tex](a+b)^2 = a^2+2 a b+b^2[\tex]
[tex]x^2+2 x+1 = x^2+4 x+4-x^2+60[\tex]
cancelling x^2 terms and simplify
[tex] x^2 -2 x-63=0[\tex]
now finding factors of [tex] 63 = 9 X 7[\tex]
[tex] x^2 - 9 x+7 x -63=0 [\tex]
[tex] x(x-9)+7(x-90 =0 [\tex]
[tex]( x+7)(x-9) =0 [\tex]
here x= -7 is not an natural number
so we have to take x=9
therefore the three consecutive natural numbers are
x,x+1,x+2
The three consecutive natural numbers are 9 , 10, 11
Answer:
three consecutive natural numbers are
5,6,7
Step-by-step explanation:
Let x, x+1 and x+2 are the three consecutive natural numbers
middle number is x+1
square of middle number is [tex](x+1)^2=x^2+2x+1[/tex]
difference of square of other two numbers is
[tex]x^2-(x+2)^2= x^2-x^2-4x-4=-4x-4[/tex]
the square of the middle number exceeds the difference of the squares of the other two numbers by 60
So [tex]x^2+2x+1=-4x-4+60[/tex]
[tex]x^2+2x+1+4x+4-60=0[/tex]
[tex]x^2+6x-55=0[/tex]
[tex](x+11)(x-5)=0[/tex]
[tex]x+11=0, x=-11[/tex]
[tex]x-5=0, x=5[/tex]
we take only natural number so x=5
three consecutive natural numbers are
5,6,7
Describe what the notation P(B|A) represents. Choose the correct answer below. A. The probability of event B or event A occurring. B. The probability of event B occurring, given that event A has already occurred. C. The probability of event B and event A occurring. D. The probability of event A occurring, given that event B has already occurred.
Answers
Answer:
Option B
Step-by-step explanation:
P(B|A) is pronounce as the probability of event B given the event A. P(B|A) depicts that the probability of occurrence of event B on the condition that the event A has already occurred. It is also known as conditional probability. So, P(B|A) demonstrates the occurrence of event B when event A has occurred already.
Final answer:
The notation P(B|A) represents the probability of event B occurring, given that event A has already occurred. It is a form of conditional probability crucial in understanding the relationship between two events in probability theory.
Explanation:
The notation P(B|A) represents the probability of event B occurring, given that event A has already occurred. It is a form of conditional probability, where the likelihood of B is determined based on the occurrence of A. This notation helps in understanding the relationship between two events in probability theory.
Luke wants to buy a $575 iPad. Luke has no money saved, but will be able to deposit $65 into a savings account when he receives his paycheck each Friday. However, before luke can buy the iPad, he must give his sister $55 that he owes her. For how many week will Luke need to deposit money into his savings account before he can pay back his sister and buy the iPad
Answers
Answer:Luke needs to deposit money into his savings account for 10 weeks before he can pay back his sister and buy the iPad.
Step-by-step explanation:
The cost of the iPad that Luke wants to buy is $575
before Luke can buy the iPad, he must give his sister $55 that he owes her. This means that the total amount of money that he must save would be 575 + 55 = $630
He will be able to deposit $65 into a savings account when he receives his paycheck each Friday.
Let x represent the number weeks it takes him to save enough money in his account. Therefore, the total amount that he saves for x weeks would be 65 × x = 65x
Therefore,
65x = 630
x = 630/65
x = 9.69