Answer:
Pi (π) is one of the most important and fascinating numbers in mathematics. Roughly 3.14, it is a constant that is used to calculate the circumference of a circle from that circle's radius or diameter.[1] It is also an irrational number, which means that it can be calculated to an infinite number of decimal places without ever slipping into a repeating pattern.[2] This makes it difficult, but not impossible, to calculate precisely.
Step-by-step explanation:
Pi (π) is one of the most important and fascinating numbers in mathematics. Roughly 3.14, it is a constant that is used to calculate the circumference of a circle from that circle's radius or diameter.[1] It is also an irrational number, which means that it can be calculated to an infinite number of decimal places without ever slipping into a repeating pattern.[2] This makes it difficult, but not impossible, to calculate precisely.
Samantha measured 40 1/2 inches. Over the 5 1/2 years, she grew to a height of 57 inches. During the 5 1/2 years, what was the average yearly change in samanthas height?
Answer:
The average yearly change in samanthas height was of 3.3 inches.
Step-by-step explanation:
She mesured 40 1/2 = 40.5 inches.
In 5 1/2 years = 5.5 years, she grew to 57 inches.
During the 5 1/2 years, what was the average yearly change in samanthas height?
The total change was of 57-40.5 = 16.5 inches
16.5/5 = 3.3
The average yearly change in samanthas height was of 3.3 inches.
f(x)=x^2 what is g(x)
Answer:
D. g(x)=4x^2
Step-by-step explanation:
Answer: g(x)=4x^2
check picture below
What do dinosaurs use to run their cars?
Answer:
Probably the engine from their helicopter
Step-by-step explanation:
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check all that apply.
Answer:
D
Step-by-step explanation:
The absolute value parent function is [tex]\mid x \mid[/tex], or answer choice D. Hope this helps!
25.2 + 800 - 427..43 × 2.4 ÷ 13
Step-by-step explanation:
25.2 + 800 - 427.43 x 2.4 ÷ 13
825.2 - 1025.832 ÷ 13
200.632 ÷ 13
= 15.44
In 2 days, 48,000 gallons of oil
Answer:
Deepwater Horizon
good movie too btw
-Hops
Answer:
48 000 gallons / 2 days = 24 000 gallons per day
24 000 gallons / 24 hours = 1 000 gallons per hour
1 000 gallons / 60 minutes = 16.(6) gallons per minute
I had the same question on a quizz, the question was:In two days, 48,000 gallons of oil gushed out of a well. At what rate did the oil flow from the well?
Hope that was helpful.Thank you!!!
VERY URGENT.
You will get Brainliest.
Here are three math questions:
1.) A rectangular prism has a volume of 2,592 cubic yards. The height of the prism is 32 yards.
What is the area of the base of the prism?
2.) A rectangular prism has a volume of 432 cubic feet and a height of 9 feet.
Which dimensions could be the length and width of the prism?
Select each correct answer.
28 ft long and 20 ft wide
3 ft long and 16 ft wide
6 ft long and 8 ft wide
13 ft long and 4 ft wide
24 ft long and 2 ft wide
3.) A rectangular prism has a volume of 960 cubic units. The area of the base is 80 square units.
What is the height of the prism?
_____ units
Answer:
(1)Base Area= 81 square yards.
(2)
3 ft long and 16 ft wide 6 ft long and 8 ft wide 24 ft long and 2 ft wide(3)Height=12 Units
Step-by-step explanation:
Question 1
Volume of the rectangular prism=2,592 cubic yards.
Height of the rectangular prism=32 yards
Volume of a rectangular prism =lbh (where lb is the Base Area)
Therefore:
lbh=2592
32lb=2592
lb=2592/32=81
Base Area= 81 square yards.
Question 2
Volume of the rectangular prism=432 cubic feet.
Height of the rectangular prism=9 feet
Volume of a rectangular prism =lbh (where lb is the Base Area)
Therefore:
lbh=432
9lb=432
lb=432/9=48
Base Area= 48 square yards.
Any dimension whose product is 48 is a possible choice.
They are:
3 ft long and 16 ft wide 6 ft long and 8 ft wide 24 ft long and 2 ft wideQuestion 3
Volume of the rectangular prism=960 cubic units.
Base Area of the rectangular prism, lb=80 Square Units
Volume of a rectangular prism =lbh (where lb is the Base Area)
Therefore:
lbh=960
80h=960
h=960/80=12
Height= 12 units.
Answer:
81 square yards.
Step-by-step explanation:
what the other guy said just less words
Trigonometry: Question 2
In triangle ABC with right angle C, the measure of angle A is 37
degrees, and the length of the hypotenuse is 10. What is the length of
AC?
Select one:
12,5
7.9
Answer:
b = 7.9
Step-by-step explanation:
A = 37 a =
B = 53 b =
C = 90 c = 10
B = 180 - 90 -37 = 53
[tex]\frac{sinB}{b} = \frac{sinC}{c}\\ \frac{sin(53)}{b} = \frac{sin(90)}{10}\\ b = \frac{10 sin(53)}{sin(90)} \\b = 7.9[/tex]
To find the length of side AC in a right-angled triangle ABC with angle A of 37 degrees and hypotenuse 10, we use the cosine function. AC equals the hypotenuse multiplied by the cosine of angle A, resulting in AC being approximately 7.9 units long.
Explanation:The student wants to know the length of side AC in a right-angled triangle ABC, where angle C is a right angle, angle A is 37 degrees, and the hypotenuse (side BC) is 10. To find the length of side AC, we will use trigonometric functions. Specifically, we will use the cosine function, which relates the adjacent side to the hypotenuse in a right-angled triangle. The cosine of angle A (cos 37°) is equal to the adjacent side (AC) divided by the hypotenuse (BC).
The formula is: Cosine of angle A = AC / BC
This can be rewritten as: AC = BC * Cosine of angle A
By substituting the given values (BC = 10 and angle A = 37°), we get:
AC = 10 * cos(37°)
To find cos(37°), we can use a calculator set to degree mode. The calculation gives us:
AC = 10 * 0.7986 (approximately)
Therefore, AC ≈ 10 * 0.7986 = 7.986
AC is approximately 7.9 units long.
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What is the area of a square with side length of 4 and one-fourth m?
Answer:18.0625m^2
Step-by-step explanation:
Length =4 1/4 m
Area= length x length
Area=4 1/4 x 4 1/4
Area=(4x4+1)/4 x (4x4+1)/4
Area=17/4 x 17/4
Area=(17x17)/(4x4)
Area=289/16
Area=18.0625m^2
when oxygen reacts with hydrogen it has the capacity to release 29 kilojoules of energy. Inside a fuel cell, oxygen reacts with hydrogen to produce 23 kilojoules of useful energy. The rest of the energy is lost as heat. Whats the efficiency percent of the fuel cell?
Answer:
79
Step-by-step explanation:
If y varies directly as x and y=8 when x=3 what is the value of y when x=9?
A 8/3
B 27/8
C 14
D 24
Answer:
24
Step-by-step explanation:
y=24 when x=3 because you * 3*3=9 so you do 8*3=24 which you your answer
The value of y when x = 9 such that the y varies directly with respect to x is 24 therefore, option (D) will be correct.
What are the ratio and proportion?Proportion is the relation of a variable with another. It could be direct or inverse.
The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given question,
y varies directly as x
y ∝ x
Removing proportion y = kx
Given that,y=8 when x=3
So, k = 8/3
Therefore, relation converts as, y = (8/3)x
At x = 9 → y = (8/3)9 = 24
Hence "The value of y when x = 9 such that the y varies directly with respect to x is 24".
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"If a ball of mass M is dropped from a height h onto a spring with spring constant k (whose equilibrium positions is at height 0), compresses the spring an additional distance (L/2), and then rebounds, what height will the ball reach? Express your answer symbolically."
So I was thinking something along the lines of h= M*k*(L/2) but I'm not sure :/ Any guidance?
Answer:[tex]h=\dfrac{kL^2}{8mg}[/tex]
Step-by-step explanation:
Given
Mass of ball is M is dropped from a height h
spring constant is k
Here we can use conservation of energy
Mass has a Potential energy of E=mgh
and when it falls on the spring then it compresses it a length of 0.5 L
Now potential energy is converted into Elastic potential energy and then spring unleashes this energy to the mass and again provide kinetic energy to mass to move upward .
In this way energy is conserved. So, mass must move to an initial height h
[tex]mgh=\frac{1}{2}k(\frac{L}{2})^2[/tex]
[tex]h=\dfrac{kL^2}{8mg}[/tex]
considering [tex]h >> 0.5L[/tex]
In order to estimate the difference between the average hourly wages of employees of two branches of a department store, the following data have been gathered. Downtown Store North Mall Store Sample size 25 20 Sample mean $9 $8 Sample standard deviation $2 $1 Refer to Exhibit 10-7. A 95% interval estimate for the difference between the two population means is
Answer:
[tex] (9-8) -2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 0.0743[/tex]
[tex] (9-8) +2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 1.926[/tex]
And we are 9% confidence that the true mean for the difference of the population means is given by:
[tex] 0.0743 \leq \mu_1 -\mu_2 \leq 1.926[/tex]
Step-by-step explanation:
For this problem we have the following data given:
[tex]\bar X_1 = 9[/tex] represent the sample mean for one of the departments
[tex]\bar X_2 = 8[/tex] represent the sample mean for the other department
[tex]n_1 = 25[/tex] represent the sample size for the first group
[tex]n_2 = 20[/tex] represent the sample size for the second group
[tex]s_1 = 2[/tex] represent the deviation for the first group
[tex]s_2 =1[/tex] represent the deviation for the second group
Confidence interval
The confidence interval for the difference in the true means is given by:
[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}[/tex]
The confidence given is 95% or 9.5, then the significance level is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. The degrees of freedom are given by:
[tex] df=n_1 +n_2 -2= 20+25-2= 43[/tex]
And the critical value for this case is [tex] t_{\alpha/2}=2.02[/tex]
And replacing we got:
[tex] (9-8) -2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 0.0743[/tex]
[tex] (9-8) +2.02 \sqrt{\frac{2^2}{25} +\frac{1^2}{20}}= 1.926[/tex]
And we are 9% confidence that the true mean for the difference of the population means is given by:
[tex] 0.0743 \leq \mu_1 -\mu_2 \leq 1.926[/tex]
35. In a simple random sample of 25 high school students, the sample mean of the SAT scores was 1450, and the sample variance was 900. Assume that the data come from a normal distribution , a 95.4 % Confidence interval for the population mean is a. 1450 +/- 180 b. 1450 +/- 18 c. 1450 +/- 12 d. 1450 +/- 360
Answer:
[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]
[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]
And the best option would be:
c. 1450 +/- 12
Step-by-step explanation:
Information provided
[tex]\bar X=1450[/tex] represent the sample mean for the SAT scores
[tex]\mu[/tex] population mean (variable of interest)
[tex]s^2 = 900[/tex] represent the sample variance given
n=25 represent the sample size
Solution
The confidence interval for the true mean is given by :
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The sample deviation would be [tex]s=\sqrt{900}= 30[/tex]
The degrees of freedom are given by:
[tex]df=n-1=2-25=24[/tex]
The Confidence is 0.954 or 95.4%, the value of [tex]\alpha=0.046[/tex] and [tex]\alpha/2 =0.023[/tex], assuming that we can use the normal distribution in order to find the quantile the critical value would be [tex]z_{\alpha/2} \approx 2.0[/tex]
The confidence interval would be
[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]
[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]
And the best option would be:
c. 1450 +/- 12
One study estimated that bears populate the Kenai Peninsula of Alaska at a rate of 424242 bears per 1,000 \text { km}^21,000 km 2 1, comma, 000, start text, space, k, m, end text, squared of available habitat. According to this study, about how many bears would you expect to find in a habitable region of this peninsula 8,500 \text { km}^28,500 km 2 8, comma, 500, start text, space, k, m, end text, squared in size?
Answer:
357 bears
Step-by-step explanation:
Given;
Population density of bears in the Kenai Peninsula of Alaska = 42 bears per 1000km^2
Area of habitable region of this peninsula = 8500 km^2
how many bears would you expect to find in a habitable region of this peninsula N;
N = population density × area
N = 42/1000 × 8500
N = 357 bears
If the original quantity is 20 and the new quantity is 18, what is the percent decrease?
Answer:
10%
Step-by-step explanation:
There are many different ways but I did 18 divided by 20 and got 0.9. I did 1 - 0.9 to get 0.1, which is 10%
There are 3 feet in 1 yard. This is equivalent to 12 feet in 4 yards. Which proportion can be used to represent this? StartFraction 12 over 1 EndFraction = StartFraction 4 over 12 EndFraction One-third = StartFraction 12 over 4 EndFraction StartFraction 3 over 1 EndFraction = StartFraction 4 over 12 EndFraction StartFraction 3 over 1 EndFraction = StartFraction 12 over 4 EndFraction
Answer:
[tex]\dfrac{3}{1}=\dfrac{12}{4}[/tex]
Step-by-step explanation:
If you write the proportion as ratios of feet to yards, you have ...
[tex]\dfrac{3\,\text{ft}}{1\,\text{yd}}=\dfrac{12\,\text{ft}}{4\,\text{yd}}\\\\\boxed{\dfrac{3}{1}=\dfrac{12}{4}}\qquad\text{without the units}[/tex]
__
Please note that a proportion is a true statement. Here, you need only pick the true statement from those offered. For example, here's the first choice written in more readable form:
[tex]\dfrac{12}{1}=\dfrac{4}{12}\qquad\text{FALSE statement}[/tex]
Answer:
d: 3/1 12/4
Step-by-step explanation:
Divide the school into classes and then randomly select students from each class is an example of:
Answer:
Stratified sampling
Step-by-step explanation:
Members of the population are divided into two or more subgroups called strata, that share similar characteristics like age, gender, or ethnicity. A random sample from each stratum is then drawn. For instance, if we divide the population of college students into strata based on the number of years in school, then our strata would be freshmen, sophomores, juniors, and seniors. We would then select our sample by choosing a random sample of freshmen, a random sample of sophomores, and so on.
This technique is used when it is necessary to ensure that particular subsets of a population are represented in the sample. Since a random sample cannot guarantee that sophomores would be chosen, we would used a stratified sample if it were important that sophomores be included in our sample. Furthermore, my using stratified sampling you can preserve certain characteristics of the population. For example, if freshmen make up 40% of our population, then we can choose 40% of our sample from the freshmen stratum. Stratified sampling is one of the best ways to enforce "representativeness" on a sample.
What is the point-slope form of a line with slope-3 that contains the point
(10,-1)?
O A. y+1 = 3(x+10)
O B. y+ 1 = 3(x-10)
O C. x+ 1 =-3(y-10)
OD. y+ 1 = -3(x-10)
Answer:
D.) [tex]y+1=-3(x-10)[/tex]
Step-by-step explanation:
The original point slope form equation is as follows:
[tex]y - y_1 = m(x-x_1)[/tex]
When you input a negative or positive value into the equation, the sign may or may not change. In this case, we input a negative y value -- this caused the sign to change to '+1' rather than stay at '-1'
A group of 52 people attended a ball game. There were three times as many children as adults in the group.
Set up a system of equations that represents the numbers of adults and children who attended the game and solve the system to find the number of children who were in the group.
Answer:
39 children and 13 adults
Step-by-step explanation:
3children = 1 adult
52 = x * (3children + 1adult)
52= x * 4
13 = x
x = 13
total children = 3x
3x = 39
The problem poses a system of linear equations where the number of attendees 'a + c = 52' and 'c = 3a'. Resolving these equations gives 'a = 13' adults and 'c = 39' children.
Explanation:This is a problem about creating and solving a system of linear equations. Let's denote the number of adults who attended the ball game as 'a' and the children who attended the game as 'c'. According to the problem, we have two parts of information that can be written as equations:
The total number of individuals who attended the game, or 'a + c = 52'. The number of children in attendance were three times the number of adults, or 'c = 3a'.You can substitute the equation for 'c' in the first equation: a + (3a) = 52. Solving this, you find that 'a' equates to 13. Substitute 'a = 13' into the second equation, you will find that 'c = 39'. This indicates that there were 13 adults and 39 children who attended the game.
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Select the graph that represent the equation (x-6)^2+(y+7)^2=16
Answer:
This is a circle with centre (6,-7) and radius 4.
Step-by-step explanation:
The equation of a circle has the following format:
[tex](x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}[/tex]
In which r is the radius(half the diameter) and the centre is the point [tex](x_{0}, y_{0})[/tex]
In this question:
[tex](x-6)^{2} + (y+7)^{2} = 16[/tex]
So
[tex]x_{0} = 6, y_{0} = -7[/tex]
[tex]r^{2} = 16[/tex]
[tex]r = \pm \sqrt{16}[/tex]
The radius is the positive value.
[tex]r = 4[/tex]
So this is a circle with centre (6,-7) and radius 4.
Answer:
Given equation
(x-6)^2+(y+7)^2=16
centre (6,-7) and radius 4.
Step-by-step explanation:
The equation of a circle is (x - a)² + (y - b)² = r²
the radius is r
the centre is (a, b)
Given equation
(x-6)^2+(y+7)^2=16
so ,
a = 6
b = - 7
r² = 16
[tex]r = \pm \sqrt{16}[/tex]
r = 4
Therefore, the circle with centre (6,-7) and radius 4.
An ice cream cone has a radius of 2 in. How much melted ice cream will the cone hold if it has a height of 6 inches?
Answer:
it will hold 25.13 cubic inches of melted ice cream
Step-by-step explanation:
first we get the cone formula because a melted ice cream cone will have a flat top, making it a cone
the cone formula is π*r^2 * h /3
so we input radius and height
π*2^2 * 6 /3
then we simplfy
π * 4 * 6 /3
12.56 *6/3
75.398/3
25.13
Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. The mean length of a bluefish is 264 millimeters with a standard deviation of 57mm. For pompano, the mean is 157mm with a standard deviation of 28mm.
Stewart caught a bluefish that was 283mm long, and Gina caught a pompano that was 152mm long. Who caught the longer fish, relative to fish of the same species?
Answer:
Due to the higher z-score, Stewart caught the longer fish, relative to fish of the same species
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Who caught the longer fish, relative to fish of the same species?
Whosoever fish's had the higher z-score.
Stewart caught a bluefish that was 283mm
The mean length of a bluefish is 264 millimeters with a standard deviation of 57mm.
So we have to find Z when [tex]X = 283, \mu = 264, \sigma = 57[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{283 - 264}{57}[/tex]
[tex]Z = 0.33[/tex]
Gina caught a pompano that was 152mm long.
For pompano, the mean is 157mm with a standard deviation of 28mm.
So we have to find Z when [tex]X = 152, \mu = 157, \sigma = 28[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{152 - 157}{28}[/tex]
[tex]Z = -0.18[/tex]
Due to the higher z-score, Stewart caught the longer fish, relative to fish of the same species
The correct answer is Stewart caught the longer fish relative to fish of the same species.
To determine who caught the longer fish relative to the average length of their respective species, we need to calculate the z-scores for both Stewart's bluefish and Gina's pompano. The z-score is a measure of how many standard deviations an observation is above or below the mean.
For Stewart's bluefish:
The mean length of a bluefish is 264 mm, and the standard deviation is 57 mm. Stewart's bluefish is 283 mm long. To find the z-score for Stewart's bluefish, we use the formula:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where X is the observed value, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation. Plugging in the values for Stewart's bluefish:
[tex]\[ z_{Stewart} = \frac{283 - 264}{57} \] \[ z_{Stewart} = \frac{19}{57} \] \[ z_{Stewart} \approx 0.333 \][/tex]
For Gina's pompano:
The mean length of a pompano is 157 mm, and the standard deviation is 28 mm. Gina's pompano is 152 mm long. To find the z-score for Gina's pompano:
[tex]\[ z = \frac{X - \mu}{\sigma} \] \[ z_{Gina} = \frac{152 - 157}{28} \] \[ z_{Gina} = \frac{-5}{28} \] \[ z_{Gina} \approx -0.179 \][/tex]
Comparing the z-scores:
Stewart's z-score is approximately 0.333, which means his bluefish is 0.333 standard deviations longer than the average bluefish. Gina's z-score is approximately -0.179, which means her pompano is 0.179 standard deviations shorter than the average pompano.
Since Stewart's z-score is positive and larger in magnitude than Gina's negative z-score, Stewart's bluefish is longer relative to its species than Gina's pompano is relative to its species. Therefore, Stewart caught the longer fish relative to fish of the same species.
. The time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal probability distribution with average time 10 minutes and a standard deviation of 2 minutes. If five individuals fill out the form on Day 1 and six individuals fill out the form on Day 2, what is the probability that the sample average time taken is less than 11 minutes for BOTH days?
Answer:
Probability that the sample average time taken is less than 11 minutes for Day 1 is 0.86864.
Probability that the sample average time taken is less than 11 minutes for Day 2 is 0.88877.
Step-by-step explanation:
We are given that the time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal probability distribution with average time 10 minutes and a standard deviation of 2 minutes.
Also, five individuals fill out the form on Day 1 and six individuals fill out the form on Day 2.
(a) Let [tex]\bar X[/tex] = sample average time taken
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 10 minutes
[tex]\sigma[/tex] = standard deviation = 2 minutes
n = sample of individuals fill out form on Day 1 = 5
Now, the probability that the sample average time taken is less than 11 minutes for Day 1 is given by = P([tex]\bar X[/tex] < 11 minutes)
P([tex]\bar X[/tex] < 11 minutes) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{11-10}{\frac{2}{\sqrt{5} } }[/tex] ) = P(Z < 1.12) = 0.86864
The above probability is calculated by looking at the value of x = 1.12 in the z table which has an area of 0.86864.
(b) Let [tex]\bar X[/tex] = sample average time taken
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean time = 10 minutes
[tex]\sigma[/tex] = standard deviation = 2 minutes
n = sample of individuals fill out form on Day 2 = 6
Now, the probability that the sample average time taken is less than 11 minutes for Day 2 is given by = P([tex]\bar X[/tex] < 11 minutes)
P([tex]\bar X[/tex] < 11 minutes) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{11-10}{\frac{2}{\sqrt{6} } }[/tex] ) = P(Z < 1.22) = 0.88877
The above probability is calculated by looking at the value of x = 1.22 in the z table which has an area of 0.88877.
If u = <-7, 6> and v = <-4, 17>, which vector can be added to u + 3v to get the unit vector <1, 0> as the resultant vector?
With u = <-7, 6> and v = <-4, 17>, we have
u + 3v = <-7, 6> + 3 <-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>
We want to find a vector w such that
u + 3v + w = <1, 0>
Subtract u + 3v from both sides to get
w = <1, 0> - (u + 3v) = <1, 0> - <-19, 57>
w = <20, -57>
To get the required vector, subtract u + 3v from the unit vector <1, 0>. The required vector is <20, -57>.
Explanation:To find the vector that can be added to u + 3v to get the unit vector <1, 0>, we need to subtract u + 3v from the unit vector. This will give us the required vector. Let's calculate:
Unit vector: <1, 0>
u + 3v: <-7, 6> + 3<-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>
Required vector = Unit vector - (u + 3v) = <1, 0> - <-19, 57> = <1 + 19, 0 - 57> = <20, -57>
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Brian makes a cleaning solution using a ratio of 4cups of water to 1 cup of vinegar. Which equationcould be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water?
A. 4/12 =c
B. 4/1 =12/c
C 4/1 = c/12
D. 4+1 = 12+c
Answer:
Option B could be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water
Step-by-step explanation:
Brian makes a cleaning solution using a ratio of 4 cups of water to 1 cup of vinegar.
Let c be the number of cups of vinegar that Brian should use with 12 cups of water.
1 cup of vinegar uses cup of water = 4
c cups of vinegar uses cup of water = 4c
We are c, the number of cups ofvinegar that Brian should use with 12 cups of water
So, 4c=12
[tex]4=\frac{12}{c}[/tex]
So, equation =[tex]\frac{4}{1}=\frac{12}{c}[/tex]
So, Option B could be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water
Kim spent 40/100 of a dollar on a snack write as a money amount she has left.
[tex]\frac{60}{100}[/tex] of a dollar
A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.
Kim spent [tex]\frac{40}{100}[/tex] of a dollar on a snack.
So, she has been left with [tex]1-\frac{40}{100}=\frac{60}{100}[/tex] of a dollar on a snack.
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Final answer:
Kim spent 40/100 of a dollar (40 cents) on a snack, so she has 60 cents left.
Explanation:
The question requires converting a fraction of a dollar into a money amount. Kim spent 40/100 of a dollar on a snack. A dollar is equivalent to 100 cents, so Kim spent 40 cents on her snack. To find out how much she has left, we subtract her spending from the total amount of one dollar.
To perform the calculation: 100 cents - 40 cents = 60 cents.
Therefore, Kim has 60 cents left after purchasing the snack.
Suppose a subdivision on the southwest side of Denver, Colorado, contains 1,400 houses. The subdivision was built in 1983. A sample of 110 houses is selected randomly and evaluated by an appraiser. If the mean appraised value of a house in this subdivision for all houses is $227,000, with a standard deviation of $8,500, what is the probability that the sample average is greater than $228,500?
Answer:
3.22% probability that the sample average is greater than $228,500
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
[tex]\mu = 227000, \sigma = 8500, n = 110, s = \frac{8500}{\sqrt{110}} = 810.44[/tex]
What is the probability that the sample average is greater than $228,500?
This is 1 subtracted by the pvalue of Z when X = 228500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{228500 - 227000}{810.44}[/tex]
[tex]Z = 1.85[/tex]
[tex]Z = 1.85[/tex] has a pvalue of 0.9678
1 - 0.9678 = 0.0322
3.22% probability that the sample average is greater than $228,500
The phone company A Fee and Fee has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 290 minutes, the monthly cost will be $87. If the customer uses 980 minutes, the monthly cost will be $225. A) Find an equation in the form y = m x + b , where x is the number of monthly minutes used and y is the total monthly of the A Fee and Fee plan.
Final answer:
The equation representing the total monthly cost of the A Fee and Fee plan based on the number of minutes used is y = 0.20x + 29, where y is the total monthly cost and x is the number of minutes.
Explanation:
To find an equation in the form y = mx + b, where x is the number of monthly minutes used and y is the total monthly cost of the A Fee and Fee plan, we first need to determine the slope (m) and the y-intercept (b).
We have two points based on the information given: (290, 87) and (980, 225). The slope (m) is calculated by the difference in cost divided by the difference in minutes:
m = (225 - 87) / (980 - 290)
m = 138 / 690
m = 0.20
Now that we have the slope, we can use one of the points to find b, the y-intercept.
Using the point (290, 87) and the slope 0.20:
87 = 0.20(290) + b
b = 87 - 58
b = 29
The equation representing the total monthly cost (y) based on the number of minutes used (x) is therefore:
y = 0.20x + 29
Giving brainliest for CORRECT awnser.
Answer:
C. F(x) = x²
Step-by-step explanation:
"Quadratic" means "second degree". The only function with an exponent of 2 is choice C.