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]
A triangular pyramid has three dimensions.
-The sides of the base are 5 centimeters, 12 centimeters, and 13 centimeters.
-The height is 12 centimeters
What is the volume of the pyramid?
A) 120 cm^3
B) 360 cm^3
C) 240 cm^3
D)720 cm^3
Answer:
A) 120 cm^3
Step-by-step explanation:
area of triangle = 1/2 x 5 x 12 = 30
volume = 1/3 x 30 x 12 = 120
Answer:
A
Step-by-step explanation:
What is the factorization of 121b4 − 49?
Answer:
( 11 b 2 + 7 ) ( 11 b 2 − 7 )
Step-by-step explanation:
Answer:
121b⁴ − 49 = (11b² + 7) • (11b² - 7)
Step-by-step explanation:
The difference of two squares.
Step 1: reformat equation
11²b² - 49
Step 2: Factoring: 121b⁴- 49
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A² - AB + BA - B² =
A² - AB + AB - B² =
A² - B²
Factorization is : (11b² + 7) • (11b² - 7)
How many decimal places are in 0.0050
Answer:
HERE IS YOUR ANSWER
Step-by-step explanation:
4
20 This spinner will be spun twice. What is the probability of
Spinning an odd number both times? (Only 0, 1, 2, 3, 4, 5,
6, 7, 8, 9, . -, and / are allowed in your answer.
Answers that are mixed numbers must be entered as
an improper fraction or decimal.)
NC 7SE
Answer: the probability is 0.25
Step-by-step explanation:
We have 10 numbers:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Of those, the odd ones are:
1, 3, 5, 7, 9
So we have 5 odd numbers.
The probability that the outcome is an odd number is equal to the number of odd numbers divided the total number of numbers:
p = 5/10 = 0.5
For the second spin the probability is the same, p = 5/10, because the first outcome does not affect the results of the second spin.
The probability of spining an odd number both times, then is the joint probability for two times this same event:
P = (5/10)(5/10) = 0.5*0.5 = 0.25
or 25% in percent form
The equation below models the height in feet h of a softball t seconds after it is hit by a batter
Answer:
It would be answer 3
Step-by-step explanation:
Because it is one in the actual maximum height
Answer:
Each value of time is associated with exactly one height.
Step-by-step explanation:
"A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.3 minutes with a standard deviation of 1.5 minutes. At the 0.01 significance level, test the claim that the mean waiting time is less than 10 minutes. Use the P-value method of testing hypotheses."
Answer:
We conclude that the mean waiting time is less than 10 minutes.
Step-by-step explanation:
We are given that a public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes.
Karen took bus number 14 during peak hours on 18 different occasions. Her mean waiting time was 7.3 minutes with a standard deviation of 1.5 minutes.
Let [tex]\mu[/tex] = mean waiting time.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] 10 minutes {means that the mean waiting time is more than or equal to 10 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 10 minutes {means that the mean waiting time is less than 10 minutes}
The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean waiting time = 7.3 minutes
s = sample standard deviation = 1.5 minutes
n = sample of occasions = 18
So, test statistics = [tex]\frac{7.3-10}{\frac{1.5}{\sqrt{18}}}[/tex] ~ [tex]t_1_7[/tex]
= -7.637
The value of t test statistics is -7.637.
Now, the P-value of the test statistics is given by the following formula;
P-value = P( [tex]t_1_7[/tex] < -7.637) = Less than 0.05%
Since, our P-values of test statistics is less than the level of significance as 0.05% < 1%, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the mean waiting time is less than 10 minutes.
Mimi needs eleven 18-inch pieces of rhinestone ribbon. she purchased 5 yards of ribbon shown at the right .
chart:$6 per yard or $55 for the whole spool
reasoning :do you need to convert measurements to determine if Mimi purchased the right amount of ribbon?explain
help me plzzzzz i need help hurry!!!!!!!!!!
Answer:
Yes we need to convert measurements to same unit to determine whether she purchased the right amount of ribbon or not.
Mimi purchased 5 yards of ribbon which is less than what she needed that is 5.5 yards
Step-by-step explanation:
Yes we need to convert measurements to same unit to determine whether she purchased the right amount of ribbon or not.
We cannot compare two different units therefore, we are always required to convert all the measurements into a single unit for the sake of comparison.
Mimi needs eleven pieces of rhinestone ribbon.
Each piece is 18-inch long.
So the total amount of ribbon that she need is
Total amount needed = 11*18
Total amount needed = 198 inches
Convert the amount of ribbon from inches to yards
1 yard is equal to 36 inches
Total amount needed = 198/36
Total amount needed = 5.5 yards
But Mimi purchased 5 yards of ribbon which is less than what she needed that is 5.5 yards.
Buying options:
$6 per yard
$55 for whole spool
Since Mimi needs 5.5 yards or round it to nearest whole because ribbon is sold in per yard basis so 6 yards of ribbon will cost
Cost = $6*6 = $36
$36 are less than $55 therefore, it is better to buy on per yard basis rather than the whole spool of ribbon.
A 2-row table with 9 columns. The first row is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. The second row is labeled f of x with entries negative 54, negative 20, negative 4, 0, negative 2, negative 4, 0, 16, 50. Which interval contains a local maximum for this function? Which interval contains a local minimum for this function?
Answer:
(-2,0) and (0,2)
Step-by-step explanation: I GOT IT RIGHT ON EDGINUITY
THANK ME LATER!!
Answer:
Step-by-step explanation:
Answer above is right!
What is the slope of
the line parallel to 3x +
y = 12?
Answer:
slope = -3
Step-by-step explanation:
1) Rearrange eqn into slope intercept form
slope intercept form: y = mx + b
where...
m = the slope
b = the y-intercept (where the line crosses the y axis)
3x + y = 12
y = -3x+12
2) Know parallel rule. A line that runs parallel has the same slope but a different y-intercept
So the slope is: -3
Jane moved from a house with 58 square feet of closet space to an apartment with 38.86 square feet of closet space. What is the percentage decrease of Jane's closet space?
Answer:
figure it out
Step-by-step explanation:
What is the approximate value of x? Round to the nearest tenth.
50°
6 cm
3.1 cm
3.9 cm
4.6 cm
5.4 cm
O
Using the sine ratio (SOH), the approximate value of x to the nearest tenth is: 4.6 cm.
What is the Sine Ratio?The sine ratio in Trigonometry is given as: sin ∅ = opposite/hypotenuse.
Thus, given:
∅ = 50°
Hypotenuse = 6 cm
Opposite = x cm
Plug in the values in to the sine ratio:
sin 50 = x/6
x = sin 50 × 6
x = 4.6 cm
Therefore, using the sine ratio (SOH), the approximate value of x to the nearest tenth is: 4.6 cm.
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foot????????¿????????¿??????¿???????
Answer:
foot = 12 inches
Step-by-step explanation:
Una pileta se vacía con una bomba que extrae agua a razón de 400 litros por minuto. Al encender la bomba, en la pileta hay 30000 litros de agua.
a) Hallar la función que indica el caudal restante de agua en función del tiempo, y
representarla gráficamente.
b) Determinar la cantidad de agua que queda en la pileta luego de media hora de
comenzar a vaciarla.
c) Determinar el tiempo necesario para vaciar la pileta por completo.
Answer:
a) The function that represents the amount of water as a function of time is
f(x) = 30,000 - 400x
b) The amount of water left in the sink after half an hour of starting to empty it
= 18,000 litres
c) The time it will take to empty the sink completely = 75 minutes.
Step-by-step explanation:
English Translation
A sink is emptied with a pump that extracts water at the rate of 400 liters per minute. when turning on the pump in the sink there were 30000 liters of water.
a) The time (in minutes) from when the pump is turned on is called x. find the function that represents the amount of water left in the sink as a function of time
b) Determine the amount of water left in the sink after half an hour of starting to empty it.
c) Determine the time it will take to empty the sink completely?
a) Speed is a quantity that is described as the rate of change of another quantity with time.
So, the speed of emptying the sink is given as
Speed = (Amount of water emptied) ÷ (Time taken to empty that amount of water).
The Speed of emptying the sink is given as 400 litres/min
Time taken to empty the sink = x
Let the amount of water left in the sink, a function of the time taken to empty the sink, be f(x)
Amount of water emptied = 30,000 - f(x)
400 = [30000 - f(x)] ÷ x
30000 - f(x) = 400x
f(x) = 30,000 - 400x
b) Determine the amount of water left in the sink after half an hour of starting to empty it.
f(x) = 30000 - 400x
x = 30 mins
f(x) = 30000 - 400(30) = 18,000 litres
c) Determine the time it will take to empty the sink completely?
f(x) = 30000 - 400x
when the sink is completely empty, the amount of water left in the sink is 0 litres, that is, f(x) = 0 litres
0 = 30000 - 400x
400x = 30000
x = (30000/400) = 75 minutes.
Hope this Helps!!!
In the diagram shown on circle A, segment CD is tangent to the circle at point D. If CD=23 and CA = 28.
then which of the following is closest to mZC?
Answer:
35°Step-by-step explanation:
The diagram is shown in the image attached.
A tangent is a line that intercepts at one unique point. When we have a tangent about a circle, an important results is that the tangent is perpendicular to the radius, because a radius can be seen as perpendicular to any point of the circle.
That means, the triangle formed ADC is a right triangle, because [tex]\angle D= 90\°[/tex].
Now, we know that [tex]CD=23[/tex] and [tex]CA=28[/tex], which are leg and hypothenuse, respectively.
So, to find [tex]m \angle C[/tex] we just need to use trigonometric reasons, specifically, the cosine funtion, because it relates the adjacent leg and the hypothenuse.
[tex]cos(C)=\frac{CD}{CA}=\frac{23}{28} \\C=cos^{-1}(\frac{23}{28} ) \approx 35 \°[/tex]
Therefore, the measure of angle C is 35°, approximately.
The question seems to seek the measure of angle mZC using properties of tangents and circles, but the provided references don't offer a clear method to find it with the given data. Therefore, it is not possible to calculate the angle without additional information or a specific figure.
Explanation:Given the information in the question, we are asked to find the measure of angle m√C in a circle where segment CD is tangent to the circle at point D, CD = 23, and CA = 28. The problem seems to be related to the properties of tangents and circles, specifically the tangent-secant theorem which states that if a tangent and a secant (or diameter) intersect at the point of tangency, the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external part (in this case, CD and DA).
However, the extracted references do not provide a clear or direct method for calculating the measure of angle m√C. The references are disjointed and relate to various other unrelated geometrical and physical contexts, like vector differences, spherical triangles, and integral segments.
Without a specific figure or more context, it is not possible to accurately determine the measure of angle m√C based solely on the information provided.
In a boutique, a $14 scarf is marked, "20% off." What is the sale price of the scarf?
Answer:
11.2
Step-by-step explanation:
20 percent of 14 is 2.8 14 minus 2.8 is 11.2
Which statement correctly describes the relationship between the graph of f(x)=4x and the graph of g(x)=f(x) 3 ?
a. the graph of g(x) is translated 3 units up from the graph of f(x) .
b. the graph of g(x) is translated 3 units right from the graph of f(x) .
c. the graph of g(x) is translated 3 units down from the graph of f(x) .
d. the graph of g(x) is translated 3 units left from the graph of f(x) .
Last year for 6 consecutive months, Sam recorded the total number of miles for each month. These miles were: 1,086, 997, 1,534, 1,637, 880 and 1,002. What was the median number of miles that Sam drove during those months? miles
Answer:
The median number of miles that Sam drove during those months is 1044 miles
Step-by-step explanation:
The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median.
For a set of n values
First we order the values in an increasing way.
If n is odd, the median is the value at the position (n+1)/2
If n is even, the median is the average of the values at the positions n/2 and (n/2) + 1
In this problem:
6 values
Ordered in an increasing way:
880, 997, 1002, 1086, 1534, 1637
6 is an even value.
6/2 = 3. The third element is 1002
6/2 + 1 = 4. The fourth element is 1086.
Average: (1002 + 1086)/2 = 1044
The median number of miles that Sam drove during those months is 1044 miles
We have 50 video gamers who share information about their favorite games. 20 people say that Borderlands II is their favorite game. 33 say their favorite game is Fortnite, while 19 declare Minecraft as their favorite game (note that a single person can have several favorite games). 15 people say that Borderlands and Fortnite are both favorites, while 10 say that both Borderlands and Minecraft are their favorites. Finally, 5 people declare all 3 of the games as their favorites. How many people declared Minecraft and Fortnite (exclusively) as their favorites?
Answer:
2 people
Step-by-step explanation:
Total number of people (n) = 50
Borderlands II (B) = 20
Fortnite (F) = 33
Minecraft (M) = 19
Borderlands and Fortnite (B&F) = 15
Borderlands and Minecraft (B&M)= 10
All games (B&M&F) = 5
The number of people that claimed more than one game as their favorite (X) is given by:
[tex]X=M+B+F-n\\X=19+20+33-50\\X=22\ people[/tex]
Those people can be divided in B&F only, B&M only, M&F only and B&M&F:
[tex]X=(B\&M-B\&M\&F)+(B\&F-B\&M\&F)+(M\&F-B\&M\&F)+B\&M\&F\\X=B\&M+B\&F+M\&F-2*B\&M\&F\\22=10+15+M\&F-2*5\\M\&F=7\ people[/tex]
7 people claimed that Minecraft and Fortnite were their favorites however, 5 of those people claimed all of the games as their favorite. Therefore, only 2 people declared Minecraft and Fortnite (exclusively) as their favorites.
Answer:
2
Step-by-step explanation:
What is cot based on the image
the answer is b I'm sure
need math help pls:))
Answer:
see below
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationships between triangle sides and trig functions. For the angle of interest, the diagram shows values for the Opposite side (12) and the Adjacent side (16.5). The mnemonic tells you that these are related to the Tangent of the angle:
Tan = Opposite/Adjacent
tan(θ) = (12/16.5)
The measure of an angle is 43.5 degrees . What is the complementary angle?
A complimentary angle has to add up two angles to equal 90 degrees.
We have one angle which is 43.5 degrees, so all we have to do is subtract 43.5 degrees from 90 degrees to find the missing angle.
90 degrees minus 43.5 degrees is 46.5 degrees.
That means the missing angle is 46.5 degrees.
It should be noted that the complementary angles is 46.5°.
From the information given, measure of an angle is 43.5 degree. It should be noted that the sum of the angles in complementary angles equal 90°.
Therefore, the value of the remaining angle will be:
= 90 - 43.5°
= 46.5°
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Find all the critical points of h(x) = x^3 − 3x^4 and categorize them as local
maximums, local minimums, or neither, using the first derivative test.
Answer:
0 is an inflection point
1/4 is a local maximum.
Step-by-step explanation:
To begin with you find the first derivative of the function and get that
[tex]h'(x) = 3x^2 - 12x^3[/tex]
to find the critical points you equal the first derivative to 0 and get that
[tex]3x^2 - 12x^3 = 0, x = 0,1/4[/tex]
To find if they are maximums or local minimums you use the second derivative.
[tex]h''(x) = 6x-36x^2[/tex]
since [tex]h''(0) = 0[/tex] is neither an inflection point, and since [tex]h''(1/4) = -3/4 <0[/tex] then 1/4 is a maximum.
When a trigonometric equation is solvable, it often has infinitely many solutions; and (depending on the context) the first solution we find may not be the one we want. Explain how, given one solution of a trigonometric equation of a trigonometric equation (say, one that reduces down to ), we can find other solutions from the first solution we find, without resorting to a calculator.'
Answer:
(See explanation for further details)
Step-by-step explanation:
An approach is handling the trigonometric equation so that number of trigonometric functions can be reduce to one, in order to determine the periodicity of complete expression and therefore, to determine the complete set of solutions.
25y = 15y +75
y= 7.5
infinite solutions
no solution
y= 750
Answer:
y= 7.5
Step-by-step explanation:
25y = 15y +75
-15y -15y
10y = 75
÷10 ÷10
y = 7.5
The Harris family and the Baker family each used their sprinklers last summer. The water output rate for the Harris family's sprinkler was 20L per hour. the water output rate for the Baker family's sprinkler was 35L per hour. The families used their sprinklers for a combined total of 75 hours, resulting in a total water output of 2025L. How long was each sprinkler used?
Answer:40 hr and 35 hr
Step-by-step explanation:
Given
Harris family sprinkler output rate is [tex]20\ L/\text{per hour}[/tex]
and Baker family sprinkler output rate is [tex]35\ L/\text{per hour}[/tex]
Total output of two is [tex]2025\ L[/tex]
Suppose Harris family sprinkler used for [tex]t_1[/tex] time and Baker family for [tex]t_2 [/tex]time then
[tex]20\times t_1+35\times t_2=2025\quad \ldots(i)[/tex]
and [tex]t_1+t_2=75[/tex]
[tex]t_1=75-t_2[/tex]
Substitute the value in [tex](i)[/tex]
[tex]\Rightarrow 20\times (75-t_2)+35t_2=2025[/tex]
[tex]\Rightarrow 1500-20t_2+35t_2=2025[/tex]
[tex]\Rightarrow 15t_2=525[/tex]
[tex]\Rightarrow t_2=\frac{525}{15}[/tex]
[tex]\Rightarrow t_2=35\ hr[/tex]
[tex]\therefore \ t_1=75-35=40\ hr[/tex]
Therefore Harris family use [tex]40\ hr[/tex] of sprinkler and Baker family use [tex]35\ hr[/tex] of sprinkler
Dozen cookies calls for 2/4 cup of flour. How much flour would be needed to triple the recipe
Answer:
1 2/4
Step-by-step explanation: 2/4 * 3 = 1 2/4
An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.82 per gallon and the population standard deviation is $0.33. You decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute the mean price for the sample.
a. what is the standard error of the mean in this experiment?
b. what is the probability that the sample mean is between $3.78 and $3.86?
c. what is the probability that the difference between the sample mean and the population mean is less than $0.01?
d. what is the likelihood the sample mean is greater than $3.92?
Answer:
(a) The standard error of the mean in this experiment is $0.052.
(b) The probability that the sample mean is between $3.78 and $3.86 is 0.5587.
(c) The probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.
(d) The likelihood that the sample mean is greater than $3.92 is 0.9726.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample mean is given by,
[tex]\mu_{\bar x}=\mu[/tex]
And the standard deviation of the distribution of sample mean is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=40\\\mu=\$3.82\\\sigma=\$0.33[/tex]
As n = 40 > 30, the distribution of sample mean is [tex]\bar X\sim N(3.82,\ 0.052^{2})[/tex].
(a)
The standard error is the standard deviation of the sampling distribution of sample mean.
Compute the standard deviation of the sampling distribution of sample mean as follows:
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=\frac{0.33}{\sqrt{40}}\\\\=0.052178\\\\\approx 0.052[/tex]
Thus, the standard error of the mean in this experiment is $0.052.
(b)
Compute the probability that the sample mean is between $3.78 and $3.86 as follows:
[tex]P(3.78<\bar X<3.86)=P(\frac{3.78-3.82}{0.052}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{3.86-3.82}{0.052})[/tex]
[tex]=P(-0.77<Z<0.77)\\=0.77935-0.22065\\=0.5587[/tex]
Thus, the probability that the sample mean is between $3.78 and $3.86 is 0.5587.
(c)
If the difference between the sample mean and the population mean is less than $0.01 then:
[tex]\bar X-\mu_{\bar x}<0.01\\\\\bar X-3.82<0.01\\\\\bar X<\$3.83[/tex]
Compute the value of [tex]P(\bar X<3.83)[/tex] as follows:
[tex]P(\bar X<3.83)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{3.83-3.82}{0.052})[/tex]
[tex]=P(Z<0.19)\\=0.57535\\\approx 0.5754[/tex]
Thus, the probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.
(d)
Compute the probability that the sample mean is greater than $3.92 as follows:
[tex]P(\bar X>3.92)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{3.92-3.82}{0.052})[/tex]
[tex]=P(Z<1.92)\\=0.97257\\\approx 0.9726[/tex]
Thus, the likelihood that the sample mean is greater than $3.92 is 0.9726.
The standard error is 0.0522. The probability of the sample mean lying in a certain range and the difference from the population mean being less than a certain value can be determined using Z-scores and a Z-table. The likelihood of the sample mean being more than a certain value can also be determined in the same way.
Explanation:An economist is using the average price of a gallon of milk to measure inflation. The average price ($3.82) and the population standard deviation ($0.33) is known. Here are answers to your questions:
a. Standard Error of the mean: The Standard error (SE) is calculated by dividing the standard deviation by the square root of the sample size. So SE = Standard Deviation / √n = 0.33 / √40 = 0.0522 per gallon.
b. Probability of the sample mean between $3.78 and $3.86: This is a Z-score question. Z = (X- µ)/SE. So, first find the Z-scores for $3.78 and $3.86, and then find the probability corresponding to these Z-scores from the Z-table. This probability is the chance that the sample mean is between $3.78 and $3.86.
c. Probability of the difference: Similarly, find the Z-score for the difference of $0.01 and look up the probability in the Z-table. This gives the likelihood of the sample mean being less than $0.01 away from the population mean.
d. Likelihood the sample mean is greater than $3.92: Use the same method to work out the Z-score for $3.92. The Z-table gives you the probability of the sample mean being less than $3.92, so subtract that from 1 to get the probability of it being more than $3.92.
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Completely factor this quadratic expression: 4x2 + 12x − 72.
Answer:
4(x-3)(x+6)
Step-by-step explanation:
Factor out the 4
4(x2 + 3x - 18)
what 2 numbers add to 3 and multiply to - 18?
-3 and 6
therefore 4x2 + 12x − 72 = 4(x-3)(x+6)
Answer:
(4x² + 24x)- (12x + 72)
4x( x+ 6)- 12(x + 6)
ans = (4x - 12)(x + 6)
Matthew invests $500 into an account with a 2.5% interest that is compounded quarterly. How much money will he have in this account if he keeps it for 10 years? Round your answer to the nearest cent. Do NOT round until you have calculated the final answer.
Answer:
Step-by-step explanation:
CORRECT ANSWER IS : $641.51
Use the compound interest formula and substitute the given values: A=$500(1+0.0254)4(10). Simplify using the order of operations: A=$500(1.00625)40=$500(1.283026821)≈ $641.51.
After ten years, Matthew will have $641.51 in the account, rounded to the closest penny.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. [tex]A = P(1 + r/n)^{nt[/tex], where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
We can use the formula for compound interest to calculate how much money Matthew will have in the account after 10 years:
[tex]A = P(1 + r/n)^{nt[/tex]
Where:
A = final amount
P = principal (initial amount invested) = $500
r = annual interest rate (as a decimal) = 0.025
n = number of times interest is compounded per year = 4 (quarterly)
t = time in years = 10
Plugging in the values, we get:
[tex]A = 500(1 + 0.025/4)^(4*10)\\A = 500(1.00625)^{40}\\A = 500(1.305011)[/tex]
A = $641.51
Therefore, Matthew will have $641.51 in the account after 10 years, rounded to the nearest cent.
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A line passes through the point (4, −9) and has a slope of 5/2.
Write an equation in slope-intercept form for this line.
The equation of the line that has a slope of 5/2 and passes through the point (4, -9) is y = 5/2x -19.
Explanation:The equation of a line in slope-intercept form is given by the formula y = mx + b, where m is the slope and b is the y-intercept. We're given that this line has a slope of 5/2 and it passes through the point (4, -9).
Plugging the known values into the equation, we get: -9 = (5/2) * 4 + b. By solving for b, we find the y-intercept of the line.
-9 = 10 + b --> b = -9 - 10 = -19
So the equation of the line in slope-intercept form is y= 5/2x - 19
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