Answer:
a) The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.
b) Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.
c) 37 cars would have to be sampled.
Step-by-step explanation:
Question a:
We have the sample standard deviation, and thus, the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{6.2}{\sqrt{15}} = 3.4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 26.7 - 3.4 = 23.3 mpg.
The upper end of the interval is the sample mean added to M. So it is 26.7 + 3.4 = 30.1 mpg.
The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.
b. What would happen to the interval if you increased the confidence level from 95% to 99%? Explain
Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.
c. The lead engineer is not happy with the interval you constructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?
Width is twice the margin of error, so a margin of error of 2 would be need. To solve this, we have to consider the population standard deviation as [tex]\sigma = 6.2[/tex], and then use the z-distribution.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How many cars would you have to sample to create the interval the engineer is requesting?
This is n for which M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 1.96\frac{6.2}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 1.96*6.2[/tex]
[tex]\sqrt{n} = \frac{1.96*6.2}{2}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*6.2}{2})^2[/tex]
[tex]n = 36.9[/tex]
Rounding up:
37 cars would have to be sampled.
What is the slope of the line that passes through the points (10,8) and (-15,18)?
Write your answer in simplest form.
Answer:
I believe it is 2/5 fraction
Answer:
-2/5
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 18-8)/(-15-10)
= 10/-25
= -2/5
How does sample size affect determinations of statistical significance? The smaller the sample size, the more confident one can be in one's decision to reject or retain the null hypothesis. The smaller the sample size, the greater the probability that the variable has an effect. The larger the sample size, the more accurate the estimation of the true population value. The larger the sample size, the greater the probability that the variable has an effect.
Answer:
The larger the sample size, the more accurate the estimation of the true population value.
Step-by-step explanation:
As large will be the sample size more data will be shown and more are the c c changes of it being an estimate of a true population. The sample size can be determined on the basis of use of experience, target variance, confidence level, and target for power.Bill and Will, starting together, ran a 400-meter race, each running at a constant speed. When Bill crossed the finish line, Will was exactly 20 yards behind Bill. They decide to run the race again, this time Bill starting 20 yards behind the original starting line and each running at his same constant speed as before. This time _______ wins by _______ yards.
Answer: Bill, 1
Step-by-step explanation:
Given
Bill and will run a 400 yard race.
Bill win by 20 yard
Suppose the speed of Bill and Will are [tex]\mathbf{v_b}, \mathbf{v_w}[/tex]
time taken for them is same for the first time
[tex]\Rightarrow t_b=t_w\\\\\Rightarrow \dfrac{400}{v_b}=\dfrac{400-20}{v_w}\\\\\Rightarrow \dfrac{v_b}{v_w}=\dfrac{400}{380}\ or\ \dfrac{20}{19}\\[/tex]
Now Bill starts 20 yards behind the starting line
Ratio of their time to cover the distances is
[tex]\Rightarrow \dfrac{t_b}{t_w}=\dfrac{\dfrac{420}{v_b}}{\dfrac{400}{v_w}}\\\\\Rightarrow \dfrac{t_b}{t_w}=\dfrac{420}{400}\times \dfrac{v_w}{v_b}\\\\\Rightarrow \dfrac{t_b}{t_w}=\dfrac{21}{20}\times \dfrac{19}{20}\\\\\Rightarrow \dfrac{t_b}{t_w}=\dfrac{399}{400}[/tex]
The obtained ratio is less than 1. Thus, the time taken by Bill is less than Will.
For the same time Bill wins
[tex]\therefore \dfrac{v_b\times t}{v_w\times t}=\dfrac{420}{x}\\\\\Rightarrow x=19\times 21\\\Rightarrow x=399\ m[/tex]
Thus, Will has covered only 399 yards.
This time Bill wins by 1 yards.
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Using the following system of equations to help, what is the value of x-2y?
3x + 2y =48
2x +3y =12
Please help.
ou invested 7000 between two accounts paying 4% and 9% annual interest, respectively. If the total interest earned for the year was $430 how much was invested at each rate? $ nothing was invested at and $ nothing was invested at
9514 1404 393
Answer:
$3000 at 9%$4000 at 4%Step-by-step explanation:
Let x represent the amount invested at 9%. Then 7000-x was invested at 4% and the interest earned was ...
9%·x +4%(7000-x) = 430
5%·x +280 = 430 . . . . . . . . . simplify
0.05x = 150 . . . . . . . . . . . subtract 280
x = 3000 . . . . . . . . . . divide by 0.05
$3000 was invested at 9%; $4000 was invested at 4%.
Find the measure of the incanted angle to the nearest degree
Answer:
34⁰
Step-by-step explanation:
let unknown angle be x
cos x=19/23
cos x=0.826
x=cos inverse of 0.826
x=34.3⁰
Larissa is ordering nachos at a restaurant, and the server tells her that she can have up to four toppings: ground beef, black beans, refried beans, and sour cream. Since she cannot decide how many of the toppings she wants, she tells the server to surprise her. If the server randomly chooses which toppings to add, what is the probability that Larissa gets just refried beans and sour cream
Answer:
0.0625
Step-by-step explanation:
Given that :
Number of toppings = 4 (ground beef, black beans, refried beans, and sour cream)
The probability of choosing any particular topping at random from the four is :
Probability = required / total possible outcomes
Hence, P = 1 / 4 = 0.25
Hence, the probability of choosing : getting refried bean and sour cream :
P(refried bean) = 1/4
P(sour cream) = 1/4
P(refried bean and sour cream) = 1/4 * 1/4 = 1/16 =
0.0625
GIVING 25 POINTS AND BRAINIER IF ANSWERED!
What is one thing you would not do when finding the question in a word problem?
A. Look for a problem similar to the word problem you are trying to solve.
B. The question may not be directly stated.
C. So you can understand what the facts are in the word problem.
D. To define your strategy or game plan to solve the word problem.
Answer:
B. The question may not be directly stated.
Help please ….. help
Answer:
Step-by-step explanation:
a) categorical
b) add all of the numbers and divide by how many numbers there were.
c) outliers means any that were far away from the rest of the data
d) not entirely, you can make an estimate based on it, but nat an exact answer.
You measure 40 watermelons' weights, and find they have a mean weight of 67 ounces. Assume the population standard deviation is 11.4 ounces. Based on this, what is the maximal margin of error associated with a 99% confidence interval for the true population mean watermelon weight.
Answer:
[tex]35.36,44.64[/tex]
Step-by-step explanation:
Sample size [tex]n=40[/tex]
Mean weight [tex]\=x =67[/tex]
Standard deviation [tex]\sigma=11.4[/tex]
Confidence Interval [tex]CI=0.99[/tex]
\alpha==0.01
Therefore
[tex]Z_{\frac{\alpha}{2}}=Z_[0.005][/tex]
From table
[tex]Z_{\frac{\alpha}{2}}=2.576[/tex]
Generally, the equation for Margin of error is mathematically given by
[tex]M.E=Z_{\frac{\alpha}{2}}*(\frac{\sigma}{sqrt{n}}[/tex]
[tex]M.E=2.576*(\frac{11.4}{\sqrt{40}}[/tex]
[tex]M.E=4.64[/tex]
Therefore Estimated mean is
[tex]\=x-M.E<\mu <\=x +E[/tex]
[tex]40-4.64<\mu< 40+4.64[/tex]
[tex]35.36<\mu < 44.64[/tex]
[tex]35.36,44.64[/tex]
A two-digit number is of the number
7
formed by reversing its digits. When the
number is increased by 2 times the sum of
its digits, it becomes 54. Find the number.
Answer:
C
Step-by-step explanation:
A bookkeeper needs to post the cost of the desk and the chair into his records. The cost of the desk is fives times the cost if the chair. The total cost of the desk and the chair is $720, what is the cost of the chair?
Answer:
120
Step-by-step explanation:
720÷6
why?
becoz 6= 1+5
1 is the cosy of the chair
5 is the cost of the desk
3/5x - 1/2x= 1, please help me to solve this
Answer:
x = - 10
Step-by-step explanation:
(6x -5x) / 10 = - 1
x = - 10
Can someone please help me with part b ? It would be so appreciated you have no idea ;)
Answer:
absolutely yes, because pythagorean theorem is used in a right triangle
and when we match a line from the tee to the hole, we have a right triangle
Step-by-step explanation:
0.5 kilograms (kg) is equal to how many ounces? Round your answer to the
Answer:
17.637 ounces
Step-by-step explanation:
35.274 ounces is 1 kilogram so divide 35.274 by 2
Question 6 plz show ALL STEPS
Step-by-step explanation:
6a. Both the x and y coordinates are negative so this means isn't must be in the Third Quadrant.
6b. The measure of this using the unt circle is
[tex] \cos(x) - \frac{1}{2} [/tex]
[tex] \sin(x) = - \frac{ \sqrt{3} }{2} [/tex]
In the unit circle, this occurs about
an angle of 240 degrees. We can find coterminal angles within the interval of 2 pi to -2 pi. Just subtract 260 from theta.( which is 240)
[tex]240 - 360 = - 120[/tex]
So the angles in the interval is
240, -120.
6c. pi/2 is the same as 90 degrees so this means that
[tex](240 + 90) = 330[/tex]
In the unit circle, we know that at 330 degrees,
[tex] \cos(330) = \frac{ \sqrt{3} }{2} [/tex]
[tex] \sin(330) = \frac{1}{2} [/tex]
So the coordinates are
(sqr root of 3/2, 1/2).
6d. pi is the same as 180 degrees so this means that
[tex](240 - 180) = 60[/tex]
In the unit circle, we know that 60 degrees,
[tex] \cos(60) = \frac{1}{2} [/tex]
[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]
So the coordinates are
(1/2, sqr root of 3/2)
Please help, I'll give brainliest to the correct answer <3
A company recently purchased a new set of laser printers.
The value of the laser printers P, in dollars, t years after the purchase can be represented by the function P(t)=1,900(0.82)t.
Interpret the meaning of the function in the context of this situation.(1 point)
The initial value of the laser printers was $1,900, and the value increases by 82% each year.
The initial value of the laser printers was $1,558, and the value decreases by 82% each year.
The initial value of the laser printers was $1,558, and the value decreases by 18% each year.
The initial value of the laser printers was $1,900, and the value decreases by 18% each year.
Answer:
The initial value of the laser printers was $1,900, and the value decreases by 18% each year.
Step-by-step explanation:
Here ya go bestie <3
The number N(t) of supermarkets throughout the country that are using a computerized checkout system is described by the initial-value problem
dN/dt = N(1 − 0.0008N), N(0) = 1.
Required:
Predict how many supermarkets are expected to adopt the new procedure over a long period of time?
Answer:
1250 supermarkets
Step-by-step explanation:
Given
[tex]\frac{dN}{dt} = N(1 - 0.0008N)[/tex]
[tex]N(0) = 1[/tex]
Required
Number of supermarkets over a long period of time
To do this, we simply set
[tex]\frac{dN}{dt} = 0[/tex]
So, we have:
[tex]N(1 - 0.0008N) = 0[/tex]
Split
[tex]N = 0\ or\ 1 - 0.0008N = 0[/tex]
Solve: [tex]1 - 0.0008N = 0[/tex]
Collect like terms
[tex]0.0008N = 1[/tex]
Make N the subject
[tex]N = \frac{1}{0.0008}[/tex]
[tex]N = 1250[/tex]
So:
[tex]\lim_{t \to \infty} N(t) = 1250[/tex]
HELP!!!!!!!!!!!!!!!!!!!
Calculate the future value of $2,500.00, earning interest at a rate of 2 1/2% that is compounded quarterly for 4 years.
A) $3,711.26
B) $2,563.09
C) $2,762.07
D) $5,910,086.00
Answer:
C) $2,762.07
you can use a compound interest calculator to find the answer
Professor Iron always gives two exams in his communications class. He only uses the lower of the two scores that a student gets on the exams when he calculates the course grade. Put the grade on the first exam on the horizontal axis and the grade on the second exam on the vertical axis. What kind of preference a student should have for these two grades. Group of answer choices Perfect Complements Perfect Substitutes Cobb-Douglas Preference Neutral Preference
Answer:
Perfect complements
Step-by-step explanation:
Since minimum score of tests is to be considered. It is a case of perfect complements.
Correct option is
Perfect complements
A product is introduced into the market. Suppose a product's sales quantity per month q ( t ) is a function of time t in months is given by q ( t ) = 1000 t − 150 t 2 And suppose the price in dollars of that product, p ( t ) , is also a function of time t in months and is given by p ( t ) = 150 − t 2 A. Find, R ' ( t ) , the rate of change of revenue as a function of time t
Answer:
[tex]r'(t) = 298t -850[/tex]
Step-by-step explanation:
Given
[tex]q(t) = 1000t - 150t^2[/tex]
[tex]p(t) = 150t - t^2[/tex]
Required
[tex]r'(t)[/tex]
First, we calculate the revenue
[tex]r(t) = p(t) - q(t)[/tex]
So, we have:
[tex]r(t) = 150t - t^2 - (1000t - 150t^2)[/tex]
Open bracket
[tex]r(t) = 150t - t^2 - 1000t + 150t^2[/tex]
Collect like terms
[tex]r(t) = 150t^2 - t^2 + 150t - 1000t[/tex]
[tex]r(t) = 149t^2 -850t[/tex]
Differentiate to get the revenue change with time
[tex]r'(t) = 2 * 149t -850[/tex]
[tex]r'(t) = 298t -850[/tex]
the camdens drove 116 miles on 5 gallons of gas. at this rate, how many miles can they drive on 7 gallons of gas
Answer:
162.4 miles
Step-by-step explanation:
We can write a ratio to solve
116 miles x miles
----------------- = ------------
5 gallons 7 gallons
Using cross products
116*7 = 5x
Divide by 5
812 /5 = 5x/5
162.4 =x
162.4 miles
Can someone please help me thanks in advance!
Step-by-step explanation:
Bro your question is quiet blur... Please help me out..
hope it Wonderful.
^_^....!_!_
(b)
The Cartesian coordinates of a point are given.
(1, -5)
(i) Find polar coordinates (r, 0) of the point, where r> 0 and 0 = 0 < 2.
(r, 0) =
(
(ii) Find polar coordinates (r, 0) of the point, where r < 0 and 0 < theta<2pi.
(r, 0) =
Answer:
Step-by-step explanation:
a) r = √(1² + (-5²)) = √26 = 5.09901...
θ = tan⁻¹(-5/1) = 4.9097... radians
(5.1, 4.9)
b) r = - 5.09901...
θ = 4.9097... - π = 1.76819...
(-5.1, 1.8)
Find the x- and y-intercept of the line
X+4y=36
Which of the following is equal to -27?
Step-by-step explanation:
here's the answer to your question
Answer: Third Choice. 3i√3
Step-by-step explanation:
Concept:
Here, we need to know the idea of radical expression and an imaginary number.
A radical expression is any mathematical expression containing a radical symbol. If you need to multiply the number outside of radical back into the radical, then you need to square the number then multiply.
For example: 2√5. We need to first square 2, which gives us 4. Then, it becomes √(4 × 5) = √20Imaginary numbers are the numbers when squared it gives the negative result. An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i² = −1.
Solve:
3√3 = √(3 × 3²) = √27 FALSE
-3√(3i) = √(3i × (-3)²) = √27i FALSE
3i√3 = √(3 × (3i)²) = √-27 TRUE
3√(3i) = √(3i × 3²) = √27i FALSE
As we can see from above, only the third choice equals √-27.
Hope this helps!! :)
Please let me know if you have any questions
Help me! Thanks!!!!!!
Answer:
there are infinite solutions
Step-by-step explanation:
if you add y-3 to both sides of the first equation, you will see that it is equal to the second equation, so they are the same line. Therefore, there are infinite solutions to this system
The diameter of a regulation soccer ball is about 8 and three-fifths inches. This number was graphed on a number line.
A number line going from negative 9 to positive 9. Point A is between negative 9 and negative 8, point B is between negative 7 and negative 6, point C is between 6 and 7, point D is between 8 and 9.
Which point could be the point representing the graph of the diameter of the ball?
A
B
C
D
Answer:
D
Step-by-step explanation:
8 and 3/5 = 8.2 and 8.2 is between 8 and 9 so the answer is D.
find the sum or difference of 4/5 - (-3 4/5)
Answer:
4 3/5
Step-by-step explanation:
4/5 - (-3 4/5)
Subtracting a negative is like adding
4/5 + 3 4/5
3 8/5
3 5/5 + 3/5
3+1+3/5
4 3/5
What is the amswerdkdmxmmdmdmdm
Answer:
HUH?
Step-by-step explanation:
