Answer:
a) -6 mpg.
b) 2.77 mpg
c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Gas mileage A: Mean 36, standard deviation 6, sample of 50:
So
[tex]\mu_A = 36, s_A = \frac{6}{\sqrt{50}} = 0.8485[/tex]
Gas mileage B: Mean 42, standard deviation 8, sample of 50:
So
[tex]\mu_B = 42, s_B = \frac{8}{\sqrt{50}} = 1.1314[/tex]
Distribution of the difference:
Mean:
[tex]\mu = \mu_A - \mu_B = 36 - 42 = -6[/tex]
Standard error:
[tex]s = \sqrt{s_A^2+s_B^2} = \sqrt{0.8485^2+1.1314^2} = 1.4142[/tex]
A. Find the point estimate.
This is the difference of means, that is, -6 mpg.
B. Find the margin of error
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 Ztable as such z has a pvalue 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 = zs = 1.96*1.4142 = 2.77[/tex]
The margin of error is of 2.77 mpg
C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)
The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg
The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg
The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).
What is the volume of this composite solid?
4 m
2 m
7 m
2 m
2 m
O A. 58 cubic meters
O B. 64 cubic meters
C. 78 cubic meters
D. 62 cubic meters
Answer:78
Step-by-step explanation:
Did it
A child pool is 3.8 feet wide 5.5 feet long and 1.2 fee deep, what is the volume of the pool?
Answer:
25.08
Step-by-step explanation:
Answer:
25.08 cubic feet
Step-by-step explanation:
v = l * w * h
v = 5.5 * 3.8 * 1.2
v = 25.08 cubic feet
1. Based on the construction below, which conclusion
is not always true?
OA. AB 1 CD
OB. AB = CD
OC. AE = EB
OD. CE = DE
Answer: B ,I just completed the assignment
AB=CD is not always true. Therefore, option B is the correct answer.
From the given construction, we need to find which conclusion is not always true.
What is a line bisector?A perpendicular bisector is defined as a line or a line segment that divides a given line segment into two parts of equal measurement. 'Bisect' is the term used to describe dividing equally. Perpendicular bisectors intersect the line segment that they bisect and make four angles of 90° each on both sides.
Here, AB⊥CD.
Since CD is the perpendicular bisector of AB.
AE=EB and CE=DE
AB=CD is not always true. Therefore, option B is the correct answer.
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You own a gas station. You are supervising the filling of the station's cylindrical fuel tank. The fuel tank has a height of
36 feet and can hold 2,500 cubic yards of fuel.
Based on these specifications, what is the radius of the fuel tank, rounded to the nearest hundredth of a yard?
0 4.70
08.15
22.12
25.58
66.35
Answer:
8.15
Step-by-step explanation:
a block of wood has a mass of 3.5 kilogram. the wood has density 0.065 kg/m3
work out the volume of the block of wood
Step-by-step explanation:
Given :-
A block of wood has a mass of 3.5 kilogram. The wood has density 0.065 kg/m³.And we need to find out the volume of the wood. Density , volume and mass are related as ,
Density :-
Mass per unit Volume .[tex]\implies\rm Density =\dfrac{Mass}{Volume}[/tex]
Substitute the respective values :-
[tex]\implies\rm Density =\dfrac{Mass}{Volume}\\\\\rm\implies 0.065 kg/m^3=\dfrac{3.5kg}{V}\\\\\rm\implies Volume = \dfrac{3.5kg}{0.065 kg/m^3}\\\\\implies\boxed{\red{\rm Volume = 53.84 m^3}}[/tex]
Hence the volume is 53.84 m³ .
Louis wants to carpet the rectangular floor. The floor has an area of 507 square feet. The width of the floor is 1/3 it's length. what is the length of the floor?
Width x Length
X = Length
[tex]\frac{1}{3}[/tex] = 507
[tex]x^{2}[/tex] = 1521 [tex]ft^{2}[/tex]
X = 39[tex]ft[/tex]
A researcher surveyed 8 people to see if there is a
relationship between years of education and starting
salaries. The data points are shown on the graph.
Which best represents the equation of the trend line
shown on the graph? (Note that the graph has a break
on the y axis
Answer: D.) y=1.25x + 7.5
Step-by-step explanation:
edg 2021
Answer: D on edg 2021. have a good day :)
Patricia needs 2 pints of purple icing to decorate cupcakes. She will use the following recipe for 1 pint of purple icing.
• 1 pint of white icing
4 1/4 teaspoons of blue food coloring
2 1/2 teaspoons of red food coloring.
explain two different ways for patricia to find total number of teaspoons of blue and red food coloring necessary to make 2 pints of purple icing
Answer:
Step-by-step explanation:
i’m thinking of the second way right now, but one way is doubling the recipe
2 pints of white icing
8 1/2 teaspoons of blue food coloring
5 teaspoons of red food coloring
Question 23 of 25
Find x. Round your answer to the nearest integer.
15
37
х
O
A. 6
B. 9
0 o o
C. 12
D. 8
Answer:
[tex]x[/tex] rounded to the nearest integer would be 12.
Step-by-step explanation:
In order to calculate the length of [tex]x[/tex], you can use the law of sines, a trigonometry rule used to solve the angles and sides of a right triangle. The law of sines states that the sine of an angle in a triangle divided by its opposite side is equivalent to all other angles taken to their sines and divided by their opposite sides. Using this rule, we can now calculate the length of [tex]x[/tex]. In this case, [tex]\frac{sin(90^{o})}{15} = \frac{sin(53^{o})}{x}[/tex] ⇒ [tex]\frac{15}{sin(90^{o})} = \frac{x}{sin(53^{o})}[/tex] ⇒ [tex]x=\frac{15*sin(53^{o})}{sin(90^{o})}[/tex] ⇒ [tex]x=15*sin(53^{o} )[/tex] ⇒ [tex]x[/tex] ≈ 12. So side [tex]x[/tex] rounded to the nearest integer would be 12.
The value of x in the given triangle is 12, Option C is correct.
The given triangle is a right angled triangle.
We need to find the value of x.
We know that cosx is adjacent side by hypotenuse.
Cos 37 = Adjacent side/ Hypotenuse
The value of cos37 degrees is 0.7654
0.7654 = x/15
15×0.7654=x
11.5 =x
12=x
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Select the correct answer.
Energized and Powercell are companies that manufacture alkaline batteries. Both companies claim that their batteries last longer than the average alkaline battery.
Anju decided to conduct a test to see whether their claims were true. He purchased 30 Energized batteries, 30 Powercell batteries, and batteries of other brands to conduct the test. The purchase selection was random, and the test was unbiased. The batteries that lasted longer than the average of all the batteries were stated to have passed the test. The batteries that did not last as long as the average of all the batteries were stated to have failed the test. The results for Energized and Powercell are displayed in this table.
Answer:
both manufactures' claims are true because most of there batteries lasted longer than the average alkaline battery.
Step-by-step explanation:
PLATO USERS
Answer:
Both companies claim that their batteries last longer than the average alkaline battery is true .
Step-by-step explanation:
Both companies claim that their batteries last longer than the average alkaline battery is true because most of the batteries of these companies did passed the test to last longer.
As we can project from that table given that around 77% Energized batteries passed the test and around 67% powered cell batteries passed the test.
hence we can also inferred from here that Energized batteries are more consistent.
Click here to know more about the sample table problem .
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Please help! Brainlyest answer!!
Answer:
The first number line
Step-by-step explanation:
.05m + 50 < 55
Subtract 50 from both sides
.05m < 5
Divide both sides by .05
m < 100
The first number line
12,000= 120 tens true or false
Answer:false
Step-by-step explanation:120 tens would be 1200
The number 12,000 does not equal 120 tens. Thus, it is false.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
12,000 = 120 tens
Simplify the equation, then we have
12,000 = 120 x 10
12,000 ≠ 1,200
The given equation is false.
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Subjects in a study by Dabonneville et al. (A-9) included a sample of 40 men who claimed to engage in a variety of sports activities (multisport). The mean body mass index (BMI) for these men was 22.41 with a standard deviation of 1.27. A sample of 24 male rugby players had a mean BMI of 27.75 with a standard deviation of 2.64. Is there sufficient evidence for one to claim that, in general, rugby players have a higher BMI than the multisport men? Let a ¼ :01.
Answer:
The responses can be defined as follows:
Step-by-step explanation:
Given:
[tex]H_o : \mu_1 = \mu_2\\\\H_a : \mu_1 < \mu_2[/tex]
Testing the hypothesis:
[tex]Z=\frac{( \bar{x_1}-\bar{x_2})}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}}}[/tex]
[tex]=\frac{(22.41-27.75)}{\sqrt{(\frac{1.27^2}{40}+\frac{2.64^2}{24})}}\\\\=-9.29\\\\[/tex]
[tex]a=0.01[/tex]
critical value [tex]Z(0.01)=-2.33[/tex] (using the standard normal table)
[tex]Z=-9.29<-2.33[/tex] so, we reject [tex]H_o[/tex].
Using the t-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, there is sufficient evidence for one to claim that, in general, rugby players have a higher BMI than the multisport men.
At the null hypothesis, it is tested that rugby players do not have a higher BMI than the multi-sport men, that is, the subtraction of the means is not greater than 0, hence:
[tex]H_0: \mu_R - \mu_M \leq 0[/tex]
At the alternative hypothesis, it is tested if they have a higher BMI, that is:
[tex]H_1: \mu_R - \mu_M > 0[/tex]
We have the standard deviation for the samples, hence, the t-distribution is used.
The standard errors are given by:
[tex]s_M = \frac{1.27}{\sqrt{40}} = 0.2008[/tex]
[tex]s_R = \frac{2.64}{\sqrt{24}} = 0.5389[/tex]
For the distribution of differences, the mean and the standard error are given by:
[tex]\overline{x} = \mu_R - \mu_M = 27.75 - 22.41 = 5.34[/tex]
[tex]s = \sqrt{s_M^2 + s_R^2} = \sqrt{0.2008^2 + 0.5389^2} = 0.5751[/tex]
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{5.34 - 0}{0.5751}[/tex]
[tex]t = 9.29[/tex]
Using a t-distribution calculator, for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05 and 40 + 24 - 2 = 62 df, the critical value is of [tex]t^{\ast} = 1.67[/tex]
Since the test statistic is greater than the critical value for the right-tailed test, there is sufficient evidence for one to claim that, in general, rugby players have a higher BMI than the multisport men.
You can learn more about the use of the t-distribution to test an hypothesis at https://brainly.com/question/16313918
what is the probability of choosing a jack or an ace from a deck of cards type your anwser as a fraction
If f(x) = 3-2x and g(x) = 1/x+5 , what is the value of (f/g) (8)
Answer: [tex]-\frac{104}{41}[/tex]
Step-by-step explanation:
[tex]f(8)=3-2(8)=-13\\\\g(8)=\frac{1}{8}+5=\frac{41}{8}\\\\\implies \left(\frac{f}{g} \right)(8)=\frac{-13}{41/8}=-\frac{104}{41}[/tex]
The circumference of circular hot tub at a hotel is 56.5 yards. What is the diameter of the hot tub?
Answer:
17.98
Step-by-step explanation:
Round it to whatever you usually do or what is in the instructions
Finding missing angles
Answer:
95
Step-by-step explanation:
[tex]x \degree = 95 \degree \\(vertical \: angles) \\ \\ x = 95[/tex]
Which numbers line correctly shows 4.5 - 2.5.? HELP FAST!!!
Answer:
Step-by-step explanation:
The answer would be the first option because it’s starting at 4.5, and if you subtracted 2.5, you would get the answer of 2, and that’s what the first option shows. Hope this helps!
A new car is purchased and a $30,000 loan is taken. The loan is for 7 years (84 months) and
the interest rate is 2.9% compounded monthly. What is the monthly payment?
Answer
around $250 per month
Step-by-step explanation:
Help !!!!!!!!!!!!!!!!!!!!!
Answer:
12 is the answer thanks for asking in
I really need help what's the answer??
i need help asap someone please help me asap
Slope = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
So taking 2 points (0,0) and (60,120)
we have slope = (120-0)/(60-0) = 120/60 = 2
general equation of linear graph is y=mx+b with m be the slope
so y=2x+b
Now to find b, just plug any point of the graph in, such as (0,0)
so we get something like 0=2(0) + b => b=0
So your equation is y=2x
Please help 50 points to whoever answers, and brainliest to best answer!!!!
Answer:
x = 26/yz
Step-by-step explanation:
Ryan is going to invest in an account paying an interest rate of 1.5%
compounded continuously. How much would Ryan need to invest, to the
nearest ten dollars, for the value of the account to reach $2,600 in 5 years?
Step-by-step explanation:
2,360×8=2,360 two thundered three hundred and sixty
Helppppp meeee llsss
Answer:
I think the answer is 6.5
What is 8.05 × 10-5 in standard notation?
Answer:
0.0000805 0.00000805 805,000 8,050,000. i think
Step-by-step explanation:
Answer:
Using PEMDAS = 75.5
Step-by-step explanation:
P - Parentheses
E - Exponents
M - Multiplication
D - Division
A - Addition
S - Subtraction
Hope this helps!
If x = -3 and y = 4 find the value of : x(3x + 4y)
Answer:
-21
Step-by-step explanation:
(−3)((3)(−3)+(4)(4))
=(−3)((3)(−3))+(−3)((4)(4))
=27−48
=−21
What single transformation was applied to triangle A to get triangle B? Links will be reported
Answer:
Rotation:
Step-by-step explanation:
Translation is usually movements like up, down, left, right.
Dilation is when one shape is bigger/smaller than the other, but still congruent.
Reflections are usually done over an axis (x or y), and don't change the degree at which a shape is turned. From looking at the triangles, you can see that one triangle was turned clockwise.
Find the area of the shape shown below.
Answer:
4
Step-by-step explanation:
k
Which expression is equivalent to 3/5?
A
3 × 5
B
3 + 5
C
3 ÷ 5
D
3 − 5