In the Fuel Economy Guide for 2018 model vehicles, the Environmental Protection Agency gives data on 1160 vehicles. There are a number of outliers, mainly hybrid gas electric vehicles. If we ignore outliers, the combined city and highway gas mileage of the other 1134 vehicles is approximately Normal with mean 22.6 miles per gallon (mpg) and standard deviation 5.2 mpg.

Required:
a. What proportion of vehicles have worse gas mileage than the 2020 Honda Civic?
b. My dad has a truck that gets around 14 mpg. How many standard deviations from the mean is my dad's truck?

Answers

Answer 1

Answer:

a) The probability is the p-value of [tex]Z = \frac{X - 22.6}{5.2}[/tex], in which X is the gas mileage of the 2020 Honda Civic.

b) Your dad's truck is 1.65 standard deviations below the mean.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Normal with mean 22.6 miles per gallon (mpg) and standard deviation 5.2 mpg.

This means that [tex]\mu = 22.6, \sigma = 5.2[/tex]

a. What proportion of vehicles have worse gas mileage than the 2020 Honda Civic?

This is the p-value of Z, given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{X - 22.6}{5.2}[/tex]

In which X is the gas mileage of the 2020 Honda Civic.

b. My dad has a truck that gets around 14 mpg. How many standard deviations from the mean is my dad's truck?

This is Z when X = 14. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{14 - 22.6}{5.2}[/tex]

[tex]Z = -1.65[/tex]

Your dad's truck is 1.65 standard deviations below the mean.


Related Questions

Simple geometry please help

Find KL. Round to the nearest hundredth.

Answers

Answer:

KL ≈ 1.94

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos48° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{JL}{KL}[/tex] = [tex]\frac{1.3}{KL}[/tex] ( multiply both sides by KL )

KL × cos48° = 1.3 ( divide both sides by cos48° )

KL = [tex]\frac{1.3}{cos48}[/tex] ≈ 1.94 ( to the nearest hundredth )

Please help me with this

Answers

9514 1404 393

Answer:

1+3x = -89x = -30

Step-by-step explanation:

If we let x represent "a number", then "three times a number" is 3x. The usm of that and 1 is ...

  1 +3x . . . . . . the sum of 1 and 3 times a number

That is said to be -89, so we have the equation ...

  1 +3x = -89

__

To solve this equation, we can subtract 1 from both sides:

  3x = -90

Then we can divide by 3 to find x.

  (3x)/3 = -90/3

  x = -30

28. A boy decided to cut 10 pieces of wood from a length of wood so tha the first piece was 5cm the second 10cm, the third 15cm, the fourth 20cm and so on until he had cut TO pieces, each one 5cm longer than the one he had cut before. What length of the wood did he use? (a) 50cm (b) 55cm (c) 70cm (d) 200cm (e) 275cm​

Answers

Step-by-step explanation:

he use 50cm length of the wood

The point A(−8,−4) is reflected over the origin and its image is point B. What are the coordinates of point b?

Answers

9514 1404 393

Answer:

  B(8, 4)

Step-by-step explanation:

Reflection across the origin negates both coordinate values.

  (x, y) ⇒ (-x, -y) . . . . . reflection across the origin

  A(-8, -4) ⇒ B(8, 4)

A person has decided to construct a frequency distribution for a set of data containing 100 numbers. The lowest number is 20 and the highest number is 80. If 5 classes are used, the class width should be approximately _______.

Answers

Answer:

The answer is "12".

Step-by-step explanation:

Lowest number[tex]=20\\\\[/tex]

highest number[tex]=80\\\\[/tex]

Number of classes[tex]=5\\\\[/tex]

Range=highest number-lowest number

          [tex]=80-20\\\\=60\\\\[/tex]

class width [tex]=\frac{Range}{\text{number of classes}}[/tex]

                   [tex]=\frac{60}{5}\\\\=12[/tex]

Can I please get asap

Answers

Answer:

Option B, cotangent is the reciprocal of tangent

That option is correct

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. A random sample of 5240 permanent dwellings on an entire reservation showed that 1613 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings on the entire reservation that are traditional hogans. Find a point estimate for p. (Round your answer to four decimal places.)
(b) Find a 99% confidence interval for p. (Round your answer to three decimal places.) What is the lower limit? What is the upper limit?

Answers

Answer:

Step-by-step explanation:

point est. 0.307824427

99% 2.58

Confidence Interval - "P" values  

(0.2914 , 0.3243 )  

КУ
11
10
A
9
8
7 구
6
5
4
A А
C
3
B'
2
1
B
C с
-6 -5 -4 -3 -2 -1
1 2 3 4 5 6
A ABC is dilated about the origin./
What scale factor was used to make the image A A'B'C?

Answers

Answer:

3

Step-by-step explanation:

The dilation factor is 3

An amortized loan of RM60,000 has annual payments for fifteen years, the first occurring exactly one year after the loan is made. The first four payments will be for only half as much as the next five payments, whereas the remaining payments are twice as much as the previous five payments. The annual effective interest rate for the loan is 5%. I If the first four payments are X each, calculate the amount of principal repaid in the eighth payment and the amount of interest in the twelfth payment.​

Answers

9514 1404 393

Answer:

  a) RM2256.09 . . . principal paid by 8th payment

  b) RM1791.10 . . . . interest paid by 12th payment

Step-by-step explanation:

First of all, we need to find the payments.

The payment amount is the amount that makes the future value of the series of payments equal to the future value of the loan at the given interest rate.

The future value of a single amount is ...

  FV = P(1 +r)^n . . . . . where r is the annual rate, and n is the number of years in the future

The future value of a series of payments is ...

  FV = P((1 +r)^n -1)/r . . . . . where n is the number of payments of P earning annual rate r

For payments in a series that does not end at the end of the loan, the future value is the product of that of the series and the effect of the accumulation of interest for the remaining time.

__

The first 4 payments will have a future value at the end of the loan period of ...

  s1 = X((1 +0.05)^4 -1)/0.05×(1 +0.05)^11 = X(1.05^15 -1.05^11)/0.05

  s1 = 7.3717764259X

The next 5 payments will have a future value at the end of the loan period of ...

  s2 = 2X((1 +0.05)^5 -1)/0.05×(1 +0.05)^6 = 2X(1.05^11 -1.05^6)/0.05

  s2 = 14.8097486997X

The last 6 payments will have a future value at the end of the loan period of ...

  s3 = 4X((1 +0.05)^6 -1)/0.05 = 27.20765125X

So, the total future value of the series of payments is ...

  payment value = 7.3717764259X +14.8097486997X +27.20765125X

  = 49.3891763756X

__

The future value of the loan amount after 15 years is ...

  loan value = 60,000(1 +0.05)^15 = 124,735.69

In order for these amounts to be the same, we must have ...

  49.3891763756X = 124,735.69

  X = 124,735.69/49.3891763756 = 2,525.57

__

At this point, it is convenient to use a spreadsheet to find the interest and principal portions of each of the loan payments. (We find the interest charge to be greater than the payment amount for the first 4 payments. So, the loan balance is increasing during those years.)

In the attached, we have shown the interest on the beginning balance, and the principal that changes the beginning balance to the ending balance after each payment. (That is, the interest portion of the payment is on the row above the payment number.)

The spreadsheet tells us ...

A) the principal repaid in the 8th payment is RM2,256.09

B) the interest paid in the 12th payment is RM1,791.10

_____

Additional comment

The spreadsheet "goal seek" function could be used to find the payment amount that makes the loan balance zero at the end of the term.

We have used rounding to sen (RM0.01) in the calculation of interest payments. The effect of that is that the "goal seek" solution is a payment value of 2525.56707 instead of the 2525.56734 that we calculated above. The value rounded to RM0.01 is the same in each case: 2525.57.

what translation was the similarity moved through ?

Answers

C & F is the answer

8. 15x - 10 = 80
a. X= 2
b. x=4
c. X= 6

Answers

Answer:

C

Step-by-step explanation:

15x-10=80

15x=90

x=90/15, x=6

Answer:

x = 6

Step-by-step explanation:

15x - 10 = 80

Add 10 to each side

15x-10+10 = 80+10

15x = 90

Divide each side by 15

15x/15 = 90/15

x = 6

If
f (x) = 3x +1 and 1-1 = *?
then f-'(7) =
O 22
O-2
02

Answers

According to my calculations answer is -2

been stuck on this for a few days now, help on even one would be greatly appreciated!!!

Answers

Answer:

-5-9i

Step-by-step explanation:

-1-8i-4-i

-1-4-8i-i

-5-9i

Find the solutions of x^2+30 = 0

please give detailed steps!

Answers

Answer:

x= i√30

Step-by-step explanation:

I'm going to go into this under the assumption that you've covered imaginary numbers based on the question. If I'm wrong then sorry about that.

Okay, so first you want to subtract 30 from both sides

x^2=-30

Then you take the square root of each side.

√(x^2)=√-30

x=√-30

Since it's impossible to square a number to get a negative number, you'll end up with an imaginary number. You have to rewrite x=-30 to get rid of the negative sign under the radical. Rewriting this will also indicate that it's an imaginary number.

Final answer: x = i√30

Can you provide a solution or a formula?

Answers

144 x 1.25 = 180

Answer: 144

Answer:

144

Step-by-step explanation:

144 × 1.25 = 180

We add the 1 to .25 to represent the original value plus the 25% increase.

Or you could have divided 180 by 1.25 to find original price.

What is the equation of the graph below?

Answers

Answer:

f(x)=5cos(1/3x) this is an equation

Rearrange to make P the subject, :)..​

Answers

Answer:  [tex]P = \frac{25}{E^2}-Q\\\\[/tex]

Work Shown:

[tex]E = 5\left(\sqrt{\frac{1}{P+Q}}\right)\\\\5\left(\sqrt{\frac{1}{P+Q}}\right) = E\\\\\sqrt{\frac{1}{P+Q}} = \frac{E}{5}\\\\\frac{1}{P+Q} = \left(\frac{E}{5}\right)^2\\\\\frac{1}{P+Q} = \frac{E^2}{25}\\\\P+Q = \frac{25}{E^2}\\\\P = \frac{25}{E^2}-Q\\\\[/tex]

A loaf of bread costs $1.40 and the markup is 30% of the selling price. Find the selling price.

Answers

Answer:

The selling price after the markup is $1.82

Step-by-step explanation:

$1.40 * .30 =

Multiply $1.40 times .30 (which is same as 30%)

$1.40 * .30 = $0.42

Add $1.40 and $0.42

= $1.82

Hope this helps.

Given the formula A = 5h (B + b); solve for B.
2

Answers

Answer:

B = A/5h - b; You could use

B = (A - 5hb)/5h  This just puts everything over a common denominator.

Step-by-step explanation:

A = 5h (B + b)          Divide both sides by 5h

A/5h = B + b             Subtract b from both sides.

A/5h - b = B

What is the value of the 2 in 4.502?

Answers

Answer:

0.002

Step-by-step explanation:

2 in 4.502 is in the thousandths place

Value is 0.002

Oak street and elm street run parallel to each other. When main street intersects them, it forms exterior 8, measuring 60. What is the measure of 1?

Answers

Answer:

0 is the answer measure 1

What information is NOT necessary to find the area of a circle?
a.
pi
c.
diameter
b.
radius
d.
height

Answers

Answer:

D. Height

General Formulas and Concepts:

Geometry

Area of a Circle: A = πr²

r is radius

Step-by-step explanation:

In order to find the area of a circle, we must follow the formula. Out of all the options given, height is not incorporated into the formula.

It wouldn't make sense to use height anyways since it would be 3-dimenional and we're talking 2-dimensional.

∴ our answer is D.

Can someone help me with this?

Answers

9514 1404 393

Answer:

CNBD -- using the given statement regarding perpendicularityΔLAW ≅ ΔWKL by ASA -- using the markings on the figure

Step-by-step explanation:

The given information tells us there is one congruent side in the two right triangles. That is not sufficient to claim congruence of the triangles.

  CNBD

__

The figure shows one congruent angle in addition to one congruent side, so the figures can be shown to be congruent using the ASA theorem.

  ΔLAW ≅ ΔWKL

_____

Additional comment

We don't know which answer is expected. You should discuss this question with your teacher, since it appears to be missing the statement that

  ∠ALW ≅ ∠KWL

verify sin2θ/1+cos2θ =tanθ

Answers

Answer:

LHS.= Sin 2x /( 1 + cos2x )

We have , sin 2x = 2 sinx•cosx

And. cos2x = 2cos^2 x - 1

i.e . 1+ cosx 2x = 2cos^2x

Putting the above results in the LHSwe get,

Sin2x/ ( 1+ cos2x ) =2 sinx•cosx/2cos^2x

=sinx / cosx

= Tanx

.•. sin2x/(1 + cos2x)= tanx

Step-by-step explanation:

What is tan 30°?
60
2
1
90°
30"
V3
O A.
B. 1
O c. 2
O D. 7/ 룸
O E
1 / 3
Eg
O E

Answers

Answer:

Hello,

What is tan 30°?

[tex]tan(30^o)=\dfrac {\sqrt{3} }{3}[/tex]

Step-by-step explanation:

[tex]sin(30^o)=\dfrac{1}{2} \\\\cos(30^o)=\dfrac{\sqrt{3} }{2} \\\\\\tan(30^o)=\dfrac{sin(30^o)}{cos(30^o)} \\tan(30^o)=\dfrac{\dfrac{1}{2} } { \dfrac{\sqrt{3} }{2} }\\\\ =\dfrac {1*2}{2*\sqrt{3} }\\\\ =\dfrac {\sqrt{3} }{3}[/tex]

The value of tan 30° is 1/√3

What is tangent of an angle?

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.

Tan 30° = sin 30° / cos 30°

We know that, sin 30° = 1/2

cos 30° = √3/2

Therefore,

Tan 30° = 1/2 ÷ √3/2

Tan 30° = 1/2 x 2/√3

Tan 30° = 1/√3

Hence, the value of tan 30° is 1/√3

Learn more about tangent of an angle, click;

https://brainly.com/question/10053881

#SPJ7

Calvin and Jamel each havr cats as pets. Calvin buys cat food in cylindrical can that are 6 centimeters in diameter and 12 centimeters high. Jamel buys cat food in cylindrical can that 12 centimeters in diameter and 6 centimeters high. What is the ratio of the volume of one of Calvin's cans of to the volume of one of Jamel's cans?​

Answers

Answer:

see below

Step-by-step explanation:

CALVIN

v=[tex]\pi[/tex]× r ² × h

v=3.14 × 3² × 12

v=3.14×9 × 12

v=3.14 × 108

v = 339.12

JAMEL

v=[tex]\pi[/tex] × r ²×h

v=3.14× 6 ² × 6

v=3.14 × 36×6

v=3.14×216

v=678.24

The curve y=2x^3+ax^2+bx-30 has a stationary point when x=3. The curve passes through the point (4,2).

(A) Find the value of a and the value of b.

#secondderivative #stationarypoints


Answers

A stationary point at x = 3 means the derivative dy/dx = 0 at that point. Differentiating, we have

dy/dx = 6x ² + 2ax + b

and so when x = 3,

0 = 54 + 6a + b

or

6a + b = -54 … … … [eq1]

The curve passes through the point (4, 2), which is to say y = 2 when x = 4. So we also have

2 = 128 + 16a + 4b - 30

or

16a + 4b = -96

4a + b = -24 … … … [eq2]

Eliminate b by subtracting [eq2] from [eq1] and solve for a, then for b :

(6a + b) - (4a + b) = -54 - (-24)

2a = -30

a = -15   ===>   b = 96

Farah is x years old. Ibtisam is 3 years younger than Farah. Muna is twice as old as Ibtisam. Write and expression in terms of x, for
(a) Ibtisam's age,
(b) The sum of their three ages, giving your answer in its simplest form.​

Answers

Answer:

Farah: x

Ibtisam: x-3

Muna: 2(x-3) or 2x-6

Sum of all their ages: 4x-6

Step-by-step explanation:

Farah is x, so we don't need an expression for that.

Ibtisam is 3 years younger than Farah, which means that we need to subtract 3 from Farah, and that would be Ibtisam's age. x-3.

Muna is 2 TIMES Ibtisam's age, so we need to multiply whatever expression taht was used for Ibtisam by 2. Put brackets around the equation with 2 outside: 2(x-3). Solve and you get 4x-6

Now, you have all their ages in expression form, now you need to simplify by adding:

x+x+2x-6

We cannot simplify -6, so we put that aside. Add all the x's and you get 4x, insert the minus 6 at the end:

4x-6

Hope this helps!

--Applepi101

Answer:

a) X -3

b) 4x - 9

Step-by-step explanation:

a) Farah's age is X so Ibtisam will be X - 3 old since he is 3years younger than Farah

b) Farah is X years old

Ibtisam is X - 3 years old

Muna is 2(X -3) since she is 2 times older than Ibtisam.

the sum of Thier ages will be

X + X -3 + 2(x-3)

= 2x - 3 + 2x - 6

= 4x - 9

what represent the area of the rectangle in cm^2??

Answers

9514 1404 393

Answer:

  d.  3x² +15x

Step-by-step explanation:

The area is the product of length and width.

  A = LW

  A = (3x)(x+5) = 3x(x) +3x(5) . . . . use the distributive property

  A = 3x² +15x

Answer: D) 3x^2 + 15

==========================================================

Explanation:

Draw a horizontal line to divide the rectangle into two parts (they don't necessarily have to be equal parts). Refer to the diagram below. The upper rectangle is x by 3x. So its area is length*width = x*3x = 3x^2

The lower rectangle is 5 by 3x, so its area is 5*3x = 15x

Combine those two sub-areas back together to get the overall area of 3x^2 + 15x

You could also use the distribution rule

3x*(x+5) = 3x*(x) + 3x*(5) = 3x^2 + 15x

Simplify: y^-3

a) 3/y
b) - 1/y^3
c) -3y
d) 1/y^3

Answers

Answer:

1/y^3

Step-by-step explanation:

We know that a^-b = 1/a^b

y ^-3 = 1/y^3

Other Questions
The lengths of two sides of the right triangle ABC shown in the illustration given b= 8ft and c= 17ft Identify the pattern in the list of numbers. Then use this pattern to find the next number.2,4,6,10,16,26,___ How does an individual enter into the devils family? Which prepositional phrase could be added to sentence 3 to best show where the eventshappen? A project to build a new bridge seems to be going very well since the project is well ahead of schedule and costs seem to be running very low. A major milestone has been reached where the first two activities have been totally completed and the third activity is 70% complete. The planners were expecting to be only57% through the third activity at this time. The first activity involves prepping the site for the bridge. It was expected that this would cost $1,427,000 and it was done for only $1,307,000. The second activity was the pouring of concrete for the bridge. This was expected to cost $10,507,000 but was actually done for $9,007,000. The third and final activity is the actual construction of the bridge superstructure. This was expected to cost a total of $8,507,000. To date, they have spent $5,007,000 on the superstructure. Calculate the schedule variance, schedule performance index, and cost performance index for the project to dat The probability I take a nap today is 4/5. The probability I will take a nap and a bubble bath todayis 1/5. What is the probability I will take a bubble bath today, given that I took a nap? You purchased XYZ stock at $50 per share. The stock is currently selling at $80. You expect the stock price to go up, but not 100% sure. Placing a ___________ may protect your current gains of $30 while at the same time keeping the opportunity open for future upward potential. In the diagram attached, ABC has coordinates A(1,1), B(4,1), and C(4,5).Given the function rulef(x, y) (x 5, y 2)Describe the transformation as completely as possible.The diagram is attached-- Thanks in advance!(No this is not homework, I was using a study guide I found online to study for a test.) 14. What was a purpose of the devshirme system?A. To convert Shi'a Muslims to SunniB. To provide soldiers and bureaucratsC. To enable efficient tax collectionD. To establish fair land distribution 10 ICTs that encourage reading...? Make x the subject of the formula y=4x-2 f(x) = -22 14Find f(9) Write a program num2rome.cpp that converts a positive integer into the Roman number system. The Roman number system has digits I 1 V 5 X 10 L 50 C 100 D 500 M 1,000 Numbers are formed according to the following rules: a. Only numbers 1 to 3,999 (inclusive) are represented. b. As in the decimal system, the thousands, hundreds, tens, and ones are express separately. c. The numbers 1 to 9 are expressed as I 1 II 2 III 3 IV 4 V 5 VI 6 VII 7 VIII 8 IX 9 As Question 4 of 10If a reader wants to evaluate a text, which is the best question to ask whilereading it?A. How long is this text, and how quickly does it get to the point?B. Where else is there a text with similar goals that used differentelements?C. What are the goals of the text, and what elements help achievethose goals?D. When did the author of this text decide on its goals, and when didhe write it?SUBMITPREVIOUS A negative slope on the velocity vs. time graph indicates a negativeacceleration.A TrueB. False What are the lengths of the legs of a right triangle in which one acute angle measures 19 and the hypotenuse is 15 units long? In cell K8, create a formula using the SUM function that calculates the total of range D17:D20 and subtracts it from the value in J8 2 angles in a triangle are 82 and 76. What is the measure of the 3rd angle. A. 38B. 22C. 82D. 76 Describe the relationship between Gilgamesh and Enkidu as it is depicted at various points throughout the epic. Include at least three specific examples from the text in your explanation. in which figure , AB || CD . determine x