Find the area of the shaded region.

Answer:

The pvalue of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.

Step-by-step explanation:

U.S. drivers spend on average, 51 minutes behind the wheel each day.

This means that at the null hypothesis we test that:

[tex]H_{0}: \mu = 51[/tex]

Is there convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes?

This means that the alternate hypothesis is:

[tex]H_{a}: \mu < 51[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

51 is tested at the null hypothesis:

This means that [tex]\mu = 51[/tex]

The study revealed that the mean time behind the wheel for the sample of 75 drivers was 46.4 minutes with a standard deviation of 18.8 minutes.

This means that [tex]n = 75, X = 46.4, \sigma = 18.8[/tex]

Value of the test-statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{46.4 - 51}{\frac{18.8}{\sqrt{75}}}[/tex]

[tex]z = -2.12[/tex]

Pvalue of the test:

The pvalue of the test is the probability of finding a sample mean less than 46.4, which is the pvalue of z when X = 46.4.

Looking at the z-table, z = -2.12 has a pvalue of 0.017.

Decision:

The pvalue of the test is 0.017 > 0.01, which means that there is not convincing evidence that the mean time behind the whell for all U.S drivers is less than 51 minutes.

No, there isn't convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes.

Given the following data:

A null hypothesis ([tex]H_0[/tex]) can be defined the opposite of an alternate hypothesis ([tex]H_a[/tex]) and it asserts that two (2) possibilities are the same.

For the null hypothesis, we would test that:

[tex]H_o : \mu =51[/tex]

For the alternate hypothesis, we would test that:

[tex]H_a : \mu < 51[/tex]

The test statistics would be calculated with this formula:

[tex]Z=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]

Where:

Substituting the given parameters into the formula, we have;

[tex]Z=\frac{46.4\;-\;51}{\frac{18.8}{\sqrt{75} } }\\\\Z=\frac{-4.6}{\frac{18.8}{8.6603} }\\\\Z=\frac{-4.6}{2.1708 }[/tex]

Z = -2.12.

In Statistics, a p-value also known as the probability value is the probability which occurs when the null hypothesis ([tex]H_0[/tex]) is true of obtaining a sample mean that is at least as unlikely as what is observed by a researcher or scientist.

From the z-table, a z-score of -2.12 corresponds to or has a p-value of 0.017. Therefore, the p-value for this test is 0.017 > 0.01.

In conclusion, there isn't convincing evidence that the mean time behind the wheel for all U.S. drivers is less than 51 minutes.

Read more on null hypothesis here: https://brainly.com/question/14913351

Answer:

113

Step-by-step explanation:

200 Customers = 45 Desserts

1 Customer = 45/200= 0.225 Desserts(Approx)

500 Customers= 0.225*500 = 113 Desserts(Approx)

Answer:

Measure of angle b is 42 degrees

Step-by-step explanation:

Since angle b is part of a right angle, we can see that part of the right and blue is 48 degrees, and the other part is b. So, we can do 90-48 to get 42 degrees.

Answer:

42

Step-by-step explanation:

since one of the lines for angle b makes a 90° angle all you have to do is subtract 48 from 90 and that is your answer

Answer:

i dont know i dont understand the question

9514 1404 393

Answer:

Step-by-step explanation:

The original side length is 14 m, so the area is (14 m)² = 196 m².

The longer side length is 14 m + 5m = 19 m, so the area is (19 m)² = 361 m².

The increase in area is ...

  361 m² -196 m² = 165 m²

The area increases from 196 m² to 361 m², which is an increase of 165 m².

Answer:

The areas from 196 m² to 361 m², which is an increase of

165 m²

Answer: 3 600 000 cm³

Step-by-step explanation: 1 m³ = 1000 dm³ = 1 000 000 cm³

Answer:

A

Step-by-step explanation:

An acute angle is an angle that is less than 90 degrees.

Answer:

Step-by-step explanation:

A

Answer:

V=pi multiplied by r^2 times height

Step-by-step explanation:

9514 1404 393

Answer:

  (2.5, -4.5)

Step-by-step explanation:

Reflection in the x-axis changes the sign of the y-coordinate

  (x, y) ⇒ (x, -y)

  (2.5, 4.5) ⇒ (2.5, -4.5)

Answer:

x=21

x=122

Step-by-step explanation:

Answer:

x= 21

x=122

I hope this will help you.

Answer:

Step-by-step explanation:

We know it must be graph A because when finding the most popularly bought item, the percentages only can go to 100%

So graphs C and D are eliminated.

Also since it never said any flavors were unknown, all the percents have to add up to 100%

So graph B is eliminated.

Only graph A follows the requirements

Based on the calculation below, the amount Max can be expected to have when he retires is $758,518.94.

The amount he will be expected to have when he retires can be calculated using the formula for calculating the future value of an ordinary annuity as follows:

FV = D * (((1 + r)^n – 1) / r) ……………………………….. (1)

Where;

FV = Future value or the expected amount when he retires = ?

D = Monthly deposit = $200

r = monthly average inflation adjusted stock market return = 7% / 12 = 0.07 / 12 = 0.00583333333333333

n = number of months = (67 -  22) * 12 = 540

Substituting the values into equation (1), we have:

FV = $200 * (((1 + 0.00583333333333333)^540 – 1) / 0.00583333333333333)

FV = $758,518.94

Learn more about future value here: https://brainly.com/question/14586629.

#SPJ1

Answer:

1.25p

Step-by-step explanation:

p = amount raised last year

amount raised this year = p +(25% of p)

=1 p+0.25p

=p(1+0.25)

=1.25p

Answer:

the answer is x=1

Step-by-step explanation:

minus 19 on both sides

then divide by 13 on both sides

Answer:

The answer is=

41887.551

9514 1404 393

Answer:

  right

Step-by-step explanation:

If you're going to be in the business of classifying triangles based on side lengths, it can be useful to know there is a "form factor" that can help. For sides a, b, c, with long side 'c', it is computed as ...

  f = a² + b² - c²

It has the following interpretation with respect to triangle shape:

  f > 0 . . . acute

  f = 0 . . . right

  f < 0 . . . obtuse

__

In this case, we have ...

  16² +63² -65² = 256 +3969 -4225 = 0

The triangle is a right triangle.

_____

Additional comment

When the triangle is a right triangle, this is equivalent to a statement of the Pythagorean theorem: c² = a² + b².

For triangles of other shapes, the interpretation is consistent with the Law of Cosines. When the form factor is divided by 2ab, the result is the cosine of the largest angle. That is why >0 means acute and <0 means obtuse.

Answer:

Step-by-step explanation:

1)

2)

3)

Answer:

2. Measure 5

3. lines m and n are parallel

4. line t is transversal

5. 8 angles are formed by transversal

6. 1, 3, 5, 7 are congruent. 2, 4, 6, 8 are congruent.

Answer:

Step-by-step explanation:

what are we looking for?/

Answer:

Bottom right does not belong.

Step-by-step explanation:

The bottom right chart does not belong.

It does not calculate the formula correctly after the first time:

y = 2/3x

y = 2/3(4)

y = 8/3

y = 2.66666...7

In the picture, it shows y = 4 instead which is untrue. When looking at the top left picture, the graph also shows that when x = 4, y = 2.66666...7.

The bottom left picture fits in because it's counting by 1's in gallons of lemonade and by 1.5's in cups of sugar. The graph is also counting by these numbers.

Answer:

C

Step-by-step explanation:

You are dividing, if you think about it every time I do it is the opposite of your equation. Plus you are supposed to multiply on both sides to get the value of d.

Answer: Mike!

Step-by-step explanation:

Answer:

18.9cm ( I rounded of and used Π as 3.14)

Step-by-step explanation:

P=distance all round

=1\2ΠD +Πd

see you have to calculate the upper length of the circle , since its half u multiply by a half. And since its not fully shaded the two semi circles are now included as the lower part of the whole shape. so you add them too. (I hope I'm making sense)

Answer:

(2+3)(2−3)(5+2)(5−2)=>(22−(3)2)(52−(22))=>(4−3)(25−2)=>(1)(23)=>23

Answer:

[tex]Pr = 32.49\%[/tex]

Step-by-step explanation:

Given

Let E represents the event of wearing glasses or contacts.

So;

[tex]P(E) =57\%[/tex]

Required

The probability that selected 2 wears glasses

This is calculated as:

[tex]Pr = P(E)\ and\ P(E)[/tex]

[tex]Pr = P(E)\ *\ P(E)[/tex]

[tex]Pr = 57\% * 57\%[/tex]

[tex]Pr = 0.57 * 0.57[/tex]

[tex]Pr = 0.3249[/tex]

[tex]Pr = 32.49\%[/tex]

Answer:

5/x = 7/x-4

5(x-4) = 7(x)

5x - 20 = 7x

5x - 7x = 20

-2x = 20

x = -20/2 = -10

Answer:

x564.99

Step-by-step explanation:

Answer:

A) [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Answer:

16^(3/2)=64

Step-by-step explanation: