A police department used a radar gun to measure the speed of a sample of cars on the highway. Assume that the distribution of speeds is approximately Normal with a mean of 71 mph and a standard deviation of 8 mph. Using this distribution what is the z-score of a 65-mph speed limit?

Answers

Answer 1

Answer:

The z-score of a 65-mph speed limit is -0.75

Step-by-step explanation:

Here, we want to calculate the z-score

To calculate the z-score, we make use of the z-score formula

Mathematically;

z-score =(x-mean)/SD

from the question we identify the values as x = 65 mph, mean = 71 mph, Standard deviation(SD) = 8 mph

Plugging these values into the equation above, we have

z-score = (65-71)/8 = -6/8 = -0.75


Related Questions

The graph below shows three different normal distributions. 3 normal distributions are shown. They all peak at the same point, but they all have different heights and widths. Which statement must be true?
A) Each distribution has a different mean and the same standard deviation.
B) Each distribution has a different mean and a different standard deviation.
C) Each distribution has the same mean and the same standard deviation.

D) Each distribution has the same mean and a different standard deviation.

Answers

Answer:

D) Each distribution has the same mean and a different standard deviation.

Step-by-step explanation:

just took test edg2020

The graph below shows three different normal distributions.

D) Each distribution has the same mean and a different standard deviation.

What is standard deviation and mean?

The spread in the provided normal curves exists due to various standard deviations. The mean for all three curves lies at the center of the curve.

Therefore, each distribution contains the same mean and a separate standard deviation.

Therefore, the correct answer is option (D) "Each distribution has the same mean and a different standard deviation."

To learn more about standard deviation and mean

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Factor the following polynomial:
5x(a - b) – 2y(a - b)

Answers

Answer:

(a - b)(5x - 2y)

Step-by-step explanation:

5x(a - b) – 2y(a - b) =

The factors in parentheses (shown in bold) are a common factor.

Factor (a - b) out from both terms.

= (a - b)(5x - 2y)

Francine has a piece of wood that is five 5 5/12 feet long she uses three 3 1/4 feet of the wood from a science project how much for just Francine have left.

Answers

Answer:

4/3 ft

Corrected question;

Francine has a piece of wood that is five 5/12 feet long she uses three 1/4 feet of the wood from a science project how much for just Francine have left.

Step-by-step explanation:

Given;

Francine has a piece of wood that is five 5/12 feet long.

Total amount of wood T = 5 × 5/12 ft = 25/12 ft

she uses three 1/4 feet of the wood from a science project.

Amount of wood Used U = 3 × 1/4 = 3/4 ft

The amount of wood left equals the total amount of wood minus the amount of wood used;

The amount of wood left L = T - U = 25/12 - 3/4

L = 25/12 - 9/12

L = 16/12

L = 4/3 ft

Pengelola layanan air minum di desaku membuat tempat penampungan air di dataran tinggi agar air dapat menjangkau seluruh desa. Tempat penampungan tersebu berbentuk kubus dengan panjang rusuk 8 meter. Jika tempat penampungan itu penuh, berapa liter air yang tertampung?

Answers

Answer:

The shelter can contain 512 cubic meters of water.

Step-by-step explanation:

This question can be translated to:

"The manager of the drinking water service in my town creates a water tank in the highlands so that the water can reach the entire town. The cube-shaped shelter is 8 meters long. If the shelter is full, how many liters of water can it contain?"

As you can observe, the volumetric form is a cube with 8 meters long each edge.

We know the volume of a cube is defined as

[tex]V=l^{3}[/tex]

Where [tex]l=8 \ m[/tex], replacing this value, we have

[tex]V=(8 \ m)^{3} \\V=512 \ m^{3}[/tex]

Therefore, the shelter can contain 512 cubic meters of water.

What two numbers have a sum of 191 and a difference of 63

Answers

Answer:

Step-by-step explanation:

a+b=191

a-b=63

i sum these

a+b+a-b=191+63

2a=254

a=254/2

a=127

b=191-127

b=64

Answer:

127 and 64

Step-by-step explanation:

To solve this, we can set up a system of equations.

We can name the first number x and the second number y.

x+y=191

x-y=63

We can use elimination to eliminate the y variable.

We do this by adding the equations together

  x+y=191

+ x-y=63

_________

2x=254

Divide both sides by 2.

x=127

Now we can plug that in to find y.

x+y=191

127+y=191

Subtract 127 from both sides.

y=64

So our two numbers are 127 and 64.

each store is offering a different promotion

Answers

Answer:

Ddddddddddddddddddddddddd

Without measuring angles what is the measure of angle A′ OB ′?

Answers

Answer:

That isn’t possible

Step-by-step explanation:

The length of a rectangular room is 5 feet longer than twice the width If the room's perimeter is 166 feet, what is the length?
A. 67 feet
B. 44 feet
C. None of these
D. 114 feet
E. 57 feet

Answers

Answer:

E. 57 feet

Step-by-step explanation:

If you draw a rectangle and label the long side 5+2x, and the short side x, then that represents the rectangular floor.

The 2x is "twice the width".

The 5 added to the 2x is "5 feet longer than"

The x is the width of the room.

                                                                                   

If the equation for the whole perimeter is 2(5+2x)+2x=166 <-(The perimeter)

                                     (Both of the long sides)^       ^(Both of the short sides)

Then we need to solve for x.

[tex]2(5+2x)+2x=166\\10+4x+2x=166\\10+6x=166\\6x=156\\x=26[/tex]

Next, we input the value we got into the equation 5+2x (The length of one side) and solve

[tex]5+2x\\5+2(26)\\5+52\\57[/tex]

So the length of the room is 57 feet.

Hope this helps!

The diagram shows AABC.
a. What is the height of AABC7 Show your work

Answers

34 I guess hope this helps

Plz Help meee!!!

Factor the Trinomial

x^2+12x+27​

Answers

Answer:

(x + 9)(x + 3)

Step-by-step explanation:

Factor 27 so that the factors, when combined, will equal 12:

x² + 12x + 27

x                9

x                3

(x + 9)(x + 3) is your answer.

Check: Use the FOIL method. Multiply the first two terms, the outside terms, the inside terms, and then the last two terms. Combine like terms:

(x + 9)(x + 3) = x² + 3x + 9x + 27 = x² + 12x + 27 (√)

~

Answer:

(x+9)(x+3)

Step-by-step explanation:

first of all, you should learn this properly, because you'll have to go back to this over and over again. anyways

you need to find two numbers so that it adds up to 12, but also multiplies to 27.

The numbers 9 and 3 fit the situation

So you add 9x and 3x because it's the same thing as 12x. you're just splitting up the term 12x into two other terms.

so now it looks like x^2 + 9x + 3x + 27. now you factor the first two terms and last two terms

x ( x + 9 ) <---factor of first two terms

3 ( x + 9) <---factor of last two terms

x(x+9)+3(x+9)

you notice that (x+9) is common in both factorized parts

so, you add x and 3 from the outside

and you get (x +3 ) (x+9)

The ratio of the leg adjacent to an angle to the hypotenuse of a right triangle is
called the ____ of the angle.

A. sine
B. tangent
C. cosine
D. cosecant

Answers

Answer:cosine

Step-by-step explanation:

Some

Of

Her

Children

Are

Having

Trouble

Over

Algebra

SOH/CAH/TOA

Sin opp/hype cos adj/hyp tan opp/hyp

If angle AOC = 40 degrees, how many degrees is angle ABC?

Answers

80........................

How many solutions does this equation have?

5 − 2k = –2k

Answers

Steps to solve:

5 − 2k = –2k

~Subtract 5 to both sides

5 - 5 - 2k = -2k - 5

~Simplify

-2k = -2k - 5

~Add 2k to both sides

-2k + 2k = -2k + 2k - 5

~Simplify

0 ≠ -5

Therefore, the equation as no solutions.

Best of Luck!

What is the sum of the interior angles of the polygon shown below?

Answers

Answer:

360

Step-by-step explanation:

Formula

Sides -2 ×180

4-2=2×180=360

Solve the equation shown for x.
2( x - 4) = 4x + 3x + 6

Answers

Answer:

-2.8

Step-by-step explanation:

I solved it thats how

I think this is answer

Someone be a homie cause I’m really tryin on this math shi thank youuuu

Answers

Answer:

The area of the shaded region is equal to difference of the sector contains that shaded region and the triangle.

The area of sector:

A_S = pi x radius^2 x 123/360

       = pi x 18.6^2 x 123/360

       = 371.346 (m2)

The area of triangle:

A_T = base x height x (1/2)

       = (18.6 x sin(123/2) x 2) x (18.6 x cos(123/2)) x (1/2)

       = 145.073 (m2)

=> Area of shaded region:

A = 371.346 - 145.073 = 226.273 = ~226.3 (m2)

Hope this helps!

:)

Answer:

First give me points and make me winner, then we can discuss the answer.

Step-by-step explanation:

someone please help :)

Answers

Answer: 25

Step-by-step explanation:

they are corresponding angles

Carl surveyed his classmates about their favorite colors. The graph shows the survey results. A circle graph titled Favorite Colors. 50 percent is blue, 25 percent is orange, 25 percent is green. Which statements about the circle graph are correct? Check all that apply.

25% of the students said blue was their favorite color.
33% of the students said green was their favorite color.
25% of the students said orange was their favorite color.
50% of the students said either green or orange was their favorite color.
66% of the students said either orange or blue was their favorite color.

Answers

Answer: 25% of the students said orange was their favorite color.

50% of the students said either green or orange was their favorite color.

Step-by-step explanation:

The statements about the circle graph are correct;

C. 25% of the students said orange was their favorite color.

D. 50% of the students said either green or orange was their favorite color.

What is a circle?

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

Given that circle graph titled Favorite Colors. 50 percent is blue, 25 percent is orange, 25 percent is green.

In total, there are 100 students.

50 %is blue,

25 %is orange,

25 %is green.

Therefore,  25% of the students said orange was their favorite color and 50% of the students said either green or orange was their favorite color.

More can be learned about circle graph at;

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What is the value of x in the equation

1/3x - 1/2 = 18 1/2


a. 6
b. 15
c. 54
d. 57
PLEASE HELP I HAVE 5 MIN LEFT ON MY TEST

Answers

Answer:

D 57

Step-by-step explanation:

The value of X

Compute the requested value. Choose the correct answer.
If the cost is $58.00 and the selling price is $63.00, then what is the percent of increase?
It is
%

Answers

Answer:

8% percent I think

Step-by-step explanation:

Use the information in the table to answer the question. A 3-column table has 1 row. The first column is labeled Species with entry Goldfish. The second column is labeled Mean with entry 7 inches. The third column is labeled Standard Deviation with entry 1.2 inches. What percentage of goldfish will have lengths between 4.6 inches and 9.4 inches?

Answers

Answer:

94% so C

Step-by-step explanation:

I did the assignment

Hope it helps

Answer:

95%

Step-by-step explanation:

Edge 2020

Calculate (full working required)

2.43 x 4 =

Answers

Answer:

The answer is 9.72 .

Step-by-step explanation:

You can do it by elaborating :

2.43×4 = (2.00×4) + (0.4×4) + (0.03×4)

= 8.00 + 1.6 + 0.12

= 9.72

Justin earned $25.67 one week and $37.85 the next
week. He also purchased a DVD for $19.99 and gas for
his car for $22.07. He started with a zero balance in his
checking account. Justin recorded all of these
transactions in his checkbook and ended up with a
balance of $105.58. Was his balance correct? If it was,
write an equation to support the answer. ​

Answers

Answer:

No, Justin isn't correct

Step-by-step explanation:

Because Justin added everything even the money he spent, and when he spent the money meaning subtracting them, he should get $21.46.

($25.67+$37.85)-($19.99+$22.07)=$21.46

↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑

Money earned      Money spend     Money left

Sorin hits a cricket ball straight up into the air. After 1.5s, the ball is falling straight down with a speed of 6.5 m/s. We want to find the initial vertical velocity of the ball. We can ignore air resistance. Which kinematic formula would be most useful to solve for the target unknown?

Answers

Step-by-step explanation:

We have, Sorin hits a cricket ball straight up into the air. After 1.5 s, the ball is falling straight down with a speed of 6.5 m/s.

We want to find the initial vertical velocity of the ball.

The relation between initial speed, final speed, acceleration and time is given by using first equation of kinematics. Let v₀ is the initial speed. So,

[tex]v=v_o +at[/tex]

Here, v = -6.5 m/s, t = 1.5 s and a = -g

[tex]v_o=v-at\\\\v_o=v+gt\\\\v_o=-6.5+9.8\times 1.5\\\\v_o=8.2\ m/s[/tex]

So, the initial velocity of the ball is 8.2 m/s and the formula used is (1).

Greg plans to purchase a bicycle. Bike A costs $270 and has an expected maintenance cost of $36 per year. Bike B costs $360 and has an expected maintenance cost of $20 per year. Which statement is true based on the average annual cost of each bike?

Answers

Answer:

Bike A costs $270 and has an expected maintenance cost of $36 per year."Bike A is the better choice if Greg plans on owning the bike for 5 years. Bike B is the better choice if Greg plans on owning the bike for 6 years."

Step-by-step explanation:

270-36x

there are 5 years so x=5

270 + 36(5) = 270 + 180 = 450  

If it were 6 years than x = 6

270 + 36(6) = 270 + 216 = 486

Bike B:

360 + 20x

For option b x = 5

360 + 20(5) = 360 + 100 = 460

for option b it would be 6 years than x = 6

360 + 20(6) = 360 + 120 = 480

Hope i helped!

This cost function of purchasing a bike A

[tex]\to f1(x) = 270+ 36 x[/tex] ( The unit of x is a year)  

A cost function for purchasing bike B:

[tex]\to f2(x) = 360+20x \\\\if \ \ f1(x)<f2(x)\\\\ \therefore\\\\ \to 270+36x-360+20x\ \ \ (transpose)\\\\\to 16x= 90 \\\\\to x=\frac{90}{16}=5.625\\\\[/tex]

If Greg plans to keep the bike for 5 years, Bike A is the superior option. If Greg plans to keep the bike for 6 years, Bike B is the superior option.

Learn more:

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Express
as a unit rate.

Betty drives her car 150 km in 2 h. Explain

Answers

Answer:

75 km per hour

Step-by-step explanation:

[tex]\frac{150km}{2hr}[/tex] divided by two is [tex]\frac{75km}{1hr}[/tex].

Mai's younger brother tells her that 10/7 equal to 2‾√ 2 2‾√ 2 . Mai knows this can't be right, because 10/7 is rational and 2‾√ 2 2‾√ 2 is irrational. Write an explanation that Mai could use to convince her brother that 10/7 cannot be the square root of 2.

Answers

Answer:

The number 10/7 is a rational number, which means it can be expressed as a fraction. Also, if we divide it would give a decimal infinite periodical number, which means it has a pattern on its decimal numbers.

On the other hand, the square root of 2 is irrational number, that means it can't be expressed as a fraction, because its decimal numbers don't have any pattern at all.

So, Mai's brother can see these type of numbers as crazy (irrational numbers) and sane (rational numbers).

At last, another important characteristic to shows that they aren't equal is that they don't have the exactly decimal numbers.

Dylan spends a total of $118.50 on 6 bags of popcorn and 12 drinks. Camden spends a total of $48.75 on 1 bag of popcorn and 6 drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a drink, to the nearest cent.

Answers

Answer:

The price of a drink is $7.25

Step-by-step explanation:

Let d represent the price of a drink

let p represent the price of a popcorn

6p+12d=118.50  equation 1

p+6d=48.75    equation 2

multiply both equation 1  by 2

multiply equation 2 by 4

12p+24d=237   equation 3

4p+24d=195 equation 4

subtract equation 4 from 3

8p=42

p=42/8

p=$5.25

Substitute for p in equation 1

(6*5.25 )+12d=118.50

31.5 +12d=118.50

12d=118.50-31.5 0

12d=87

d=87/12

d=$7.25

21.14,7.2,4.5 are these irrational or rational?

Answers

Answer:

Rational. They have termination decimals, so the next digit can be predicted. Therefore, those numbers are rational.

Step-by-step explanation:

[tex] {75}^{2} + 25 - 750[/tex]

Answers

your answer is 4900
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