Suppose that the average speed of cars on a busy section of a local highway was normally distributed with a mean of 65 mph and standard deviation of 4 mph. What is the probability that the speed of a random car in this data set was less than 53 mph?

0.025
0.0015
0.16
0.475

Answers

Answer 1
Answer: Choice B)  0.0015

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Explanation:

mu = 65 = population meansigma = 4 = population standard deviation

Let's convert x = 53 to its corresponding z score

z = (x-mu)/sigma

z = (53-65)/4

z = -12/4

z = -3

This indicates we're 3 standard deviations below the mean.

Recall that the Empirical Rule states that roughly 99.7% of the data items in a normal distribution are within 3 standard deviations of the mean. That leaves 100% - 99.7% = 0.3% outside this range. This small percentage is the combined percentage in both tails. Take half of this to find the amount in the left tail only.

(0.3%)/2 = 0.15%

This then converts to 0.0015 when we move the decimal point 2 spots to the left.


Related Questions

Use the Pythagorean Theorem to find the distance between the point (1,4) and (-5,-4) on the coordinate plane? (FREE RESPONSE)
no pic ANSWER IT

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Answer:

12?

Step-by-step explanation:

Answer:The Answer is 10!!!

Step-by-step explanation:

If you plot (1,4) and (-5,-4) on a graph, you can see that you can form a right triangle.

you would count the values on the X-axis and on the Y-axis. The values are 6 and 8 respectively.

You put the values on the second power and add them. So the equation would be 6^2 + 8^2. The answer would be 100.  Because the Pythagorean Theorem is a^2 + b^2= c^2, you would square root would be 10. The distance between the two points is 10.

Can someone pls help me
Ill give Brainly
NO BOTS OR ILL REPORT YOU

Answers

The first one 3y = 2x - 12.

The graph is the line y = 2/3 - 4. And the first answer describes the same line multipled by 3.

solve the matrix equation

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Answer:

c

Step-by-step explanation:

if someone writes "/" does it mean Division or a Fraction Line

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Fraction line is what it means like 1/2 is the fraction 1 half

HEY THERE!! CORRECT ANSWER+EXPLANATION SHALL BE MARKED BRAINLIEST+43 POINTS
-solve the equation
[tex] \frac{1}{x} + \frac{1}{3x} = 4[/tex]
(pls have your answer as a fraction in its simplest form)

Thanks xx)​

Answers

[tex]\displaystyle \frac{1}{x} +\frac{1}{3x} =4 \ \ ; \ \ x\neq 0 \\\\\\ \frac{3+1}{3x} =4 \\\\\\12x=4 \\\\ \boxed{x=\frac{1}{3} }[/tex]

Factor Completely. (and please show work)
-10x^2 + 3x + 4

Answers

Step-by-step explanation:

=>-10x²+3x+4

=>-10x²-5x+8x+4

=>-5x(2x+1)+4(2x+1)

=>(2x+1)(4-5x)

hope this helps you.

PLEASE PLEASE HELP ILL MARK BRAINLIEST!!!!

Answers

Answer:

done this before

Step-by-step explanation:

cant see full picture but of what i know of is he spent 35 dollars on apples for his shop...?

Answer: 3x+5y=$33

X+y=9

Step-by-step explanation: X= number of pounds of apples y= number of ponds of oranges.

Can anyone help me with this?

Answers

Answer:

x = 42 degrees

y = 37 degrees

Step-by-step explanation:

Those are right angle triangles. So you know the right angles are 90 degrees, and each triangle gives you the measurement of another angle.

So, take the triangle in the top left (x):

180 - 90 - 48 = x

Same with the other triangle (y)

180 - 90 - 53 = y

Can someone explain this to me ​

Answers

Angle ADB is a right angle --- Given

Angle ADB is 90 degrees --- Definition of a Right Angle

Angle CDB is 90 degrees --- Definition of Supplementary Angles

Angle ADB = Angle CDB --- Definition of Congruent Angles

Proofs can be tricky! What helps me is thinking through them step by step and how I would prove I did something. While I'm not entirely sure what options you have for this proof, I've given my best guess.

Hope this helps!! :)

Please help me out!!!!!

Answers

Answer:

D. 9

Step-by-step explanation:

9 is the degree of polynomial

Ski rental is $45 for 3 hours and $10 for each additional hour. You pay $75. How many additional hours did you pay

Answers

Answer:3

Step-by-step explanation:Its really easy?

willie's school is selling tickets to the annual talent show. On the first day of ticket sales the school sold 10 adult tickets and 4 student tickets for a total of $194. The school took in $182 on the second day selling 7 adult tickets and 7 student tickets. What is the price each one adult ticket and one student ticket? ​

Answers

Adult tickets - $15

Student tickets - $11

First day:

10 tickets * $15 = $150

4 tickets * $11 = $44

Total: $194

Second day:

7 tickets * $15 = $105

7 tickets * $11 = $77

Total: $182

I need help please!!!

Answers

Answer:

yes (the given angles are co-interior {130+50=180} )yes( corresponding angles are equal) .....yes (exterior alternate angles are equal)yes ( vertically opposite angles are equal)

7) 3x=45( corresponding angles formed on parallel lines)

x=45/3

x=15

8)120=2x+10(corresponding angles formed on parallel lines)

or,120-10=2x

or,110/2=x

or,x=55

pls help me i don’t get this at all

Answers

Step-by-step explanation:

oh, come on ! you don't understand what ordered pairs or point coordinates stands for ?

it is simple, the first number is the x value, and the second number is the y value.

so, all we need to do here is to take every pair, put their values in the places of x and y in the inequality, and see if it is true with these specific values or not.

if yes, then that pair is a solution.

(6, -33)

-33 >= -8×6 +7

-33 >= -48 + 7

-33 >= -41 true, -33 is indeed bigger than -41

in the same way as -1 is bigger than -2.

(-1, 12)

12 >= -8×-1 + 7

12 >= 8 + 7

12 >= 15 false

(8, -65)

-65 >= -8×8 + 7

-65 >= -64 + 7

-65 >= -57 false

(2, -1)

-1 >= -8×2 + 7

-1 >= -16 + 7

-1 >= -9 true, -1 is bigger than -9

(-6, 47)

47 >= -8×-6 + 7

47 >= 48 + 7

47 >= 55 false

A retiree has $200,000 to invest and needs to make $13,000 with her investments. If she can invest in government bonds at 6% or investment-grade bonds at 8%, how much should she invest in each?

Answers

Answer:

$50,000 at 8%; $150,000 at 6%

Step-by-step explanation:

$50,000 x .08 = $4000

$150,000 x .06 = $9000

$4000 + $9000 = $13,000

On a graph, points form a curved line.
Using the scatterplot, determine the association.

Answers

Answer:

Nonlinear association, B

Step-by-step explanation:

Answer:

strong  

Step-by-step explanation:

Solve for x, y and z ( help ♡ )

Answers

Ans of your question . in which class do u read?

help plz i will give brainliest

Answers

Answer:

12

(If needed explanation ask in the comments! ty)

Hope This Helps! •v•

Omar wants to open an account for his grandchildren that he hopes will have
$80,000 in it after 20 years. How much must he deposit now into an account
that yields 1.75% interest, compounded monthly, so he can be assured of
reaching his goal?

Answers

Using compound interest, it is found that he must deposit $56,389.

Compound interest:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

A(t) is the amount of money after t years.  P is the principal(the initial sum of money).  r is the interest rate(as a decimal value).  n is the number of times that interest is compounded per year.  t is the time in years for which the money is invested or borrowed.

In this problem:

Hopes to have $80,000 in 20 years, thus [tex]t = 20, A(t) = 80000[/tex].Interest rate of 1.75%, thus [tex]r = 0.0175[/tex].Compounding monthly, thus [tex]n = 12[/tex]The investment is of P, for which we have to solve.

Then:

[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]

[tex]80000 = P(1 + \frac{0.0175}{12})^{12(20)}[/tex]

[tex]P = \frac{80000}{(1 + \frac{0.0175}{12})^{12(20)}}[/tex]

[tex]P = 56389[/tex]

He must deposit $56,389.

A similar problem is given at https://brainly.com/question/25263233

Someobe pleaseeee help I need it​

Answers

Answer:

its 35

Step-by-step explanation:


How many gallons of pure water should be added to 10 gallons of a solution containing 15% juice so that
the remaining solution contains 5% juice?
Fill in the table:
What is the amount of juice in the original solution? a =
What is the original amount of solution in gallons? b =
How much juice is added? c =
How much total solution is added? d =
Original
Added
New
Amount of juico
a
Total solution

Answers

Answer:

A = 1.5, B = 10, C = 0, D = 20

Step-by-step explanation:

A = 10 * 15% = 1.5

b = 10

c = 0

(10 + x) * 5% = 1.5

0.5 + 0.05x = 1.5

0.05x = 1

x = 20

(assume 'x' is added solution)

d = 20

Answer: A. 1.5 B. 10 C. 0 D. X

8th grade math!!! Help ILL BRAINLIST

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The answer is 10 8 8 10

Help!!!!!!!!!!!!!!!!!!!

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Answer:

Slope of a line perpendicular to y=4x+3 is −14 .

Step-by-step explanation:

...............

If you need the graph here it is

plsss help me with this:(((​

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Answer:

[tex] \frac{2 {a}^{2} }{3 {b}^{3} } \div \frac{6 {a}^{3} }{5 {b}^{2} } = \frac{2 {a}^{2} }{3 {b}^{3} } \times \frac{5 {b}^{2} }{6 {a}^{3} } = \frac{5}{9ab} \\ \\ \frac{ {x}^{2} - 5x + 6}{ {x}^{2} - 6x + 9} + \frac{4x - 12}{{x}^{2} - 6x + 9} \\ = \frac{{x}^{2} - 5x + 6 + 4x - 12}{{x}^{2} - 6x + 9} \\ = \frac{{x}^{2} - x - 6}{{x}^{2} - 6x + 9} \\ = \frac{(x - 3)(x + 2)}{(x - 3)(x - 3)} \\ = \frac{(x + 2)}{(x - 3)} \\ \\ \frac{3a}{a - b} - \frac{a + 2b}{a - b} \\ = \frac{3a - a + 2b}{a - b} \\ = \frac{2a - 2b}{a - b} \\ = 2\frac{a - b}{a - b} \\ = 2[/tex]

what would be the answer to this problem [tex]\frac{7x-3}{9} \geq 8-2x[/tex]

Answers

Answer:

[tex]x\geq 3[/tex]

Step-by-step explanation:

Solve the following equation for v in terms of all other variables involved.
2(v-h)/k=r

Answers

Answer:

[tex]v = \frac{rk}{2} + h[/tex]

Step-by-step explanation:

Given the equation, [tex]r = \frac{2(v - h)}{k}[/tex], in order to solve for v:

Start by multiplying both sides by k:

[tex](k)r = \frac{2(v - h)}{k} (k)[/tex]

rk = 2(v - h)

Divide both sides by 2:

[tex]\frac{rk}{2} = \frac{2(v-h)}{2}[/tex]

[tex]\frac{rk}{2} = v - h[/tex]

Add h to both sides to isolate v :

[tex]\frac{rk}{2} + h = v - h + h[/tex]

[tex]\frac{rk}{2} + h = v[/tex]

Find the GCF for the pair of numbers. ​9,4

Answers

The GCF of numbers is the greatest common factor of the numbers.

The numbers are given as: 4 and 9.

Factorize both:

[tex]\mathbf{4 = 1 \times 2 \times 2}[/tex]

[tex]\mathbf{9 = 1 \times 3 \times 3}[/tex]

The common factor between  both is 1.

So, we have:

[tex]\mathbf{GCF = 1 }[/tex]

Hence, the GCF of 4 and 9 is 1

Read more about GCFs at:

https://brainly.com/question/20061154

so I'm not sure how to draw a square with the area of 3 units

Answers

The area of a square is width x height where both the width and height is the same length because a square has the same lengths on all four sides.

So we can say “3 = L x L” where L is any side length of the square

L times L is just simplified to L squared: “3 = L^2”

We can take the square root of both sides to get rid of the L squared. We are left with “the square root of 3 equals L”.
Sqrt(3) = L

And on a calculator the square root of 3 is 1.73205080757.

1.73205080757 = L.

The square is 4 lines in a box each with the length of 1.73205080757 units.

helppppppppppppppppppppppppppppppppp

Answers

Answer:

You want to find how much it cost for 1kg of potatoes, which in this case is .45 cents. After that you want to multiply the price of 1kg by 50, to get your cost for 50 kg of potatoes, which would be $22.50 I hope this helps! :)

Answer:

$22.50

Step-by-step explanation:

If one. again is 10k and it costs 4.50, then you would do 4.50 multiplied by 5 because each 10k is 4.50 and thier is 50 in total so 5 bags of 4.50 meaning 4.5x5 which would get you $22.50

75.3325 round to the tenth

Answers

75.3 the first 3 [.3] is the tens place and since the number after it [3] isn’t higher the 5 you round down making it 75.3
75.3

the first 3 is in the tenths place, the second 3 is in the hundredths place, the 2 is in the thousandths place, and the 5 is in the ten thousandths place.

now since you know that the 3 is in the tenths place you have to look at the number in the hundredths place so you know what to round it to. since the number in the hundredths place is below 5, it stays the same. if it were a 5 or above, that 3 would be rounded to a 4 making the answer 75.4, but since it’s a 3, the answer stays 75.3
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