John finds that there is a scholarship available to all personals scoring in the top 5% on the ACT test. If the mean score on the ACT is 21 with a standard deviation of 4.7, what score does he need in order to qualify for the scholarship

Answers

Answer 1

Answer:

He needs a score of 28.7315 to qualify for the scholarship

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.

The mean score on the ACT is 21 with a standard deviation of 4.7

This means that [tex]\mu = 21, \sigma = 4.7[/tex]

What score does he need in order to qualify for the scholarship?

The top 5%, so the 100 - 5 = 95th percentile, which is X when Z has a p-value of 0.95, so X when Z = 1.645.

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

[tex]1.645 = \frac{X - 21}{4.7}[/tex]

[tex]X - 21 = 4.7*1.645[/tex]

[tex]X = 28.7315[/tex]

He needs a score of 28.7315 to qualify for the scholarship


Related Questions

This equation shows how the total number of pieces Lamar has learned depends on the number of weeks he has taken piano lessons. P = w The variable w represents the number of weeks he has taken piano lessons, and the variable p represents the total number of pieces he has learned. In all, how many weeks of piano lessons will Lamar need before he will be able to play a total of 19 pieces?

Answers

Answer:

19 weeks

Step-by-step explanation:

Given equation:

P = w

Where,

w = the number of weeks he has taken piano lessons

p = the total number of pieces he has learned

how many weeks of piano lessons will Lamar need before he will be able to play a total of 19 pieces?

Find w when p = 19

P = w

p = 19

Since P = w

19 = w

Therefore,

w = 19

Lamar need 19 weeks before he will be able to play a total of 19 pieces

What is the value for the expression (-5)(3 + 4) ?

Answers

Answer:

-35

Step-by-step explanation:

Since there are  parentheses, you start with that. 3+4=7

Now, -5 x 7 =-35

Answer:

-35

hope this helps

have a good day :)

Step-by-step explanation:

3+4=7

-5 x 7=-35

Question 9 You are rushing out to get to your appointment in 30 minutes. From experience you know that most of the time you travel this distance in 30 minutes. However, half of the time there is heavy traffic. In the past, there has been heavy traffic and you have made it to your appointment within 30 minutes 34% of the time. You get out on the street and see that there is heavy traffic. What is the chance you will get to your appointment on time

Answers

Answer:

0.68

Step-by-step explanation:

According To the Question,

Let, H ⇒ "heavy traffic" & T ⇒  "get there on time".

Then, "half of the time there is heavy traffic" ⇔ P(H)=0.5.

Given, In the past, there has been heavy traffic and you have made it to your appointment within 30 minutes 34% of the time. This has to be taken to mean P(H and T) = 0.34.

Now, you are given that there is heavy traffic, so We need to find P(T I H).

 P(T l H) = P(H and T) / P(T)

P(T l H) = 0.34/0.5 ⇒ 0.68

Omar runs 3 miles everyday. He runs a mile in 4 minutes 30 seconds. How many miles did he run in the month of February?​

Answers

Answer:

so he ran 84 miles and if you need 378.

Step-by-step explanation:

3*28=84miles

and then 84*4.5=378

If f (x) = 6x - 6, find f(-1).

Answers

Answer:

Step-by-step explanation:

1

Answer:

-12

Step-by-step explanation:

Hi Alyssa!,

For any x we multiply it by 6 and subtract 6 from it to get the F. The function tells us this. To find f(-1) it bassicly says what's f when x is -1. Well we know that. f is 6(-1)-6 whis is -12.

F is -12

JoeLouis2

The product of two consecutive even integers is 36 less than 18 times their sum. Find the two integers

Answers

Answer:

34 and 36

Step-by-step explanation:    7  1  17   15

product of two consecutive even integer   x(x+2)      x is even

product of two consecutive even integer  x(x + 2) plus 36 equal 18(x +x + 2)

x(x+2) + 36 = 18(x +x +2)

x² + 2x + 36  = 18x + 18x + 36    36's cancel, 2x - 36x = -34x

x² - 34x = 0     solve for x

x( x - 34) = 0        x = 0 and 34    only 34 is an even number!

x = 34  and 36  

On a number line, graph all the temperature that are warmer than -2 degrees Celsius

Answers

The inequality would be x>2

(a) A temperature of -2 °C is warmer than a temperature of -5 °C as the temperature on the graph decreases.

(b)The inequality -2>-5 will be used to illustrate the connection between -2 and -5.

What is a graph?

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

On a number line, graph all the temperature that are warmer than -2°C.

(a)-2 °C  temperature is warmer,As the temperature in the graph is decreasing,-2 °C temperature is warmer than -5 °C.

The inequality to express the relationship between -2 and -5 will be -2>-5.

Hence,temperature of -2 °C is warmer than a temperature of -5 °C as the temperature on the graph decreases.

To learn more about the graph, refer to the link;

https://brainly.com/question/14375099

#SPJ2

Victor wanted to know the height of a tree at his friend’s house. On Saturday morning, he measured the shadow of the tree along the ground to be 24 feet long. At the same time, he measured his own shadow to be 3 feet long. Victor is 6 feet tall. Find the height of the tree

Answers

The shadow of the tree is 12ft long. Divide the height of the tree (24) by Victors height (6), which will equal 4. Then multiple 4 and the height of victors shadow. (this is my first time doing this, hope it helped:)

Ratio remains same

Let that be x

[tex]\\ \rm\rightarrowtail \dfrac{6}{3}=\dfrac{x}{24}[/tex]

[tex]\\ \rm\rightarrowtail 2=x/24[/tex]

[tex]\\ \rm\rightarrowtail x=48[/tex]

Question 16. Use the Triangle Inequality Theorems to determine if a triangle can exist with the given side lengths. (HINT: A triangle with sides a, b and c
exists if and only if the sum of any two sides of the triangle is greater than
the third side.) *
7,16, 6

Answers

Answer:

no

Step-by-step explanation:

7 squared plus 6 squared is 85 while 16 squared is 256

please help me!!!!! please

explaining your answer = brainliest

Answers

Answer:

42.39 sq.cm

Step-by-step explanation:

Ф = 135°

r  = 6 cm

Area of the sector = [tex]\frac{theta}{360}*\pi *r^{2}\\[/tex]

  [tex]= \frac{135}{360}* 3.14 *6 * 6\\\\= \frac{135}{10}*3.14\\\\= 27 * 1.57\\\\=42.39[/tex]

The area of sector bounded by 135 ° arc is 42.42 cm ².

Step-by-step explanation:

Given :-

Radius of the circle , r = 6 cm

Angle of the circle, θ = 135 °

To Find :-

Area of circle bounded by a 135 ° arc.

Solution :-

We know that

[tex]\small \sf \: Area \: of \: sector \: = \frac{θ}{360} \: \times \pi \times r {}^{2} \\ [/tex]

Substitute the values of r and θ , we get

Area of sector =

[tex]\small \sf \: Area \: of \: sector \: = \frac{135 °}{360} \: \times \pi \times {6cm}^{2}\\ [/tex]

[tex]\small \sf \: Area \: of \: sector \: = \frac{135°}{360} \: \times \frac{22}{7} \times 6cm \times 6cm \\ \\ \small \: \sf Area \: of \: circle \: = \frac{135}{360} \times \frac{22}{7} \times 36cm {}^{2} \\ \sf \: \: = \frac{135}{10} \times \frac{22}{7} \\ \sf \: = 42.42cm \: {}^{2} [/tex]

Therefore, The area of sector bounded by 135 ° arc is 42.42 cm ².

Let g(x) = 2x and h(x) = x^2 +4 evaluate (h*g)(-2)

Answers

Answer:

-32

Step-by-step explanation:

Firstly, what we have to do is to multiply g(x) by h(x)

We have this as;

2x(x^2 + 4)

We then proceed to substitute the value of x with -2 as follows

2(-2)(-2^2 + 4)

= -4(8) = -32

A retailer sells a refrigerator for a list price of $1,200. The retailers cost was $850. What is the percentage of the markup?

Answers

Answer:

41%

Step-by-step explanation:

1200-850=350

350 is the markup, now we need the percentage

the orginal price was 850 so we just need to divide 350 by 850

we get 0.4117...

convert that to a percentage and we have 41% markup

The cost of 10 donuts and 2 cakes is the same. If the cost of 3 cakes and 5 donuts is $8, find the cost of a cake.

Answers

Answer:

$2

Step-by-step explanation:

Let the cost of a donut and a cake be $d and $c respectively.

10d= 2c

Dividing both sides by 2:

5d= c -----(1)

3c +5d= 8 -----(2)

Substitute (1) into (2):

3c +c= 8

Simplify:

4c= 8

Divide both sides by 4:

c= 8 ÷4

c= 2

∴ The cost of a cake is $2.

Help me emergency please

Answers

I think it's the second one since the line goes the whole way through the circle. but it's hard to tell.

do you happen to know if it's the radius it diameter?

Answer:

Step-by-step explanation:

radius=diameter/2

=11/2

=5.5 mm

circumference=2πr

=2*3.14*5.5

=34.54 mm


While attempting to multiply the expression (3x + 7)" a student made mistakes. Explain and write the correct way.

Answers

Answer:

9x²+42x+49

Step-by-step explanation:

that is not the correct way to foil.

the correct way would be (3x+7)²= (3x+7)(3x+7)

simplifying that would give us 9x²+42x+49

his mistake was multiplying wrong because he did not foil

what is 12.8% of 250?​

Answers

Answer:

32

put 12.8% as a decimal which is 0.128 and times it by 250

Answer:

32

Step-by-step explanation:

[tex]\frac{y}{250} :\frac{12.8}{100}[/tex]

y × 100 = 250 × 12.8

100y = 3200

100y ÷ 100 = 3200 ÷ 100

y = 32

Tiny's Tattoo Parlor sold 389 tattoos this month. 43 of those tattoos were arm tattoos.
Based on this data, what is a reasonable estimate of the probability that the next customer does not get an
arm tattoo?
Choose the best answer.
Choose 1 answer.
43
346
43
389
43
43
346
389
St Watch video or use a hint
Report a problem

Answers

Answer:

346/389

Step-by-step explanation:

First determine how many were not arm tattoos

389-43

346

P( not arm) = not arm /total

                   = 346/389

Answer:

346/389

Step-by-step explanation:

Khan

SOMEBODY PLEASE HELP ME! I'M HORRIBLE AT GEOMETRY!

Answers

Answer:

Step-by-step explanation:

From graph :

IF = 59

MJ = 26

MJ/IF = 26/59

FGHI is sumilar to JKLM

So JK/FG = 26/58

So 26/59 = Jk/28

JK =( 28*26)/(59)=12.33 ~12

I need help. Please 30 points if you know no links, or I will report you.

Answers

Answer: for first question answer is second option and other question answer is again b

Step-by-step explanation:

Firstly you already see that the median is increasing because it is first 403 and changing to 553. We can understand it increased

help pls i will give brain list to whoever answers first

Answers

Answer:

not a answer

Step-by-step explanation:

try using demos graphing calculator

As the other person stated, use desmos!

Need help with this....

Answers

Answer:

m ∠S = 43°

Step-by-step explanation:

Exterior angle = Sum of opposite interior angles

(6x)° = 77° + (2x + 3)°

6x = 77 + 2x + 3

6x - 2x = 77 + 3

4x = 80

x = 20

m ∠S = (2x + 3)° = 2(20) + 3 = 40 + 3 = 43°

Answer:

∠ S = 43°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ PQR is an exterior angle of the triangle, then

6x = 77 + 2x + 3 ( subtract 2x from both sides )

4x = 80 ( divide both sides by 4 )

x = 20

Then

∠ S = 2x + 3 = 2(20) + 3 = 40 + 3 = 43°

Is the graph increasing, decreasing, or constant?
O A. Decreasing
ООО
B. Increasing
O C.
Constant
Can someone please help

Answers

B. increasing
explanation from left to right, the graph is steadily increasing

simplify an expression
(x^2y^4z)^5/(xy)^2
A) y10z5
B) x6y7z5
C) x7y9z5
D) x8y18z5

Answers

Answer:

d

Step-by-step explanation:

I WILL GIVE YOU BRAINLIEST, PLEASE HELP! I

Answers

Answer:

Amber has a total of $1225.54 after 10 years. Jin has a total of $1225.35 after 10 years. So, Amber earns $0.19 more

Step-by-step explanation:

A: Amber

First, convert 8 percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 rate per year

P = Principal

e = 2.71828(mathematical constant)

t = time  

Then solve the equation for A

A = P*e^(r*t)

A = 1,000.00(2.71828)^(0.08)(10)

A = $2,225.54  

The total amount accrued, principal plus interest, with compound interest on a principal of $1,000.00 at a rate of 8% per year compounded continuously over 10 years for Amber is $2,225.54.

J: Jin

First, convert 8 as a percent to r as a decimal

r = R/100

r = 8/100

r = 0.08 rate per year

n = 365 days

Then solve the equation for A

A = P(1 + r/n)^n*t

A = 1,000.00(1 + 0.08/365)(365)(10)

A = 1,000.00(1 + 0.000219178)(3650)

A = $2,225.35

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $1,000.00 at a rate of 8% per year compounded 365 times per year over 10 years for Jin is $2,225.35.

$2,225.54-1000=A($1225.54)

$2,225.35-1000=J($1225.35)

Answer:

I think the person above explained it best. I just needed to answer a question to keep my streak going and since I know you irl, this is easy. Give that person brainliest bestie <3 they did good job

Step-by-step explanation:

Can someone help me with this please :,)

Answers

Answer: 43.07

Step-by-step explanation:

Anne is painting her house light blue. To make the color she wants, she must add 3 cans of white paint to every 2 cans of blue paint. How many cans of white paint will she need to mix with 6 cans of blue?

Answers

Answer:

9 cans of white paint

Step-by-step explanation:

To solve this you can set up a ratio.

The ratio right now is 3 : 2, you have 3 cans of white paint for every 2 cans of blue paint. This question is asking how many white paint cans would be needed for 6 cans of blue paint. You can see the relationship between the number of blue paint cans and the new number of blue paint cans, maybe it's multiplying by 4 or 2 for example, and once we find that out we can do the same exact thing to the white cans.

[tex]\frac{3}{2} = \frac{?}{6}[/tex]

We can see that to get from 2 to 6 you multiply by 3, so now we do that to the other side of the fraction as well, we multiply by 3. 3 multiplied by 3 is 9, so if we were to have 6 cans of blue paint we would need 9 cans of white paint to get that perfect shade of light blue. Anne would need 9 cans of white paint if she had 6 cans of blue paint to make her shade of blue.

What is the value of √(18-6)^2+(17-1)^2

Answers

Answer:

20

Step-by-step explanation:

sqrt((18-6)^2+(17-1)^2)

Inside parentheses first

sqrt((12)^2+(16)^2)

Then square inside the parentheses

sqrt(144+256)

Sqrt(400)

Taking the square root

20

Problem:

What is the value of:

[tex]\quad \quad \quad \quad\tt{ \sqrt{(18 - {6)}^{2}+ (17 - {1)}^{2}} }[/tex]

Let's try!

[tex]\quad \quad \quad \quad\tt{ \sqrt{(18 - {6)}^{2}+ (17 - {1)}^{2}} }[/tex]

[tex]\quad \quad \quad \quad\tt{ \sqrt{{(12)}^{2}+ {(16)}^{2}} }[/tex]

[tex]\quad \quad \quad \quad\tt{ \sqrt{144+ 256} }[/tex]

[tex]\quad \quad \quad \quad\tt{ \sqrt{400} }[/tex]

[tex]\quad \quad \quad \quad\tt{ = 20}[/tex]

Hence, The answer is:

[tex]\quad \quad \quad \quad \huge\boxed{ \tt{ \color{green}20}}[/tex]

________

#LetsStudy

Amy has a rectangular garden that is 23 feet wide. If the length of the garden is 12 feet, what is the length of its diagonal, in feet? Round to the nearest tenth​

Answers

Answer:

25.9 feet

Step-by-step explanation:

If you split a rectangle into 2 pieces with a diagonal, each piece will be a right triangle

Therefore we can use the pythagorean theorem to solve this problem

The two legs of the right triangle will be 23 and 12

The formula is a^2 +b^2=c^2

c^2 is the diagonal squared ( the hypotenuse)

So:

12^2+23^2=c^2

144+529=c^2

673=c^2

To find just c we need to find the square root of 673, rounded to the nearest tenth

[tex]\sqrt{673}=25.9[/tex]

(the equation is rounded)

So the diagonal is 25.9

6th grade math help me pleaseeee

Answers

Answer:

First one.

Step-by-step explanation:

0.3/3=0.1 ==> 0.1$ per meter

0.77/7 ==> 0.11$ per meter

The first option is cheaper, therefore better to buy if you agree with "the cheaper. the better".

what are the coefficients in the expansion of (x+y)^6​

Answers

Answer:

6 is the coefficient

Step-by-step explanation:

brainliest?

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