Someone please help!! Solve for X, Y, and Z!

Complete Question

The SAT are scored so as to yield a mean of 500 and a standard deviation of 100. These scores are close to being normally distributed. An exclusive club wishes to invite those scoring in the top 5% on the College Boards to join. a. Find percentages of scores that is between 480 and 590. b. What score is required to be invited to join the club? c. What score separates the top 60% of the population from the bottom 40%? What do we call this value? (hint: the score that separates the top 20% of the population from the bottom 80% is called the 80th percentile)

Answer:

a

 [tex]P(480 < X  <  590) =  0.3952[/tex]  

b  

  [tex]x =  664.5 [/tex]

c

 [tex]x_1 =  474.67[/tex]

The value is called the [tex]40^{th}[/tex] percentile

Step-by-step explanation:

From the question we are told that

The mean is [tex]\mu = 500[/tex]

The standard deviation is [tex]\sigma = 100[/tex]

Generally the percentage of the score that are between 480 and 590 is mathematically represented as

[tex]P(480 < X < 590) = P(\frac{ 480 - 500}{ 100} < \frac{ X - \mu }{ \sigma } < \frac{ 590 - 500}{ 100} )[/tex]

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

=> [tex]P(480 < X < 590) = P(\frac{ 480 - 500}{ 100} < Z < \frac{ 590 - 500}{ 100} )[/tex]

=> [tex]P(480 < X < 590) = P(-0.2< Z < 0.9 )[/tex]

=> [tex]P(480 < X < 590) = P(Z < 0.9 ) - P(Z<-0.2) [/tex]

From the z table (reference calculator dot net )

[tex] P(Z < 0.9 )= 0.81594 [/tex]

And

[tex] P(Z < -0.2 )= 0.42074 [/tex]

=> [tex]P(480 < X < 590) = 0.81594 - 0.42074 [/tex]

=> [tex]P(480 < X < 590) = 0.3952[/tex]

Converting to percent

[tex]P(480 < X < 590) = 0.3952 * 100[/tex]

[tex]P(480 < X < 590) = 39.52\% [/tex]

The percentage invited to join the club is the top 5% , this can be mathematically represented as

[tex]P(X > x ) = 0.05[/tex]

Here x is the score that is within the top 5%

=> [tex]P(X > x) = P( \frac{X - \mu }{\sigma } > \frac{ x - 500}{100} )= 0.05[/tex]

Generally the critical value of 0.05 from the normal distribution table is

[tex]Z_{0.05} = 1.645[/tex]

So

[tex]\frac{ x - 500}{100} = 1.645[/tex]

=> [tex]x - 500 = 164.5[/tex]

=> [tex]x = 664.5 [/tex]

Generally the probability of having a score that separates the top 60% of the population from the bottom 40%

[tex]P(X > x_1 ) = 0.60[/tex]

=> [tex]P(X > x_1) = P(\frac{ X - \mu }{\sigma } > \frac{x - 500}{100} ) = 0.60[/tex]

The critical value of 0.60 from the normal distribution table is

[tex]Z_{0.60} = - 0. 2533[/tex]

So

[tex]\frac{x_1 - 500}{100} = -0.2533[/tex]

=> [tex]x_1 = 474.67[/tex]

From the hint given we can see that this value is called the [tex]40^{th}[/tex] percentile

Answer:

A. 6.95+8t=24.95;t=2.25

Step-by-step explanation:

24.95 minus 6.95 of the canvas equals 18 dollars left for the 8 tubes of paint, but then you have to figure out how much money for each which would equal 18 divided by 8, and that equals 2.25 dollars.

Answer:

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Answer:

4. 180

5. PQ

Step-by-step explanation:

Answer:0.4

Step-by-step explanation:

4 is bigger than one so it would be like 400>127

Answer:

0.4 would be the greater number

Answer:

The answer is D, 45.

Step-by-step explanation:

How to find the Interquartile Range

After doing that, write out your list, and and subtract the medians to get 45.

Answer:

D

Step-by-step explanation:

Answer:

f(3)= 3+1

=4

gf(3) is attached.

Answer:

see below

Step-by-step explanation:

the circumference of a circle is

[tex]2\pi r[/tex]

in our problem

r=11

[tex]C=2\pi (11)\\\\=22\pi[/tex]

rounded to the nearest tenth

[tex]C\approx69.1[/tex]

the area of a circle is

[tex]\pi r^2[/tex]

so the area is

[tex]A=\pi(11)^2\\\\=121\pi[/tex]

rounded to nearest tenth

[tex]A\approx 380.1[/tex]

Answer:

7.6

Step-by-step explanation:

(4−(−3))2+(−2−1)2

=7^2+(−2−1)2

=49+(−2−1)2

=49+(−3)^2

=49+9

=58

=7.6

Answer:

480

Step-by-step explanation:

In each box there is 32. Well, we know there is 15 boxes, so we multiply 32 and 15 to get 480.

She bought 480 total bananas :D

Answer:

She would've eaten 480 bananas

Step-by-step explanation:

Answer:

10.7 grams

Step-by-step explanation:

hey there, again!

this is a similar process the mass is denisty*area HOWEVER keep in mind it's flat so the area is just x deltax while denisity is 3 + sin(x)

mass of rod = integral 0 to 3pi/4 of (3 + sin(x))*x deltax

= integral 0 to 3pi/4 of 3x + xsin(x) deltax

= 0 to 3pi/4 [3/2*x^2 + x(-cos(x)) + sin(x)]

= 10.7 grams

Answer:

$1.25

Step-by-step explanation:

15 divided by a dozen (12) is 1.25

Have a great day!

Answer:

$1.25.

Step-by-step explanation:

15/12 = $1.25

Answer:

23

Step-by-step explanation:

117 - 94 should be the correct answer

Answer:

There are NO solutions

Step-by-step explanation:

On the left hand side, we have an absolute value;

which means that the left hand side will always be greater than or equal to 0

On the right hand side, we have a negative value;

Since the LHS can NEVER be negative, it will never be less than a negative number

Hence, No value of y can make this equation true

Answer:

is this a trick question cause how can you have 5.3 thermometers?

The total inventory of the inventory shows 2, 4, 2,5,3, and 1 will be 17.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, thousand, or a million. There are summations with an infinite set of parameters.

In another word, the summation is to add or subtract any two or more terms by doing that operation we will get a new result which could be big or small depending upon the number.

Given the inventory 2, 4, 2,5,3,1 if we add this inventory to the total then it will come out to be

2+ 4+ 2+5+3+1 =17 hence 17 will be the correct answer.

For more information about summation

https://brainly.com/question/10777222

#SPJ2

Answer:

a) H1: µ < 7.5

Step-by-step explanation:

From the given information:

mean = 7.5

sample size = 50

sample mean = 9.3

The main task we are to carry out is to identify the correct alternative hypothesis:

Now to do that, let's state the null and the alternative hypothesis from the given study.

The null hypothesis can be computed as:

[tex]\mathbf{H_o: \mu \geq 7.5}[/tex]

The alternative hypothesis can be computed as:

[tex]\mathbf{H_1: \mu < 7.5}[/tex]

Thus, this test hypothesis is a one-tailed test (left tailed).

Answer:

A. r^10

Step-by-step explanation:

r^2/r^12

1/r^-10

r^10

Answer:

Please see the attached picture.

Answer:

[tex]g(n-7)=\frac{n^{2}-14n+43}{7n-49}[/tex]  → (a)

Step-by-step explanation:

We need to evaluate g(n - 7), where

Replace x by (n - 7) to evaluate it

∵ x = (n - 7)

∴ [tex]g(n-7)=\frac{(n-7)^{2}-6}{7(n-7)}[/tex]

→ Let us find (n - 7)²

∵ (n - 7)² = (n - 7)(n - 7) = (n)(n) + (n)(-7) + (-7)(n) + (-7)(-7)

∴ (n - 7)² = n² + (-7n) + (-7n) + 49 = n² + -14n + 49

∴ (n - 7)² = n² - 14n + 49

→ Find 7(n - 7)

∵ 7(n - 7) = 7(n) - 7(7)

∴ 7(n - 7) = 7n - 49

→ Now let us write then in the form above

∵ [tex]g(n-7)=\frac{n^{2}-14n+49-6}{7n-49}[/tex]

→ Add the like terms in the numerator

∴  [tex]g(n-7)=\frac{n^{2}-14n+43}{7n-49}[/tex]

The correct answer is (a)

Answer:

5.31

Step-by-step explanation:

Given the regression line equation, [tex] y = 10 - 0.67x [/tex], where,

x = number of slices of pizza eaten

y = number of laps run immediately

Number of laps run by a player who ate 7 slices of pizza can be predicted by plugging in x = 7 into the regression line equation to find y:

[tex] y = 10 - 0.67x [/tex]

[tex] y = 10 - 0.67(7) [/tex]

[tex] y = 10 - 4.69 [/tex]

[tex] y = 5.31 [/tex]

Answer:

6) 130

7) x = 35

8) y = 100

9) 50

10) 130

11) DEF = 29

12) FEG = 61

13) DEF = 91

14) FEG = 89

Step-by-step explanation:

angle AEB is 50°

supplementary is when 2 angles add together to make 180°

50 + x = 180

x = 180 - 50

x = 130

angles AEB and DEC are vertical angles

vertical angles are equal.

50 = x + 15

50 - 15 = x

35 = x

AEB and AED are supplementary angles

supplementary angles add together to make 180

50 + (y + 30) = 180

y + 30 = 180 - 50

y + 30 = 130

y = 130 - 30

y = 100

DEC is vertical to AEB

vertical angles are equal.

AEB = 50

DEC = 50

AED = y + 30

as established earlier, y = 100

substitute Y for 100

AED = 100 + 30

AED = 130

DEF and FEG are complimentary.

complimentary means they add together to make 90

(3x - 4 ) + (5x + 6 ) = 90

3x - 4 + 5x + 6 = 90

8x + 2 = 90

8x = 90 - 2

8x = 88

x = 88/8

x = 11

substitute x into the equations

DEF = 3x - 4

DEF = 33 - 4

DEF = 29

FEG = 5x + 6

FEG = 55 + 6

FEG = 61

DEF and FEG are supplementary.

supplementary means they add together to make 180

(9x + 1) + (8x + 9) = 180

9x + 8x + 1 + 9 = 180

17x + 10 = 180

17x = 170

x = 10

substitute x into the equations

DEF =  9x + 1

DEF = 90 + 1

DEF = 91

FEG = 8x + 9

FEG = 80 + 9

FEG = 89

Answer:

5

Step-by-step explanation:

2/4=y/10

=> 2x10=yx4

=> 20=yx4

=>y=5

9514 1404 393

Answer:

  Jesse

Step-by-step explanation:

Jesse's distance in 60 seconds would be ...

  (60 s)(15 m)/(6 s) = 150 m

Peyton's distance in 60 seconds would be ...

  (60 s)(22 m)/(10 s) = 132 m

Jesse travels farther in the same amount of time, so Jesse is moving faster.

__

You might find it simpler just to compute the rate of each.

  Jesse: (15 m)/(6 s) = 2.5 m/s

  Peyton: (22 m)/(10 s) = 2.2 m/s

Jesse's speed is higher.

Answer:

Step-by-step explanation:

800

Answer:

oh we late

Step-by-step explanation:

Answer: it’s =

i just got the test results