MATHEMATICS COLLEGE

The Graduate Record Examination (GRE) is a standardized test that students usually take before entering graduate school. According to the document Interpreting Your GRE Scores, a publication of the Educational Testing Service, the scores on the verbal portion of the GRE are (approximately) normally distributed with mean 462 points and standard deviation 119 points. (6 p.) (a) Obtain and interpret the quartiles for these scores. (b) Find and interpret the 99th percentile for these scores

Answers

Answer 1

Answer:

Answer:

(a) The first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.

The second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.

The third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.

(b) The 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.

Step-by-step explanation:

The first, second the third quartile are the values that let a probability of 0.25, 0.5 and 0.75 on the left tail respectively.

So, to find the first quartile, we need to find the z-score for which:

P(Z<z) = 0.25

using the normal table, z is equal to: -0.67

So, the value x equal to the first quartile is:

$z=(x-m)/(s)\n x=z*s +m\nx =-0.67*119 + 462\nx=382.27$

Then, the first quartile is 382.27 and it means that at least el 25% of the scores are less than 382.27 points.

At the same way, the z-score for the second quartile is 0, so:

$x=0*119+462\nx=462$

So, the second quartile is 462 and it means that at least el 50% of the scores are less than 462 points.

Finally, the z-score for the third quartile is 0.67, so:

$x=z*s +m\nx =0.67*119 + 462\nx=541.73$

So, the third quartile is 541.73 and it means that at least el 75% of the scores are less than 541.73 points.

Additionally, the z-score for the 99th percentile is the z-score for which:

P(Z<z) = 0.99

z = 2.33

So, the 99th percentile is calculated as:

$x=z*s +m\nx =2.33*119 + 462\nx=739.27$

So, the 99th percentile is 739.27 and it means that at least el 99% of the scores are less than 739.27 points.

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A spherical tank has a radius of 6 yards. It is filled with a liquid that costs $7.50 percubic yard. What is the total value of the liquid in the tank? Use 3.14 for
$1695.60
$6782.40
$904.32
$565.20

Answers

The solution is Option B.

The total cost of the liquid in the spherical tank is $ 6782.40

What is a Sphere?

A sphere has a spherical, symmetrical shape. It is a three-dimensional solid with equal distances between each surface point and the center. On the basis of its radius, it has a surface area and a volume. There are no faces, corners, or edges on it.

The volume of a sphere is given by the formula

Volume of Sphere = ( 4/3 )πr³

where r is the radius of the sphere

Given data ,

Let the total cost of the liquid in the spherical tank be = A

Let the radius of the spherical tank be = R

The value of R = 6 yards

Now the cost of the liquid in the tank per cubic yard = $ 7.50

And ,

The volume of spherical tank = ( 4/3 )πR³

Substituting the values in the equation , we get

The volume of spherical tank = ( 4/3 ) x 3.14 x ( 6 )³

The volume of spherical tank = 25.12 x 6 x 6 x 6

The volume of spherical tank = 904.32 yards³

Now ,

The total cost of the liquid inside the spherical tank A = cost of the liquid in the tank per cubic yard x volume of spherical tank

Substituting the values in the equation , we get

The total cost of the liquid inside the spherical tank A = 7.50 x 904.32

The total cost of the liquid inside the spherical tank A = $ 6782.40

Therefore , the value of A is $ 6782.40

Hence , the volume of sphere is 904.32 yards³ and the cost of the liquid inside the tank is $ 6782.40

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Katelyn had 2 dogs and 3 cats. Which of the following shows the ratio written correctly for the number of dogs to cats?A) 3:2
B) 3-2
C) 2:3
D) 3 x 2

Answers

Answer:

2:3

Step-by-step explanation:

Ratio is indicated by :

Its dogs to cats, right so ratio is number of dogs:number of cats which is 2:3

Hope this helps plz mark brainliest if correct :D

Answer:

2:3

Step-by-step explanation:

2 is first and 3 is the second number so you put them in order

Determine the circumference of the base of the tin?

Answers

By answering the given question, we may state that We can apply the formula if we know the radius: C = 2πr where the radius r is.

what is diameter?

In geometry, a circle's diameter is any straight line segment whose endpoint is on the circle and which passes through its centre. Another name for it is the circle's longest chord. The diameter of a sphere can be defined using either idea. The diameter is the length of the line perpendicular to the two points at either end of the circle. If you think of length as the distance between two points, then diameter is length. The diameter of a circle is the separation between its two farthest points.

We must know the base's diameter or radius in order to calculate the circumference of the tin.

If we know the diameter, we can apply the following formula to determine the circle's circumference:

C = πd

where d is the diameter and C is the circumference.

We can apply the formula if we know the radius:

C = 2πr

where the radius r is.

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