The figure above shows a square inscribed in a rectangle.
What is the area of the orange colored part of the figure? (Include only numbers, not words or labels, in your answer.)

Answer:

1. 90.49% of test takers scored less than Alison.

2.

Kamal scored in the 82th percentile.

Kamal's score was of 510.8.

3. 15.52% of test takers scored between 505 and 510 on the MCAT.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

For the current version of the MCAT, the population mean is 501.1 and the population standard deviation is 10.6 points.

This means that [tex]\mu = 501.1, \sigma = 10.6[/tex]

1. Alison scored 515 on the MCAT. What is the percentage of test takers who scored less than Alison (what is the percentile rank associated with a raw score of 515)?

The proportion is the pvalue of Z when X = 515. So

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

[tex]Z = \frac{515 - 501.1}{10.6}[/tex]

[tex]Z = 1.31[/tex]

[tex]Z = 1.31[/tex] has a pvalue of 0.9049

0.9049*100% = 90.49%

90.49% of test takers scored less than Alison.

2. Kamal scored higher than 82% of the test takers. What is Kamal's percentile—what is Kamal's score on the MCAT?

Kamal scored in the 82th percentile.

His score is the value of Z when Z has a pvalue of 0.82. So X when Z = 0.915.

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

[tex]0.915 = \frac{X - 501.1}{10.6}[/tex]

[tex]X - 501.1 = 0.915*10.6[/tex]

[tex]X = 510.8[/tex]

Kamal's score was of 510.8.

3. What percentage of test takers scored between 505 and 510 on the MCAT?

The proportion is the pvalue of Z when X = 510 subtracted by the pvalue of Z when X = 505. So

X = 510

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

[tex]Z = \frac{510 - 501.1}{10.6}[/tex]

[tex]Z = 0.84[/tex]

[tex]Z = 0.84[/tex] has a pvalue of 0.7995

X = 505

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

[tex]Z = \frac{505 - 501.1}{10.6}[/tex]

[tex]Z = 0.37[/tex]

[tex]Z = 0.37[/tex] has a pvalue of 0.6443

0.7995 - 0.6443 = 0.1552

0.1552*100% = 15.52%

15.52% of test takers scored between 505 and 510 on the MCAT.

Answer:

3.16

Step-by-step explanation:

4.42 - 1.26 = 3.16

Answer:

the answer is 184570

Step-by-step explanation:

Answer:

D. 12

Step-by-step explanation:

The average rate of change between the interval, x = 2 to x = 4, in the given function is: D. 12.

Average rate of change = change in y / change in x = (y2 - y1)/(x2 - x1).

Given the interval of the function, as x = 2 to x = 4, we have:

(x1, y1) = (2, 8)

(x2, y2) = (4, 32)

Average rate of change = change in y / change in x = (32 - 8)/(4 - 2) = 24/2

Average rate of change = 12

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The weights that round to 7.43 pounds are:

7.429 pounds and 7.425 pounds

Option A and E are the correct options.

The place value of a number is given as:

Example:

1234.567

1 = thousand place value

2 = hundred place value

3 = tens place value

4 = ones place value

5 = tenths place value

6 = hundredths place value

7 = thousandths place value

We have,

Rounding to the nearest hundredths.

A.

7.429 pounds

= 7.43 pounds

B.

7.437 pounds

= 7.44 pounds

C.

7.433 pounds

= 7.43 pounds

D.

7.413 pounds

= 7.41 pounds

E.

7.425 pounds

= 7.43 pounds

Thus,

7.429 and 7.425 rounds to 7.43 pounds.

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Answer:

Step-by-step explanation:

A linear function has the form

y=mx+b, where m=slope and b=y intercept ( the value of y when x=0)

We are given the point (0,5) so we know b is 5. So we just need to find the slope m

m=(y2-y1)/(x2-x1), we have two points (0,5) and (2,-3)

m=(-3-5)/(2-0)

m=-8/2

m=-4 so our line is

y=-4x+5

Answer:

c. 12

Step-by-step explanation:

PA² = (BC + PB) × PB => tangent-secant theorem

PA = 8

PB = 4

BC = ?

Substitute

8² = (BC + 4) × 4

64 = 4BC + 16

64 - 16 = 4BC + 16 - 16

48 = 4BC

48/4 = 4BC/4

12 = BC

BC = 12

Answer:

Area of sector = 4.88 m ²

Step-by-step explanation:

Given:

Angle = 140°

Radius = 2 m

Find:

Area of sector

Computation:

Area of sector = [θ/360][πr²]

Area of sector = [140/360][(22/7)(2)²]

Area of sector = 4.88 m ²

Answer:

Its the first one 2^(x-1) -3

Answer:

a)2.7

b)1.65289256

c)3.12

Answer:

20

Step-by-step explanation:

20 is the least common denominator

2/5, 1/2, and 3/4 fractions have a Least Common Denominator of 20.

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

We have to determine the Least Common Denominator of fractions  2/5, 1/2, and 3/4

We need to calculate the factors of the denominators 5, 2, and 4.

⇒ 5 = 5 × 1

⇒ 2 = 2 × 1

⇒ 4 = 2 ×2 × 1

The LCD would be:

⇒ 5 × 2 ×2 × 1 = 20

Hence, 2/5, 1/2, and 3/4 fractions have a Least Common Denominator of 20.

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The tree is 20 feet tall if the 6-foot tall man has a 9-foot shadow at the same time a tree standing next to him as a 30-foot shadow.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

From the right angle triangle,

The ratio of the man height and his shadow is equal to the tree height(h) and its shadow.

6/9 = h/30

h = 20 feet

Thus, the tree is 20 feet tall if the 6-foot tall man has a 9-foot shadow at the same time a tree standing next to him as a 30-foot shadow.

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Answer: 6 in

Step-by-step explanation:

[tex]a^{2}= c^{2} - b^{2}[/tex]

[tex]a=\sqrt{10^{2}-8^{2} }[/tex]

a=6 in

Step-by-step explanation:

so first you have 8 and 6 and a triangle the third side should be a equal number it should me 14 combined but I dont know if im wrong but the other side should me 7×2 which is 14

Answer:

-9

Step-by-step explanation:

dude just use some math app tbh, youre doing algebra it should give you answers faster than brainly can

Answer:

it could be 49cm

Step-by-step explanation:

you didnt really say which is the base and the side so i dont know if this is right

Step-by-step explanation:

p=2s+b

p=2×9+20

p=38cm

Answer: 53.8

Step-by-step explanation:

Answer: 22.5

Step-by-step explanation:

math

Answer:

A= 60, B= 33%, C= 66%

Step-by-step explanation:

A=60 because 1/3 of 180 is 60

B=33% because thats the closest you can get to 1/3 of 100 unless you wanna add .3 to it

C= Same explanation for B

Answer:

5.

Step-by-step explanation: Because when you flip a coin it has 2 sides, a 50/50 to get heads or tails. But theoretically it could be infinitely any combination. Though 5 tails would be the best choice.

Answer:

C. 48

Step-by-step explanation:

since it's the perimeter is 112 and the width is 8 ft you add 8 + 8 which is 16 and then you subtract it by 112 which gives you 96 then you divide 96 / 2 which gives you the answer of 48

Answer:

35

Step-by-step explanation:

Answer:

The answer is 35

Hope this helps :>

Answer:

See the answers below

Step-by-step explanation:

Given data

Discount=12%

VAT= 13%

Amount paid= Rs. 3,57,984

The amount of VAT

=13/100*3,57,984

=0.13*357984

= Rs. 46537.92

The amount of discount

=12/100*3,57,984

=0.12*357984

= Rs. 42958.08

Answer:

State City ZIP Code(s)

Arizona (AZ) Phoenix 85001 thru 85055

Arkansas (AR) Little Rock 72201 thru 72217

California (CA) Sacramento Los Angeles Beverly Hills 94203 thru 94209 90001 thru 90089 90209 thru 90213

Colorado (CO) Denver 80201 thru 80239

Step-by-step explanation:

Hope This Helps!!!!!!!

Answer:

The value of c is [tex]c = \frac{1}{3}[/tex]

Step-by-step explanation:

Point of inflection:

A function f(x) has a point of inflection at the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

Has a point of inflection at (1, f(1))

This means that [tex]f^{\prime}(1) = 0[/tex]

f(x) = cx^2 + 1/x^2

This means that, applying the derivative of a power rule:

[tex]f^{\prime}(x) = 2cx - \frac{2}{x^3}[/tex]

Since [tex]f^{\prime}(1) = 0[/tex]

[tex]2c - \frac{2}{3} = 0[/tex]

[tex]2c = \frac{2}{3}[/tex]

[tex]c = \frac{2}{2*3} = \frac{1}{3}[/tex]

The value of c is [tex]c = \frac{1}{3}[/tex]