Probability and Statistics
Suppose the x-axis of a density graph represents someone's height in inches. If the area under the density curve from 60 inches to 70 inches is 0.65, what is the probability of someone's height being anywhere from 60 inches to 70 inches?
A. 70%
B. 65%
C. 75%
D. 60%

Answer:

It's 35

Step-by-step explanation:

I took a test that had this question on it and it said this was the right answer.

Different combination to pulls out 4 coins each time from 7coins is equals to 35.

" Combination is defined as the selection of the objects from the given set where arrangement of order does not matter."

Formula used

[tex]nC_{r} = \frac{n!}{(n-r)!r!}[/tex]

According to the question,

Total number of coins 'n' = 7

Number of coins pulls out each time 'r' = 4

Substitute the value in the formula to get different combination,

[tex]7C_{4} = \frac{7!}{(7-4)!4!}[/tex]

      [tex]= \frac{(7)(6)(5)(4!)}{(3!)(4!)} \\\\=\frac{(7)(6)(5)}{(3)(2)(1)}\\\\=(7)(5)\\\\=35[/tex]

Hence, different combination to pulls out 4 coins each time from 7coins is equals to 35.

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Answer:

No teen sent texts fewer than 1630 or more than 1854 texts in a month

Step-by-step explanation:

margin of error gives the difference that may come in the sample results from the actual population results.

Given:

Average teen sends 1742±112 texts per month

here ±112 is margin of error, calculating maximum difference:

1742+112=1854

1743-112=1630

No teen sent texts fewer than 1630 or more than 1854 texts in a month !

Answer:

option C is the correct answer

Step-by-step explanation:

System A:                                                  System B:

-x - 2y = 7    ........(1)                               -x - 2y = 7    .......(3)  

5x - 6y = -3  ........(2)                                  -16y= 32  ........(4)

Solution for system A: ( -3, -2)

For option A

Multiply the first equation by 3

3(- x - 2y) = 3(7)         ⇒     - 3x - 6y = 21 ........... (5)

Add equation 2 and 5

  5x - 6y = -3

- 3x - 6y = 21

  2x -12y = 18   ⇒  2( x - 6y ) = 2( 9 )    ⇒   x - 6y = 9

Option A is not equal to equation in system B so now we check option B.

 For option B

Multiply the first equation by -5

-5(- x - 2y) = -5(7)         ⇒    5x + 10y = -35 ........... (6)

Add equation 2 and 6

  5x - 6y = -3

  5x + 10y = -35

  10x + 4y = -38   ⇒   2( 5x + 2y ) = 2(-19)    ⇒  5x + 2y = -19

Option B is not equal to equation in system B so now we check option C.

For option C

Multiply the first equation by 5            

5(- x - 2y) = 5(7)         ⇒   - 5x - 10y = 35 ........... (7)

Add equation 2 and 7

  5x - 6y = -3

- 5x - 10y = 35

    0 - 16y = 32   ⇒   -16y = 32

Option C is equal to equation in system b so now we check if the solution to system B is same as system A.  

Solution to system B:

First, we find value of y from equation 4:

-16y = 32   ⇒    y = [tex]\frac{32}{-16}[/tex]   ⇒    y = -2

Now, we put value of y in equation 3 to find value of x:

-x - 2y = 7  ⇒  -x - 2(-2) = 7   ⇒  -x + 4 = 7   ⇒  -x = 7 - 4  ⇒  -x = 3

multiply both sides by -1

-1 × (-x) = -1 × (3)       ⇒     x = -3

Solution of system B = (-3, -2)

Solution of system B is the same as system A, so option C is correct.

ANSWER

The number who are not enrolled in either Chorus or Band is 53

EXPLANATION

The given information can be represented on a Venn diagram as shown above.

Let x represent the number of students who are not enrolled in either chorus or band.

Then

[tex]x + 14 + 10 + 23 = 100[/tex]

[tex]x + 43 = 100[/tex]

This implies that

[tex]x = 100 - 43[/tex]

[tex]x = 57[/tex]

The number who are not enrolled in either Chorus or Band is 53

Final answer:

Discrimination, particularly in the labor market as demonstrated by disparities in job callbacks and opportunities based on race, gender, and disability, represents a systemic issue that persists despite legal protections against such practices.

Explanation:

Discrimination is the unfair treatment of individuals or groups based on characteristics such as race, gender, or religion. One of the most common forms of discrimination occurs in the labor market, where individuals may face disparities in job opportunities and wages. An example of this is how studies have shown that individuals with white sounding names receive more callbacks for interviews than African-American names, indicating racial discrimination. Furthermore, women and those disclosing a disability also face significant hurdles in the job market, highlighting gender discrimination and disability discrimination. Despite the existence of laws against discrimination in the United States and global conventions from the United Nations aimed at eliminating all forms of discrimination, these practices unfortunately persist. Institutional discrimination extends beyond individual acts of prejudice to include systemic issues such as white privilege, which confers benefits upon the dominant group often without their conscious acknowledgment.

Answer:

[tex]x= 11.47[/tex]

Step-by-step explanation:

By definition the cosine of an angle is the quotient between the side adjacent to the angle and the hypotenuse.

In other words:

[tex]cos (\alpha) = \frac{adjacent}{hypotenuse}[/tex]

In this triangle the length of the side adjacent to the 55 degree angle is x, and the length of the hypotenuse is 20

So:

[tex]cos(55\°) = \frac{x}{20}[/tex]

Now we solve the equation to find the value of x

[tex]x = 20cos(55\°)[/tex]

Finally

[tex]x= 11.47[/tex]

Answer:

11.47

Step-by-step explanation:

Given

Two angles of 90 and 55 degrees

and a side of length 20

Finding third angle= 180-(90+55)

                              = 35

Finding x:

Using Law of Sines to find length of side x

x/sinX=y/SinY

x/sin35=20/sin90

x=20sin35

x=11.47 !

Answer:

q^12

Step-by-step explanation:

To raise a power to a power you multiply the powers together. That would be 6*2=12.

You didn’t give the question

For distributions C and D, the median represents the centre most accurately.

Given that the median is a robust statistic—that is, skewed data and outliers have little effect on it—it is the best estimate of centre for skewed or outlier-filled distributions.

Since the mean is not robust, it serves as a useful proxy for the centre in symmetric distributions.

Answer B has a uniform distribution, whereas answer A has a distribution that is nearly symmetric.

Given that the right tail is longer than the left, solution D appears to have a right-skewed distribution, while answer C has a left-skewed distribution.

Thus, for options C and D, the median would be the most appropriate way to measure the centre.

The question probable maybe:

For which distributions is the median the best measure of center? Select each correct answer:

(Given in the attachment)

Mean is the average so just add up all the numbers in your data set and divide by the total for numbers that there are.

Ex. (5, 7, 8, 9)

5+7+8+9=29

29/4=7.25

7.25 is the Mean.

Median is the number that is directly in the middle so just count inwards from each side after you ordered your data set. If you get two numbers just add them both and divide by two.

Answer:

8*8*8 if thats what you mean. Same outcome as 8^3

Step-by-step explanation:

Final answer:

To simplify 8³ on a scientific calculator, input 8, press the exponentiation key, enter 3, and press '=' to get the result of 512, or 5.12 x 10² in scientific notation.

Explanation:

To simplify 8² using a scientific calculator, you would typically follow these steps:

Ensure that the calculator is turned on and in the correct computational mode.

Enter the number 8.

Press the exponentiation key, often labeled as '^', 'exp', or represented by a caret symbol.

Enter the number 3 to represent the power to which you are raising 8.

Press the '=' or 'Enter' key to execute the calculation.

The calculator will give you the answer, which is 512. When simplifying further, if we were to represent this number in scientific notation, it would be written as 5.12 times 10², as it has three significant figures.

The answer is 3/28

-1/4 x -3/7

-1 x -3 = 3

4 x 7 = 28

3/28

Answer: 3/28

Step-by-step explanation:

Answer:

x = - 6.4 or

x = - 6 2/5

Step-by-step explanation:

3 = 5*x + 7*5              Remove the brackets

3 = 5x + 35                 Subtract 35 from both sides

3 - 35 = 5x + 35-35    Combine

- 32 = 5x                     Divide by 5

-32/5 =5x/5

-6.4 = x

or

- 6 2/5

Answer:

11

Step-by-step explanation:

3/7 x 14/1 = 42/7 = 6

5/8 x 8/1 = 40/ 8 =5

6+5= 11

Hope this helps

Sorry if it's wrong

If it's right please mark brainliest :D

y= x^2+20x+21

( x+3)(x+7)

or (x+7)(x+3)

Doesn't matter which one comes first

(x+3)(x+7) Answer

(x+7)(x+3) Answer

Answer:

( x + 7 ) ( x + 3 )

Solutions are -7 , -3

Step-by-step explanation:

x² + 10 x + 21

x ( x + 3 ) + 7 ( x + 3 ) = 0

( x + 7 ) ( x + 3 )

Factors = 3 , 7

Sum = 21

Product = 10

[tex] \frac{5}{60} = \frac{8}{x} \\ 5x = 60 \times 8 \\ x = \frac{60 \times 8}{5} \\ x = 12 \times 8 \\ x = 96[/tex]

So x=96.

Hope it helps...

Regards;

Leukonov/Olegion.

[tex]

\frac{5}{60}=\frac{8}{x} \\

5x=8\cdot60 \\

5x=480 \\

\boxed{x=96}

[/tex]

Hope this helps.

r3t40

Answer:

6

Step-by-step explanation:

To solve for e, it must be alone on one side of the equation

Your equation is:

e/2 = 3

To get rid of the divided by 2, you multiply both sides by 2 since multiplication is the opposite of divison.

So:

e/2 = 3

[Multiply both sides by 2]

e = 6

So, e = 6

I hope this helps! :)

Answer:

x =  2.5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

here m = - 2 and c = 5, so

y = - 2x + 5 ← equation of line

To find the x- intercept let y = 0, that is

- 2x + 5 = 0 ( subtract 5 from both sides )

- 2x = - 5 ( divide both sides by - 2 )

x =  2.5 ← x- intercept ⇒ (2.5, 0 )

Hello There!

Number 2

3.50x=40

Then, divide both of the numbers by 3.50.

You end up with X=11.42 is greater or equal to 12 movies

Number 3

5h+3

5 ‘5’ + 3 = 30

Number 4,5,6 are attached in images below.

You just have to split the figures in different parts...

- First Picture:

- the total length is 130, so the upper and bottom rectangles have 50ft. as showed, and the middle one is 130-(50x2) = 30

- The second step is get the 2 holes área to subtract from the “total rectangle without holes area” (30x40=1200)x2 and then (20,150-1400=18,750) so, the total area from the rectangle with the holes is 18,750!

Answer:

Volume=2.2*10^10  km^3

Step-by-step explanation:

Given

Diameter of moon=d=3476 km

The formula for the volume of sphere is:

V=4/3 πr^3

As it can be clearly seen that the formula uses radius, and we are given diameter. So we have to find the radius first

So,

radius=r=d/2

=3476/2

=1738 km

Now putting the value of r and pi in the formula:

V=4/3*3.14*(1738)^3

=12.56/3* 5249879272

= 21979494552.106

Rounded off to two significant digits:

Volume=2.2*10^10  km^3

Answer:

[tex]V=2.2\ x\ 10^{10} km^3[/tex]

Step-by-step explanation:

The formula to calculate the volume of a sphere is:

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where r is the radius of the sphere.

In this case we do not know the radius of the sphere, but we know the diameter.

By definition the diameter of a sphere is equal to twice the radius. This is:

[tex]d = 2r[/tex]

[tex]r = \frac{d}{2}[/tex]

In this case d= 3,476 km

So

[tex]r = \frac{3,476}{2}[/tex]

[tex]r = 1738\ km[/tex]

Finally

[tex]V=\frac{4}{3}\pi (1738)^3[/tex]

[tex]V=2.20\ x\ 10^{10} km^3[/tex]

Answer:

The answer is 8.

Step-by-step explanation:

Go from left to right.

2x2x2

Take the first two numbers: 2 x 2; this equals 4.

Take that number and multiply by the next number (2): 4 x 2 = 8

Hope this helps! :)

The value of 2 x 2 x 2 using the multiplication operation gives the result 8.

The expression 2 x 2 x 2 represents the multiplication of three 2's together.

To simplify the expression, perform the multiplication operation:

= 2 x 2 x 2

= 4 x 2

= 8

Therefore, 2 x 2 x 2 is equal to 8.

In other words, multiplying three 2's together results in the value of 8.

This can be visualized as multiplying 2 by 2 to get 4 and then multiplying that result by 2 again to obtain 8.

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Answer:

445.2 square cm

Step-by-step explanation:

The surface area consists of  area of two bases and area of three leteral faces. Each lateral face is a rectangle with length of 23 cm and width of 6 cm.

The area of rectangle is

[tex]A_{rectangle}=\text{length}\times\text{width}[/tex]

So,

[tex]A_{rectangle}=23\times 6=138\ cm^2[/tex]

The area of base is given as [tex]15.6\ cm^2[/tex]

Thus, the surface area is

[tex]SA=2A_{base}+3A_{lateral\ face}\\ \\SA=2\cdot 15.6+3\cdot 138=445.2\ cm^2[/tex]

Answer:

Option 1: 0.32

Step-by-step explanation:

Let

P(A) be the experimental probability of getting two

And

P(B) be the experimental probability of getting three

The dice is rolled 360 times.

So the sample space is n(S) = 360

P(A) = n(A)/n(S)

= 54/360

= 0.15

And

P(B) = n(B)/n(S)

= 62/360

= 0.172

As both the events A and B are mutually exclusive,

P(A or B)  = P(A) + P(B)

= 0.15 + 0.172

=0.322

Rounding of to one decimal gives us:

0.32

So the probability of rolling a two or three is 0.32 ..

ANSWER

[tex]{i}^{20} + 1 =2[/tex]

EXPLANATION

The given expression is;

[tex] {i}^{20} + 1[/tex]

Recall that, in complex numbers

[tex] {i}^{2} = - 1[/tex]

We use this identity to simplify the given expression:

[tex]{i}^{20} + 1 =( {i}^{2})^{10} + 1[/tex]

This implies that:

[tex]{i}^{20} + 1 =( - 1)^{10} + 1[/tex]

[tex]{i}^{20} + 1 =1+ 1[/tex]

[tex]{i}^{20} + 1 =2[/tex]

Answer:

B) y = 5x

Step-by-step explanation:

We need to find the slope

m = (y2-y1) /(x2-x1)

We have 2 points (0,0) and (6,30)

m = (30-0)/(6-0)

  = 30/6

  =5

The slope is5

y = mx+b

The y intercept is 0

y = 5x+0

y = 5x

Answer:

B:)

Step-by-step explanation:

ANSWER

|SU|=3ft

EXPLANATION

Triangle TSU is an isosceles right triangle.

Because one of the angles in the right triangle is 45°.

This means that the third angle is also 45°.

This implies that that |ST|=|SU|

The reason is that isosceles triangle has the base angles equal and the arms on these angles are equal.

[tex] \frac{9}{8} [/tex]

Step-by-step explanation:

you would want to get rid of the -1/2 so you have to add one half to the other side of the equation and since 1/2 equals 4/8 the equation would be

4/8 plus 5/8 which equals 9/8

What is AD? There is no picture...

Final answer:

The length of AD is calculated using the given formula, which is a proportion involving the length of AC and the variables a, c, and d. One must plug in the values for these variables and solve the equation to find the length of AD.

Explanation:

To find the length of AD, we use the given formula which indicates a proportional relationship between the lengths on a line segment. The formula involves variables that define the lengths of specific segments of the line, as well as the ratios between them. In this case, the formula is (Length AD) = (Length AC) × (a-d)/(a-c). Here's a step-by-step explanation:

This formula can be used to calculate the length of a line segment extending beyond the segment AC or that lies between points A and C, depending on the values of the variables involved.

Answer:

• mathematical: y ≤ 52

• reasonable: 0 ≤ y ≤ 52

Step-by-step explanation:

The reasonable range is the set of heights between the maximum height and the ground (y=0).

___

The maximum height is about 44.51 meters, so values between that and 52 meters are not in the reasonable range. A maximum height of 52 meters requires an initial velocity of about 15.4 m/s.

Answer:

Step-by-step explanation:

C