The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between x(height) and y(arm span) is shown in the scatterplot below. The equation of the line of best fit modeling this relationship is given.
Y=4.5x + 0.977x

Mike is 175cm tall and George is 170cm tall.
Using the model, how many centimeters longer would we expect Mike's arm span to be than George's?

____Cm

Answer:

[tex]A = 234mm^{2}[/tex]

Step-by-step explanation:

A rectangular prism (or orthohedron) is a polyhedron whose surface is formed by two equal and parallel rectangles called bases and by four lateral faces that are also parallel rectangles and equal two to two.

The orthohedron is a straight prism and also a particular case of irregular quadrangular prism.

In a rectangular prism you can differentiate the following elements:

Bases: are two parallel and equal rectangles.

Faces: the four rectangles of the lateral faces and the two bases. Therefore, it has six faces.

Height : distance between the two bases of the prism. The height h coincides with any of the edges of the lateral faces.

Vertices: the eight points where three faces of the prism converge.

Edges: segments where two faces of the prism are found.

The surface area of ​​the rectangular prism (or orthohedron) is calculated by the following formula:

[tex]A=2(wh+lw+lh)[/tex] where w is width, l is length, and h is height.

Solving with l = 15mm, w = 3mm, and h = 4mm

[tex]A=2[(3mm)(4mm)+(15mm)(3mm)+(15mm)(4mm)][/tex]

[tex]A=2(12mm^{2}+45mm^{2} +60mm^{2}) \\A=2(117mm^{2})\\A= 234mm^{2}[/tex]

Answer:

Step-by-step explanation:

Look at the net of the prism in the picture.

We have

two rectangles 4mm × 15mm

two rectangles 3mm × 15mm

two rectangles 3mm × 4mm

The formula of an area of a rectangle: A = lw

l - length

w - width

l × w

Calculate the areas:

A₁ = 4mm · 15mm = 60mm²

A₂ = 3mm · 15mm = 45mm²

A₃ = 3mm · 4mm = 12mm²

The surface area:

S.A. = 2A₁ + 2A₂ + 2A₃

Substitute:

S.A. = 2 · 60 + 2 · 45 + 2 · 12 = 120 + 90 + 24 = 234mm²

ANSWER

4 units.

EXPLANATION

Triangle RQT is a right isosceles triangle.

This implies that:

RQ=RT=x.

Triangle RTS is also a right angle triangle with hypotenuse, RT=x.

Also, the side with length , 2√3 units is opposite to the 60° angle.

We use the sine ratio, to obtain:

[tex] \sin(60 \degree) = \frac{opposite}{hypotenuse} [/tex]

[tex] \sin(60 \degree) = \frac{2 \sqrt{3} }{x} [/tex]

Solve for x to obtain;

[tex]x= \frac{2 \sqrt{3} }{ \sin(60 \degree)} [/tex]

This gives us:

[tex]x= \frac{2 \sqrt{3} }{ \frac{ \sqrt{3} }{2} } = 4[/tex]

Therefore the value of x is 4 units.

The answer is D because all of the dots are in the same place except for 2.

Answer:

Step-by-step explanation:

d

For this case, we have: If we have a root polynomial -6, 1, and 4. Then, the previous step was:

[tex](x + 6) (x-1) (x-4) = 0[/tex]

To build the polynomial we must multiply:

[tex](x + 6) (x-1) (x-4) =\\(x ^ 2-x + 6x-6) (x-4) =\\x ^ 3-4x ^ 2-x ^ 2 + 4x + 6x ^ 2-24x-6x + 24 =[/tex]

Adding similar terms:

[tex]x ^ 3 + x ^ 2-26x + 24[/tex]

Answer:

[tex]x ^ 3 + x ^ 2-26x + 24[/tex]

Its C, you have to add all the numbers up and divide by how many numbers there are

Answer:

y = (x + 9)² - 83

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

y = x² + 18x - 2

Obtain vertex form by using the method of completing the square

add/subtract (half the coefficient of the x- term )²

y = x² + 2(9)x + 81 - 81 - 2

  = (x + 9)² - 83

The ANSWER IS Y=(x+9)^2-83

Answer:

Step-by-step explanation:

A.

First spin         Second Spin

____ Red   |---------Red

|                  |---------Green

|                  |--------Yellow

|

____Blue   |---------Red

                  |----------Green

                  |---------Yellow

B.    Probability of getting a red on the first spin = 1 /2.

Answer:

8

Step-by-step explanation:

The required value in the fill-in-the-blank is 8, which is completely factored into the product of two binomials: (x-7) and (x-8).

To fill in the blank in the expression x²-15x+56=(x-7)(x-____), we need to find the missing factor that, when multiplied by (x-7), gives us the original quadratic expression.

Factor the quadratic expression x²-15x+56 by finding two numbers that multiply to 56 and add up to -15, which are -7 and -8.

Therefore, we can rewrite the quadratic expression as:

x² - 15x + 56 = (x - 7)(x - 8)

This means that the quadratic expression can be completely factored into the product of two binomials: (x-7) and (x-8).

Thus, the required value in the fill-in-the-blank is 8.

Learn more about quadratic function here:

brainly.com/question/14083225

#SPJ2

Answer:

Step-by-step explanation:

First step:

Calculate, what fraction of 75 is 33:

[tex]\dfrac{33}{75}=\dfrac{33:3}{75:3}=\dfrac{11}{25}[/tex]

Second step:

Convert to the percent:

[tex]\dfrac{11}{25}\cdot100\%=(11)(4\%)=44\%[/tex]

33 is 44% of 75.

To determine what percent of 75 is 33, you can use the formula: (part/total) × 100. In this case, the part is 33 and the total is 75.

Thus, 44% of 75 is 33.

Subtract 0.2 by both sides and the your answer is f = -3.2

Answer:

the answer is f=-3.2

Step-by-step explanation:

because with solving linear equations you have to do the opposite of what your doing do like  f+0.2=−3 since your adding you want to subtract instead you want to subtract on both sides so we know 0.2-0.2= 0 so 0.2- -3= -3.2 so that gives us our answer -3.2

Answer:

y=1/3x+1

Step-by-step explanation:

y=mx+b

y=1/3x+b

2=1/3(3)+b

2=1+b

1=b

y=1/3x+1

Answer:

36 cubic cm.

Step-by-step explanation:

To find volume, you multiply width by length by height, so 3x4x3, which is 36.

20+h=42 is the answer

Answer: Melissa made 22 striped hats

(Hope this helps) :D

Step-by-step explanation: You get this answer by subtracting 20 from 42 to get 22

Answer:

the answer would be A.  a measure of center, such as the median

Step-by-step explanation:

A measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Some examples of a measure of center are median and mode. Some examples of a measure of variation are interquartile range and mean absolute deviation.

The salon manager wants one number to summarize all the values of the data set.

Answer:

The answer would have to be VELOCITY which is distance / time.

That answer is NOT on your list.

Step-by-step explanation:

Answer:

frequency

Step-by-step explanation:

To find the probability that A occurs given B occurs, multiply the Probability of A by the probability of B.

3/4 x 5/8 = 15/32

Answer:

40%

Step-by-step explanation:

you would take the number of magicians and divide that number by the total number of performers like this:

4 / 10 = 0.4

which equals 40%

so the probability of selecting a performer and them being a magician would be 40% exactly

i hope this helps :)

The probability of randomly selecting a magician from a group of 10 performers with 4 magicians is [tex]\frac{2}{5}[/tex].

The probability that a randomly selected performer from a circus with 10 performers and 4 magicians will be a magician is calculated by dividing the number of magicians by the total number of performers. Therefore, the probability P(magician) is:

P(magician) = number of magicians / total number of performers
P(magician) = [tex]\frac{4}{10}[/tex]
P(magician) = [tex]\frac{2}{5}[/tex]

Answer:

The function is  [tex]f(x)=2x-1[/tex]

Step-by-step explanation:

If a function has a zero of [tex]\frac{1}{2}[/tex].

The we can write  [tex]x=\frac{1}{2}[/tex].

We need to work backwards to obtain the function:

We multiply through by 2 to get:

[tex]2x=1[/tex].

This implies that:

[tex]2x-1=0[/tex]

Hence a function with such zero is  [tex]f(x)=2x-1[/tex]

Answer:

The function is [tex]f(x)=4x-2[/tex]

Step-by-step explanation:

That a function has a zero at a certain number x means that [tex]f(x)=0[/tex]

Let's see an example,

If we have [tex]f(x)=x+2[/tex] (this is what we call function)

and we choose any value for the x,

x = 3

Now we replace it in our function

[tex]f(3)=3+2[/tex]

[tex]f(3)=5[/tex] (this is the image of 3)

Now if we say that x = -2, and replace it in our function

[tex]f(-2)=(-2)+2[/tex]

[tex]f(-2)=0[/tex] , this means that our function has a zero at x = -2

We can find the zeros of our function equaling it to zero and clearing the x, let's see

[tex]x+2=0[/tex]

[tex]x=-2[/tex]  this means that our function has a zero at x = -2

To find a function that has a zero at  [tex] \frac{1}{2}[/tex] , let's think that the result must be [tex]f(x)=0[/tex]

If we have 4 and multiply it by 1/2.

[tex]4)(\frac{1}{2})=2[/tex], now we subtract 2 from this result

[tex]-2 = 0[/tex] , the complete process would be

[tex]4)(\frac{1}{2})-2=0[/tex], we said that [tex] \frac{1}{2}[/tex], then

[tex]4x-2[/tex], now we write it as a function

[tex]f(x)=4(x)-2[/tex]  we know that by replacing the x by 1/2 the result will be zero, which means that [tex] \frac{1}{2}[/tex] is zero of this function

Answer:

solution  (-∞,4.25)

Step-by-step explanation:

Given inequality is [tex]4m +16.5 < 33.5[/tex].

Now we need to solve the given inequality. Describe the solution set using the set-builder or interval notation. Then, graph the solution set on a number line.

[tex]4m +16.5 < 33.5[/tex]

[tex]4m < 33.5 - 16.5[/tex]

[tex]4m < 17[/tex]

[tex]m < \frac{17}{4}[/tex]

[tex]m < 4.25[/tex]

Hence solution set using interval notation is given by (-∞,4.25).

Graph will be an arrow pointing to the left of 4.25

Answer:

m < 4.25; (-∞, 4.25).

Step-by-step explanation:

Part 1. Solve the inequality

4m + 16.5 < 33.5

         4m  < 17         Subtracted 16.5 from each side

            m < 4.25     Divided each side by 4

Part 2. Interval notation

The solution set consists of all numbers less than 4.25. We use parentheses to denote numbers that are not included in the interval.

4.25 is not included, because m < 4.25.

-∞ is not included, because we can never reach it.

In interval notation, the solution set is (-∞, 4.25).

Step 3. Number line

The solution set consists of all numbers less than 4.25. We use an open circle to show that  4.25 is not included in the set.

Answer:

5 1/3

Step-by-step explanation:

16 - (2z-4)/3

Let z = 18

16 - (2*18-4)/3

Multiply inside the parentheses first

16 - (36-4)/3

Subtract inside the parentheses

16 - (32/3)

Divide inside the parentheses and change to a mixed number

16 - 10 2/3

Borrow 1 from 16 in the form of 3/3

15 3/3 - 10 2/3

5 1/3

Answer:

Your answer would be 5 1/3.

Step-by-step explanation:

16- (2(18)-4)/3

16- (36-4)/3

16/1 - 32-3

48/3 - 32/3 = 16/3

16/3 converted to a mix number is 5 1/3

Hope I helped :)

The area of the paper is Length x width = 8 x 11 = 88 square inches.

Each game piece was 1 inch in diameter.,so you could cut it out of a 1 inch square.

So each square inch of the paper could be a game piece.

You could make 88 game pieces.

You can make 88 pieces

Acute triangle is the answer

Answer:

The answer is a. right.

Step-by-step explanation:

GIVEN:

hypo=25

opposite and adjacent=15 and 20.

FORMULA:

hypotenuse^2 =opposite side^2 + adjacent side^2

25^2=15^2+20^2

625=225+400

400+225=625

(Got this from yahoo answers, everybody said right.)

Answer:

The square root of 25 is 5 because whenever it's a number multiplied by the same number like 4×4, 5×5, 8×8 and so on, you are squaring that number since you are multiplying the same number twice. Hope this helps and I'm sorry if my explanation is not that clear:)

Answer:

x=8

Step-by-step explanation:

The two angles are complementary angles, so they add together to make 90 degrees

x+50 + 4x = 90

Combine like terms

5x+50 = 90

Subtract 50 from each side

5x+50-50= 90-50

5x = 40

Divide by 5

5x/ 5 = 40/5

x = 8

If this helps you please make it brainliest.

14. She has 12 possible choices.

15. $96

16. I don’t know about this one, sorry.

I7. 4/7

18. 1/3

Hope this helps!

ANSWER

[tex]{f}^{ - 1}(x) = ln(x)[/tex]

EXPLANATION

The given function is

[tex]f(x) = {e}^{x} [/tex]

Let

[tex]y={e}^{x} [/tex]

We interchange x and y.

[tex]x={e}^{y} [/tex]

Solve for y.

[tex]y = ln(x) [/tex]

This implies that,

[tex] {f}^{ - 1}(x) = ln(x) [/tex]

The correct answer is C

Answer:

[tex]f^{-1}(x)=ln(x)[/tex]

Step-by-step explanation:

Given function is [tex]f\left(x\right)=e^x[/tex].

Now we need to find it's inverse so follow these steps:

Step 1: replace f(x) with y.

[tex]y=e^x[/tex]

Step 2: Switch x and y.

[tex]x=e^y[/tex]

Step 3: Solve for y.

[tex]x=e^y[/tex]

[tex]ln(x)=ln(e^y)[/tex]

[tex]ln(x)=y[/tex]

[tex]y=ln(x)[/tex]

Step 4: Replace y with [tex]f^{-1}(x)[/tex].

[tex]f^{-1}(x)=ln(x)[/tex]

Hence final answer is [tex]f^{-1}(x)=ln(x)[/tex].

Answer:

x = - 9, x = 4

Step-by-step explanation:

The x- intercepts are the values of x where the graph of the function crosses the x- axis.

To obtain them set f(x) = 0, that is

x² + 5x - 36 = 0

To factor the quadratic.

Consider the factors of the constant term (- 36) which sum to give the coefficient of the x- term (+ 5)

The factors are + 9 and - 4, since

9 × - 4 = - 36 and 9 - 4 = + 5, thus

(x + 9)(x - 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x - 4 = 0 ⇒ x = 4

Answer:

x=(4,0) and x=(9,0)

hope this helps

Answer:

5/12

Step-by-step explanation:

The probability of throwing an even number (2 4 6) out of six numbers on the die (1 2 3 4 5 6) is

3/6

The probability of throwing a number greater than 1 is 5 out of 6.

The probability of both events occurring is 1/2 * 5/6 = 5/12 or just under 1/2

Answer:

-3≤x<4

Step-by-step explanation:

First you divide 3 on all sides of the equation.

So,

Answer:

x= (-3,-2,-1,0,1,2,3)

Step-by-step explanation:

You would divide 3 from both which you would get:

-3< x <4

x can represent any number above because the numbers I listed above is greater than -3 or less than 4.

3*-1=-3

3*0=0 ....... -3 <0 >4

3*1=3

x⁶; multiplying monomials means adding their exponents in this case.