In Hillcrest School, 36% of middle school students are in Grade 6, 31% are in grade 7, and 33% are in grade 8.

If a middle school student is selected randomly, what is the probability that the student is either in grade 6 or in grade 7?

Answer:

24x^4- 12x^2  or 12x^2 (2x^2-1)

Step-by-step explanation:

We are given the length and width of the rectangle:

Length=l=4x^2

and

Width=w=6x^2-3

The formula for the area of rectangle is:

Area=length*width

Area=l*w

Putting the values of l and w into the formula:

area=(4x^2 )(6x^2-3)

=24x^(2+2)-12x^2

=24x^4- 12x^2

It can also be written as: taking 12x^2 as common:

=12x^2 (2x^2-1)

Given the line of best fit equation Y = 4.5X + 0.977, we would expect Mike's arm span to be approximately 23 cm longer than George's, assuming their respective heights are 175cm and 170cm.

The given equation appears to have a typo, as it seems to contain two x terms, which is unusual for a line of best fit in this context. I believe it should be Y = aX + b, where 'a' represents the slope and 'b' the y-intercept.

Assuming the correct equation is Y = 4.5X + 0.977, we can calculate Mike's and George's arm spans by plugging in their respective heights (in cm) for X:

So, we would expect Mike's arm span to be longer than George's by about:

788.977 cm - 765.977 cm = 23 cm

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Answer:

A) C = 29*d + 0.15*m

B) C = $88.75

Step-by-step explanation:

Givens

Let the cost of the rental = C

Let the most of the daily rental = d

Let the cost of the mileage driven = m

Equation

Cost = 29*d + 0.15*m

C = 29*d + 0.15m

Part B

d = 2

m = 205

C = ?

C = 29*2 + 205*0.15

C = 58 + 30.75

C = $88.75

Answer:

B. 25

Step-by-step explanation:

10+6=16

if it is proportional, then it would be 25 to get 15.

Answer:

25

Step-by-step explanation:

y = kx

10 = 6k

5

3

= k

y =

5

3

(15)

y = 25

Answer:

Gretchen: 18

Judith: 23

Trina: 28

Step-by-step explanation:

Do reverse math. to find the average you would normally add up each age and divide your answer by the amount of ages provided. but in this case we don't have enough information so you do it opposite.

23x3=69.

Trina is clearly the oldest and Gretchen is the youngest, leaving Judith in the middle.

Gretchen: 18

Judith: 23

Trina: 28

it takes some experimenting with numbers but this is correct because all three numbers add up to 69 and they are each 5 years apart.

                                                            :)

Answer:

4 quarters and 20 nickels

Step-by-step explanation:

4 quarters= 1.00

4x5=20 nickels =1

1+1=2.00

Margie has 4 quarters and 20 nickels, which amounts to $2.00. The solution was found by setting up and solving a system of equations.

The question involves solving a system of equations to find out how many nickels and quarters Margie has if she has 5 times as many nickels as quarters and the total value is $2.00. Let's define two variables: n for the number of nickels and q for the number of quarters. Now, we have two equations based on the information provided:

Substitute the first equation into the second: 0.05(5q) + 0.25q = 2.00, which simplifies to 0.25q + 0.25q = 2.00, meaning that 0.50q = 2.00. Divide both sides by 0.50 to find that q = 4. Since q = 4, we substitute it back into the first equation to find that 5n = q gives us n = 4/5, which results in n = 20. Therefore, Margie has 4 quarters and 20 nickels.

ANSWER

a=1

b=-12

EXPLANATION

The function has a hole at

x=3

The function also have a vertical asymptote at

x=-4.

This implies that, the denominator of the function is

[tex](x - 3)(x + 4) [/tex]

[tex] {x}^{2} + 4x - 3x - 12[/tex]

[tex]{x}^{2} + x - 12[/tex]

Comparing this to the function in the denominator,

[tex] {x}^{2} + ax + b[/tex]

we have

a=1 and b=-12

Answer:

Negative infinity,12

Hope this helps you out!

Yes is going to be negative

Answer:

5

Step-by-step explanation:

Put the numbers in order then find the middle number. 334677

Here there are two middle numbers, 4, and 6. Add 4 and 6 together, 10 then divide by 2, 5. So the median is 5! Hope this was helpful have a Great day!!!

12.50 is what he got paid each hour

Answer:

$9.75 per hour

Step-by-step explanation:

243.75/25= 9.75

Answer:

Week 1:  15

Week 2: 21

Step-by-step explanation:

5 x 3 = 15

7 x 3= 21

hope it helps you!!!!!!!!!!!!!!

Start with

[tex]8x+2(x-7)=7x+3x-14[/tex]

Apply the distributive property to expand the left hand side:

[tex]8x+2x-14=7x+3x-14[/tex]

Sum like terms:

[tex]10x-14=10x-14[/tex]

Apply the additive property of equality to add 14 to both sides:

[tex]10x=10x[/tex]

Apply the additive property of equality to subtract 10x to both sides:

[tex]0=0[/tex]

This means that the equation was actually an identity, i.e. the left and right hand sides were actually the same expression.

Since they are the same expression, it doesn't matter which values you plug into x, it will always be a solution of this equation.

Solution: infinite. All numbers are solutions of this equation.

Property used: Listed while solving the equation.

Answer:    6x-4

Step-by-step explanation:  The number 6 is multiplied by another variable so it would be written as 6x and then 4 is less than whatever 6x is so it would be 6x-4.

Answer:

The volume of each cube  = (side)^3  = (1/3)^3  = 1/27 cubic units

The number of cubes  that will fill the prism  =

Vol of prism            4

__________  =    _____  =    4 * 27   =   108 cubes

Vol of cube            (1/27)

Step-by-step explanation:

Approximately 108 cubes, each with side lengths of 1/3 unit, can fit into a rectangular prism that has a volume of 4 cubic units.

The subject of this question covers volume and dimension within 3D Geometry, particularly recognizing cubic units as a measure of volume. Given a rectangular prism with a volume of 4 cubic units, which is filled with cubes, each with side lengths of 1/3 unit, the idea is to understand how many smaller cubes would fit into the larger prism.

When calculating, we first need to figure out the volume of one small cube: (1/3)^3 = 1/27 cubic units. Then, you would divide the total volume of the rectangular prism by the volume of one of the small cubes: 4 divided by 1/27. This gives approximately 108, meaning around 108 cubes with a side length of 1/3 can fit into a rectangular prism with a volume of 4 cubic units.

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Hello - let's do this step by step. Show your work.

You're asking: 9(8−x)=3x.

Now, simplify both sides of the equation.

9(8−x)=3x

(9)(8)+(9)(−x)=3x (To do that, distribute)

72+−9x=3x

−9x+72=3x

Now,  subtract 3x from both sides.

−9x+72−3x=3x−3x

Simplify,

−12x+72=0

After, subtract 72 from both sides.

−12x+72−72=0−72

−12x=−72

Last thing, divide both sides by -12.

-12x/12 = -72/-12

Divide.

Therefore, you have x = 6 as your final answer.

Hello there!

9(8-x)=3x

Use the Distributive Property to distribute 9:

72-9x=3x

Move all the variables to the left side. Be sure to use the opposite operation!

-9x-3x=-72

-12x=-72

Divide both sides by 12 in order to isolate x:

         x=6

Hope this helps you!

~Just a joyful teen

[tex]SilentNature[/tex]

Answer:

4 5/6

Step-by-step explanation:

m = 9/2

1 + ( - 2/3) - (- m)

= 1 + (-2/3) - ( - 9/2)

= 1 - 2/3 + 9/2

= 1/3 + 9/2

= 29/6

= 4 5/6

Answer:

4 5/6

Step-by-step explanation:

A is the most common

are they supposed to look like 1x10^-20 lb?? that would make it easier for you to determine the answer

i hope this helps

Answer:

There is 1 way to vote for 0 people. There are 8 ways to vote for 1 person. There are 8⋅7/ 2 ways to vote for 2 people. There are 8⋅7⋅6 /2⋅3 ways to vote for 3 people. There are 8⋅7⋅6⋅5/ 2⋅3⋅4 ways to vote for 4 people. This is all because you can choose people but there are ways you can order the people.  

Does this help

Answer:

c.

Step-by-step explanation:

The answer to your question is C

Answer:

[tex]45\ games[/tex]

Step-by-step explanation:

we know that

If the probability of winning a game is 75%

that means-----> of every 100 games wins 75

Using proportion

[tex]\frac{100}{75}=\frac{60}{x} \\ \\ x=75*60/100\\ \\x=45\ games[/tex]

Answer:

[tex]4x^{3} y^{2} (\sqrt[3]{4 x y})[/tex]

Step-by-step explanation:

Another complex expression, let's simplify it step by step...

We'll start by re-writing 256 as 4^4

[tex]\sqrt[3]{256 x^{10} y^{7} } = \sqrt[3]{4^{4} x^{10} y^{7} }[/tex]

Then we'll extract the 4 from the cubic root.  We will then subtract 3 from the exponent (4) to get to a simple 4 inside, and a 4 outside.

[tex]\sqrt[3]{4^{4} x^{10} y^{7} } = 4 \sqrt[3]{4 x^{10} y^{7} }[/tex]

Now, we have x^10, so if we divide the exponent by the root factor, we get 10/3 = 3 1/3, which means we will extract x^9 that will become x^3 outside and x will remain inside.

[tex]4 \sqrt[3]{4 x^{10} y^{7} } = 4x^{3} \sqrt[3]{4 x y^{7} }[/tex]

For the y's we have y^7 inside the cubic root, that means the true exponent is y^(7/3)... so we can extract y^2 and 1 y will remain inside.

[tex]4x^{3} \sqrt[3]{4 x y^{7} } = 4x^{3} y^{2} \sqrt[3]{4 x y}[/tex]

The answer is then:

[tex]4x^{3} y^{2} \sqrt[3]{4 x y} = 4x^{3} y^{2} (\sqrt[3]{4 x y})[/tex]

Answer:

Step-by-step explanation:

Lateral Area:

We have four congruent triangles with base b = 16cm and height h = 12cm.

The formula of an area of a traingle:

[tex]A_\triangle=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_\triangle=\dfrac{(16)(12)}{2}=(8)(12)=96\ cm^2[/tex]

[tex]L.A.=4A_\triangle=4(96)=384\ cm^2[/tex]

Surface Area:

[tex]S.A.=B+L.A.[/tex]

In the base we have the square with side s = 16cm. The formula of an area of a square:

[tex]A_\square=s^2[/tex]

Substitute:

[tex]B=16^2=256\ cm^2[/tex]

[tex]S.A.=256\ cm^2+384\ cm^2=640\ cm^2[/tex]

Answer:

80 pages

Step-by-step explanation:

First, work out how many minutes are in two hours.

2 hours = 120 minutes.

Multiply 2/3 by 120

2/3 × 120 = 240/3

Simplify the the fraction

240/3 = 80/1 = 80.

Answer:

Step-by-step explanation:

page read in 1 minute =2/3 40 pgs

page read in 2 hours=(1 hrs = 60 min) 2hrs =120 min

2/3 *120 = 80 pgs

Answer:

[tex]x=38.56[/tex]

Step-by-step explanation:

First, we'll solve for the missing angle.

The interior angles of a triangle add up to 180, so let's make an equation.

[tex]35+90+x=180 \\ \\ 125+x=180 \\ \\ x=55[/tex]

Now we can use the law of sines.

[tex]\frac{a}{sin(A)}=\frac{b}{sin(B)}[/tex]

Where the lowercases are the side lengths and the uppercases are the angle measures.

Plug in the values we know.

[tex]\frac{27}{sin(35)}=\frac{x}{sin(55)}[/tex]

Solve using a calculator.

[tex]x=38.55999618 \\ \\ x=38.56[/tex]

Answer:

The second one

Step-by-step explanation:

Subtract 190 minus 40 to find the miles traveled: 190-40=150

Now divide the miles by the time: 150/2.5

Step-by-step explanation:

[tex]\dfrac{6}{8}=\dfrac{6:2}{8:2}=\dfrac{3}{4}\\\\\dfrac{6}{8}=\dfrac{6\cdot2}{8\cdot2}=\dfrac{12}{16}\\\\\dfrac{6}{8}=\dfrac{6\cdot3}{8\cdot3}=\dfrac{18}{24}\\\\\dfrac{6}{8}=\dfrac{6\cdot4}{8\cdot4}=\dfrac{24}{32}\\\\\dfrac{6}{8}=\dfrac{6\cdot5}{8\cdot5}=\dfrac{30}{40}\\\vdots[/tex]

The answer would be 186.2.

Answer:

The correct answer is  133% of 140  = 186.2

Step-by-step explanation:

Points to remember

X % of Y is given by

(X/100)*Y

To find 133 % of 140

We have to find 133 % of 140,

According to the formula we can write,

133% of 140 = (133/100) * 140

 = 1.33 * 140

 = 186.2

133% of 140 = 186.2

Therefore the correct answer is  133% of 140  = 186.2

A geometric ray has one endpoint and extends from the endpoint to infinity in one direction on a line. Rays are written with a right-facing arrow over two capital letters. The first letter represents the endpoint, and the second letter represents another point on the ray.

hope this helps :)

Answer:

Step-by-step explanation:

Point r

Answer: 14/4

Step-by-step explanation:

since 4/4 is one three would be 12/4. Adding 2/4 to 12/4 is 14/4. So the answer is 14/4

3 2/4 as a mixed number is 14/4

3 multiplied by 4 is 12 and you just add 2 to that and it'll be 14/4

[tex]\(i^{223}\)[/tex] is equal to -i.

To find the value of [tex]\(i^{223}\)[/tex], we can use the cycle of powers of i:

[tex]\(i^1 = i\), \(i^2 = -1\), \(i^3 = -i\)[/tex], and [tex]\(i^4 = 1\)[/tex]

The powers of i repeat every four steps.

Therefore, we can express [tex]\(i^{223}\)[/tex] in terms of [tex]\(i^4\)[/tex]:

[tex]\[i^{223} = (i^4)^{55} \cdot i^3\][/tex]

Since [tex]\(i^4 = 1\)[/tex] and [tex]\(i^3 = -i\)[/tex], we have:

[tex]\[i^{223} = 1^{55} \cdot (-i) = -i\][/tex]