The PE class has 12 boys and 8 girls. What is the maximum number of teams that the teacher can divide the class into so that each team has an equal number of boys and girls, the greatest common factor of the numbers of girls and boys? Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 8: 1, 2, 4, 8

2

4

24

96

Answer:

a. 2016-112x

Step-by-step explanation:

because each month he need to pay $112 so it have to be multiplied to the number of month and then answer should be subtracted from 2016

Answer:

The diameter of circle d is 9.03

Step-by-step explanation:

Circumference of Circle = 28.36

We need to find the diameter of circle.

The formula used to find the circumference of circle is:

C = 2πr

we know that radius is half of diameter

so r = d/2

Putting value of r in above equation

C = 2π(d/2)

C = πd

The value of π is 3.14. finding value of d

28.36 = 3.14 * d

=> d = 28.36 / 3.14

d = 9.03

So, the diameter of circle d is 9.03

Answer:

The diameter is approximately 9 units

Step-by-step explanation:

Circumference is given by

C = pi *d

28.36 = pi *d

Let use 3.14 for pi

28.36 = 3.14 *d

Divide each side by 3.14

28.36 /3.14 = 3.14 d/3.14

9.031847134 = d

The diameter is approximately 9 units

Answer: -2, 2, -1, 4

Step-by-step explanation:

The domain are all the x-coordinates in the ordered pair.

The domain of the list is {-2, 2, -1, 4} if the list of ordered pair is (-2, 1), (2, 0), (-1, -3), (4, 6).

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

List of ordered pairs is:

(-2, 1), (2, 0), (-1, -3), (4, 6)

As we know: order pair can be represented as:

(x, y) here x shows the domain of the function

and y shows the range of the function.

So the domain of the function:

= {-2, 2, -1, 4}

Thus, the domain of the list is {-2, 2, -1, 4} if the list of ordered pair is (-2, 1), (2, 0), (-1, -3), (4, 6).

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Answer:

See below.

Step-by-step explanation:

The zeroes of the equation will  not be real so the graph will not pass through the x-axis.

Answer:True

Step-by-step explanation:

Answer:

false

Explanation:

square root of x= -7

the equation would be -7 x -7

-7 x -7= 49 not -49

Answer: false

Answer:

[tex]\boxed{\text{A. 7 in}}[/tex]

Step-by-step explanation:

The formula for the arc (s) of a circle is

[tex]s = r\theta \times \dfrac{\pi}{180^{^{\circ}}}[/tex]

where θ is measured in degrees.

Data:

r = 5 in

θ = 75°

Calculation:

[tex]s = \text{5 in} \times 75^{^{\circ}}\times\dfrac{\pi}{180^{^{\circ}}} = \textbf{7 in}\\\\\text{The length of the arc is }\boxed{\textbf{7 in}}[/tex]

Answer:

3V2

Step-by-step explanation:

V18

V9 times 2 equals 18

V3 to the second power because 3 times 3=9 so we get 3V2

1. Carl's constant rate of speed is the slope of the straight line graph.

This straight line passes through: (0,0), (5,1), (10,2) etc

We can use the slope formula with any two points to find the slope of this line.

The slope formula is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

Let [tex](x_1,y_1)=(0,0)[/tex] and [tex](x_2,y_2)=(5,1)[/tex]

Then [tex]m=\frac{1-0}{5-0}[/tex], [tex]\implies m=\frac{1}{5}[/tex].

Carl's speed is [tex]\frac{1}{5}[/tex] miles per minute.

But we must leave our answer in miles per hour

Hence Carl's speed is [tex]\frac{1}{5}\times 60=12[/tex]  miles per hour

After 2 hours, Carl will travel [tex]12\times 2=24[/tex] miles.

2. The given line has equation [tex]-4x+y=10[/tex]

We write this in slope-intercept form by solving for y.

[tex]\implies y=4x+10[/tex]

This is in the form [tex]y=mx+c[/tex], where [tex]m=4[/tex] is the slope.

When x=3,  [tex]y=4(3)+10[/tex]

[tex]\implies y=12+10=22[/tex]

When x=3, y=22

3. The given straight line graph that models the situation passes through:

(0,0) and (20,30).

The slope of this line is [tex]\frac{Rise}{Run}=\frac{300}{20}=15[/tex]

Therefore the rate is $ 15 per ticket.

If the theater sells 150 tickets, the earnings will be: [tex]150\times 15=2,250[/tex] dollars.

Answer:

17

Step-by-step explanation:

QS and RS equal the same

5x - 8 = 3x + 2

-3x  +8    -3x +8

2x = 10

x = 5 you would then plug x into QS

5(5) - 8

25 - 8

17

Answer:

17

YA

Step-by-step explanation:

Answer:

Option C.

Step-by-step explanation:

Domain of any function is always represented by x - values when graphed.

Option A.

it has only one x value that is x = 2

Not correct.

Option B.

In this graph straight line doesn't intersect x - axis at x = -2 and -4.

So Not correct.

Option C.

If we see the x- values of the given set of coordinates, we find domain of the given function is { -4, -2, 2, 4}

Therefore, it's correct option.

Option D.

Given set with the coordinates shows domain set as {1, 0, 2, 6}

So it's not the answer.

Therefore, option C is correct.

Answer:

The book value for the van at the end of first year will be $30400

Step-by-step explanation:

Cost of van = $38,000

Amount of depreciation after one year = 20%

Finding 20% of 38,000

=38,000 *(20/100)

= 7600

so, amount of van after 1 year = 38,000 - 7600

= 30400

So, the book value for the van at the end of first year will be $30400

The book value of the Shining Star Preschool's van at the end of the first year is $30,400, after depreciating 20% of its original cost of $38,000 using the MACRS method.

Using the Modified Accelerated Cost Recovery System (MACRS), the van is depreciated over 6 years with fixed percentages assigned to each year. The first year's depreciation is 20% of the purchase price.

To calculate the depreciation expense for the first year, we multiply the purchase price by the first year's depreciation rate:

Depreciation Expense (Year 1) = Purchase Price  imes Depreciation Rate

Depreciation Expense (Year 1) = $38,000  imes 20%

Depreciation Expense (Year 1) = $7,600

Now, we subtract this depreciation expense from the purchase price to find the book value at the end of the first year:

Book Value (End of Year 1) = Purchase Price - Depreciation Expense (Year 1)

Book Value (End of Year 1) = $38,000 - $7,600

Book Value (End of Year 1) = $30,400

Therefore, the book value of the van at the end of the first year is $30,400.

Answer:

c = $5.00

Step-by-step explanation:

Let c = the cost of each candy bar

3 + 8c = 43

8c = 40

The standard equation of a circle is in the form:

(x-a)^2 + (y-b)^2 = r^2

where; a is the x coordinate of the center, b is the y coordinate of the center, and r is the radius of the center.

In this case, a is -5, b is 2, and r is 7.

Therefore, the equation of this circle would be

(x+5)^2 + (y-2)^2 = 49

Answer:

Second option: [tex](x +5)^2 + (y -2)^2 =49[/tex]

Step-by-step explanation:

The center-radius form of the circle equation is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Where "r" is the radius and the center is at the point [tex](h,k)[/tex]

Since the center of this circle is at the point [tex](-5, 2)[/tex], we can identify that:

[tex]h=-5\\k=2[/tex]

We know that the radius is 7, then:

[tex]r=7[/tex]

Now we must substitute these values into the equation  [tex](x - h)^2 + (y - k)^2 = r^2[/tex] to find the equation of this circle.

This is:

 [tex](x - (-5))^2 + (y - 2)^2 = (7)^2[/tex]

 [tex](x +5)^2 + (y -2)^2 =49[/tex]

The order of choosing doesn't matter, so it's a combination.

[tex]_{60}C_5=\dfrac{60!}{5!55!}=\dfrac{56\cdot57\cdot58\cdot59\cdot60}{120}=5,461,512[/tex]

Answer:

12/5

Step-by-step explanation:

tan(F)    =opposite side to angle F  over (Fraction Bar) adjacent side to angle F

[tex] \tan(F)=\frac{\text{ opposite side to angle F } }{ \text{ adjacent side to angle F} } [/tex]

The side that is opposite is the side that doesn't include F.

The side the is adjacent will include F (this is not the hypotenuse which is opposite the 90 degree angle).

So

[tex]\tan(F)=\frac{12}{5}[/tex]

Area of a rectangle is Length times width.

The Width is given as X and the length is 2x+3

Now you have x * 2x+3 = 230

Multiplying x to 2x+3 = 2x^2 +3x

2x^2 +3x = 230

Subtract 230 from both sides:

2x^2+3x-230 = 0

Factor the polynomial:

(x-10) (2x+23) = 0

Solve for each x:

x = 10 and X = -11.5

Since a side of a rectangle can't be a negative number x = 10.

The width = x = 10 yards.

The length = 2(10) +3 = 23 yards.

Answer: 5/6

Step-by-step explanation:

2/3=4/6

1/6 + 4/6 = 5/6

Answer:

5/6

Step-by-step explanation:

you can rewrite 2/3 plus 1/6 as:

2/3+1/6

To add fractions you need to have a common denominator (the bottom half of the fraction). In this case 6 is a common denominator. To convert 2/3 we need to multiply it by the appropriate form of 1. We can multiply by 1 because 1 times anything does not change the value:

(2/2⋅2/3)+1/6⇒2/2⋅2/3+1/6⇒4/6+1/6⇒5/6

[tex]\log1000=3[/tex]

[tex]\bf \cfrac{15\sqrt{6}}{3\sqrt{5}}\implies \cfrac{15\sqrt{6}}{3\sqrt{5}}\cdot \cfrac{\sqrt{5}}{\sqrt{5}}\implies \cfrac{15\sqrt{6}\cdot \sqrt{5}}{3(\sqrt{5})^2}\implies \cfrac{15\sqrt{6\cdot 5}}{3(5)} \\\\\\ \cfrac{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\sqrt{30}}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \sqrt{30}[/tex]

Answer:

6

Step-by-step explanation:

I added 2 cracker jacks to get how much money he had left the kept subtracting. 99 from the money he had left

Your question asks to make an equation with the information that was given.

In order to make an equation for your question. We would be making an equation with the formula: y = mx + b.

Formula: y = mx + b

m = change

x = amount of ice cream

b = starting value

We would need to gather the key information from the question.

Key information:

You have $30

Each ice cream cost $5

With the information above, we can make an equation for the question.

What we know is that you started with $30, so that means that 30 would be your b value (starting value).

Your equation should look like this:

y = mx + 30

Now, we know that each ice cream cost $5, but since we're paying for the ice cream, we would subtract that from our starting value. This means that our change would be -5, since we are taking away $5 each time we buy ice cream.

Your equation should look like this:

y = -5x + 30

The equation above would be the equation for your question.

We would do nothing to x but just leave it as is, since we don't know how many ice creams you're going to buy.

y = -5x + 30 should be your FINAL answer.

Answer:

It's A-all real numbers less than or equal to 7

Step-by-step explanation:

I just took the unit test and got a 100 on it!

The range of the function f(x) = -(x + 3)² + 7 is {y: y ∈ R, y ≤ 7}. So, option A is correct.

Given that,

f(x) = -(x + 3)² + 7

⇒ y = -(x + 3)² + 7

⇒ (x + 3)² = 7 - y

⇒ (x + 3) = √(7 - y)

⇒ x = (√(7-y)) - 3

Thus, all the real values less than or equal to 7 for y define the function. So, the domain for the obtained function is {y: y ∈ R, y ≤ 7}.

Therefore, the range of the given function is {y: y ∈ R, y ≤ 7}.

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Angles whose terminal sides lie on the x and y axis are Quadrantal angels.

Hope it helps.

Answer:

The correct answer option is c) quadrantal angles.

Step-by-step explanation:

When the terminal sides lie on the x axis or the y axis in the standard position, the angles are called as quadrantal angles.

For example when one of the sides lie on the x axis and one lies on the y axis, it makes an angle of 90 degrees which is a quadrantal angle (as shown in the picture attached).

[tex]\bf m-2c~:~m+c~~=~~1:k\qquad \implies \cfrac{m-2c}{m+c}=\cfrac{1}{k}\implies k(m-2c)=m+c \\\\\\ mk-2kc=m+c\implies mk-m-2kc=c\implies mk-m=2kc+c \\\\\\ \stackrel{\textit{common factor}}{m(k-1)=c(2k+1)}\implies m=\cfrac{c(2k+1)}{k-1}[/tex]

Answer:

6e^2f (3f^2-2e)

Step-by-step explanation:

18 e^2 f^3 - 12 e^3 f

18 e^2 f^3 = 2*3*3 ee fff

12 e^3 f = 2*2*3 eee f

The common terms are 2 *3*eef

Factor that out

2*3*eef (3ff - 2e)

Combine like terms

6e^2f (3f^2-2e)

Answer:

0.625N

Step-by-step explanation:

                                        0.50N

0.80M = 0.50N, so M = ------------

                                          0.80

and so:

                0.50N

N*M = N*------------ = (5/8)N, or 0.625N

                   0.80

Answer:

Step-by-step explanation:

Solve the system:

8x−4y=20

4x−8y=4

Reduce the first equation by dividing every term by -2:

-4x + 2y = -10

and then combine this result with the second equation:

4x−8y=4

-4x + 2y = -10

--------------------

      -6y = -6, and so y = 1.  

According to the first equation, if y = 1, then 4x - 8 = 4, or x = 3.

Then x = 3 and y = 1.

So, finally, x - y = 3 - 1 = 2

Answer:

T'={1}

Step-by-step explanation:

Definition:

Given a set T, the complement of T is the set of all elements in the universal set U, but not in T.

We can write T^c  

You can also say complement of T in U

Complement of T( T')= U-T

where U={1,2} and T={2}

Now put the sets of U and T in the formula:

T'=U-T

T'={1,2}-{2}

T'{1}

Thus the Complement of T(T')={1}....

The complement of a set T in a universal set U is all the elements in U that are not in T. If U={1,2} and T={2}, the all the elements in U that are not in T corresponds to {1}. So, the complement of T is {1}.

In the field of Mathematics, specifically in set theory, the complement of a set T in a universal set U is the set of all elements in U that are not in T. When we say complement of T, we are referring to the set of all outcomes in the universal set U that are NOT in T.

In this case, the universal set U={1,2}, and the event T={2}. Therefore, the complement of the set T in relation to U would be the set of all elements in U that are not in T. Hence, since 2 is in T, the only number left in U that is not in T is 1. So, the complement of T is {1}.

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Answer:the cost of the cell phone is a function of the number of features

Step-by-step explanation:

Because the cost depends on the features

Answer:179.95in

That is the awnser so how it helped

Step-by-step explanation:

Answer:

15.00 inches

Step-by-step explanation:

Recall the formula for the surface area of a sphere and a radius of r

A = 4πr²

In our case, we are given that A = 2826 ft² = 406944 in²

so,

406944 = 4πr²

r² = 406944 / (4π)      (use π=3.142)

r² = 406944 / (4π)  = 32383.57

r = √32383.57 = 179.95 in