There are 25 students in the class. 36% of the students ate hot dogs for lunch. How many students ate hot dogs?

Option A

[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}} = \left(y^{2}\right)^{\frac{-1}{2}}[/tex]

Solution:

Given expression is:

[tex]\left(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]

Product of powers property:

The product of powers property tells us that when you multiply powers with the same base you just have to add the exponents

Which is represented as,

[tex]a^m.a^n = a^{m+n}[/tex]

Therefore, the given expression becomes,

[tex]\left(y^{\frac{4}{3}+\frac{2}{3}}\right)^{\frac{-1}{2}}[/tex]

Now add the exponents, we get

[tex]\left(y^{\frac{4+2}{3}}\right)^{\frac{-1}{2}}[/tex]

Simplify the above expression

[tex]\left(y^{\frac{6}{3}}\right)^{\frac{-1}{2}}[/tex]

Simplify the exponent of y, we get

[tex]\left(y^{2}\right)^{\frac{-1}{2}}[/tex]

Thus Option A is correct

Answer:

The answer is A

Step-by-step explanation:

Answer:

700

Step-by-step explanation:

Hope this helps!

The problem is a mathematical exercise in determining the total number of movies rented from the provided percentage of those returned. By setting up an equation and solving it, we find that the total number of movies rented was 700.

The student's question is on a mathematical concept related to percentages and determining the whole from a percentage portion. From the information provided, 434 movies, which represent 62% of the total number of movies rented last week, were returned. To calculate the total number of movies rented, we can let the total be x. With this, the equation representing the scenario is 0.62x = 434.

By solving for x, we get x = 434 / 0.62. After the calculation, we find that the total number of movies rented last week was 700. Therefore, the store originally rented out 700 movies.

Remember that when dealing with percentages, the percentage value (in this case, 62%) must be converted into decimal form before performing any calculation. This is done by dividing the percentage by 100, thus 62% becomes 0.62. For clarity, here's the step-by-step procedure:

Answer:

8 3/5

Step-by-step explanation:

subtract the whole numbers first and then the fractions. you have 10 4/5-2 1/5. subtract the whole numbers and you have 8(put that off to the side). then do 4/5-1/5. 4-1=3 and the denominators stay the same so you have 3/5. you don’t need to simplify so your final answer is 8 3/5.

Answer:

43 / 5 or 8 3/5

Step-by-step explanation:

Answer:

15: 1

Step-by-step explanation:

Please see attached picture for full solution.

Answer:

x=8

Step-by-step explanation:

17=x+9

-9     -9

8=x

Answer:

x=8

Step-by-step explanation:

17-9=8

8+9=17

Answer:

17

Step-by-step explanation:

a[2]+b[2]=c[2]

8*8+15*15=hypotenuse.

64+225=289

[tex]\sqrt{x} 289[/tex]

hypotenuse=17

Answer:

It is NOT possible for a solution to be both x<9 and x>9

It IS possible for a solution to be both x≤9 and x≥9

Step-by-step explanation:

Because for x<9 and x>9 the GREATER than symbol means it less than 9 and cannot be 9 or it is greater than 9 but cannot be 9.

With x≤9 and x≥9 the greater than or EQUAL sign makes a big difference. Because x≥9 may be the actual solution but since it is possible to be  equal to 9 so can x≤9.

(Sorry if this seemed very confusing to explain).

Answer:

I think its B. because if you put 6/4and reduce it it would be 3/2

Step-by-step explanation:

Answer:

C. 5/8

Step-by-step explanation:

P(red) = 6/16

p(blue) = 4/16

p(red or blue) = P(red) + p(blue) = (6+4)/16 = 10/16 = 5/8

Answer:

if you're solving for inequality its y>2

Option B

The factored form by grouping is:

[tex]xy+2y^2+3x+6y = (x+2y)(y+3)[/tex]

Solution:

Given that we have to factor the given polynomial by grouping

Given polynomial is:

[tex]xy+2y^2+3x+6y[/tex]

Factoring by grouping means that you will group terms with common factors before factoring.

This is done by grouping a pair of terms. Then factor each pair of two terms

In the given polynomial, group the terms that has "x" as common and group the terms that has "y" as common

[tex](xy+3x)+(2y^2+6y)[/tex]

Factor out "x" from first group and factor out "2y" from second group

[tex]x(3+y)+2y(y+3)[/tex]

Factor out y + 3

[tex]x(3+y)+2y(y+3) = (x+2y)(y+3)[/tex]

Thus the factored form by grouping is:

[tex]xy+2y^2+3x+6y = (x+2y)(y+3)[/tex]

Answer:

Option a

- x + 2y = −10

3x − y = 12

Step-by-step explanation:

step 1

Find the equation of the line with negative slope

we know that

The line with negative slope has a y-intercept at (0,-5)  and passes through the point (2,-6)

Find the slope

[tex]m=(-6+5)/(2-0)=-\frac{1}{2}[/tex]

The equation in slope intercept form is

[tex]y=-\frac{1}{2}x-5[/tex]

Convert to standard form

Multiply by 2 both sides

[tex]2y=-x-10\\x+2y=-10[/tex]

step 2

Find the equation of the line with positive slope

The line with positive slope has a x-intercept at (4,0)  and passes through the point (2,-6)

Find the slope

[tex]m=(-6-0)/(2-4)=3[/tex]

The equation of the line in point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=3\\point\ (4,0)[/tex]

substitute

[tex]y-0=3(x-4)[/tex]

Convert to standard form

[tex]y=3x-12\\3x-y=12[/tex]

therefore

The system of equations is

- x + 2y = −10

3x − y = 12

Answer:

infinite solution

Step-by-step explanation:

no matter what you have for x, 3x still equals 3x, so it is infinite

Answer:

Step-by-step explanation:

Letters are variables and those variable can store a number

Ex: x=5  y=2

evaluate : 3x+2y

we know that x is 5, so we know that 3x would be 15

we know that y is 2, so we know that 2x would be 4

then it says to add 3x and 2y, we would add 15 and 4 to get 19

(This is a very simple example, when you get older, the expression would be much more confusing.

Answer:

Step-by-step explanation:

1) pentagon; n= 5

Sum of interior angles = 180*(n -2) = 180* (5-2) = 180 * 3 = 540

2) Sum of interior angles of a polygon = 1080

180*(n-2) = 1080

n - 2 = 1080/180

n -2 = 6

n = 6+2

n = 8

Polygon has 8 sides

3) Sum of interior angles of a polygon = 6840

180*(n-2) = 6840

n - 2 =6840/180

n -2 = 38

n = 38 + 2

n = 40

Polygon has 40sides

4)Sum of interior angles of an octagon = 180*(n-2) = 180* (8-2) = 180 - 6 = 1080

The sum of the interior angles of the 10-sided polygon on the left is 1440 °.

The answer is : 1440

Answer:

The slope is 2

Step-by-step explanation:

y = 2x + 7

Comparing with y = mx + c

Where m is the slope = 2

Answer:

B

Step-by-step explanation:

The equation of line is y=2x+7

Comparing it with the standard equation y=mx+c

Where m is the slope and c is the y-intercept

Hence we get

Slope,m =2

Answer:

24 sweets

Step-by-step explanation:

Total amount of sweets is 36

Goal to divide into 3 (1+2) and give out the sections.

36/3 = 12

Tina sweets = 12(1) = 12

Penny sweets = 12(2) = 24

12:24

1:2

Answer:

24

Step-by-step explanation:

2/3 ×36/1 3 ÷3=1 and 36÷3=12 and 12×2=24

Answer:

[tex]\left\{\begin{array}{l}x+y=200\\ \\xy=9,600\end{array}\right.[/tex]

Step-by-step explanation:

The diagram shows rectangular parking lot with sides of [tex]x[/tex] feet and [tex]y[/tex] feet.

1. The area of the rectangle is

[tex]A=Length\times Width=xy.[/tex]

If the area of the parking lot os [tex]9,600\ ft^2,[/tex] then

[tex]xy=9,600[/tex]

2. A parking lot has  a [tex]200\ ft[/tex] fence built along two adjacent sides of lengths [tex]x[/tex] and [tex]y[/tex], then

[tex]x+y=200[/tex]

3. The system of two equations describing this situation is

[tex]\left\{\begin{array}{l}x+y=200\\ \\xy=9,600\end{array}\right.[/tex]

Answer:

45°

Step-by-step explanation:

We know ∠ Y +∠ S = 90

and ∠ S= 5 ( ∠ Y)-180  so

leave S alone for both

90- ∠Y = 5 ( ∠Y) -180

270 = 6( ∠Y )

45= ∠ Y

∠S = 5( 45) -180

     =225-180

     =45

Final answer:

The measure of angle Y (m∠Y) is 45°, following the equation derived from the facts that angles S and Y are complementary and m∠S equals 5 times m∠Y minus 180°.

Explanation:

If ∠S and ∠Y are complementary angles, then the sum of their measures is 90°. According to the given information, m∠S = 5(m∠Y) − 180°. Since m∠S + m∠Y = 90°, we can set up the equation:

5(m∠Y) − 180° + m∠Y = 90°

Combining like terms to solve for m∠Y:

6(m∠Y) = 90° + 180°

6(m∠Y) = 270°

m∠Y = 270° / 6

m∠Y = 45°

The measure of angle Y, m∠Y, is 45°.

The tending of rabbits, known as rabbit farming or rabbit husbandry, involves providing adequate resources for the rabbits to mature and reproduce. This could be for the purposes of obtaining meat, fur, or wool from the rabbits. It's also important to monitor for signs of infection to prevent communicable diseases.

The tending or caring of rabbits is commonly referred to as rabbit husbandry or rabbit farming. This involves the raising and breeding of rabbits, often for their meat, fur, or sometimes, for their wool in the case of certain breeds like the Angora Rabbit.

Aspects of rabbit husbandry can include providing an adequate food source, healthcare, and a suitable living environment. It is imperative to watch out for any signs of infection, as some diseases can be transmitted from the rabbits to humans through eating or handling infected rabbits. Some such infections could be vector-borne, passing through ticks or flies, or potentially through aerosols in a laboratory setting.

These caretaking measures help ensure that a young rabbit can develop into a healthy adult rabbit, capable of reproducing or providing the intended resource, whether it be meat, fur, or wool.

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Answer:

Any equation that cannot be written in standard form form in nonlinear.

Step-by-step explanation:

Considering the equation in standard form as

[tex]ax + by = c[/tex]

For example here is the sample equation [tex]3x - 2y = 4[/tex] is in standard form.

Very much every linear equation can be written in standard form.

There are certain rules that need to be followed for any lines to be in standard form, violation of which would not let certain lines to be written in standard form. These rules are:

Any equation that cannot be written in this form in nonlinear.

Keywords: linear equation, standard form, nonlinear equation

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Answer: 60 ounces of pebbles

Answer:

The Area of the Ferris wheel is 31400 Square feet

Step-by-step explanation:

The AREA formula for a circle:

The Area formula for the circle is [tex]\pi r^2[/tex]

where

r is the radius of the circle

The area of the Ferris Wheel:

The Height of the Ferris wheel =  200 foot

Here height of the Ferris wheel is the diameter

So the Diameter = 200

Then Radius =[tex]\frac{200}{2}[/tex] = 100 foot

Now the area of the Ferris wheel is

=> [tex]\pi (100)^2[/tex]

=> [tex]\pi \times 10000[/tex]

=> 31400 square feet

Answer:

The answer to your question is  (4/3, -1)

Step-by-step explanation:

Convert both equations to the same base

                                    [tex]27^{x - 2} = 9^{y}[/tex]

        27 = 3 x 3 x 3 = 3³  

          9 = 3 x 3 = 3²

Substitution

                                   [tex]3^{3(x - 2)} = 3^{2y}[/tex]

Simplify

                                      3x - 6 = 2y                         Equation l

                                   [tex]32^{y - 3/5} = \frac{1}{8^{2x}}[/tex]

            32 = 2 x 2 x 2 x 2 x 2 = 2⁵

             8 = 2 x 2 x 2 = 2³          

                                   2[tex]^{5(y - 3/5)} = 2^{-3(2x)}[/tex]

Simplify

                                  5y - 3 = -6x                            Equation ll

Equal to zero both equations

                                3x - 2y - 6 = 0                         Equation l

                                6x + 5y - 3 = 0                          Equation ll

Solve by elimination

Multiply equation l by 5 and equation ll by 2

                               15x - 10y - 30 = 0

                               12x + 10y - 6 = 0

                                27x        -36 = 0

Solve for x

                                 27x = 36

                                     x = 36 / 27

Simplify                        x = 4/3

Find the y value

                                6(4/3) + 5y - 3 = 0

                                8 + 5y - 3 = 0

                                      5y = -8 + 3

                                      5y = -5

                                        y = -5/5

                                        y = -1

Solution

                                  (4/3, -1)

Answer:

5/12

Step-by-step explanation:

1/4×3/3=3/12

1/3×4/4=4/12

4/12+3/12=7/12

12/12-7/12=5/12

Answer:

  20

Step-by-step explanation:

Let x represent the number of rentals. Then the cost will be the same when ...

  105 +9.50x = 14.75x

  105 = 5.25x

  105/5.25 = x = 20

Each would have to rent a boat 20 times in order to pay the same amount.

The answer to that problem is:

[tex]36 {a}^{8} {b}^{8} [/tex]

Hope This Helps! :)

Answer:

Step-by-step explanation:

A = 3/4B

A = 72.75

3/4B = 72.75

B = 72.75 * 4/3

B = 291/3 = 97

you would save (97 - 72.75) = $ 24.25 when buying them at store A

By calculating the original price of the headphones at Store B and subtracting the price at Store A, we find that you would save $24.25 by purchasing the headphones at Store A.

To find out how much you save by buying the headphones at Store A, we need to determine the original price of the headphones at Store B.

Let's denote the price at Store B as P. According to the information given, the price at Store A is 3/4 of the price at Store B. We can write the following equation:

P × (3/4) = $72.75

Solving for P, we get:

P = $72.75 ÷ (3/4)
  P = $72.75 ÷ 0.75
  P = $97.00

Therefore, the price of the headphones at Store B is $97.00. To find the savings, subtract the price at Store A from the price at Store B:

Savings = Price at Store B - Price at Store A
  Savings = $97.00 - $72.75
  Savings = $24.25

By buying the headphones at Store A, you save $24.25.

Answer: 146.12 m/s (to the right)

Step-by-step explanation:

The Conservation of Linear Momentum principle states that the initial momentum [tex]p_{i}[/tex] (before the elastic collision) must be equal to the final momentum [tex]p_{f}[/tex] (after the elastic collision):

[tex]p_{i}=p_{f}[/tex] (1)

Being:

[tex]p_{i}=m_{r}V_{r} + m_{b}V_{b}[/tex]

[tex]p_{f}=m_{r}U_{r} + m_{b}U_{b}[/tex]

Where:

[tex]m_{r}=0.311 kg[/tex] is the mass of the racket

[tex]V_{r}=30.3 m/s[/tex] is the velocity of the racket before the collision

[tex]m_{b}=0.057 kg[/tex] is the mass of the ball

[tex]V_{b}=-19.2 m/s[/tex] is the velocity of the ball before the collision

[tex]U_{r}=0 m/s[/tex] is the velocity of the racket after the collision  (assuming it is at rest after hitting the ball)

[tex]U_{b}[/tex] is the velocity of the ball the collision

So, we have the following:

[tex]m_{r}V_{r} + m_{b}V_{b}=m_{r}U_{r} + m_{b}U_{b}[/tex]  (2)

Finding [tex]U_{b}[/tex]:

[tex]U_{b}=\frac{m_{r}V_{r} + m_{b}V_{b}}{m_{b}}[/tex] (3)

[tex]U_{b}=\frac{(0.311 kg)(30.3 m/s) + (0.057 kg)(-19.2 m/s)}{0.057 kg}[/tex] (4)

Finally:

[tex]U_{b}=146.12 m/s[/tex] This is the velocity of the ball after the collision

Answer:

38m/s

Step-by-step explanation: