When a survey was conducted among 100 students to find their favorite pizza topping, 45 students voted for pepperoni, 25 for mushrooms, and 30 voted for cheese. If a pie chart were made showing the number of votes for each topping, the central angle for the cheese sector would be __________.

Answer:

x=3.9 or 39/10 and   y=3.13333 or 47/15

Step-by-step explanation:

Since both expressions (6x-3y) and (3-2x+6y) are equal to 14, separate the equations:

       6x-3y=14 and 3-2x+6y=14

Simplify the equations

       6x-3y=14 and -2x+6y=11

Now, line the equations up and pick a variable (either x or y) to eliminate

        6x-3y=14

        -2x+6y=11

In this case, let's eliminate y first. To do so make the y values in both equations the same but with opposite signs. Make both be 6y but one is +6y and the other -6y

Multiply (6x-3y=14) by 2 to get:

      12x-6y=28

Line the equations up and add or subtract the terms accordingly

      12x-6y=28

      -2x+6y=11

This becomes:

     10x+0y=39

Isolate for x

   x= 39/10 or x= 3.9

Now substitute the x value into either of the original equations

    6x-3y=14

    6(3.9)- 3y=14

Isolate for y

   23.4-14=3y

   3y= 9.4

  y= 3.1333 (repeating)  or y= 47/15

Answer: x = 39/10, y = 94/30

Step-by-step explanation:

6x - 3y = 3 - 2x + 6y,

Now solving this becomes

6x + 2x -3y - 6y = 3

8x - 9y = 3 ------------------- 1

3 - 2x + 6y. = 14

-2x + 6y = 14 - 3

-2x. + 6y = 11

Now multiply both side by -1

2x. - 6y = -11 ----------------- 2

Solve equations 1 & 2 together

8x - 9y. = 3

2x - 6y = -11

Using elimination method

Multiply equation 1 through by 2 ,and equation 2 be multiplied by 8

16x - 18y = 6

-16x - 48y = -88 ------------------------- n, now subtract

30y = 94

Therefore. y = 94/30.

Now substitute for y in equation 2

2x - 6y = -11

2x - 6(94/30) = -11

2x - 94/5 = -11

Now multiply through by 5

10x - 94 = -55

10x = -55 + 94

10x = 39

x = 39/10

Answer:

y = 3x + 4

Step-by-step explanation:

We can use the equation y = mx + b to find the equation:

Plug in the slope and the point into the equation, and we can find b:

-5 = 3(-3) + b

-5 = -9 + b

4 = b

Now, we can plug in the slope and y-intercept into the equation:

y = 3x + 4 will be our equation

Answer:

The options that have two angles, which are A and D prove both triangles to be similar.

Step-by-step explanation:

The postulate AA is exactly what it sounds like, and you can find the two angles, which will prove the similarity of two triangles sharing those two angles.

The reason being is if two angles are the same between the two triangles, the third can't be different.

Answer: x=2 y=-2

(2,-2) one solution

Step-by-step explanation:

Solve by substitution

[tex]\begin{bmatrix}x^2+y^2=8\\ y=x-4\end{bmatrix}[/tex]

[tex]\mathrm{Subsititute\:}y=x-4[/tex]

[tex]\begin{bmatrix}x^2+\left(x-4\right)^2=8\end{bmatrix}[/tex]

[tex]2x^2-8x+16=8[/tex]

[tex]\mathrm{Isolate}\:x\:\mathrm{for}\:2x^2-8x+16=8:\quad x=2[/tex]

[tex]\mathrm{For\:}y=x-4[/tex]

[tex]\mathrm{Subsititute\:}x=2[/tex]

[tex]y=2-4[/tex]        [tex]2-4=-2[/tex]

[tex]y=-2[/tex]

[tex]The\:solutions\:to\:the\:system\:of\:equations\:are[/tex]

[tex]x=2,\:y=-2[/tex]

Answer:

Random variable

Step-by-step explanation:

The reason it is a random variable is because a, the definition fits, and b you can use context clues as well, such as 'determined by chance' which is another example of random! So, the answer is random, because random variables are determined by chance. Hope this helped.

Answer:

"A random variable is a variable that has a single numerical value, determined by chance, for each outcome of a procedure."

A random variable is distinct on the off chance that it takes on a countable number of quantities.

Answer:

19)

[tex]\frac{1}{2}*\frac{1}{4}*\frac{1}{8}*\frac{1}{16} = 2^n[/tex]

Notice that in the left side, all the numbers are powers of 2.

2 = 2^1

4 = 2^2

8 = 2^3

16 = 2^4

remember that:

(a^x)*(a^y) = a^(x+y)

then the denominator in the left is:

(2*4*8*16) = 2*(2^2)*(2^3)*(2^4) = 2^(1 + 2 + 3+ 4) = 2^8

Then we have:

[tex]\frac{1}{2}*\frac{1}{4}*\frac{1}{8}*\frac{1}{16} = \frac{1}{2^8} = 2^n[/tex]

[tex]1 = 2^8*2^n = 2^{8 + n}[/tex]

then 8 + n = 0

then n = -8.

18)

here we have:

x = (x/9) + (x/6) + (x/2) + 4 + (x/12) + 2

now in the left side we can use the common factor x and write it as:

x = x*( 1/12 + 1/9 + 1/6 + 1/2) + 6

x = x*(0.861) + 6

x - x*(0.861) = 6

x*(1 - 0.861) = 6

x = 6/(1 - 0.861) = 43.2

Answer:

P = 0.0714

Step-by-step explanation:

If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.

Additionally, from the 28 cubes painted only 4 have exactly two painted faces.

Then, to calculate the number of ways in which we can select x elements from a group of n, we can use the following equation:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

So, the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces is:

[tex]P=\frac{4C1*36C1}{64C2}=0.0714[/tex]

Because there are 64C2 ways to select 2 cubes from the 64, and from that, there are 4C1*36C1 ways to select one cube with exactly two painted faces and one cube with no painted faces.

Answer:

y = 3/8x

or

3/8 cups of sugar for every 1/2 batch of muffins

Step-by-step explanation:

Since we are only making 1/2 of the full batch of muffins, we only need to use 1/2 the cups of sugar:

[tex]\frac{3}{4} (\frac{1}{2} )= \frac{3}{8}[/tex] cups of sugar.

Answer:

[tex]\frac{x}{2} = \frac{3y}{8}[/tex]

Step-by-step explanation:

Let the batch be x and the amount of sugar be y

Condition:

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

Multiplying both sides by 1/2

[tex]\frac{1}{2} x = \frac{3}{4}y * \frac{1}{2}[/tex]

[tex]\frac{x}{2} = \frac{3y*1}{4*2}[/tex]

[tex]\frac{x}{2} = \frac{3y}{8}[/tex]

So, For 1/2 batch of muffins, Farid need 3/8 cups of sugar.

Answer:it is 6 trust

Step-by-step explanation:yah know

Answer:

Real Estate Deals

The best "payoff deal:"

B. Office Building

Step-by-step explanation:

A) Payoff Table

                                  Good Economic         Bad Economic

                                     Conditions                 Conditions

Probability                          (.60)                          (.40)

Apartment Building         $50,000                    $30,000

Office Building               $100,000                   $-40,000

Warehouse                     $30,000                     $10,000

B) Calculation of Expected Values:

                             Good Economic      Bad Economic    Expected Values

                                  Conditions          Conditions

Probability                       (.60)                    (.40)

Apartment Building     $30,000             $12,000             $42,000

Office Building            $60,000            $-16,000             $44,000

Warehouse                  $18,000               $4,000            $22,000

b) The expected value for these real estate deals can be derived as the sum of the payoffs under the two economic conditions after they have been weighed with their odds of occurrence.  The office building, in this example, showed the best payoff deal as the expected payoff from it results to a payoff of $44,000, which is higher than the expected payoff from the Apartment and Warehouse.  However, it is also the riskiest, especially when bad economic conditions occur.  This also accords with the general economic risk-return pattern that higher risky investments attract higher returns.

Answer:

12/13

Step-by-step explanation:

First we must calculate the hypotenus using the pythagoran theorem

Now let's calculate sin0

So the exact value is 12/13

Answer:

C.) 12/13

Step-by-step explanation:

In a right angle triangle MN = 12, ON = 5 and; angle N = 90°

Now,

For hypotenuse we will use Pythagorean Theorem

(MO)² = (MN)² + (ON)²

(MO)² = (12)² + (5)²

(MO)² = 144 + 25

(MO)² = 169

MO = √169

MO = 13

now,

Sin O = opp÷hyp = 12÷13

Answer:

3200ft^2

Step-by-step explanation:

1 inch = 4ft

so 20 inches = 80ft

and 10 inches = 40ft

Area = 80ft*40ft

Area = 3200ft^2

Answer:

B (4, 2+3)

Step-by-step explanation:

To do this you fill in x with 4 so the equation becomes y = (4)2 - 3

You then solve to y = 8 - 3

then 8 - 3 is 5.

Making the coordinates (4, 5) and in this case with the answers (4, 2+3)

Answer:

A. (4, 4^2 – 3)

Answer:

4.42 ounces

Step-by-step explanation:

Given:

The solid food Stacie has eaten in the noon meal:

1. [tex]\frac{1}2[/tex] of a 3-ounce serving of meatloaf.

2. [tex]\frac{3}4[/tex] of her 3-ounce serving of mashed potatoes

3. [tex]\frac{1}3[/tex] of a 2-ounce serving of green beans

To find:

How many ounces of solid food was consumed by Stacie (upto 2 decimal places) ?

Solution:

Let us convert the given fractions to decimal form upto 2 decimal places:

1. [tex]\frac{1}{2}\ of\ 3\ ounces[/tex] [tex]= \frac{1}{2}\times 3 =1.50\ ounces[/tex] meatloaf .

2. [tex]\frac{3}{4}\ of\ 3\ ounces[/tex] [tex]= \frac{3}{4}\times 3 =2.25\ ounces[/tex] mashed potatoes .

3. [tex]\frac{1}{3}\ of\ 2\ ounces[/tex] [tex]= \frac{1}{3}\times 2 =0.67\ ounces[/tex] green beans.

Let us add the above 3 quantities to get total solid food consumed.

Total solid food consumed = 1.50 + 2.25 +0.67 = 4.42 ounces.

So, the answer is 4.42 ounces.

Answer:

The p-value is 2.1%.

Step-by-step explanation:

We are given that a study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed.

The sample average age was 24.2 with a standard deviation of 3.7.

Let [tex]\mu[/tex] = true average age a "child" moves permanently out of his parents' home in the United States.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 23      {means that the average age a "child" moves permanently out of his parents' home in the United States is at most 23}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 23      {means that the average age a "child" moves permanently out of his parents' home in the United States is greater than 23}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                            T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average age = 24.2

            s = sample standard deviation =3.7

            n = sample of U.S. Adults = 43

So, the test statistics =  [tex]\frac{24.2-23}{\frac{3.7}{\sqrt{43} } }[/tex]  ~  [tex]t_4_2[/tex]

                                    =  2.127

The value of t-test statistics is 2.127.

Now, the p-value of the test statistics is given by;

         P-value = P( [tex]t_4_2[/tex] > 2.127) = 0.021 or 2.1%

Step-by-step explanation:

(ax + b)² = a²x² + 2abx + b²

In this case, a = 1, so:

14 = 2b

b = 7

(x + 7)² = x² + 14x + 49

Answer:

  As x increases, y decreases and then increases

Step-by-step explanation:

You need only understand your own description of the graph:

  begins above the x-axis, extends below the x-axis, and ascends above the x-axis

This is a description of decreasing, then increasing:

  As x increases, y decreases and then increases

Answer:

C. As x increases, y increases and then decreases.

Step-by-step explanation:

Just took the Unit Test and got it correct on Edge.

Answer:

[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]

which agrees with the first answer in the list of possible options.

Step-by-step explanation:

We can use the fact that the addition of all four internal angles of a quadrilateral must render [tex]360^o[/tex]. Then we can create the following equation and solve for the unknown "h":

[tex]2h+2h+h+h = 360^o\\6h=360^o\\h=60^o[/tex]

Therefore the angles of this quadrilateral are:

[tex]120^o,\,120^o,\,60^o,\,\,\,and\,\,\,60^o[/tex]

Answer:60,60,120,120

Step-by-step explanation:All qualdrilaterals equal to 360, so if you add all of the different numbers you should get 360

Answer:

width of the garden is 50 ft and the length is 70 ft

Step-by-step explanation:

Solution:-

- We will denote the width and and the length of the rectangular garden as:

   Width: x

   Length: x + 20

- We are given the area ( A ) of the garden is 3500 ft^2. We are to determine for what dimensions is the area A = 3500 ft^2.

- Recall that the area ( A ) of a rectangle is the product of length and width as follows:

                      A = Length * width

                      A = x*( x + 20 )

                      3500 = x^2 + 20x

                      x^2 + 20x - 3500 = 0

- Use the quadratic formula to determine the value of ( x ):

                     [tex]x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a} \\\\x = \frac{-20 +/- \sqrt{20^2 - 4*-3500} }{2}\\\\x = \frac{-20 +/- 120 }{2} = -10 +/- 60\\\\x = -70 , 50[/tex]

- Ignore the negative value of ( - 70 ft ). Physical impractical to have a negative value. Hence, the width of the garden is 50 ft and the length is 70 ft

Answer:

the answer is 750 because there are 30 days in the month of april and you just need to multiply it by how much meat they need to have per day.

Step-by-step explanation:

30 x 25 = 750

Answer:  $323.33

Step-by-step explanation:

($17,000 + $4,900 - $2,500) ÷ 60 months = $323.33 per month

    ↓                ↓              ↓

 price        finance      down payment

Answer:

549

Step-by-step explanation:

Remember PEMDAS (this is the order of operations).

P = Parentheses

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

So, lets do multiplication first.

33*2 = 66

So, our new expression is 486 - 9 + 6 + 66.

Remember that addition and subtraction are reversible.

486 - 9 = 477

477 + 6 = 483

483 + 66 = 549

Answer:

404

Step-by-step explanation:

P-parenthesis

E-exponents

M-multiplication

D-division

A-addition

S-subtraction

486-9+6+33*2

486-9+6+66

486-81=404

Answer:

Below

Step-by-step explanation:

The initial length of the road was 56. 56 is the y-intercept assuming that the graph of this function is a line.

so the equation is:

y= mx+56

m is the slope of the function wich is by how much the function grows.

By analogy, m is the distance added to the road each day.

● y= 3x+56

X is the number of days.

■■■■■■■■■■■■■■■■■■■■■■■■■■

To find the length of the road after 33 days, replace x by 33.

y= 3*33+56 = 155

So after 33 days the road is 155 miles.

Answer:

(Y-3)= -1/3(x-7)

Or

(Y-4)= -1/3(x-4)

Steb by step explanation:

The condition for the line is (7,3) and (4,4).

Point slope form of equation is in this format below.

(Y-y1)= m(x-x1)

We have the given parameters in the above format except the m

M = gradient

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

Gradient=(4-3)/(4-7)

Gradient= 1/-3

Gradient= -1/3

So

(Y-y1)= m(x-x1)

(Y-3)= -1/3(x-7)

Or

(Y-4)= -1/3(x-4)

Answer:

1/36

Step-by-step explanation:

the fair die has 6 equal parts which means its the total

the probability of rolling a 6 is 1/6

the probability of rolling another 6 is 1/6

so u multiply 1/6 times 1/6 which is 1/36

hope this helps

Hey there

Answer: C. Interest will be charged

Step-by-step explanation:

Answer:

Step-by-step explanation:

Interest will be charged is your answer!

Answer:

20 students per row

Step-by-step explanation:

person per each row=180/9=20

Answer:

20

Step-by-step explanation:

Take the number of students and divide by the number of students

180/9

20

There are 20 students in each row

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            Hi my lil bunny!

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Let's solve your equation step-by-step.

[tex]\frac{1}{3} (x+1)+2x=2[/tex]

Step 1: Simplify both sides of the equation.

[tex]\frac{1}{3} (x+1)+2x=2[/tex]

[tex](\frac{1}{3}) (x) + (\frac{1}{3} ) (1) + 2x = 2[/tex] (Distribute)

[tex]\frac{1}{3} x + \frac{1}{3} + 2x = 2[/tex]

[tex]( \frac{1}{3} x + 2x ) + (\frac{1}{3}) = 2[/tex] (Combine Like Terms)

[tex]\frac {7}{3} x + \frac{1}{3} = 2\\\frac{7}{3} x + \frac{1}{3} = 2[/tex]

Step 2: Subtract 1/3 from both sides.

[tex]\frac{7}{3} x + \frac{1}{3} - \frac{1}{3} = 2 - \frac{1}{3} \\\\\frac{7}{3} x = \frac{5}{3}[/tex]

Step 3: Multiply both sides by 3/7.

[tex]( \frac{3}{7} ) * (\frac{7}{3}x) = ( \frac{3}{7}) * \frac{5}{3} \\\\x = \frac{5}{7}[/tex]

So the answer is : [tex]x = \frac{5}{7}[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

Answer:

460

Step-by-step explanation:

Answer:

460

Step-by-step explanation: