In a survey, 300 adults and children were asked whether they preferred hamburgers or pizza. The survey data are shown in the relative frequency table.

4.5 + 1.5k = 18 - 3k

Bring -3k to the other side by adding 3k to both sides

4.5 + (1.5k + 3k) = 18 + (-3k + 3k)

4.5 + 4.5k = 18 + 0

4.5 + 4.5k = 18

Bring 4.5 to the other side by subtracting it to both sides

(4.5 - 4.5) + 4.5k = 18 - 4.5

0 + 4.5k = 13.5

4.5k = 13.5

Isolate k by dividing 4.5 to both sides

4.5k / 4.5 = 13.5 / 4.5

k = 3

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The solution of the equation are 3 , -11

Step-by-step explanation:

* Lets revise how to make the completing square

- The form of the completing square is a(x - h)² + k, where a , h , k

 are constant

- The general form of the quadratic is ax² + bx + c, where a , b , c

 are constant

- To change the general form to the completing square form equate

  them and find the constant a , h , k

* Now lets solve the problem

∵ x² + 8x = 33 ⇒ subtract 33 from both sides

∴ x² + 8x - 33 = 0

- lets change the general form to the completing square

∴ x² + 8x - 33 = a(x - h)² + k ⇒ solve the bracket of power 2

∴ x² + 8x - 33 = a(x² - 2hx + h²) + k ⇒ multiply the bracket by a

∴ x² + 8x - 33 = ax² - 2ahx + ah² + k ⇒ compare the two sides

∵ x² = ax² ⇒ ÷ x²

∴ a = 1  

∴ -2ah = 8 ⇒ substitute the value of a

∴ -2(1)h = 8 ⇒ -2h = 8 ⇒ ÷ (-2)

∴ h = -4

∵ ah² + k = -33 ⇒ substitute the value of a and h

∴ (1)(-4)² + k = -33

∴ 16 + k = -33 ⇒ subtract 16 from both sides

∴ k = -49

∴ x² + 8x - 33 = (x + 4)² - 49

* Now lets solve the completing square

∵ (x + 4)² - 49 = 0 ⇒ add 49 to both sides

∴ (x + 4)² = 49 ⇒ take square root for both sides

∴ (x + 4) = ± 7

∵ x + 4 = 7 ⇒ subtract 4 from both sides

∴ x = 3

∵ x + 4 = -7 ⇒ subtract 4 from both sides

∴ x = -11

* The solution of the equation are 3 , -11

Answer:

{-11, 3}

Step-by-step explanation:

Answer:

Distance divided by time

I would say that’s correct

OOF yes it's correct...

Answer:

Option 3 (angle WXY + angle YXZ = 180) is the answer.

The last one. It goes and touches the most points.

The 4th line is the line of best fit for this given scatter plot.

"A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed."

Here, 4 different lines are drawn for a given scatter plot.

We know, a line drawn on a scatter plot fits it the best is the line that is closer to most of the points.

Here, the 4th line is closer to most of the points on the scatter plot.

Therefore, 4th line is the best fit.

Learn more about scatter plot here: https://brainly.com/question/19741330

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Answer:

FICA Tax =$8170.2

Step-by-step explanation:

Given

Total income=$165000

Taxable income=$106800

FICA tax includes Social security tax and medicare tax.  

Medicare tax is 1.45% of the taxable wage and social security tax is6.2% of the taxable wage.  

1.45% of medicare is paid by the employer and similarly 6.2% social security tax is paid by the employer.

0.9% of medical surtax is deducted if the employee earns more than $200000

So,

Medicare  Tax=Taxable income*1.45/100

=106800*0.0145

=$1548.6  

Social Security Tax=Taxable Income*6.2/100

=106800*0.062

=$6621.6

As the income of the employee is less than $200000, so there will be no medical surtax.  

Total FICA tax=$1548.6+$6621.6

=$8170.2

Answer: The graph is shifted 2 units to the right.

Step-by-step explanation:

Given a function f(x), we know that one transformation rule is:

If [tex]f(x-k)[/tex] then the function is shifted "k" units to the right.

 Therefore, for the function [tex]f(x)=x^{2}[/tex], when we subtract 2 from the input, then we get the function g(x) in the form:

 [tex]g(x)=(x-2)^{2}[/tex]

We can conclude that subtracting 2 from the input of the function [tex]f(x)=x^{2}[/tex], then the graph is shifted 2 units to the right.

The answer is right graph shifted 2 units to the right

Answer:

A.

⇒The slope of the function f(x) is greater than the slope of the function g(x).

This is so because using the slope intercept form equation, the slope of f(x) is 6 while that of g(x) is 5

B.

⇒The function f(x) has a greater y-intercept than the function g(x)

⇒The y intercept for the function f(x) is -1 where as that of the function g(x) is -4

Step-by-step explanation:

This question is on the standard equation of a linear function using the slope-intercept form

y=m x+c----------where m is the gradient/slope of the line and c is the y-intercept.

Given the values in function f(x) we can identify the points in the line as;

(-1,-7), (0,-1) , (1,5)............plot the points to obtain the graph as indicated in the attachment.

Find the gradient  of the graph ;

m₁=Δy/Δx

m₁= 5--1/1-0 =6/1 =6

Equation of line will be;

y-5/x-1 = 6

y-5=6(x-1)

y-5=6x-6

y=6x-1.........................m₁=6 and c₁= -1

Given that;

g(x)=5x-4.........................m₂=5   c₂= -4

⇒The slope of slope of the function f(x) is greater than the slope of the function g(x).

This is so because using the slope intercept form equation, the slope of f(x) is 6 while that of g(x) is 5

B.

⇒The function f(x) has a greater y-intercept than the function g(x)

⇒The y intercept for the function f(x) is -1 where as that of the function g(x) is -4

In the attached graph;

Red line graph, y=5x-4

Blue line graph, y=6x-1

Answer:

g(x) =   y=5x-4

f(x) =.    y= 6x-1

I know the slope of f(x) is greater than the slope of g(x) since the slope of f(x)=6 and g(x)=5 and 6>5.

I also know that the y-intercept of f(x) is greater because f(x)=-1 and g(x)=-4 and -1>-4.  

Step-by-step explanation:

First, I will put both functions into slope-intercept form.

Next, I will use  by picking two points on the table.  and

this equals  or 6.

So, I know the slope is 6.

To find the y-intercept I have to do, -7=6(-1)+b

So, the y-intercept is -1.

From this, I know the slope of f(x) is greater than the slope of g(x) since the slope of f(x)=6 and g(x)=5 and 6>5.

I also know that the y-intercept of f(x) is greater because f(x)=-1 and g(x)=-4 and -1>-4.  

Answer:

15) f(x) + g(x)  = -x + 8

17) f(x) - g(x) = x + 9

Step-by-step explanation:

15)

f(x) = 3x + 5

g(x)= - 4x + 3

Find f(x) + g(x)

f(x) + g(x)  = 3x + 5  + ( - 4x + 3 )

f(x) + g(x)  = 3x + 5   - 4x + 3

f(x) + g(x)  = -x + 8

17)

f(x) = 2x +4

g(x)= x - 5

Find f(x) - g(x)

f(x) - g(x) = 2x +4  - (x - 5 )

f(x) - g(x) = 2x +4  - x +  5

f(x) - g(x) = x + 9

[tex]

f(x)=3x+5 \\

g(x)=-4x+3 \\

(f+g)(x)=f(x)+g(x)=(3x+5)+(-4x+3) \\

3x+5-4x+3=\boxed{-x+8} \\ \\

f(x)=2x+4 \\

g(x)=x-5 \\

(f-g)(x)=f(x)-g(x)=(2x+4)-(x-5) \\

2x+4-x+5=\boxed{x+9}

[/tex]

Hope this helps.

r3t40

you just cancel out the x variable first since 4x-4x is 0 then you bring down your y variable and solve for x then you plug x into either equation then solve for x.

Answer:

Answer is B - 290.

Step-by-step explanation:

The idea here is that we're assuming the frequency each colour is drawn is a reflection of the proportion of marbles in the bag that are that colour. The more of a particular colour you have, the more likely you are to draw it, and vice versa.

Therefore we can assume the proportion of blue, gree, and red marbles is 13%, 29%, and 58% respectively based on the first 100 draws.

These percents should stay relatively similar as more draws are done, approaching the true proportions of each colour better the higher the number of draws. That means 29%, or 290, of the 1000 draws will be green.

Answer: 290

Step-by-step explanation:

36-(4+2a)^2=0

36-16+4a^2=0

4a^2+20=0

a^2+5=0 <— Factored form

Answer:

Step-by-step explanation:

3.14 x 10.6^2= 352.81 pi

Answer is...

Volume = 4988.92

See attached photo

1 = a

2 = h

have a good day

Answer:

[tex]x=5(+/-)\sqrt{17}[/tex]

Step-by-step explanation:

we have

[tex]x^{2}-10x+8=0[/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex]x^{2}-10x=-8[/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side.

[tex]x^{2}-10x+5^{2}=-8+5^{2}[/tex]

[tex]x^{2}-10x+25=-8+25[/tex]

[tex]x^{2}-10x+25=17[/tex]

Rewrite as perfect squares

[tex](x-5)^{2}=17[/tex]

Take square root both sides

[tex](x-5)=(+/-)\sqrt{17}[/tex]

Adds 5 both sides

[tex]x=5(+/-)\sqrt{17}[/tex]

Answer:

x = 18

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{x+x+3}{x+3}[/tex] = [tex]\frac{14+12}{14}[/tex]

[tex]\frac{2x+3}{x+3}[/tex] = [tex]\frac{26}{14}[/tex] ( cross- multiply )

14(2x+3) = 26(x + 3) ← distribute both sides

28x + 42 = 26x + 78 ( subtract 26x from both sides )

2x + 42 = 78 ( subtract 42 from both sides )

2x = 36 ( divide both sides by 2 )

x = 18

The answer would be 20

You multiply 62.5% by 32

32*0.625=20

They are correct it is 20.

5:55am

Start by finding how long the stand was open. Add 5 hours + 1 hour + 6 hours 15 minutes to get 12 hours 15 minutes.

Now, just find the time that is 12 hours and 15 minutes before 6:10pm. Start by subtracting 12 hours, which just switches the time from a.m. to p.m. This brings you to 6:10am. Finally, subtract the 15 minutes to get 5:55am.

1210÷4=302.5 and u can have a half of a dog so there would be 302

Answer:

Step-by-step explanation:

D

Answer: 56.25

Step-by-step explanation:

You just need to use common sense.

Answer:

[tex]\$16,021[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]V=P(1-k)^{x}[/tex]  

where  

V is the depreciated value  

P is the original value  

k is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$20,000\\k=0.105\\x=2\ years[/tex]

[tex]V=\$20,000(1-0.105)^{2}=\$16,020.50[/tex]  

round to the nearest dollar

[tex]\$16,020.50=\$16,021[/tex]  

the value of the car after 2 years will be approximately $16,212.

To find the value of the car after 2 years with continuous depreciation, we will use the formula for continuous exponential decay:

[tex]V(t) = V_0 \times e^{-kt}[/tex]

Where V(t) is the value after time t V_0 is the initial value, k is the decay constant and t is time

Plugging in the values:

[tex]V(2) = 20000 \times e^{-0.105 \times 2}[/tex]

Simplifying the exponent:

[tex]V(2) = 20000 \times e^{-0.21}[/tex]

[tex]V(2) = 20000 \times 0.8106 \approx 16212[/tex]

Thus, the value of the car after 2 years will be approximately $16,212.

1 quart = 2 pints.

This means a 4 pint container is 2 quarts.

To find the price for 1 quart divide the price by 2:

12.04 / 2 = $6.02 per quart.

ANSWER:

The 100 one is 10 and the 1,728 one is 12!

I think this is right and I hope I helped!

Tell me if it was right!

The diameter of a circle is the radius times 2.

Diameter = 3 x 2 = 6 meters.

Answer:

6 is the answer.

3 x 2 = 6

Step-by-step explanation:

Answer: Option A

P(B and V)=10%

Step-by-step explanation:

To solve this poroblema we use the formula of combinations:

[tex]nCr =\frac{n!}{r!(n-r)!}[/tex]

Where n is the number of objects that can be chosen and you choose r from them.

There are 5 colors of shirts.

The number of shirts that can be made by combining 2 of the 5 possible colors is calculated as:

[tex]5C2[/tex]

[tex]5C2=\frac{5!}{2!(5-2)!}[/tex]

[tex]5C2=10[/tex]

The number of shirts that can be made by combining 2 of the 2 possible colors (B) and (V) is calculated as:

[tex]2C2 = 1[/tex]

Then the probability is:

[tex]P(B\ and\ V)=\frac{2C2}{5C2}\\\\P(B\ and\ V)=\frac{1}{10}\\\\P(B\ and\ V)=0.1=10\%[/tex]

Answer: the answer is D

Step-by-step explanation:

Cause you have to do 100% divided by 5 you will get 20%

So if you have two of the five colors you will have two multiple 20% times 2 and get 40%

Answer:

Step-by-step explanation:

The volume of a box with dimensions length x, width (x+1), and height (x+2), is given by the formula x^3 + 3x^2 + 2x cubic units.

The volume of the box can be calculated by multiplying its length, width, and height together. Given that the length is x, width is (x+1), and height is (x+2), the volume would be x*(x+1)*(x+2).

To further expand this, apply the distributive law which first multiplies x*(x+1), resulting in x^2 + x. Then multiply this result by (x+2), giving the final volume V = x^3 + 3x^2 + 2x.

Therefore, the volume of the box given the stated dimensions is x^3 + 3x^2 + 2x cubic units.

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Add the total number of rolls that were greater than 3.

This would be the number 4, 5 and 6.

8 + 11 + 10 = 29 rolls higher than 3.

Now divide the number of rolls higher than 3 by the total number of rolls which is given as 50:

29 / 50 = 0.58

Multiply by 100 to get the percent:

0.58 x 100 = 58% of the rolls were higher than 3.

Answer:

[tex]g^2+ 3g -10=(x-2)(x+5)[/tex]

Step-by-step explanation:

The trinomial is the following

[tex]g^2+ 3g -10[/tex]

Look for two numbers b and d that when multiplying them get as a result -10 and when you add up these numbers you get 3 as a result.

This is.

[tex]b * d = -10\\\\b + d = 3[/tex]

Then you can write the trinomial as the product of two factors:

[tex](x+b)(x+d)[/tex]

You can check that the numbers that meet this condition are:

[tex]b = -2\\d = 5[/tex]

Then the trinomial is written as

[tex]g^2+ 3g -10=(x-2)(x+5)[/tex]

tan 24 = x/12

0.4452 · 12 = X

5.34 = X