Math

You are the first person to see a video and you share the link with three friends. Each new person who views the video shares it with three new people. Assume it takes 3 hours to share the video. Complete the following table to determine how many new viewers the video will have every 3 hours.

3, 9, 27, 81 -(start with how many people it's shared with (3) and then keep multiplying each new number by 3 to get answers).

If a star increases its luminosity by 1.6 orders of​ magnitude, by what factor does its luminosity​ increase?

40 -(to solve you would do 10^1.6 and then round to the next whole number).

Use dimensional analysis to convert as indicated. 5.4 square yards=​_______ square feet

48.6 -(1 square yd=9square ft, so multiply 5.4 by 9 to get answer)

If y varies inversely as​ x, find the constant of variation k and the inverse variation equation for the situation. y=10 when x=5 Find the constant of variation k.

50-(multiply 10 and 5 for first part), y=50/x (place y=and then 50 over x).

Simplify the expression using exponent rules. Then write the answer in scientific notation. (8×10^4)(9×10^6)

7.2x10^11 -(multiply 8 and 9, keep 10, then add the exponents. Then plug 72x10^10 into calculator to get answer).

Find the deviations from the mean for the set of​ data: 24​, 28​, 19​, 22​, 22.

1, 5, -4,-1,-1 (find the mean by adding all the products and then dividing by the amount of numbers (5), then subtract the mean (23) from each given number).

Complete the ordered pairs so that each is a solution to the equation. Then choose two of the points to graph the equation. y=−5x+4

14, 4, -6 -(plug numbers in x column into actual equation) then graph.

Using the​ graph, find the rate of change of the tuition and fees at private​ four-year colleges.

1500-(subtract 11500-10000=1500 then put 1500/1 to get answer)

Use the vertical line test to determine if the graph is a function.

Yes, the relation is a function because every vertical line intersects the graph at no more than one point.

Use the function machine to find ​f(4​) and x when ​f(x)=2. f(x)=10x+13

f(4)=53, f(2)=-11/10 -(to solve the first, just plug 4 into the equation for x, but for the second, subtract 13 from 2 which is -11 and place 10 under to form a fraction).

Use the graph to determine the allowed inputs and possible outputs of the function.

part 1: all real numbers, part 2: all real numbers

Use the function and its graph to determine the allowed inputs and possible outputs of the function. y=x^2-3

part 1: all real numbers, part 2:y>-3

Complete the factoring. x2+ 8x ​+ 7=(x+7)(x+? )

x+1 (see what 8-7 is and then what 7/7 is. They should be equal the same thing, which would be one and that is your answer)

Verify that the value is a solution to the equation. 2x−5=4−x; x=3

yes, because both sides of the equation equal 1. -(plug 3 into equation to see if both sides of equation equal the same thing).

Convert to scientific notation. 15,050

1.505x10^4 (plug into calculator to get answer)

A fair​ 12-sided die is rolled. The equally likely outcomes are​ 1, 2,​ 3, 4,​ 5, 6,​ 7, 8,​ 9, 10,​ 11, and 12. Find the probability of rolling a 12 or a 2.

1/6 (put in calculator 2/12 and simplify it)

Evaluate the expression. (1/9)^-3

729-(plug into calculator as is to get answer)

Solve the following equation. 36−11=5(x−9)

14-(multiply 5 and 9=5x-45 then add 45 to the left side to get x alone on the right, 36-11+45=70, then divide by 5x=14).

Find the following given f(x)=−7x−3.

a.-45, b.11, c.-3, d.-22/5

Find the volume and surface area of a sphere of radius 10 inches. Use π≈3.14. The volume of a sphere of radius r is V=4/3πr3. The surface area of a sphere of radius r is S=4*3.14^2

4186.7 in.^3, 1256 in.^2 (plug given number 10 into correct formulas..)

In City​ A, 4,238 of 5,820 ​residents, have reliable​ high-speed internet access. In City​ B, 15,221 of 20,389 residents have reliable​ high-speed internet access. In which town are residents more likely to have reliable​ high-speed internet​ access?

72.8%, 74.7%, City B is more likely to have high-speed internet access. (divide 4,238/5,820 and multiply by 100 to get percentages. Take higher percentage of the two for the most reliable internet access).

A family has an annual income of ​$32,400. Of​ this, 1/4 is spent for​ food, 1/5 for​ housing, 1/10 for​ clothing, 1/9 for​ savings, 1/4 for​ taxes, and the rest for other expenses. How much is spent for​ taxes?

8,100- multiply the fraction for taxes (1/4) by 32,400.

Assuming equal​ rates, 44 miles in 8 hours implies how many miles in 9 ​hours?

49.5-divide 44/8 and then multiply by 9

Complete the table by continuing the pattern. Then use the table to create the graph. x 0 1 2 3 4 5

subtract each number by two to get new answers. Then graph.

Write an equation to describe the variation. Use k for the constant of variation. w varies inversely as s

w=k/s (place w= and place k over s)

Find the value of the following expression. −​|35​|

-35 (keep the same number without the brackets)

Determine if the graph shows direct variation. If it​ does, state the constant of variation.

No, y does not vary directly as x

Solve the following equation. Check your solution. 8​(x+2​)=2​(4x+5​)+6

The solution is all real numbers.

What does it mean to say that data have a positive​ correlation?

When the value of one variable​ increases, the value of the other variable tends to increase.

The sales tax rate in New York City is 8.3​%. Find the tax charged on a purchase of $261​, and the total cost.

$21.66, $282.66-(take given percent 8.3 divide by 100, then multiply that answer by $261. Then add that answer to the given price $261.

Kyle's credit-card bill indicates that he owes ​$548. He sends a check to the​ credit-card company for ​$75​, charges another ​$118 in​ merchandise, and then pays off another ​$218 of the bill. What is the new amount that Kyle​ owes?

$373 (plug in calculator 548-75+118-218)

The following data represent the monthly cell phone bill for a​ person's phone for six randomly selected months. $35.76​, $41.75​, $39.21​, $38.53​, $43.68​, $48.24. Compute the​ mean, median, and mode phone bill.

$41.20-mean, $40.48-median, there is no mode. (to find the mean, add all numbers up and then divide by how many numbers there are. To find the median, put numbers least to greatest, cross off until you find the two middle numbers, add them up and then divide by 2. For the mode, it's the most occurring number).

A ​'70​% off​ sale' begins today at​ Wanda's Women's Wear. What is the sale price of​ women's wool coats normally priced at ​$260​?

$78-(change percent to decimal by dividing by 100, then take that answer and multiply by $260. Then take that answer and subtract it from $260 to get answer).

State the ordered pair of the point on the grid. Then state the axis or quadrant where it is located.

(-3,-5) quadrant 3

Decide which is the correct factored form of the polynomial. 4y2+29y−63

(4y-7)(y+9) -(keep the first number with letter (4y) and then it'l be the number with a minus and then plus sign.

Solve the equation. x+17+2x=−20−2x−23

-12-(combine like terms on each side-don't forget invisible one in front of x, then start to get rid of terms on the right side. once you have, divide by x to get answer).

Simplify. (−6x^3)(8x^9)

-48x^12 (multiply -6x and 8x which equals -48x, then add the exponents which is 12).

Select the lesser of the two given numbers. −7/4​, −9/5

-9/5-choose the number that's more into the negative.

Simplify. Write the answer using positive exponents only. (x^3)^−2

1/x^6 -(multiply exponents (6) and then put into fraction with 1 on top and x to the 6th on bottom).

If a grain of sand decreased in volume by 6 orders of​ magnitude, by what factor would its volume​ decrease?

1000000 -(to solve you would do 10^6)

Find the distance between the two points. ​(1​,9) and ​(−4​,21)

13-(-4-1)^2+(21-9)^2=169, then find square root

For the following​ table, compute the mass of 1,440 grams of radioactive element D left each day if element D loses half its mass every day. What type of decay is​ this?

1400, 720, 360, 180, 90, exponential-(multiply first given number by 1/2 and then continue to multiply answers by 1/2).

Combine like terms. 8x+10y+7x−2y

15x+8y

There are 110 calories per 28.4 grams of Cereal X. Find how many calories are in 45.44 grams of this cereal.

176-(take 110 and multiply it by 45.44, then divide by 28.4 to get answer).

The low temperatures for the past 6 days were −4​, 17​, 1​, −11​, −6​, and 15. Find the average low temperature for the past 6 days.

2-(plug all numbers into calculator as they are given and then divide by 6)

A police car is driving down the highway at 79 miles per hour. The average speed of the drivers on the highway is 61 miles per​ hour, with a standard deviation of 8 miles per hour. What is the police​ car's z-score? Is the speed of the police car unusually​ high?

2.25, unusually high-(subtract 79-61 and the divide by 8. If the answer is above 2, then it is unusually high).

Find the standard deviation of the set of data. 16​, 24​, 22​, 18​, 20

2.828 -(first find the mean, add up all the numbers and divide by 5, then subtract the mean from each individual given number, then square each of those answers in parentheses (-4)^2, after doing that with all the squares, add squared answers up and then divide by 5 (how many numbers total like with the mean) then find the square root of that answer to get final answer.

Add the polynomials. −6x2−10x+2+8x2−7x+8

2x^2-17x+10

A box of gumdrops was found to contain the number of gumdrops listed in the table. If one gumdrop is drawn at random from the​ box, what is the probability of drawing​ a(n) cherry ​gumdrop? TypeNumberLemon3Orange2Cherry6Grape9

3/10-(add up all the numbers and then take number from cherry and place it in a fraction and simplify it).

Use the quadratic formula to solve the equation. 2x2−x−3=0

3/2, -1

The​ day's high temperature in Phoenix, Arizona was recorded as 95°F. Use the formula C=5/9(F−32) to write 95°F as degrees Celsius.

35 degrees C (divide 5/9(95-32) to get answer).

How tall is this​ tree? 36ft, 5ft, h?

35.7 ft -(square both 36 and 5, then subtract 25 from 1296=1271. Then find square root of 1271 and round to get answer).

Factor the GCF. 6s^2+3s

3s(2s+1) -(start with 3s after the plus sign, then divide 6 by 3 to get 2s and then add 1).

Convert to standard notation. 5.63×10^5

563000 (type into calculator to get answer)

Solve for x. ​Don't forget to perform a check. 4/13x=20

65-(multiply 13 and 20, then divide by 4).

Jennifer decides to take a bike ride on a trail that is 15 kilometers long. Use dimensional analysis to convert this distance to miles.​ (One kilometer is approximately equal to 0.62​ miles).

9.3 -(multiply 15 and 0.62 to get answer)

The weight W of an aluminum flatboat varies directly with the length L of the boat. If a 11​-foot boat weighs 154 pounds, then what is the weight of a 7​-foot boat?

98 pounds-(divide 154/11, and then multiply answer by 7 to get final answer).

Find the following given f(x)=6x^2+13 a. f(8), b. f(-7), c. f(0), d. f(1/3) -(4 parts):

a. 397, b.307, c.13, d.41/3 (plug given numbers into equation in parentheses to get answers).

Solve the equation. square root7x=35

x=175-(square 35 and then divide by 7 to get answer)

Write an equivalent expression with positive exponents only. x^4y^-2

x^4/y^2 -(make the negative number positive and place them in fraction form)

Apply the vertical line test to determine if the graph represents a function.

y is not a function of x

Find the​ slope-intercept equation of the line that has the given characteristics. Slope −3 and​ y-intercept ​(0,8​)

y=-3x+8