The surface area of a cube varies directly as the square of the length of an edge. true or false

Answers

Answer 1

The surface area of a cube is 6 times the surface area of one face.

If the side of the cube is x, then the surface area of one side is x^2, and the total surface area is 6x^2 (because there are 6 squares making up the surface of the cube).

Here, we have A(x) = 6 x^2, which DOES vary directly as the square of the length of an edge, denoted by x.

Related Questions

A gas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month. the total of gas pumped at the station in a month is a random variable y (measured in 10,000 gallons) with a probability density function (p.d.f.) given by compute e(y)

Answers

Given that a gas station operates two pumps, each of which can pump up to 10,000 gallons of gas in a month and that the total of gas pumped at the station in a month is a random variable y (measured in 10,000 gallons) with a probability density function (p.d.f.) given by

[tex]f(y)=\begin{cases} cy, & \text{if} \ \ 0\ \textless \ y\ \textless \ 1 \\ (2-y), & \text{if} \ \ 1\leq y\ \textless \ 2 \\ 0, & \text{elsewhere} \end{cases}[/tex]

Part A:

The value of c that makes f(y) a pdf is obtained as follows:

[tex]F(\infty)= \int\limits^{\infty}_{-\infty} {f(y)} \, dy=1 \\ \\ \Rightarrow \int\limits^1_0 {cy} \, dy +\int\limits^2_1 {(2-y)} \, dy=1 \\ \\ \Rightarrow \left. \frac{cy^2}{2} \right]^1_0+\left[2y- \frac{y^2}{2} \right]^2_1=1 \\ \\ \Rightarrow \frac{c}{2} +4-2-2+ \frac{1}{2} =1 \\ \\ \Rightarrow \frac{c}{2} = \frac{1}{2} \\ \\ \Rightarrow \bold{c=1} [/tex]

Part B:

We compute E(y) as follows:

[tex]E(y)=\int\limits^{\infty}_{-\infty} {yf(y)} \, dy \\ \\ =\int\limits^1_0 {y^2} \, dy +\int\limits^2_1 {(2y-y^2)} \, dy \\ \\ =\left. \frac{y^3}{3} \right]^1_0+\left[y^2- \frac{y^3}{3} \right]^2_1 \\ \\ = \frac{1}{3} +4- \frac{8}{3} -1+ \frac{1}{3} \\ \\ =1[/tex]

Therefore, E(y) = 1.

Final answer:

The expected value E(y) cannot be computed without the given probability density function for the random variable y. The computation involves integrating the product of the variable and its probability density over its range. An example has been provided for how to compute the expected value with a hypothetical p.d.f.

Explanation:

To answer the student's question, it appears there may be a missing probability density function (p.d.f.) for the random variable y, which represents the total amount of gas pumped at the station in a month. Without the actual function, we cannot compute E(y), which is the expected value (mean) of the random variable y. In general, if we had the p.d.f., we would compute the expected value by integrating the product of the variable and its probability density over its range.

An example of how to compute the expected value if we had a p.d.f. f(y) might look like this:

E(y) = ∫ y × f(y) dy

For instance, if the p.d.f. were f(y) = ay (a being a constant) over the interval [0, 1], then:

Integrate the product of y and the p.d.f. over the interval:E(y) = ∫01 y × ay dy = a × ∫01 y² dyAfter computing the integral you would find the expected value E(y).

However, without the p.d.f. provided, we can only state the method, not the actual expected value.

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Your favorite football team has three games left to finish the season. the outcome of each game can be win, lose or tie. the number of possible outcomes is ____.

Answers

There are usually 16 games in a football season.
Since there's three more games, they've had 13 so far.

There are 27 combinations of outcomes.

There are 27 possible outcomes for your favorite football team's remaining three games.

What is probability?

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

If each game can have one of three possible outcomes (win, lose, or tie), then the total number of possible outcomes for all three games can be calculated by multiplying the number of possible outcomes for each individual game.

Since each game has three possible outcomes, the total number of possible outcomes for all three games is:

3 x 3 x 3 = 27

So there are 27 possible outcomes for your favorite football team's remaining three games.

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Determine whether the variable is qualitative or quantitative. explain your reasoning. miles per gallon that a car gets for highway driving

Answers

Miles per gallon that a car gets for highway driving is a quantitative variable. This is because a quantitative variable is something that can be quantified, or measured. For instance, you can say your car gets 22 miles per gallon. It is not a qualitative observation because a qualitative observation is something that is merely observed, not measured.

Kurt and Maria’s high school is having a newspaper drive.The goal is to collect 3,585 pounds of newspapers. So far, 21% of the goal has been reached. Kurt estimated the number of pounds of newspapers collected by finding 10% of 3,600 and then multiplying the result by 2. Maria estimated the number of pounds of newspapers collected by finding mc006-1.jpg of 3,600. Who is right, and why?

Answers

Both Kurt and Maria are right, because 3585 will be rounded up to 3600 durning intermediate calculations and 21% of this amount can be approximated by either finding 10% of 3600 and multiplying the result by 2 or by finding [tex]\frac{1}{5}[/tex] of 3600.

Kurt and Maria were both right

perform the following conversions convert 5.0 cm to m

Answers

5 centimeters is 0.05 meters

To convert 5.0 cm to m, use the conversion factor of 1 m = 100 cm to get the result of 0.05 m.

Convert 5.0 cm to m:

1 m = 100 cm, which means 1 cm is 0.01 m.

Therefore, 5.0 cm is equal to 5.0 x 0.01 m = 0.05 m.

Which shows the correct simplification of product of powers?
1.) 78 · 7-4 = 78· (–4) = 7–32
2.)78 · 7–4 = 78 ÷ (–4) = 7–2
3.)78 · 7–4 = 78 + (–4) = 74
4.)78 · 7–4 = 78 - (–4) = 712

Answers

The power symbols are missing.

I can infere that the product intended to simplify is (7^8) * (7^-4)., because that permits you to use the rule of the product of powers with the same base.

That rule is that the product of two powers with the same base is the base raised to the sum of the powers is:

(A^m) * (A^n) = A^ (m+n)

=>(7^8) * (7^-4) = 7^ [8 + (- 4) ] = 7^ [8 - 4] = 7^4, which is the option 3 if the powers are placed correctly.

The answer choice which shows the correct simplification of product of powers is:

78 · 7–4 = 78 + (–4) = 74

What is Product of Powers?

This refers to the mathematical property which states that when there is a multiplication of two powers that have the same base, then there would be the addition of exponents.

From the given choices, we can see that the powers are not given, so we can solve using inference.

This posits that (7^8) * (7^-4) was the product that was intended to be simplified and this law shows:

(A^m) * (A^n) = A^ (m+n)

Hence, if we add the powers, then the correct answer would be option C because they are of the same base.

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jake said he has 8/100 of a dollar in his pocket Margie said that the decimal for 8/100 is 0.8 what error did she make. what is the decimal form for 8/100?

Answers

The 8 is in the tenths place it would look like 8/10 .8 its .08 for 8/100

margie's mistake was where she placed the decimal point. the correct answer is 0.08.

Graph the line y+3=2(x-1) first identify the slope of the line

Answers

First you need to simplify the equation.

y + 3 = 2(x - 1)
y + 3 = 2x - 2

Then you need to put that into slope-intercept form (y = (slope)x + (y intercept))

y + 3 = 2x - 2
-3 -3
y = 2x - 5

The slope is the coefficient of x, so 2 is the slope of the line.

which number is greater 67.89 and 67.98

Answers

67.98 lol what king of question is that??

.98 is greater than .89
so 67.98 is greater than 67.89

answer
67.98 is greater

Use the chinese remainder theorem to solve the systems of congruences:
a. find x mod 77 if x ≡ 2 (mod 7) and x ≡ 4 (mod 11).
b. x ≡ 2 (mod 3), x ≡ 3 (mod 4), x ≡ 1 (mod 5).

Answers

(a) Suppose we let

[tex]x=2+4=6[/tex]

Modulo 7, we're left with [tex]x\equiv2+4\pmod7=6\mod7[/tex], but we want a remainder of 2, so multiply 4 by 7 to assure that that remainder vanishes. So now

[tex]x=2+4\cdot7=30[/tex]

and [tex]x\equiv2\pmod7[/tex], but modulo 11, we have [tex]x=\equiv2+28\equiv2+4\equiv6\pmod{11}[/tex]. But we want the remainder to be 4, so multiply the first term by 11 to guarantee this. So we write

[tex]x=2\cdot11+4\cdot7=50[/tex]

but now, we get a remainder of 1 modulo 7 and 6 modulo 11. To fix the first case, multiply the first term by 2. For the second case, first find the inverse of 6 modulo 11. We have [tex]2\cdot6=12[/tex], and [tex]12\equiv1\pmod{11}[/tex], so the inverse is 2. Multiply the second term by 2, so that the second term's remainder modulo 11 becomes 1. Then multiply by 4, so that now

[tex]x=2\cdot11\cdot2+4\cdot7\cdot2\cdot4=268[/tex]

We have

[tex]x=268=3\cdot77+37\implies x\equiv37\pmod{77}[/tex]

(b) This is done similarly. Modulo 3, we want a remainder of 2, so we can start with

[tex]x=2+3+3=8[/tex]

Then taken modulo 4, we need to multiply the first term by 2 and the third term by 4 to ensure the remainder becomes 3. The second term can be left alone.

[tex]x=2\cdot2+3+3\cdot4=19[/tex]

Now taken modulo 5, we can multiply the first two terms by 5 and the third term by the inverse of [tex]3\times2\equiv12\equiv2\pmod5[/tex]. We have [tex]3\cdot2\equiv6\equiv1\pmod5[/tex], so we multiply by 3.

[tex]x=2\cdot2\cdot5+3\cdot5+3\cdot4\cdot3=71[/tex]

Now

[tex]x=71=1\cdot(3\cdot4\cdot5)+11=1\cdot60+11[/tex]

which means the smallest positive solution for the system would be [tex]x=11[/tex].

What type of solution does the system of linear equations have? 2x - 6y = 8 -x + 3y = 10

Answers

Let's actually find the solution of

2x - 6y = 8
-x + 3y = 10

Let's use the addition/subtraction method. Multiply the 2nd equation by 2, obtaining

2x - 6y = 8
-2x + 6y = 20
--------------------
0 + 0 = 28

Since this can never be true, the system of linear equations

2x - 6y = 8
-x + 3y = 10

has no solution.

Answer:

No Solution

Step-by-step explanation:

Did the test and got this question correct :>

Ignore the bottom...the top question is what I’m struggling with

Answers

check the picture below.

so, an approximation could just be 48,000,000.

If Mr. Khans buys 15 staplers, it would cost him $254.85. How would you write this using function notation?

Answers

f(x) = 15x.......with f(x) being the total cost and x being the number of staplers

254.85 = 15x
254.85/15 = x
16.99 = x.....so each stapler costs $ 16.99

Answer:

f(x) = don't spend more than 200 dollars on staplers

Step-by-step explanation:

What is the slope of the line represented by the equation y = 1/4x – 3?

Answers

The slope is always the number before the x variable, so the slope is 1/4.

Suppose you buy a piece of office equipment for $17,000. After 3 years you sell it for a scrap value of $3,000. The equipment is depreciated linearly over 3 years. The rate of depreciation of the piece of equipment is

Answers

Depreciation amount = Purchase Price - Scrape Value
Depreciation amount = $17,000 - $3,000
Depreciation amount = $14,000

depreciation rate = $14,000/3 years
depreciation rate= $4667.67

The rate of depreciation of the piece of equipment is 27.45%.

Given that,

The cost of office equipment is $17,000.The number of years is 3And, the scrap value is $3,000.

Based on the above information, the depreciation should be

= (Office equipment cost - scrap value) ÷ (Office equipment cost × number of years)

= ($17,000 - $3,000) ÷ ($17,000 × 3)

= $14,000 ÷ $51,000

= 27.45%

Therefore we can conclude that the rate of depreciation of the piece of equipment is 27.45%.

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an airplane approaching its destination has begun it's final descent into the airport. if the plane descends at a rate of 300 feet per minute. what is the change in altitude of the plane after 4 minutes?

Answers

300 * 4 = 1200
you have descended 1200 feet in 4 minutes

Joanne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months there is $300 in the account. Determine the constant rate of change of the account.

Answers

The constant rate is 50 dollars per month. I hope this helps!

Answer:

The constant rate of change of the account is $50 or Increasing by $50 per month.

Step-by-step explanation:

Consider the provided information.

Joanne is depositing money into a bank account. After 3 months there is $150 in the account. After 6 months there is $300 in the account.

Rate of change is known as how one quantity change in relation to other.

The rate of change can be calculated as:

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Now use the above formula to calculated the rate of change.

[tex]\frac{300-150}{6-3}[/tex]

[tex]\frac{150}{3}[/tex]

[tex]50[/tex]

Hence, the constant rate of change of the account is $50 or Increasing by $50 per month.

linear graphing y= -2x

Answers

Let x = 0. What do you get for y?
This gives you one point.

Then let x = 1. What do you get for y.
This gives you a second point.

A theater can seat 864 people. The number of rows is 5 less than the number of seats in each row. How many rows of seats are there?

Answers

There should be 27 rows of 32 seats.

Final answer:

To determine the number of rows in a theater that can seat 864 people, with the number of rows being 5 less than the number of seats per row, we set up the equation x(x-5)=864. Solving this quadratic equation, we find that there are 31 rows of seats.

Explanation:

To solve for the number of rows in the theater, let's denote the number of seats in each row as x and the number of rows as x - 5. Since the product of the number of seats in each row and the number of rows will give us the total seating capacity, we can write down the equation:

x(x - 5) = 864

Expanding the equation, we get:

x2 - 5x - 864 = 0

Using the quadratic formula or factoring, we find that x = 36. Therefore:

The number of rows is x - 5 = 36 - 5 = 31.

So, the theater has 31 rows of seats.

what is the answer ×-(-150)=200

Answers

x - (-150) = 200

x + 150 = 200

x + 150 (-150) = 200 (-150)

x = 200 - 150

x = 50

hope this helps

a few questions i need help with.

Answers

question 1:
The first step is getting rid of the denominators by multiplying all terms by 3. This is done using multiplicative property.
The second step is getting rid of the brackets using the distributive property.
The third and fourth steps are isolating the term containing the x on one side of the inequality using addition or subtraction property of order
The last step is getting rid of the coefficient of the x using the division property of order.

So, the correct order of choices is:
1- multiplicative property..
2- distributive property.
3- addition or subtraction property of order
4- addition or subtraction property of order
5- division property of order.

question 2:
The first step is getting rid of the brackets using the distributive property.
The second and third steps are isolating the term containing the x on one side of the inequality using addition or subtraction property of order
The last step is getting rid of the coefficient of the x using the division property of order.

So, the correct order of choices is:
1- distributive property.
2- addition or subtraction property of order
3- addition or subtraction property of order
4- division property of order.

Students can take MATH 080 between one and four times. The student's tuition for MATH 080 is $ 548.00 If the tuition is increased 6% AFTER 2 ATTEMPTS, what is the student's one semester tuition after the 2nd attempt? In this situation what is the total tuition for taking MATH 080 the allowed four times

Answers

2nd attempt carries a price of 6% extra, so (6/100) * 548 is 32.88, so 548 + 32.88, the price is 580.88.

for the 3rd attempt 6% extra of that, (6/100) * 580.88, is 34.8528, so the price is 615.7328.

4th attempt is 6% extra of that, (6/100) * 615.7328, 36.943968, adding that will give us 652.676768.

At 1pm, there was 16 seagulls on the beach. At 3pm, there were 60 seagulls. What is the constant rate of change

Answers

22 seagulls per hour... cx

1/3 = 16/60
Cross Multiply
48/60=4/5
The constant rate of change is 4/5

Which equation has no solution?
A) 2.3y + 2 + 3.1y = 4.3y + 1.6 + 1.1y + 0.4
B) 32x + 25 - 21x = 10x
C) 5/8 x + 2.5 = 3/8 x + 1.5 + 1/4 x
D) 1/3 + 1/7 y = 3/7 y
PLEASE HELP!!
| THANK YOU SO MUCH |

Answers

the equation that have no solution is c

Answer: c

Step-by-step explanation:

Carly is making 3 1/2 batches of biscuits. If one batch calls for 2 1/3 cups of floor, how much flour will she need?

Answers

In this question, Carly needs to make 3.5 batches of biscuit and one batch equal to 2 1/3 cups of flour. Then you will get an equation look like this:

1 batch of biscuit= 2 1/3 cups of flour

Then 3.5 batches of cookies would be:
3.5 batches of biscuit * (2 1/3 cups of flour/ batch of biscuit)= 49/6 cups of flour= 8.16 cups of flour

What was the most direct effect of the establishment of the Queen’s Men?

a. New plays were written every year.

b. The queen visited Whitehall Palace.

c. The Puritans were outraged.

d. Drama received royal approval.

Answers

Answer:

C) The Puritans were outraged.

Step-by-step explanation:

Answer:

Step-by-step explanation:

trust

Is the subset w = {(x, y, z) | z = 1} ⊂ r 3 a vector subspace of r 3 ? explain why or why not?

Answers

No, [tex]W[/tex] is not a subspace of [tex]\mathbb R^3[/tex] because it doesn't contain the zero vector.

an equation is shown below. 3x-10x+5=5x+17 what is the value of x that makes the equation true?

Answers

collect like terms;

3x-10x=-7x

-7x+5=5x+17

move the variable to the left and change sign

-7x+5=5x+17

move the constant to the right and change sign

-7x-5x+17-5

collect the like terms

-12x=17-5

subtract the numbers

-12x=12

divide both sides by -12

your answer is: x= -1

Find the prime factorization of the follwing numbers: (write p0 if a prime does not appear in the given number.)

Answers

18. There are Personal Muth Trainer library. The 318 fiction books in the class ne number number of nonfiction books is 47 less than of fiction books. Part A About how many nonfiction books are there in the class library? Explain. Part B How many fiction and nonfiction books are there in the class library altogether? Show your work.

a pump is running at 6.4 quarts per minute. how many gallons per hour is this?

Answers

60*6.4 quarts = 384 quarts = 96 Gallons/hr

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