Han has 10 cubes, each 5 inches on a side. A) Find the total volume of Han’s cubes. Express your answer as an expression using an exponent. B) Find the total surface area of Han’s cubes. Express your answer as an expression using an exponent.

Answers

Answer 1

Answer:

A) Vol_10_cubes  = 2*(5^4) inch^3

B) Area_10_cubes = (2^2)*3*(5^3)  inch^2

Step-by-step explanation:

A)The volume of a cube, as all sides are equal:

Vol_cube = (side)^3

side = 5 inches

Vol_cube  = 5^3 inch^3

Since we have 10 cubes

10 = 2*5

Vol_10_cubes  = 2*(5^4) inch^3

B) A cube has six faces, each with area equal to its squared side

Area_cube = 6*(side)^2

Area_cube = 6*(5)^2  inch^2

Area_10_cubes = 2*5*6*(5)^2  inch^2

Area_10_cubes = (2^2)*3*(5)^3  inch^2

Answer 2
Final answer:

The total volume of Han's cubes is given by the expression 10 × 5³ cubic inches, and the total surface area can be expressed as 10 × 6 × 5² square inches.

Explanation:

The question asks for the calculation of volume and surface area of cubes with a given side length.

Volume Calculation

To find the volume of a single cube, we use the formula V = s³, where s is the length of a side of the cube. Because each side of the cube is 5 inches, the volume of one cube is V = 5³ inches³, which equals 125 cubic inches. Now, Han has 10 cubes, so the total volume is 10 times the volume of one cube, which can be expressed as:

Total Volume = 10 × 5³ inches³

Surface Area Calculation

The surface area of a single cube is found using the formula SA = 6s², since there are six sides to a cube. With a side length of 5 inches, the surface area of one cube is SA = 6 × 5² square inches, which equals 150 square inches. For 10 cubes, the total surface area is 10 times the surface area of one cube, which can be expressed as:

Total Surface Area = 10 × 6 × 5² square inches


Related Questions

The conditional relative frequency table below was generated by column using frequency table data comparing the number of calories in a meal to whether the meal was prepared at home or at a restaurant.

A nutritionist attempts to determine an association between where food is prepared and the number of calories the food contains. Which is most likely true?

A. An association cannot be determine because the value 0.55 is similar to the value 0.45
B. There is an association because the value 0.15 is not similar to the value 0.55
C. There is an association because the sum of each column is 1.0.
D. An association cannot ve determined because the sum of the rows going across is not 1.0.

Answers

Answer:

B. There is an association because the value 0.15 is not similar to the value 0.55

Step-by-step explanation:

Based on the above picture, for the nutritionist to determine whether there is an association between where food is prepared and the number of calories the food contains, there must be an association between two categorical variables.

The conditions that satisfy whether there exists an association between conditional relative frequencies are:

1. When there is a bigger difference in the conditional relative frequencies, the stronger the association between the variables.

2. When the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables.

For the given conditional relative frequency, we can see that there exists a significant difference between the columns of the table in the picture because 0.15 is significantly different from 0.55 and 0.85 is significantly different from 0.45

We can conclude that there is an association because the value 0.15 is not similar to the value 0.55

Answer:There is an association because the value 0.15 is not similar to the value 0.55.

Step-by-step explanation:

Which ordered pair is a solution of the equation? 7x-2y=-5

Answers

answer X= 5 over 7 and 2 over 7y step by step explaination add 2y on both sides u cancelled -2y and positive 2y u bring down 7X u get 7X=-5+3 then u divide and u get that answer yw have a nice day mark me brainliest

Answer:

2y=-x7

Love mORgan

Find the missing number: 8.4(1.5 + 2.3) = 12.6 +

Answers

Answer:

19.32

Step-by-step explanation:

One way to find the missing number is to get the value of the left side of the equation first.

8.4(1.5 + 2.3) = 31.92

Now we need to take that value and subtract it to the value on the right side of the equation.

31.92 - 12.6 = 19.32

So we have:

8.4(1.5 + 2.3) = 12.6 + 19.32

31.92 = 31.92

Answer:

The required number is 19.32

Step-by-step explanation:

Consider the provided expression.

Let the missing number is x.

[tex]8.4(1.5 + 2.3) = 12.6 +x[/tex]

Add the numbers as shown.

[tex]8.4(3.8) = 12.6 +x[/tex]

Open the parentheses.

[tex]31.92= 12.6 +x[/tex]

Subtract 12.6 from both the sides.

[tex]31.92-12.6= 12.6-12.6 +x[/tex]

[tex]x=19.32[/tex]

Hence, the required number is 19.32

What is the area of this triangle? please help me.

Answers

Answer:

6

Step-by-step explanation:

Area of a triangle: bh/2

4*3/2=6

Answer:

6 units²

Step-by-step explanation:

The area (A) of a triangle is calculated using the formula

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = DE = 3 units and

h is the distance from the vertex F to DE = 4 units, hence

A = [tex]\frac{1}{2}[/tex] × 3 × 4 = 6 units²

Javier’s Bakery sells donuts in packages of 3 and cookies in packages of 5 today the backers sold the same number of donuts and cookies . What is the smallest number of donuts that the bakery could have sold?please help me

Answers

The answer is A.) 5 because it’s the smaller number

suppose that 17 inches of wire cost $0.85 at the same rate how many inches of wire can be bought for $0.55​

Answers

Answer:

11 inches

Step-by-step explanation:

17/0.85 * 0.55

20 * 0.55

11.

An Antique Collector want to know the age of a particular chair in a shop Statistical or not statistical

Answers

Answer:

[tex]\boxed{\bold{Not \ Statistical}}[/tex]

Step By Step Explanation:

Statistical: A survey, branch or mathematics consisting of data collection, organization, analysis, interpretation and presentation.

A statistical question deals with social problems, people, or something that must be studied and data gained. Statistical questions must have data sets and data gained. They also must have answers that vary from side to side or opinion to opinion, in order to be qualified as a 'statistical question'.

"An Antique Collector wants to know the age or a particular chair in a shop"

                                                V

Statistical                       Not Statistical

[tex]\boxed{\bold{>}}[/tex] This is not a statistical question because there is no data that needs to be collected, no surveys that need to be filled out and no analysis, interpretation and presentation. The answer to this question does not vary. It is simply a fact.

Find the area thanks

Answers

16 x 14 = 224

[tex]answer = {224cm}^{2} [/tex]

One of the roots of the equation 10x2−33x+c=0 is 5.3. Find the other root and the coefficient c.

Answers

Answer:

1. The other root is [tex]-2[/tex]

2. c=-106

Step-by-step explanation:

The given equation is [tex]10x^2-33x+c=0[/tex].

If [tex]5.3[/tex] is a solution to the given quadratic equation, then [tex]x=5.3[/tex] must satisfy this equation.

[tex]10(5.3)^2-33(5.3)+c=0[/tex]

[tex]280.9-174.9+c=0[/tex]

[tex]106+c=0[/tex]

[tex]c=0-106=-106[/tex]

We now substitute [tex]c=-106[/tex] into the given equation to obtain;

[tex]10x^2-33x-106=0[/tex].

Comparing to the general equation;

[tex]ax^2+bx+c=0[/tex], we have a=10, b=-33 and c=-106.

Recall the quadratic formula;

[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]

We now use the quadratic formula to obtain;

[tex]x=\frac{--33\pm \sqrt{(-33)^2-4(10)(-106)} }{2(10)}[/tex]

This implies that;

[tex]x=\frac{33\pm \sqrt{5329} }{20}[/tex]

[tex]x=\frac{33\pm73}{20}[/tex]

[tex]x=\frac{33-73}{20}[/tex] or [tex]x=\frac{33+73}{20}[/tex]

[tex]x=\frac{-40}{20}[/tex] or [tex]x=\frac{106}{20}[/tex]

[tex]x=-2[/tex] or [tex]x=5.3[/tex]

Hence the other root is [tex]-2[/tex]

Claire made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Claire doesn’t touch the money in her account, she can find the amount she’ll have the next year by multiplying her current amount by 1.03. A) how much money will Claire have in her account after 1 year? After 2 years? B) how much money will Claire have in her account after 5 years? Explain your reasoning. C) Write an expression for the amount of money Claire would have after 30 years if she never withdraws money from that account.

Answers

We can make and use the equation: A = 160( 1.03 )^y: A = amount, 160 = amount put in, 1 + .03 = 1.03 = interest, and y as the number of years, as the money is compounded every year. (This is the compound interest equation, but I put in the numbers)

A) 160 * 1.03 = $164.80, 160 * 1.03² = $169.744 ≈ $169.74

B) 160 * 1.03⁵ = 185.48385 ≈ $185.48

The expression is the same as saying (((((160 * 1.03)1.03)1.03)1.03)1.03). This is like multiplying 160 * 1.03, which gives the amount for the first year. Then, that amount is multiplied by 1.03, which is the amount for the second year. This isi repeated until 5 years.

C) 160(1.03)³⁰

Final answer:

Claire will have $164.80 after 1 year and $169.74 after 2 years in her savings account due to the 3% interest rate. After 5 years, she will have $185.86. The expression for the amount after 30 years is $160 × (1.03)³⁰.

Explanation:

When Claire deposited $160 into her savings account at a 3% interest rate per year, she initiated a process of compound interest. This means each year, the amount of money in her account will increase by 3% of the amount from the previous year. The way to find out how much money she will have after a certain number of years is to multiply the initial amount by 1.03 raised to the power of the number of years.

Interest After 1 Year

After 1 year: $160 × 1.03 = $164.80

Interest After 2 Years

After 2 years: $160 × (1.03)² = $169.74

Interest After 5 Years

After 5 years: $160 × (1.03)⁵ = $185.86. This is calculated using the formula for compound interest: $160 × 1.03 raised to the fifth power.

Interest After 30 Years

To write an expression for the amount of money she will have in 30 years: $160 × (1.03)³⁰. This follows the general formula for compound interest, which is the initial amount times one plus the interest rate raised to the number of years.

The numbers of hours that 12 students say they typically spend on homework in a week are 2, 0, 10, 8,10, 8, 8, 8, 10, 10, 8, and 8. What is the mean number of hours? What are the outliers in the data set?

Answers

Answer:

The mean is 7.5 and the outliers are 0 and 2

Step-by-step explanation:

To find the mean, add all of the numbers together and divide by the amount of numbers.

2 + 0 + 10 + 8 + 10 + 8 + 8 + 8 + 10 + 10 + 8 + 8 = 90

90/12 = 7.5

To see the outliers, look for the numbers far away from the mean.

What is the axis of symmetry for f(x) = 2x2 + 4x + 2?
Choices
x = −3

x = −1

x = 1

x = 3

Answers

Answer:

-1

Step-by-step explanation:

to find the axis of symmetry, the formula is X= -b/ 2a

a is the 2 from 2x2

and b is 4 from 4x

then plug them to the formula

-b= -4 because of the negative in -b

and 2a is 2(2)

-4/4 is -1

so x= -1

hope im right

hope it helps

6/10+39/100 find the sum

Answers

The answer is-

Exact form: 99/100

Decimal form: 0.99

what is 3(x-4)-7=(2x-3)

Answers

Solve for x by simplifying both sides of the equation, then isolating the variable.

So the answer to your question is :

x = 16.

Hope this helps,

Davinia.

Answer:

x = 16

Step-by-step explanation:

distribute parenthesis on both sides and simplify

3x - 12 - 7 = 2x - 3

3x - 19 = 2x - 3 ( subtract 2x from both sides )

x - 19 = - 3 ( add 19 to both sides )

x = 16

A jar contains balls numbered 1 to 10. Two balls are drawn with replacement. What is the probability that both balls are numbered 2 or less?


Answers

Answer:

Step-by-step explanation:

The number of ways that you can draw 2 balls without restriction is 10 * 10 = 100

Two balls will give you 2 or less (meaning 1) or 2*2 = 4

Four ways are possible

2  and 2

2 and 1

1 and 2

1 and 1

4/100 = 1/25 is the probability of making this happen.

6....................

Answers

Answer:

option (a)

x - √7x / x - 7

Step-by-step explanation:

Given the expression in the question

  √x / (√x + √7)

 There are 3 steps to follow

Multiply numerator and denominator by a radical that will get rid of the radical in the denominator. Make sure all radicals are simplified. Simplify the fraction if needed.

Step 1

Multiply by √x - √7

√x (√x - √7) /  (√x + √7)(√x - √7)

√x .√x - √7.√x / (√x + √7)(√x - √7)

Step 2

a² - b² = (a+b)(a-b)

√x² - √7x / √x² - √7²

Step 3

x - √7x / x - 7

Graph the solution for the following system of inequalities. Click on the graph until the correct solution is displayed. x + y > 3 x + y < -4

Answers

Answer:

The graph for the following system of inequalities is attached below.

Step-by-step explanation:

The given system of inequalities is

[tex]x+y>3[/tex]                    .... (1)

[tex]x+y<-4[/tex]                  .... (2)

From inequality (1) and (2) it is clear that (x+y) is greater than 3 adn 3 is not less than -4. So, the given system of inequality has no feasible reason or solution.

The related equation of first inequality is

[tex]x+y=3[/tex]

Put x=0 to find the y-intercept.

[tex]0+y=3\Rightarrow y=3[/tex]

The y-intercept is 3.

Put y=0 to find the x-intercept.

[tex]x+0=3\Rightarrow x=3[/tex]

The x-intercept is 3.

The related equation of second inequality is

[tex]x+y=-4[/tex]

Put x=0 to find the y-intercept.

[tex]0+y=-4\Rightarrow y=-4[/tex]

The y-intercept is -4.

Put y=0 to find the x-intercept.

[tex]x+0=-4\Rightarrow x=-4[/tex]

The x-intercept is -4.

The related lines are dotted line because the sign of inequalities are > and <.

Check each inequality be (0,0).

[tex]0+0>3[/tex]

[tex]0>3[/tex]

This statement is false. So the shaded region of first inequality is opposite sides of the origin.

[tex]0+0<-4[/tex]  

[tex]0<-4[/tex]  

This statement is false. So the shaded region of first inequality is opposite sides of the origin.

The graph for the following system of inequalities is attached below.

Answer:

This is the correct graph on Odyssey :)

Choose the correct answer. Distance between 2 airports = 1,450 miles. Average speed of airplane = 350 mph. Travel time by bus after arrival at airport = 20 minutes. Total travel time = _____ hours.

Please do not round

Answers

Final answer:

Using the given information, the total travel time by airplane and bus is calculated as 4.47616 hours, which includes flying time and additional travel time by bus.

Explanation:

To calculate the total travel time by airplane including the additional travel time by bus, we must first find out the time taken by the airplane to cover the distance between the two airports. This can be done by dividing the distance by the airplane's average speed. Afterward, we add the bus travel time to get the total travel time.

The time taken by the airplane to cover 1,450 miles at an average speed of 350 mph is calculated by dividing distance by speed: 1,450 miles ÷ 350 mph = 4.142857 hours. Note that we do not round this number to maintain accuracy.

Next, we convert the bus travel time of 20 minutes into hours: 20 minutes ÷ 60 minutes per hour = 0.3333 hours.

Now, we add both the airplane and bus travel times together: 4.142857 hours + 0.3333 hours = 4.47616 hours total travel time.

Solve for the roots in the equation below. In your final answer, include each of the necessary steps and calculations. Hint: Use your knowledge of polynomial division and the quadratic formula.

x3 - 27 = 0

Answers

Answer:   3

Step-by-step explanation:

[tex]x^3-27=0\\\\x^3=27\\\\\sqrt[3]{x^3}=\sqrt[3]{27}\\\\x=\sqrt[3]{3\cdot 3\cdot 3} \\\\x=3[/tex]

What is the range of the graph

Answers

Answer:

Range: all real numbers greater than or equal to  2

Step-by-step explanation:

The range is the possible numbers that the output can take

Y can be any number greater than or equal to 2

Range: all real numbers greater than or equal to  2

As part of your training schedule you plan to jog once a week around the reservoir shown below on the map.


One lap along the perimeter of the reservoir is 25 cm. What is the actual length of a lap?

Answers

Final answer:

The actual length of a lap cannot be determined without the scale of the map. The 25 cm measurement seems to be from the map, so without knowing the real-world equivalent of the map's measurements, we can't find the actual distance.

Explanation:

The length of a lap around the reservoir cannot be directly determined from the information given. The measurement provided (25 cm) appears to be a distance measured on a map or plan of the area, and not in real life. In order to convert that measurement into a real-world distance, we need the scale of the map. A map's scale is typically represented as a ratio that indicates the relationship between a certain distance on the map and the real-world distance it represents.

For example, if the map's scale was 1 cm : 1 km, then a measurement of 25 cm on the map would represent a real-world distance of 25 km. However, without the scale, we cannot accurately determine the actual length of a lap around the reservoir. This concept is extremely important in geography and cartography as well as in mathematical problems dealing with maps and scales.

Learn more about Map Scale here:

https://brainly.com/question/24486949

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Which of the following rules is true for all values in the input-output table below?

A x + 1 = y


B x + 2 = y


C 2x = y


D 3x − 2 = y

Answers

The answer is B.
If you multiply x by 2 then you should get y.

Answer:

The answer is b

thank you

What is 6x^2-12x+y+13=0 in vertex form of parabolas

Answers

Answer:

[tex]y=-6(x-1)^{2}-7[/tex]

Step-by-step explanation:

we have

[tex]6x^{2} -12x+y+13=0[/tex]

Convert to vertex form

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

[tex]y+13=-6x^{2} +12x[/tex]

Factor the leading coefficient

[tex]y+13=-6(x^{2} -2x)[/tex]

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

[tex]y+13-6=-6(x^{2} -2x+1)[/tex]

[tex]y+7=-6(x^{2} -2x+1)[/tex]

Rewrite as perfect squares

[tex]y+7=-6(x-1)^{2}[/tex]

[tex]y=-6(x-1)^{2}-7[/tex] -----> equation of the parabola in vertex form

The vertex is (1,-7) is a maximum, the parabola open downward

Final answer:

To convert 6x^2 - 12x + y + 13 = 0 to vertex form, follow the steps to complete the square and rewrite the equation as (x - 1)^2 = -y/6 - 7/6.

Explanation:

The equation 6x^2-12x+y+13=0 is in the general form of a quadratic equation. To convert it into the vertex form, we need to complete the square.

First, let's group the x terms together: 6x^2 - 12x = -(y + 13).

Next, let's complete the square: 6(x^2 - 2x) = -(y + 13).

Now, we can add (2/2)^2 = 1 to both sides to complete the square: 6(x^2 - 2x + 1) = -(y + 13) + 6.

Simplifying further, we get 6(x - 1)^2 = -y - 7.

Finally, we can write the equation in vertex form by dividing both sides by 6: (x - 1)^2 = -y/6 - 7/6.

Learn more about Quadratic equations here:

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Help plz !! Need this to graduate

Answers


[tex] \sqrt[3]{x {}^{5} } = x \sqrt[3]{x {}^{2} } [/tex]

Find the area of the triangle that has a base of 5in -‘d a height of 3 3/4

Answers

Answer:

its either c or b

Step-by-step explanation:

formula: 1/2*b*h or 1/2*5*3+3/4

the answer i got was 33/4

There are bytes in a gigabyte. There are bytes in a megabyte. How many times greater is the storage capacity of a 1-gigabyte flash drive than a 1-megabyte flash drive?

Answers

Answer: third option.

Step-by-step explanation:

You know that:

- There are 10⁹ bytes in a gigabyte.

- There are 10⁶  bytes in a megabyte.

Then, to know how many times greater  the storage capacity of a 1-gigabyte flash drive is than a 1-megabyte flash drive, you must divide 10⁹ bytes by 10⁶ bytes.

Remember the quotient of powers property:

[tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex]

Then:

[tex]=\frac{10^9}{10^6}=10^3=1,000[/tex] times greater

 

Answer:

1,000

Step-by-step explanation:

1.simplifyyyyyyyyyyyy

Answers

Answer:

Choice A

Step-by-step explanation:

We apply the law of exponents;

[tex](a^{b})^{c}=a^{bc}[/tex]

[tex]\sqrt{0.08^{12}}=(0.08^{12})^{\frac{1}{2}}[/tex]

applying the law of exponents we simply multiply 12 and 1/2 to get;

[tex]0.08^{6}[/tex]

riddle time I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I? if hard text me and i will give you the answer

Answers

Answer:

Is it a map? To me that makes the most logical sense.

Answer:

A map

Step-by-step explanation:

A map has cities, mountains, and water. It doesn't show houses, trees, or fish because it doesn't show specific things.

Please !!! Someone help me

Answers

answer is the last one D

pls mark brainliest

The answer is D good luck

Point P is the image of P -2,-2 under a translation by 1 unit to the left and 3 units down.

Answers

Answer:

(- 3, - 5)

Step-by-step explanation:

A translation of 1 unit left, subtract 1 from x- coordinate

A translation of 3 units down, subtract 3 from y- coordinate

The translation rule is

(x, y) → (x - 1, y - 3), hence

(-2, - 2) → (- 2 - 1, - 2 - 3) → (- 3, - 5)

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