A large rectangular prism has a length of 2 and 1/2 inches, a width of 4 inches, and a height of 1 and 1/2 inches. A smaller cube has a length, width, and height of 1/2 of an inch. How many of the smaller cubes will fit into the larger rectangular prism?

Answers

Answer 1

Answer:

120 cubes

Step-by-step explanation:

Volume of prism and cube:

We can find the number of smaller cubes that will fit into larger rectangular prism by dividing the volume of prism by the volume of cube.

Rectangular prism:

[tex]\sf l = 2\dfrac{1}{2} =\dfrac{5}{2} \ inches\\\\w = 4 \ inches\\\\h =1\dfrac{1}{2}=\dfrac{3}{2} \ inches\\[/tex]

[tex]\sf \boxed{\text{\bf Volume of rectangular prism= l * w * h}}[/tex]

[tex]\sf =\dfrac{5}{2}*4*\dfrac{3}{2}\\\\= 5*1*3\\\\= 15 \ in^3[/tex]

Cube:

[tex]\sf side = \dfrac{1}{2} \ inches\\[/tex]

[tex]\sf \boxed{\text{ \bf Volume of cube = side * side *side}}[/tex]

[tex]\sf =\dfrac{1}{2}*\dfrac{1}{2}*\dfrac{1}{2}\\\\ =\dfrac{1}{8} \ in^3[/tex]

Number of cubes = Volume of prism ÷ volume of a cube

[tex]\sf = 15 \div \ \dfrac{1}{8}\\\\=15 *\dfrac{8}{1}\\\\= 120[/tex]

120 cubes will fit

Related Questions

Yes or no math questions will give brainlest

Answers

Answer:

Problem 13: NO

Problem 14: YES

Step-by-step explanation:

HOPE IT HELPS YOU IN YOUR LEARNING PROCESS.

solve it by using high order derivative
y=1÷(X+2)(x^2+4)

Answers

Answer:

I think it is ± 2y−2X1 −22y− 2X1−2+4=x2=x

Step-by-step explanation:

hope this helps if not let me know

The diagram show a solid cube.
The cube has a mass of 16 grams.
Work out the density of the cube.

Answers

Answer:

density: 0.25 g/cm³

Explanation:

density = mass/volume

Here given:

· mass: 16 grams

· volume: side³ = 4³ = 64 cm³

Find density:

· mass/volume

· 16/64

· 0.25 g/cm³

Which shows how to solve the equation -4/5 x = 80 for x in one step

Answers

Answer:

[tex] - \frac{1}{100} [/tex]

Step-by-step explanation:

[tex] - \frac{4}{5x} = 80 \\ - \frac{4}{80 } = 5x \\ x = - \frac{1}{100} [/tex]

Tyler believes that an 8-sided die can be used to predict whether customers at his store will use a coupon when making their purchases, with a roll of 1 indicating a coupon and all other outcomes indicating no coupon. Today, 4 of the first 48 customers in the store used a coupon. How does the experimental probability of a customer using a coupon compare to the theoretical probability of Tyler’s die? The experimental probability is greater than the theoretical probability by more than 2%. The experimental probability is less than the theoretical probability by more than 2%. The experimental probability is greater than the theoretical probability, but within 2%. The experimental probability is less than the theoretical probability, but within 2%.

Answers

The correct answer choice is; The experimental probability is less than the theoretical probability by more than 2%.

How does the experimental probability of a customer using a coupon compare to the theoretical probability of Tyler’s die?

It follows from the task content that, upon evaluation;

The experimental probability = 4/48 = 1/12.

The theoretical probability = 1/8.

On this note, it follows that the experimental probability is less than the theoretical probability by more than 2%.

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Answer:

B. The experimental probability is less than the theoretical probability by more than 2%.

Step-by-step explanation:

have a good day peep's :]

A bag contains 3 red marbles, 7 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?

Answers

Probability helps us to know the chances of an event occurring. The exact probability that all three marbles are drawn will be green is 0.02198.

What is Probability?

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Given the bag contains 3 red marbles, 7 blue marbles and 5 green marbles, therefore, a total of 15 marbles. Therefore, the exact probability that all three marbles are drawn will be green can be written as,

[tex]\rm Probability = \dfrac{5}{15} \times \dfrac{4}{14} \times \dfrac{3}{13} = \dfrac{60}{2730} = 0.02198[/tex]

Hence, the exact probability that all three marbles are drawn will be green is 0.02198.

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Marco invested $3000 into a fund that is expected to grow by 4.23% per year. How long will it take the fund to be worth $6000?

Answers

Answer:

[tex]6000 = 3000(1+0.0424)^{t}[/tex]

t = 16.73 years

Step-by-step explanation:

This can be solved using the "exponential growth" formula.

Steps:

A = Final Amount

S = Starting Value

r = rate

c = times in a year ( c = 1 in this equation which is why it's not shown in the actual equation )

1. [tex]A=S(1+\frac{r}{c})^{ct}[/tex] → cancel out S → [tex]\frac{A}{S} = \frac{S(1+\frac{r}{c})^{ct} }{S}[/tex]

2. [tex]\frac{A}{S} = {(1+\frac{r}{c})^{ct} }[/tex] → sperate ct from equation by logging both sides (logging a value with an exponent brings the exponent in front of log) → [tex]log(\frac{A}{S}) = ctlog(1+\frac{r}{c})[/tex]

3. [tex]log(\frac{A}{S}) = ctlog(1+\frac{r}{c})[/tex] → transfer right side log to left side along with the c value to only have t remaining → [tex]\frac{log(\frac{A}{S})}{clog(1+\frac{r}{c})} = \frac{ctlog(1+\frac{r}{c})}{clog(1+\frac{r}{c})}[/tex]

4. Solve for answer: [tex]\frac{log(\frac{A}{S})}{clog(1+\frac{r}{c})} = t[/tex]

Answer: its option D) 17 years

Step-by-step explanation: the answer is 16.7 but you round it up because thats not an option

Find the area of the shape.
Either enter an exact answer in terms of it or use 3.14 for TT and enter your answer as a decimal.

Answers

Answer:

what was the answer?? I am also needing to know!

Two angles of a triangle are the same size. The third angle is 12 degrees smaller than the first angle. Find the measure the angles

Answers

Answer:12, 84 and 84

Step-by-step explanation:

since we know 3 angles of a triangle = 180 degrees

1 angle = 12 degrees

12 + x + x = 180

12 + 2x = 180

2x= 180 - 12

2x = 168

x = 168/2

x = 84 degrees

Hope it helps! Mark it as Braniest

Answer:

64° , 64° , 52°

Step-by-step explanation:

Angle sum property of triangle:

The two angles that are same be 'x'

Third angle = x - 12

Sum of all angles of triangle = 180

x + x + x -12 = 180

3x - 12 = 180

3x = 180 + 12

3x = 192

x = 192/3

x = 64

x - 12 = 64 - 12

= 52

The three angles are 64° , 64° , 52°

If 15 is equal to 20% how much is 100%???

Answers

Answer:

75=100%

Step-by-step explanation:

15=20%

30=50%

75=100%

help please, this is supposed to be done with a calculator but i don’t have one

Answers

Answer:

x = {7, -1}

Step-by-step explanation:

assuming that you are to find the zeros of the equation you dont need a calculator to do this

you can set both sides to zero

(x - 7) = 0

(x + 1) = 0

and then solve for the zeros

x = {7, -1}

that is your answer

Somerset Corporation just completed its fiscal year ended January 31, 2021. All sales were on account and totaled 650,000 for the year. The accounts receivable balance on February 1, 2020 was 60,000 and the balance was 55,000 on January 31, 2021. What is the accounts receivable turnover ratio? Round and enter to one decimal place only.

Answers

The accounts receivable turnover ratio for the year ended January 31, 2021, for Somerset Corporation is 11.3 times.

What is the accounts receivable turnover ratio?

The accounts receivable turnover ratio is a financial measurement of the effectiveness of a company to extend credits and collect debts.

The ratio, which shows the number of times per period that Somerset Corporation can collect its credit sales, can be computed as net credit sales divided by average accounts receivable.

Data and Calculations:

Sales on account = $650,000

Accounts receivable balances:

February 1, 2020 = $60,000

January 31, 2021 = $55,000

Average receivable = $57,500 ($60,000 + $55,000)/2

Accounts receivable turnover ratio = Net credit sales/Average receivables

= 11.3 x ($650,000/$57,500)

Thus, the accounts receivable turnover ratio for the year ended January 31, 2021, for Somerset Corporation is 11.3 times.

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Once a month, volunteers from the Green Sea Club clean up litter at the beach. Last month, the volunteers picked up 8 pounds of trash in 4 hours. This month, the same group of volunteers will spend 3 hours picking up trash.
If they pick up trash at the same rate, how many pounds of trash should the volunteers pick up this month?
pounds

Answers

69 pounds of trash I think

Answer:

6 pounds

Step-by-step explanation:

2 pounds per hour

2(8 + t)* 6 when s = 3 and t = 2.

Answers

Answer:

120

Step-by-step explanation:

Plug in variables with numbers

2(8+2)*6

2(10)*6

20*6

120

Please mark brainliest!

PLEASE HELP I NEED HELP I don’t get this

Answers

Answer: The first question is a corrosponding angle, which means the measure is the same. So, angle KRQ is 146°.

And QRN is 128°.

3,045 ÷ 85
Estimate:
Quotient:
Remainder:

Answers

Answer:

[tex]85 \sqrt{(3045})35.823\\ - 2975 \\ 700 \\ - 680 \\ 200 \\ - 10 \\ 300 \\ - 255 \\ ......[/tex]

PLEASE HELP WILL MARK BRAINLIEST

Answers

Answer:

3.1

Step-by-step explanation:

sine 70= x/4

sin= opposite/hypotenuse

Given that 5 miles is 8 km, convert 32.7 km to miles.
help im stuck

Answers

Answer:

20.4375 miles

Step-by-step explanation:

5 miles / 8 km * 32.7 km = 20.4375 miles

( see how the units 'km' cancel out and you are left with 'miles' as your answer?)

Travis drew this graph to plan his rectangular garden. The points on the graph mark the four corners of the fence around the garden. What will be the length and width of the fence around the garden? Explain your answer.

Answers

The length of the rectangular garden which Travis drew on graph is equal to the large side of the rectangle made by four points and width is equal to short side.

What is the perimeter of a rectangle?

The measure of the boundary of the sides of a rectangles called its perimeter. The perimeter of a rectangle is twice the sum its length and width.

P=2(l+w)

Here, (l) is the length of the rectangle and (w) is the width of the rectangle.

Travis drew a graph to plan the rectangular garden he has. The points over the graph marked are the four corners of the fence around the garden.

Now let suppose the two corner marked are with total distance of x while other two with total distance of y. Then the length will be x and width will be y.

Thus, the length of the rectangular garden which Travis drew on graph is equal to the large side of the rectangle made by four points and width is equal to short side.

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find the minimum product of two numbers whose difference is 17.
what are the numbers?

Answers

A number is an arithmetic value that is used to represent a quantity and calculate it. The two numbers will be 17 and 0, so the product of the two is minimal.

What are Numbers?

A number is an arithmetic value that is used to represent a quantity and calculate it. Numericals are written symbols that represent numbers, such as "3."

Given the difference between the two numbers is 17. Let the first number be zero, then the second number will be 17. Thus, the product of the two numbers will be 0, which is the minimum.

If the first number is further increased such as 1, then the other number will be 18, and the product of the two will be 18, which is greater than zero.

Hence, the two numbers will be 17 and 0, so the product of the two is minimal.

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A hot dog costs $1 at the ballpark. Which equation shows the total cost, C, of n hot dogs?
⚫️n = 1c
⚫️n = 1+c
⚫️c = 1n
⚫️c = 1 + n

Answers

c=1n is the answer because the cost of hotdogs equals the price times the number of hotdogs

Answer:

C=1n

Step-by-step explanation:

So first you look for keywords, the most noticeable one is "total cost." C will be at the end of the equation.

C= ? + ?

Then, each hot dog costs $1 which means no matter how many hot dogs there will be, it will be multiplied by the cost. So, the answer is:

c=1n

Which of the following are solutions to the equation below?
Check all that apply.
(5x- 2)2 = 10
m A. x=-2 +2
B. x = -V12
m c. x- 42
0 D. X=2 +2
E. x= v10 +2
0 F. x- 10+2
5

Answers

The provided equations are not a solution to the given equation, which is (5x - 2)2 = 10

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have given a linear equation in one variable:

(5x - 2)2 = 10

Finding the solution to the above equation

5x -2 = 5

5x = 7

x = 7/5

For checking A:

x= -2+2

x = 0