Match each three-dimensional figure to its volume based on the given dimensions. (Assume T = 3.14.)
a right cylinder with radius 4 cm
and height 3 cm
314 cu cm
a cone with radius 5 cm and
height 12 cm
160 cu cm
a pyramid with base area
16 sq cm and height 30 cm
48 cu cm
a pyramid with a square base of
length 3 cm and height 16 cm
150.72 cu cm

The original number is 64

Step-by-step explanation:

The given is:

We need to find the original number

Assume that the unit digit of the number is x and the ten digit is y

∵ The unite digit of the number is x

∵ The ten digit of the number is y

∵ The sum of the two digits is 10

- Add x and y, then equate the sum by 10

∴ x + y = 10 ⇒ (1)

∵ The value of the number is x + 10y

- Reverse the digits means y will be the unit digit and x will

   be the ten digit

∴ The new number is y + 10x

∵ The new number is 18 less than the original number

- That means their difference is 18, (the original number minus

   the new number = 18)

∴ (x + 10y) - (y + 10x) = 18

- Simplify the left hand side

∴ x + 10y - y - 10x = 18

- Add the like terms in the left hand side

∴ -9x + 9y = 18

- Divide both sides by 9

∴ -x + y = 2 ⇒ (2)

Now we have a system of equation to solve it

Add equation (1) and (2) to eliminate x

∴ 2y = 12

- Divide both sides by 2

∴ y = 6

- Substitute the value of y in equation (1) to find x

∵ x + 6 = 10

- Subtract 6 from both sides

∴ x = 4

∵ The original number is x + 10y

∵ x = 4 and y = 6

∴ The original number = 4 + 10(6) = 4 + 60 = 64

The original number is 64

To check the answer reverse the digits of the number

∵ The new number is y + 10x

∴ The new number = 6 + 10(4) = 6 + 40 = 46

∵ The original number is 64

∵ The new number is 46

∵ 64 - 46 = 18

∴ The new number is less than the original number by 18

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Answer:

The original number is 64.

Answer:

The number of comic books did they have in all   = 56

Step-by-step explanation:

The ratio of comics with Susan : Abe = 3 : 5

Let us assume the common factor on this ratio = m

So, the number of comics Susan has  = 3 m

The number of comics Abe has  = 5 m

Also, given:  Abe had 14 more comic books than Susan

So, the number of comics Abe had  = 14 + 3 m

⇒  5 m  =  3 m + 14

or,   2 m = 14, or m = 7

So, the number of books Susan has = 3 m = 3 x 7 = 21 books

The number of books Abe has  = 5 m = 5 x 7 = 35

So, the book they have in all = 21 +  35 = 56

Option A

[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6}) = 6.9977 \times 10^{-3}[/tex]

Solution:

Given expression is:

[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6})[/tex]

To evaluate the expression, let us make the exponent of 10 same

[tex]2.3 \times 10^{-6} = 0.0023 \times 10^{-6+3} = 0.0023 \times 10^{-3}[/tex]

[ Here, decimal point is moved three times left, so add 3 ]

Therefore,

[tex](7 \times 10^{-3}) - (2.3 \times 10^{-6}) = (7 \times 10^{-3}) - (0.0023 \times 10^{-3})[/tex]

[tex]\text{Take the } 10^{-3} \text{ as common }[/tex]

[tex](7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 10^{-3}(7-0.0023)\\\\\text{ Solve for terms inside the bracket }\\\\(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 10^{-3} \times 6.9977\\\\\text{Therefore, the simplified expression is: }\\\\(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 6.9977 \times 10^{-3}[/tex]

Thus Option A is correct

The area of the gray portion in the room, after subtracting the area of the central linoleum from the total area of the room, is 112 sq. ft.

To calculate the area of the gray portion in the room, first subtract the area of the linoleum from the total area of the room. The area of the room is given as 12 x 16 sq. ft. and the linoleum is 8 x 10 sq. ft.. To find the total area of the room, multiply the length by the width (12 x 16 = 192 sq. ft.). Then do the same for the linoleum (8 x 10 = 80 sq. ft.). Subtracting the area of the linoleum from the total area of the room gives us the gray area (192 - 80 = 112 sq. ft.). Hence, the area of the gray portion is 112 sq. ft.

Answer:

[tex]y=3(x+4.5)(x+2.8)[/tex] or  [tex]y=3x^2+21.9x+37.8[/tex]

Step-by-step explanation:

we know that

The equation of a vertical parabola in factored form is equal to

[tex]y=a(x-x_1)(x-x_2)[/tex]

where

a is a coefficient

x_1 and x_2 are the roots or x-intercepts of the quadratic equation

In this problem we have

[tex]x_1=-4.5\\x_2=-2.8[/tex]

substitute

[tex]y=a(x+4.5)(x+2.8)[/tex]

Find the value of a

we have the y-intercept (0,37.8)

substitute the value of x and the value of y of the y-intercept in the equation and solve for a

[tex]37.8=a(0+4.5)(0+2.8)[/tex]

[tex]a=37.8/12.6\\a=3[/tex]

so

[tex]y=3(x+4.5)(x+2.8)[/tex]

Convert to expanded form

[tex]y=3(x^2+2.8x+4.5x+12.6)[/tex]

[tex]y=3x^2+21.9x+37.8[/tex]

Answer:

Go to the link below :)

Step-by-step explanation:

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Final answer:

The correct solution to the equation 5x+10=24-2x is x=2, which is verified by substitution and results in an identity, confirming the solution is accurate.

Explanation:

The equation 5x+10=24-2x is a simple linear equation that can be solved by collecting like terms and isolating the variable x. Begin by adding 2x to both sides to get 7x + 10 = 24, then subtract 10 from both sides to obtain 7x = 14. Dividing both sides by 7 yields x = 2, which is the sole solution to the equation. Checking the solution, 24 - 2(2) does indeed equal 5(2) + 10, giving an identity of 20 = 20. This illustrates the solution is correct and verifies our process.

Answer:

D) 24.

Step-by-step explanation:

The solution is 24 routes. To determine the number of different routes we multiply the routes for each part of the trip. 4(3)(2) = 24 routes.

He can take 24 different routes for his trip

The correct option is option D)

What is permutation and combination?

an arrangement of objects in a definite order is known as permutation. The members or elements of sets are arranged here in a sequence.  a combination is a selection of items from a set which has distinct members, and the order of selection does not matter. even though the terms are used together they are different and formula for calculating them is also different

We are given that,

Jacksonville to Atlanta: 4 routes

Atlanta to Knoxville: 3 routes

Knoxville to Indianapolis: 2 routes

Also Sammy is traveling from Jacksonville to Atlanta to Knoxville to Indianapolis

To find the different routes sammy can take can be computed as

4*3*2=24ways

Hence Sammy can take 24 routes

The correct option is option D)

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Answer:

$158.74

Step-by-step explanation:

A sound system has a regular price of $249. Now, we have to find the total cost of it if there is a sale for 40% off and the sales tax is 6.25%.

Now, if there is 40% off on price $249, then the discounted price will be

[tex]249(1 - \frac{40}{100}) = 149.4[/tex] dollars.

Then the after-tax value of the sound system at the rate of 6.25% will be [tex]149.4(1 + \frac{6.25}{100}) = 158.74[/tex] dollars (Approximate)

(Answer)

Answer:

23/12x+7

Step-by-step explanation:

2 3/4=11/4

8 2/5=42/5

----------------

11/4x-5/6(x-42/5)

11/4x-5/6x+210/30

11/4x-5/6x+7

33/12x-10/12x+7

23/12x+7

Answer:

Step-by-step explanation:

X + 61° = 90° {right angle}

X = 90° - 61°

X = 29°

Answer:

Step-by-step explanation:

Let the number be x and y

xy = 378.......(1)

x + y = 41......(2)

Making y as subject in (2)

y = 41 - x......(3)

Substitute it in (1)

x(41 - x) = 378

41x - x² = 378

x² - 41x + 378 = 0

x² - 27x - 14x + 378 = 0

(x² - 27x) - (14x - 378) = 0

x(x - 27) - 14(x - 27) = 0

(x -14)(x - 27) = 0

x - 14 = 0 or x - 27 = 0

x = 14 or x = 27

And y = 41 - x

When x = 14

y = 41 - 14 = 27

y = 27

When x = 27

y = 41 - 27 = 14

y = 14

The two numbers are 14 and 27.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Let the numbers are x and y.

Then,

the system of equations

xy = 378  {equation 1}

x + y = 41   {equation 2}

y = 41 - x

Then

x(41 - x) = 378

41x - x² = 378

x² - 41x + 378 = 0

x² - 27x - 14x + 378 = 0

(x² - 27x) - (14x - 378) = 0

x(x - 27) - 14(x - 27) = 0

(x -14)(x - 27) = 0

x - 14 = 0 or x - 27 = 0

x = 14 or x = 27

And y = 41 - x

When x = 14

y = 41 - 14 = 27

y = 27

When x = 27

y = 41 - 27 = 14

y = 14

Therefore, the  14 and 27 are the numbers.

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The expression of multiplication used will be 26x = 1300.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Miranda was asked to solve the problem 1300 divided by 26. The expression will be written as,

26x = 1300

x = 1300 / 26

x = 50

Hence, the expression of multiplication used will be 26x = 1300.

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Miranda can solve 1300 divided by 26 by using multiplication – specifically, by finding what number multiplies with 26 to result in 1300. She can break down the number 26 into smaller factors for easier estimation, using inverse operations to eventually find that 50 is the correct answer.

Using Multiplication to Solve Division Problems

Miranda was asked to solve the problem 1300 divided by 26. To use multiplication to solve this division problem, she can apply the reciprocal approach. Essentially, she can multiply 1300 by the reciprocal (the inverse) of 26. The reciprocal of a number 'a' is 1/a, so the reciprocal of 26 is 1/26. However, finding the reciprocal of 26 directly can be challenging, so we can use intuitive steps that simplify the problem.

For example, we could productively think about what number, when multiplied by 26, gives us 1300. This is a form of inverse operations. One way to approach this is to break down 26 into factors like 2 and 13, which might lead to simpler multiples to work with. She may start by estimating and refining her estimations by multiplying different numbers by 26 and seeing how close she gets to 1300. It’s a trial and error process, but eventually, she will find the correct answer of 50, as 26 multiplied by 50 equals 1300.

Answer:

28

Step-by-step explanation:

Plug in the corresponding numbers to the corresponding variables. Note that:

m = 7

r = 8

t = 2

mr/t = (7 * 8)/2

(7 * (8/2)) = 7 * 4 = 28

28 is your answer.

~

The system of inequalities is x+y≥250 and 3x+2y≤800.

Step-by-step explanation:

Given,

People to invite = at least 250

At least 250 means that the number can increase from 250.

Cups to be provided = only 800

It means the number cannot exceed 800.

Number of adults = A

Number of children = C

According to given statement;

x+y≥250

3x+2y≤800

The system of inequalities is x+y≥250 and 3x+2y≤800.

Keywords: linear inequalities, addition

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Answer

overlapping

explanation:

This is overlapping set because at least one common element (5) is present in both set.

-8, 3.5, -1.15. -9 1/4

I hope this helped!

Answer:

#2 486

#3 25

#4 25

#5 1,000,000

Step-by-step explanation:

Sequences like this always have some rule that determines the next number, a pattern that needs to be followed. Sometimes the pattern is easy to find, sometimes really hard.

#2 One of the first things to check is the ratio of adjacent numbers. Here we have 2 then 6 then 18 then 54 etc.

The most prominent feature of these numbers is that the next number is always three times bigger than the previous. It's safe to assume that the missing number will be 162 • 3 = 486.

#3 Of course numbers can be arranged in the decreasing order as well. However, that does not change their ratio. In this example, carefully examining, we can see that each number in the sequence is exactly twice smaller than the previous:

800 -> 400 -> 200 -> 100  etc.

Following this pattern, we can say that the next number will be 50 / 2 = 25.

#4 Of course, ratio is not the only way to help us find the pattern. One of the very often used methods is also the difference between adjacent numbers. Let's subtract each adjacent pair:

4 - 1 = 3

9 - 4 =5

16 - 9 = 7

Longer the sequence is, greater are the chances to see the pattern, but from this we could conclude that the difference between adjacent numbers is always an odd number (3, 5, 7). We could say that the next odd number is 9, so the missing number is 16 + 9 = 25

There is another pattern that could be found. This sequence could also represent the sequence of squared numbers:

1^2, 2°2, 3°2, 4^2

In this case, the next number would be 5^2 which is also 25.

#5 Again, we can find a pattern established on the ratio of numbers, but this time with repetitive symbol L. After every L, the number is a thousand times bigger than the previous number:

0.001 -> 1 -> 1000

So, following this pattern, the missing number would be 1000 • 1000 which equals to 1000000 (a million).

Answer:

The total amount that Beyonce will pay for the chair is $9100.

Step-by-step explanation:

The Principal amount of chair  = $6500

Rate of interest  = 8%

Time = 5 years

Now, SIMPLE INTEREST  = [tex]\frac{P\times R \times T}{100}[/tex]

So, here calculating the interest on the chair, we get:

[tex]SI = \frac{6500 \times 5 \times 8}{100} = 2600[/tex]

So, the interest on the amount of chair for 5 years  is $2600.

Total amount of chair  = Original Amount of Chair + Interest Amount

                                      = $6500 + $2600 = $9100

Hence, the total amount that Beyonce will pay for the chair is $9100.

To find the total amount, calculate the interest and add it to the principal amount.

Simple interest is calculated using the formula: I = P * r * t, where I is the interest, P is the principal amount (loan), r is the annual interest rate, and t is the time in years. In this case, the principal amount (loan) is $6500, the annual interest rate is 8%, and the time is 5 years. So, the interest can be calculated as: I = 6500 * 0.08 * 5 = $2600.

To find the total amount that Beyonce will pay for the chair, we need to add the interest to the principal amount. The total amount is given by the formula: Total Amount = Principal + Interest. Therefore, Total Amount = 6500 + 2600 = $9100.

So, Beyonce will pay a total amount of $9100 for the chair, including the principal amount and interest.

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Answer:

x=0.9

Step-by-step explanation:

1. You first have to isolate the x term so you subtract 6.814 from both sides which makes the equation 1.54x=1.386

2. Then, to isolate "x", you divide 1.54 on both sides to get rid of the 1.54 which makes x=.9

Answer:

Area = π×(3.5)^2+ π×(3.5)^2

=76,96902001295 inch²

Answer:

1.12*10^(-15)

Step-by-step explanation:

Answer:

1.12e-15

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

Step-by-step explanation:

buys it for $ 45

well...you know the business is gonna want to make a profit...so they would have to sell it for more then they bought it for.

I would say $ 60 or $ 80

Final answer:

Given the wholesale price of $45, the sensible retail prices to charge customers would be $60 and $80, as they both allow for covering costs and earning a profit, unlike $20 and $40, which would incur losses.

Explanation:

The question involves understanding wholesale and retail prices, essential concepts in economics and business mathematics. When a company buys an item at a wholesale price, it usually marks up the price when selling it at retail to cover costs and generate profit. Given the wholesale price of $45, the retail prices that make sense to charge customers would be those higher than $45 because selling at a lower price would result in a loss.

Both $60 and $80 are above the wholesale price and would allow the company to cover additional costs and earn a profit. $20 and $40 would not make sense as they are below the wholesale price, leading to a loss per item sold.

Answer:

11.25 miles/hour

Step-by-step explanation:

Recall, speed = Distance ÷ Time

We are given :

Distance = 45 miles

Time = 4 hours

Hence,

Speed = Distance ÷ Time

= 45 miles ÷ 4 hours

= 11.25 miles/hour

Answer:

Step-by-step explanation:

Convert into improper fractions

Add numerators and denominators

Simplify

Hope this helps :)

p = 32

Solution:

Given p represents the amount of air pressure in a tire.

t represents the time it takes for the tire to go flat and t = –8.

To find the value of p, if [tex]\frac{p}{t}=-4[/tex].

⇒ [tex]\frac{p}{t}=-4[/tex]

Substitute t = –8 in the above equation.

⇒ [tex]\frac{p}{-8}=-4[/tex]

Do cross multiply, we get

⇒ p = (–8) × (– 4)

⇒ p = 32

Hence, the value of p is 32 if the quotient [tex]\frac{p}{t}[/tex] is –4.

Answer:

Step-by-step explanation:

l = -2.4t + 75

what this equation is saying is that the initial height of the anchor is 75 meters (thats also ur y intercept), and it drops at a rate of 2.4 meters per second.

another way u could look at it is the initial height is before u drop the anchor....0 seconds...meaning sub in 0 for t

l = 2.4(0) + 75

l = 0 + 75

l = 75 meters <=====

Answer:

Step-by-step explanation:

three angles measuring 40°, 70°, and 65 cannot create a triangle because sum of all the angles should be 180

Answer:

The rate of change for the interval shown in the table is 1 , so the function is a linear function.

Step-by-step explanation:

See the table attached.

The table shows selected points from a function.

Now, the given interval is x = 1 to x = 4.

For, x = 1, f(x) = 2 and for x = 4. the function f(x) = 5.

Therefore, the rate of change for the interval shown in the table i.e slope of the line is [tex]\frac{5 - 2}{4 - 1} = 1[/tex] and it is constant throughout the interval so the function is a linear function. (Answer)

The rate of change for the interval shown in the table is constant , so the function is a linear function.

Note the following important points:

1. Linear Function:

If the difference between y values remains constant for any pair of consecutive points ([tex]y_2-y_1 = y_3-y_2 = y_4-y_3,[/tex]and so on), the function exhibits a constant rate of change, indicating a linear function. In this case, the rate of change would be the difference between two y values divided by the difference between their corresponding x values (e.g., [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]).

2. Non-Linear Function:

If the difference between y values varies between consecutive points, the function would be non-linear. The specific type of non-linear function (e.g., quadratic, exponential) would require further analysis with more data points or additional information about the function's behavior.

In this case, as shown in the attached table, it is clear that

For [tex]x_1=1, y_1=f(x)=2[/tex].

For [tex]x_2=2, y_2=f(x)=3[/tex].

For[tex]x_3=, y_3=f(x)=4[/tex].

For [tex]x_4=, y_4=f(x)=5[/tex], and so on.

Thus the rate of change for the interval shown in the table or its slope is constant as evident from the following calculation.

[tex]\frac{(y_2-y_1)}{(x_2-x_1)}=\frac{3-2}{2-1}=1\\ \frac{(y_3-y_2)}{(x_3-x_2)}=\frac{4-3}{3-2}=1\\\frac{(y_4-y_3)}{(x_4-x_3)}=\frac{5-4}{4-3} =1[/tex].

So it is clear that, the rate of change for the interval shown in the table is constant , so the function is a linear function.

Answer:

2 BTUs/cubic foot.

Step-by-step explanation:

Suppose that 2 people exercising in an enclosed room are each generating about 2,400 BTUs of body heat per hour.

So, 2 people will produce (2400 × 2) = 4800 BTUs for 1 hour.

Now, the volume of the room with dimensions (20 ft by 12 ft by 10 ft) will be (20 × 12 × 10) = 2400 cubic feet.

Therefore, the number of BTUs per cubic foot will be produced  by [tex]\frac{4800}{2400} = 2[/tex] BTUs/cubic foot. (Answer)