how can you decide if finding common multiples and common factors is helpful in solving a problem?explain.

Answer:

Quadrant

Step-by-step explanation:

Given cylinder has diameter 16ft and height 10ft.

Radius of the cylinder = 16/2 = 8 ft.

We need to find the volume of cylinder.

Volume of the cylinder (V) = [tex]\pi r^2h[/tex]

Where r is the radius of the cylinder and h is the height of the cylinder.

Plugging values of r=8 and height h=10 in above formula, we get

V =  [tex]\pi (8)^2(10)[/tex]

V= [tex]\pi 64 \times 10[/tex]

V=[tex]\pi \ times 640[/tex]

Plugging π =3.142

V= 3.142 × 640

V ≈2010.88.

In the given options it's nearly equal to 2010.62.

Subtraction is a mathematical operation that reflects the removal of things from a collection.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The given blanks can be written as,

1)When adding two negative numbers, add the absolute value of the numbers and keep the negative sign.

2)When adding two different signed numbers, subtract the absolute values of the numbers and keep the sign of the number with the larger absolute value.

3)When subtracting, change the subtraction to addition and change the sign of the number being taken away.

Learn more about Subtraction:

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One way the barber could cut 3 people's hair in 35 minutes is by spending 15 minutes on the first haircut and 10 minutes each on the second and third haircuts.

If a barber cuts 3 people's hair in 35 minutes and each haircut takes at least 10 minutes, the timing could look as follows: The first haircut, taking the most time, could be 15 minutes. The second haircut could take 10 minutes, which is the minimum time per haircut. The third haircut would also take 10 minutes. This allocation adheres to the conditions that the first haircut takes the most time, and each haircut takes at least 10 minutes.

Total time spent would be 15 minutes + 10 minutes + 10 minutes, which equals 35 minutes.

To divide 6.25 by 2.5, you can multiply both numbers by 10 to make it 62.5 divided by 25, which equals 2.5. Thus, 6.25 divided by 2.5 is 2.5.

To find this, we divide 6.25 by 2.5. First, we can make the divisor a whole number by multiplying both the divisor and dividend by 10, which will not change the value of the quotient:

6.25 × 10 = 62.5

2.5 × 10 = 25

Now, we divide 62.5 by 25:

62.5 ÷ 25 = 2.5

Therefore, 6.25 divided by 2.5 is 2.5.

The probability that it will snow and Amy will be late for school is found by multiplying the individual probabilities of each event, which are 60% and 10% respectively, resulting in 6%.

The probability that both events (it snowing and Amy being late for school) will occur is found by multiplying the probabilities of each independent event. As Amy states, there is a 60% chance of snow (which can be expressed as a probability of 0.60) and a 10% chance she will be late for school (expressed as a probability of 0.10). To find the probability that both events happen, we calculate:

Probability(snow and late) = Probability(snow) × Probability(late)

Probability(snow and late) = 0.60 × 0.10 = 0.06

Therefore, the probability that it will snow tomorrow and Amy will be late for school is 6%.

a. What is the cost expression for the newspaper? 

The cost would be the sum of fixed cost and the variable cost. The fixed cost is 70 while the variable cost is 0.40 x, where x stands for the number of copies made. That is:

Cost = 70 + 0.40 x            

where x = number of copies made

b. What is the revenue expression for the newspaper? 

The revenue would simply be the product of selling price and number of copies sold or made, that is:

Revenue = 0.50 x

c. Put the cost and revenue expressions into an inequality that would represent a successful newspaper. 

To have a successful newspaper, the difference of revenue and cost must be greater than 0, that is:

Revenue – Cost > 0

0.50 x – (70 + 0.40 x) > 0


d. How many copies should be sold to make a profit? Show all work! An answer with no work will receive 0 points. 

From the above equation, we solve for x.

0.50 x – (70 + 0.40 x) > 0

0.50 x – 70 – 0.40 x > 0

0.10 x > 70

x > 700

Number of copies made should be more than 700 copies


e. Now go back to your answer for d. On every line of your solution write what property of math you would use to justify the transformation that occurred. 

0.50 x – (70 + 0.40 x) > 0                Distribution property

0.50 x – 70 – 0.40 x > 0                    Addition property

0.10 x > 70                                           Addition property

x > 700                                                  Division property

Final answer:

The cost expression for the newspaper is $70 + $0.40c. The revenue expression is $0.50c. A successful newspaper would have $0.50c > $70 + $0.40c. To make a profit, 700 copies should be sold.

Explanation:

a. The cost expression for the newspaper can be calculated by adding the fixed production cost per edition to the cost of printing and distributing each copy. So the cost expression is:

Cost = $70 + $0.40c

where 'c' represents the number of copies.

b. The revenue expression for the newspaper can be calculated by multiplying the selling price per copy by the number of copies sold. So the revenue expression is:

Revenue = $0.50c

c. To represent a successful newspaper, the revenue should be greater than the cost. So the inequality would be:

$0.50c > $70 + $0.40c

d. To calculate the number of copies needed to make a profit, we need to find the point where the revenue is equal to or greater than the cost. So we set the inequality from part c to equality and solve for 'c':

$0.50c = $70 + $0.40c

$0.10c = $70

c = $700

e. At every step in the solution, we used the property of equalizing the equation by adding or subtracting the same value on both sides, and also dividing by the same value on both sides.

Final answer:

To translate a polygon 3 units down and 4 units left, subtract 4 from the x-coordinate and 3 from the y-coordinate of each vertex. For example, the vertex (3, 0.4) would become (-1, -2.6) in prime notation after the translation.

Explanation:

If a polygon is translated 3 units down and 4 units left, the coordinates of the new image would change respectively. To find the new coordinates after the translation, the x-coordinate of each vertex will decrease by 4 (since it is moving left) and the y-coordinate will decrease by 3 (since it is moving down). For example, if the coordinates of a vertex are (x, y), after the translation, the new coordinates will be (x - 4, y - 3), which we denote using prime notation as (x', y').

So, if we are given the initial coordinates of the first vertex as (3, 0.4), then after the translation, the new coordinates will be:

x' = 3 - 4 = -1

y' = 0.4 - 3 = -2.6

Therefore, the new coordinates are (-1, -2.6), using prime notation to represent the translated vertex.

Final answer:

To solve the algebraic equation stated as 'six times the sum of a number and 7 equals 2,' we distribute, subtract 42 from both sides, and then divide by 6, leading to the solution x = -20/3 or approximately -6.67.

Explanation:

The question involves solving an algebraic equation to find an unknown number. When the problem states that six times the sum of a number and 7 equals 2, it can be represented mathematically as 6(x + 7) = 2. To find the value of x, you need to follow these steps:

First, distribute the 6 to both x and 7, which gives 6x + 42 = 2.

Next, to isolate the variable term (6x), you would subtract 42 from both sides of the equation, resulting in 6x = 2 - 42, which simplifies to 6x = -40.

Finally, to find the value of x, divide both sides by 6, giving x = -40 / 6, which simplifies to x = -20 / 3 or approximately x = -6.67.

5/13t = -9

Isolate the t. Multiply 13/5 to both sides

5/13t(13/5) = -9(13/5)

t = -9(13/5)

t = -117/5

Simplify.

t = -23.4

t = 23.4 is your answer

hope this helps