5% of what number is 63?

Answers

Answer 1

Answer: To find the percentage of a number, you take the percent - 5% - and change it to a decimal by moving the percent over 2 times to the left and multiplying it by the number. So...

.05 x 63
= 3.15

Answer: 5% of 63 is 3.15

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2 mi. yd. I'm confused

Answers

Answer && Step-by-step explanation:

Obtain yards by multiplying miles by 1760

== 3520 yards

Consider the optimization problem of maximizing Cobb–Douglas production function: Q = 20 K1/2 L1/2, subject to cost constraint: K + 4L = 64. a/ Use the method of Lagrange multipliers to find the maximum value of the production function;
b/ Estimate the change in the optimal value of Q if the cost constraint is changed to K + 4L = 65, and state the new maximum value of the production function.

Answers

Answer:

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Find the perimeter and area of the regular polygon. Round answers to the nearest tenth.

Answers

Answer: perimeter = 26.5

Area = 106

Step-by-step explanation:

The given polygon is an octagon. The apotherm which is the perpendicular line from the midpoint of the octagon is 8,

The formula for determining the area of a polygon is expressed as

Area = a² × n × tan 180/n

Where n represents the number of sides of the polygon.

n = 8

Therefore,

Area = 8² × 4 × tan(180/8)

Area = 256 × tan 22.5

Area = 106

The formula for determining the perimeter of a regular polygon is

P = 2 × area/apotherm

Perimeter = 2 × 106/8

Perimeter = 26.5

Find the greatest common factor of 108d^2 and 216d

Answers

Answer:

$\boxed{108d}$

Step-by-step explanation:

Part 1: Find GCF of variables

The equation gives d ² and d as variables. The GCF rules for variables are:

The variables must have the same base.
If one variable is raised to a power and the other is not, the GCF is the variable that does not have a power.
If one variable is raised to a power and the other is raised to a power of lesser value, the GCF is the variable with the lesser value power.

The GCF for the variables is d.

Part 2: Find GCF of bases (Method #1)

The equation gives 108 and 216 as coefficients. To check for a GCF, use prime factorization trees to find common factors in between the values.

Key: If a number is in bold, it is marked this way because it cannot be divided further AND is a prime number!

Prime Factorization of 108

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 108 is 2 * 2 * 3 * 3 * 3, or simplified as 2² * 3³.

Prime Factorization of 216

216 ⇒ 108 & 2

108 ⇒ 54 & 2

54 ⇒ 27 & 2

27 ⇒ 9 & 3

9 ⇒ 3 & 3

Therefore, the prime factorization of 216 is 2 * 2 * 2 * 3 * 3 * 3, or simplified as 2³ * 3³.

After completing the prime factorization trees, check for the common factors in between the two values.

The prime factorization of 216 is 2³ * 3³ and the prime factorization of 108 is 2² * 3³. Follow the same rules for GCFs of variables listed above and declare that the common factor is the factor of 108.

Therefore, the greatest common factor (combining both the coefficient and the variable) is $\boxed{108d}$ .

Part 3: Find GCF of bases (Method #2)

This is the quicker method of the two. Simply divide the two coefficients and see if the result is 2. If so, the lesser number is immediately the coefficient.

$(216)/(108)=2$

Therefore, the coefficient of the GCF will be 108.

Then, follow the process described for variables to determine that the GCF of the variables is d.

Therefore, the GCF is $\boxed{108d}$ .

Answer:

Below

Step-by-step explanation:

If d is a positive number then the greatest common factor is 108d.

To get it isolate d and d^2 from the numbers.

108 divides 216. (216 = 2×108)

Then the greatest common factor of 216 and 108 is 108.

For d^2 and d we will follow the same strategy

d divides d^2 (d^2 = d*d)

Then the greatest common factor of them is d.

So the greatest common factor will be 108d if and only if d is positive. If not then 108 is the answer

A ferryboat makes four trips to an island each day.The ferry can hold 88 people.If the ferry is full on each trip,how many passengers are carried by the ferry each day?