A cylinder has a diameter of 5 centimeters and a height of 50 millimeters. Which of the following steps should be done first in order to find the surface area of the cylinder?

convert the diameter and the height to the same unit
determine the radius and multiply by 2
calculate the circumference of the circle
multiply the circumference of the circle by the height of the cylinder

Answer:

For the green one the answer is 8 square units

For the red one the answer is 9 square units

Hope this helps

The area of the shaded green polygon is equal to 8 square units.

The area of the shaded red polygon is equal to 9 square units.

In Mathematics and Geometry, the area of a triangle can be calculated by using the following mathematical equation (formula):

Area of triangle = 1/2 × b × h

Where:

Note: When the green polygon is dissected, three triangles would be formed.

By substituting the given side lengths into the formula for the area of a triangle, we have the following;

Area of triangle = (1/2 × 1 × 1) + (1/2 × 3 × 1) + (1/2 × 3 × 4)

Area of triangle = 0.5 + 1.5 + 6

Area of triangle = 8 square units.

In order to determine the area of the shaded red polygon, we would have to apply Pick's theorem;

Area of polygon = (b/2 + i) - 1

where:

By substituting the number of lattice points, we have the following;

Area of polygon = (b/2 + i) - 1

Area of red polygon = (4/2 + 8) - 1

Area of red polygon = 10 - 1

Area of red polygon = 9 square units.

For this case we have that by definition, the volume of a cone is given by:

[tex]V = \frac {1} {3} * \pi * r ^ 2 * h[/tex]

Where:

r: It is the radius of the cone

h: Is the height of the cone

We must find the radius knowing that the circumference of the base of the cone is[tex]19.1 \ ft[/tex]

[tex]2 \pi * r = 19.1\\r = \frac {19.1} {2 \pi}\\r = 3.04 \ ft[/tex]

Thus, we substitute in the formula:

[tex]V = \frac {1} {3} * \pi * (3.04) ^ 2 * 5.3\\V = \frac {1} {3} * \pi * 9.25 * 5.3\\V = \frac {1} {3} * 154.0165\\V = 51.34[/tex]

Thus, the volume of the cone is: [tex]51.34 \ ft ^ 3[/tex]

Answer:

[tex]51.3 \ ft ^ 3[/tex]

Answer:

51.3 ft^3

Step-by-step explanation:

Answer:

4a+6

Step-by-step explanation:

To find the answer to this problem, you need to combine the like terms. (3a+7)+(a-1)=(3a+a)+(7-1)=4a+6. Hope this helps!

The of the given expression is 4a+6.

An algebraic expression is formed by using integers, constants, variables, and arithmetic operations. Variables and constants can be combined in an algebraic expression through mathematical operations.

Given that, an expression (3a+7)+(a−1), we need to find sum,

So,

(3a+7)+(a−1)

Opening the brackets,

3a+7+a-1

Combining the like terms,

3a+a+7-1

= 4a+6

Hence, the of the given expression is 4a+6.

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Answer:

(x-2)(x+1)

Step-by-step explanation:

x²-x-2 can be factored into:

(x-2)(x+1)

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Answer:

6.46 mm

Step-by-step explanation:

Answer:

3:30 pm

Step-by-step explanation:

Games : 1 hour

Cleaning : 1 hour

Homework: 30 minutes

Total time

1+1+ 30 minutes

She started at 1 pm

1 + 2 hour 30 minutes

1 +2 hours = 3 pm

3+30 minutes = 3:30

Answer:

1:00 pm + 1 hr = 2:00pm

2:00pm + 1 hr= 3:00pm

3:00pm +30 mins = 3:30 pm

Answer:

D)

9 units

Step-by-step explanation:

[tex]distance = 6 - ( - 3) = 6 + 3 = 9 \: units[/tex]

Answer:

A) -9 units is the distance between -3 and 6

Marvin would need 6.25 cans of paint for square 1.

Using ratio of paint used

We are given that it takes 4 cans of paint to paint square 3 and 5 cans of paint to paint square 2.

This suggests a possible ratio between the amount of paint needed for different squares. Let's assume this ratio remains constant.

If the ratio between squares 2 and 3 is r, then:

Paint needed for square 2 = 5 cans = r * Paint needed for square 3

Paint needed for square 3 = 4 cans

Solving for r: r = 5 cans / 4 cans = 1.25

Assuming the same ratio applies to square 1 and 2:

Paint needed for square 1 = r * Paint needed for square 2

Paint needed for square 1 = 1.25 * 5 cans = 6.25 cans

Therefore, Marvin would need 6.25 cans of paint for square 1.

Complete question:

Marvin is painting three squares shaped like the one below. If it takes him exactly four cans of paint to paint square 3 and five cans of paint to paint square 2, how many cans of paint should he need to paint square 1?

Answer:

d. 4 ft

Step-by-step explanation:

1/2h(b1+b2)

1/2h(10)=20

multiply both sides by 2

h(10)=40

divide both sides by 10

h=4

Answer:

m=0.19

Step-by-step explanation:

To work this out you would divide 0.95 by 5. this is because 0.95 is equal to 5*m and so so work out m you would divide 0.95 by 5.

[tex]0.95/5=0.19\\m=0.19[/tex]

Answer:

25.9666 m

Step-by-step explanation:

The 4 arches combine to for a circle, so then you can find the area of the shaded region by subtracting the area of the square from the area of the circle.

The formula for area of a circle is A=[tex]\pi[/tex]r^2

Since the radius of the circle would be 11/2 or 5.5, the area if the circle would be [tex]\pi[/tex] x 5.5^2. This equals 95.0334.

The area of the square would be 11 x 11 = 121.

The 121-95.0334= 25.9666 m

We can't see any choices but it doesn't matter.  That's the factorization of the difference of two squares.  It's important to recognize either side when you see it; the usual next move is to replace it with the other side.

(x + y)(x – y) = x² - y²

Answer: x² - y²

Answer:

8.64 feet squared

Step-by-step explanation:

The formula for calculating the area of a triangle is 1/2(bh) or base * height divided by 2,

So first multiply 4.8 and 3.6

(4.8) (3.6) = 17.28

Then divide that by 2

17.28/2 = 8.64

Answer:

A. 8.64 feet squared

Step-by-step explanation:

A = 1/2bh

A = 1/2(4.8 x 3.6)

A = 1/2(17.28)

A = 8.64 feet²

Answer:

81

Step-by-step explanation:

9*7 = 63

6*3 = 18

63 + 18 = 81

Answer:

B

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = (x - 2)² + k ← is in vertex form

with (h, k) = (2, 4)

Thus the minimum value is 4 when x = 2 → B

Step-by-step explanation:

P(t) = 12,000 (2)^(-t/15)

9,000 = 12,000 (2)^(-t/15)

0.75 = 2^(-t/15)

ln(0.75) = ln(2^(-t/15))

ln(0.75) = (-t/15) ln(2)

-15 ln(0.75) / ln(2) = t

t = 6.23

The time it would take for Sawyerville's population to decrease to 9000 can be calculated by setting the population function equal to 9000 and solving for 't'. After a series of algebraic transformations, you can isolate 't' and calculate its value with a scientific calculator.

To find the amount of time it will take for Sawyerville's population to fall to 9000 people, we can set up the equation: P(t) = 9000. Therefore, we have 9000 = 12,000 - 2-t/15.

To solve this equation, we first need to isolate the exponential term by subtracting 9000 from both sides, getting 3000 = 2-t/15. Then, we take the natural logarithm (ln) of both sides to remove the exponential term, resulting in ln(3000) = -t/15*ln(2). Divide both sides by -ln(2) and multiply them by 15 to find 't'. The final equation is: t = -15*ln(3000)/ln(2).

In this particular problem, you may need the help of a scientific calculator to compute the value of 't'.

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Answer:

mme 3 is 20

Step-by-step explanation:

i dont like to do work

Answer:

V= 103.9 mm^3 and 72.7 mg

Step-by-step explanation:

Edge

Answer:

-14

Step-by-step explanation:

-10-18=-28 -28/2=-14

Answer:

P = 0.0909

Step-by-step explanation:

To know the number of ways or combinations in which we can select x elements from a group of n elements, we can use the following equation:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

So, if you sat down at your computer and randomly loaded 4 of the 12 problems, there are 495 different possibilities and it is calculated as:

[tex]12C4=\frac{12!}{4!(12-4)!}=495[/tex]

Then, from 495 different possibilities, there are 45 possibilities that both this problem and Richard Rusczyk's problem were among the four you loaded. This 45 possibilities are calculated as:

[tex](1C1)*(1C1)*(10C2)=(\frac{1!}{1!(1-1)!})*(\frac{1!}{1!(1-1)!})*(\frac{10!}{2!(10-2)!})=45[/tex]

Because you need to select: this problem and there is only one, the problem that Richard Rusczyk wrote and there is only one, and 2 problems from the other 10.

Finally, the probability that both this problem and Richard Rusczyk's problem were among the four you loaded is equal to:

[tex]P=\frac{45}{495}=0.0909[/tex]

Answer:

1/9

Step-by-step explanation:

There are 30 pens in total, 1/3 of the pens are each the following colours: blue; black; red.

This will result in a one in three chance of picking up a red pen. As Mr.Lopez puts the pen back, the fractions stay the same as it's the same possibility both times.

As it's again a one in three chance, we just have to multiply it for the possibility of him picking a blue pen, which is 1/3.

1/3 * 1/3 = 1/9

Final answer:

To find the number of possible codes, we can use the concept of permutations. There are 7 digits to choose from and we need to select all of them. Therefore, there are 5,040 possible registration codes.

Explanation:

To find the number of possible codes, we can use the concept of permutations.

Since the code must be made up of 7 digits and each digit can only be used once, we can calculate the number of permutations of the 7 digits. The formula to use is nPr = n! / (n - r)!, where n is the total number of elements and r is the number of elements to be selected.

In this case, there are 7 digits to choose from and we need to select all of them.

So we plug in n = 7 and r = 7 into the formula:

nPr = 7! / (7 - 7)! = 7! / 0! = 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5,040

Therefore, there are 5,040 possible registration codes.

Answer:

[tex]\pi \: {r}^{2} \\ \pi \: {6}^{2} \\ = 36\pi[/tex]

Answer:

[tex] 8 {x}^{3} + 3 {x}^{2} - 5x + 4[/tex]

Step-by-step explanation:

[tex](6 {x}^{3} + 3 {x}^{2} + 3) + (2 {x}^{3} - 5x + 1) \\ = 6 {x}^{3} + 2 {x}^{3} + 3 {x}^{2} - 5x + 3 + 1 \\ = 8 {x}^{3} + 3 {x}^{2} - 5x + 4[/tex]

Answer:

Option A

Step-by-step explanation:

If you take a look at the translation described in option A, the x value is increased by 1 (from -2 to -1), and the y value is decreased by 5 (from -5 to -10), meaning that you have made this jump with just one translation. Hope this helps!

Answer:

360

Step-by-step explanation:

The sum exterior angles of any number of side polygon is always 360

Answer:

24*(1-0.5^n)/0.5

Step-by-step explanation:

Answer:

Square root of 36.

Step-by-step explanation:

The square root of 36 = 6  so this is rational.

Recall that a rational number is one that can be written as a/b  where a and b are not 0. 6 can be written as 6/1.

Answer:

6

Step-by-step explanation:

The square root of 36 is 6

Answer:

932.58 in ^ 2 is needed

Step-by-step explanation:

What we need to do is calculate the area of all the circles and add it up, so we know how many square inches of paint are going to be needed.

We know that the area of a circle has the following formula:

A = pi * r ^ 2

there are 4 circles:

radio of 2 inches:

A = 3.14 * 2 ^ 2 = 12.56 in ^ 2

radio of 4 inches:

 A = 3.14 * 4 ^ 2 = 50.24 in ^ 2

radio of 9 inches:

A = 3.14 * 9 ^ 2 = 254.34 in ^ 2

radio of 14 inches:

A = 3.14 * 14 ^ 2 = 615.44 in ^ 2

12.56 + 50.24 + 254.34 + 615.44 = 932.58

a total of 932.58 in ^ 2 is needed