A cylinder has a radius of 12.2 inches and a height of 6.1 inches.

What is the approximate volume of the cylinder?

Use 3.14 for pi.


74.4 in³

148.8 in³

2850.9 in³

4961.2 in³

Final answer:

To find the price of one drink, we create a system of equations based on the purchases at the movie theater and solve it using the elimination method. The calculated price of one drink is $3.75, to the nearest cent.

Explanation:

David and Ryan's purchases at the movie theater can be represented by the following system of equations to find the price of one bag of popcorn (p) and one drink (d):

3p + 5d = 24.75

9p + 4d = 33.00

We'll solve this system using the substitution or elimination method. For this example, we will use the elimination method.

Multiply the first equation by 9 and the second by 3 to equalize the coefficients for p:

(3p + 5d) × 9 → 27p + 45d = 222.75

(9p + 4d) × 3 → 27p + 12d = 99.00

Subtract the second equation from the first:

27p + 45d - (27p + 12d) = 222.75 - 99.00

33d = 123.75

Divide by 33 to find the price of one drink:

d = 123.75 / 33

d = 3.75

So, the price of one drink is $3.75, to the nearest cent.

Answer:

Its 131, I did the test, and got it right.

Explanation:

Let's assume Ken arranged his sandwiches in a rectangular shape with length 'L' and width 'W'. Now Sarah arranged her sandwiches to form a border around Ken's rectangle. The solution diagram is attached below.

Ken needs as much sandwiches as area of rectangle i.e. number of Ken's sandwiches would be = LW.

It is clear that Sarah needs as much sandwiches as perimeter of rectangle and extra four sandwiches to put on corners. It means number of Sarah's sandwiches would be = 2·(L+W) + 4.

Given that all of the sandwiches are the same size and they are all used.

Ken and Sarah bought same number of sandwiches. So we need to solve the following equation :-

Number of Ken's sandwiches = Number of Sarah's sandwiches

LW = 2·(L+W) + 4

Using trial and error approach, we get 6 x 4 = 2 x (6 + 4) + 4.

So number of Ken's sandwiches would be LW = 6 x 4 = 24 sandwiches.

Hence, final answer is "Each person could have 24 sandwiches".

In this Pythagorean theorem question, The value of pq in the right triangle is 8 cm. Therefore, the correct answer is option C.

The given triangle is a right triangle, with two sides measuring 17 cm and 15 cm. The side opposite the right angle (perpendicular) is represented by the variable pq.

To find the value of pq, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. So, applying the Pythagorean theorem:

a2 + b2 = c2

(15 cm)2 + pq2 = (17 cm)2

225 cm2 + pq2 = 289 cm2

pq2 = 289 cm2 - 225 cm2

pq2 = 64

pq = √64

pq = 8 cm

Learn more about Pythagorean theorem here:

https://brainly.com/question/28361847

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Answer:

8 meters per second

Step-by-step explanation:

Hi, to answer this question we simply have to substitute k=32 in the formula given and solve for v.

K= (v ^ 2) /2

Substituting K=32

32 = (v ^ 2) /2

Solving for v:

32x2= v ^ 2

64 =v ^ 2

√64 =v

8 =v

v= 8 meters per second

When the kinetic energy is 32 joules, the apple is traveling at a speed of 8 m/s.

Feel free to ask for more if needed or if you did not understand something.

Answer: 10 bugs.

Step-by-step explanation:

Answer:

Step-by-step explanation:

p must be a whole number because $5 which is the cost of socks per pair is a perfect divisor of the expression 5p.

i.e 5p/5 = p

And in the expression p represent number of pairs

Two angles are complementary if they add up to 90 degrees. If one angle measures 32 degrees, the other angle measures 58 degrees, which is found by subtracting 32 from 90.

The question is asking about complementary angles, which are two angles that add up to 90 degrees. If one angle measures 32 degrees, we can find the measure of the second angle by subtracting 32 degrees from 90 degrees since the two angles must sum to 90 degrees.

The calculation would be: 90 degrees - 32 degrees = 58 degrees.

Therefore, the measure of the second angle is 58 degrees, making the correct answer:

Option: A is the correct answer.

         A)     change  direction but remain parallel.

We know that when same rigid transformation is applied  to two lines which are parallel to each other ,then after rigid transformation they will behave the same i.e. same relationship hold between the two the only difference will be in their location.

Given is a parallelogram whose base is b = 10 inches and it says height is 2 more than half-value of base i.e. h = 2 + (b ÷ 2).

So height is h = 2 + (10 ÷ 2) = 2 + 5

⇒ h = 7 inches.

We know the formula for area of parallelogram is given as follows :-

Area of parallelogram = base x height

Area of parallelogram = 10 inches x 7 inches

Area of parallelogram = 70 squared inches.

Hence, the final answer is 70 squared inches.

Final answer:

To get the area of the parallelogram, first determine the height, which is 5 inches plus 2 inches, totaling 7 inches. Using the formula (base × height), the area is calculated as 10 inches times 7 inches, resulting in 70 square inches.

Explanation:

To find the area of the parallelogram, we need to identify its base and height. The base is already given as 10 inches. Next, we calculate the height, which the problem states as '2 inches more than half the base.' First, we find half of the base: 10 inches / 2 = 5 inches. Then, add 2 inches to get the height: 5 inches + 2 inches = 7 inches. Now we have the height of the parallelogram.

Using the formula for the area of a parallelogram (base × height), we can now calculate the area.

Area = 10 inches × 7 inches = 70 square inches.

Thus, the area of the parallelogram is 70 square inches.

Answer:

16 mph

Step-by-step explanation:

Jim is just as likely to get a head as Jane is to get an even number since the chance or probability of getting a head for Jim and getting a even number for Jane are equal i.e. 1/2=0.5

In a quarter there are just two outcomes-- Head and Tail

The probability of getting a head is: 1/2

Similarly in a number cube that has six possible outcomes i.e. {1,2,3,4,5,6}

The number of outcomes that represents a even number are: 3  

(Since outcomes are: 2,4 and 6)

Hence, the probability of getting a even number is: 3/6=1/2

Hence, we see that the probability of getting a head and a even number is same.

An oblique prism can be thought of as a leaning prism where the altitude or height of the prism is not the same as the lateral edge of the prims.