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3 years ago

A cylinder has a radius of 8 cm and a height of 14 cm. What is the volume of the cylinder?

1 answer:

6 0

The volume of a cylinder is represented by the following equation...

V=<span><span>πr^2 x </span><span>h
</span></span>
Volume = π(64)(14)

Your volume is 896π

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Find the angle made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest in

prohojiy [21]

<h2>Answer:</h2>

55°

<h2> Step-by-step explanation:</h2>

To solve this, follow these steps:

i. <em>Make a sketch of the problem</em>.

The sketch has been attached to this response.

ii. <em>Label the sketch properly</em>

As shown in the sketch, θ is the angle between the x-axis and the terminal side resulting from connecting the origin to (5,7).

iii. <em>Solve using the tangent trigonometric ratio</em>

With the proper sketch and labelling, a right triangle is formed with the adjacent and opposite sides to the angle being 5 units and 7 units respectively.

Using the tangent formula,

tan θ = opposite / adjacent

tan θ = 7 / 5

θ = tan⁻¹ (7/5)

θ = tan⁻¹ (1.4)

θ = 54.46

θ = 55° to the nearest integer.

Therefore, the angle made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest integer is 55°

3 0

2 years ago

3. Cameron's car averages 25 miles

Triss [41]

Answer:15.2

Step-by-step explanation:380/25

8 0

3 years ago

Read 2 more answers

The movie theater in town has 4 rooms. Each room has 58 seats on the left side and 32 seats on the right side. Which equation co

saveliy_v [14]

Answer:

The right option is (C) (58 + 32)×4

Step-by-step explanation:

Total number of rooms = 4

Number of seats on left = 58 seats in each room

Number of seats on right = 32 seats in each room

Total number of seats in a room = 58 + 32 seats

Total number of seats in the movie theater = Number of rooms × Number of seats in each room

Total number of seats in the movie theater = 4 × (58 + 32) = 360 seats

Hence the right option is (C) (58 + 32)×4

7 0

3 years ago

Write the following sentence into an expression using x as your variable: Myrna and Tom collect stamps. Tom has four more than h

balandron [24]

Answer: f(x) = x/2 + 4.

where f(x) is the number of stamps that Tom has, and x is the number of stamps that Myrna has.

Step-by-step explanation:

The statement is:

"Tom has four more than half the stamps that Myrna has"

For how is written, we can model the number of stamps that Tom has as a function f(x).

f(x) represents the number of stamps that Tom has, and x is the number of stamps that Myrna has.

Then:

"four more than a number" is written as:

N + 4 (where N is the number)

"Half the stamps that Myrna has" is written as:

x/2.

Then the whole statement can be modeled as:

f(x) = x/2 + 4.

notice that we have x/2, and f(x) must be a whole number, so Myrna must have an even number of stamps (in that case x/2 will be integer)

8 0

3 years ago

A professor has learned that three students in his class of 20 will cheat on the final exam. He decides to focus his attention o

balu736 [363]

Answer:

$P(X \ge 1) = 0.509$

$P(X \ge 1) = 0.6807$

Step-by-step explanation:

From the question we are told that

The number of students in the class is N = 20 (This is the population )

The number of student that will cheat is k = 3

The number of students that he is focused on is n = 4

Generally the probability distribution that defines this question is the Hyper geometrically distributed because four students are focused on without replacing them in the class (i.e in the generally population) and population contains exactly three student that will cheat.

Generally probability mass function is mathematically represented as

$P(X = x) = \frac{^{k}C_x * ^{N-k}C_{n-x}}{^{N}C_n}$

Here C stands for combination , hence we will be making use of the combination functionality in our calculators

Generally the that he finds at least one of the students cheating when he focus his attention on four randomly chosen students during the exam is mathematically represented as

$P(X \ge 1) = 1 - P(X \le 0)$

Here

$P(X \le 0) = \frac{ ^{3} C_0 * ^{20 - 3} C_{4- 0}}{ ^{20}C_4}$

$P(X \le 0) = \frac{ ^{3} C_0 * ^{17} C_{4}}{ ^{20}C_4}$

$P(X \le 0) = \frac{ 1 * 2380}{ 4845}$

$P(X \le 0) = 0.491$

Hence

$P(X \ge 1) = 1 - 0.491$

$P(X \ge 1) = 0.509$

Generally the that he finds at least one of the students cheating when he focus his attention on six randomly chosen students during the exam is mathematically represented as

$P(X \ge 1) = 1 - P(X \le 0)$

$P(X \ge 1) =1- [ \frac{^{k}C_x * ^{N-k}C_{n-x}}{^{N}C_n}]$