A cone has a diameter of 6 centimeters and a height that is 3 times the diameter. Using 3.14 for pi, which of the following can be used to calculate the volume of the cone?one over three(3.14)(3cm)2(18cm)
one over three(3.14)(6cm)2(18cm)
one over three(3.14)(18cm)2(3cm)
one over three(3.14)(18cm)2(6cm)

Answers

Answer 1

Answer: The volume of the cone is calculated by the formula:

V = B*H/3
r=D/2 = 6/3 = 2
where B is surface area of basis and H is height.

B is circle which fomula for surface is:
B = r^2 * pi = 3^2*3,14 = 9*3,14 = 28.26

from condition of height we write:
H = 3*D = 3*6 = 18

now volume is:

If we express all of that in equation of volume we get:

V = 1/3* 3^2*3,14*18

Answer is first option.

Answer 2

Answer:

Answer:

Answer is first option.

Step-by-step explanation:

V = 1/3* 3^2*3,14*18

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Consider a situation in which P(X) = and P(Y) = . If P(X and Y) is = , which best describes the events?They are independent because P(X) · P(Y) = P(X and Y).
They are independent because P(X) + P(Y) = P(X and Y).
They are dependent because P(X) · P(Y) = P(X and Y).
They are dependent because P(X) + P(Y) = P(X and Y).

Answers

Answer:

They are independent because P(X) · P(Y) = P(X and Y).

Step-by-step explanation:

Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event. This means that the probability of both events happening is equal to the product of the probabilities of each event happening individually.

In the given situation, we have:

P(X) = 1/2

P(Y) = 1/2

P(X and Y) = 1/4

If we calculate the product of P(X) and P(Y), we get:

P(X) · P(Y) = 1/2 · 1/2 = 1/4

This is equal to P(X and Y), which means that the events X and Y are independent.

P(X) + P(Y) = P(X and Y) is not a necessary condition for independence. For example, the events of flipping a coin and rolling a die are independent, but P(X) + P(Y) ≠ P(X and Y).

Therefore, the best description of the events is that they are independent because P(X) · P(Y) = P(X and Y).

A gardener is planting two types of trees:Type A is three feet tall and grows at a rate of 15 inches per year.
Type B is four feet tall and grows at a rate of 10 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.

Answers

First convert the feet to inches:

3 feet= 36 in.; 4 feet=48 in.

Make an equation for each one:

Type A: h=36+15x

Type B: h=48+10x

Since the questions wants the heights to be equal, h=h so you can substitute so you have:

36+15x=48+10x

5x=12

x=2 2/5 years or 2.4 years

Marina saved $80 from her babysitting job. She wants to buy some shirts and pants that are on sale at her favourite store for $17 each. How many items of clothing can she buy?

Answers

Answer:

Step-by-step explanation:

Total amount of money that Marina saved from her babysitting job is $80.

She wants to buy some shirts and pants that are on sale at her favourite store for $17 each. To determine how many items of clothing that she can buy, we would divide the total amount that she saved by the cost of each clothing. It becomes

80/17 = 4.7.

Since the number of clothing must be whole number, the number of clothing that she can buy would be 4

Solve this linear equations: x + y + z = 34 1x + 10y + 5z = 100

Answers

Answer

To solve this system of linear equations, we can use the method of substitution.

First, let's solve the first equation for x:

x = 34 - y - z

Now, we substitute this value of x into the second equation:

1(34 - y - z) + 10y + 5z = 100

34 - y - z + 10y + 5z = 100

34 + 9y + 4z = 100

Next, we simplify the second equation:

9y + 4z = 100 - 34

9y + 4z = 66

We can rewrite this equation as:

9y = 66 - 4z

y = (66 - 4z) / 9

Now, we substitute this value of y back into the first equation:

x + (66 - 4z) / 9 + z = 34

Multiplying through by 9 to eliminate the fraction:

9x + 66 - 4z + 9z = 306

9x + 5z = 240

Now we have a system of two equations in two variables:

9x + 5z = 240

9y + 4z = 66

We can solve this using the method of substitution or elimination. Let's use the method of elimination:

Multiplying the first equation by 4 and the second equation by 5, we get:

36x + 20z = 960

45y + 20z = 330

Subtracting the second equation from the first, we eliminate z:

36x - 45y = 630

We can simplify this equation by dividing through by 9:

4x - 5y = 70

Now, let's solve the new system of equations:

4x - 5y = 70

9y + 4z = 66

We can multiply the first equation by 9 and the second equation by 4 to eliminate x:

36x - 45y = 630

36y + 16z = 264

Now, subtracting the first equation from the second, we eliminate y:

36y + 16z - 36x + 45y = 264 - 630

81y + 16z = -366

Dividing through by 3, we get:

27y + 16z = -122

Now, we have a system of two equations in two variables:

4x - 5y = 70

27y + 16z = -122

We can solve this system using the method of substitution or elimination.

Which of the following are vertical asymptotes of the function y = 3cot(1/2x) - 4?

Answers

A vertical asymptote is a line that the graph of the function does not cross.
If: $\lim_(x \to a) 3 cot (1/2 x)-4 =$ +/- ∞
then the line x = a is a vertical asymptote.
For x = 0:
f ( 0 ) = 3 * cot 0 - 4 = ∞
For x = +/- 2 π :
f ( 2 π ) = 3 * cot π - 4 = - ∞
Answer:
A ) x = 0 and C ) x = +/- 2π

Answer:

x=0 or ±2 nπ where n belongs to natural numbers.

Step-by-step explanation:

The " vertical asymptote " is a vertical line that the graph of a function approaches but never touches. To find the vertical asymptotes of a rational function we set denominator=0.

We are given function y=3 cot((1/2)x)-4

which could also be written as $y=3*(cos((1/2)x))/(sin((1/2)x)) -4\n\ny=(3 cos((1/2)x)-4 sin((1/2)x))/(sin((1/2)x))$

for denominator to be equal to 0 we must have sin((1/2)x)=0

⇒ (1/2)x=0

⇒ x=0 or ±2 nπ where n belongs to natural numbers.

Hence, the vertical asymptotes of the given function is x=0 or ±2 nπ where n belongs to natural numbers.

A necklace has and matching bracelet have two types of beads. The necklace has 12 large beads and 8 small beads and weighs 88 grams. The bracelet has 5 large beads and 2 small beads and weighs 25 grams. Write and solve a system of equations to find the weight of a large bead and weight of a small bead.