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2 years ago

Which proportion satisfies the geometric mean (altitude) theorem for the triangle?

Mathematics

2 answers:

Snezhnost [94]2 years ago

8 0

Answer:

D. $\frac{2}{h}=\frac{h}{3}$

Step-by-step explanation:

We have been given an image of a triangle. We are asked to choose the proportion that satisfies the geometric mean (altitude) theorem for the triangle.

The geometric mean (altitude) theorem states that altitude drawn from the right angle to hypotenuse divides the hypotenuse into two segments such that their product is equal to the altitude times altitude.

$\frac{2}{h}=\frac{h}{3}$

Therefore, option D is the correct choice.

Degger [83]2 years ago

3 0

D is the correct answer

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Tim was given a large bag of sweets and ate one third of the sweets before stopping as he was feeling sick. The next day he ate

mars1129 [50]

Answer: In the beginning he was given 27 sweets.

Step-by-step explanation: The most logical thing to do is to solve it backwards, that is, from what he had at the end of the third day up till the beginning of the first day.

On the third day he ate one-third and had 8 sweets left over. To determine how many he started with on the third day, let the total on day three be called a. If one-third of a is eaten, then the left over which is two-thirds is 8. That is;

8/a = 2/3

By cross multiplication we now have

8 x 3 = 2a

24/2 = a

a = 12

Let the number of sweets he had on day two be called b. If he ate one-third of b and he had 12 left over, then the two-thirds left over is 12 and we now have;

12/b = 2/3

By cross multiplication we now have

12 x 3 = 2b

36 = 2b

36/2 = b

b = 18

Let the number of sweets he had on day one be called x. If he ate one-third of x and he had 18 left over, then the two-thirds left over is 18, and we now have;

18/x = 2/3

By cross multiplication we now have

18 x 3 = 2x

54 = 2x

x = 27

Therefore Tim was given 27 sweets at the beginning.

3 0

2 years ago

Carl bought some stock at $25 a share it increased 1 1/2 times its value. How much is the stock per share ?

jolli1 [7]

Answer: $37.50 per share

Step-by-step explanation:

Take the difference in the final price and the original price. Divide by the original price and multiply by 100.

37.5-25= 12.5

12.5/25= .50

.50*100= 50%

The other answers are $12.50 per share, and

The new stock is worth $37.50 per share.

4 0

2 years ago

Read 2 more answers

A class with n kids lines up for recess. The order in which the kids line up is random with eachordering being equally likely. T

Elis [28]

Answer:

A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

B) The method used is Relative frequency approach.

Step-by-step explanation:

From the question, we are told a sample of n kids line up for recess.

Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).

Since we are being asked about 3 kids from the class, let's assign a letter to each kid:

J: John

B: Betty

M: Mary

A) Now, we want to find the probability that Betty is first in line or Mary is last in line.

In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;

P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))

Where;

The suffix 1 refers to the first position while the suffix n refers to the last position.

Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)

This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.

B) The method used is Relative frequency approach.

In this method, the probabilities are usually assigned on the basis of experimentation or historical data.

For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.

Also, let n_A be the number of times that A did occur.

Now, the relative frequency would be written as (n_A)/n.

Thus, in this method, we will define P(A) as:

P(A) = lim:n→∞[(n_A)/n]

7 0

2 years ago

the mean height of the team is 200.3 .a new player joins and raises the mean average height to 201cm. work out the height of the

ivann1987 [24]

Question

The table shows the heights in a basketball team.

Height: 198, 199, 200, 201, 202

a.) Work out the mean height of the team. Round you answer to 1d.p.

That, I have worked out is 200.3

b.) A new player joins the team and raises the mean average height to 201cm. Work out the height of the new player.

Answer:

206 cm

Step-by-step explanation:

The sum of the fiven numbers, 198+199+200+201+202=1000

For a mean of 201, the product should be 201*6=1206

The difference of the two is equivalent to the height of the other person hence 1206-1000=206 cm

Therefore, the height is 206 cm

8 0

1 year ago

Now imagine that instead of walking along the path 1→2→3→4→1, ann walks 80 meters on a straight line 33∘ north of east starting

stealth61 [152]

Answer:

Anna's walk as a vector representation is $80\cos 33^{\circ}\hat{i}+80 \sin33^{\circ}\hat{j}$ and refer attachment.

Step-by-step explanation:

Let the origin be the point 1 from where Ann start walking.

Ann walks 80 meters on a straight line 33° north of the east starting at point 1 as shown in figure below,

Resolving into the vectors, the vertical component will be 80Sin33° and Horizontal component will be 80Cos33° as shown in figure (2)

Ann walk as a vector representation is $80\cos 33^{\circ}\hat{i}+80 \sin33^{\circ}\hat{j}$

Thus, Anna's walk as a vector representation is $80\cos 33^{\circ}\hat{i}+80 \sin33^{\circ}\hat{j}$

7 0

2 years ago

Read 2 more answers