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3 years ago

An equilateral triangle has an altitude length of 33 feet. Determine the length of a side of the triangle.

Mathematics

1 answer:

Murrr4er [49]3 years ago

4 0

The side of this triangle is about 23.3345237792

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Write the expression as one<br> involving only sin x and cos x.<br> sin 2x + cos x

AfilCa [17]

Answer:

sin 2x + cos x = 2 sin x cos x + cos x = (2 sin x + 1)cos x

Step-by-step explanation:

Given the expression: sin 2x + cos x,

then we can use the formula: sin 2x = 2 sin x cos x, which gives:

sin 2x + cos x = 2 sin x cos x + cos x = (2 sin x + 1)cos x

So there you have two expressions in terms of sin x and cos x, as requested. :D

6 0

2 years ago

A function models the growth of a sample starting with 40 bacteria with the ability to double every two hours. Which graph

natima [27]

Answer:

The function is y = 40 * 2^(x/2)

The graph is in the image attached

Step-by-step explanation:

The function that models this growth is an exponencial function, that can be described with the following equation:

y = a * b^(x/n)

Where a is the inicial value, b is the rate of growth, x is the time and n is the relation between the time and the rate (the rate occurs for every two hours, so n = 2).

Then, using a = 40, r = 2 and n = 2, we have:

y = 40 * 2^(x/2)

If we plot this function, we have the graph shown in the image attached,

It is an exponencial graph, where the value of y increases very fast in relation to the increase of x.

7 0

3 years ago

An exit poll in an election is a survey taken of voters just after they have voted. One major use of exit polls has been so that

3241004551 [841]

Answer:

P(A) = 0.39

Step-by-step explanation:

We are given;

P(W|A) = 0.7

P(W|A^c ) = 0.3

We are told that 60% of the respondents said they voted for A. Thus;

P(A|W) = 60% = 0.6

Now, using the principle of drawing lots, we can be able to find the probability of the event that they are willing to participate in the exit poll which is P(W).

Thus;

P(W) = [P(W|A) × P(A)] +[P(W∣A^c) × P(A^c)]

Now, P(A^c) can be expressed as 1 - P(A)

Thus, we now have;

P(W) = [P(W|A) × P(A)] + [P(W∣A^c) × (1 - P(A)]

Plugging in the relevant values gives;

P(W) = 0.7P(A) + 0.3(1 - P(A))

P(W) = 0.7P(A) + 0.3 - 0.3P(A)

P(W) = 0.3 + 0.4P(A)

Now,using Baye's theorem, we can find an expression for P(A|W)

Thus;

P(A|W) = [P(A ∩ W)]/P(W)

This can be further expressed as;

P(A|W) = [P(A) × P(W|A)]/P(W)

Plugging in relevant values, we have;

0.6 = 0.7P(A)/(0.3 + 0.4P(A))

Cross multiply to get;

0.6(0.3 + 0.4P(A)) = 0.7P(A)

0.18 + 0.24P(A) = 0.7P(A)

0.18 = 0.7P(A) - 0.24P(A)

0.46P(A) = 0.18

P(A) = 0.18/0.46

P(A) = 0.39

7 0

3 years ago

Find the midpoint of the segment with the following endpoints.<br> (4,5) and (9,2)

viktelen [127]

Answer:

(13/2,7/2)

Step-by-step explanation:

7 0

4 years ago

The grap

Mila [183]

Answer:

Step-by-step explanation:

Just look at the graph....................

6 0

4 years ago