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aev [14]
3 years ago
15

Solve the equation for 0° ≤ x ≤ 90°. Round to the nearest degree. 8cotθ + 3 = 5

Mathematics
1 answer:
galina1969 [7]3 years ago
5 0

<u><em>Answer:</em></u>

θ = 76°

<u><em>Explanation:</em></u>

<u>The given equation is:</u>

8 cotθ + 3 = 5

8 cotθ = 5-3

8 cotθ = 2

cot θ = \frac{2}{8} = \frac{1}{4}

<u>Now, we find θ</u>

We know that the cot function is the inverse of the tan function.

The tan of an angle is positive in the first and third quadrants, therefore, the cot will be <u>positive</u> in the <u>first and third quadrants</u> as well

<u>Now, we are given the condition:</u>

0° ≤ x ≤ 90°

<u>Therefore, we know for sure that our angle is in the first quadrant</u>

θ = cot⁻¹(\frac{1}{4}) = 75.96° = 76° to the nearest degree

Hope this helps :)

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A survey was conducted of 880 college students attending the same university. They were offered a list of 10 different internet
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Answer: Yes

Step-by-step explanation:

From the question, we are informed that a survey was conducted of 880 college students attending the same university and that they were offered a list of 10 different internet service providers and were asked to select the one they prefer.

Basee on this information, if everyone selected equal numbers, each service provider will get (880 / 10 = 88 students). In this case, if someone has 89 votes, this means that another person will get 87 votes while the remaining 8 service providers gets 88 students each. Therefore, the device provider with 89 votes can come out on top.

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2 years ago
If (k,6k) and (3k,10k) are two points on the graph of a line and K is not equal to 0, what is the slope of the line?
Nataliya [291]

Answer:

Step-by-step explanation:

slope = y2-y1/x2-x1

Given the coordinates (k,6k) and (3k,10k)

x1 = k

y1 = 6k

x2 = 3k

y2 = 10k

Substitute

slope = 10k-6k/3k-k

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slope = 4/2

slope  = 2

Hence the slope of the line is 2

7 0
2 years ago
Two athletic teams play a series of games; the first team to win 4 games is declared the overall winner. Suppose that one of the
kodGreya [7K]

Answer:

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  • p=0.6480 (2-game series)

Step-by-step explanation:

Let X be the random variable equal the the first 4 straight wins. An overall win for the stronger team implies a negative binomial function with the parameters  n=4, p=0.6:

P(X=4)={{i-1}\choose {4-1}}0.6^40.4^{i-4},\  i=4,5,6,7

#We find probabilities for the different values of i:

P(X=4)={3\choose 3}0.6^4=0.1296\\\\P(X=5)={4\choose 3}0.6^40.4^1=0.2074\\\\P(X=6)={5\choose 3}0.6^40.4^2=0.2074\\\\P(X=4)={6\choose 3}0.6^40.4^3=0.1659

Hence, probability of the stronger team winning overall is:

=P(X=4)+P(X=5)+P(X=6)+P(X=7)\\\\=0.7103

#Define Y as the random variable for winning 2/3 games.:

P(Y=2)={1\choose 1}0.6^2=0.3600\\\\P(Y=3)={2\choose3}0.6^20.4=0.2880\\\\P(win)=0.2880+0.3600=0.6480

Hence, probability of the stronger team winning in 2 out 3 game series is 0.6480

The stronger team has a higher chance of winning in a 4-game series(0.7103>0.6480)

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2 years ago
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Answer:

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Coefficient of x should be 5 so first ? should be 5 let the second ? = z

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