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2 years ago

Helppppp !NO LINKS, NO FILES! please :)

Mathematics

1 answer:

lukranit [14]2 years ago

5 0

Answer:

Step-by-step explanation:

brainly.com/question/23396982?answering=true&answeringSource=greatJob%2FquestionPage%2F1

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How to solve these two problems ？

puteri [66]

8) $\theta$ is -0.896 radians

9) length of arc is 41.91 cm

Solution:

Given that,

$tan\ \theta = \frac{-5}{4}$

$\theta$ is in quadrant 4

To find: $\theta$

From given,

$tan\ \theta = \frac{-5}{4}\\\\\theta = tan^{-1} \frac{-5}{4}\\\\\theta = tan^{-1} (-1.25)\\\\\theta = -51.34$

Thus value of $\theta$ is -51.34 degrees

Convert degrees to radians

$-51.34\ degree = -51.34 \times \frac{ \pi }{180}\ radian\\\\-51.34\ degree = -0.896\ radian$

Thus $\theta$ is -0.896 radians

From given,

radius = 15.4 cm

$\theta = \frac{13 \pi }{15}$

The length of arc when angle in radians is:

$arc\ length = r \times \theta\\\\arc\ length = 15.4 \times \frac{ 13 \pi }{15}\\\\arc\ length = 15.4 \times 2.721\\\\arc\ length = 41.91$

Thus length of arc is 41.91 cm

4 0

3 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 16) = C_{20,16}.(0.75)^{16}.(0.25)^{4} = 0.1897$

$P(X = 17) = C_{20,17}.(0.75)^{17}.(0.25)^{3} = 0.1339$

$P(X = 18) = C_{20,18}.(0.75)^{18}.(0.25)^{2} = 0.0669$

$P(X = 19) = C_{20,19}.(0.75)^{19}.(0.25)^{1} = 0.0211$

$P(X = 20) = C_{20,20}.(0.75)^{20}.(0.25)^{0} = 0.0032$

$P(X \geq 16) = P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20) = 0.1897 + 0.1339 + 0.0669 + 0.0211 + 0.0032 = 0.4148$

c. If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.

The expected value of the binomial distribution is:

$E(X) = np$

In this question, we have $n = 22$

$E(X) = 22*0.75 = 16.5$

The closest integer to 16.5 is 17.

7 0

3 years ago

Pam wants to buy a DVD player. The original price is $50. What is the sale price? with a 90% off

qaws [65]

Answer:

5 dollars

Step-by-step explanation:

If the price is 90 % off, we will pay 100 - 90 or 10 %

Take the original price times 10 %

50 * 10 %

50 * .10

5 0

3 years ago

Pls help me plssssssssss

MariettaO [177]

Step-by-step explanation:

what type of help u want......

7 0

3 years ago

James and Amy play 3 more games.They have played the same number of games as last week .Fill in the blanks to make the equation

Fiesta28 [93]

Question is Incomplete; Complete question is given below;

James and Amy played 12 games of checkers last week. This week they played 7 games on Monday and 2 games on Wednesday.James and Amy play 3 more games. They have played the same number of games as last week. Fill in the blanks to make the equation true. Use +,-, or =. 12_7_2_3 Explain how you chose the symbols.

Answer:

12 = 7 + 2 + 3

Step-by-step explanation:

Given:

Number of games played last week = 12

Number of games played on Monday this week = 7

Number of games played on Wednesday this week = 2

Also given:

James and Amy play 3 more games.

So Number of games played more = 3

We need to fill in the blanks 12 __ 7__2__3 with signs '+', '-','='.

Solution:

It is given that they have played the same number of games as last week.

So we can say that;

Number of games played last week is equal to Number of games played on Monday this week plus Number of games played on Wednesday this week plus Number of games played more.

framing in equation form we get;

$12 = 7 + 2+3$

Hence we have fill the blanks as 12 = 7 + 2 + 3.

8 0

3 years ago