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2 years ago

AC CE and D is the midpoint of CE. IF CE 10x + 18, DE =7x -1, and BC = 9x - 2, find AB, AB =

Mathematics

1 answer:

Anastasy [175]2 years ago

4 0

Answer:

<h3> If you mean: AC=CE, the answer is: AB = 24</h3>

Step-by-step explanation:

D is the midpoint of CE, then

CD = DE = 0.5CE = 0.5(10x+18) = 5x + 9

So: 5x + 9 = 7x - 1

-9 -9

5x = 7x - 8

-7x -7x

-2x = -8

÷(-2) ÷(-2)

x = 4

AC = CE = 10x + 18 = 40 + 18 = 58

BC = 9x - 2 = 36 - 2= 34

AB = AC - BC = 58 - 34 = 24

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n 2019, approximately 97.4% of all the runners who started the Boston Marathon (in Boston, Massachusetts, USA) were able to comp

Zarrin [17]

Answer:

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

Step-by-step explanation:

For each runner, there are only two possible outcomes. Either they finished the marathon, or they did not. The probability of a runner completing the marathon is independent of any other runner. This means that the binomial probability distribution is used 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.

97.4% finished:

This means that 100 - 97.4 = 2.6% = 0.026 did not finish, which means that $p = 0.026$

100 runners are chosen at random

This means that $n = 100$

Find the probability that at least 5 of them did not finish the marathon

This is:

$P(X \geq 5) = 1 - P(X < 5)$

In which

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

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

$P(X = 0) = C_{100,0}.(0.026)^{0}.(0.974)^{100} = 0.0718$

$P(X = 1) = C_{100,1}.(0.026)^{1}.(0.974)^{99} = 0.1916$

$P(X = 2) = C_{100,2}.(0.026)^{2}.(0.974)^{98} = 0.2531$

$P(X = 3) = C_{100,3}.(0.026)^{3}.(0.974)^{97} = 0.2207$

$P(X = 4) = C_{100,4}.(0.026)^{4}.(0.974)^{96} = 0.1429$

$P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0718 + 0.1916 + 0.2531 + 0.2207 + 0.1429 = 0.8801$

$P(X \geq 5) = 1 - P(X < 5) = 1 - 0.8801 = 0.1199$

0.1199 = 11.99% probability that at least 5 of them did not finish the marathon

4 0

1 year ago

In a study of crime, the FBI found that 13.2% of all Americans had been victims of crime during a 1-year period. This result was

Mkey [24]

Answer: The lower bound of confidence interval would be 0.116.

Step-by-step explanation:

Since we have given that

p = 13.2%= 0.132

n = 1105

At 90% confidence,

z = 1.645

So, Margin of error would be

$z\sqrt{\dfrac{p(1-p)}{n}}\\\\=1.645\times \sqrt{\dfrac{0.132\times 0.868}{1152}}}\\\\=0.0164$

So, the lower bound of the confidence interval would be

$p-\text{margin of error}\\\\=0.132-0.0164\\\\=0.116$

Hence, the lower bound of confidence interval would be 0.116.

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1 year ago

Which statements are true about the graph of y < Two-thirdsx + 1? Check all that apply. The slope of the line is 1. The line

Marina CMI [18]

The answer would be:

The x-intercept of the boundary line is (-3/2, 0).

The area below the line is shaded.

The slope of the line should be 2/3. The area below the line shaded because the function using y<.....

Coordinate 2,3 doesn't fulfill the function.

y < 2/3x + 1

3 < 2/3(2)+1

3< 4/3+1

3< 2.3 ---->false

X intercept is when the y variable is zero. If you put it to the equation

y = 2/3x + 1

0= 2/3x+1

2/3x= -1

x= -3/2

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Answer:

Step-by-step explanation:

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If the growth rate is a number greater than 1, we have exponential growth; if the growth rate is a number greater than 0 but less than 1, we have exponential decay.

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So the rate of growth is 7%

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1 year ago

y - 5 = 0.5x2 + 6x - 3 How many x-intercepts does the graph of this quadratic have? Two x-intercepts One x-intercept No x-interc

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2 years ago

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