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2 years ago

The value of r? Do not round your answer.

Mathematics

1 answer:

bearhunter [10]2 years ago

8 0

Answer:

r = 31.2

Step-by-step explanation:

Δ ACE and Δ BCD are similar, thus the ratios of corresponding sides are equal, that is

$\frac{AE}{BD}$ = $\frac{CE}{CD}$ , substitute values

$\frac{r}{19.5}$ = $\frac{64}{40}$ ( cross- multiply )

40r = 1248 ( divide both sides by 40 )

r = 31.2

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Write the equation of the line that passes through (3, 4) and 2, -1) in slope-intercept form

Marat540 [252]

Answer:

Step-by-step explanation:

(-1 -4)/(2 - 3) = -5/-1 = 5

y - 4 = 5(x - 3)

y - 4 = 5x - 15

y = 5x - 11

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2 years ago

A public health organization reports that 40%of baby boys 6-8 months old in the United

Sveta_85 [38]

Using the binomial distribution, the probabilities are given as follows:

0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.

0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.

Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.

<h3>What is the binomial distribution formula?</h3>

The formula is:

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

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

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

The values of the parameters for this problem are:

n = 10, p = 0.4.

The probability that more than 4 weigh more than 20 pounds is:

$P(X > 4) = 1 - P(X \leq 4)$

In which:

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

Then:

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

$P(X = 0) = C_{10,0}.(0.4)^{0}.(0.6)^{10} = 0.0061$

$P(X = 1) = C_{10,1}.(0.4)^{1}.(0.6)^{9} = 0.0403$

$P(X = 2) = C_{10,2}.(0.4)^{2}.(0.6)^{8} = 0.1209$

$P(X = 3) = C_{10,3}.(0.4)^{3}.(0.6)^{7} = 0.2150$

$P(X = 4) = C_{10,4}.(0.4)^{4}.(0.6)^{6} = 0.2502$

Hence:

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0061 + 0.0403 + 0.1209 + 0.2150 + 0.2502 = 0.6325$

$P(X > 4) = 1 - P(X \leq 4) = 1 - 0.6325 = 0.3675$

0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.

The probability that fewer than 3 weigh more than 20 pounds is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0061 + 0.0403 + 0.1209 = 0.1673

0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.

For more than 7, the probability is:

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10)$

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

$P(X = 8) = C_{10,8}.(0.4)^{8}.(0.6)^{2} = 0.0106$

$P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016$

$P(X = 10) = C_{10,10}.(0.4)^{10}.(0.6)^{0} = 0.0001$

Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.

More can be learned about the binomial distribution at brainly.com/question/24863377

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4 0

1 year ago

1. The function h = - 4.9x2 + 40x + 1 gives the height of a baseball after it has been hit

pickupchik [31]

The ball will hit the ground between 8 and 9 seconds

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2 years ago

tony is taking a 5 year loan in the amount of $15,000. The interest is continuously compounded at an annual rate of 7%. How much

kobusy [5.1K]

Answer:

$21,038.28

Step-by-step explanation:

Use the equation 15000(1.07)^5 since 1.07 equals to 7% and you are loaning more money to Tony's account for 5 years. You should get $21,038.28 as your result.

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago