If BC = 4 and CD = 27, find AC.

Answers

Answer 1

Answer: $\Delta ABC\sim\Delta DAC\n\nthen\n\n(|AC|)/(|BC|)=(|CD|)/(|AC|)\n\n|AC|^2=|BC|\cdot|CD|\n\n|AC|^2=4\cdot27\n\n|AC|=√(4\cdot27)\n\n|AC|=\sqrt4\cdot√(27)\n\n|AC|=2\cdot√(9\cdot3)\n\n|AC|=2\sqrt9\cdot\sqrt3\n\n|AC|=2\cdot3\sqrt3\n\n|AC|=6\sqrt3$

Answer 2

Answer:

31 is the answer I think..

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its cost 50 to make a bracelet and 1$ to make a necklace to make a profit the total cost for bracelets and necklaces must be less than 10$ the jeweler can make no more than 14 pieces of jewelry each day write a system of inequalities to model the number of bracelets and necklaces to be made each day

Answers

b + n ≤ 14 and .50b + 1n < 10 This is because the total number of bracelets added to the total number of necklaces made each day must be less than or equal to 14. Also, the price of each bracelet (.50b) added to the price of each necklace (1n) must be less than $10.

Weather records show that the probability of rainfall in Florida in June is 0.86. What is the probability that it rains there in June at least 9 times in a decade?

Answers

0.5816 = 58.16% probability that it rains there in June at least 9 times in a decade.

For each June 9 in Florida, there are only two possible outcomes. Either it rains, or it does not. The probability of raining on June 9 of an year is independent of rain on June 9 on any other year, which means that the binomial probability distribution is used to solve this question.

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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.

$C_(n,x) = (n!)/(x!(n-x)!)$

And p is the probability of X happening.

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0.86 probability of rain means that $p = 0.86$
A decade means 10 years, so $n = 10$

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What is the probability that it rains there in June at least 9 times in a decade?

This is:

$P(X \geq 9) = P(X = 9) + P(X = 10)$

In which

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

$P(X = 9) = C_(10,9).(0.86)^(9).(0.14)^(1) = 0.3603$

$P(X = 10) = C_(10,10).(0.86)^(10).(0.14)^(0) = 0.2213$

Thus

$P(X \geq 9) = P(X = 9) + P(X = 10) = 0.3603 + 0.2213 = 0.5816$

0.5816 = 58.16% probability that it rains there in June at least 9 times in a decade.

A similar question is found at brainly.com/question/9631195

R - it is rain (probablity: 0.86)
N - it is not rain (probablity: 1-0.86 = 0.14)
You've got these cases:

R R R R R R R R R N
R R R R R R R R N R
R R R R R R R N R R
. . .
N R R R R R R R R R - it is 10 cases. Probablity each case is
(0.86)^9 * 0.14 - it is approximately 0.036 (9R and 1N - you multiply everything)

It is 10 cases so you have to multiply by 10 and you get 0.36

There is also eleventh case:

R R R R R R R R R R

Probablity is (0.86)^10 approximately 0.22

Add these cases and you'll get your probablity: 0.36 + 0.22 = 0.58

Variable y varies directly with variable x, and y = 6 when x = 20.What is the constant of variation in decimal form?

Answers

In a direct proportion, the equation can be set up as
y = kx
k = y/x
k = 6/20
k = 0.3

If a sheep eats 1/6 of a bale a day how many sheep can be fed off of 1bale of hay?

Answers

To find out how many $\frac { 1 }{ 6 }$ there are in $1$ you should divide $1$ by $\frac { 1 }{ 6 }$ so :
$\frac { 1 }{ \frac { 1 }{ 6 } } =1\cdot 6=6$
6 sheep can be fed with 1 bale hay

6 because 6/6 is a whole and each sheep only eats 1/6.

A 7-foot tall stop sign creates a shadow that is 2 feet long. At the same time, a utility pole creates a shadow that is 9.6 feet long. How tall, in feet, is the utility pole?

Answers

Answer:

33.6

Step-by-step explanation:

Divide 9.6 by 2

9.6/2

4.8

Multiply that by 7

4.8x7

33.6 feet tall

A pie was cut into 8 equal slices. If Ruben ate 3/4 of the pie, how many slices did he ate? Explain your answer using a number line and words.

Answers

Answer:

Step-by-step explanation:

A pie was cut into 8 equal slices. Ruben ate 3/4 of the pie.

We have tell how many slices Ruben ate.

Since a pie was cut in 8 pieces that means 1 piece is 1/8th part of pie.

Since Ruben ate 3/4 of pie that means 6/8 of pie was finished by Ruben.

This clearly says that out of 8 pieces 6 pieces Ruben has eaten.

If Ruben ate 3/4 of the pie, that means that he ate 6/8 of it, because 3/4 = 6/8, that is, he ate 6 of the 8 slices of the pie.

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