Which pairs of angles are congruent?

If $560 is invested at an interest rate of 9% per year and is compounded continuously, how much will the investment be worth in

koban [17]

Answer:

$878.25

Step-by-step explanation:

Continuously compounded interest is:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the number of compoundings.

Here, P = 560, r = 0.09, and t = 5.

A = 560e^(0.09×5)

A = 878.25

5 0

2 years ago

Two families go to a zoo.

Alisiya [41]

Adult ticket=£17 and child ticket=£9 hope this helps

3 0

2 years ago

Helen is putting a fence around her flower garden, which is in the shape of half of a circle and a rectangle. If the semicircle

erastova [34]

Answer:

Part 1) Helen will need 38 feet of fencing

Part 2) The perimeter around the three sides of the rectangular section of the garden is 27 feet

Part 3) The approximate distance around half of the circle is 11 feet

Step-by-step explanation:

Part 1) How much fencing will Helen need?

Find out the perimeter

we know that

The perimeter of the figure is equal to the sum of three sides of the rectangular section plus the circumference of a semicircle

so

$P=2L+W+\frac{1}{2}\pi D$

we have

$L=10\ ft\\W=7\ ft\\D=7\ ft\\\pi =\frac{22}{7}$

substitute

$P=2(10)+7+\frac{1}{2}(\frac{22}{7})(7)$

$P=20)+7+11=38\ ft$

therefore

Helen will need 38 feet of fencing

Part 2) What is the perimeter around the three sides of the rectangular section of the garden?

$P=2L+W$

we have

$L=10\ ft\\W=7\ ft$

substitute

$P=2(10)+7$

$P=20+7=27\ ft$

therefore

The perimeter around the three sides of the rectangular section of the garden is 27 feet

Part 3) What is the approximate distance around half of the circle?

Find the circumference of semicircle

$C=\frac{1}{2}\pi D$

we have

$D=7\ ft\\\pi =\frac{22}{7}$

substitute

$C=\frac{1}{2}(\frac{22}{7})(7)$

$C=11\ ft$

therefore

The approximate distance around half of the circle is 11 feet

4 0

2 years ago

Read 2 more answers

Use the distributive property to write an equivalent expression.<br> 3(8-9)

yulyashka [42]

The solution to this is 3(8)-3(9).

8 0

2 years ago

According to national data, 5.1% of burglaries are cleared with arrests. A new detective is assigned to six different burglaries

blagie [28]

Answer:

26.95% probability that at least one of them is cleared with an arrest

Step-by-step explanation:

For each burglary, there are only two possible outcomes. Either it is cleared, or it is not. The probability of a burglary being cleared is independent of other burglaries. 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.

5.1% of burglaries are cleared with arrests.

This means that $p = 0.051$

A new detective is assigned to six different burglaries.

This means that $n = 6$

What is the probability that at least one of them is cleared with an arrest?

Either none are cleared, or at least one is. The sum of the probabilities of these events is 100% = 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

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

$P(X = 0) = C_{6,0}.(0.051)^{0}.(0.949)^{6} = 0.7305$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7305 = 0.2695$

26.95% probability that at least one of them is cleared with an arrest

8 0

2 years ago