For a Right triangle with 30-60-90 degrees, the sides have specific ratios. If we assign a length of 1 to the short side (opposite 30), the hypotenuse will be 2, and the other leg will be square root 3.

Given that the hypotenuse is 16 in this triangle, we will need to multiply each of our ratios given above by 8 (16/2)

So, the short side is 8, the hypotenuse is 16 and the last leg is 8(square root 3). Adding these three sides we get

8 + 16 + 8 sqrt(3)
24 + 8 sqrt(3)

The answer is B

3 0

3 years ago

What is the value of y in the equation 4y – 2(1 – y) = –44?<br> –23<br> –15<br> –14<br> –7

user100 [1]

Answer:

-7

Step-by-step explanation:

4 0

3 years ago

Find the 66th term of the arithmetic sequence -10, 7, 24

zavuch27 [327]

Answer:

1095

Step-by-step explanation:

There is a common difference between consecutive terms , that is

7 - (- 10) = 24 - 7 = 17

This indicates the sequence is arithmetic with n th term

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 10 and d = 17 , thus

$a_{66}$ = - 10 + (65 × 17) = - 10 + 1105 = 1095

5 0

3 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.

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