What’s the answer to this problem that I can not figure out

Please Help! Math help Needed

Sholpan [36]

ANSWER

The exact value is 24√3

The approximate value is 41.6 to the nearest tenth.

x=52.1 units.

EXPLANATION

Let the blue dotted line be h units.

This line is opposite to the 60° angle.

The side length of the triangle which is 24 units is adjacent to the 60° angle.

So we use the tangent ratio,

$\tan(60 \degree) = \frac{opposite}{adjacent}$

$\tan(60 \degree) = \frac{h}{24}$

$\sqrt{3} = \frac{h}{24}$

$h = 24 \sqrt{3}$

This is the exact value.

$h = 41.6$

This is that approximate value to the nearest tenth.

To find the side length , x, we need to use the second triangle.

$\sin(53\degree) = \frac{h}{x}$

$\sin(53\degree) = \frac{41.6}{x}$

$x = \frac{41.6}{\sin(53\degree)}$

$x = 52.1$

3 0

3 years ago

Let X be the number of accidents per week at the Hillsborough Street roundabout by the NCSU Bell Tower. Assume X varies with mea

Eduardwww [97]

Answer:

1) 0.1587 = 15.15% probability that x is less than 2

2) 7.64% probability that there are fewer than 100 accidents at the roundabout in a year

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the Central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .