Given that TS is a midsegment of PQR, find x<br> A. 5<br> B.9<br> C.10<br> D.13

A bird leaves its nest and travels 20 miles per hour downwind for x hours. On the return trip, the bird travels 4 miles per hour

Reil [10]

Answer:

The correct answers are:

A) 60 miles; and B) 3.375 hours.

Explanation:

We will use the equation d = rt for this.

For the first leg of the trip, the bird travels 20 miles per hour for x hours. This gives us the equation

d = 20x

For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour. He also travels 6 miles less than the return distance, for x hours:

d-6 = 16x

To isolate d, we will add 6 to each side:

d-6+6 = 16x+6

d = 16x+6

We will set the two equations equal to one another, since they both equal d:

20x = 16x+6

Subtract 16x from each side:

20x-16x = 16x+6-16x

4x = 6

Divide both sides by 4:

4x/4 = 6/4

x = 1.5

He travels for 1.5 hours both times.

The first time, 1.5 hours at 20 miles per hour is:

d = 1.5(20) = 30 miles

The original trip is 30 miles. This makes the entire trip 30(2) = 60 miles.

On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:

24 = 16x

Divide both sides by 16:

24/16 = 16x/16

1.5 = x

If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:

24/1.5 = 30/x

Cross multiplying,

24*x = 1.5(30)

24x = 45

24x/24 = 45/24

x = 1.875

This gives him a total time of 1.5+1.875 = 3.375 hours

Step-by-step explanation:

7 0

3 years ago

The price for each pizza size at a local pizzeria is listed below. The dimension is the diameter of the pizza. Find the best buy

Morgarella [4.7K]

I think the 8in pizza

3 0

4 years ago

Which of the following statements must be true about this diagram? Check all that apply.

galben [10]

The following are the true statements are

m<4 is greater than m<2

m<4 is greater than m<1

m<1 + m<2= m<4

<h3>What is exterior angle property?</h3>

If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

As, by property

m<1 + m<2= m<4

and, the measure of each individual angle is less than angle 4.

Learn more about exterior angle property here:

brainly.com/question/2406986

#SPJ1

6 0

2 years ago

A cylinder has a base radius of 7in and a height of 18in. What is its volume in cubic inch to the nearest tenths place?

Delvig [45]

Answer:

2770.9 in³

Step-by-step explanation:

A cylinder has a base radius of 7in and a height of 18in. What is its volume in cubic inch to the nearest tenths place?

The formula for the volume of a cylinder is given as:

πr²h

r = radius = 7 in

h = height = 18 in

Hence:

Volume of the cylinder = π × 7² × 18

= 2770.88472 in³

Approximately to the nearest tenth = 2770.9 in³

8 0

3 years ago

A film distribution manager calculates that 9% of the films released are flops. If the manager is right, what is the probability

ioda

Answer:

0.9884 = 98.84% probability that the proportion of flops in a sample of 469 released films would be greater than 6%.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$