3. Brian paid $27 for 12 gallons of gasoline. To the nearest

Find UV (Pic Stated Below)

natta225 [31]

Answer:

UV=29

Step-by-step explanation:

In right triangles AQB and AVB,

∠AQB = ∠AVB ...(i) {Right angles}

∠QBA = ∠VBA ...(ii) {Given that they are equal}

We know that sum of all three angles in a triangle is equal to 180 degree. So wee can write sum equation for each triangle

∠AQB+∠QBA+∠BAQ=180 ...(iii)

∠AVB+∠VBA+∠BAV=180 ...(iv)

using (iii) and (iv)

∠AQB+∠QBA+∠BAQ=∠AVB+∠VBA+∠BAV

∠AVB+∠VBA+∠BAQ=∠AVB+∠VBA+∠BAV (using (i) and (ii))

∠BAQ=∠BAV...(v)

Now consider triangles AQB and AVB;

∠BAQ=∠BAV {from (v)}

∠QBA = ∠VBA {from (ii)}

AB=AB {common side}

So using ASA, triangles AQB and AVB are congruent.

We know that corresponding sides of congruent triangles are equal.

Hence

AQ=AV

5x+9=7x+1

9-1=7x-5x

8=2x

divide both sides by 2

4=x

Now plug value of x=4 into UV=7x+1

UV=7*4+1=28+1=29

<u>Hence UV=29 is final answer.</u>

7 0

3 years ago

Find the median of the baseball batting averages.

Charra [1.4K]

Answer:

0.236

Step-by-step explanation:

First put it in order

0.199, 0.211, 0.225, 0.236, 0.257, 0.264, and 0.283

Then find the middle number

0.236

7 0

3 years ago

Read 2 more answers

Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 8. If 100 people are

Sergeu [11.5K]

Answer:

D. 0.9938.

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.

Mean of 115 and a standard deviation of 8.

This means that $\mu = 115, \sigma = 8$

100 people are randomly selected

This means that $n = 100, s = \frac{8}{\sqrt{100}} = 0.8$

Find the probability that their mean blood pressure will be less than 117.

This is the p-value of Z when X = 117, so:

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

By the Central Limit Theorem

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

$Z = \frac{117 - 115}{0.8}$

$Z = 2.5$

$Z = 2.5$ has a p-value of 0.9938, and thus, the correct answer is given by option D.

8 0

3 years ago

A ladder is leaning against a wall. The top of the ladder is 9 feet (ft) above the ground. If the bottom of the ladder is moved

Dmitriy789 [7]

The ladder is 9.5 feet

8 0

3 years ago

Simplify 2(5x – 4) + 3x

guapka [62]

To simplify, you must distribute the 2 into the 5x and -4 by multiplying 2 with 5x and 2 with -4.

<span>2(5x – 4) + 3x

2 x 5x = 10x

2 x -4 = -8

You will get 10x - 8 + 3x

Now you must combine like terms or add like terms. In this case we must add 10x and 3x

10x + 3x = 13x

Finally the answer would be 13x - 8</span>

6 0

3 years ago

Read 2 more answers