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3 years ago

Which expression is equivalent to 6r - 10 + 3r – 2?

Mathematics

2 answers:

katovenus [111]3 years ago

6 0

The answer is c

9r - 12

Because it is just the simplified expression

EastWind [94]3 years ago

5 0

Answer: There are no choices so unfortunately I can't give you an answer

Step -by-step explanation:

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A study investigating the relationship between age and annual medical expenses randomly samples 400 individuals in a city. It is

ICE Princess25 [194]

Answer:

The probability is 0.789

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 $s = \frac{\sigma}{\sqrt{n}}$ .

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

In this problem, we have that:

$\sigma = 16, n = 400, s = \frac{16}{\sqrt{400}} = 0.8$

Find the probability that the mean age of the individuals sampled is within one year of the mean age for all individuals in the city.

Using $\mu = 30$ , this is the pvalue of Z when X = 31 subtracted by the pvalue of Z when X = 29. So

X = 31

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

By the Central Limit Theorem

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

$Z = \frac{31 - 30}{0.8}$

$Z = 1.25$

$Z = 1.25$ has a pvalue of 0.8944

X = 29

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

$Z = \frac{29 - 30}{0.8}$

$Z = -1.25$

$Z = -1.25$ has a pvalue of 0.1056

0.8944 - 0.1056 = 0.7888

Rounded to three decimal places, 0.789

The probability is 0.789

4 0

3 years ago

Read 2 more answers

A factory has two types of employees line workers and Mananger

denis-greek [22]

Step-by-step explanation:

Read this article to learn about the types, functions, advantages and conflicts of line and staff organisation.

Types of Staff:

1. Personal Staff:

Personal staff is attached to individual line officers. The Personal Assistant or the Private Secretary etc. form personal staff of line managers. These persons help their bosses in every possible way. The routine work of line officers is mostly handled by the personal staff. They fix routine meetings, open the post, maintain diaries and accompany the boss on official visits. The line officers are spared of routine works and are able to devote much time for planning and execution.

2. Specialist Staff:

These are technically qualified persons who provide service to the whole organisation. They serve line and other staff in planning, organizing and coordinating their work. Their specialized knowledge is an asset to the organisation. The appointment of a legal advisor may be helpful to every department where his advice is required.

3. General Staff:

ADVERTISEMENTS:

This staff consists of persons attached to the key executives. They have the same background as that of line officers. They are attached to important functionaries as their deputies, etc. They may be appointed as Deputy Managers, Assistant Managers, Special Assistants, etc.

Functions of Staff Authority:

The staff authority is assigned the following functions:

1. Agency of Control:

It has to discharge the functions such as:

(a) Organisation;

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3 0

3 years ago

In the diagram, the measure of angle 6 is 98°. A transversal intersects 2 lines to form 8 angles. Clockwise from top left, the a

OLga [1]

We need a picture to
Solve this

7 0

3 years ago

Read 2 more answers

Camilias as backyard is in the shape of a rectangle and has a length of 16.5 feet. It costs her $976 to fence in the yard. If fe

Bumek [7]

Answer:

14 feet

Step-by-step explanation:

To calculate the width of the patio, we will use the formula of the perimeter, in the case of the rectangle it has the formula of:

p = 2 * l + 2 * w

Now we know that the total fencing value is $ 976 and that per foot is $ 16

that is, we can calculate the value of the perimeter, like this:

976/16 = 61

We know that the perimeter is 61 feet and that the length is 16.5, therefore it only remains to replace:

61 = 16.5 * 2 + 2 * w

solving for w:

w = (61 - 33) / 2

w = 14

which means that the width of the patio is 14 feet.

8 0

3 years ago

Find the area of the shaded region.

taurus [48]

Answer:

$426.96 \: {km}^{2}$

Step-by-step explanation:

Area of the shaded region = Area of triangle with base 40 km and height 27 km - Area of circle with radius (12/2) 6 km.

$= \frac{1}{2} \times 40 \times 27 - 3.14 \times {(6)}^{2} \\ \\ = 20 \times 27 - 3.14 \times 36 \\ \\ = 540 - 113.04 \\ \\ = 426.96 \: {km}^{2}$

5 0

3 years ago