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PilotLPTM [1.2K]
2 years ago
13

use the elimination method to solve the system of equations. choose the correct ordered pair x-y=2 2x+3y=14

Mathematics
1 answer:
Salsk061 [2.6K]2 years ago
3 0
Solve using the p method
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Is it is it possible to have 43 pencils and divide the pencils into groups with the same number of pencils with none left over
anastassius [24]

we have given 43 pencils

we need to divide it equally so that none can be without groups.

we need to find the factors of 43.

we know that 43 is a prime number. which cannot be divided.so it is not possible to divide the 43 pencils with none left over .

6 0
3 years ago
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wires are attached to a pole to make it more secure. the diagram shows one of those wires having a length of 220 feet the angle
MariettaO [177]
In(36)=h/220ft
220ftsin(36) = h
h=129.3 ft
7 0
3 years ago
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Write an absolute value inequality that represents the situation. The area, A, in square inches of a square photo is required to
xz_007 [3.2K]

Answer:

|A - 8.7| < 0.4

Step-by-step explanation:

Given

8.5 < A < 8.9

Required

Write as an absolute value inequality

The absolute value inequality can be derived using

|A - Mid| < Length

First Step: Get the middle of the interval

Mid = \frac{1}{2}(8.5 + 8.9)

Mid = \frac{1}{2}(17.4)

Mid = 8.7

Next: Get the Length of the interval

Length = 8.9 - 8.5

Length = 0.4

Substitute values for Mid and Length in  |A - Mid| < Length

|A - 8.7| < 0.4

Hence:

<em>The absolute inequality is </em>|A - 8.7| < 0.4<em></em>

7 0
3 years ago
The CEO of a large manufacturing company is curious if there is a difference in productivity level of her warehouse employees ba
blsea [12.9K]

Answer:

The test statistic is z = -2.11.

Step-by-step explanation:

Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.

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.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Group 1: Sample of 35, mean of 1276, standard deviation of 347.

This means that:

\mu_1 = 1276, s_1 = \frac{347}{\sqrt{35}} = 58.6537

Group 2: Sample of 35, mean of 1439, standard deviation of 298.

This means that:

\mu_2 = 1439, s_2 = \frac{298}{\sqrt{35}} = 50.3712

Test if there is a difference in productivity level.

At the null hypothesis, we test that there is no difference, that is, the subtraction is 0. So

H_0: \mu_1 - \mu_2 = 0

At the alternate hypothesis, we test that there is difference, that is, the subtraction is different of 0. So

H_1: \mu_1 - \mu_2 \neq 0

The test statistic is:

z = \frac{X - \mu}{s}

In which X is the sample mean, \mu is the value tested at the null hypothesis and s is the standard error.

0 is tested at the null hypothesis:

This means that \mu = 0

From the two samples:

X = \mu_1 - \mu_2 = 1276 - 1439 = -163

s = \sqrt{s_1^2+s_2^2} = \sqrt{58.6537^2+50.3712^2} = 77.3144

Test statistic:

z = \frac{X - \mu}{s}

z = \frac{-163 - 0}{77.3144}

z = -2.11

The test statistic is z = -2.11.

7 0
3 years ago
Which equation of the least squares regression line most closely matches the data set?
Rudiy27

Answer: y = 3.5 x+ 43.8

Step-by-step explanation:

Here x represents the number of years after 1990

Thus, we get the table that is used to find the equation will be,

x             0                  2                4               6                8

y             45                51               57            61               75

Let the equation that shows the above data,

y = b + a x ---------(1)

\text{Where, }a=\frac{\sum y \sum x^2-\sum x \sum xy}{n(\sum x^2)-(\sum x)^2}

\text{And, }b = \frac{\sum xy - \sum x\sum y}{n\sum x^2 - (\sum x)^2}

By the above table,

\sum x = 20

\sum xy = 1296

\sum x^2 = 120

\sum y = 289

By substituting these values in the above value of a and b,

We get b = 43.8 and a = 3.5

Substitute this value in equation (1)

we get, the equation that shows the given data is,

y = 3.5 x + 43.8

⇒ Option (3) is correct.

4 0
3 years ago
Read 2 more answers
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