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3 years ago

Solve the following system of equations using elimination (multiplication)

Mathematics

1 answer:

Alecsey [184]3 years ago

6 0

X= 3 y=3

(3)2x+y=9
4x-3y=3

6x+3y=27
4x-3y=3
——————
10x=30
—————-
10
x=3

2(3)+y=9
6+y=9
-6. -6
y=3

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A computer manufacturing company has sent a mail survey to 2,800 of its randomly selected customers that have purchased a new la

vodka [1.7K]

Answer:

The 96% confidence interval for the population proportion of customers satisfied with their new computer is (0.77, 0.83).

Step-by-step explanation:

We have to calculate a 96% confidence interval for the proportion.

We consider the sample size to be the customers that responded the survey (n=800), as we can not assume the answer for the ones that did not answer.

The sample proportion is p=0.8.

$p=X/n=640/800=0.8$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.8*0.2}{800}}\\\\\\ \sigma_p=\sqrt{0.0002}=0.014$

The critical z-value for a 96% confidence interval is z=2.054.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=2.054 \cdot 0.014=0.03$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.8-0.03=0.77\\\\UL=p+z \cdot \sigma_p = 0.8+0.03=0.83$

The 96% confidence interval for the population proportion is (0.77, 0.83).

4 0

3 years ago

How do you solve: 2(7-x)+4x=20

Angelina_Jolie [31]

First expand it
Next subtract 14 - 2x + 4x so it can be 14 + 2x
Next subtract 14 from both sides
Next subtract 20 - 14 so it can be 6
Then divide both sides by 2
And lastly reduce the fraction 6/2 and once u reduce it u have your answer which is x = 3.

5 0

3 years ago

What is the height of the triangle? 12 units 24 units 36 units 72 units.

konstantin123 [22]

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side. The height of the tringle is 24 units. Hence option 2 is the correct option.

<h3>Given information-</h3>

The triangle for the given problem is shown in the image below.

Form the figure the length of the each side is $16 \sqrt{3}$ units.

As all the sides are equal thus the $\Delta MNO$ is a equilateral triangle in which the height of the divides the triangle into two equal part of the length $8\sqrt{3}$ at point <em>R.</em>

<h3>Height of the triangle-</h3>

Height of the triangle is the altitude of the triangle and which is drawn perpendicular from the vertex of the triangle to the opposite side.

Now in the $\Delta MRN$ , the length of the hypotenuse is $16 \sqrt{3}$ units and the length of the base is $8\sqrt{3}$ units. Let <em>h </em>is the height of the triangle thus by the Pythagoras theorem,

$(16\sqrt{3})^2 =(8\sqrt{3})^2+h^2$

Solve for <em>h,</em>

<em />

<em /> $\begin{aligned}h^2 &=(16\sqrt{3})^2 -(8\sqrt{3})^2\\h^2 &=16\times16\times3 -8\times8\times3\\h^2 &=576\\h &=\sqrt{576}\\h &=24\\\end$ <em />

<em />

Thus the height of the tringle is 24 units. Hence option 2 is the correct option.

Learn more about the equilateral triangle here;

brainly.com/question/4268382

5 0

2 years ago

The temperature outside Monday morning was -14. On Tuesday morning it was 4 degrees colder. Create an equation to show temperatu

Illusion [34]

Answer:

Temperature on Tuesday morning is $-18^{o}$ .

Step-by-step explanation:

Temperature is the measure in degrees how cold or hot a substance is. The three scale of measurements are: Celsius, Fahrenheit, and Kelvin.

In the given question, temperature on Monday morning is -14 degrees. Since it was given that the temperature on Tuesday morning is 4 degrees colder than that of Monday, then;

Temperature on Tuesday = -14 + (-4)

= -14 -4

= -18

Therefore, the temperature on Tuesday morning is $-18^{o}$ .

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3 years ago

Liz's website has been getting more popular, primarily through word-of-mouth advertising. Each month, she sees a 5% increase in

muminat

Step-by-step explanation:

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3 years ago