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3 years ago

Solve the system of equations algebraically. Verify your

Mathematics

2 answers:

xz_007 [3.2K]3 years ago

8 0

Answer:

The solution is the point (0.5,-3)

Step-by-step explanation:

we have

$y=4x-5$ ----> equation A

$y=-3$ ----> equation B

Solve the system by substitution

Substitute equation B in equation A

$-3=4x-5$

Solve for x

Adds 5 both sides

$-3+5=4x$

$2=4x$

Divide by 4 both sides

$x=0.5$

therefore

The solution is the point (0.5,-3)

<em>Verify your answer using the graph</em>

using a graphing tool

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (0.5,-3)

therefore

The solution is the point (0.5,-3)

see the attached figure

Arada [10]3 years ago

8 0

Answer:

Since y= -3, just put that in the equation.

-3 = 4x - 5

+5 +5

2 = 4x

/4 /4

x=1/2

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3 years ago

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At Western University the historical mean of scholarship examination scores for freshman applications is 900. A historical popul

vampirchik [111]

Answer:

a) Null Hypothesis: $\mu =900$

Alternative hypothesis: $\mu \neq 900$

b) The 95% confidence interval would be given by (910.05;959.95)

c) Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d) $z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750$

Since is a bilateral test the p value is given by:

$p_v =2*P(Z>2.750)=0.0059$

Step-by-step explanation:

a. State the hypotheses.

On this case we want to check the following system of hypothesis:

Null Hypothesis: $\mu =900$

Alternative hypothesis: $\mu \neq 900$

b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean x¯¯¯= 935?

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=935$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=180$ represent the population standard deviation

n=200 represent the sample size

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=3278.222$

The sample deviation calculated $s=97.054$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$935-1.96\frac{180}{\sqrt{200}}=910.05$

$935+1.96\frac{180}{\sqrt{200}}=959.95$

So on this case the 95% confidence interval would be given by (910.05;959.95)

c. Use the confidence interval to conduct a hypothesis test. Using α= .05, what is your conclusion?

Since we confidence interval not ocntains the value of 900 we fail to reject the null hypothesis that the true mean is 900.

d. What is the p-value?

The statistic is given by:

$z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

If we replace we got:

$z=\frac{935 -900}{\frac{180}{\sqrt{200}}}=2.750$

Since is a bilateral test the p value is given by:

$p_v =2*P(Z>2.750)=0.0059$

So then since the p value is less than the significance we can reject the null hypothesis at 5% of significance.

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3 years ago

Which number is between 0.5 and 8/9?

GalinKa [24]

To know which number is between 0.5 and 8/9, let us convert all numbers in the same form, the decimal form. 8/9 is equivalent to 0.89.
Option A is 0.29. Option B is 0.14. Option C is 0.21 and option D is 0.29. From the given choices above, THERE IS NO CORRECT ANSWER. None of the choices given fits to be a number that is between 0.50 and 8/9. Hence, the given choices may be incorrect.

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3 years ago

A simple random sample of the sitting heights of 36 male students has a mean of 92.8cm. The population of males has sitting heig

Naily [24]

Answer:

there is sufficient evidence to support the claim that male student have a sitting height different of 91.4 cm.

Step-by-step explanation:

p value = 0.0198

level of significance = 0.05

hypothesis:-

$H_{0}:\mu=91.4$

$H_{1}:\mu\neq91.4$

decision:-

p value = 0.0198 <0.05

so, we reject the null hypothesis.]

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3 years ago

The new patio at Tonya's house is 5 yards long by 10 feet wide. She is going to cover the patio with square bricks that measure

Klio2033 [76]

Answer:

Step-by-step explanation:

Steps to take to determine the answer

Because the length is in yards, it has to be converted to foot
Find the area of the patio using the length and width measured in foot
Determine the area of the square brick
Multiply the cost of the brick by the area

1 yards = 3 foot

5 x 3 = 15 foot

Area of a rectangle = length x breadth

15 x 10 = 150 ft^2

Cost = 150 x 4 = $600

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3 years ago