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2 years ago

5

Determine whether the system of equations has one solution, no solution, or infinitely many solutions by graphing. If the system

has one solution, name it.
3x-y = 14
-6+ 2y = -28

A. One solution (2,2)
B. Infinitely many solutions
C. No solutions
D. No Solutions

2 answers:

Svetlanka [38]2 years ago

8 0

One solution

I’m pretty sure that’s right

Juli2301 [7.4K]2 years ago

5 0

Answer:

One solution

Step-by-step explanation:

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Sarah has 25 candies. Sarah gave 2/5 of the candies to her sister. Of the amount left she gave 2/3 to her friend. How many candi

satela [25.4K]

Answer:

5 candies

Step-by-step explanation:

Total of candy Sarah has = 25candies

If Sarah gave 2/5 of the candies to her sister, the total amount she gave her sister will be 2/5 of 25

2/5 of 25 = 10

The remaining candy left will be 25-10 which is 15.

If she gave 2/3 of amount left to her friend, the amount she gave her friend will be 2/3×15 = 10candies.

The amount of candy Sarah have left will be 15- 10 which is 5candies.

3 0

2 years ago

Suppose that a random sample of 10 newborns had an average weight of 7.25 pounds and sample standard deviation of 2 pounds. a. T

frosja888 [35]

Answer:

$z=\frac{7.25-7.5}{\frac{1.4}{\sqrt{10}}}=-0.565$

$p_v =P(Z$

a) If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true average is not significantly less than 7.5.

b) $\chi^2 =\frac{10-1}{1.96} 4 =18.367$

$p_v =P(\chi^2 >18.367)=0.0311$

If we compare the p value and the significance level provided we see that $p_v >\alpha$ so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 1.96.

Step-by-step explanation:

Assuming this info: "Suppose birth weights follow a normal distribution with mean 7.5 pounds and standard deviation 1.4 pounds"

1) Data given and notation

$\bar X=7.25$ represent the sample mean

$s=1.2$ represent the sample standard deviation

$\sigma=1.4$ represent the population standard deviation

$n=10$ sample size

$\mu_o =7.5$ represent the value that we want to test

$\alpha=0.05,0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is less than 7.5, the system of hypothesis would be:

Null hypothesis: $\mu \geq 7.5$

Alternative hypothesis: $\mu < 7.5$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{7.25-7.5}{\frac{1.4}{\sqrt{10}}}=-0.565$

4)P-value

Since is a left tailed test the p value would be:

$p_v =P(Z$

5) Conclusion

Part a

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true average is not significantly less than 7.5.

Part b

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

$n=10$ represent the sample size

$\alpha=0.01$ represent the confidence level

$s^2 =4$ represent the sample variance obtained

$\sigma^2_0 =1.96$ represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance increase, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 \leq 1.96$

Alternative hypothesis: $\sigma^2 >1.96$

Calculate the statistic

For this test we can use the following statistic:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

$\chi^2 =\frac{10-1}{1.96} 4 =18.367$

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case 9. And since is a right tailed test the p value would be given by:

$p_v =P(\chi^2 >18.367)=0.0311$

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(18.367,9,TRUE)"

Conclusion

If we compare the p value and the significance level provided we see that $p_v >\alpha$ so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 1.96.

4 0

3 years ago

omar will donate up to $500 to charity. the money will be divided between two charities: the city of youth fund and educational

marshall27 [118]

Answer:

Please refer to the attached graph

Step-by-step explanation:

Knowing the following:

X = amount of money donated to the city youth fund

Y = amount of money donated to the educational growth foundation

We can write the statements in form of equations:

"Will donate up to $500, the money will be divided between two charities"

(a) $X + Y = \$ 500$

"The amount donated to the educational growth foundation to be at least four times the amount donated to the city youth fund"

(b) $Y \geq 4X$

If we graph both equations we can see the area where both conditions are met (see graph attached)

Where the blue line is (a) and the red line is (b)

Shaded area represent all the possible solutions for the donations, for example:

X=100 and Y=400 or

X=50 and Y=200, etc.

6 0

2 years ago

I don't know how to do this. Can someone explain how to please?

Natalija [7]

Answer:

f(5) = -2

Step-by-step explanation:

You look on the x-axis for 5 because f(5) means let x = 5. Then go down to the graph (the red zig-zaggy line) At the red line (you're still directly under the 5) look over to the y-axis to find the value. That's your answer. It is -2. The point (5, -2) is on the red graph.

f(5) = -2

3 0

2 years ago

Can someone please explain this for me, thank you.

r-ruslan [8.4K]

just divide Atlantic/Mississippi

$\frac{3.1 \times {10}^{17} }{6.3 \times {10}^{11} } = \frac{3.1}{6.3} \times \frac{ {10}^{17} }{ {10}^{11} } \\ = 0.492 \times {10}^{17 - 11} \\ = 0.492 \times {10}^{6} \\ = 4.92 \times {10}^{5}$

7 0

2 years ago