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3 years ago

What does X to the second power minus 14x plus 49 equals

Mathematics

2 answers:

Rina8888 [55]3 years ago

5 0

X= 3.5 because 14 times 3.5= 49?

SashulF [63]3 years ago

3 0

X^2 - 14x + 49

2 numbers that multiplied equal 49
2 number that added equal -14

-7 times -7 = 49
-7 plus -7 = -14

(x-7) (x-7)

x=7

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A circle has the equation x^2−8y−6x+y^2=4.

mylen [45]

Hello here is a solution :
x²-8y-6x+y²=4....(1)
A)
x²-6x = x²-2(3)x+9-9
= x²-2(3)x+3²-9
x²-6x =(x-3)² -9
B)
y²-8y = y²-2(4)y +4²-16
y²-8y = (y-4)²-16
C)
in (1) :

(x-3)² -9 +(y-4)²-16 = 4
(x-3)² +(y-4)² = 29 ...is the standard form of the equation

 Select answer 1 :
A: 3
B: 4
C: (x−3)2+(y−4)2=29

8 0

3 years ago

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.

8 0

3 years ago

Which graph represents the solution set of the inequality Negative 14.5 less-than x?

Natalka [10]

Answer:

I think Its C

Step-by-step explanation:

I did it on unit test so idk if its right or wrong

4 0

3 years ago

Read 2 more answers

A garden hose emits 9 quarts of water in 6 seconds how much did the water emit in 10seconds

jarptica [38.1K]

Answer:

In 10 seconds, the garden hose will emit 15 quarts of water.

Step-by-step explanation:

The amount of water emitted by the garden hose over time can be expressed as a ratio: 9/6, or 9 quarts of water for every 6 seconds of time. We can then simplify this ratio to 3/2, or 3 quarts of water for every 2 seconds of time. Since the ratio will remain constant, or the same, over time, we can set up an equivalent ratio, or fraction to find the amount of water emitted in 10 seconds: 3/2 = x/10. We look at the denominators and see that 2 x 5 = 10. In order to make the ratios equivalent, we would also multiply the numerator by 5: 3 x 5 = 15, which gives us the amount of water emitted in 10 seconds.

7 0

2 years ago

If anyone could help that would be greatly appreciated!

Serggg [28]

B. rational means it does not go on forever.

4 0

3 years ago