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2 years ago

Find the value of x and y.

Mathematics

1 answer:

spayn [35]2 years ago

7 0

By the geometric mean theorem,

$\frac{y}{4}=\frac{12}{y} \\ \\ y^{2}=48 \\ \\ \boxed{y=4\sqrt{3}}$

So, by the Pythagorean theorem,

$12^{2}+(4\sqrt{3})^{2}=x^{2}\\\\144+48=x^{2}\\\\192=x^{2}\\\\\boxed{x=8\sqrt{3}}$

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Which of the following phrases would represent this expression?

aivan3 [116]

I think its (the quotient of 3 and x)
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3 0

4 years ago

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A random sample of 50 recent college graduates results in a mean time to graduate of 4.58 years, with a standard deviation of 1.

Anna007 [38]

Answer:

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

Yes, this confidence interval contradict the belief that it takes 4 years to complete a bachelor’s degree.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean μ, when the population standard deviation is not known is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

The information provided is:

$\bar x=4.58\\s=1.10\\\alpha =0.10$

Compute the critical value of t for 90% confidence interval and (n - 1) degrees of freedom as follows:

$t_{\alpha/2, (n-1)}=t_{0.10/2, (50-1)}=t_{0.05, 49}=1.671$

*Use a t-table for the probability.

Compute the 90% confidence interval for population mean μ as follows:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

$=4.58\pm 1.671\times \frac{1.10}{\sqrt{50}}\\=4.58\pm 0.26\\=(4.32, 4.84)$

Thus, the 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32, 4.84).

If a hypothesis test is conducted to determine whether it takes 4 years to complete a bachelor’s degree or not, the hypothesis will be:

Hₐ: The mean time it takes to complete a bachelor’s degree is 4 years, i.e. μ = 4.

Hₐ: The mean time it takes to complete a bachelor’s degree is different from 4 years, i.e. μ ≠ 4.

The decision rule based on a confidence interval will be:

Reject the null hypothesis if the null value is not included in the interval.

The 90% confidence interval for the mean time to graduate with a bachelor’s degree is (4.32 years, 4.84 years).

The null value, i.e. μ = 4 is not included in the interval.

The null hypothesis will be rejected at 10% level of significance.

Thus, it can be concluded that that time it takes to complete a bachelor’s degree is different from 4 years.

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3 years ago

PLEASE HELP WILL MARK BRAINLY

Alenkinab [10]

Answer:

1: $53750

2: $15975

3: 40

4: 90

5: 51

6a: 20%

6b:204

Step-by-step explanation:

1: to calculate this mulitply 50000*1.075= 53750

2: same deal 15000*1.065=15975

3: We have a ratio of 3:2 and then 60:x because we multiplied the first ratio by 20 to get the 60 in the second we multiply the 2 by 20 as well and get x=40

4: This one is kind of tricky. we know that there are 4 dogs for every 3 cats. We also know that there are 210 animals. This means that 4x+3x=210 solve this and get x=30 you then multiply the ratio 4:3 by 30 and get 120:90

5: 1/5*255=51

5a: 1/5=.2=20%

5b: 255-51=204

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3 years ago

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Solve the System of Equations -5x+4y=3 x=2y-15

hjlf

Answer:

Point Form:

(9,12)

Equation Form: