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4 years ago

How do you solve this?? Please help!

Mathematics

1 answer:

Aleks04 [339]4 years ago

5 0

f = (f1 f2) / (f1 + f2)

f(f1 + f2) = f1 f2

f f 1 + f f 2 = f1 f 2

f1 f2 - f f2 = f f1

f2 (f1 - f) = f f1

f2 = (f f1) / (f1 - f) <==== solution

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Sarah claims that the thickness of the spearmint gum she produces is 7.5 one-hundredths of an inch. A quality control specialist

satela [25.4K]

Answer:

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

$p_v =2*P(t_{(9)}>1.539)=0.158$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

Step-by-step explanation:

Data given and notation

Data: 7.65, 7.60, 7.65, 7.7, 7.55, 7.55, 7.4, 7.4, 7.5, 7.5

We can begin calculating the sample mean given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

And the sample deviation given by:

$s=\sart{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And we got:

$\bar X=7.55$ represent the sample mean

$s=0.103$ represent the sample standard deviation

$n=10$ sample size

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

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

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 7.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 7.5$

Alternative hypothesis: $\mu \neq 7.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-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".

Calculate the statistic

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

$t=\frac{7.55-7.5}{\frac{0.103}{\sqrt{10}}}=1.539$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=10-1=9$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(9)}>1.539)=0.158$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis.

3 0

4 years ago

A total of $12,000 is invested in two corporate bonds that pay 7.5% and 9% simple interest. The invest wants an annual interest

nlexa [21]

Answer:

$13,200

Step-by-step explanation:

You need to use the simple interest formula

I = P * r * t

I = Interest accrued

P = Principal amount invested

r = Interest rate you need to divide by 100 to get it in decimal form

t = time, in years if you are given a partial year, divide the months by 12

P = $12,000

r = 7.5% = .075

t = 1

But, because we want I to equal $990 then I is

I = $990

So we ignore our P and instead solve for the P that will give us the desired result.

I = P * r * t

$990 = P * .075 * 1

$990 = P.075 Divide each side by .075

$990/.075 = P.075/.075

$990/.075 = P

$13,200 = P

So, to earn an annual interest income of $990, $13,200 will have to be invested in the 7.5% bond.

6 0

3 years ago

Which logarithmic equation is equivalent to the exponential below ? e^5x=6

Aneli [31]

$\bf \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b~\hfill e^{5x}=6\implies \log_e(6)=5x$

3 0

3 years ago

What is the midpoint of the segment with two endpoints (4,-6) and (-2,-3)? Put your answers in decimal from, if applicable.

Ber [7]

Answer: 1,-4.5

Explanation: you can find this by finding the difference in y and the difference in x. The difference in x is -6, and the difference in y is +3. All you have to do after that is divide that by 2: -3,1.5, than add that to the first coordinate. That should be the midpoint.

4 0

2 years ago

In quadrilateral XWZY, name the angles which are consecutive with angle W

Aleksandr [31]

The consecutive angles are

Angle x

And

Angle z

3 0

3 years ago