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3 years ago

Can someone help me with 1-4

Mathematics

1 answer:

Lady_Fox [76]3 years ago

5 0

Answer:

For question 1.

Sin B= 3/7

CosB=5/7

Step-by-step explanation:

Sin: opposite over hypotenuse

Cosine: adjacent over hypotenuse

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Write the first five terms of the the sequence defined by the explicit formula an=72(1/3)^n-1

lisabon 2012 [21]

$a_n=72\left(\dfrac{1}{3}\right)^{n-1}\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}:\\\\n=1\to a_1=72\left(\dfrac{1}{3}\right)^{1-1}=72\left(\dfrac{1}{3}\right)^0=72(1)=72\\\\n=2\to a_2=72\left(\dfrac{1}{3}\right)^{2-1}=72\left(\dfrac{1}{3}\right)^1=72\left(\dfrac{1}{3}\right)=\dfrac{72}{3}=24\\\\n=3\to a_3=72\left(\dfrac{1}{3}\right)^{3-1}=72\left(\dfrac{1}{3}\right)^2=72\left(\dfrac{1}{9}\right)=\dfrac{72}{9}=8\\\\n=4\to a_4=72\left(\dfrac{1}{3}\right)^{4-1}=72\left(\dfrac{1}{3}\right)^3=72\left(\dfrac{1}{27}\right)=\dfrac{72}{27}=\dfrac{8}{3}\\\\n=5\to a_5=72\left(\dfrac{1}{3}\right)^{5-1}=72\left(\dfrac{1}{3}\right)^4=72\left(\dfrac{1}{81}\right)=\dfrac{72}{81}=\dfrac{8}{9}\\\\Answer:\ \boxed{72,\ 24,\ 8,\ \dfrac{8}{3},\ \dfrac{8}{9}}$

8 0

3 years ago

Read 2 more answers

A counselor at a community college claims that the mean GPA for students who have transferred to State University is more than 3

Lena [83]

Answer:

$t=\frac{3.25-3.1}{\frac{0.3}{\sqrt{36}}}=3$

If we compare the p value and the significance level for example $\alpha=1-0.99=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

And the best conclusion would be:

a) Yes. The counselor's claim is valid

Because we reject the null hypothesis in favor to the alternative hypothesis.

Step-by-step explanation:

Data given and notation

$\bar X=3.25$ represent the sample mean

$s=0.3$ represent the sample standard deviation

$n=36$ sample size

$\mu_o =3.1$ represent the value that we want to test

$\alpha$ 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 more than 3.1, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.1$

Alternative hypothesis: $\mu > 3.1$

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:

$t=\frac{3.25-3.1}{\frac{0.3}{\sqrt{36}}}=3$

P-value

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

$df=n-1=36-1=35$

Since is a one right tailed test the p value would be:

$p_v =P(t_{(35)}>3)=0.00247$

Conclusion

If we compare the p value and the significance level for example $\alpha=1-0.99=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

And the best conclusion would be:

a) Yes. The counselor's claim is valid

Because we reject the null hypothesis in favor to the alternative hypothesis.

5 0

3 years ago

If UW = 9x – 9, what is UW in units?

Tju [1.3M]

I will answer this question to the best of my ability, because you have not provided a value of x to plug in.

UW is always equal to 9x-9 or 9(x-1) whenever x is a real number. By plugging in x, we can get the value. For example, if x was 4, we plug in x, giving us 9*4-9=36-9=27 units or 9(4-1)=9(3)=27 units
Don't forget to include units when you complete your answer!

Hope this helps! I did as much as I could!

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3 years ago

Select the two binomials that are factors of this trinomial x^20 - x - 20

Mashcka [7]

Answer:

$(x-5)(x+4)$

Step-by-step explanation:

To factor the equation, break it into two binomials which multiply to make the equation. To write these binomials (x+a)(x+b), find factors which multiply to -20 and add to -1 for a and b.

20: 1, 2, 4, 5, 10, 20

-5+4 = -1

$x^2-x-20 = (x-5)(x+4)$

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3 years ago

Nelson purchased a 3 pound bunch

sveticcg [70]

Step-by-step explanation:

you would do 3 ÷ .99 and then when you get the answer from that you would multiply it by 5.

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3 years ago

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