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3 years ago

Factor the expression. 48g2 – 22gh – 15h2

Mathematics

2 answers:

IrinaVladis [17]3 years ago

8 0

It’s B because it’s the right answer

kiruha [24]3 years ago

3 0

Answer:

Step-by-step explanation:

FOIL:First,Inner,Outer,Last

After the polynomial operations are done we can see that A is the answer.

6g*8g=48g^2

6g*3h=18gh

8g*-5h=-40gh

-5h*3h=-15h

After combining like terms we get :

48g^2-22gh-15h^2

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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

The function f (t) = 12(1 +0.03) can be used to determine the population, in thousands of a town t years

Alja [10]

f= the original amount of people, a steady growth throughout the years

t=time

In 1955 the population was 12 thousand. Compared to the current population of 12.36 thousand, the population then was roughly 77%.

5 0

3 years ago

There is a bag filled with 3 blue and 4 red marbles.

tresset_1 [31]

Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.

The marbles are chosen without replacement, hence the <em>hypergeometric </em>distribution is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

There is a total of 3 + 4 = 7 marbles, hence N = 7.

Of those, 3 are blue, hence k = 3.

2 marbles will be taken, hence n = 2.

The probability of getting 2 of the same colour is the sum of P(X = 0), which is both red, with P(X = 2), which is both blue, then:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,7,2,3) = \frac{C_{3,0}C_{4,2}}{C_{7,2}} = 0.2857$

$P(X = 2) = h(2,7,2,3) = \frac{C_{3,2}C_{4,0}}{C_{7,2}} = 0.1429$

Hence:

$p = P(X = 0) + P(X = 2) = 0.2857 + 0.1429 = 0.4286$

0.4286 = 42.86% probability of getting 2 of the same colour.

You can learn more about the hypergeometric distribution at brainly.com/question/4818951

3 0

2 years ago

A monkey is swinging from a tree. On each swing, she travels along an arc that is 75% as long as the previous swing's arc. The t

mr_godi [17]

Answer:

Total length of the first swing=64 m

Step-by-step explanation:

The total length of all four swings can be expressed as;

Total length of all 4 swings=Length of first swing+length of second swing+length of third swing+length of fourth swing

where;

Total length of all 4 swings=175 m

Length of first swing=x

Length of second swing=75% of length of first swing=(75/100)×x=0.75 x

Length of third swing=75% of length of second swing

Length of third swing=(75/100)×0.75 x=0.5625 x

Length of fourth swing=75% of length of third swing

Length of fourth swing=(75/100)×0.5625 x=0.421875 x

replacing;

Total length of all 4 swings

175=x+0.75 x+0.5625 x+0.421875 x

2.734375 x=175

x=175/2.734375

x=64

Total length of the first swing=x=64 m

3 0

4 years ago

Read 2 more answers

What is 10/8 in simplest form

aliya0001 [1]

10/8 in simplest form:

First, we can start off by finding the GCF of the denominator and the numerator. To do so, we need to list the factors of each of them and find the common ones.

Factors of 10: 1, 2, 5, 10
Factors of 8: 1, 2, 4, 8

We can see that our common factors are 1 and 2, considering that both the numerator and denominator has the same factors (1 and 2). Since we have our common factors, we need to find the greatest. Which is the greatest out of 1 and 2? The GCF is 2 because it is bigger than 1.

Second, divide the numerator and the denominator by the GCF (2).
$10 \div 2 = 5 \\ 8 \div 2 = 4$

Third, now we can revise our fraction and turn it into the simplest form. Take the two numbers you just got above us and put them in their numerator and denominator spot. You should get: $\frac{5}{4}$

Answer in fraction form: $\fbox {5/4}$
Answer in decimal form: $\fbox {1.25}$
Answer in mixed number form: $\fbox {1 1/4}$

4 0

3 years ago

Read 2 more answers