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Marysya12 [62]
3 years ago
5

Simplify: 18q2−45q+25/9q2−25.

Mathematics
1 answer:
Svet_ta [14]3 years ago
5 0

Answer:

\frac{(6q-5)}{(3q+5)}

Step-by-step explanation:

Given: \frac{18q^{2}-45q+25 }{9q^{2}-25 }

Factorizing the numerator and the denominator, we have:

18q^{2} - 45q + 25 = 18q^{2} - 30q - 15q + 25

                         = (3q - 5)(6q - 5)

and

9q^{2} - 25 = (3q - 5)(3q + 5)

So that,

\frac{18q^{2}-45q+25 }{9q^{2}-25 } = \frac{(3q-5)(6q-5)}{(3q-5)(3q+5)}

                 = \frac{(6q-5)}{(3q+5)}

Therefore,

\frac{18q^{2}-45q+25 }{9q^{2}-25 } = \frac{(6q-5)}{(3q+5)}

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It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken if the desir
Ksju [112]

Answer:

We need a sample size of at least 75.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, we find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

The standard deviation is the square root of the variance. So:

\sigma = \sqrt{484} = 22

With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is

We need a sample size of at least n, in which n is found when M = 5. So

M = z*\frac{\sigma}{\sqrt{n}}

5 = 1.96*\frac{22}{\sqrt{n}}

5\sqrt{n} = 43.12

\sqrt{n} = \frac{43.12}{5}

\sqrt{n} = 8.624

(\sqrt{n})^{2} = (8.624)^{2}

n = 74.4

We need a sample size of at least 75.

6 0
3 years ago
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Which correlation coefficient indicated the strongest linear relationship between the variables?
Anna35 [415]

Answer:

-0.87 has the strongest linear relationship

Step-by-step explanation:

-0.87, since it is the closest value to either one or negative one,

0.8 is the second strongest

0.65 is the third strongest

-0.52 is the least strongest

7 0
3 years ago
If your Indiana trip is 375 km, how many cm is this ?
Ivan

Answer:

The answer is 3.75e+7

Step-by-step explanation:

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In an experiment you do a chi-square test comparing observed and expected progeny. Your calculated chi square is 0.375. With 1 d
myrzilka [38]

Answer:

It mean that the observed progeny is similar than the expected progeny. There is no a relationship between the categorical variables.

Step-by-step explanation:

The Chi-squared test is used to test the relationship between categorical variables. A categorical variable is a non-numerical variable. The null hypothesis of the Chi-squared test is that categorical variables are independent; it means that the frequencies are not dependent on the variable. It is important to know that the Chi-squared test does not measure causality, it only measures the relationship. To reject the null hypothesis, you usually need a probability lower than 0.05, but in this case, the probability was way higher than 0.05, it was between 0.5 and 0.9.

4 0
3 years ago
8.46 If 100 is decreased by a% and the result is decreased by b%, then what is the total percent decrease (in terms of a and b)?
Marysya12 [62]

Answer:

The total percent decrease is $a+b-\frac{a b}{100}$

Step-by-step explanation:

  • We are given with a word problem
  • We are asked to find the total percentage decrease
  • We can do this in two steps

         Step 1: Finding the two percentage decrease

         Step 2: Finding their difference

Step 1 of 2

Let the decrease by a% be 100-a

Then b% decrease is

$$\begin{aligned}\frac{b}{100} \times(100-a) &=\frac{100 b-a b}{100} \\\frac{100 b}{100}-\frac{a b}{100} &=b-\frac{a b}{100}\end{aligned}$$

Step 2 of 2

The percentage difference between the two percentages is,

$$\begin{aligned}&(100-a)-\left(b-\frac{a b}{100}\right)=100-a-b+\frac{a b}{100} \\&100-a-b+\frac{a b}{100}=100-\left(a+b-\frac{a b}{100}\right)\end{aligned}$$

Since 100 is the total percent $a+b-\frac{a b}{100}$ is the percentage decrease.

3 0
1 year ago
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