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From a group of 12 students, we want to select a random sample of 4 students to serve on a university committee. How many combin

borishaifa [10]

Answer:

495 combinations of 4 students can be selected.

Step-by-step explanation:

The order of the students in the sample is not important. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

How many combination of random samples of 4 students can be selected?

4 from a set of 12. So

$C_{n,x} = \frac{12!}{4!(8)!} = 495$

495 combinations of 4 students can be selected.

8 0

3 years ago

What is the simplified form of the following expression? 10abc^2 sqrt 49a^2b^2c^2

Elodia [21]

$10abc^2\sqrt{49a^2b^2c^2}=70a^2b^2c^3$

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

$10abc^2\sqrt{49a^2b^2c^2}$

$\sqrt{49a^2b^2c^2}=7abc$

$7\cdot \:10aabbc^2c$

$70aabbc^2c$

$70a^2bbc^2c$

$70a^2b^2c^2c$

$70a^2b^2c^3$

4 0

3 years ago

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In an orchard, there are 18 apple trees, 23 orange trees, and a cherry tree. What is the ratio of orange trees to cherry trees?

Nikitich [7]

Answer:

18:23

Step-by-step explanation:

18:23 (cannot be simplified further as there is no common factor)

7 0

3 years ago

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g A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is cha

leva [86]

Answer:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

$z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502$

$p_v =2*P(Z>2.502)= 0.0123$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=410$ represent the number of people indicating that their financial security was more than fair for the recent year

$X_{2}=245$ represent the number of people indicating that their financial security was more than fair for the year before

$n_{1}=1000$ sample 1 selected

$n_{2}=700$ sample 2 selected

$p_{1}=\frac{410}{1000}=0.410$ represent the proportion estimated of indicating that their financial security was more than fair this year

$p_{2}=\frac{245}{700}=0.35$ represent the proportion estimated of indicating that their financial security was more than fair the year before

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

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

$\alpha$ significance level given

Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{410+245}{1000+700}=0.385$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.410-0.35}{\sqrt{0.385(1-0.385)(\frac{1}{1000}+\frac{1}{700})}}=2.502$

Statistical decision

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

$p_v =2*P(Z>2.502)= 0.0123$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportion analyzed is significantly different between the two groups at 5% of significance.

7 0

3 years ago

Calculate the size of θ in the given diagram ( see image).<br>O is the center of the circle.

mariarad [96]

Answer:

∅ = 42°

Step-by-step explanation:

90 - 48 = 42° because 48 and 42 are complimentary angles (add up to 90°)

because the radii lines form an isosceles triangle, ∠∅ also = 42°

3 0

3 years ago

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