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3 years ago

From a group of five boys and seven girls, two boys and three girls will be selected to attend a conference. In

Mathematics

1 answer:

babunello [35]3 years ago

3 0

Step-by-step explanation:

Number of combinations

= 5C2 * 7C3

= 10 * 35

= 350.

Hence there are 350 possible ways.

P.S.

5C2 = 5! / (2!3!) = 120 / (2 * 6) = 10.

7C3 = 7! / (3!4!) = 5040 / (6 * 24) = 35.

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1. Find the 90% Cl for the population mean if sample

Elden [556K]

Answer:

The answer is below

Step-by-step explanation:

mean (μ) = 12, SD(σ) = 2.3, sample size (n) = 65

Given that the confidence level (c) = 90% = 0.9

α = 1 - c = 0.1

α/2 = 0.05

The z score of α/2 is the same as the z score of 0.45 (0.5 - 0.05) which is equal to 1.65

The margin of error (E) is given as:

$E=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } =1.65*\frac{2.3}{\sqrt{65} } =0.47$

The confidence interval = μ ± E = 12 ± 0.47 = (11.53, 12.47)

mean (μ) = 23, SD(σ) = 12, sample size (n) = 45

Given that the confidence level (c) = 88% = 0.88

α = 1 - c = 0.12

α/2 = 0.06

The z score of α/2 is the same as the z score of 0.44 (0.5 - 0.06) which is equal to 1.56

The margin of error (E) is given as:

$E=Z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} } =1.56*\frac{12}{\sqrt{45} } =2.8$

The confidence interval = μ ± E = 23 ± 2.8 = (22.2, 25.8)

8 0

3 years ago

A company wants to select 1 project from a set of 4 possible projects. Which of the following constraints ensures that only 1 wi

Elza [17]

Given:

A company wants to select 1 project from a set of 4 possible projects.

Consider the options are:

a. $X_1+X_2+X_3+X_4=1$

b. $X_1+X_2+X_3+X_4\leq 1$

c. $X_1+X_2+X_3+X_4\geq 1$

d. $X_1+X_2+X_3+X_4\geq 0$

To find:

The constraints that ensures only 1 will be selected.

Solution:

It is given that the company wants to select 1 project from a set of 4 possible projects. It means the sum of selected projects must be equal to 1.

$X_1+X_2+X_3+X_4=1$

Therefore, the correct option is (a).

8 0

3 years ago

Find the measure of an angle who's measure is 20 less than the measure of its supplement.

Dvinal [7]

supplementary angles add up to 180°.

x = measure of such angle

x + 20 = measure of her sibling.

since "x" has 20 less than her sibling, then clearly her sibling has to have 20 more than "x".

$\bf (x)+\stackrel{sibling}{(x+20)}=180\implies 2x+20=180\implies 2x=160 \\\\\\ x=\cfrac{160}{2}\implies x=80$

7 0

3 years ago

Select all that apply. Which of the following are proportions? 25/10=5/2,3/4=8/10,2/8=3/12,3/4=15/20

8_murik_8 [283]

Answer:

$\frac{25}{10} = \frac{5}{2}$ is in proportion.

$\frac{3}{4} = \frac{8}{10}$ is not in proportion.

$\frac{2}{8} = \frac{3}{12}$ is in proportion.

$\frac{3}{4} = \frac{15}{20}$ is in proportion.

Step-by-step explanation:

The first example is $\frac{25}{10} = \frac{5}{2}$ and it is in proportion.

This is because, you will get the same simplest fraction ( $\frac{5}{2}$ ) from the fraction $\frac{25}{10}$ by dividing its numerator and denominator by 5.

The second example is $\frac{3}{4} = \frac{8}{10}$ and it is not in proportion.

This is because, you can not get the simplest fraction ( $\frac{3}{4}$ ) from the fraction $\frac{8}{10}$ after simplification.

The third example is $\frac{2}{8} = \frac{3}{12}$ and it is in proportion.

This is because, you will get the same simplest fraction ( $\frac{1}{4}$ ) from the fraction $\frac{2}{8}$ by dividing its numerator and denominator by 2 and from the fraction $\frac{3}{12}$ by dividing its numerator and denominator by 3.

The fourth example is $\frac{3}{4} = \frac{15}{20}$ and it is in proportion.

This is because, you will get the same simplest fraction ( $\frac{3}{4}$ ) from the fraction $\frac{15}{20}$ by dividing its numerator and denominator by 5. (Answer)

3 0

3 years ago

Read 2 more answers

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 3 to 5. If there were 7

Zinaida [17]

Answer:

2967 yes votes

Step-by-step explanation:

Welcome to Brainly!

One way of doing this problem follows:

Find the ratio, r, mentioned in the problem statement. To do this,

write the equation 3r + 5r = 7912 and solve this for r:

8r = 7912, so that r = 989.

Then the number of yes votes was 3(989), or 2967, and the number of no votes was 5(989), or 4947.

check: Does the ratio 2967/4947 equal 3/5? yes.

There were 2967 yes votes.

8 0

3 years ago