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2 years ago

Find the coordinate plane that represents the solution of this system y > -x - 1 y + 4 ≤ x

Mathematics

1 answer:

gulaghasi [49]2 years ago

8 0

Answer:

The graph will open to the right and will be mostly in quadrant 1

Step-by-step explanation:

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3. university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standa

gregori [183]

Answer:

A sample of 17 must be selected.

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:

$\alpha = \frac{1 - 0.96}{2} = 0.02$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.02 = 0.98$ , so Z = 2.054.

Now, 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 from a previous study is 4 hours.

This means that $\sigma = 4$

How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours?

A sample of n is required.

n is found for M = 2. So

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

$2 = 2.054\frac{4}{\sqrt{n}}$

$2\sqrt{n} = 2.054*4$

Simplifying both sides by 2:

$\sqrt{n} = 2.054*2$

$(\sqrt{n})^2 = (2.054*2)^2$

$n = 16.88$

Rounding up:

A sample of 17 must be selected.

8 0

3 years ago

In how many ways can a subcommittee of 6 students be chosen from a committee which consists of 10 senior members and 12 junior m

givi [52]

Answer:

The number of ways is 13860 ways

Step-by-step explanation:

Given

Senior Members = 10

Junior Members = 12

Required

Number of ways of selecting 6 students students

The question lay emphasis on the keyword selection; this implies combination

From the question, we understand that

4 students are to be selected from senior members while 2 from junior members;

The number of ways is calculated as thus;

Ways = Ways of Selecting Senior Members * Ways of Selecting Junior Members

$Ways = ^{10}C_4 * ^{12}C2$

$Ways = \frac{10!}{(10-4)!4!)} * \frac{12!}{(12-2)!2!)}$

$Ways = \frac{10!}{(6)!4!)} * \frac{12!}{(10)!2!)}$

$Ways = \frac{10 * 9 * 8 * 7 *6!}{(6! * 4*3*2*1)} * \frac{12*11*10!}{(10!*2*1)}$

$Ways = \frac{10 * 9 * 8 * 7}{4*3*2*1} * \frac{12*11}{2*1}$

$Ways = \frac{5040}{24} * \frac{132}{2}$

$Ways = 210 * 66$

$Ways = 13860$

Hence, the number of ways is 13860 ways

7 0

3 years ago

A police officer wants to know the proportion of crimes that are burglaries within the last five years. She randomly selects 40

svlad2 [7]

Answer:

a. Yes

See explanation below.

Step-by-step explanation:

Assuming that if the question is if we can use the normal approximation for the true proportion.

For this case we have n = 40 and p = 0.3 (probability of success)

We need to check some conditions:

1) Random sample : This condition is satisfied since the problem says that she randomly select 40 records

2) $n \hat p = 40*0.3 =12 \geq 10$

$n(1-\hat p)= 30 *(1-0.3) = 28 \geq 10)$

3) 10% condition: the random sample is assumed to be less than 10% of the original population size (assumed)

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

So then as we can see the normal approximation for this case makes sense since we have all the 3 conditions satisfied so then the answer would be:

a. Yes

7 0

3 years ago

If N=10 then what is 2n+4

SOVA2 [1]

If n is ten then the expression would change to
2(10)+4
20+4
so your answer would be 24

3 0

3 years ago

Read 2 more answers

George is twice as old as Edward, and Edward’s age exceeds Robert’s age by 4 years. If the sum of the three ages is at least 56

vova2212 [387]

Answer:

Step-by-step explanation:

if george is 30 than edward would be 15 as he is twice younger than george

and robert would be 11 as he is 4 year younger than edward.

4 0

3 years ago