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3 years ago

10

Use any model you choose to solve the story problem. The band director is splitting 1/4 of the band into 4 equal rehearsal group

s. What fraction of the entire band will be in each rehearsal group?

2 answers:

ahrayia [7]3 years ago

5 0

Answer:

The answer is 1/16

nika2105 [10]3 years ago

4 0

1/16 of the group is in each rehersal group

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At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen

guajiro [1.7K]

Answer:

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

p1 -> 1993

20 out of 100, so:

$p_1 = \frac{20}{100} = 0.2$

$s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04$

p2 -> 1997

10 out of 100, so:

$p_2 = \frac{10}{100} = 0.1$

$s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03$

Distribution of p1 – p2:

$p = p_1 - p_2 = 0.2 - 0.1 = 0.1$

$s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05$

Confidence interval:

$p \pm zs$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a p-value of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower bound of the interval is:

$p - zs = 0.1 - 1.645*0.05 = 0.01775
$

The upper bound of the interval is:

$p + zs = 0.1 + 1.645*0.05 = 0.18225
$

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

6 0

3 years ago

What are the restrictions of the domain of the function F(x) = 1/x^2-9

Sonbull [250]

$f(x)=\frac{1}{x^2-9}$

The denominator can't be equal to 0.
$x^2-9 \not= 0 \\
x^2 \not= 9 \\
x \not= -3 \ \land \ x \not= 3$

The domain is all numbers except -3 and 3.
$x \in \mathbb{R} - \{-3, 3 \}$

6 0

3 years ago

Which of the following theorems verifies that ABC ~ STU?

Lunna [17]

Answer:

B. AA

Step-by-step explanation:

The diagram given shows that two angles in ∆ABC are congruent to two corresponding angles in ∆STU.

Invariably, the third unknown angle of both triangles would also be equal going by the third angle theorem.

Thus, based on the AA Similarity Theorem which says that two triangles are similar to each other if two corresponding angles of one is congruent to two angles in the other, ∆ABC ~ ∆STU.

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3 years ago

What is the place vaule of the 7 in 9.357

kumpel [21]

The 7 is in the Ones place

4 0

3 years ago

Read 2 more answers

Is the negative square root of 9 rational or irrational

Nana76 [90]

Answer:

Rational

Step-by-step explanation:

-9 is rational because 9 is a perfect square and all perfect squares are rational.

6 0

3 years ago