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2 years ago

7

Three student representatives, a president, a secretary, and a treasurer, are to be chosen from a group of five students: Andrew

, Brenda, Chad, Dorothy, and Eric. In how many different ways can the representatives be chosen if the president must be a woman and the secretary and treasurer must be men

1 answer:

damaskus [11]2 years ago

8 0

Answer:

Hence there are 6 different ways can the representatives be chosen if the president must be a woman and the secretary and treasurer must be men.

Step-by-step explanation:

We know that,

Total males = 3,

Total Females = 2,

Now we want 2 males and a female.

Then the choices are,

$= ^{3} C_{2} \times ( ^{2} C_{1} )\\\\= 3 \times 2\\\\=6$

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"Immediately after a ban on using hand-held cell phones while driving was implemented, compliance with the law was measured. A r

sergiy2304 [10]

Answer:

(a) Null Hypothesis, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$

Alternate Hypothesis, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$

(b) We conclude that there is a statistical difference in these two proportions measured initially and then one year later.

Step-by-step explanation:

We are given that a random sample of 1,250 drivers found that 98.9% were in compliance. A year after the implementation, compliance was again measured to see if compliance was the same (or not) as previously measured.

A different random sample of 1,100 drivers found 96.9% compliance."

<em />

<em>Let </em> $p_1$ <em> = proportion of drivers that were in compliance initially</em>

$p_2$ <em> = proportion of drivers that were in compliance one year later</em>

(a) <u>Null Hypothesis</u>, $H_0$ : $p_1-p_2=0$ or $p_1= p_2$ {means that there is not any statistical difference in these two proportions measured initially and then one year later}

<u>Alternate Hypothesis</u>, $H_A$ : $p_1-p_2\neq 0$ or $p_1\neq p_2$ {means that there is a statistical difference in these two proportions measured initially and then one year later}

The test statistics that will be used here is <u>Two-sample z proportion statistics</u>;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{ \frac{\hat p_1(1-\hat p_1)}{n_1} + \frac{\hat p_2(1-\hat p_2)}{n_2}} }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of drivers in compliance initially = 98.9%

$\hat p_2$ = sample proportion of drivers in compliance one year later = 96.9%

$n_1$ = sample of drivers initially = 1,250

$n_2$ = sample of drivers one year later = 1,100

(b) So, <u><em>the test statistics</em></u> = $\frac{(0.989-0.969)-(0)}{\sqrt{ \frac{0.989(1-0.989)}{1,250} + \frac{0.969(1-0.969)}{1,100}} }$

= 3.33

<u>Now, P-value of the test statistics is given by;</u>

P-value = P(Z > 3.33) = 1 - P(Z $\leq$ 3.33)

= 1 - 0.99957 = <u>0.00043</u>

Since in the question we are not given with the level of significance so we assume it to be 5%. Now at 5% significance level, the z table gives critical values between -1.96 and 1.96 for two-tailed test.

<em>Since our test statistics does not lies within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><u><em>we reject our null hypothesis.</em></u>

Therefore, we conclude that there is a statistical difference in these two proportions measured initially and then one year later.

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2 years ago

What is the domain of validity for csctheta =start fraction 1 over sine theta end fraction? (1 point) all real numbers all real

dem82 [27]

We know the following relationship:

$csc(\theta)=\frac{1}{sin(\theta)}$

The domain of a function are the inputs of the function, that is, a function $f$ is a relation that assigns to each element $x$ in the set A exactly one element in the set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function $csc(\theta)$ we can write its domain as follows:

1. D<span>omain of validity for $csc(\theta)$ :
</span>
$D: \{\theta \in R/ sin(\theta) \neq 0 \} \\ In words: All \ \theta \ that \ are \ real \ values \ except \ those \ that \ makes \ sin(\theta)=0$

When:

$sin(\theta)=0$ ?

when:

$\theta=..., -2\pi,-\pi,0,\pi,\2pi,3pi,...,k\pi$

where k is an integer either positive or negative. That is:

$sin(k\theta)=0 \ for \ k=...,-2,-1,0,1,2,3,...$

To match this with the choices above, the answer is:

<span>"All real numbers except multiples of $\pi$ "

</span>
2. which identity is not used in the proof of the identity $1+cot^{2}(\theta)=csc^{2}(\theta)$ :

This identity can proved as follows:

$sin^2{\theta}+cos^{2}(\theta)=1 \ Dividing \ by \ sin^{2}(\theta) \\ \\ \therefore \frac{sin^2{\theta}}{sin^{2}(\theta)}+\frac{cos^{2}(\theta)}{sin^{2}(\theta)}=\frac{1}{sin^{2}(\theta)} \\ \\ \therefore 1+cot^{2}(\theta)=csc^{2}(\theta)$

The identity that is not used is as established in the statement above:

<span>"1 +cos squared theta over sin squared theta= csc2theta"

Written in mathematical language as follows:

</span> $\frac{1+cos^{2}(\theta)}{sin^{2}(\theta)}=csc^{2}(\theta)$ <span>

</span>

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2 years ago

Read 2 more answers

Wyatt went to soda city to get vegetables for herself and her friends. She collected $30 and boxes are $10 each. Fill in the equ

sergey [27]

Answer:

$Budget = 3 b$

Step-by-step explanation:

Given

$Budget = \$30$

$Cost\ of\ box (b) = \$10$

Required

Represent as an equation;

$Budget = \$30$

Expand the above

$Budget = 3 * \$10$

<em>Recall that b = $10 ----given</em>

$Budget = 3 * \$10$ becomes

$Budget = 3 * b$

$Budget = 3 b$

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2 years ago

The diagram shows the sequence of three rigid transformations used to map TriangleABC onto TriangleA"B"C". What is the sequence

Igoryamba

Answer:

Rotation, then reflection, then translation

Step-by-step explanation:

The sequence of three rigid transformations that is used to map Triangle ABC onto TriangleA"B"C" are what we called ROTATION ,REFLECTION AND TRANSLATION

ROTATION can be defined as the process or waysbin which an object tend to rotate about a fixed point without the object changing either its size or shape.

REFLECTION occur in a situation where an object is been flipped across a line without the object changing either its size or shape.

TRANSLATION can be defined as the process or ways of sliding a figure in any or various direction without the figure changing either its size or shape .

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2 years ago

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Exercise 6.12 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they canno

tensa zangetsu [6.8K]

<h2>Answer with explanation:</h2>

As per given , we have

$\hat{p}=0.48$ , n=331

Critical value for 90% Confidence interval : $z_{\alpha/2}=1.645$

a) Confidence interval :

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$0.48\pm (1.645)\sqrt{\dfrac{0.48(1-0.48)}{331}}\\\\\approx 0.48\pm0.02746\\\\=(0.48-0.02746,\ 0.48+0.02746)\\\\=(0.45254,\ 0.50746)$

Hence, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot a ord it : $(0.45254,\ 0.50746)$

b) Margin of error : E=1.5%=0.015

Formula for sample size : $n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2$

For p =0.48 , we have

$n=0.48(1-0.48)(\dfrac{1.645}{0.015})^2=3001.88373333\approx3002$

Hence, the required sample size to survey = 3002

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2 years ago