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Effectus [21]
3 years ago
14

Chang and Cal both collect pearls. Chang has three more pearls in her collection than Cal. Write an expression to represent the

total number of pearls in both collections.
Mathematics
1 answer:
natta225 [31]3 years ago
6 0
Let <em>x</em> be the number of pearls in Chang's collection.  Let <em>y</em> be the number of pearls in Cal's collection.<em />

Chang has 3 more than Cal, so <em>x</em> = <em>y</em> + 3.
Adding both collections would be <em /><em>x</em> + <em /><em>y.</em>  It's easier to have an expression in one variable, so we will substitute what we had written about Chang in for <em>x</em>.
(<em>y</em> + 3) + <em>y</em> = 2<em>y</em> + 3.
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Answer:

3 sqrt 5     ( or  6.7082039    as posted in earlier A )

Step-by-step explanation:

sqrt ( 5) ( 5-2)   = 3sqrt 5

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2 years ago
The manager at a sports radio station will be covering several football games over the weekend. She knows that most of her liste
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Complete Question:

The manager at a sports radio station will be covering several football games over the weekend. She knows that most of her listeners are at least 22 years old and wants to know what age group she should gear her advertisements to for the games. She takes a random sample of 46 listeners from age 22-39 and 57 listeners who are 40 and older and asks them if they are likely to tune in to football games. The "yes" responses are recorded in the file attached below.

1. At the 0.05 level of significance, is there a significant difference in the proportion of listeners based on age?

2. Is there evidence to suggest that there is a significant difference in the proportion of listeners based on age?

Answer:

1) There is no significant difference in the proportion of listeners based on age

2) No, there is no evidence

Step-by-step explanation:

Sample size of group 1, n_1 = 46

Sample size of group 2, n_2 = 57

Number of Yes in group 1,  X_1 = 32

Number of Yes in group 2, X_2 = 47

Proportion of Yes in group 1:

\hat{p_1} = \frac{X_1}{n_1} \\\hat{p_1} = \frac{32}{46}\\\hat{p_1} = 0.6957

Proportion of Yes in group 2:

\hat{p_2} = \frac{X_2}{n_2} \\\hat{p_2} = \frac{47}{57}\\\hat{p_2} = 0.8246

Null Hypothesis, H_0: p_1 = p_2

Alternate Hypothesis,H_a: p_1 \neq p_2

\hat{p} = \frac{X_1 + X_2}{n_1 + n_2}  \\\\\hat{p} = \frac{ 32+47}{46+57} \\\\\hat{p}= 0.767

Significance level,

Calculate the test statistic

z = (\hat{p_1} - \hat{p_2})/\sqrt{(\hat{p} * (1-\hat{p}) * (\frac{1}{N_1}  + \frac{1}{N_2})}\\\\z = (0.6957-0.8246)/ \sqrt{(0.767*(1-0.767)*(1/46 + 1/57))}\\\\z = -1.54

Get the P-value from the probability distribution table:

At z = -1.54, P-value = 0.1236

Since (P-value = 0.1236) > (α = 0.05), we will accept the null hypothesis. This means that there is no evidence to suggest that there is difference in the proportion of listeners based on age.

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Answer:

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Step-by-step explanation:

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