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2 years ago

Joey makes 20 less dollars than Jeremy. If they make a total of $72, how much does

Mathematics

1 answer:

svetoff [14.1K]2 years ago

7 0

Answer:

Joey makes 52 dollars

Step-by-step explanation:

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Alex drew a scale drawing of an auditorium. He used the scale 3 inches = 2 feet. If the stage is 30 inches in the drawing, how w

White raven [17]

Answer:

20 feet

Step-by-step explanation:

The scale is 3 inches is to 2 feet

As a ratio, it would be:

$\dfrac{3}{2}$

The question is what is the actual length of the stage if the drawing is 30 inches. All we need to do is find a ratio proportional to the scale ratio:

$\dfrac{3inches}{2feet} = \dfrac{30inches}{xfeet}$

Now to find the missing number, cross multiply the fractions first:

$\dfrac{3}{2}=\dfrac{30}{x}$

$(3)(x)=(2)(30)$

$3x=60$

Then solve for x:

$3x=60$

$x=\dfrac{60}{3}$

$x=20$

The answer is 20 feet

8 0

2 years ago

Multiply (x + 2y)(x2 − xy + 3y).

erma4kov [3.2K]

Answer:

${x}^{3} + {x}^{2} y + 3xy - 2x {y}^{2} + 6 {y}^{2}$

4 0

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

Paraphin [41]

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.