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3 years ago

A radio is being discounted 40%. If the sale price of the radio is $31.02, what was the original price of the radio?

Mathematics

1 answer:

kobusy [5.1K]3 years ago

8 0

Answer:

$51.70 is the original price

Step-by-step explanation:

Step 1:

Turn 40% into a decimal which makes it 0.40

ex. 50% would be 0.50, 5% would be 0.05 etc.

Step 2:

Put the numbers into this formula: Original Price (x) - Percent Off times Original Price = Sales Price

x - 0.40x = 31.02 this is basically 1x - 0.40x = 31.02 so,

Solving the left side of our equation gives us 1x - 0.40x = 0.60x

so now you have: 0.60x = 31.02

Step 3:

Divide both sides by 0.60 which gets x by itself and gives us the original price which is $51.70

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According to the U.S. Census Bureau, 42% of men who worked at home were college graduates. In a sample of 480 women who worked a

Likurg_2 [28]

Answer:

1) $0.327 - 0.539 \sqrt{\frac{0.327(1-0.327)}{480}}=0.315$

The point estimate for the proportion of college graduates among women who work at home is 0.327

2) $0.327 - 0.539 \sqrt{\frac{0.327(1-0.327)}{480}}=0.315$

$0.327 + 0.539 \sqrt{\frac{0.327(1-0.327)}{480}}=0.339$

The 80% confidence interval is given by (0.315; 0.339)

Step-by-step explanation:

For this case we have the following info given:

$X = 157$ represent the women who worked at home who were college graduates

$n = 480$ the sample size selected

Part 1

In order to find the proportion of college graduates among women who work at home and we can use the following formula:

$\hat p=\frac{X}{n} = \frac{157}{480}= 0.327$

The point estimate for the proportion of college graduates among women who work at home is 0.327

Part 2

Construct an 80% confidence interval for the proportion of women who work at home who are college graduates. Round the answer to three decimal places. An 80% confidence interval for the proportion of women who work at home Is < p <

The confidence interval for the true proportion would be given by this formula

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

For the 80% confidence interval the value for the significance is $\alpha=1-0.8=0.2$ and $\alpha/2=0.1$ , the critical value would be given by:

$z_{\alpha/2}=0.539$

And replacing we goot:

$0.327 - 0.539 \sqrt{\frac{0.327(1-0.327)}{480}}=0.315$

$0.327 + 0.539 \sqrt{\frac{0.327(1-0.327)}{480}}=0.339$

The 80% confidence interval is given by (0.315; 0.339)

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