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2 years ago

During a sale, fidget spinners 1/4 off the regular price. If a spinner regularly costs 5.90, what is the sale price

Mathematics

1 answer:

garik1379 [7]2 years ago

8 0

price - (1/4)×price = price×(1 - 1/4) = (3/4)×price

... = (3/4)×5.90 = 4.425 ≈ 4.43 . . . . . sale price

_____

The sale price could be 4.42 if the discount is rounded up, rather than the price being rounded up. If you first compute the discount as (1/4)×5.90 = 1.475 ≈ 1.48, then the half-penny goes to the customer, not the shop-keeper.

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2 years ago

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3 years ago

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2 years ago

Consider the following hypothesis test. : : The following results are for two independent samples taken from two populations. Ex

I am Lyosha [343]

Answer:

$z = -1.53$ --- test statistic

$p = 0.1260$ --- p value

Conclusion: Fail to reject the null hypothesis.

Step-by-step explanation:

Given

$n_1 = 80$ $\bar x_1= 104$ $\sigma_1 = 8.4$

$n_2 = 70$ $\bar x_2 = 106$ $\sigma_2 = 7.6$

$H_o: \mu_1 - \mu_2 = 0$ --- Null hypothesis

$H_a: \mu_1 - \mu_2 \ne 0$ ---- Alternate hypothesis

$\alpha = 0.05$

Solving (a): The test statistic

This is calculated as:

$z = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2} }}$

So, we have:

$z = \frac{104 - 106}{\sqrt{\frac{8.4^2}{80} + \frac{7.6^2}{70} }}$

$z = \frac{104 - 106}{\sqrt{\frac{70.56}{80} + \frac{57.76}{70}}}$

$z = \frac{-2}{\sqrt{0.8820 + 0.8251}}$

$z = \frac{-2}{\sqrt{1.7071}}$

$z = \frac{-2}{1.3066}$

$z = -1.53$

Solving (b): The p value

This is calculated as:

$p = 2 * P(Z < z)$

So, we have:

$p = 2 * P(Z < -1.53)$

Look up the z probability in the z score table. So, the expression becomes

$p = 2 * 0.0630$

$p = 0.1260$

Solving (c): With $\alpha = 0.05$ , what is the conclusion based on the p value

We have:

$\alpha = 0.05$

In (b), we have:

$p = 0.1260$

By comparison:

$p > \alpha$

i.e.

$0.1260 > 0.05$

So, we fail to reject the null hypothesis.

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2 years ago