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viva [34]
3 years ago
8

You have several purchases you need to make from the grocery store. from the grocery store you need to purchase 1/2 lb of cheese

, 2lbs sliced ham, 2 laoves od bread, 3 bags of potato chips, and 2 comtainers of salsa. you have a coupon for $3.00 off if your purchase totals more than $25.00 or 10% off if the toral is more than $30. the sales tax is 4%. what is your total purchase?
Mathematics
1 answer:
MArishka [77]3 years ago
3 0

The subtotal before tax and coupons is

... (2.99/lb × 1/2 lb) + (4.29/lb × 2 lb) + (2 loaves × 2.49/loaf) + (3 bags × 3.00/(2 bags)) + (2 salsa × 3.39/salsa) = 1.50 +8.58 +4.98 +4.50 +6.78

... = 26.34

This total is more than 25.00, but less than 30.00, so you get 3.00 off. The amount before tax is

... 26.34 - 3.00 = 23.34

4% tax is 0.04 × 23.34 = 0.93

so the total purchase comes to

... $23.34 + 0.93 = $24.27

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Pyramid A is a square pyramid with a base side length of 14 inches and a height of 6 inches. Pyramid B has a volume of 3,136 cub
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The Volume of PYRAMID A is 8 times greater than the Volume of PYRAMID B as obtained by taking the ratio of the volume of both pyramids.

Volume of a square based pyramid is given as :

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Hence, Volume of PYRAMID A :

V = 14^2 * (6/3)\\\\V = 392 in^3

Volume of PYRAMID B = 3,136 in³

Divide Volume of pyramid B by pyramid A :

3136 in^3 / 392 in^3

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8 * 100% = 800%

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2.A production process manufactures items with weights that are normally distributed with mean 10 pounds and standard deviation
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Answer:

Step-by-step explanation:

Given that:

population mean = 10

standard deviation = 0.1

sample mean = 9.8 < x > 10.2

The z score can be computed as:

z = \dfrac{\bar x - \mu}{\sigma}

if x > 10.2

z = \dfrac{10.2- 10}{0.1}

z = \dfrac{0.2}{0.1}

z = 2

If x < 9.8

z = \dfrac{9.8- 10}{0.1}

z = \dfrac{-0.2}{0.1}

z = -2

The p-value = P (z ≤ 2) + P (z ≥ 2)

The p-value = P (z ≤ 2) + ( 1 -  P (z ≥ 2)

p-value = 0.022750 +(1 -   0.97725)

p-value = 0.022750 +  0.022750

p-value = 0.0455

Therefore; the probability of defectives  = 4.55%

the probability of acceptable = 1 - the probability of defectives

the probability of acceptable = 1 - 0.0455

the probability of acceptable = 0.9545

the probability of acceptable = 95.45%

4.55% are defective or 95.45% is acceptable.

sampling distribution of proportions:

sample size n=1000

p = 0.0455

The z - score for this distribution at most 5% of the items is;

z = \dfrac{0.05 - 0.0455}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}

z = \dfrac{0.0045}{\sqrt{\dfrac{0.04342975}{1000}}}

z = \dfrac{0.0045}{\sqrt{4.342975 \times 10^{-5}}}

z = 0.6828

The p-value = P(z ≤ 0.6828)

From the z tables

p-value = 0.7526

Thus, the probability that at most 5% of the items in a given batch will be defective = 0.7526

The z - score for this distribution for at least 85% of the items is;

z = \dfrac{0.85 - 0.9545}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}

z = \dfrac{-0.1045}{\sqrt{\dfrac{0.04342975}{1000}}}

z = −15.86

p-value = P(z ≥  -15.86)

p-value = 1 - P(z <  -15.86)

p-value = 1 - 0

p-value = 1

Thus, the probability that at least 85% of these items in a given batch will be acceptable = 1

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