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PSYCHO15rus [73]
2 years ago
9

Volume: The base of a pyramid is a rectangle with a length of 3 centimeters and a width of 6 centimeters. If the height of the p

yramid is 12 centimeters, what is the volume of the pyramid?​
Mathematics
1 answer:
il63 [147K]2 years ago
3 0

Answer:

72 cm³

Step-by-step explanation:

Volume of a pyramid = Area of base * height / 3

= 3 * 6 * 12/3 = 72 cm³

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\frac{1}{7} \ is\ rational\ number. \\\\ Every\ number\ which\ can\ be\ written\ as\ fraction\ (quotient)\ of\ two\\numbers\ is\ rational.
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3 years ago
Read 2 more answers
5. Abbey Road Motors pays a percent commission to its sales people. They are paid
ira [324]

Answer:

c(p) = {0.2 p ⇒ p < 1000

           0.24 p - 40 ⇒ 1000 ≤ p ≤ 2000

           0.29 p - 140 ⇒ p > 2000}

Step-by-step explanation:

* Lets explain how to solve the problem

- The profit is represented by p

1. If the profit is under $1,000,  the commission rate is 20%

∵ The profit is p < 1000

∵ 20% of p = \frac{20}{100}*p = 0.2 p

∵ c(p) is the function of the commission

∴ c(p) = 0.2 p when p < 1000

2. If the profit is at least $1,000 and less than or equal to  $2,000, the

  commission rate is 20% of the first $1,000 and 24% of the remainder

  of  the profit

- At least means greater than or equal

∵ The profit 1000 ≤ p ≤ 2000

- The commission is divided into 20% of first $1000 and 24% of

  the reminder

∵ 20% of 1000 = \frac{20}{100}*1000 = 200

∵ The remainder of the profit = p - 1000

∵ 24% of the remainder profit = \frac{24}{100}*(p-1000)

  = 0.24(p - 1000) = 0.24 p - 240

∴ The total commission = 200 + 0.24 p - 240

∴ The total commission = 0.24 p - 40

∴ c(p) = 0.24 p - 40 when 1000 ≤ p ≤ 2000

3. If the profit is above $2,000, the rate is 20% of the first $1,000

   of profit,  24% of the next $1,000 of profit, and 29% of the amount

   of profit over $2,000

∵ The profit p > 2000

- The commission is divided into 20% of first $1000 and 24% of the

  next $1,000 of profit, and 29% of the amount of profit over $2,000

∵ 20% of 1000 = \frac{20}{100}*1000 = 200

∵ 24% of 1000 = \frac{24}{100}*1000 = 240

- The amount of profit over $2,000 = p - 2000

∵ 29% of the amount of profit over $2,000 =

   \frac{29}{100}*(p-2000) = 0.29(p - 2000)

   = 0.29 p - 580

∴ The total commission = 200 + 240 + 0.29 p - 580

∴ The total commission = 0.29 p - 140

∴ c(p) = 0.29 p - 140 when p > 2000

* The commission function is:

c(p) = {0.2 p ⇒ p < 1000

            0.24 p - 40 ⇒ 1000 ≤ p ≤ 2000

            0.29 p - 140 ⇒ p > 2000}

6 0
3 years ago
(a) 12 is 15% of what?
OlgaM077 [116]
80


hope this helps mate
8 0
2 years ago
Quadrilateral KLMN is similar to quadrilateral OPQR. Find the measure of side QR.
Shalnov [3]

Answer:   12.6=13

Step-by-step explanation:

7 0
2 years ago
An investigator compares the durability of two different compounds used in the manufacture of a certain automobile brake lining.
jeka94

Answer:

The point estimate is 5,617.

The margin of error of a confidence interval for the difference between the two population means is 454.18386 .

The 98% confidence interval for the difference between the two population means is (5163, 6071).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.  

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Compound 1:

127 brakes, average brake life of 42,814 miles, population standard deviation of 1819 miles. This means that:

\mu_1 = 42814

s_1 = \frac{1819}{\sqrt{127}} = 161.41

Compound 2:

163 brakes, average brake life of 37,197 miles, population standard deviation of 1401 miles. This means that:

\mu_2 = 37197

s_2 = \frac{1401}{\sqrt{163}} = 109.73

Distribution of the difference:

\mu = \mu_1 - \mu_2 = 42814 - 37197 = 5617

The point estimate is 5,617.

s = \sqrt{s_1^2 + s_2^2} = \sqrt{161.41^2 + 109.73^2} = 195.18

Confidence interval

The confidence interval is:

\mu \pm zs

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is:

M = zs

98% confidence level

So \alpha = 0.02, z is the value of Z that has a p-value of 1 - \frac{0.02}{2} = 0.99, so Z = 2.327.  

Margin of error:

M = zs = 195.18*2.327 = 454.18386&#10;

The margin of error of a confidence interval for the difference between the two population means is 454.18386 .

For the confidence interval, as we round to the nearest whole number, we round it 454. So

The lower bound of the interval is:

\mu - zs = \mu - M = 5617 - 454 = 5163

The upper bound of the interval is:

\mu + zs = \mu + M = 5617 + 454 = 6071

The 98% confidence interval for the difference between the two population means is (5163, 6071).

3 0
3 years ago
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