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2 years ago

What is the volume of this rectangular prism?

Mathematics

2 answers:

Natali [406]2 years ago

8 0

The answer is 1/24 because 1/4 times 1/3 is 1/12. Then times that by 1/2.

OLEGan [10]2 years ago

3 0

Answer:

1/24

Step-by-step explanation:

khan.

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you have 5 red crayons, 3 yellow crayons, 4 blue crayons and purple crayons. what multiplication would you do to find the probab

almond37 [142]

Answer:

3/46

Step-by-step explanation:

7 0

3 years ago

1. What is the correct reason for statement #3?

r-ruslan [8.4K]

Answer:

1) B. Combine-like terms

2) A. Subtraction Property of Equality

3)D. Division Property of Equality

Step-by-step explanation:

8 0

3 years ago

Solve the equation by factoring: x2 − 7x + 12 = 0

Gnoma [55]

Answer:

x = 3 . . . or . . . x = 4

Step-by-step explanation:

The factored form is ...

(x -3)(x -4) = 0

The zero product rule tells you the solutions are the values of x that make the factors be zero:

x = 3

x = 4

_____

Comment on factoring

When the leading coefficient is 1, the coefficient of the x-term is the sum of the constants in the binomial factors, and the constant term is their product. You can see this by multiplying out the generic case:

(x +a)(x +b) = x^2 +(a+b)x + ab

What this means is that when you're factoring, you're looking for factors of the constant that add up to give the coefficient of the x-term. Here, the x-term is negative and the constant is positive, so both factors will be negative.

12 = -1×-12 = -2×-6 = -3×-4

The sums of these factor pairs are -13, -8, -7. Clearly, the last pair of factors of 12 will be useful to us, since that sum is -7. So, the binomial factors of our equation are ...

(x -3)(x -4) = 0

___

If the leading coefficient is not zero, the method of factoring is similar, but slightly different. Numerous videos and web sites discuss the method(s).

7 0

2 years ago

4- A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produ

galben [10]

Answer:

$\\ \mu = 118\;grams\;and\;\sigma=30\;grams$

Step-by-step explanation:

We need to use z-scores and a standard normal table to find the values that corresponds to the probabilities given, and then to solve a system of equations to find $\\ \mu\;and\;\sigma$ .

<h3>First Case: items from 100 grams to the mean</h3>

For finding probabilities that corresponds to z-scores, we are going to use here a <u>Standard Normal Table </u><u><em>for cumulative probabilities from the mean </em></u><em>(Standard normal table. Cumulative from the mean (0 to Z), 2020, in Wikipedia) </em>that is, the "probability that a statistic is between 0 (the mean) and Z".

A value of a z-score for the probability P(100<x<mean) = 22.57% = 0.2257 corresponds to a value of z-score = 0.6, that is, the value is 0.6 standard deviations from the mean. Since this value is <em>below the mean</em> ("the items produced weigh between 100 grams up to the mean"), then the z-score is negative.

Then

$\\ z = -0.6\;and\;z = \frac{x-\mu}{\sigma}$

$\\ -0.6 = \frac{100-\mu}{\sigma}$ (1)

<h3>Second Case: items from the mean up to 190 grams</h3>

We can apply the same procedure as before. A value of a z-score for the probability P(mean<x<190) = 49.18% = 0.4918 corresponds to a value of z-score = 2.4, which is positive since it is after the mean.

Then

$\\ z =2.4\;and\; z = \frac{x-\mu}{\sigma}$