MATHEMATICS COLLEGE

10 ) Which Property of Multiplication is shown? (5 + 3) x 2 = 5 x 2 + 3 x 2A. Identity Property
C. Associative Property
B. Distributive Property
D. Commutative Property

Answers

Answer 1
Answer:

Property of Multiplication that is shown on the expression (5 + 3) x 2 = 5 x 2 + 3 x 2 is Distributive Property (option b)

The property of multiplication that is shown in the given equation is the Distributive Property. The Distributive Property states that multiplication distributes over addition. In other words, when we multiply a number by the sum of two other numbers, it is the same as multiplying the number by each of the individual addends and then adding the results together.

In the given equation, we have "(5 + 3) x 2 = 5 x 2 + 3 x 2." Let's break down the left-hand side first. "(5 + 3)" represents the sum of 5 and 3, which is 8. So, we have "8 x 2." By applying the Distributive Property, we can rewrite this as "5 x 2 + 3 x 2."

Now, on the right-hand side, we have "5 x 2 + 3 x 2." Here, we are multiplying 5 by 2 and 3 by 2 individually and then adding the products together. This aligns with the Distributive Property, which states that the result will be the same as on the left-hand side.

So, the Main Answer is option B. Distributive Property

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Answer 2
Answer:

Answer:

B. Distributive Property of Multiplication

Step-by-step explanation:

The given equation shows that two similar expressions are equal to each other.

How? Well, they both equal 16 to start. These are the same expressions - one is just distributed out!

2 \cdot (5 + 3) \n2 \cdot 5 + 2 \cdot3 \n10 + 6 = 16

and...

5 \cdot 2 + 3 \cdot 2\n10 + 6\n16

In the equations, the only difference is that we distributive 2 and multiplied in by 5 and 3!

I hope I was of assistance! #SpreadTheLove <3

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This year, a small business had a total revenue of $81,900 . If this is 26% more than their total revenue the previous year, what was their total revenue the previous year?

Answers

Answer:

total revenue was $65,000

Step-by-step explanation:

A small business had a total revenue this year = $81,900

This is 26% more than their total revenue the previous year.

Let the revenue of previous year be 'r'.

r + ( 26% of r ) = $81,900

r + ( 0.26r ) = 81,900

1.26r = 81,900

r = (81,900)/(1.26)

r = 65,000

Their total revenue was $65,000 the previous year.
$65000 was the total revenue for the previous year.
65000 x .26 = 16900
65000 + 16900 = 81,900

The surface of a mountain is modeled by the equation h(x, y) = 5000 - 0.001x² - 0.004y². A mountain climber is at the point (500, 300, 4390). In what direction should the climber move in order to ascend at the greatest rate?

Answers

Answer:

i-2.4j

Step-by-step explanation:

Given that,

The surface of a mountain is modeled by the equation as follows :

h(x,y)=5000 -0.001x^2-0.004y^2

A mountain climber is at the point (500, 300, 4390).

We need to find the direction in which he should move in order to ascend at the greatest rate.

To find direction, first finding the gradient of h as follows :

\nabla h(x,y)=-0.002xi-0.008yj

Now put x = 500 and y = 300

So,

\nabla h(x,y)=-0.002(500)i-0.008(300)j\n\n\nabla h(x,y)=i-2.4j

The direction of the climber is i-2.4j

At a farm, there are two huge pits for storing hay. 90 tons of hay is stored in the first pit, 75 tons in the second pit. Then, three times as much hay was removed from the first pit as was removed from the second pit. After that, there was half as much hay in the first pit as there was now in the second pit. How many tons of hay was taken from the first pit?

Answers

Answer:

63 tons

Step-by-step explanation:

The problem statement asks for the tons of hay removed from the first pit. It is convenient to let a variable (x) represent that amount. This is said to be 3 times the amount removed from the second pit, so that amount must be x/3.

The amount remaining in the first pit is 90-x.

The amount remaining in the second pit is 75 -x/3.

Since the first pit remaining amount is half the second pit remaining amount, we can write the equation ...

... 90 -x = (1/2)(75 -x/3)

... 180 -2x = 75 -x/3 . . . . multiply by 2

... 105 - 2x = -x/3 . . . . . . subtract 75

... 315 -6x = -x . . . . . . . . multiply by 3

... 315 = 5x . . . . . . . . . . . add 6x

... 63 = x . . . . . . . . . . . . . divide by 5

63 tons of hay were taken from the first pit.

_____

Check

After removing 63 tons from the first pit, there are 27 tons remaining. After removing 63/3 = 21 tons from the second pit, there are 54 tons remaining. 27 is half of 54, so the answer checks OK.

What is 32% of 60 as a decimal.

Answers

Answer:

19.2

Step-by-step explanation:

32% as a decimal is 0.32.

60x0.32 is 19.2.

Which relation is not a function?

Answers

It would be 3 beacuse w=3

*4.8.21Question Help
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After the release of radioactive material into the atmosphere from a nuclear power plant in a country in 2000, the hay in that country was contaminated by a radioactive
isotope (half-life 7 days). If it is safe to feed the hay to cows when 14% of the radioactive isotope remains, how long did the farmers need to wait to use this hay?
The farmers needed to wait approximately days for it to be safe to feed the hay to the cows.
(Round to one decimal place as needed.)
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Answers

Answer:

  19.9 days

Step-by-step explanation:

The amount remaining after d days is ...

  a = (1/2)^(d/7)

We want to find d when a = 0.14

  log(a) = (d/7)log(1/2)

  d = 7·log(0.14)/log(1/2) ≈ 19.855 ≈ 19.9

The farmers need to wait about 19.9 days for it to be safe.
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