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Ipatiy [6.2K]
3 years ago
7

A town uses positive numbers to track incresses in population and negitive numbers to track decresses in population. The populat

ion had decressed by 300 residents over the past 5 years. The same numbers of residents left each year. What was the change in towns population each year?
Mathematics
1 answer:
schepotkina [342]3 years ago
5 0

Answer:

60 people left each year so -60

Step-by-step explanation:

-300 is the total population change over the past 5 years

The population decreased.

Divide 300/5 to find the amount of people who left each year

300/5= 60

60 people left each year.

The change in the towns population is (-60)

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What is the simplified form of 12x/900x²y4z6?
zalisa [80]

Answer:

360xy^2|xz^3|

Step-by-step explanation:

Given expression:

12x \sqrt{900x^2y^4z^6}

\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:

\implies 12x \sqrt{900}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}

Replace 900 with 30² :

\implies 12x \sqrt{30^2}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}

\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:

\implies 12x \cdot 30|x|\sqrt{y^4}\sqrt{z^6}

\implies 360x|x|\sqrt{y^4}\sqrt{z^6}

(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).

\textsf{Apply exponent rule} \quad \sqrt{a^m}=a^{\frac{m}{2}}:

\implies 360x|x|\cdot y^{\frac{4}{2}}\cdot z^{\frac{6}{2}}

Simplify:

\implies 360xy^2|xz^3|

(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).

7 0
2 years ago
The area of a rectangular painting is 5/8 square yard. The width is 3/4 yard. What is the length of the painting?
vfiekz [6]

Answer:

The answer is

<h2>\frac{5}{6}  \:  \:  \:  \: yards \\</h2>

Step-by-step explanation:

Area of a rectangle = length × width

Since we are finding the length of the rectangle

length =  \frac{area}{width}  \\

From the question

area = 5/8 square yards

width = 3/4 yard

So we have

length =  \frac{5}{8}  \div  \frac{3}{4}  \\  =  \frac{5}{8}  \times  \frac{4}{3}  \\  =  \frac{5}{2}  \times  \frac{1}{3}

We have the final answer as

\frac{5}{6}  \:  \:  \:  \: yards \\

Hope this helps you

3 0
3 years ago
A=student is female
Aleks04 [339]
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4 0
3 years ago
Suppose your entertainment budget is 30% of your weekly wages from a job. You plan to spend $10.50 on a movie night. How much wi
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You would need C) $35 to stay within your budget.
7 0
2 years ago
Miller Company’s total sales are $123,000. The company’s direct labor cost is $14,760, which represents 30% of its total convers
lana66690 [7]

1.

Direct labor cost = $14760

This is 30% of total conversion cost so, conversion cost = 14760/30%

= $49200

Total conversion cost = Direct labor + Manufacturing overhead

Manufacturing overhead = Total conversion cost - Direct labor

=49200-14760 = $34440

Hence, The total manufacturing overhead cost= $34440

2.

Direct labor = $14760

This is 40% of prime cost. So total prime cost = 14760/40%

= $36900

Total prime cost = Direct material + Direct labor

Direct material = Total prime cost - Direct labor

= 36900 - 14760 = 22140

Hence, the total direct materials cost = $22140

3.

Total manufacturing cost = Direct materials + Direct labor + Manufacturing overhead

= 22140+14760+34440 = $71340

4.

Variable selling and administrative cost = 5% of 123000

=$ 6150

5.

Total variable cost = Direct materials + Direct labor + Sales commission

= 22140 + 14760 + 6150 =$43050

6.

Fixed selling and administrative expense = Total selling and administrative expense - Sales commission = 18450-6150 = $12300

Total fixed cost = Manufacturing overheads + Fixed selling and administrative expense

= 34440+12300 = $46740

7.

Total contribution margin = Sales - Total variable cost

= 123000 - 43050 = $79950

6 0
3 years ago
Read 2 more answers
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