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Kobotan [32]
11 months ago
12

A salesperson makes a base salary of $15,000 per year plus a 8% commission on total sales for the year. The yearly salary can be

expressed as a linear function.
Mathematics
1 answer:
allochka39001 [22]11 months ago
4 0

The salary of the salesperson can be represented as "y" and the number of sales for the year will be represnted as "x". With this in mind the salary will be the fixed part (15000) plus the number of sales per year multiplied by 8 percent. With this in mind we have:

\begin{gathered} y(x)=15000+8\text{\%}\cdot x \\ y(x)=15000+\frac{8}{100}\cdot x \\ y(x)=15000+0.08\cdot x \end{gathered}

The function that represents his yearly salary is "y(x)=15000+0.08*x".

To find his salary when he sells $500,000 in a year we need to make x equal to that value. Therefore:

\begin{gathered} y(500000)=15000+0.08\cdot500000 \\ y(500000)=15000+40000 \\ y(500000)=55000 \end{gathered}

His salary will be $55,000 for that year.

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Very quickly pleasee!!! What is the remainder when 3 to the power of 2020 is divided by 30
Misha Larkins [42]
<h3>Answer:  21</h3>

===============================================

Explanation:

Let's see if we can find a pattern where we divide powers of 3 over 30

In other words, let's see if we can find a pattern for (3^n)/30 where n is a natural number {1,2,3,4,...}

We only care about the remainders so ignore the quotients.

This is the pattern of remainders:

  • 3^1 = 3. When divided over 30, we get remainder 3.
  • 3^2 = 9. When divided over 30, we get remainder 9.
  • 3^3 = 27. When divided over 30, we get remainder 27.
  • 3^4 = 81. When divided over 30, we get remainder 21.
  • 3^5 = 243. When divided over 30, we get remainder 3.
  • 3^6 = 729. When divided over 30, we get remainder 9.

We see the pattern repeating again after we get to remainder 3 a second time. The pattern of remainders is {3, 9, 27, 21} which repeats forever.

The length of this cycle is 4. So what we do is divide the exponent by 4 to see what the remainder is. For instance, both 1 and 5 lead the same remainder when we divide by 4. This tells us 3^1 and 3^5 lead to the same remainder as shown in the pattern above.

Similarly, 3^2 and 3^6 lead to the same remainder. These items are spaced exactly four units apart, which is the length of the cycle.

For the exponent 2020, we get 2020/4 = 505 remainder 0

Having a remainder 0 is the same as having remainder 4, when dividing by 4.

So we'll be looking in the fourth slot of the cycle {3,9,27,21} to see the answer is 21.

Dividing 3^2020 over 30 leads to a remainder of 21.

6 0
3 years ago
If x + sin^2 theta + cos^2 theta = 4, then what is the value of x?
Ray Of Light [21]

Answer:

x = 3

Step-by-step explanation:

x + sin^2  \theta + cos^2  \theta = 4 \\ x + 1 = 4 \\ ( \because \: sin^2  \theta + cos^2  \theta = 1) \\ x = 4 - 1 \\  x = 3

4 0
3 years ago
Hich equation correctly applies the distributive property?
Rashid [163]
The answer is c. 0.7 is in every set of pairs so you would get the same product by multiplying all of them the way c has it.
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3 years ago
If the diameter of a circle is 10 inches, find the radius.
Serjik [45]

Answer:

5 inches

Step-by-step explanation:

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2 years ago
6x - 5y = 15, x=y+3 what does x and y equal
Natasha_Volkova [10]

Answer:

Step-by-step explanation:

6x - 5y = 15....... (1)

x=y+3..........(2)

Putting (2) in (1)

6(y + 3) - 5y = 15

6y + 18 - 5y = 15

6y - 5y = 15 - 18

y = -3

And x = y + 3

x = -3 + 3

x = 0

3 0
3 years ago
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