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Anvisha [2.4K]
3 years ago
15

A sales person is paid a weekly salary of $760, plus a commission of 7.5% of all her sales for the week. Express her weekly inco

me in terms of the weekly sales amount. Is this a function? How do you know? What is an appropriate domain?
Mathematics
1 answer:
Elis [28]3 years ago
6 0

Answer:

1. We can see that salesperson's weekly income is the sum of her constant weekly salary ($760) and a commission which is variable and depends on her weekly sales.

So, if we say that y is her weekly income and x is her weekly sales, we can write this as:

y = 760 + 0.075x

Note that we had to change percentage to decimal number dividing it by 100.

2  Since for each value of x there is only one corresponding value of y, we can say that this is a function. For any value of x we input there is only one solution we get - that is the main feature of function and a way to tell if something is really a function.

Since this is a function, it can also be written as:

f(x) = 760 + 0.075x

3. Domain of a function is, basically, set of all values of x for which the function can work. That practically means that, since x is weekly sale, it can not be negative (one cannot make -$500 sale, for example). However, it is possible that she doesn't make a sale one week, making it possible for x to be 0. Also, the value of her sales doesn't have to be integer (it is quite possible that she makes $673.50 sale).

All this means that appropriate domain for this function are positive real numbers including 0.

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Write each ratio in simplest fractional form. 1. 16 dogs and 9 cats 2. 99 miles to 6 gallons 3. 4 frogs to 9 lily pads 4. 6 cups
soldi70 [24.7K]

Answer:

1. 16/9

2. 33/2

3. 4/9

4. 3/2

5. 6/13

Step-by-step explanation:

1. 16 dogs and 9 cats  

16/9

2. 99 miles to 6 gallons  

99/6

Divide by 3 on the top and bottom

33/2

3. 4 frogs to 9 lily pads

4/9

4. 6 cups of milk to 4 cups of flour

6/4

Divide the top and bottom by 2

3/2

5. 6 girls to 13 boys

6/13

6 0
3 years ago
What is the probability of rolling a 1 with a number cube that has the numbers 1, 2, 3, 4, 5, and 6 and tossing heads with a coi
Helga [31]
Probablity is (desired outcomes)/(total) possible outcomes so the dice 1 is desired and the total poassible outcomes is 6 since 6 numbers so probailty of rolling a 1 is 1/6 then flippin heads desired outcome=1 total possible=2 probabilty is 1/2 so we have 1/6 and 1/2 now we mulitply them 1/6 times 1/2=1/12 the answer is A
7 0
3 years ago
Read 2 more answers
Evaluate Dx / ^ 9-8x - x2^
Solnce55 [7]
It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for \sqrt x.

In that case, you want to find the antiderivative,

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}

Complete the square in the denominator:

9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2

Now substitute x+4=5\sin y, so that \mathrm dx=5\cos y\,\mathrm dy. Then

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy

which simplifies to

\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy

Now, recall that \sqrt{x^2}=|x|. But we want the substitution we made to be reversible, so that

x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)

which implies that -\dfrac\pi2\le y\le\dfrac\pi2. (This is the range of the inverse sine function.)

Under these conditions, we have \cos y\ge0, which lets us reduce \sqrt{\cos^2y}=|\cos y|=\cos y. Finally,

\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C

and back-substituting to get this in terms of x yields

\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C
4 0
3 years ago
5/12 expressed as a decimal fraction is? (Round to the nearest thousandths)
Makovka662 [10]

Answer:

5/12 = 0.416666667 if you round up to the nearest thousandths it would be 0.417

7 0
3 years ago
Read 2 more answers
In ΔXYZ, ∠Y=90° and ∠X=73°. ∠ZWY=80° and XW=80. Find the length of ZY to the nearest 100th.
lawyer [7]

Answer:

Solution given:

Y=90°

∠X=73°.

∠ZWY=80°

and XW=80.

ZY=?

We know that

In right angled triangle ∆ XYZ

Tan 73=\frac{p}{h}

3.27=\frac{yz}{xy}

3.27×[xy]=yz

xw+wy=\frac{yz}{3.27}

wy=\frac{yz}{3.27}-80...........(1)

again

In right angled triangle WYZ

Tan 80=\frac{yz}{wy}

5.67×wy=yz

wy=\frac{yz}{5.67}

yz=5.67×wy............................................(2)

E<u>q</u><u>u</u><u>a</u><u>t</u><u>i</u><u>n</u><u>g</u><u> </u><u>equation</u><u> </u><u>1</u><u>&</u><u>2</u>

\frac{yz}{5.67}=\frac{yz}{3.27}-80

\frac{yz}{3.27}-\frac{yz}{5.67}=80

5.67yz-3.27yz=80*5.67*3.27

2.4yz =1483.272

yz=\frac{1483.272}{2.4}

yz=618.03

:.y=618.03unit.<u>the length of ZY to the nearest 100</u><u>th</u><u> </u><u>is</u><u> </u><u>6</u><u>1</u><u>8</u><u>.</u>

8 0
3 years ago
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