MATHEMATICS COLLEGE

When hired at a new job selling jewelry, you are given two pay options:Option A: Base salary of $16,000 a year, with a commission of 7% of your sales

Option B: Base salary of $25,000 a year, with a commission of 2% of your sales

In order for option A to produce a larger income, you would need sell at least $_______ of jewelry each year

Answers

Answer 1

Answer:

You are required to sell a minimum of 180,001 of jewelry each year.

Given that,

The base salary is $16,000 per year and there is a 7% commission on sales for option A.
The base salary is $25,000 per year and there is a 2% commission on sales for option B.
Also, let us assume the sales be x

Based on the above information, the following expression should be made:

16,000 + 0.07x > 25,000 + 0.02x

0.07x - 0.02x > 25,000 - 16,000

0.05x > 9000

x > 9000 ÷ 0.05

x > 180,000

Therefore we can conclude that you are required to sell a minimum of 180,001 of jewelry each year.

Learn more: brainly.com/question/12127730

Answer 2

Answer: 16,000 + 0.07x > 25,000 + 0.02x
0.07x - 0.02x > 25,000 - 16,000
0.05x > 9000
x > 9000 / 0.05
x > 180,000....so they would need to sell at least 180,001

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A piece of rope there is 28 feet long is cut into two pieces. One is use to form a circle and others used to form a square. Write a function G representing the area of the square as a function of the radius of the circle R

Answers

The function g representing the area of the square as a function of the radius of the circle r is given as:

$g(r) = 49 - 22r + (121r^2)/(49)$

Solution:

Given that,

length of rope = 28 feet

Let "c" be the circumference of circle

Let "p" be the perimeter of square

Therefore,

length of rope = circumference of circle + perimeter of square

c + p = 28 ------- eqn 1

The circumference of circle is given as:

$c = 2 \pi r$

Where, "r" is the radius of circle

Substitute the above circumference in eqn 1

$2 \pi r + p = 28$

$p = 28 - 2 \pi r$ ----------- eqn 2

If "a" is the length of each side of square, then the perimeter of sqaure is given as:

p = 4a

Substitute p = 4a in eqn 2

$4a = 28 - 2 \pi r\n\na = (28 - 2 \pi r)/(4)\n\na = 7 - ( \pi r)/(2)$

The area of square is given as:

$area = (side)^2\n\narea = a^2$

Substitute the value of "a" in above area expression

$area = (7 - ( \pi r)/(2))^2$ ------ eqn 3

We know that,

$(a - b)^2 = a^2 - 2ab + b^2$

Therefore eqn 3 becomes,

$area = 7^2 -2(7)((\pi r)/(2)) + (( \pi r)/(2))^2\n\narea = 49 - 7 \pi r + ( (\pi)^2 r^2 )/(4)$

$\text{ substitute } \pi = (22)/(7)$

$area = 49 - 7 * (22)/(7) * r + ((22)/(7))^2 * (r^2 )/(4)\n\narea = 49 - 22r + (121)/(49) * r^2\n\narea = 49 - 22r + (121r^2)/(49)$

Let g(r) represent the area of the square as a function of the radius of the circle r, then we get

$g(r) = 49 - 22r + (121r^2)/(49)$

Thus the function is found

Suppose you have 18 objects (10 of type A, 5 of type B, and 3 of type C). Objects of type A are indistinguishable from each other; objects of type B are indistinguishable from each other; and objects of type C are indistinguishable from each other. In how many ways can you Pick 5 of the 18 objects (order does not matter)

Answers

Answer:

$\binom{18}{5}= 8568$

Step-by-step explanation:

Note that we have in total 18 items. Even though we are given information regarding the amounts of items per type, the general question asks the total number of ways in which you can pick 5 out of the 18 objects, without any restriction on the type of chosen items. Therefore, the information regarding the type is unnecessary to solve the problem.

Recall that given n elements, the different ways of choosing k elements out of n is given by the binomial coefficient $\binom{n}{k})$ .

Therefore, in this case the total number of ways is just $\binom{18}{5}=8568$

Answer:

Given:

Number of objects: n = 18

Type A objects: 10

Type B objects: 5

Type C objects: 3

To find:

In how many ways can you Pick 5 of the 18 objects (order does not matter)

Step-by-step explanation:

When the order does not matter we use Combination.

Formula to calculate combination:

C(n,r) = n! / r! ( n - r )!

n = 18

r = 5

Putting the values:

C(n,r)

= C(18,5)

= 18! / 5! ( 18 - 5 )!

= 18! / 5! ( 13 )!

= ( 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 ) / ( 5 * 4 * 3 * 2 * 1 ) * (13 * 12 * 11 * 10 *9* 8 * 7 *6 * 5 * 4 * 3 * 2 *1 )

Cancel 13!

= (18 * 17 * 16 * 15 * 14 ) / ( 5 * 4 * 3 * 2 * 1 )

= 1028160 / 120

= 8568

So you can pick 5 of the 18 objects in 8568 ways.

What can you say about a solution of the equation y' = - y2 just by looking at the differential equation? The function y must be decreasing (or equal to 0) on any interval on which it is defined. The function y must be increasing (or equal to 0) on any interval on which it is defined.

Answers

Answer:

The function y must be decreasing (or equal to 0) on any interval on which it is defined.

Step-by-step explanation:

The derivative of a function gives us the rate at which that function is changing. In this case, -y^2, yields a negative value for every possible value of y, thus, the rate of change is always negative and the function y is decreasing (or equal to 0) on any interval on which it is defined.

Final answer:

The differential equation y' = - $y^2$ implies that y is either decreasing or constant wherever it is defined, because the derivative y' is non-positive.

Explanation:

By examining the differential equation y' = - $y^2$ , we can infer some characteristics about the solutions without solving it. If y is a solution to this equation, then y' represents the derivative of y with respect to x. This derivative tells us about the rate of change of the function y.

Since the right side of the equation is - $y^2$ , and a square of a real number is always non-negative, multiplying by -1 makes it non-positive. This implies that the derivative y' is either less than or equal to zero. Therefore, wherever the function y is defined, it must be either decreasing or constant (equal to zero). If y is positive, y will decrease because of the negative sign in front of the square. If y is negative, squaring it results in a positive number, but the negative sign still ensures that the rate of change is non-positive.

Conclusion: the function y is decreasing or remains constant on any interval it is defined; it cannot be increasing.

Learn more about Differential Equation Behavior here:

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80 orders in 10 days = 8 orders in days

Answers

Answer:

8 orders in 1 day

Step-by-step explanation:

80 divided by 8 is 10. 8 divided by 8 is 1.

Levi Jeans Company at the Silverthorne, Colorado Outlet store sells bootcut jeans for $40 and straight leg jeans for $60. If customer’s bought 5 times more bootcut than straight leg jeans and last month’s sales totaled $6,500, how many of each pair of jeans were sold?

Answers

okay so we know the ratio of jeans sold is 5/1 so lets put that into an equation.

6,500 = $40(5*x) + $60(1*x) so lets solve for x.

so lets merge 40(5x) + 60(x) = 260(x)
6,500 = 260(x)

Divide both sides by 260. 6,500/260 = (260(x))/260 = 25

so lets plug it in. 6,500 = 40(5*25) + 60(1*25) = 5,000 + 1,500 = 6,500.

So the answer is 25!

Write down the equations you know!

40x + 60y = 6500
x = 5y

x = bootcut jeans
y = straight leg jeans

Replace 'x' with it's equation, then solve for y.

40(5y) + 60y = 6500
200y + 60y = 6500
260y = 6500
y = 25

Now plug that back into one of the original equations:

x = 5y
x = 5(25)
x = 125

125 = bootcut jeans
25 = straight leg jeans

A bridge in the shape of a parabolic arch is modelled by this function (see pic).

Answers

Answer:

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