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1 year ago

14

Caitlin Grasso is a salesperson in the kitchen and bath department at Morris Supplies, Inc. She makes 5.5% straight commission o

n her total sales. What were her total week's sales, if her gross pay was $560?

1 answer:

miskamm [114]1 year ago

7 0

10% of $560 is $56

So 5% is $28

1% of $560 is $5.60

So now half $5.60 is $2.80

$2.80 is 0.05%

Now add

$28 + $2.80 = $30.80

Total is $30.80

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Determine which equations below, when combined with the equation 3x-4y=2, will form a system with no solutions. Choose all that

svetoff [14.1K]

Two equations will not have solution if they are parallel and have different y-intercepts. Parallel lines have the same slope. In a slope-intercept form, the equation of the line can be expressed as,

y = mx + b

where m is slope and b is the y-intercept.

Given: 3x - 4y = 2
Slope-intercept: y = 3x/4 - 1/2

A. 2y = 1.5x - 2
Slope-intercept: y = 3x/4 - 1

B. 2y = 1.5x - 1
Slope-intercept: y = 3x/4 - 1/2

C. 3x + 4y = 2
Slope-intercept: y = -3x/4 + 1/2

D. -4y + 3x = -2
Slope-intercept: y = 3x/4 + 1/2

Hence, the answers to this item are A and D.

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2 years ago

Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |

Bas_tet [7]

Answer:

$M=168k$

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

$M=\int\int \rho dA$

Now, we know the limits of the integrals of x and y, and also know that ρ = ky², so we will have:

$M=\int^{9}_{1}\int^{4}_{1}ky^{2} dydx$

Let's solve this integral:

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx$

$M=k\int^{9}_{1}21dx$

$M=21k\int^{9}_{1}dx=21k*x|^{9}_{1}$

So the mass will be:

$M=21k*8=168k$

Now we need to find the x-coordinate of the center of mass.

$\bar{x}=\frac{1}{M}\int\int x*\rho dydx$

$\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx$

$\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx$

$\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx$

$\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}$

$\bar{x}=\frac{21}{168}*40=5$

Now we need to find the y-coordinate of the center of mass.

$\bar{y}=\frac{1}{M}\int\int y*\rho dydx$

$\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx$

$\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx$

$\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx$

$\bar{y}=\frac{255}{672}\int^{9}_{1}dx$

$\bar{y}=\frac{255}{672}8=\frac{2040}{672}$

$\bar{y}=\frac{85}{28}$

Therefore the center of mass is:

$(\bar{x},\bar{y})=(5,\frac{85}{28})$

I hope it helps you!

3 0

2 years ago

ALGEBRA Jake Duffy drove 12,568 miles

kirza4 [7]

Answer:

The cost per mile that Jack Duffy charge $0.278 per miles , i.e option B

Step-by-step explanation:

Given as :

The distance drove by Jack Duffy = d = 12,568 miles

The fixed costs totaled = $1,485.00

The variable cost totaled = $2,015.75

Let The cost per mile that Jack Duffy charge = $x cost per miles

Now, According to question

The totaled cost = The fixed costs + The variable cost

Or, The totaled cost = $1,485.00 + $2,015.75

I.e The totaled cost = $3500.75

Now,

The cost per mile that Jack Duffy charge = $\dfrac{\extrm Total cost}{\textrm Total Distance}$

I.e x = $\dfrac{3500.75}{12568}$

∴ x = $0.278 per miles

So,The cost per mile that Jack Duffy charge = x = $0.278 per miles .

Hence,The cost per mile that Jack Duffy charge $0.278 per miles , i.e option B Answer

5 0

2 years ago

A print shop makes bumper stickers for election campaigns. If x stickers are ordered (where x < 10,000), then the price per s

Sergeu [11.5K]

Answer:

P(x) = (0.049x - 0.0000015x²)

Step-by-step explanation:

price per sticker is 0.14 − 0.000002x dollars

total cost of producing the order is 0.091x − 0.0000005x² dollars.

P(x) = profit = Revenue - Cost

Let the number of units of stickers made be x

Revenue = (price per sticker) × (total units sold) = (0.14 − 0.000002x) × (x)

= (0.14x - 0.000002x²) dollars.

Cost of producing x units in the order = (0.091x − 0.0000005x²)

P(x) = 0.14x - 0.000002x² - (0.091x − 0.0000005x²) = 0.14x - 0.091x - 0.000002x² + 0.0000005x²

= (0.049x - 0.0000015x²)

P(x) = (0.049x - 0.0000015x²)

Hope this Helps!!!

3 0

2 years ago

Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month,

den301095 [7]

Zach time of reading every weekend forms a sequence with these terms: 10, 20, 40, 80. On the other hand, that of Victoria forms a sequence with terms: 35, 50, 65, 80. By keenly observing the sequences, Zach's sequence is a geometric sequence with a common ratio equal to 2 and Victoria's sequence is an arithmetic or linear sequence with a common difference of 15. Thus, the answer is letter B.

5 0

1 year ago

Read 2 more answers