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nadya68 [22]
3 years ago
15

Darcy and Harper work for different catering companies. Darcy earns a weekly salary of $982 and an 18% commission on her food

Mathematics
1 answer:
PilotLPTM [1.2K]3 years ago
8 0

Answer:

$2500

Step-by-step explanation:

Given that:

Darcy's weekly earning = $982 plus 18% commission on food sales

Harper's weekly earning = $807 plus 25% commision

amount of food sales will result in Darcy and Harper earning the same amount for the week

Let amount of food sales = f

Darcy's earning = Harper's earning

(982 + 18%*f) = (807 + 25% * f)

(982 + 0.18f) = (807 + 0.25f)

982 + 0.18f = 807 + 0.25f

982 - 807 = 0.25f - 0.18f

175 = 0.07f

f = 175 / 0.07

f = 2500

Hence amount of food sales that will result in both Darcy and Harper earning the same amount = $2500

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A book falls from a shelf that is 5 feet above the floor. A model for the height h in feet if an object dropped from an initial
Brums [2.3K]

Answer:

About 0.559 seconds

Step-by-step explanation:

The height equation is:

h=-16t^2+h_0

Where h_0 is the initial height of the book, which is 5, so we can write:

h=-16t^2+5

Now, we want time it took for the book to reach ground (h = 0)

So, we substitute h = 0 and solve for t:

h=-16t^2+5\\0=-16t^2+5\\16t^2=5\\t^2=0.3125\\t=0.5590\\t=0.559

It took about 0.559 seconds for the book to reach the ground

5 0
3 years ago
x - 2y = 3 5x + 3y = 2 The lines whose equations are shown intersect at which point? (1, -1) (-1, 1) (0, 3/2)
gtnhenbr [62]
I would solve the first equation for x and then sub that value into x in the second equation.  That's the easiest way.  x - 2y = 3 solved for x is x = 2y+3.  Now sub that in for x in the second equation: 5(2y+3)+3y=2 and 10y + 15 + 3y = 2.  13y = -13, and y = -1.  Now sub that y value into either equation to solve for x: x = 2(-1) + 3 gives us an x value of x = 1.  Therefore, your solution to this system is (1, -1), first choice above.
4 0
3 years ago
Determine if each of the following sets is a subspace of Pn, for an appropriate value of n.
snow_tiger [21]

Answer:

1) W₁ is a subspace of Pₙ (R)

2) W₂ is not a subspace of Pₙ (R)

4) W₃ is a subspace of Pₙ (R)

Step-by-step explanation:

Given that;

1.Let W₁ be the set of all polynomials of the form p(t) = at², where a is in R

2.Let W₂ be the set of all polynomials of the form p(t) = t² + a, where a is in R

3.Let W₃ be the set of all polynomials of the form p(t) = at² + at, where a is in R

so

1)

let W₁ = { at² ║ a∈ R }

let ∝ = a₁t² and β = a₂t²  ∈W₁

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t²) + c₂(a₂t²)

= c₁a₁t² + c²a₂t²

= (c₁a₁ + c²a₂)t² ∈ W₁

Therefore c₁∝ + c₂β ∈ W₁ for all ∝, β ∈ W₁  and scalars c₁, c₂

Thus, W₁ is a subspace of Pₙ (R)

2)

let W₂ = { t² + a ║ a∈ R }

the zero polynomial 0t² + 0 ∉ W₂

because the coefficient of t² is 0 but not 1

Thus W₂ is not a subspace of Pₙ (R)

3)

let W₃ = { at² + a ║ a∈ R }

let ∝ = a₁t² +a₁t  and β = a₂t² + a₂t ∈ W₃

let c₁, c₂ be two scalars

c₁∝ + c₂β = c₁(a₁t² +a₁t) + c₂(a₂t² + a₂t)

= c₁a₁t² +c₁a₁t + c₂a₂t² + c₂a₂t

= (c₁a₁ +c₂a₂)t² + (c₁a₁t + c₂a₂)t ∈ W₃

Therefore c₁∝ + c₂β ∈ W₃ for all ∝, β ∈ W₃ and scalars c₁, c₂

Thus, W₃ is a subspace of Pₙ (R)

8 0
3 years ago
What types of shelter did hunter gather's have
stiv31 [10]
Animal skins, animal bones, wood, and more. Depending on what era they were in.
8 0
3 years ago
5/18 • 3/20 • 6/12 please help
wlad13 [49]

Step-by-step explanation:

1. (5/18) × (3/20)=

(5×3)/(18×20)=

15/360=1/24

2. (1/24) × (6/12)=

1/48

4 0
2 years ago
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