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LenKa [72]
3 years ago
5

Natalie works in a department store selling clothing. She makes a guaranteed salary of $300 per week, but is paid a commission o

n top of her base salary equal to 30% of her total sales for the week. How much would Natalie make in a week in which she made $225 in sales? How much would Natalie make in a week if she made x dollars in sales?
Mathematics
1 answer:
Sergio039 [100]3 years ago
7 0

Answer:

The answer is below

Step-by-step explanation:

a) Natalie basic salary is $300 per week. She is paid a commission of 30% of her total sales for the week. Therefore her total weekly salary per week is given by:

Total weekly salary = Basic salary + Commissions

If Natalie makes $225 in sales, her commission = 30% of $225 = 0.3 × $225 = $67.5

Total weekly salary = Basic salary + Commissions = $300 + $67.5

Total weekly salary = $367.5

b) If Natalie makes $x in sales, her commission = 30% of $x = 0.3 × $x = $0.3x

Total weekly salary = Basic salary + Commissions = $300 + $0.3x

Total weekly salary = $(300 + 0.3x)

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John Tucker is interested in purchasing stock. He wants to determine the costs.
Delvig [45]

Answer: a0 =$97.5  ; a1 =$87.96 ; a2=$282.48; a3=$1,722.5 ; a4=$1,553.96 ; a5=$4,990.48

Step-by-step explanation:

Hi, to solve this problem we have to multiply each total by the commission in decimal form (6 / 100= 0.06).

So:

$1625 x 0.06 = $97.5

$1,466 x 0.06 =$87.96

$4,708 x 0.06 =$282.48

And finally, to obtain the total costs we have to add to each total the commission of the total.

$1625 + $97.5 = $1,722.5

$1,466 +$87.96 = $1,553.96

$4,708 +$282.48 = $4,990.48

Feel free to ask for more if it´s necessary or if you did not understand something.

8 0
2 years ago
Read 2 more answers
Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 9t + 9 cot(t/2), [π/4, 7π/4]
agasfer [191]

Answer:

the absolute maximum value is 89.96 and

the absolute minimum value is 23.173

Step-by-step explanation:

Here we have cotangent given by the following relation;

cot \theta =\frac{1 }{tan \theta} so that the expression becomes

f(t) = 9t +9/tan(t/2)

Therefore, to look for the point of local extremum, we differentiate, the expression as follows;

f'(t) = \frac{\mathrm{d} \left (9t +9/tan(t/2)  \right )}{\mathrm{d} t} = \frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9  \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2}

Equating to 0 and solving gives

\frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9  \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2} = 0

t=\frac{4\pi n_1 +\pi }{2} ; t = \frac{4\pi n_2 -\pi }{2}

Where n_i is an integer hence when n₁ = 0 and n₂ = 1 we have t = π/4 and t = 3π/2 respectively

Or we have by chain rule

f'(t) = 9 -(9/2)csc²(t/2)

Equating to zero gives

9 -(9/2)csc²(t/2) = 0

csc²(t/2)  = 2

csc(t/2) = ±√2

The solutions are, in quadrant 1, t/2 = π/4 such that t = π/2 or

in quadrant 2 we have t/2 = π - π/4 so that t = 3π/2

We then evaluate between the given closed interval to find the absolute maximum and absolute minimum as follows;

f(x) for x = π/4, π/2, 3π/2, 7π/2

f(π/4) = 9·π/4 +9/tan(π/8) = 28.7965

f(π/2) = 9·π/2 +9/tan(π/4) = 23.137

f(3π/2) = 9·3π/2 +9/tan(3·π/4) = 33.412

f(7π/2) = 9·7π/2 +9/tan(7π/4) = 89.96

Therefore the absolute maximum value = 89.96 and

the absolute minimum value = 23.173.

7 0
3 years ago
you have a piece of wood that is 72 inches long u cut the wood into three pieces the second piece is 6 inches longer than the fi
tangare [24]

Let

x---------> the length of the first piece

y---------> the length of the second piece

z---------> the length of the third piece

we know that

x+y+z=72 -------> equation 1

y=x+6 -----> solve for x

x=y-6 -------> equation 2

z=6+y -------> equation 3

substitute equation 2 and equation 3 in equation 1

[y-6]+y+[6+y]=72

3y=72

y=(72/3)=24 in

<u>Find the value of x</u>

x=y-6 -------> equation 2

x=24-6=18 in

<u>Find the value of z</u>

z=6+y -------> equation 3

z=6+24=30 in

therefore

<u>the answer is</u>

the length of the first piece is 18 in

the length of the second piece 24 in

the length of the third piece is 30 in

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3 years ago
A grocery store is selling 12 bananas for $2.40 at this rate what is the cost of 15 bananas
lorasvet [3.4K]
C. $3.00
To find how many bananas you get for a dollar, do 12/2.4 to get 5 bananas per dollar. Since you want to find how much it costs for 15 bananas, you'll do 15/5, which gives you $3

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3 years ago
Solve the equation 8-2x=-8x+14
Salsk061 [2.6K]

Answer:

x= -3/5

Step-by-step explanation:

6 0
3 years ago
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