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3 years ago

9

While shopping for clothes, Daniel spent $34 less than 3 times what Jaclyn spent. Daniel spent $14. Write and solve an equation

to find how much Jaclyn spent. Let x represent how much Jaclyn spent.
___x - ___ = ___

Jaclyn spent $____

1 answer:

topjm [15]3 years ago

4 0

Answer: Jaclyn spent $48

Step-by-step explanation:

3x - 34 = 14

3x = 14+34

X = 48/3 = 16

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Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = x^3 – 3x^2 + 2x

castortr0y [4]

Answer: The correct option is second, i.e. ,"2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".

Explanation:

The given equation is,

$y=x^3-3x^2+2x$

It can be written as,

$f(x)=x^3-3x^2+2x$

Find the zeros of the equation. Equation the function equal to 0.

$0=x^3-3x^2+2x$

$x(x^2-3x+2)=0$

$x(x^2-2x-x+2)=0$

$x(x-2)(x-1)=0$

So, the three zeros are 0, 1 and 2.

The graph of the equation is shown below.

From the given graph it is noticed that the enclosed by the curve and x- axis is lies between 0 to 2, but the area from 0 to 1 lies above the x-axis and area from 1 to 2 lies below the x-axis. So the function will be negative from 1 to 2.

The area enclosed by curve and x-axis is,

$A=\int_{0}^{1}f(x)dx+\int_{1}^{2}[-f(x)]dx$

$A=\int_{0}^{1}f(x)dx-\int_{1}^{2}f(x)dx$

From the graph it is noticed that the area from 0 to 1 is symmetric or same as area from 1 to 2. So the total area is the twice of area from 0 to 1.

$A=2\int_{0}^{1}f(x)dx$

$A=2\int_{0}^{1}[x^3-3x^2+2x]dx$

Therefore, The correct option is "2 times the integral from 0 to 1 of the quantity x cubed minus 3 times x squared plus 2 times x, dx".

3 0

3 years ago

19. The marked price of an oven is 30% above its cost. In a sale, it is

yaroslaw [1]

a) Marked price: $884, Cost: $680

b) 2.5 %

Step-by-step explanation:

a)

Let's call:

P = marked price of the oven

C = cost of the oven

We know that:

- The marked price of the oven is 30% above the cost, which means

$P=(1+\frac{30}{100})C=1.30C$ (1)

- In the sale, the oven is sold at a discount of 25% on its marked price; so the price of the sale is (we call it S)

$S=(1-\frac{25}{100})P=0.75P$ (2)

- We also know that the discount, which is the difference between the makerd price (P) and the discounted price (S) is

$P-S=\$221$ (3)

Substituting (2) into (3) we find marked price

$P-0.75P=\$221\\0.25P=\$221\\P=\frac{221}{0.25}=\$884$

Therefore, the cost of the oven is (from eq(1)):

$C=\frac{P}{1.30}=\frac{884}{1.30}=\$680$

b)

The percentage loss in this situation is given by the difference between cost of the oven and the final price at which the oven is sold.

In this case, we have:

C = $680 (cost of the oven)

The discounted prices is S, and can be f ound using eq(3):

$S=P-221=884-221=\$663$

Therefore, the oven costs 680$ but it is sold at 663$.

Therefore, we can calculate the percentage loss using the equation:

$Loss=\frac{C-S}{C}\cdot 100 = \frac{680-663}{680}\cdot 100 =0.025\cdot 100 = 2.5\%$

So, a percentage loss of 2.5%.

4 0

3 years ago

Compute the multifactor productivity measure for each of the weeks shown for production of chocolate bars. What do the productiv

liq [111]

Answer:

Week 1 =3.03

Week 2 =2.99

Week 3=2.9

Week 4=2.83

Step-by-step explanation:

Computation for the multifactor productivity measure for each of the weeks shown for production of chocolate bars.

Using this formula

Week Multifactor productivity measure = (Output / Total Cost)

Where:

Output represent Quantity produced

Total cost represent Labor cost + Material cost + Overhead

Let plug in the formula

Week 1= 30,000/(40*12*6)+[(40*12*6)1.5]+(450*6)

Week 1 =30,000/(2,880)+(2,880*1.5)+2,700

Week 1 =30,000/(2,880+4,320+2,700)

Week 1=30,000/9,900

Week 1 =3.03

Week 2= 33,600/(40*12*7)+[(40*12*7)1.5]+(470*6)

Week 2 =33,600/(3,360)+(3,360*1.5)+2,820

Week 2=33,600/(3,360+5,040+2,820)

Week 2=33,600/11,220

Week 2 =2.99

Week 3= 32,200/(40*12*7)+[(40*12*7)1.5]+(460*6)

Week 3 =32,200/(3,360)+(3,360*1.5)+2,760

Week 3=32,200/(3,360+5,040+2,760)

Week 3=32,200/11,160

Week 3=2.9

Week 4= 35,400/(40*12*8)+[(40*12*8)1.5]+(480*6)

Week 4 =35,400/(3,840)+(3,840*1.5)+2,880

Week 4=35,400/(3,840+5,760+2,880)

Week 4=35,400/12,480

Week 4=2.83

Therefore the multifactor productivity measure for each of the weeks shown for production of chocolate bars is :

Week 1 =3.03

Week 2 =2.99

Week 3=2.9

Week 4=2.83

4 0

3 years ago

Its complete solution <br>and answer is 45

lora16 [44]

Answer:

8

Step-by-step explanation:

6 0

3 years ago

Please help asap 20 pts + brainliest to right/best answer

AleksAgata [21]

Answer:

(-1,-2)

Step-by-step explanation:

The vertex of the parabola is the minimum or maximum point of the parabola. It is located along the line of symmetry.

Looking at the graph, the minimum point is (-1,-2)

5 0

4 years ago