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3 years ago

11

Harrison mows lawns and rakes leaves for his summer and fall weekend jobs. He gets $10 an hour to mow lawns and $8 an hour to ra

ke leaves. If, during September, Harrison mows for m hours and rakes for 12 hours, which expression represents the amount of money he makes? Harrison mows lawns for 11 hours, so m = 11. How much money does he make in September?

2 answers:

Airida [17]3 years ago

8 0

Answer:

first one is 10m+8(12)

second one is 206

Step-by-step explanation:

i took it alrr..

earnstyle [38]3 years ago

7 0

Total money= 10m+8(12)

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Account A and Account B both have a principal of $2,000 and an annual interest rate of 2%. No additional deposits or withdrawals

GuDViN [60]

Answer:

Account B earns more interest.

After 20 years, account B will have earned $171.89 more.

Step-by-step explanation:

Let's calculate the total for each account.

Account A:

Account A earns simple interest. We know that the principal value is $2000 and the interest rate is 2% or 0.02. We can use the simple interest formula:

$A=P(1+rt)$

Where A is the future value, P is the principal, r is the rate, and t is the time in years.

So, let's substitute 2000 for P, 0.02 for r, and 20 for t. This yields:

$A=2000(1+0.02(20))$

Multiply and add:

$A=2000(1+0.4)=2000(1.4)$

Multiply. So, the total amount of money in Account A after 20 years is:

$A=\$2800$

Since we initially deposited $2000 and our total is now $2800, this means that we earned an interest of $2800-2000=\$ 800$

Account B:

Account B earns compound interest. Like Account A, Account B has a principal value of $2000 and the interest rate is 2% or 0.02. We also know that it's compounded annually, so once per year. We can use the compound interest formula:

$B=P(1+\frac{r}{n}})^{nt}$

Where B is the future value, P is the principal, r is the rate, n is the times compounded per year, and t is the time in years.

So, let's substitute 2000 for P, 0.02 for r, n for 1 (since it's compounded annually), and t for 20. This yields:

$B=2000(1+\frac{0.02}{1})^{(1)(20)}$

Simplify this to acquire:

$B=2000(1.02)^{20}$

Evaluate. Use a calculator. So, after 20 years, the amount of money in Account B is:

$B\approx\$2971.89$

Since our principal was $2000, this means that we earned an interest of approximately $2971.89-2000=\$ 971.89$ .

So, Account A earned an interest of $800 and Account B earned an approximate interest of $971.89.

So, Account B earned more interest.

And it earned $971.89-800=\$ 171.89$ more than Account A.

And we're done!

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3 years ago

What is the value of z?<br><br> Enter your answer in the box.

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Answer:

23

Step-by-step explanation:

Because the angles of a triangle always add up to 180°, you can set up an equation like this.

$62+95+z=180$

$157+z=180$

$157-157+z=180-157$

$z=23$

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2 years ago

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Whats 0.4 as a percentage?

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2 years ago

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Solve 2x + 3y = C, for y

natta225 [31]

Answer:

y= $\frac{c-2x}{3}$

Step-by-step explanation:

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3 years ago

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A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of the box at x= 1.59:

$V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of the box at x= 0.53:

$V = \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0

3 years ago