Hey, I have some questions on some math problems for Algebra 2. Think you can help? Here's the first one :)

Some investments in the stock market have gained 10% annually. the total value of the investment, A, and this rate can be found using A= P(1.10)^n where P is the initial value of this investment, and N is the number of years the money is invested. if $1,000 is invested in the stock market at this annual rate of return, what is the expected total value after 18 years?

1. $4,054.47
2. $5,559.92
3. $18,700.00
4. $19,800.00

I originally thought it was $18,700.00 but I don't know

Answer:

[tex]f(-1)>g(-1)[/tex]

Step-by-step explanation:

we are given

[tex]f(x)=-x^2+1[/tex]

We can plug x=-1 and find f(x)

we get

[tex]f(-1)=-(-1)^2+1[/tex]

[tex]f(-1)=-1+1[/tex]

[tex]f(-1)=0[/tex]

now, we can find g(-1)

we can look at the table and find g(-1)

so, we get

[tex]g(-1)=-4[/tex]

we know that

-4 is less than 0

so,

[tex]g(-1)<f(-1)[/tex]

or we get

[tex]f(-1)>g(-1)[/tex]

Answer:

[tex](1.12 x 10^5) (6.06 x 10^5) = 6.787 x 10^{10}\\[/tex]

 [tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2} = 6.14 * 10 ^ {-3}\\[/tex]

Step-by-step explanation:

To solve this problem we must solve all 4 operations.

For the first one we have:

[tex](1.12 x 10^5) (6.06 x 10^5)[/tex]

When we have multiplication of powers of equal base (10) the same base is placed and the exponents are added

So:

[tex]1.12 * 6.06 x 10^{5+5} = 6.787 x 10^{10}\\[/tex]

Therefore the answer to this question is correct.

For the second question we have:

[tex](2 x 10^1) (3.0 x 10^1)[/tex]

Then following the same procedure as in the previous question we have:

[tex]2 * 3.0 x 10 ^ {1 + 1} = 6 x 10 ^ 2\\[/tex]

Then the answer shown in the statement is not correct, because 10 must be squared, product of the sum of its exponents (1 + 1)

For the third question we have:

[tex](2,775 x 10^{-4}) (4,775 x 10^4)\\2.775 * 4.775 x 10 ^{(- 4) +4} = 13.251 x10 ^ 0\\[/tex]

Then it is verified that the answer for this operation is no correct

[tex]13.25\neq 1.325[/tex]

Finally, for the fourth question we have:

[tex]\frac{5}{(8.14 x 10 ^ 2)}\\[/tex]

This we can write it as:

[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2}\\[/tex]

In division of powers of equal base (10 in this case) the same base is placed and the exponents are subtracted:

[tex]\frac{0.5}{8.14 x 10 ^ {1-2}} = 0.0614 x 10 ^ {-1} = 6.14 * 10 ^ {-3}\\[/tex]

Finally, the problems that show correct answers are:

[tex](1.12 x 10^5) (6.06 x 10^5) = 6.787 x 10^{10}\\[/tex]

[tex]\frac{0.5 x 10 ^ 1}{8.14 x 10 ^ 2} = 6.14 * 10 ^ {-3}\\[/tex]

The smaller sail has a height of 10.5 inches.

We know that for the two sails of the sailboat,

the right angle will be equal,

the angles at the top of the sail are congruent, {given}

therefore, the third angle will be equal for both the triangles.

thus, both the triangles will be similar to each other.

The sides will be in ratio.

[tex]\dfrac{12}{8}=\dfrac{x}{7}[/tex]

[tex]\dfrac{12\times 7}{8}=x\\x = 10.5[/tex]

Hence, the smaller sail has a height of 10.5 inches.

Learn more about Similar triangles:

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The problem describes a case of exponential decay. The car's value decreases by 20% each year, so after 5 years of depreciation, the value of the car can be calculated by repeatedly applying this 20% reduction each year. The car will be worth approximately $8,437.76 after 5 years of depreciation.

The problem is a very typical example of exponential decay. The car depreciates in value by 20% each year. This means that after each year, the car is worth 80% (or 0.8) of its value from the previous year. After five years, we can calculate how much the car is worth by simply applying these percentages to the car's initial cost.

To calculate the value of the car after 5 years, you multiply the initial cost of the car by 0.8 (representing the 80% remaining value after depreciation) five times:

So after 5 years, the car will be worth approximately $8,437.76.

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The minimum value of the parabola y = x^2 + 5x is -25/4.

The minimum value of the parabola y = x^2 + 5x can be found by completing the square.

Rewrite the equation as y = (x^2 + 5x + 25/4) - 25/4, which is equivalent to y = (x + 5/2)^2 - 25/4.

Since the square of a real number is always non-negative, the minimum value of the parabola is -25/4.

Answer:

I did the quiz

Step-by-step explanation:

The correct statement is,

⇒ Terrell ran 3,000 meters more than Victor.

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

We have to given that;

Victor ran 3 kilometers.

And, Terrell ran 4,000 meters.

Now,

We know that;

1 kilometer = 1000 meters

Hence, We get;

Victor ran = 3 kilometers

                 = 3 x 1000

                 = 3000 meters

Thus, Difference of distance are,

= 4000 - 3000

= 1000 meters

Therefore, The correct statement is,

⇒ Terrell ran 3,000 meters more than Victor.

Learn more about the measurement unit visit:

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Consider cases where the number of withholding allowances is less than 6.

The amount of federal income tax withheld will increase if the

1. Gross pay increases and withholding allowances remains the same or

2. Gross pay remains the same and withholding allowances decreases

Option B is correct. The amount of federal income tax withheld will increase when Gross pay increases by more than $20 and withholding allowances stay the same

Hope this helps..!!

Thank you :)

Federal income tax, when withholding allowances is less than 6, the Gross pay increases by more than $20 and withholding allowances stay the same.

Federal income tax is the tax which is used to develop and run the city or country and charged on the citizen resides their.

The value of  federal income tax changes with change in withholding allowances and gross pay as-

Given information-

The number of withholding allowances is less than 6.

As the number of withholding allowances is less than 6. Thus the withholding allowances is fixed here.

Now the value of federal income tax increases gross pay increases as discussed in first property above.

Hence, Gross pay increases by more than $20 and withholding allowances stay the same. Thus the option B is the correct option.

Learn more about the federal income tax here;

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Answer:

h = x + 1.5

Step-by-step explanation:

Start with the width. The width = x

The length is 5 times the width = 5*x or 5x

The volume of this is

5x^3 + 7.5x^2 = 5x * x * h

5x^3 + 7.5x^2 = 5x^2 * h                          Divide both sides by 5x^2

5x^3 / 5x^2    +    7.5x^2 / 5x^2   =   5x^2*h/ 5x^2

x + 1.5  = h <<<< Answer

Given is a Right Triangular Prism whose height is 8 feet, and whose base is a right triangle with legs 4 feet and 6 feet.

To find the volume of the prism, we must find the area of its base. Its base is in shape of right triangle. We know the formula for area of Right triangle is given as follows :-

[tex] Area = \frac{1}{2} bh \\\\
Area = \frac{1}{2} *4*6 \\\\
Area = \frac{24}{2} \\\\
Area = 12 \;\;feet^{2} [/tex]

So Prism's base area, B = 12 squared feet.

and Prism's height, H = 8 feet.

We know the formula for volume of Prism is given as follows :-

Volume of Prism = (Base Area) x (Height of Prism)

Volume = B x H

Volume = 12 feet² x 8 feet

Volume = 96 feet³

Hence, option C is correct i.e. 96 cubic feet.

Answer:

he means 5 2/3

Step-by-step explanation:

Answer: Fourth option is correct.

Step-by-step explanation:

Since we have given that

Distance traveled by Brian = [tex]4\frac{1}{4}\ miles=\frac{17}{4}\ miles[/tex]

Time taken by him = [tex]\frac{3}{4}[/tex] of an hour

So, Speed at which Brian is running fast is given by

[tex]Speed=\dfrac{Distance}{Time}\\\\\\Speed=\dfrac{\dfrac{17}{4}}{\dfrac{3}{4}}\\\\\\Speed=\dfrac{17}{3}\\\\\\Speed=5\dfrac{2}{3}\ mph[/tex]

Hence, Brian was running fast at [tex]5\dfrac{2}{3}\ mph[/tex]

Therefore, Fourth option is correct.

Answer: 575-d

Step-by-step explanation:

1). 8/15

2). 1/3

3). B. equally likely

4). A

5). D

Final answer:

To make 3000 pounds of raisins, you would need 12000 pounds of grapes, as it takes 4 pounds of grapes to make 1 pound of raisins.

Explanation:

The question asks us to find out how many pounds of grapes are needed to make 3000 pounds of raisins.

Given that it takes 4 pounds of grapes to make 1 pound of raisins, we can set up a proportion to solve for the total weight of grapes needed. The proportion will be:

4 pounds of grapes / 1 pound of raisins = x pounds of grapes / 3000 pounds of raisins

Multiplying both sides of the proportion by 3000 pounds of raisins gives us:

4 pounds of grapes x 3000 pounds of raisins = x pounds of grapes x 1 pound of raisins

So,

x = 4 x 3000

x = 12000 pounds of grapes.

Therefore, you would need 12000 pounds of grapes to make 3000 pounds of raisins.

Answer:   Its B for short

First we get 30% ounces of peanuts in mixed nuts:

(0.3) * (32) = 9.6

To find the percentage of peanut concentration of the final mix if you add x ounces of peanuts:

% of peanuts = ((x + 9.6) / (x + 32)) * (100)

Answer:

An expression can be used is:

% of peanuts = ((x + 9.6) / (x + 32)) * (100)

Step-by-step explanation:

yea