What is compound interest?
A - the interest earned on the principal of an investment
B - the interest earned on both the principal and interest of an investment or savings account
C - the interest earned on a mutual fund
D - the interest earned on a loan

Correct Answer:

z1= 2(cos 56 deg + i sin 56 deg)

z2= 2(cos 128 deg + i sin 128 deg)

z3 = 2(cos 200 deg + i sin 200 deg)

z4 = 2(cos 272 deg+ i sin 272 deg)  

z5 = 2(cos 344 deg+ i sin 344 deg)

Step-by-step explanation:

De Moivre's Theorem--> e^i theta = cos theta + i sin theta

The fifth root of 32 is 2 and 280/5 is 56

z1= 2(cos 56 deg + i sin 56 deg)

360deg/ 5 = 72 deg

(If it was asking for cubed root u would do 360/3. whatever the root is you divide that by 360)

z2= 2(cos 56 + 72) + (i sin 56 + 72)

z2= 2(cos 128 deg + i sin 128 deg)

z3 = 2(cos 128 + 72) + ( i sin 128 + 72)

z3 = 2(cos 200 deg + i sin 200 deg)

z4 = 2(cos 200 + 72) + (i sin 200 + 72)

z4 = 2(cos 272 deg + i sin 272 deg)  

z5 = 2(cos 272 + 72) + (i sin 272 + 72)

z5 = 2(cos 344 deg + i sin 344 deg)

deg means degrees

We have been given that the company spent 32% of its annual budget developing a new machine.

Let us convert the percentage to fraction.

[tex]32 \%=\frac{32}{100} \\ \\ 32 \%=\frac{4\times 8}{4\times 25}\\ \\ \text{Cancel 4 from numerator and denominator}\\ \\ 32 \%=\frac{8}{25}[/tex]

Thus, when we convert 32% to fraction that will be equal to 8/25.

Hence, [tex]\frac{8}{25}[/tex] company's budget was spent developing the new machine.

The fraction of the sector of a circle in radians is (θπ/180). Substituting this fraction into the formula for the area of a circle, and simplifying, results in the formula for the area of the sector being A = (θπ/360) * r^2.

In a circle, the angle in degrees is often converted to radians for calculations. A full circle is equivalent to 360 degrees or 2π radians. Therefore, if the sector angle is θ degrees, then in radians, the equivalent is (θ/360) * 2π = θπ/180.

Inserting this into the formula for the area of a circle, which is A = πr2, the area A of the sector becomes a fraction of the full circle's area, which is calculated as follows: (θ/360) * A = (θ/360) * πr2 = (θπ/180) * r2. Simplifying this results in the formula A = (θπ/360) * r2.

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For a sector in a circle, the fraction is θ/2π in radians. After substituting this into the formula for circle's area, we get the area of sector as Area = (θr²)/2.

The fraction in radians for a sector in a circle is θ/2π, because there are 2π radians in a whole circle. As the formula for the area of circle A is Area=πr², when we insert this fraction, which represents the proportion of the circle that Sector CAB occupies, we get the formula for the area of a sector: Area= (θ/2π) * πr². This simplifies to Area= (θr²)/2, as the π's cancel out. This formula says that the area of a sector is proportionate to its central angle and the square of the radius of the circle.

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The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).

Hence, option D) is the correct answer.

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

To solve for x using the quadratic formula;

x = (-b±√(b² - 4ac)) / (2a)

The correct form of the quadratic formula is x = (-b±√(b² - 4ac)) / (2a).

Hence, option D) is the correct answer.

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The circumference of the parachute is Option A (100.48 feet).

To find the circumference of the parachute, we use the circumference formula for a circle:

C = 2πr

Given the radius (r) is 16 feet, we substitute it into the formula:

C = 2π(16) = 32π

Using the approximate value of π (3.1416), we get:

C ≈ 32 × 3.1416 = 100.48 feet

Thus, the measurement closest to the circumference of the parachute in feet is 100.48 feet (Option A).

Complete question:

In PE a parachute is laid out on the gym floor. The parachute has a radius of 16 feet. Which measurement is closest to the circumference of the parachute in feet?

A. 100.48ft

B. 198.4ft

C. 49.6ft

D. 803.84ft

The expression is equivalent to [tex]\rm 3m^2+7m-6[/tex].

Given

Expression; [tex]\rm 2m \left (\dfrac{3}{2}m+1 \right )+3\left ( \dfrac{5}{3}m-2\right )[/tex]

To find the equivalent expression first multiply by term then combine like terms and simplify.

Therefore,

The expression is equivalent to;

[tex]\rm =2m \left (\dfrac{3}{2}m+1 \right )+3\left ( \dfrac{5}{3}m-2\right )\\\\=2m \times 3m + 1\times 2m + 5m \times 1-3\times 2\\\\=3m^2+2m+5m-6\\\\= 3m^2+7m-6[/tex]

Hence, the expression is equivalent to [tex]\rm 3m^2+7m-6[/tex].

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The experimental probability of winning a free gallon of milk will be calculated as under -

It is given that, total number of outcomes = 156

Non-winning customers = 147 (it is given in the question)

Thus, the winning customers will be = Total outcomes - Non-winning customers

Expected winning customers = 156 - 147 = 9

The probability is calculated as -

Probability (Winning customer) = [tex] \frac{Winning Customers}{Total Customers} [/tex]

Probability (Winning customer) = [tex] \frac{9}{156} [/tex] = [tex] \frac{3}{52} [/tex]

Answer:

0.00105

Step-by-step explanation:

Given that AB is the bisector of DC. The third options of all the options are True.

B is the midpoint of DC.

In geometry, to bisect an entity means to disassociate it into two equal parts. A bisector is a line, ray, or segment that divides an entity into two equal parts. For illustration, a line that bisects an angle divides the angle into two angles with equal measures. A segment that bisects a line segment divides the line segment into two segments with equal lengths. A ray that bisects an angle extends from the vertex of the angle and divides the angle into two angles with equal measures.

As it is given that AB is the bisector of DC,

therefore, B, being the foot of AB on CD is the midpoint of DC.

Since DC is bisected by AB,

therefore, [tex]\angle[/tex] ABD = [tex]\angle[/tex] ABC.

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Final answer:

The solution to f(g(x)) when x = 9 is -6.

Explanation:

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain), where each input is related to exactly one output.

Given:

f(x) = x2 - 4x - 3, g(x) = (x + 3) / 4

To find f(g(x)) when x = 9:

Therefore, f(g(x)) when x = 9 is -6.

Fixed costs, such as rent, remain constant regardless of production levels, while variable costs, like raw material expenses, will fluctuate based on the level of production.

Firms classify their costs into two categories: fixed costs and variable costs. Fixed costs are expenses that do not change regardless of the level of production. For instance, a lease on a retail space would be considered a fixed cost as it remains the same whether you sell a lot or a little. On the other hand, variable costs are directly tied to the level of production. For example, the cost of buying materials to produce a product tends to rise as the level of production increases. It's variable because the more you produce, the more materials you would need, and therefore the cost varies with the level of output.

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