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1. A wooden plank is leaning against an outside wall of a building. The bottom of the plank is 3 ft from the wall. Find each of the following values, and show all your work.
(a) Find the approximate length of the plank. Round to the nearest tenth of a foot.
(b) Find the height above the ground where the plank touches the wall. Round to the nearest tenth of a foot.

2. A support wire is strung from a tree. The bottom of the wire is 24 ft from the tree. The length of the wire is 30 ft. Find each of the following values, and show all your work.
(a) Find the value of x. Round to the nearest tenth of a degree.
(b) Find the approximate height where the wire touches the tree. Round to the nearest foot.

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]

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.

Answer:   1/4

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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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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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Answer:

0.00105

Step-by-step explanation:

Answer:

the answer is 180 degrees

Step-by-step explanation:

i used my head and my google maths

Answer:

Katy bought 12 cakes

Gugu bought 36 cakes

Deanna bought 14 cakes

Step-by-step explanation:

Final answer:

To divide 2y² + 8 by 2y + 4, use long division to find the quotient and remainder.

Explanation:

To divide 2y² + 8 by 2y + 4, we can use long division. Here are the steps:

Divide the first term of the dividend by the first term of the divisor, which gives us y.

Multiply the entire divisor by y to get 2y² + 4y.

Subtract 2y² + 4y from the dividend 2y² + 8 to get 4.

Next, divide 4 by 2y + 4, which gives us 2.

Finally, we have a remainder of 0.

Therefore, the quotient is y + 2 and the remainder is 0.

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

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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