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The area of the mural is 1056 in² and the base is 32 inches. We have to determine the height of the mural.

Area of parallelogram = [tex] b \times h [/tex]

where 'b' is the base and 'h' is the height.

1056 [tex] in^{2} [/tex] = 32 [tex] \times h [/tex]

[tex] h=\frac{1056}{32} [/tex] in

Therefore, the height of the mural is 33 inch.

Final answer:

The total volume of the candies in the machine is approximately 0.981 cubic inches.

Explanation:

To find the total volume of the candies in the machine, we first need to calculate the volume of one candy. The diameter of each candy is 0.25 inches, so the radius is half of the diameter, which is 0.125 inches. The formula for the volume of a sphere is V = (4/3)πr³. Plugging in the values, we get V = (4/3)π(0.125)³ = 0.0081777 cubic inches.

Since there are 120 candies in the machine, we can multiply the volume of one candy by the number of candies to get the total volume. Total Volume = 120 * 0.0081777 = 0.981324 cubic inches.

The first step to solve this problem is to formulate equations. Since the triangle has two equal sides, you can conclude that the angles adjacent to the sides are equal which means:

3x – 11 = 2x + 11

We can now solve for the value of x:

3x – 2x = 11 + 11

x = 22

The sum of the angles of a triangle is 180 so we can formulate another equation:

3x – 11 + 2x + 11 + 2y = 180

5x + 2y = 180

Remember that the value of x is 22 so you should substitute the value of x:

5(22) + 2y = 180

110 + 2y = 180

2y = 180 – 110

2y =70

y = 35

Answer:

254,000,000

Step-by-step explanation:

As it's 212,610 you round it down

The value of number rounded to nearest million is,

⇒ 254,000,000

Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.

Given that;

There are 254 212 610 registered cars in the United States.

Hence, The value of number rounded to nearest million is,

⇒ 254,000,000

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Answer:

Ken worked 4 hours overtime.

Step-by-step explanation:

Ken earns $11 for an hour in his regular pay.

He receives time-and-a-half for overtime =  $11 + (11/2) = 11 + 5.50 = $16.50

Ken worked 40 hours plus overtime and he made $66.00 in his overtime.

So he worked overtime = $66.00 ÷ 16.50 = 4 hours

Ken worked 4 hours overtime.

The annual appreciation rate for the Marriott family's apartment they bought three years ago for $65,000, now worth $86,515, is 10%.

The subject matter of this question is the calculation of the appreciated rate of the Marriott family's apartment. They bought this apartment three years ago for $65,000, and now it is worth $86,515. We want to find a constant rate of growth over these three years.

To determine the annual rate of appreciation, we need to use the formula for exponential growth: final value = initial value × (1 + annual growth rate) ^ number of years.

Let's plug in the given values: $86,515 = $65,000 × (1 + growth rate)³.

First, we divide the final value by the initial value: $86,515/$65,000 = 1.33177.

Second, we must calculate the cubic root of 1.33177 (since we have three years), which is 1.1. Therefore, the annual growth rate is 1.1 - 1 = 0.1 or 10%.

Hence, the yearly rate of appreciation for the apartment is 10%.

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The height of the second triangle is 4 feet, which is found by using the formula for the area of a triangle (A = bh/2) and equating the area of the first triangle to that of the second.

To find the height of the second triangle with the same area as the first, we use the formula for the area of a triangle, A = bh/2, where b is the base and h is the height. The area of the first triangle with a base of 20 feet and height of 5 feet is:

Since the second triangle must have the same area, we can set up the equation:

Solving for the height (h2) of the second triangle:

Therefore, the height of the second triangle is 4 feet.

The GCF of 95, 42, and 97 is 1 because the prime factorizations of these numbers do not share any common factors other than 1.

To find the Greatest Common Factor (GCF) of the numbers 95, 42, and 97, we need to look for the highest number that can divide all three numbers without leaving any remainder. When considering 95, 42, and 97, we notice that:

Since the prime factorization of these numbers does not share any common factors other than 1, the GCF of 95, 42, and 97 is 1.

4 / 10  = 2 / 5

The fraction equivalent to 4 /10 can be gotten by reducing the actual fraction to it lowest term.

Therefore, let's divide the numerator and denominator by 2.

4 / 10 ÷ 2 / 2 = 2 / 5

The fraction equivalent to 4 / 10 is 2 /5 .

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The Greates Common Factor (GCF) is:   2 x 2 x 2 = 8

The decimal equivalent to 50/100 is 0.50, which is found by dividing 50 by 100.

The decimal equivalent to 50/100 is 0.50. This is because 50/100 is the same as dividing 50 by 100, which gives you 0.50.

This conversion is a standard way of expressing fractions where the denominator is 100, and it's commonly used to convert fractions into percentages or decimals.

For example, to convert 1/4 to a percent, you multiply by 25 (since 4 times 25 equals 100) to get 25 percent, which is equivalent to the decimal 0.25.

So, 50/100 is equivalent to 0.5 as a decimal.