The base of a pyramid covers an area of 13.3 acres (1 acre = 43,560 ft2) and has a height of 473 ft. if the volume of a pyramid is given by the expression v = bh/3, where b is the area of the base and h is the height, find the volume of this pyramid in cubic meters.

A variable is an object that you are trying to measure. It has two types; independent and dependent variable. An independent variable is a variable that is not affected by other variables. A dependent variable on the other hand is a variable that depends on the other variables. Suppose you want to know the quality of sleep of the students in their academic performance. The quality of sleep is the independent variable and the academic performance is the dependent variable. There are also controlled variables in an experiment. A controlled experiment is an experimental setup designed to test the hypotheses. It has one or more conditions (independent variables) and measures (dependent variables). It is necessary to change more than one variable, but all of the experimental conditions will be controlled so that only the variables being examined change and the amount or way of change is measured.

To isolate the variable in x + 5 = -12, subtract 5 from both sides of the equation. This leads to the equation x = -12 - 5.

In order to isolate the variable x in the equation x + 5 = -12, you should subtract 5 from both sides of the equation. This gives us the equation in a simplified form that allows us to determine the value of x. The idea here is to cancel out the +5 on the left side by subtracting 5 from both sides, resulting in x = -12 - 5. Hence, the answer is option b.

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find area of larger figure

then subtract area of cut out

 larger figure 40 *36 = 1440 square yards

cut out = 20 *10 = 200 square yards

1440-200 = 1240 square yards total

Each pair has the inverse points corresponding to the points in the original set.

To match the sets of points representing one-to-one functions with the sets of points representing their inverse functions, we need to find the pairs where each point in one set corresponds to the inverse point in the other set.

Here are the matches:

1. Set of Points Representing Function: [tex]\( h = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\} \)[/tex]

  Set of Points Representing Inverse Function: [tex]\( h^{-1} = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\} \)[/tex]

2. Set of Points Representing Function: [tex]\( g = \{(1,3), (2,6), (3,9), (4,12), (5,15), (6,18)\} \)[/tex]

  Set of Points Representing Inverse Function: [tex]\( g^{-1} = \{(3,1), (6,2), (9,3), (12,4), (15,5), (18,6)\} \)[/tex]

3. Set of Points Representing Function: [tex]\( f = \{(1,2), (2,3), (3,4), (4,5), (5,6), (6,7)\} \)[/tex]

  Set of Points Representing Inverse Function: [tex]\( f^{-1} = \{(2,1), (3,2), (4,3), (5,4), (6,5), (7,6)\} \)[/tex]

4. Set of Points Representing Function: [tex]\( i = \{(1,1), (2,3), (3,5), (4,7), (5,9), (6,11)\} \)[/tex]

  Set of Points Representing Inverse Function: [tex]\( i^{-1} = \{(1,1), (3,2), (5,3), (7,4), (9,5), (11,6)\} \)[/tex]

Each pair has the inverse points corresponding to the points in the original set.

Answer:

True

Step-by-step explanation:

The required pair of number are -3 and -6

The factored form of the trinomial is (x-3) and (x-6)

The standard form of a quadratic equation is expressed as:

[tex]ax^2+bx+c=0[/tex]

Given the expression [tex]x^2 - 9x + 18.[/tex]

[tex]a=1\\b=-9\\c=18[/tex]

We are to get two values that we must add to get b, and that we will multiply that will give c.

The given values are -6 and -3

Check:

[tex]-6+(-3)=-6-3=-9\\-6(-3) = 18[/tex]

Factorize the trinomial

[tex]x^2-9x+18\\x^2-6x-3x+18\\x(x-6)-3(x-6)\\(x-3)(x-6)[/tex]

Hence the factored form of the trinomial is (x-3) and (x-6).

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The volume of the cone is 56.52 cubic inches.

Having a flat base and a smooth tapering tip or vertex, a cone is a three-dimensional geometric object.

Given, the radius of the cone is 3 inches and the height of the cone is 6 inches.

The volume of a cone is given by,

V=(1/3)πr²h

V = (1/3) × 3.14 × 3² ×6

V = 56.52 cubic inches

Hence, the volume of the cone is 56.52 cubic inches.

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Answer:

Option C is correct

The expression [tex](1215)^{\frac{1}{5}x}[/tex]  is equivalent to [tex]\sqrt[5]{1215^x}[/tex]

Step-by-step explanation:

Simplify the radical Expression: [tex]\sqrt[5]{1215^x}[/tex]

A radical expression can be written by using the exponents and also using the following procedure:

[tex]\sqrt[n]{x} = x^{\frac{1}{n}}[/tex]

when x be non-negative then n can be any index

when x is negative, then n can be odd.

The following radical expression can be written as:

[tex]\sqrt[5]{1215^x} = (1215^x)^{\frac{1}{5}}[/tex] = [tex](1215)^{\frac{1}{5}x}[/tex]

Therefore, the expression [tex](1215)^{\frac{1}{5}x}[/tex]  is equivalent to [tex]\sqrt[5]{1215^x}[/tex]

Final answer:

To determine the slope, solve for y in terms of x, resulting in the equation y = (-3/2)x. Hence, the slope of the line described by the equation 2/x + 3/y = 0 is -3/2.

Explanation:

To find the slope of the line determined by any two solutions to the equation 2/x + 3/y = 0, let's begin by solving for y in terms of x.

First, we isolate the term 3/y:

2/x = -3/y

Then we cross-multiply and get:

2y = -3x

Now we solve for y:

y = (-3/2)x

This is now in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. In this case, there is no y-intercept since the line passes through the origin.

The slope m is -3/2. So any two solutions to the original equation will yield a line with a slope of -3/2.

The statement that "the distance between your houses is negative three (-3) miles" is correct.

A Cartesian coordinate system on a plane is a coordinate system in which each point is uniquely specified by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicularly oriented lines measured in the same unit of length.

If we assume that your house is the origin of a graph, and each unit square on the graph is equal to 1 square mile. Therefore, if your friend's house is exactly south of your house then it will be on the y-axis that too in the negative direction.

Therefore, the statement that "the distance between your houses is negative three (-3) miles" is correct.

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One of either the circumference or distance across is not rational. If you have a bit of string precisely 1 inch long and you make it into an idealize circle, the distance across of that circle will be an irrational value. You could try to measure it, however regardless of how precisely you measured it, it would in any case not be very sufficiently precise. So, you can never know precisely what the diameter is just by measuring.

What's more, on the off chance that you took that string and made a width with it, the circumference would be irrational and you could never have the capacity to measure the circumference precisely enough. Whatever you quantified would be close however not correct.

Since we have chosen 2 letters, then the total probability of winning the game is the sum of the probabilities of each letter. Therefore:

Total probability of winning = Probability of D + Probability of H

Total probability of winning = 5% + 10%

Total probability of winning = 15%

Since we are playing the game for 20 turns, therefore out of those 20 games, we will win 15% of the time. So:   

15% = 0.15

Winning times = 0.15 * 20

Winning times = 3

Therefore we have a chance or probability to win at least 3 games out of 20 turns.

Answer:

C: 3

Step-by-step explanation:

An angle of elevation of 58 degrees with the ground means that the angle started at the x-axis and terminates on the first quadrant region through a counter clockwise direction. Imagining a triangle, the string of the kite becomes the hypotenuse, the angle 58 degrees is the angle between the hypotenuse and the ground, and the height of the kite is the side opposite to the angle.

Therefore, we can calculate for the height of the kite using the sin function:

sin θ = opposite side / hypotenuse

sin 58 = opposite side / 50 m

opposite side = 50 m * sin 58

opposite side = 42.4 m

Therefore the kite is about 42.4 m above the ground.

The change in elevation of the rock is 290 feet.

The change in elevation of the rock can be calculated by finding the difference in height between the top of the cliff and the sea floor.

Given that the top of the cliff is 250 feet above sea level and the sea floor is 40 feet below sea level, we can calculate the change in elevation by subtracting the elevation of the sea floor from the elevation of the top of the cliff.

The change in elevation is therefore 250 feet - (-40 feet), which simplifies to 250 feet + 40 feet = 290 feet. So, the number that represents the change in elevation of the rock is 290 feet.

Answer:

The answer is 20 and it represents the monthly fee.

Step-by-step explanation:

Final answer:

For Rome, both the mean and the median are almost identical, suggesting a well-balanced data set and either can be used to describe the center. For New York, the median might be a better measure if the data are skewed or contain outliers, but more information would be needed to make a definitive judgment.

Explanation:

When considering the best measure to describe the center of a data set, we should look at the presence of outliers and the distribution of the data. The mean is the numerical average and is sensitive to extreme values, while the median is the middle value that splits the data set in half and is less affected by outliers.

For Rome, the mean is 6.4 and the median is 6.5, which are very close to each other, indicating that the data is likely symmetric without extreme outliers. Thus, in Rome's case, either the mean or the median could serve as a good measure of center. On the other hand, New York's mean is 6.1 and the median is 5.5, suggesting slightly skewed data or the presence of outliers. However, without more data points or visual representation, it's difficult to determine which is more representative solely based on these summary statistics.

Considering the provided values and common statistical practice, the centers can potentially be described as follows:

The Rome data center can be best described by either the mean or the median as they are similar.

The New York data center might be best described by the median if outliers or skewness are present.

The system of equations are 3y − x = −6 and 4y − x = 4

Two or more expressions with an Equal sign is called as Equation.

One third x − 2 = one fourth x + 11

1/3x - 2 = 1/4x + 11

Now let us take y as 1/3x - 2

y= 1/3x - 2

3y=x-6

Subtract x on both sides

3y-x=-6

and Let us consider the right side equation

y=1/4x + 11

4y=x+44

Subtract x on both sides

4y-x=44

Hence, the system of equations are 3y − x = −6 and 4y − x = 44

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Answer

THE AVERAGE OF THE 30 STOCKS IN THE DOW JONES INCREASED

Step-by-step explanation:

To solve this problem, we use the tan function. The distance across the river is the adjacent side, the distance drownstream is the opposite side while the direction of the boat is the hypotenuse.

tan θ = opposite side / adjacent side

tan 10 = opposite side / 420 ft

opposite side = 74.06 ft

Therefore the boat will move about 74 ft downstream.