A tapered bar is 10. 0 inches long. The diameter of the circular cross section decreases linearly from 4. 0 inches at one end to 2. 0 inches at the other end. Determine the equation that expresses the cross-sectional area of the bar as a function of the position, x, along the length. The area of a circle is given by A=πr2.

what is the meaning of the cross-sectional area of the bar ? ( with drawing )

Answer:

The perimeter of a square is given by the formula P = 4s, where s is the length of one side.

Here, one side of the square is given as 14x + 14 feet. Substituting this into the formula, we get:

P = 4(14x + 14) feet

P = 56x + 56 feet

Therefore, the answer is option B: 56x + 1 feet.

After 71 years we will no longer have enough natural resources to support the growing population.

What is a population?

The population of a given place is the total number of people who typically reside there as of January 1 of a given year.

Total population supported by resources = 9 billion = 9 x [tex]10^9[/tex]

Because resources are being depleted 1% per year = 90000000000 x 1%

= 9 x [tex]10^7[/tex]

Total world population = 6.4 x [tex]10^9[/tex]

Now, for to find time of resource depletion,

Resource problem = 6.4 x [tex]10^9[/tex] ÷ 9 x [tex]10^7[/tex]

On solving we get 71 years

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Answer:

Step-by-step explanation:

You want the solutions to the absolute value equations ...

The absolute value function is defined piecewise:

This means each of the equations can be rewritten as two equations on different domains.

For a ≥ 0, this is ...

  a = -a

  2a = 0 . . . . . add a

  a = 0

For a < 0, the equation is ...

  -a = -a . . . . for all a < 0

The solution to the equation is the union of these solutions:

  a ≤ 0

For (a-5) ≥ 0, this is ...

  a -5 = 5 -a

  2a = 10

  a = 5

For (a-5) < 0, this is ...

  -(a -5) = 5 -a

  a = a . . . . for all a < 5

The solution to the equation is the union of these solutions:

  a ≤ 5

__

Additional comment

When a-5 ≥ 0, the value of a is a≥5.

When a-5 < 0, the value of a is a<5.

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The surface area οf the sphere is apprοximately 82,203.84 square yards.

Let's start by using the fοrmula fοr the circumference οf a circle C = 2πr

where C is the circumference, π is the cοnstant pi (which is apprοximately equal tο 3.14), and r is the radius οf the circle. We knοw that the circumference οf the widest circle οf the sphere is 508.68 yards, sο we can set up an equatiοn as fοllοws:

508.68 = 2πr

Sοlving fοr r, we get:

r = 508.68 / (2π)

r = 80.99 yards (rοunded tο twο decimal places)

Nοw that we knοw the radius οf the sphere, we can use the fοrmula fοr the surface area οf a sphere:

A = 4πr²

Plugging in the value οf r, we get:

A = 4π(80.99)²

An ≈ 82,203.84 square yards

Therefοre, the surface area οf the sphere is apprοximately 82,203.84 square yards.

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CIRCUMFERENCE OF A CIRCLE : 2πr

2×3.142×7.5

47.13 cm

To solve the system using the elimination method (AKA combining the equations), you want to first set up the system so that one variable will be eliminated when you add the equations together.

The first equation has -2x, while the second one has -8x.  If we multiply the entire first equation by -4, we'd turn that -2x into 8x, which would cancel out when you add that with the -8x in the second equation:

   -4 ( -2x +   y = 10 )    –>       8x - 4y = -40

         -8x + 3y = 32     –>      -8x + 3y = 32

And if you add the new equations on the right, you'll end up with
    0x - y = -8    
which means y = 8.

We could do the something similar to eliminate the y's.  The first equation has y, while the second one has 3y.  If we multiply the entire first equation by -3, we'd turn that y into -3y, which would cancel out when you add that with the 3y in the second equation:

   -3 ( -2x +   y = 10 )    –>      6x - 3y = -30

         -8x + 3y = 32     –>      -8x + 3y = 32

And if you add the new equations on the right, you'll end up with
    -2x + 0y = 2
which means x = -1.

Putting those together, we have a solution of (-1, 8), which checks in both equations.

There are 60,466,176 different sequences that are possible.

Permutation represents a method of arranging things in order. In a fair 6-sided die rolled 10 times and the resulting sequence of 10 numbers is recorded, the different possible sequences are calculated as shown below:

When rolling a die, the possible outcomes are 1, 2, 3, 4, 5, and 6. As there are ten rolls, each roll has six possible outcomes. Thus, the total number of different sequences will be calculated as follows:6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 = 60,466,176. Therefore, there are 60,466,176 different sequences that are possible.

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The probability of X = 2 can be found using the binomial probability formula, with p ≈ 0.119 obtained by solving for p using the equation P(X = 4) = 0.9724. The resulting probability is approximately 0.193.

We can use the binomial probability formula to find P(X = 2):

P(X = 2) = (7 choose 2) * p² * (1-p)⁽⁷⁻²⁾

We know that P(X = 4) = (7 choose 4) * p⁴ * (1-p)⁽⁷⁻⁴⁾ = 0.9724

Solving for p in this equation, we get p ≈ 0.119

Substituting this value of p in the formula for P(X = 2), we get:

P(X = 2) = (7 choose 2) * 0.119² * 0.881⁽⁷⁻²⁾ ≈ 0.193

Therefore, the probability that X = 2 is approximately 0.193.

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Step-by-step explanation:

[tex] - \frac{1}{2} [/tex]

a. The solution to the system of equations that is graphed in the diagram is: (6, -1).

b. This is the point where the lines intersect each other.

To find the solution of the system of equations graphically, we plot the equations as lines on a coordinate plane and look for the point of intersection, which represents the solution to the system. If the lines are parallel, there is no solution, and if they overlap, there are infinitely many solutions.

a. The solution as shown in the graph given is: (6, -1).

b. We know this because the point where the two lines intersect is the solution of a system of equations.

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keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]x-y=3\implies -y=-x+3\implies y=\stackrel{\stackrel{m}{\downarrow }}{1}x-3\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ 1 \implies \cfrac{1}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{1} \implies \text{\LARGE -1}}}[/tex]

Answer: 6√√/2

Step-by-step explanation: just did it

Answer:

Step-by-step explanation:

[tex]-\sqrt{72}=-\sqrt{2*6*6}=-6\sqrt{2}[/tex]

Alexis made 63 foul shots during the season.

If Alexis made 73% of her foul shots, then she made 0.73 * 86 = 62.78 foul shots during the season.

However, since foul shots must be whole numbers, Alexis would have made either 62 or 63 shots.

We know that Alexis and her team won 15 out of 17 games during the season. This means that Alexis made foul shots in each of these 15 games, for a total of 15 * 2 = 30 foul shots.

If Alexis made a total of 62 foul shots during the season, she would have had to make an additional 32 foul shots in the two games they lost (17 games - 15 games they won = 2 games they lost). That would mean she made 16 foul shots in each of the two games they lost, which is unlikely.

Therefore, Alexis must have made 63 foul shots during the season, leaving only 23 foul shots missed (86 total foul shots - 63 made foul shots).

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The sample space for this compound event consists of 6 possible outcomes, which can be represented by a table with 3 toppings and 2 crusts. Mathematically, this sample space can be represented by the formula nCr(3,2) × nCr(2,1) which simplifies to 3 × 2 = 6.

The sample space for this compound event can be represented by a table where each row represents one possible outcome. The number of outcomes is the product of the number of toppings and the number of crusts. In this case, the sample space consists of 3 toppings and 2 crusts, so there are 6 possible outcomes. The sample space is:

Table A

Topping 1 | Crust 1

Topping 1 | Crust 2

Topping 2 | Crust 1

Topping 2 | Crust 2

Topping 3 | Crust 1

Topping 3 | Crust 2

Mathematically, this sample space can be represented by the formula nCr(3,2) × nCr(2,1), where nCr(3,2) is the number of combinations of 3 toppings and 2 crusts, and nCr(2,1) is the number of combinations of 2 crusts and 1 topping. The formula can be simplified to 3 × 2 = 6, which is the same number of outcomes in the sample space.

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From the given data, the answer is approximately 26.5 cubic inches. The closest option is b. 70.65 inches³.

The volume of each coin can be calculated as follows:

Volume of a coin = π × radius² × height

Volume of a coin = 3.14 × (1.2 inches)² × 0.0625 inches

Volume of a coin = 0.106 cubic inches

The total volume of all the coins can be found by multiplying the volume of one coin by the number of coins:

Total volume of coins = 0.106 cubic inches/coin × 250 coins

Total volume of coins = 26.5 cubic inches (rounded to the nearest tenth)

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Answer: 1= 6/6 and 2=12/6

Step-by-step explanation: Just Think and use your brain

The evidence which supports the fact that the shape ABCD is a parallelogram is; ABCD is a parallelogram because both pairs of opposite sides are parallel.

From the features of parallelograms, it can be inferred that the opposite sides of a parallelogram are parallel.

Also, parallel lines are lines whose slopes are equal.

On this note;

slope of AB-2/5 slope of BC = -4

slope of CD-2/5 slope of AD = -4

Hence, it can be inferred that opposite sides AB and CD as well as BC and AD are parallel.

Ultimately, ABCD is a parallelogram because both pairs of opposite sides are parallel.

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weight, color, and clarity ratings

In a regression model, the price of diamonds can be predicted by using a number of predictor variables. The predictor variables that are commonly used to predict the price of diamonds include the weight of the stone, the color rating, and the clarity rating. The weight of the stone is typically measured in carats, where one carat is equivalent to 0.2 grams.The color rating of the diamond is typically measured on a scale of D to I, where D is the most colorless and I is the most yellow. The clarity rating of the diamond is typically measured on a scale of IF to VS2, where IF is the most flawless and VS2 is the most included. By using a regression model to predict the price of diamonds, it is possible to identify which of these predictor variables are most important in determining the price of a particular diamond. The regression model can also be used to estimate the price of a diamond based on its weight, color, and clarity ratings.

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The area of the composite figure is the sum of the whole area of each shape. Therefore, the area of the figure is 151.585 ft².

The figure above is a composite figure. A composite figure is a shape that has two or more shapes in it.

Therefore, the composite figure can be divided into two rectangles and a quarter circle.

Hence, the area of the composite figure is the sum of the whole individuals area of the shapes.

Hence, the area of the composite figure is the sum of the area of the two rectangle and area of the quarter circle.

area of the composite figure = area of rectangle + area of rectangle + area of quarter circle

area of the composite figure = 5 × 8 + 8 × 6 + 1 / 4 × π × 9²

area of the composite figure =  40 + 48 + 81π / 4

area of the composite figure = 88 + 254.34 / 4

area of the composite figure = 88 + 63.585

area of the composite figure = 151.585 ft²

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Answer:  -4 to the 7th power.

Step-by-step explanation:

Answer:

-45,000

Step-by-step explanation:

According to the given information, the value(s) of x for which[tex]$f(G(x)) = g(f(x))$[/tex] is x = 1 or x = -2/3.

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

[tex]To find the inverse of $G(x)$:Replace $G(x)$ with $y$: $y = x - x^2 + 1$Solve for $x$: $x^2 - x + (1 - y) = 0$Apply the quadratic formula: $x = \frac{1 \pm \sqrt{1 - 4(1)(1-y)}}{2} = \frac{1 \pm \sqrt{-3 + 4y}}{2}$The inverse of $G(x)$ is therefore: $G^{-1}(x) = \frac{1 \pm \sqrt{-3 + 4x}}{2}$To find the value of $x$ for which $f(G(x)) = g(f(x))$:Start with $f(G(x))$: $f(G(x)) = f(x^2 - x + 2)$[/tex]

[tex]Replace $f(x)$ with $3 - 2x$: $f(G(x)) = 3 - 2(x^2 - x + 2) = -2x^2 + 2x - 3$Replace $G(x)$ with $y$: $y = x^2 - x + 2$Replace $g(y)$ with $y - x^2 + 1$: $g(y) = y - x^2 + 1$Set $f(G(x))$ equal to $g(f(x))$ and solve for $x$:$-2x^2 + 2x - 3 = (3 - 2x) - x^2 + 1$Simplify and solve for $x$: $x = 1$ or $x = -\frac{2}{3}$[/tex]

Therefore, according to the given information, the value(s) of x for which [tex]$f(G(x)) = g(f(x))$[/tex]is x = 1 or x = -2/3.

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The total percentage increase in the investor's stock account is 3.7%.

What is the percentage increase?

Percentage increase refers to the amount by which a value or quantity has grown or increased, expressed as a percentage of its original value. It is calculated by dividing the difference between the new value and the original value by the original value, and then multiplying by 100 to express the result as a percentage. The formula for calculating percentage increase is:

Percentage increase = [(New value - Original value) / Original value] x 100%

To find the total percentage increase in the investor's stock account, we need to first calculate the new value of each stock and then add them together.

For Company A:

The stock has increased by 1%, which means its new value is 1% higher than $2000.

The increase in value is 0.01 * $2000 = $20.

The new value of the stock in Company A is $2000 + $20 = $2020.

For Company B:

The stock has increased by 5%, which means its new value is 5% higher than $4240.

The increase in value is 0.05 * $4240 = $212.

The new value of the stock in Company B is $4240 + $212 = $4452.

Now, we can find the total value of the investor's stock account by adding the new values of both stocks:

$2020 + $4452 = $6472

To find the percentage increase, we need to compare the total new value to the original total value:

The original total value was $2000 + $4240 = $6240

The total percentage increase is [(New total value - Original total value) / Original total value] x 100%

Plugging in the numbers: [(6472 - 6240) / 6240] x 100% = 3.7%

Therefore, the total percentage increase in the investor's stock account is 3.7%.

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The value of x, considering that 3x and 99º are supplementary angles, is given as follows:

x = 27.

Supplementary angles are a pair of angles that add up to 180 degrees. In other words, if two angles are supplementary, then the sum of their measures is 180 degrees.

Supplementary angles can be adjacent (share a common vertex and a common side) or non-adjacent (do not share a common vertex or side). When two angles are supplementary, they form a straight line, and are sometimes referred to as a linear pair of angles.

For this problem, the angles 3x and 99º are a linear pair, hence the value of x is obtained as follows:

3x + 99 = 180

3x = 81

x = 81/3

x = 27.

The image is presented at the end of the answer.

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Answer:add pic

Step-by-step explanation:

The chord of the sphere is represented by OT.

The geometrical equivalent of a two-dimensional circle in three dimensions is a sphere. The collection of points in three-dimensional space that are all located at the same r distance from one another is known as a sphere.

The line segment connecting any two locations on a circle's circumference is referred to as the chord of the sphere. It should be emphasized that the diameter is the circle's longest chord, which runs through its center.

So, if L, M, and N lie on the surface of a sphere with its center at point O. Point T lies in the interior of the sphere, then OT would connect two points on the circumference of the sphere.

Hence, the chord of the sphere is represented by OT.

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A relative frequency is obtained with the division of the number of desired outcomes by the number of total outcomes.

For hamburguers, the outcomes are given as follows:

Hence:

58/300 x 100% = 19.33%.

For cheeseburger and onion rings compared to the total amount of orders for onion rings, the outcomes are given as follows:

Hence:

74/103 = 71.84%.

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Answer:

216 cubic cm

Step-by-step explanation:

Answer:

3174.538707cm³

Step-by-step explanation:

SurfaceArea of Cube=S²

volume of cube=S³

SA=216cm²

S=

[tex] \sqrt{216} [/tex]

S=

[tex]6 \sqrt{6} [/tex]

Volume of cube =S³

V=

[tex](6 \sqrt{6} )^{3} [/tex]

: . V= 3174.538707cm³

The area for the parallelogram is equal to 255 square centimeters and the correct option is A = 255 cm²

In calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.

we shall calculate for the height h using Pythagoras rule for the triangle as follows:

h² + 9² = 15²

h² + 81 = 225

h² = 225 - 81 {subtract 81 from both sides}

h² = 144

h = √144 {take square root of both sides}

h = 12

area of parallelogram = 21 cm × 12 cm

area of parallelogram = 254 cm²

Therefore, the area for the parallelogram is equal to 255 square centimetres.

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Answer:

[tex]2^{6}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex]

then

[tex]2^{15}[/tex] ÷ [tex]2^{9}[/tex] = [tex]2^{(15-9)}[/tex] = [tex]2^{6}[/tex] ( with k = 6 )