Find the value of an investment of $10,000 for 13 years at an annual interest rate of 3.15% compounded continuously.

Answer:

324 cm³

Step-by-step explanation:

Square based pyramid volume formula:
[tex]V=a^2\frac{h}{3}[/tex]

with a being the base length and h being the height

We can substitute in our values:

[tex]V=a^2\frac{h}{3} \\V=9^2\frac{12}{3}\\V=81(4)\\V=324[/tex]

So, the volume is 324 cm³.

Hope this helps! :)

The width of the dog run is 20 feet.

In the given problem, the length of the dog run is given as 30 feet.

The area of the dog run is also given as 240 square feet.

Using the formula for the area of a rectangle (A = lw), we can solve for the width (w).

Rearranging the formula, we have w = A / l.

Plugging in the values, we get w = 240 / 30 = 8 feet.

Since the width is given as (30 minus x) feet, we can set up an equation:

30 - x = 8. Solving for x, we find x = 22.

Therefore, the width of the dog run is 20 feet (30 - 22 = 8).

In this problem, the length and width of the dog run are defined by the dimensions of the fence being built around it.

The area of the dog run is given as 240 square feet.

By using the formula for the area of a rectangle, we can solve for the width. We are also given that the length is 30 feet.

Setting up an equation with the given width (30 minus x) and solving for x, we find that x is equal to 22.

This means that the width of the dog run is 8 feet. The main answer to the problem is that the width of the dog run is 20 feet (30 - 22 = 8).

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To simplify the expression 12(3k-3)k^5, we can use the distributive property and simplify each term.First, let's apply the distributive property:

[tex]12 * 3k * k^5 - 12 * 3 * k^5[/tex]

This simplifies to:

[tex]36k * k^5 - 36 * k^5[/tex]

To combine like terms, we add the exponents when multiplying variables with the same base. In this case, both terms have k as the base:

36k * k^5 can be simplified to 36k^6.

Therefore, the expression becomes:

[tex]36k^6 - 36k^5[/tex]

This is the simplified form of the expression 12(3k-3)k^5.

It's important to note that if you have any specific values for k, you can substitute those values into the expression to get the numerical result. Without a specific value for k, we can't simplify it further.

Remember to always double-check the original expression and any specific instructions or context given to ensure you've applied the correct simplification techniques.

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By evaluating f(6) and confirming that it equals zero, we can determine that x - 6 is a factor of the polynomial f(x) = x^4 - 32x^2 - 144.

To determine if x - 6 is a factor of f(x) = x^4 - 32x^2 - 144 using the Factor Theorem, we need to check if f(6) equals zero. If f(6) is zero, then x - 6 is a factor of f(x); otherwise, it is not a factor.

Let's calculate f(6):

f(6) = (6)^4 - 32(6)^2 - 144

= 1296 - 32(36) - 144

= 1296 - 1152 - 144

= 0

Since f(6) equals zero, we can conclude that x - 6 is indeed a factor of f(x).

The Factor Theorem states that if f(c) equals zero, where c is a constant, then x - c is a factor of f(x). In this case, since f(6) is zero, x - 6 is a factor of f(x).

Therefore, the answer is: Yes, x - 6 is a factor of f(x).

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114 is 95% of 120

100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.

114 is 95 Percent of What Number?

Formula = Number x 100

Percent = 114 x 100

95 = 120

The following shows the steps to derive this formula and find out 95% of the number is 114.

Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.

114

95% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

95Y = 114 x 100

95Y = 11400

Y = 11400

100 = 120

The correct equation for the parabola is [tex]x^2 = 16(y - 4)[/tex].

The standard equation of the parabola in the graph can be determined based on its characteristics.

Given:

Vertex: (0, 4)

Focus: (4, 4)

P (the distance from the vertex to the focus or directrix): 4

We can conclude that the parabola opens to the right because the axis is horizontal.

The standard equation of a parabola with a horizontal axis and vertex (h, k) is given by:

[tex](x - h)^2 = 4p(y - k)[/tex]

In this case, the vertex is (0, 4), so the equation becomes:

[tex](x - 0)^2 = 4p(y - 4)[/tex]

Now, we need to determine the value of p. The distance from the vertex to the focus is p, which is 4 in this case.

Therefore, the standard equation of the parabola in the graph is:

[tex]x^2 = 4(4)(y - 4)\\x^2 = 16(y - 4)[/tex]

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The domain of the function f(x) = -3x + 2 is (-∞, +∞), representing all real numbers, and the range is (-∞, 2], representing all real numbers less than or equal to 2.

The function f(x) = -3x + 2 is a linear function defined by a straight line. To determine the domain of this function, we need to identify the range of values for which the function is defined.

The domain of a linear function is typically all real numbers unless there are any restrictions. In this case, there is no explicit restriction mentioned, so we can assume that the function is defined for all real numbers.

Therefore, the domain of the function f(x) = -3x + 2 is (-∞, +∞), which represents all real numbers.

Now, let's analyze the range of the function. The range of a linear function can be determined by observing the slope of the line. In this case, the slope of the line is -3, which means that as x increases, the function values will decrease.

Since the slope is negative, the range of the function f(x) = -3x + 2 will be all real numbers less than or equal to the y-intercept, which is 2.

Therefore, the range of the function is (-∞, 2] since the function values cannot exceed 2.

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Answer:

19.0285

Step-by-step explanation:

For this, we have to work backwards.

First, the equation for the circumference of a circle is:
[tex]2\pi r[/tex]

We already know the circumference, so we can solve for r:
[tex]119.56=2\pi r[/tex]

divide both sides by 2

[tex]59.78=\pi r[/tex]

divide both sides by pi

[tex]19.0285...=r[/tex]

So, depending on the answer choices, the answer is 19.0285 rounded to the according decimal place.

Hope this helps! :)

Answer:

Step-by-step explanation:

Let x be 1 shirt price

Let y be 1 pant price

we have the following equation

3x+2y = 104.81$ (1)

2x+y = 61.33$ => multiply two sides by 2 => 4x + 2y = 122.66 (2)

=> (2) - (1) => x = 17.85$

So one shirt is 17.85$

The value of the improper integral ∫[0 to 1] arctan(√(x/(1-x))) dx is π/4.

To evaluate the improper integral

∫[0 to 1] arctan(√(x/(1-x))) dx,

we can use a trigonometric substitution. Let's substitute x = sin²θ, which gives dx = 2sinθcosθ dθ and modifies the limits of integration as well.

When x = 0, sin²θ = 0, and when x = 1, sin²θ = 1. Therefore, the new limits of integration are θ = 0 to θ = π/2.

Now, let's substitute these expressions into the integral:

∫[0 to 1] arctan(√(x/(1-x))) dx

= ∫[0 to π/2] arctan(√(sin²θ/(1-sin²θ))) * 2sinθcosθ dθ

= 2∫[0 to π/2] arctan(√(sin²θ/cos²θ)) * sinθcosθ dθ.

Simplifying inside the arctan, we have:

√(sin²θ/cos²θ) = √tan²θ = tanθ.

Substituting this back into the integral, we get:

2∫[0 to π/2] arctan(tanθ) * sinθcosθ dθ.

Since arctan(tanθ) is equivalent to θ for 0 ≤ θ < π/2, the integral becomes:

2∫[0 to π/2] θ * sinθcosθ dθ.

We can rewrite sinθcosθ as (1/2)sin(2θ):

2∫[0 to π/2] θ * (1/2)sin(2θ) dθ

= ∫[0 to π/2] θ * sin(2θ) dθ.

Now, we can integrate by parts with u = θ and dv = sin(2θ) dθ:

∫ u dv = uv - ∫ v du.

Differentiating u = θ gives du = dθ, and integrating dv = sin(2θ) dθ gives v = -(1/2)cos(2θ).

Applying the formula for integration by parts:

∫[0 to π/2] θ * sin(2θ) dθ = [-(1/2)θ * cos(2θ)] from 0 to π/2 - ∫[0 to π/2] (-(1/2)cos(2θ)) dθ

= [-(1/2)(π/2) * cos(π)] - [-(1/2)(0) * cos(0)] - [-(1/2) ∫[0 to π/2] cos(2θ) dθ]

= [-(π/4)(-1)] - [0] - [-(1/2) ∫[0 to π/2] cos(2θ) dθ]

= π/4 + (1/4) ∫[0 to π/2] cos(2θ) dθ.

Now, let's integrate ∫[0 to π/2] cos(2θ) dθ:

∫ cos(2θ) dθ = (1/2)sin(2θ).

Evaluating this integral from 0 to π/2:

∫[0 to π/2] cos(2θ) dθ = (1/2)sin(π) - (1/2)sin(0)

= (1/2)(0) - (1/2)(0)

= 0.

Substituting this result back into the previous expression:

π/4 + (1/4) ∫[0 to π/2] cos(2θ) dθ = π/4 + (1/4)(0)

= π/4.

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The calculated value of the improper integral [tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx[/tex] is 0.7853

From the question, we have the following parameters that can be used in our computation:

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx[/tex]

The above expression can be integrated using integration by parts method

When integrated, we have

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = \arctan\left(\frac{\sqrt{x}}{\sqrt{1-x}}\right)\,x+\frac{\sqrt{1-x}\sqrt{x}+\arctan\left(\frac{\sqrt{1-x}}{\sqrt{x}}\right)}{2}[/tex]

When simplified, we have

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = \frac{\left(2x-1\right)\arctan\left(\sqrt{\frac{x}{1-x}}\right)+\left(1-x\right)\sqrt{\frac{x}{1-x}}}{2}[/tex]

Recall that the x values are from 0 to 1

This means that

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = \frac{\left(2(1)-1\right)\arctan\left(\sqrt{\frac{1}{1-1}}\right)+\left(1-1\right)\sqrt{\frac{1}{1-1}}}{2}- \frac{\left(2(0)-1\right)\arctan\left(\sqrt{\frac{0}{1-0}}\right)+\left(1-0\right)\sqrt{\frac{0}{1-0}}}{2}[/tex]

When evaluated, we have

[tex]\int\limits^{1}_0 \arctan\sqrt{\frac{x}{1 - x}} \, dx = 0.7853[/tex]

Hence, the value of the integral is 0.7853

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Answer

a=93

b=74

Step-by-step explanation:

a=180-87=93 b=180-106=74

The probability that the proportion of polled voters supporting the incumbent candidate is less than 0.37 is approximately 0.6915, and the probability that the proportion is between 0.32 and 0.38 is approximately 0.3004.

To complete the boxes accurately, we need to use the given information and the normal distribution to determine the appropriate values.

The normal distribution is characterized by its mean (μ) and standard deviation (σ). In this case, the mean proportion of voters supporting the incumbent candidate is given as 35% or 0.35. However, we need to calculate the standard deviation.

To calculate the standard deviation, we can use the formula:

σ = √(p(1-p)/n),

where p is the proportion supporting the incumbent candidate (0.35) and n is the sample size (140).

σ = √(0.35(1-0.35)/140)

= √(0.35(0.65)/140)

= √(0.2275/140)

≈ √0.001625

≈ 0.04031.

Now that we have the standard deviation, we can determine the probabilities in the given normal distribution.

In the first box, we need to find the probability that the proportion is less than 0.37. We can use the standard normal distribution table or a calculator to find the corresponding z-score and its probability. The z-score can be calculated using the formula:

z = (x - μ)/σ,

where x is the value (0.37), μ is the mean (0.35), and σ is the standard deviation (0.04031).

z = (0.37 - 0.35)/0.04031

≈ 0.02/0.04031

≈ 0.4953.

Using the z-table or calculator, we can find that the probability corresponding to a z-score of 0.4953 is approximately 0.6915.

Therefore, the probability that the proportion of polled voters supporting the incumbent candidate is less than 0.37 is approximately 0.6915.

In the second box, we need to find the probability that the proportion is between 0.32 and 0.38. We can repeat the process for each value and find the corresponding z-scores:

z1 = (0.32 - 0.35)/0.04031 ≈ -0.07448,

z2 = (0.38 - 0.35)/0.04031 ≈ 0.7445.

Using the z-table or calculator, we can find the probabilities corresponding to these z-scores:

P(z < -0.07448) ≈ 0.4698,

P(z < 0.7445) ≈ 0.7702.

The probability that the proportion of polled voters supporting the incumbent candidate is between 0.32 and 0.38 is approximately 0.7702 - 0.4698 ≈ 0.3004.

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The graph that correctly represents Marie's situation is the graph B or the second graph.

For the graph to correctly represent Marie's situation the followin elements are needed:

Note: This question is incomplete; below are the missing graphs:

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The domain of the function shown in the graph is given as follows:

B. x ≥ 0.

The values of x in this graph are to the right of x = 0, including x = 0, hence the domain is given as follows:

B. x ≥ 0.

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Answer:

37.5

Step-by-step explanation:

the therom of a parallelogram is width*height

so 7.5*5

=37.5

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Answer:

A = 37.5

Step-by-step explanation:

The area of a parallelogram is:

Area = base × height

In your picture the base is 7.5 and the height is 5.

So multiply 7.5×5 and you get 37.5.

The area is 37.5cm^2

The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

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Answer:

56

Step-by-step explanation:

The sample size is given by :

[tex]n = (z_{_{\frac{\alpha}{2} }} \frac{\sigma }{E})^2\\[/tex]

We have c = 0.95

⇒ 1 - α = 0.95

⇒ α = 1 - 0.95

⇒ α = 0.05

⇒

[tex]\frac{\alpha}{2} = \frac{0.05}{2} \\\\\frac{\alpha}{2} = 0.025 \\[/tex]

By lookat at the table values,

[tex]z_{_{\frac{\alpha}{2} }} = 1.96[/tex]

So the sample size n is

[tex]n = (z_{_{\frac{\alpha}{2} }} \frac{\sigma }{E})^2\\\\=(1.96 * \frac{7.6}{2})^2 \\\\= (\frac{14.896}{2} )^2\\\\=(7.448)^2\\\\= 55.47[/tex]

n ≈ 56

Answer:

Let x be the number we are looking for.

We know that 12 is at most a number decreased by 7, which can be written as:

x - 7 >= 12

To solve for x, we add 7 to both sides of the inequality:

x - 7 + 7 >= 12 + 7

Simplifying, we get:

x >= 19

Therefore, the solution to the inequality is x >= 19.

The answer is:

Work/explanation:

Let w be the number. Now, let's write an inequality to solve for w.

Let's focus on the part that says "at most a number". At most means that the number can't be greater than something, it can only be less than. So the symbol for "at most" is ≤, which also means "less than".

Now, decreased by 7 means we subtract 7 from w.

With all this information, we are ready to write the inequality.

The inequality is:

[tex]\sf{12\leqslant w-7}[/tex]

Now, let's solve it for w.

_________________________

Add 7 on each side

[tex]\sf{12+7\leqslant w}[/tex]

[tex]\sf{19\leqslant w}[/tex]

Answer:

Step-by-step explanation:  -3.655 hopefully that works

The fourth table of values represents an exponential function (Correct choice: D).

Herein we find four tables of values, three representing a linear function and one representing an exponential function. Each function is introduced below:

Linear equation:

n = m + r · n

Exponential function

n = m · rⁿ

Where:

Common rate is the most appropriate criterion to distinguish linear equations of exponential equations. Now we proceed to summarize the results of each table of values:

Case A: Linear equation, r = 8.

Case B: Linear equation, r = 1.

Case C: Linear equation, r = 5.

Case D: Exponential equation: r = 2.

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Answer:

इगिइक्सिइत्क्स्हंह्होय्फोय

The farmer should use 660 pounds of the 75% protein supplement and 440 pounds of the 25% protein ration to make 1100 pounds of a high-grade 55% protein ration.

Let 75% protein supplement be x and 25% protein ration be y

The total weight of the mixture is x + y = 1100

The second equation related  to the protein in the mixture is 0.75x + 0.25y = 0.55 × 1100

= 0.75x + 0.25y = 605

By using the elimination method multiply the first equation by 0.25 to match the coefficients of y:

0.25x + 0.25y = 0.25 × 1100

0.25x + 0.25y = 275

by subtracting this equation from the second equation:

0.75 x + 0.25 y - {0.25 x + 0.25y} = 605 - 275

0.75 x - 0.25 x = 330

0.5x = 330

x = 660

by substituting this in the first equation:

660 + y = 1100

y = 440

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You invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

Let's assume you invested an amount, x, at 3% annual interest rate. This means the amount invested at 4% annual interest rate would be $4000 - x.

To calculate the interest earned from the investment at 3%, we multiply x by 3% (0.03). Similarly, the interest earned from the investment at 4% is calculated by multiplying ($4000 - x) by 4% (0.04).

According to the given information, the total interest earned from both investments is $130. So we can set up the equation:

0.03x + 0.04($4000 - x) = $130

Simplifying the equation:

0.03x + 0.04($4000 - x) = $130

0.03x + $160 - 0.04x = $130

-0.01x = $130 - $160

-0.01x = -$30

x = -$30 / -0.01

x = $3000

Therefore, you invested $3000 at 3% annual interest rate, and the remaining amount of $4000 - $3000 = $1000 was invested at 4% annual interest rate.

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The graph can represent a normal curve because it represent a normal density function. The Option C.

The answer is yes. While these characteristics may deviate from the ideal properties of a normal distribution, they do not necessarily invalidate the possibility of the graph representing a normal density function.

A normal curve can have tails that extend indefinitely allowing for the graph to increase as x becomes very large or very small. Negative values can occur if the graph represents a standard normal distribution which is centered at zero.

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Answer:

What is the equation?

Step-by-step explanation:

Can't solve it without knowing where c is in the equation

After 3 days, the two friends will earn the same profit.

To find the number of days after which the two friends will earn the same profit, we need to set the profit functions P(x) and Q(x) equal to each other and solve for x.

P(x) = Q(x)

−x^2 + 5x + 12 = 6x

Rearranging the equation:

−x^2 + 5x + 12 - 6x = 0

Combining like terms:

−x^2 - x + 12 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's factor the equation:

-(x - 3)(x + 4) = 0

Setting each factor equal to zero:

x - 3 = 0 or x + 4 = 0

Solving for x:

x = 3 or x = -4

Both x = 3 and x = -4 are solutions to the equation. However, we need to determine which one is a viable answer and which one is a nonviable answer.

The question asks for the number of days, which cannot be negative. Therefore, x = -4 is a nonviable answer since it represents a negative number of days. The viable answer is x = 3.

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Answer:

First you draw the lines zjkl and then you make an archs to bisect the line using a compass and a pencil first you go to each point and it's corresponding letter you arch then draw a straight line which passes through the arch

Answer:

1428

Step-by-step explanation:

Area=L×B/W

34×42

=1428