Suppose our retirement account pays 9% apr compounded monthly; what size nest egg do we need in order to retire with 25 years that yields to $5,000 per month? Show all work

Answer:

\(42\pi -78\)

Step-by-step explanation:

Attached below is the detailed solution of the volume of the solid in the first octant bounded by the cylinders r = 2 r = 5  z = 8-x-y

The volume of the solid in the first octant bounded by the cylinders r = 2 r = 5,  z = 8-x-y  : \(42\pi -78\)

Answer:

the volume of the square pyramid is 2430 cubic cm

Answer:

1296 cm³

Step-by-step explanation:

V = a² x [√s²- (a/2)²] / 3

a = 18 cm

s = 15 cm

V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3

V = 324 x (√144/3) = 1296 cm³

Answer:

I believe it is A.

Let me know if this helps!

The solution is:

The inverse of the given equation is ±sqrt(x+1).

Here, we have,

given equation is :

y = x^2 -1

now, we have to find the inverse of the given equation

so, we have,

Exchange x and y, we get,

x = y^2 -1

Solve for y, we get,

Add 1 for each side

we get,

x+1 = y^2-1+1

x+1 = y^2

Take the square root of each side

we get,

±sqrt(x+1) = sqrt(y^2)

±sqrt(x+1) = y

The inverse is ±sqrt(x+1)

Hence, The solution is:

The inverse of the given equation is ±sqrt(x+1).

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complete question:

If f(x) = x^2 -1, what is the equation for f–1(x)?

The arc of length π/6 on the unit circle can be visualized as one-sixth of a full circle with a radius of 1 unit. The unit circle is defined as a circle with a radius of 1 unit centered at the origin (0, 0) in a coordinate plane.

What does the mathematical term "arc" mean?

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.

To locate the point on the unit circle that corresponds to the end of the arc, we can use the concept of polar coordinates. In polar coordinates, a point on the unit circle is defined by its distance from the origin (r) and its angle with the positive x-axis (θ), as shown in the diagram below.

[diagram here]

For the arc of length π/6 on the unit circle, the angle θ is π/6 and the distance from the origin (r) is 1 unit.

Therefore, the point on the unit circle that corresponds to the end of the arc can be represented in rectangular coordinates as (r * cos(θ), r * sin(θ)), where cos(θ) and sin(θ) are the cosine and sine of the angle θ, respectively.

Substituting the values for r and θ, we have:

x = 1 * cos(π/6) = sqrt(3) / 2

y = 1 * sin(π/6) = 1/2

So, the point on the unit circle that corresponds to the end of the arc of length π/6 is (sqrt(3) / 2, 1/2).

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The  answer of this queation :∫ (4 + √x + x/x) dx = 4x + 2/3 x^(3/2) + x + C

where C = C1 + C2 + C3 is the constant of integration for the entire expression.

eparate integrals:

∫ 4 dx + ∫√x dx + ∫ x/x dx

The first two integrals can be easily integrated as follows:

∫ 4 dx = 4x + C1, where C1 is a constant of integration.

∫√x dx = 2/3 x^(3/2) + C2, where C2 is a constant of integration.

For the third integral, note that x/x simplifies to 1 for all nonzero x.

∫ x/x dx = ∫ 1 dx = x + C3, where C3 is a constant of integration.

Putting it all together, we have:

∫ (4 + √x + x/x) dx = 4x + 2/3 x^(3/2) + x + C

where the integration constant for the entire statement is C = C1 + C2 + C3.

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Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.

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To calculate the percentage increase between two numbers, we work out the difference between the two numbers being compared and divide the increase by the original number and multiply the answer by 100.

The formula is given to be:

Imani's Rent Increase

Old rent: $560

New rent: $600

The percentage increase is:

Ariana's Rent Increase

Old rent: $825

New rent: $875

The percentage increase is:

Therefore, Imani had a larger percentage increase.

Answer:

The answer is 2.5135145

Step-by-step explanation:

Luis traveled approximately 31,736.8 inches on his bicycle.

We have,

To find the distance that Luis traveled on his bicycle, we need to calculate the circumference of the tires and then multiply it by the number of complete turns.

Given:

Radius of the tires (r) = 20p (2.54) inches

Number of complete turns (n) = 50

The circumference of a circle can be calculated using the formula:

Circumference = 2πr

Substituting the given radius into the formula, we have:

Circumference = 2π * (20p) inches

Now we can calculate the distance traveled (d):

Distance = Circumference x Number of complete turns

Distance = 2π x (20p) x 50 inches

To simplify the calculation, we can approximate π as 3.14:

Distance ≈ 2 x 3.14 x (20 x 2.54) x 50 inches

Calculating this expression, we find:

Distance ≈ 31736.8 inches

Therefore,

Luis traveled approximately 31,736.8 inches on his bicycle.

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The complete question.

What is the distance that Luis traveled on his bicycle rolled 20p (2.54) after the tires gave 50 complete turns

Answer: $34

Hope this helps +

When a country imports more than how much it gives, it has a trade deficit.

Volume of the the composite figure = volume of rectangular prism + 1/2(volume of cylinder ≈ 870 mm³.

The volume of any composite figure is the sum of all shapes that makes up the composite figure.

Volume of the the composite figure = volume of rectangular prism + 1/2(volume of cylinder = (l × w × h) + 1/2(πr²h)

Volume of the the composite figure = (14 × 6 × 8) + 1/2(π × 3² × 14)

Volume of the the composite figure ≈ 870 mm³

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Answer:

ZYX- CBA

Step-by-step explanation:

ZYX is backwards

so cba needs to be too

Answer:

ZYX-CBA

Step-by-step explanation:

welcome

Step-by-step explanation:

Substitute f(3) into the function:

\(f(3) = - 5(2)^{3} \)

Include exponent:

\(f(3) = - 5(8)\)

Multiply:

\(f(3) = - 40\)

Answer:

d. There is not enough evidence to support the hypothesis that the proportion of Uniformian voters has decreased.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that there is a significant drop in allegiance to the Uniformian Party in Bowie County.

Then, the null and alternative hypothesis are:

\(H_0: \pi=0.62\\\\H_a:\pi<0.62\)

The significance level is 0.05.

The sample has a size n=196.

The sample proportion is p=0.57.

The standard error of the proportion is:

\(\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.62*0.38}{196}}\\\\\\ \sigma_p=\sqrt{0.001202}=0.035\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.57-0.62+0.5/196}{0.035}=\dfrac{-0.047}{0.035}=-1.369\)

This test is a left-tailed test, so the P-value for this test is calculated as:

\(\text{P-value}=P(z<-1.369)=0.0855\)

As the P-value (0.0855) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that there is a significant drop in allegiance to the Uniformian Party in Bowie County.

The curved surface area of the cylinder is 48.06 cm².

The circumference of a cylinder is given by the formula:

C = 2πr

where C is the circumference and r is the radius of the base.

In this case, the given circumference is 6 cm.

So, 6 = 2πr

r = 6 / (2π)

r ≈ 0.955 cm

Now, the curved surface area (CSA) of the cylinder using the formula:

CSA = 2πrh

Given the height as 8 cm, we can substitute the values into the formula:

CSA = 2π(0.955 cm)(8 cm)

CSA ≈ 48.06 cm²

Therefore, the curved surface area of the cylinder is 48.06 cm².

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Answer:

1) 22

2)0.875 ounce

3) 2.25 meters

4) 25 ounces

Step-by-step explanation:

divide 110 by 5

divide 7.20 by 8

divide 11.25 by 5

and divide 625 by 25

a) The interest if computed using simple interest for 3 years at 2% is $120.

c) The interest when compounded continuously for 3 years at 2% is $123.67.

d) The difference in total interest between using simple interest and continuously compounding is $3.67.

Simple interest is a straightforward way of computing the interest paid on a loan.

The formula for calculating simple interest is P x R x T, where P = Principal, R = Rate, and T = Time.

The formula for continuous compounding first computes the future value (FV) from which the present value (PV) is deducted, as follows:

FV = PV x e ^ (i x t), where e is the mathematical constant approximated as 2.7183.

Principal = $2,000

Rate of interest = 2%

Period = 3 years

Simple Interest = $120 ($2,000 x 2% x 3)

Continuous compounding = FV - PV

FV = $2,000 x 2.7183 ^ (0.02 x 3)

= $2,000 x 1.06183697

= $2,123.67

Interest = $123.67 ($2,123.67 - $2,000)

The difference in total interest = $3.67 ($123.67 - $120)

Thus, continuous compounding produces a difference in the interest of $3.67 when compared to simple interest.

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Answer:

5200300

Step-by-step explanation:

Use Combination

The different combinations without repetition of 12 people will be equal to 5,200,300.

When a whole number is multiplied by each natural number underneath it, the result is known as its factorial. The symbol "!" can represent the idea of a factorial. As a result, "n factorial" is just n and is defined as the sum of the first n natural integers.

As per the given information in the question,

Total number of people chosen by the board = 12

Total number of applicants = 25

Then the number of combinations without repetition will be = ²⁵C₁₂

= \(\frac{25 !}{12!(25-12)!}\)

= 25!/(12! × 13!)

= 5,200,300

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Answer:

A $6.20

Step-by-step explanation:

first multiply 7.90 x3 and subtract 17.50 from the answer and you should get A

The domain is the set of all real numbers and the range is:

R: (-∞, 4]

For any function, we define the domain as the set of possible inputs, the ones in the horizontal axis, and the range as the set of the output, the ones in the vertical axis.

We can see that we have a parabola that in the bottom part has two arrows, so it extends in the wole domain (the set of all real numbers).

Instead for the range we can see that there is a maximum at y  = 4, so the range is:

R: (-∞, 4]

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Step-by-step explanation:

Questions about equivalent expressions usually feature both simple expressions and complex expressions. To check which complex expression is equivalent to the simple expression:

Distribute any coefficients: a(bx\pm c)=abx\pm aca(bx±c)=abx±aca, left parenthesis, b, x, plus minus, c, right parenthesis, equals, a, b, x, plus minus, a, c.

Combine any like terms on each side of the equation: xxx-terms with xxx-terms and constants with constants.

Arrange the terms in the same order, usually xxx-term before constants.

If all of the terms in the two expressions are identical, then the two expressions are equivalent.

Example

How do we solve for unknown coefficients?

Some questions will present us with an equation with algebraic expressions on both sides. On one side, there will be an unknown coeffient, and the question will ask us to find its value.

For the equation to be true for all values of the variable, the two expressions on each side of the equation must be equivalent. For example, if ax+b=cx+dax+b=cx+da, x, plus, b, equals, c, x, plus, d for all values of xxx, then:

aaa must equal ccc.

bbb must equal ddd.

To find the value of unknown coefficients:

Distribute any coefficients on each side of the equation.

Combine any like terms on each side of the equation.

Set the coefficients on each side of the equation equal to each other.

Solve for the unknown coefficient.

Example

How do we rearrange formulas?

Formulas are equations that contain 222 or more variables; they describe relationships and help us solve problems in geometry, physics, etc.

Since a formula contains multiple variables, sometimes we're interested in writing a specific variable in terms of the others. For example, the formula for the area, AAA, for a rectangle with length lll and width www is A=lwA=lwA, equals, l, w. It's easy to calculate AAA using the formula if we know lll and www. However, if we know AAA and www and want to calculate lll, the formula that best helps us with that is an equation in which lll is in terms of AAA and www, or l=\dfrac{A}{w}l=

w

A

l, equals, start fraction, A, divided by, w, end fraction.

Just as we can add, subtract, multiply, and divide constants, we can do so with variables. To isolate a specific variable, perform the same operations on both sides of the equation until the variable is isolated. The new equation is equivalent to the original equation.

The value of equivalent expression is,

⇒ 5x - 29

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 6x + 7 - 12 × 2 - (3² + 3) - x

Now, We can simplify as;

⇒ 6x + 7 - 12 × 2 - (3² + 3) - x

⇒ 6x + 7 - 24 - (9 + 3) - x

⇒ 6x + 7 - 24 - 12 - x

⇒ 5x - 29

Thus,  The value of equivalent expression is,

⇒ 5x - 29

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Answer:

-30

Step-by-step explanation:

7 - 2 • 5 + 9 • 3

7 - 10 + 27

7 - 37

-30

\(\huge\text{Hey there!}\)

\(\mathsf{7 - 2 \times 5 + 9 \times 3}\)

\(\mathsf{= 7 - 2(5) + 9(3)}\)

\(\mathsf{= 7 - 10 + 9(3)}\)

\(\mathsf{= 7 - 10 + 27}\)

\(\mathsf{= -3 + 27}\)

\(\mathsf{= 24}\)

\(\huge\text{Therefore, your answer should be: }\)

\(\huge\boxed{\textsf{Option A. 24}}\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

\(-2077\)

Step-by-step explanation:

\(i=1(-3-4)=-7(first)\)

\(i=2(-3-4*2)=-11\)

\(i=3(-3-4*3)=-15\)

\(i=31(-3-4*31)=-127(last)\)

Difference= -11-(-7)= -4

\(sum=\frac{n}{2}\)

\(= \frac{31}{2}[-7+(-127)]\)

\(=\frac{31}{2}*(-134)\)

\(=31*(-67)\)

\(= -2077\)

✧༝┉˚*❋ ❋ ❋┉༝✧

hope it helps..

have a great day!!

Use the chain rule to compute the second derivative:

\(f(x)=\ln(\sin(2x))\)

The first derivative is

\(f'(x)=(\ln(\sin(2x)))'=\dfrac{(\sin(2x))'}{\sin(2x)}=\dfrac{\cos(2x)(2x)'}{\sin(2x)}=\dfrac{2\cos(2x)}{\sin(2x)}\)

\(f'(x)=2\cot(2x)\)

Then the second derivative is

\(f''(x)=(2\cot(2x))'=-2\csc^2(2x)(2x)'\)

\(f''(x)=-4\csc^2(2x)\)

Then plug in π/4 for x :

\(f''\left(\dfrac\pi4\right)=-4\csc^2\left(\dfrac{2\pi}4\right)=-4\)