With a present value of $150,000, what is the size of the withdrawals that can be made at the end of each quarter for the next 10 years if money is worth 7.4%, compounded quarterly? (Round your answer to the nearest cent) 312271.67

This query relates to prices. Let's use the rate for a cold tap to represent Rc and hot water to represent Rh.

Therefore,

Since R = V/t, where t is the fill-in time, determines the rate at which the volume V tab is filled. The following can be written for both of them:

Rc = V/17

Rh = V/t

Rc + Rh = V/7

where t is the time that we need to find.

V/17 + V/t = V/7

Divide both sides by V to get:

1/17 + 1/t = 1/7

Rearrange:

1/t = 1/7 - 1/17

Bring to common denominator:

1/t = (17 - 7)/(7*17) = 10/119

Take an inverse:

t = 119/10 = 11.9 minutes.

The complete question is?

Left on together, the cold and hot water faucets of a certain bathtub take 7 minutes to fill the tub. If it takes the cold water faucet 17 minutes to fill t?

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The function that convolved with -2cos(t) would produce 6sin(t) is g(t) = -3 * e^(-jt)/(2π).

To determine the function that, when convolved with -2cos(t), would produce 6sin(t), we can use the convolution theorem. According to the convolution theorem, the Fourier transform of the convolution of two functions is equal to the product of their individual Fourier transforms.

Let's denote the function we are looking for as g(t). Taking the Fourier transform of g(t) yields G(ω), and taking the Fourier transform of -2cos(t) yields -2πδ(ω - 1), where δ(ω) is the Dirac delta function.

Using the convolution theorem, we have:

G(ω) * -2πδ(ω - 1) = 6πδ(ω + 1)

To solve for G(ω), we divide both sides of the equation by -2πδ(ω - 1):

G(ω) = -3δ(ω + 1)

Now, we take the inverse Fourier transform of G(ω) to obtain g(t):

g(t) = Inverse Fourier Transform[-3δ(ω + 1)]

The inverse Fourier transform of δ(ω + a) is given by e^(-jat)/(2π), so applying this to our equation:

g(t) = -3 * e^(-jt)/(2π)

Therefore, the function that convolved with -2cos(t) would produce 6sin(t) is g(t) = -3 * e^(-jt)/(2π).

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Answer:

3x+5

Step-by-step explanation:

1/2 (8 x + 4) + 1/3 (9 - 3 x)

Distribute

4x+2 + 3-x

Combine like terms

4x-x  +2+3

3x +5

From the cumulative Frequency graph given, the answers to the questions posed are :

The median mark is the at the 50th percentile of the cummlative frequency distribution.

For School A , the mark which falls on the 50th percentile from the graph given is 44.

B.)

Percentage of students from school B who gained more than 80.

Trace 80 on the cummlative frequency axis to the point on the x-axis where it intersects the school B trendline. The number of students in school B who scored 80 is 150.

Hence, students who scored more than 80;

Hence, 150 students scored more than 80.

C.)

The median score for school A is 44

The median score for school B is 150

Since the median score for school B is greater than School A , then School B performed better.

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Answer:

Even if a right solid became oblique, the volume would not change, because the cross sectional area and height would remain the same. Therefore, by Cavalieri's principle, the volume is the same as the original solid.

Step-by-step explanation:

sample answer

The given triangles are obtuse = 36 m, right angled = 225 m and right angled = 2500 m.

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

7.) This triangle is obtuse.

To see this, we can use the Pythagorean theorem:

4*4 + 5*5 = 16 + 25 = 41

6*6 = 36 m

Since 41 > 36, we know that the triangle is obtuse.

8.) This triangle is right.

To see this, we can again use the Pythagorean theorem:

11*11 + 12*12 = 121 + 144 = 265

15*15 = 225 m

Since 265 = 225 + 40, we know that the triangle is right.

9.) This triangle is also right.

We can use the same method as before:

30*30 + 40*40 = 900 + 1600 = 2500

50*50 = 2500 m

Since 2500 = 2500, we know that the triangle is right.

Therefore, The given triangles are obtuse , right angled and right angled.

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Answer:

The population is 34,000. The sample is 2,000

Step-by-step explanation:

Population in statistics can be explained as the group or set of all elements which are of particular interest to a researcher or a study. In the scenario above, the research interest concerns customers who pay with a debit card, whose number amounts to 34,000, this value refers to the population. The sample is referred to as the subset of the population or larger sample, the sample from the study corresponds to number of debit card users who were selected at random to participate in the survey. This value is 2000.

\Answer:

\(\displaystyle \frac{(x-7)^2}{4}+\frac{(y+2)^2}{36}=1\)

Step-by-step explanation:

Equation of The Ellipse

Given the center (h,k) and the length of the major and minor axis, we can write the equation of the ellipse as follows:

\(\displaystyle \frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\)

If the major axis is a, then the ellipse is horizontal, if the major axis is b, then the ellipse is vertical.

The ellipse shown in the figure is centered at (7,-2). The major axis is b and it can be found by measuring the distance from the center up or down to any vertex. We find b=6 and a=2.

Thus, the equation of the ellipse is:

\(\displaystyle \frac{(x-7)^2}{2^2}+\frac{(y+2)^2}{6^2}=1\)

Operating:

\(\mathbf{\displaystyle \frac{(x-7)^2}{4}+\frac{(y+2)^2}{36}=1}\)

5a. A function to show p, the number of parrots t years after 2010 is \(P(t) = 515(1.54)^t\\\\\).

5b. The number of parrots that is expected to be there in 2016 is 6,870 parrots.

In Mathematics and Statistics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:

\(P(t) = I(1 + r)^t\\\\\)

Where:

Part a.

By substituting the given parameters into the formula, an exponential function to show p, the number of parrots t years after 2010 is given by;

\(P(t) = I(1 + r)^t\\\\\)

4418= 515(1 + r)⁵

(1 + r)⁵ = 4418/515

(1 + r)⁵ = 8.5786407766990

1 + r = 1.54

Therefore, the required exponential function to show p is given by;

\(P(t) = 515(1.54)^t\\\\\)

Part b.

When t = 6 years, the number of parrots can be calculated as follows;

\(P(6) = 515(1.54)^6\)

P(6) = 6,869.60 ≈ 6,870 parrots.

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Those activities that enable a person to describe in the detail the system that solves the need is called "System design".

The method of defining the components of a system consists, modules, and components, the various interfaces of those components, and the data that flows through that system is known as system design.

Some key features regarding the system design are-

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Answer:

A

Step-by-step explanation:

The definition of a parrelelogram is "a four-sided plane rectilinear figure with opposite sides parallel". Since you already know that EH and Fg are equal because of the black ticks on them. Now you only need to find out wheter or not  EF≅HG to meet the criteria of a parrelologram.

Answer:

Step-by-step explanation:

A

Answer: -4

Step-by-step explanation:

Answer:

13 for 4 and 26 for 8 I believe is the answer

Answer:

88 birdhouses

6 new boxes

226 postcards

Answer:

1. 88

2. 6

that's all, and when you do problems like this later, don't forget the order of operations!

The Pythagorean theorem is not satisfied since dAB² + dBC² ≠ dAC². Therefore, AABC is not a right triangle.

AABC is a scalene triangle with no sides of equal lengths. A triangle is said to be scalene when it has all its sides with different lengths. The side lengths of the AABC triangle can be calculated using the distance formula, which is given by'd = √((x2 - x1)² + (y2 - y1)²)Where d is the distance between two points (x1, y1) and (x2, y2).

Using the distance formula, we can calculate the length of each side of the AABC triangle. For side AB: dAB = √[(5 - (-6))² + (-1 - 2)²]= √(11² + (-3)²)= √130For side AC:dAC = √[(4 - (-6))² + (4 - 2)²]= √(10² + 2²)= √104For side BC:dBC = √[(4 - 5)² + (4 - (-1))²]= √((-1)² + 5²)= √26Since all the three sides have different lengths, the triangle AABC is a scalene triangle.

As for the second part of the question, we will check if it is a right triangle by determining if it has a right angle. We know that a right triangle is one that has one angle measuring exactly 90 degrees, and in such a triangle, the side opposite to the 90-degree angle is called the hypotenuse.

To determine if AABC is a right triangle, we can calculate the length of all the sides. Then we can check if the Pythagorean theorem holds, that is, the sum of the squares of the two smaller sides equals the square of the hypotenuse.If the Pythagorean theorem holds, then the triangle is a right triangle. If it doesn't, then the triangle is not a right triangle.

Using the distance formula above, we can determine the length of the three sides of the AABC triangle. Then we will compare the sides to determine if they satisfy the Pythagorean theorem. We have:dAB² + dBC² = √130² + √26²= 13,000 + 676= 13,676dAC² = √104²= 10,816

The Pythagorean theorem is not satisfied since dAB² + dBC² ≠ dAC².

Therefore, AABC is not a right triangle.

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To prove that n^3 + 2n is divisible by 3 for all integers n using mathematical induction, we need to show that it holds for the base case (n = 0) and then demonstrate that if it holds for any arbitrary integer k, it also holds for k + 1.

**Base Case (n = 0):**

When n = 0, we have 0^3 + 2(0) = 0 + 0 = 0. Since 0 is divisible by any integer, including 3, the base case is satisfied.

**Inductive Step:**

Assume that for some arbitrary integer k, k^3 + 2k is divisible by 3.

Now, we need to prove that it holds for k + 1, which means showing that (k + 1)^3 + 2(k + 1) is also divisible by 3.

Expanding (k + 1)^3 using the binomial theorem, we get:

(k + 1)^3 = k^3 + 3k^2 + 3k + 1

Substituting this back into (k + 1)^3 + 2(k + 1), we have:

(k + 1)^3 + 2(k + 1) = k^3 + 3k^2 + 3k + 1 + 2k + 2

                               = k^3 + 3k^2 + 5k + 3

Now, we can rewrite this expression as:

k^3 + 2k + 3k^2 + 3k + 3

Using the assumption that k^3 + 2k is divisible by 3 (inductive hypothesis), we can express this as a multiple of 3:

3m + 3k^2 + 3k + 3 = 3(m + k^2 + k + 1)

Since (m + k^2 + k + 1) is an integer, we have shown that (k + 1)^3 + 2(k + 1) is divisible by 3.

By satisfying the base case and demonstrating the inductive step, we have proven that n^3 + 2n is divisible by 3 for all integers n using mathematical induction.

we have proven that n³ + 2n is divisible by 3 for all integers n by mathematical induction.

To prove that the expression n³ + 2n is divisible by 3 for all integers n, we will use mathematical induction.

Let's first verify the statement for the base case, which is n = 0.

When n = 0, we have

0³ + 2(0) = 0 + 0 = 0,

which is divisible by 3 since 0 divided by any non-zero number is always 0 with no remainder.

Assume that the statement holds true for some arbitrary integer \(k\), where k is a non-negative integer. That is, assume that \(k^3 + 2k\) is divisible by 3.

We need to prove that the statement also holds true for k+1. That is, we need to show that (k+1)³ + 2(k+1) is divisible by 3.

Expanding (k+1)³ + 2(k+1), we get:

(k+1)³ + 2(k+1) = k³ + 3k² + 3k + 1 + 2k + 2

= k³ + 3k² + 5k + 3.

Now, let's express (k+1)³ + 2(k+1) in terms of our inductive hypothesis:

k³ + 3k² + 5k + 3 = (k³ + 2k) + (3k² + 3k + 3).

By our inductive hypothesis, we know that k³ + 2k is divisible by 3. Therefore, we can write k^3 + 2k as 3m for some integer m.

Substituting this back into our expression, we have:

(k³ + 2k) + (3k² + 3k + 3) = 3m + 3(k² + k + 1)

= 3(m + k² + k + 1)

The expression 3(m + k² + k + 1) is a multiple of 3 since it can be written as 3(m + k² + k + 1). Therefore, we have shown that (k+1)³ + 2(k+1) is divisible by 3.

By completing the base case and the inductive step, we have proven that n³ + 2n is divisible by 3 for all integers n by mathematical induction.

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Answer:

6x -2 is the solved answer for the bracketed question.

Step-by-step explanation:

6x- 2 is not = to -6x -2

Answer: x=0

Step-by-step explanation:

if you are sloving fo x

2(3x-1) = -6x-2 cancel equal terms

6x-2=-6x-2 move the variable to the left

6x=-6x  collect like terms

12x=0 divide both sides

x=0

0.3814  is the probability that a standard normal random variable .

What is the probability equation?

The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula.

                      P(E) = positive outcomes/total outcomes is how it's expressed mathematically. The probability of an event occurring, or P(E), is defined as the ratio of the number of favorable outcomes to the total number of outcomes in the probability formula. Mathematically speaking, it seems as follows: P(E) stands for positive outcomes/total outcomes.

P(0.3 < z < 3.2)

= P(z < 3.2) - P(z < 0.3)

= 0.9993 - 0.6179

 = 0.3814

Probability = 0.3814

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According to the Consecutive Interior Angle Theorem, the sum of Angles 4 and 6 is 180 degrees if Lines AB and CD are parallel.

Co-interior angles, often referred to as consecutive interior angles, are found inside the two lines but on one side of the transversal.

According to the consecutive interior angles theorem, the consecutive interior angles are complementary to one another when the two lines are parallel. Supplementary denotes that the sum of the two angles is 180 degrees.

Interior angles on the same side of a transversal are understood to be supplementary. Similarly, B + C, C + D, and A + B all add up to 180 degrees. As a result, the sum of any two adjacent parallelogram angles equals 180°.

The smaller angle should be "x" while the larger angle should be "8x." Since A and B are adjacent angles, A plus B equals 180 degrees. This suggests that x + 8x Equals 180°. The smaller angle therefore has a value of 20°.

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★To Solve :

\(\rm\blue{13(y+7) = 3(y-1)}\)

⠀⠀⠀⠀⠀

★SOLUTION :

\(\rm\red\leadsto{13(y+7) = 3(y-1)}\)

\(\rm\red\leadsto{13\times{y}+13\times7= 3\times{y}-3\times1}\)

\(\rm\red\leadsto{13y+91=3y-3}\)

\(\rm\red\leadsto{13y-3y=-3-91}\)

\(\rm\red\leadsto{10y=-94}\)

\( \rm\red\leadsto{} y =\dfrac{ { \cancel{-94}}^{ \:-45 } }{ { \cancel{10}}^{ \: 5} } \)

\(\rm\red\leadsto{y=}\dfrac{-47}{5}\)

____________________

Answer:L x b

              98ft x 56ft =5488

                                  =5488 / $3.75= $1463.47

Step-by-step explanation: Play ground is more like a rectangle so we use the formula for the rectrectangle to get total area . A=Lxb

Divide  the total with the cost since it say each per sqr feet

A=lxb

98x56=5488

5488/3.75= 1463.47

Experimental probability refers to the probability of an event occurring when an experiment was conducted. Mathematically, this can be represented as shown below

It should be noted that in order for experimental probability to be meaningful in research, the sample size must be sufficiently large. The reason why it is important to use a large number of trials when using experimental probability to predict the result is the law of large numbers.

In statistics and probability theory, the law of large numbers is a theorem that describes the result of repeating the same experiment a large number of times. The large numbers theorem states that if the same experiment or study is repeated independently a large number of times, the average of the results of the trials must be close to the expected value. The result becomes closer to the expected value as the number of trials is increased.

Hence, it is important to use a large number of trials when using experimental probability to predict results because the result becomes closer to the expected value as the number of trials is increased

Answer:

Step-by-step explanation:

The formula to find the tangent line to a curve at a given point is y = f'(x) (x - x₀) + f(x₀).

The derivative of the function, f'(x) is calculated at the given point, x₀. Then, the equation of the tangent line is found by substituting the x₀ and f'(x) values into the formula.

To find the tangent line to a curve at a given point, the formula for the slope of the tangent line must be used. The slope of a tangent line is equal to the derivative of the function at that point. The resulting equation is a line with a slope equal to the derivative of the function at the given point, and a y-intercept equal to the value of the function at the given point. For example, if you want to find the tangent line to the function f(x) = 4x² + 3 at the point (2, 19), the derivative of the function at that point is f'(x) = 8x = 8(2) = 16. Then, the equation of the tangent line is y = 16(x - 2) + 19.

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The answers that  best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.

The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.

To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.

Therefore the correct option is C.

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Answer:

You cannot solve this

Step-by-step explanation:

you need at least one value given like x=something or y=something so you can plug it in

if you meant solve for x, then x= -4y+32

The symmetric difference, denoted by the symbol ⊕, between two sets A and B is defined as the set of elements that are in either A or B, but not in both.

a) If a is a subset of u, then a⊕a will contain all elements that are in a and not in a, which is an empty set (∅). Therefore, a⊕a=∅.
b) The symmetric difference between a and an empty set (∅) is simply a, because there are no elements in ∅ that are not in a. Thus, a⊕∅=a.
c) The symmetric difference between a and the universal set u will contain all elements that are in either a or u, but not in both. Since a is already a subset of u, a⊕u will simply be all elements in u that are not in a, which is just a. Therefore, a⊕u=a.
d) The symmetric difference between a and itself (a⊕a) will contain all elements that are in either a or a, but not in both. This is equivalent to the set of elements that are not in a, which is the complement of a in u. Therefore, a⊕a is equal to u-a, or simply the universal set u. Hence, a⊕a=u.
In conclusion, if a is a subset of a universal set u, then a) a⊕a=∅, b) a⊕∅=a, c) a⊕u=a, and d) a⊕a=u.

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Answer:

yes, but the assignment is not here