is there an ordered pair that is in the solution to both of these linear equations


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To accumulate $2,176,097.00 in his retirement account by age 65, Derek needs to make annual deposits of $5,000.00 starting on his 27th birthday and ending on his 65th birthday, assuming an 8.00% interest rate.

To determine the annual deposits Derek needs to make, we can use the future value of an ordinary annuity formula. First, we calculate the number of years between Derek's 25th and 65th birthdays, which is 65 - 25 = 40 years. Next, we calculate the future value of the retirement account using the given interest rate of 8.00%. Using the formula:

Future Value = Present Value * (1 + interest rate)^number of periods

In this case, the future value is $2,176,097.00, the interest rate is 8.00%, and the number of periods is 40. We can rearrange the formula to solve for the present value:Present Value = Future Value / (1 + interest rate)^number of periods

Substituting the values:Present Value = $2,176,097.00 / (1 + 0.08)^40 = $123,529.31 (rounded to 2 decimal places)

Now, we need to find the annual deposit amount. Since Derek starts making deposits on his 27th birthday and ends on his 65th birthday, he makes deposits for 65 - 27 = 38 years.Annual Deposit = Present Value / ((1 + interest rate)^number of periods - 1)Substituting the values:

Annual Deposit = $123,529.31 / ((1 + 0.08)^38 - 1) = $5,000.00 (rounded to 2 decimal places)Therefore, Derek must make annual deposits of $5,000.00 into his retirement account starting on his 27th birthday and ending on his 65th birthday to accumulate $2,176,097.00 by the time he turns 65.

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The given statement " If two sounds can form a minimal pair, they are allophones of two distinct phonemes." is true. because when two sounds can form a minimal pair, it demonstrates that the difference between the sounds is crucial for distinguishing the meaning of the words in the language as a result these sounds cannot be considered as allophones of the same phoneme, as they do not share the same underlying representation.

A minimal pair refers to two words that differ in only one sound but have different meanings. For example, "bat" and "pat" differ only in their initial consonants, /b/ and /p/, but have distinct meanings. This difference in meaning indicates that the two sounds are part of separate phonemes.

Phonemes are the basic, abstract units of sound in a language that can change the meaning of a word when substituted for one another. Allophones, on the other hand, are the various concrete realizations of a phoneme that do not change the meaning of a word. They are considered to be different surface forms of the same underlying phoneme.

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Step-by-step explanation:

I want you to fart in your hand and eat it like a sandwich

Answer:

80.95

Step-by-step explanation:

Percentage increase = \(\frac{New Value - Old Value}{Old Value}\) *100

=> (38-21)* 100/21 = 80.9523%

The answer round it to the nearest 100th = 80.95%

Answer:

Step-by-step explanation:

Answer:

Point K is located at -6.

Step-by-step explanation:

-15+9=-6

Point K is located at -6.

The margin of error in a sample of 100 people with a standard deviation of 12.5 is 2.45.

Let us assume a confidence of 95%.

Given that the confidence level (C) = 95% = 0.95

α = 1 - C = 0.05

α/2 = 0.05/2 = 0.025

The z score of α/2 corresponds with the z score of 0.475 (0.5 - 0.025) which is equal to 1.96

The margin of error (E) is:

\(E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.96*\frac{12.5}{\sqrt{100} } =2.45\)

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Answer:

6 possible outcomes

Step-by-step explanation:

To solve this problem, we have to make use of the Fundamental Counting Principle formula.

The formula counting principle states that when we are given two or more distinct events, in order to get the total number of possible outcomes, we multiply such events together.

In the above question, we are given two events.

Event 1

3 varieties of cheese: Cheddar, Gouda, and Swiss.

Event 2

2 styles of cheese: Shredded and Sliced

The possible outcomes for the variety and style of cheese = Event 1 × Event 2

= 3 × 2

6 possible outcomes.

These 6 Possible outcomes are listed below:

1) Cheddar cheese , Shredded

2) Cheddar cheese , Sliced

3) Gouda cheese , Shredded

4) Gouda cheese , Sliced

5) Swiss cheese , Shredded

6) Swiss cheese , Sliced

Answer:

23.88 cm squared

Step-by-step explanation:

3.6 x 5.9 = 21.24

1.1 x 4.8 x 1/2 = 2.64

21.24 + 2.64 = 23.88

Answer:

9a is equivalent to 11a - 2a because 11a-2a is 9a.

Step-by-step explanation:

The probability that for the second​ sample, the mean number of hours worked will be greater than 15.2​ is 0.567.

What is probability?

The probability of an event can be determined using probability. Only the likelihood that an event will occur can be estimated using it. A scale from 0 to 1, where 0 represents impossibility and 1 represents a specific occurrence.

We are given that among a random sample of 250 college​ students, the mean number of hours worked per week at​ non-college related jobs is 15.2 and that this mean lies 1.5 standard​ deviation(s) above the mean of the sampling distribution.

So, here Z = 1.5

Therefore,

⇒ P (X > 15.2) = 1 - P (X < 15.2)

⇒ P (X > 15.2) = 1 - 0.433

⇒ P (X > 15.2) = 0.567

Hence, the probability that for the second​ sample, the mean number of hours worked will be greater than 15.2​ is 0.567.

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ANSWER:

x° = 24°

y° = 72°

Analysis on picture hope it helps

Answer:

A) √3/4

Step-by-step explanation:

Eccentricity describes how closely a conic section resembles a circle:

\(e=\sqrt{1-\frac{b^2}{a^2}}\\\\e=\sqrt{1-\frac{52}{64}}\\\\e=\sqrt{\frac{12}{64}}\\\\e=\sqrt{\frac{3}{16}}\\\\e=\frac{\sqrt{3}}{4}\)

Note that \(a^2 > b^2\) in an ellipse, so the decision of these values matter.

Hank will take approximately 6.6 years to recover from his loss.

In the question, we are given that to go to college, Hank goes from working full-time making $28,000 per year to working part-time at half the salary for two years. The cost of his education will be $5,000.

We are asked for the time in which Hank recovers his loss if he makes $33,000 per year after getting his degree.

He will lose $14,000 every year he works part-time since his annual income drops from $28,000 to $14,000. He plans to do this for two years, which will result in a loss of $28,000 ($14000(2)).

The price of his degree will be added to this: 28,000+5,000 Equals $33,000.

By the time he graduates, he will be earning $33,000 annually. This is 5000 more a year than he was previously paid or 33000-28000.

We divide the amount he loses, 33,000, by the additional amount he will earn annually, 5000, to determine the number of years it will take him to recoup his investment:

33000/5000 = 6.6.

Thus, Hank will take approximately 6.6 years to recover from his loss.

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Answer:

C

Step-by-step explanation:

Took the test

The glasses + no glasses must = the total of people he has in his chart which is 32.

We have given that,

Marcos makes a table to show how many students in his class wear glasses. There are 18 boys and 14 girls in the class. There are 5 boys and 7 girls who wear glasses.

The first one

Boys 5-13-18

glasses + no glasses must = the total of people

Girls 7-7-14

Total 12-20

make sure that when the 18+14 is 32.

Therefore the glasses + no glasses must = the total of people he has in his chart which is 32.

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Answer:

A

Step-by-step explanation:

Answer:

\(\frac{-x^{2}+5x-1}{2x^{2} -x-1}\)

Step-by-step explanation:

Answer:

if x was 4 then the answer would be 36.

Step-by-step explanation:

28+8(4−3)

=28+(8)(1)

=28+8

=36

Answer:

Step-by-step explanation:

10:3 i believe

Answer:

9:31

Step-by-step explanation:

I guess since there arent any other mentioned its only black and brown horses so it would be 9:31

Partial fraction decomposition of \(x^6/(x^2-4) is {x^6}/{x^2-4}\)=\({A_1}/{x+2} + {A_2}/{x-2}\) where \(A1 and A2\) are constants and -2 and 2 are the roots of the denominator \(x^2 - 4.\)

Partial fraction decomposition involves breaking a fraction down into simpler fractions. These simpler fractions consist of terms with denominators that are factors of the original denominator. It is often used in calculus when integrating rational functions.

The form of partial fraction decomposition is as follows:

\({P(x)}/{Q(x)}\)= \({A_1}/{x-x_1} +{A_2}/{x-x_2} + {A_3}/{x-x_3} + ... + {A_n}/{x-x_n}\)where \(A1, A2, A3, ..., An\) are constants, and\(x1, x2, x3, ..., xn\) are the roots of the polynomial \(Q(x)\).

Now let's apply this form to the given function, \(x^6/(x^2-4)\): \({x^6}/{x^2-4} ={A_1}/{x+2} + {A_2}/{x-2}\)where A1 and A2 are constants and -2 and 2 are the roots of the denominator\(x^2 - 4.\)

This is the partial fraction decomposition of\(x^6/(x^2-4).\)

Note that we have not determined the numerical values of the coefficients A1 and A2.

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The required answer is

Ali traveled 20 miles per hour during the first interval and 40 miles per hour during the second interval.

Rafael traveled 35 miles per hour consistently during each interval.

Given that, the table relates the distance travelled by Ali, in miles and the time taken in hours,

Time(hour) , Distance travelled (miles)

1, 30

2, 50

3, 90

The table shows the distance travelled by Rafael in mile and time taken in hours

Time(hour) ,Distance travelled (miles)

2, 70

3, 105

4, 140

5, 175

To determine the distance traveled per hour for both Ali and Rafael, we can calculate the difference in distance for each hour.

For Ali:

Between hour 1 and hour 2: 50 miles - 30 miles = 20 miles

Between hour 2 and hour 3: 90 miles - 50 miles = 40 miles

Ali traveled a distance of 20 miles in one hour during the first interval and 40 miles in one hour during the second interval.

For Rafael:

Between hour 2 and hour 3: 105 miles - 70 miles = 35 miles

Between hour 3 and hour 4: 140 miles - 105 miles = 35 miles

Between hour 4 and hour 5: 175 miles - 140 miles = 35 miles

Rafael traveled a consistent distance of 35 miles in one hour during each interval.

Therefore, the required answer is

Ali traveled 20 miles per hour during the first interval and 40 miles per hour during the second interval.

Rafael traveled 35 miles per hour consistently during each interval.

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If a lawn sprinkler sprays water 7 feet in every direction as it rotates, the area of the watered lawn is approximately 153.94 square feet.

Assuming the sprinkler is placed at the center of the lawn, the area of the watered lawn can be found by calculating the area of a circle with a radius of 7 feet. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

Plugging in the given value of the radius, we get:

A = π(7 feet)^2

A = 153.94 square feet (rounded to two decimal places)

It's important to include the correct unit of measure, which is square feet in this case, to avoid confusion.

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Answer: (-9,18) , (1,8)  and (5,4)

Step-by-step explanation:

If  the x coordinate is -9 then plot it into the equation and solve for y.

y = -1(-9) + 0

y = 9 + 9

y = 18

Same for the second one plot in the value of x and solve for y

y= -1(1) + 9

y = -1 + 9

y = 8

Again same for the last one

y = -1(5) + 9

y = -5 + 9

y = 4

The solution to the given  is y(t) = -1/15, which is defined on the interval (-∞, ∞).

The initial-value problem given is dy/dt = 2(t-1)y2 with the initial condition y(0) = -1/15. The solution of this problem is y(t) = -1/15, which is a constant. This means that the solution is defined on the entire real line, which can be written in interval notation as (-∞, ∞).

To derive this solution, we can start by taking the antiderivative of both sides of the equation. Doing so yields \(∫dy/2(t-1)y2 = ∫dt\). Applying the integral law of substitution yields \(∫dy/y2 = ∫(2(t-1))dt\). Solving this integral yields y = -1/15 + c, where c is an arbitrary constant. Since the initial condition is y(0) = -1/15, we can set c = 0 to get the solution y(t) = -1/15. This means the solution is a constant, so the largest interval on which the solution is defined is (-∞, ∞).

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Answer:

B.

Step-by-step explanation:

The measurement which is closest to the number of miles between these two cities is 113 miles.

Given the distance between two cities is 180 kilometers.

If there are approximately 8 kilometers in 5 miles, we can use this conversion factor to convert 180 kilometers to miles, then one kilometer is approximately equal to 5/8 miles (0.625 miles).

To find the number of miles between the two cities, we can convert 180 kilometers to miles by multiplying by the conversion factor:

180 kilometers × (5/8 miles per kilometer) ≈ 112.5 miles = approximately 113 miles

Therefore, the closest measurement to the number of miles between these two cities is approximately 113 miles.

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Answer: The average rate of change from (-3,5) is 4.

Step-by-step explanation: This question is incomplete there a function is needed

So, suppose f(x) = 2x²-5

Given that, x= -3 to x= -5

let a = -3 and b=5

F(a) = F(-3) = 2(-3)²-5 = 13

F(b) = F(5) = 2(5)² -5 = 45

Step-by-step explanation:

2524 ÷ 23 = 24a6u= 7

bengek hyung

Answer:

m=-1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Once you move the -x to the other side of the equation, it becomes +x, making the slope 1

~theLocoCoco

Answer:

Cylinder

Step-by-step explanation:

A cylinder has two parallel,congruent bases that ate circles. A cylinder is round. It does not have a base,the others do.

Hope it helps.