Adam deposited $50,000 in a savings account with simple interest. Three years later, he had earned $6,000 in interest. What was the interest rate

Answer:3000

Step-by-step explanation:

You need to find the LCM of 500 and 600

The aluminum parallel-flow plate-and-fin evaporator has several key advantages over the standard round copper tube plate-and-fin evaporator are Lighter Weight, Improved Heat Transfer Efficiency.

An evaporator is a device used in air conditioning and refrigeration systems to remove heat from the refrigerant, which helps to cool down the air. There are two main types of evaporators: the aluminum parallel-flow plate-and-fin evaporator and the standard round copper tube plate-and-fin evaporator.

The parallel-flow design of the aluminum evaporator provides a larger surface area for heat transfer, which results in more efficient cooling. This means that less energy is required to achieve the same cooling effect.

Reduced Pressure Drop: The parallel-flow design also reduces the pressure drop in the refrigerant, which can improve the overall efficiency of the air conditioning or refrigeration system.

Aluminum is lighter than copper, which makes the aluminum evaporator easier to handle and install. This can be especially important in large air conditioning or refrigeration systems where weight and handling can be a significant concern.

Increased Durability: Aluminum is a more durable material than copper, which means that the aluminum evaporator is less likely to suffer from corrosion or other types of damage over time.

Better Resistance to Leakage: The parallel-flow design of the aluminum evaporator provides a tighter seal, which reduces the risk of refrigerant leakage. This helps to maintain the efficiency of the air conditioning or refrigeration system.

Lower Maintenance Costs: The increased durability and better resistance to leakage of the aluminum evaporator can help to lower maintenance costs over time.

Improved Environmental Performance: The improved efficiency and reduced pressure drop of the aluminum evaporator can help to lower the energy consumption of the air conditioning or refrigeration system. This can result in a reduction in greenhouse gas emissions and other environmental impacts.

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Answer:

The 95% confidence interval for the mean amount of the increase is ($541.6, $588.4). This means that we are 95% sure that the mean amount of increase of all customers who charge at least $3,000 in a year is between these two values.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.96\frac{267}{\sqrt{500}} = 23.4\)

The lower end of the interval is the sample mean subtracted by M. So it is 565 - 23.4 = $541.6

The upper end of the interval is the sample mean added to M. So it is 565 + 23.4 = $588.4

The 95% confidence interval for the mean amount of the increase is ($541.6, $588.4). This means that we are 95% sure that the mean amount of increase of all customers who charge at least $3,000 in a year is between these two values.

Answer:

Infinitely many

Step-by-step explanation:

Given:

\(y + 12 = y + 10 + 2\)

Solve:

Subtract y from  both sides

\(y+12-y=y+10+2-y\)

Simplify

\(12=10+2\)

Now add : 10 + 2

\(12=12\)

Both side are equal

Since both sides are equal then answer = Infinitely many

[RevyBreeze]

Answer:

1,264

Step-by-step explanation:

a = 1000(1.06)^4

a = 1,262.47696

1,264

Answer:

\(\frac{4}{30}\) or \(\frac{2}{15}\)

Step-by-step explanation:

30 students

8 earned A

9 earned B

6 earned C

3 earned D

30 - (8 + 9 + 6 + 3)

30 - 26 = 4

So out of 30 people, 4 people didn't pass

The probability is \(\frac{4}{30}\) or \(\frac{2}{15}\)

The probability that the student chosen did not pass the exam is 7 / 15

What is Probability?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is between 0 and 1

Given data ,

Total number of students for calculus exam = 30 students

Students who passed and earned A = 8 students

Students who passed and earned B = 9 students

Students who passed and earned C = 6 students

Students who passed and earned D = 3 students

And , Total students who passed = Students passed ( A + B + C + D )

                                                       = 8 + 9 + 6 + 3

                                                       = 26 students

Total students who passed = 26 students

Therefore , total students who failed the exam =
Total number of students - Total number of students who passed

Total students who failed the exam = 30 - 26

                                                          = 4 students

And the probability that the chosen student has failed =
Total number of students who failed / Total number of students

Probability that the student has failed = 4 / 30

                                                               = 2 / 15

Hence , The probability that the student did not pass the exam is 2 / 15

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Answer:

39.55

Step-by-step explanation:

24.99+15=39.55

That is how you get your answer :)

Answer:

1.89

Step-by-step explanation:

.15 x 24.55=1.89

Answer:

√9

Step-by-step explanation:

√9 because 3×3 =9

and the sum of the number 3+3=6

3 is the number

9514 1404 393

Answer:

  y +2 = (1/3)(x -6)

Step-by-step explanation:

When given a point and a slope, it is convenient to use the point-slope form of the equation for a line.

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

For your point and slope, this is ...

  y +2 = 1/3(x -6)

__

The slope of 1/3 means the graph has a "rise" of 1 for each "run" of 3:

  slope = m = rise/run = 1/3

A graph of it is attached.

Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:

5 nickels

10 dimes

5 quarters

Step-by-step explanation:

n = number of nickels

d = number of dimes

q = number of quarters

q = n

d = 2n

0.05n + 0.10d + 0.25q = 2.50

substitute

0.05n + 0.10(2n) + 0.25(n) = 2.50

0.05n + 0.20d + 0.25n = 2.50

0.50n = 2.50

n = 5

d = 10

q = 5

Each step of this theorem is proved below.

Given that,

S is finite,

Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).

According to the cancellation rule,

This product is independent of the order of the factors.

As a result, we can define the identity element e as this product.

It is simple to demonstrate that e meets the criteria of an identity element.

Now, let's show that every element of S has an inverse.

Let a be any element of S. Consider the set {a, a, a, ...}.

Since S is finite,

There exist positive integers m and n such that

am = an   for some m > n.

By the cancellation law,

We can cancel a power of a from both sides to get a\({(m-n)}\) = e.

This means that a has an inverse, and we can conclude that S is a group.

Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.

This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.

As a result, this is not a group.

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Answer:

d) 1/12

Step-by-step explanation:

if d = 14 cm ----> r = d/2

hence, circumference of a circle is:

\(c = 2\pi \: r \\ c = 2 \times \pi \times \frac{14}{2} = 14\pi \: cm\)

and its unit is centimeters or cm

Integral that would give the volume V generated by rotating the region bounded by the given curves will be 200 pi unit³

Finding the volume of rotation is similar to finding the area of the bounded region of the graphs of the functions. The only difference is the added component added due to the rotation of the bounded region. Now whether we are using disk method or cylindrical shell method to find the volume, we will first set up the integral and its limits of integration, then evaluate this integral.

To find the volume of the solid generated by rotating the region bounded by curves:

(y = x^3 and y = 0) around the y-axis

We use the Cylindrical Shells Method.

First, we need to set up the integral.

We have:

2π∫\(0^5\) x (\(x^3\)) dx.

To solve this integral, we use the power rule for integration.

This states that if we have an integral of \(x^n\), the antiderivative is

x^(n+1)/(n+1).

Therefore, the antiderivative of our integral is 2π∫\(0^5\) x (\(x^3\)) dx.. Now that we have the antiderivative, we can solve the integral by applying the fundamental theorem of calculus.

This states that the integral of a function is equal to the difference between the evaluated antiderivative at the upper and lower limits of the integral.

Therefore, the volume of the solid generated is

V = \([x^5/5]^5_0\) = 2π(\(5^5/5\)) = 200π\(unit^3\).

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Find the factors of each number:

72 = 1,2,3,4,6,8,9,12,18,24,36

84 = 1,2,3,4,6,7,12,14,21,28,42

The Greatest common factor of both numbers is 12

divide by 12, and apply common factor

12 ( 7m-6n)

Step-by-step explanation:

The definite integral of sin^5(x)dx from 0 to pi/2 can be evaluated using the method of substitution.

Let u = sin(x), then du = cos(x)dx

The integral becomes:

∫sin^5(x)dx = ∫u^5du from 0 to sin(π/2)

= (u^6)/6 evaluated at sin(π/2) and 0

= (sin^6(π/2))/6 - 0

= (1^6)/6

= 1/6

So, the definite integral of sin^5(x)dx from 0 to pi/2 is equal to 1/6.

Answer:

f(2) = 1

x = 0

Step-by-step explanation:

f(2) = 1 since y=1 when x=2.

f(0) = -3 since x=0 when y=-3

Answer:

B

Step-by-step explanation:

y-intercept is where x is zero, so we must look at where the y-iterceot is crossed

Answer:

You hace to find x first

Step-by-step explanation:

6x+1=4

6×=3

here i subtract 1 on each side

6x/6 = 3/6

here you have to divide

×= 0.5

Answer: x=0.5 or 1/2

Answer:

Step-by-step explanation:

False.

The correct identity is:

cos^2(x/3) = 1/2[1+cos(2x/3)]

To see why, use the double angle formula for cosine:

cos(2x/3) = 2cos^2(x/3) - 1

Substitute this into the original equation:

cos(x/3)cos(x/3) = 1/2[1+2cos^2(x/3)-1]

Simplify:

cos^2(x/3) = 1/2[1+cos(2x/3)]

Answer:

Statement is true!

Step-by-step explanation:

Required to Prove:

\(\Large \textsf{$\cos \left(\frac{x}{3}\right)\cos \left(\frac{x}{3} \right)=\frac{1}{2} \left[1+\cos(\frac{2x}{3})\right]$}\)

This is a special property, used in integral calculus, that can be derived and hence proved, from the double angle formula of cosine.

\(\large \textsf{Given that cos(A+B) = cosA\,cosB $-$ sinA\,sinB,}\\ \\\large \textsf{Hence cos(A+A) = cosA\,cosA $-$ sinA\,sinA}\\ \\\large \textsf{$\therefore$ cos2A = cos$^2$A $-$ sin$^2$A}\\ \large \textsf{$\rm \phantom{\therefore cos^2A}=$ 1 $-$ 2sin$^2$A}\\ \large \textsf{$\rm \phantom{\therefore cos^2A}=$ 2cos$^2$A $-$ 1 (using Pythagorean Identity $\Rightarrow cos^2A+sin^2A = 1$)}\)

This property, can be quoted in exams and only has to be derived, not proved. Now using the Cos2A property, we can manipulate the formula:

\(\large \textsf{$\cos2\rm A = \cos^2A - \sin^2A$}\\ \\ \large \textsf{$\rm \phantom{\cos 2A}=2\cos^2A-1$}\\ \\ \large \textsf{$\rm \therefore \cos2A+1 = 2\cos^2A$}\\ \\ \large \textsf{$\rm \cos^2A=\frac{\cos2A+1}{2}$}\\ \\ \large \textsf{$\rm \phantom{\cos^2A}=\frac{1}{2}(\cos2A+1)$}\\ \\ \large \textsf{$\rm \phantom{\cos^2A}=\frac{1}{2}(1+\cos2A)$}\)

And since:

\(\large \textsf{$\cos \left(\frac{x}{3}\right)\cos\left(\frac{x}{3}\right)=\cos^2\left(\frac{x}{3}\right)$}\)

Therefore, inputting the value of A = \(\Large \textsf{$\frac{x}{3}$}\) into the formula we derived above, hence:

\(\Large \boxed{\boxed{\textsf{$\cos \left(\frac{x}{3}\right)\cos \left(\frac{x}{3} \right)=\frac{1}{2} \left[1+\cos(\frac{2x}{3})\right]$}}} \Large \textsf{ , as required}\)

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Answer:

there would be 8 sides if there are 20 diagonals

The product that is represented with the algebra tiles is (2x + 2)(2x + 3)

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

The algebra tiles

Representing the red tile with digit 1

So, we have

Vertical = 2x + 1 + 1 = 2x + 2

Horizontal = 2x + 1 + 1 + 1 = 2x + 3

The product that is represented with the algebra tiles is then calculated as

Product = Vertical * Horizontal

So, we have

Product = (2x + 2)(2x + 3)

Hence, the product is (2x + 2)(2x + 3)

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Answer:

-7x^3+39x^2+136x

Step-by-step explanation:

= x(x-8) (-7x - 17)

( x - 8 ) ( -7 x - 17) : -7x^2 + 39x+136

= x( -7x^2 + 39x + 136)

= x( -7x^2) + x * 39x * 136

= -7x^3 + 39x^2 + 136x

Answer:

I think its c but not really sure but ill calculate it if I ever had the chance

Answer:

how would you want your answer

Therefore, the solution to the equation \((z + 1)^7 + (z + 1)^7 = 0\) in the complex number system is z = -1.

To solve the equation\((z + 1)^7 + (z + 1)^7 = 0\) in the complex number system, we can simplify the equation and then find the values of z that satisfy it.

Let's start by simplifying the equation:

\((z + 1)^7 + (z + 1)^7 = 0\)

We notice that both terms on the left side of the equation are identical, so we can rewrite it as:

2(z + 1)^7 = 0

Now, we can divide both sides of the equation by 2 to isolate the term\((z + 1)^7:\)

\((z + 1)^7 = 0\)

To find the solutions, we set each factor of \((z + 1)^7\)equal to zero. In other words, we set the exponent 7 to be a multiple of 2:

z + 1 = 0

From this equation, we find that z = -1.

It's important to note that complex numbers have a real and imaginary part.

In this case, since the equation simplifies to a real number, the solution is a real number (-1).

If the equation involved complex terms or the roots of unity, the solutions could include complex numbers as well.

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Answer:

1/14

Step-by-step explanation:

all together the probability would be 1/21 because we're adding all the color eyes together. After that, it narrows to only blue and hazel which is 14 so the new probability is 1/14, so the answer is 1/14.

Answer: 1/8

Step-by-step explanation:

First make the bottom half the same:

3/4*2/2=6/8

We don’t need to change the first portion since they have a common factor

7/8-6/8=1/8