4,400 is placed in an account with an annual interest rate of 8. 25%. How much will be in the account after 22 years to the nearest cent

The work required to stretch the spring from its natural length to a distance of 9 inches beyond its natural length is 2.25 lb-ft.

The problem involves calculating the work required to stretch a spring from its natural length to a distance of 9 inches beyond its natural length, given that a force of 192 lb is required to hold the spring stretched 3 ft beyond its natural length.

To solve the problem, we use the formula for the work done by a force that varies with distance, which is given by:

W = (1/2) k (x2^2 - x1^2)

where W is the work done, k is the spring constant, x1 is the initial distance, and x2 is the final distance.

In this case, the initial distance is the natural length of the spring, which is 0 ft, and the final distance is 9/12 ft. To find the spring constant, we use the fact that a force of 192 lb is required to hold the spring stretched 3 ft beyond its natural length, which gives us:

192 = k * 3

Solving for k, we get k = 64 lb/ft.

Substituting the values into the formula, we get:

W = (1/2) * 64 * (9/12)^2

Simplifying, we get:

W = 2.25 lb-ft

This calculation shows how the work done by a force that varies with distance can be calculated using the spring constant and the distances involved.

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Answer:

2 • (10ab + 35a - 12b2 - 42b)

Step-by-step explanation:

(20ab + 70a - 84b) - (23•3b2)

20ab + 70a - 24b2 - 84b =

2 • (10ab + 35a - 12b2 - 42b)

Answer:

the answer is : m= -1/3

Step-by-step explanation:

you need the steps?

=4t + 8

=4×3 + 8

= 12 +8

= 20

[tex]...[/tex]

Answer:

The aeroplane will fly 2000 km if travelling at the same average speed.

Step-by-step explanation:

To calculate the distance an aeroplane will fly in 2 h 30 min if it flies 1400 km in 1 h 45 mins, use the Speed Distance Time formula.

[tex]\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]

There are 60 minutes in one hour.  Therefore:

To calculate the speed of the aeroplane, divide the distance by the time it takes to travel that distance.  Therefore, if an aeroplane flies 1400 km in 1.75 hours then its average speed is:

[tex]\sf Speed=\dfrac{1400\;km}{1.75\;h}=800\;km/h[/tex]

To determine the distance the aeroplane will travel in 2.5 hours, multiply the found speed of 800 km/h by the time:

[tex]\sf Distance=800\;km/h \times 2.5\;h=2000\;km[/tex]

Therefore, the aeroplane will fly 2000 km in 2 h 30 min if travelling at the same average speed.

The graph states that there are 2 number of gallons of lemonade in a container, y, after drinking 12 glasses of lemonade.

How to interpret a graph?

The horizontal scale across the bottom and the vertical scale along the side tell us how much or how many. The points or dots on the graph show us the facts. The lines connecting the points give estimates of the values between the points.

since , it is a decreasing graph because it has a negative slope . Therefore , as no of glasses increases the gallons numbers decreases.

Hence , the graph states that there are 2 number of gallons of lemonade in a container, y, after drinking 12 glasses of lemonade.

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Answer:

no run hide

Step-by-step explanation:

hide run boo

Answer:

(36/5)

Step-by-step explanation:

y=x^2+36/5

Since x is squared, the result will always be a positive number, regardless of the actual value of x.  Starting with a value of x of zero, the x^2 term will only grow as one moves away from 0.  E.g., (-1)^2 = 1, (-2)^2 = 4, etc.

So the minium for this equation will occur when x = 0.  It only gets larger from that point.  The minimum is (36/5).

See the attached graph.

The value of m is 40 degrees, the value of x is 6 and value of y is 9.

Parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

To find the value of variable m.

Forming an equation:

3m = 120°

m = 120/3

m = 40

Therefore the value of m is 40.

Finding x:

x is opposite to the side of measure 6.

As per the first property.

x = 6

So, x = 6

Therefore the value of x is 6.

Finding y.

5y is opposite the angle measuring 45°.

Forming an equation.

5y = 45°

y = 45/5

y = 9

Therefore the value of y is 9.

Hence, the value of m is 40 degrees, the value of x is 6 and value of y is 9.

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The complete question is given below and in attachment

Find the value of each variable in the parallelogram. explain step by step

The probability that at least one component does not function properly when 2 components are randomly selected from 8 is 1/4, or 0.25.

The total number of ways to select 2 components from 8 is:

C(8,2) = 8! / (2! (8-2)!) = 28

Now, let's find the probability that at least one component does not function properly. We can find this probability by subtracting the probability that both components function properly from 1.

The probability that the first component functions properly is 7/8, since there are 7 working components out of 8. The probability that the second component also functions properly, given that the first component does, is 6/7, since there are 6 working components left out of 7. Therefore, the probability that both components function properly is:

(7/8) * (6/7) = 6/8 = 3/4

So the probability that at least one component does not function properly is:

1 - 3/4 = 1/4

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The probability that Anthony is on time for work and takes the train is 0.76.

What is probability?

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

Here, we have

Given: the probability that Anthony is on time for work is 0.90. the probability that Anthony takes the train to work is 0.80. given that Anthony takes the train to work, the probability that he is on time is 0.95.

We let

A: Anthony being on time for work

B: Anthony will take the train to work

P(A) = 0.9

P(B) = 0.8

P(A/B) = 0.95

P(Anthony is on time for work and takes the train):

P(A∩B) = P(A/B). P(B)

P(A∩B) = 0.95×0.8

P(A∩B) = 0.76

Hence, the probability that Anthony is on time for work and takes the train is 0.76.

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For all n that is higher than or equal to 4, this statement is true.

By taking the cubes of both sides of the inequality, we can demonstrate this.

log2(n3) = [tex]3\sqrt{n}[/tex]

n^(3/2) <= 3 * log2(n) (n)

Since log2(n) > 2 for n >= 4, we can write:

3 * 2 * (log2(n)) = 3 * n where n(3/2) = 3 * log2(n)

This suggests that:

[tex]\sqrt{n} =( \frac{3}{n{log 2}} + n) (n)[/tex]

We come to the conclusion that the square root of n will eventually be less than or equal to log2(n3) for all n higher than or equal to 4 since the right-hand side of this inequality approaches zero as n goes to infinity. The assertion is accurate as a result.

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Part (a)

4/15 is the probability of getting a rotten orange

After one is taken and not put back, there are

meaning 3/14 is the probability of a second rotten orange.

Two rotten in a row has the probability (4/15)*(3/14) = 2/35. I skipped a few steps so let me know if you need to see in more detail how I got to that result.

=====================================================

Part (b)

We want to calculate the probability exactly one of the two oranges selected is rotten.

There are two possible cases here:

Let's determine the probability for case 1.

4/15 was mentioned earlier in part (a) as the probability of a rotten orange. There are 15-4 = 11 non-rotten oranges and 15-1 = 14 remaining since we aren't replacing the first selection. That gives 11/14 as the probability the 2nd selection is fresh.

We get (4/15)*(11/14) = 22/105 as the probability for case 1 to happen.

Through similar calculations, the probability for case 2 is (11/15)*(4/14) = 22/105

Cases 1 and 2 are mutually exclusive. Both cannot happen simultaneously. There is no overlap. This fact allows us to add the results to get:

22/105 + 22/105 = 44/105

That fraction cannot be reduced.

This is a probability problem. To find the probability of removing two blue counters, we need to calculate the number of possible outcomes of removing two blue counters out of seven counters (3 blue and 4 yellow).

The number of possible outcomes of removing two blue counters is 3C2 = 3! / (2! * (3-2)!) = 3.

So, the probability of removing two blue counters is 3/7C2 = 3/21.

To find the probability of X being equal to 2, we need to calculate the probability of removing two blue counters.

Therefore, the probability of X being equal to 2 is 3/21.

A rectangular piece of cardbord has 3D dimensions.

Rectangles are enclosed 2-D shapes with four sides, four corners, and four right angles.Equal and parallel opposite sides make up a rectangle.

The rectangle's properties are listed below:

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Answer: $4.75 for each pen

Step-by-step explanation:

$28.50/6= 4.75$

Answer:

B

Step-by-step explanation:

the zeros are the values of x on the x- axis where the graph crosses.

the graph crosses the x- axis at x = 3 and x = 6

then

the zeros are x = 3 and x = 6

Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.

P(A) = f / N.

probability = 2%/100=0.0002

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.

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The information provided by a source in a graph is C. Who put the data together.

The information provided by a source in a graph can include various aspects such as the data being displayed, the method used to collect the data, and who put the data together (also known as the data source).

The data source is important because it provides context and credibility to the data being presented. It helps to understand the reliability and accuracy of the data, as well as any potential biases that may be present. In this case, the source is the Human Resources Department.

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The system of linear equations represented in the graph have (b) ne solution at (-3, 1)

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

0 = y - x - 4

3y + 9 = -4x

The above system represents two linear functions

The point of intersection of the linear functions represent the solution

In this case, the linear functions intersect at (-3, 1)

See attachment for graph

Hence, it has one solution at (-3, 1)

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The area of the aperture storing light is 0.196 [tex]m^{2}[/tex].

Mathematical figures which have a set of pre defined properties are known as shapes. For example, Square shape is a mathematical figure who has four sides and all of them are equal in length and all the four corner of square have an angle of 90 degree. Similarly if there a figure who  has been formed by the help of four lines of equal length but the corners are not 90 degrees then it will be Rhombus and not Square.

Now for the given question:

Diameter of the mirror=50 cm

we convert dia. unit in meter as area is asked in meter.

Dia.= [tex]\frac{50}{100}[/tex]

      = [tex]\frac{1}{2}[/tex]

Area of a circle=π× [tex](\frac{dia}{2} )^{2}[/tex]

               =π×[tex](\frac{1}{4} )^{2}[/tex]

Area= π/16

π=3.14

Area=[tex]\frac{3.14}{16}[/tex]

       = 0.196 [tex]m^{2}[/tex]

Hence area of the aperture is 0.196 [tex]m^{2}[/tex].

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The 92nd term of the arithmetic sequence 8, 25, 42, ..... is equal to 1,555.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 25 - 8

Common difference, d = 17

Substituting the given parameters into the formula, the 92nd term of this arithmetic sequence is given by;

a₉₂ = a₁ + (92 - 1)d

a₉₂ = 8 + (91)(17)

a₉₂ = 8 + 1,547

a₉₂ = 1,555.

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Part A: The  inequality to find the possible number of students, n, who ate the school lunch n > 542 students

Part B: The number of students, that possibly eat lunch at school is 542 or more students

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

Part A; The number of students who bring lunch, B > 485 students

The number of students who eat lunch in school, E = B + 57

∴ E > 485 + 57

The number of students who can possibly eat lunch in school;

E > 542 students

Part B;

The number of students, n, that possibly eat lunch at school, are;

n = 542 or more students.

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The linear regression of the data is given as follows:

y = 25.1x + 150.4.

The estimate for the year in which the profit would reach $482,000 is of:

2019.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points for this problem are given as follows:

(0, 147), (1, 167), (2, 209), (3, 239), (4, 250), (5, 267).

Hence the equation is of:

y = 25.1x + 150.4.

The estimate for the year in which the profit would reach $482,000 is x years after 2006, when y = 482, hence:

482 = 25.1x + 150.4.

x = (482 - 150.4)/25.1

x = 13.

2006 + 13 = 2019 -> year.

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The values on the stem are {5, 5, 4, 3, 4, 3} and the leaf of the data set is represented by {6, 4, 1, 2, 7, 9}.

A stem and leaf plot, also known as a stem and leaf diagram, is a way to arrange data so that it is simple to see how frequently various sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf.

According to the stem leaf plot the first digit is the stem and the second digit is the leaf.

Hence, the values on the stem are {5, 5, 4, 3, 4, 3} and the leaf of the data set is represented by {6, 4, 1, 2, 7, 9}.

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The unknown angle in the cyclic quadrilateral is as follows:

m∠B = 121 degrees.

In a cyclic quadrilateral, the sum of a pair of opposite angles is 180° (supplementary). The sum of angles in a cyclic quadrilateral is 360 degrees.

Therefore, let's find the angle m∠B in the cyclic quadrilateral.

m∠D = 59 degrees

m∠A = 33 degrees

Therefore,

m∠B = 180 - m∠D

This is because the angle m∠B is opposite to the angle m∠D.

Hence,

m∠B = 180 - 59

m∠B = 121 degrees.

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Answer:

73°

Step-by-step explanation:

Vertical angles are congruent.  They have the same measurement.

To solve the equation cos²x + sin x = 1, we can use the trigonometric identity cos²x = 1 - sin²x. By substituting this identity into the equation, we get:

1 - sin²x + sin x = 1

Combining like terms, we get:

1 - sin²x = 0

Solving for sin x, we get:

sin x = 1

However, the sine function has a range of [-1, 1], so the only solution in the interval [0, 2π] is sin x = 1, which corresponds to x = π/2. So the solution to the equation cos²x + sin x = 1 in the interval [0, 2π] is x = π/2.

The length of the side c of the right-angled triangle is equal to 6.5 to the nearest tenth using the trigonometric ratio of sine of angle 50°.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle ABC, we shall calculate for the length c by application of the trigonometric ratio of sine for the angle 50°.

sin 50° = 5/c {opposite/hypotenuse}

by cross multiplication

c = 5/sin 50°

c = 6.5270

Therefore, the length of the side c of the right-angled triangle is equal to 6.5 to the nearest tenth using the trigonometric ratio of sine of angle 50°.

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Answer: s≥3

Step-by-step explanation: fist you need to get the variable by itself on one side. So subtract the 10 from each side and you have 3s≥9. Then you divide each side ny 3 to get s by itself, divide 9 by 3. Then your answer is s≥3