An office machine purchased new for $3600 loses $400 each year.
Assume the value continues to decrease the same amount
each year. If f(x) represents the value of the office machine
after x years, which linear function models the given situation?

a. The solution to the system is shown in the graph given below, which is (3, 8).

b. Plugging in the values of x and y into each equation, both sides of each equation are balanced.

To find the solution to a system of equations, plot both equations on a coordinate plane, then find the coordinates of the point where the two lines intersect, which is the solution.

a. Given the system, 3y = x + 21 and y + 2/3x = 10, the image below show each line where 3y = x + 21 is represented as the blue line, and y + 2/3x = 10 is represented as the red line.

The lines of both equations intersect at point (3, 8) which shows that the solution of the system is solved graphically as (3, 8).

b. 3y = x + 21 --> eqn. 1

y + 2/3x = 10 --> eqn. 2

Substitute x = 3 and y = 8 into equation 1:

3(8) = 3 + 21

24 = 24 [true]

Substitute x = 3 and y = 8 into equation 2:

8 + 2/3(3) = 10

8 + 2 = 10

10 = 10 [true]

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IQ is normally distributed with a mean and Standards deviations .

a) The probability that this person has an iq greater than 95 is 0.6306 or 63.1%

b) The probability that this person has an IQ less than 125 is 0.9522 or 95.2 %.

c) In a sample of 700 people, the number of people would have an IQ less than 110 is 598 people.

d)In a sample of 700 people, how many people would have an IQ greater than 140 is three in count.

We have normal distribution here with

Mean , u = 100

Standard deviations, s = 15

let X be random variable, X~ N(15, 100)

a) P(X > 95)

From Z- statistic, Z = (X - u) /s

Converting to standard normal variable,

P( X- u/sd <( 95 - u)/s)

P(Z > (95 - 100) / 15)

= P(Z > -0.3333)

Using standard normal tables, value of P(Z > -0.3333) = 0.6306

Therefore 63.1% is the required percentage here.

b) P(X < 125)

= P(Z < (125 - 100) / 15)

= P(Z < 1.6667)

Using standard normal tables,

= 0.9522

Therefore 95.2% is the required percentage here.

c) The probability here is computed as:

P(X < 110)

= P(Z < (110 - 100) / 15)

= P(Z < 0.6667 )

Using the standard normal tables,P(Z < 0.6667 ) = 0.7475

Therefore expected number of people:

= 800×0.7475

= 598

Therefore 598 is the required expected number of people here.

d) P(X > 140)

= P(Z > (140 - 100) / 15)

= P(Z > 2.6667)

Getting from standard normal tables,

= 0.0038

Therefore expected number of people here:

= 800×0.0038

= 3.04

Therefore 3 is the expected number of people here. Hence, we get the required probability for each case

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Complete question:

IQ is normally distributed with a mean of 100 and a standard deviation of 15. a) Suppose one individual is randomly chosen. Find the probability that this person has an IQ greater than 95. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ greater than 95) = % b) Suppose one individual is randomly chosen. Find the probability that this person has an IQ less than 125. Write your answer in percent form. Round to the nearest tenth of a percent. P (IQ less than 125) = % c) In a sample of 700 people, how many people would have an IQ less than 110? people d) In a sample of 700 people, how many people would have an IQ greater than 140? people

If you had originally set the alpha level at 0.10 then conclusion is same as the in case of where alpha level of 0.01, i.e reject the null hypothesis.

Hypothesis testing is a statistical process by which analysts test assumptions about population parameters. Every analyst uses a random population sample to test two different hypotheses of hers: the null hypothesis and the alternative hypothesis. The null hypothesis is usually the hypothesis that the population parameters are equal. We have , alpha level = 0.01

We reject the null hypothesis when the p value of a test is less than the level of significance that is alpha. In the case of alpha =0.01, the null hypothesis was rejected implies p value was less than 0.01. In the provide case originally the alpha value is 0.10, Still at this level of alpha p value is less than 0.10(as p value less than 0.01 implies p value less than 0.10). As the p value is less than 0.10 we reject the null hypothesis. So the correct option is '' Reject the null hypothesis''.

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If we are rolling a six-sided dice, where. a = get a roll that is even, then the value of [tex]$P\left(A^c\right)^$[/tex]  will be 1/2

Option (c) is the correct choice.

As we know,

A dice has 6 faces on which 6 different numbers (1,2,3,4,5 and 6) are printed on each of the six faces of the dice.

Now, considering an unbiased die the probability of any of the faces appearing in a single roll is 1/6.

So, we can write it as:

P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6

Now that number to be even is 2,4,6

And for each individual number, the probability will be 1/6

So, the value of P(A) =P(2) + P(4)+ P(6)

= 1/6 + 1/6 +1/6 =3/6

P(Ac) = 1 - P(A) = 1 - ( 3/6 ) = 1/2.

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The complete question may be:

Suppose that you are rolling a six sided dice.

Let A= get a roll that is even

What is [tex]$P\left(A^c\right)^$[/tex] ?

(a) 1 / 3

(b) 1 / 4

(c) 1 / 2

(d) 1 / 6

Answer:

7

Step-by-step explanation:

Answer:  The first bolt he bought is 7/8 inches long. The second bolt he bought is 5/8 inches long.

Step-by-step explanation:

The bolt he already has: 3/4 inches, or this can be written as 6/8 inches.

Since the the first bolt he bought was 1/8 inches longer than the original one, we can do 1/8 + 3/4 (6/8) and we get the sum of 7/8.

The first bolt he bought is 7/8 inches long.

The second bolt he bought was 1/8 inch shorter than the first one, so we just take 1/8 from 3/4,

==> 6/8 - 1/8 = 5/8

The second bolt he bought was 5/8 inches long.

Hope this helped, have a good day :D

Answer:3.33%

Step-by-step explanation:

Her annual income will be 3.33%

The average rate of change of the function at the interval x = 5 and x = 7 is 22.5

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

The graph (see attachment)

The interval is given as

x = 5 and x = 7

This can be represented as

5 ≤ x ≤ 7

On the graph, we have

x = 5 and y = 3

x = 7 and y = 48

This means that

f(5) = 3 and f(7) = 48

The average rate of change is then calculated as

Average rate of change = [f(7) - f(5)]/[7 - 5]

Substitute the known values in the above equation, so, we have the following representation

Average rate of change = [48 - 3]/[2]

Evaluate the expression

Average rate of change = 22.5

Hence, the rate is 22.5

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Complete question

The function y=f(x) is graphed below. Plot a line segment connecting the the points on f where x=5 and x=7. Use the line segment to determine the average rate of change of the function f(x) on the interval 0≤x≤ 4.

See attachment for graph

Answer:

-1.8f-19

Step-by-step explanation:

2.5f-0.7f=1.8 and 16+3=19

make both negative

After solving the percentage, the height of flower stem after two months is found to be 10 feet.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

To solve this question, we will do 40% x 25.

= (40/100) x 25

= 10 feet

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Answer:

The discount on the barbecue grills is 75.11%.

Step-by-step explanation:

To calculate the discount as a percentage, we first need to find the total discount amount by subtracting the new price of the barbecue grills from the old price. This gives us $844 - $211 = $633.

To find the discount as a percentage, we divide the discount amount by the old price and multiply the result by 100%. This gives us $633 / $844 * 100% = 75.11%.

Therefore, the discount on the barbecue grills is 75.11%.

The z-score for that condition is 0.38. To be exact, the z-score is 0.38461538461.

First we have to extract mean and standard deviation from x~n(145, 13) where mean (μ) = 145 and standard deviation(б) = 13. As per given corresponding to an observation(x) is directly given = 150 we can start to find the z-score with formula z-score = (x - μ) :  б. So

z = (x - μ) :  б.

z = [tex]\frac{150-145}{13}[/tex]

z = [tex]\frac{5}{13}[/tex]

z = 0.38461538461

Normally z written in 2 to 4 digit after decimal, so z-score = 0.38

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The probability that all three will be in box 1 will be  [tex]\frac{1}{8}[/tex] or 0.125.

As per the given data the three balls which are labeled as A, B, C are placed into two different boxes of box 1 and box 2.

Box 1 has 10 balls and box two has 5, if all the arrangements are equally likely we have to determine the probability that all the three will be in box 1.

Formula for finding the probability:

Probability = The total number of outcomes ÷ The favorable number of outcomes.

The total number of outcomes:

= [tex]$${ }^3 C_3+{ }^3 C_2+{ }^3 C_1+{ }^3 C_0$$[/tex]

= 1+3+3+1

=8

The favorable number of outcomes:

= [tex]{ }^3 C_3[/tex]

=1

The probability that all the three will be in box 1:

= [tex]\frac{1}{8}[/tex]

= 0.125

Therefore the probability is  [tex]\frac{1}{8}[/tex] or 0.125.

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The properties of the angles and sides of a triangle are as follows:

1. The sum of the three angles of any triangle is 180°

2. The longest side of a triangle is opposite the largest angle and the smallest side is opposite the smallest angle.

3. The sum of any two sides of a triangle is always greater than the third side.

These properties can be used to solve problems involving triangles by working out the angles or lengths of sides. For example, let's say we have a triangle with two sides of length 5 and 8, and we need to find the length of the third side. Using the third property listed above, we can set up the following equation:

5 + 8 > x

13 > x

Therefore, the length of the third side is greater than 13.

A triangle (of any kind) has a total angle of 180°. A triangle's two sides add up to a length bigger than its third side. In the same way, the length of the third side of a triangle's third side is shorter than the difference between its two sides.

Triangulus, which means "three-cornered" or "having three angles," is a Latin word with roots in tri-, "three," and angulus, "angle or corner."

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Answer: i say 36.2 mph but this is my option i could be wrong :)

Step-by-step explanation:

To determine the minimum number of subjects needed for a z-test with a power of at least 80% and a type 1 error rate of 0.05, you can use a sample size calculator or perform the calculations manually.

Assuming that the population of differences is approximately normal, the z-test is appropriate to use. The z-test allows you to test whether the mean of a population differs significantly from a specified value (the null hypothesis) based on a sample taken from the population.

To perform the calculations manually, you will need to know the following:

Once you have this information, you can use the following formula to calculate the minimum sample size:

n = (Z_alpha/2 + Z_beta)^2 * (SD / effect size)^2

where:

For example, let's say the desired power of the test is 80%, the type 1 error rate is 0.05, the effect size is 0.5, and the standard deviation of the population is 1. Using the formula above, we can calculate the minimum sample size as follows:n = (1.96 + 0.84)^2 * (1 / 0.5)^2

= 3.8236^2 * 2^2

= 14.52 * 4

= 58.08

Therefore, the minimum sample size needed for this test would be 59 subjects.

It's important to note that this is just a rough estimate, and the actual sample size may need to be adjusted based on the specific characteristics of the population and the research question being addressed.

Answer:

x = 4.5

Step-by-step explanation:

2x = 9 ( isolate x by dividing both sides by 2 )

x = [tex]\frac{9}{2}[/tex] = 4.5

The difference between a line and a line segment is, a line is extended in both directions infinitely but a line segment has two endpoints.

Lines are the geometrical picture with non-terminating ends. A line runs in two opposite directions with endless. Both the points of a line can be extended to infinity.

The line is non-ending but it can be fractionally divided into different segments. These segments are known as the line segment which has two endpoints.

Difference between line and line segment:

A line segment can be taken as the shortest distance between two endpoints and they are the distance between two defined endpoints.

A line segment can be measured in length as it has two fixed endpoints, which are denoted by ‘_’ or \overline{xy}

A line extends up to infinity as it does not have any starting or endpoint, Which can be measured as it has no end and extends up to infinity, and is denoted by any two points lying on the line.

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When data records are not in any desired sequence for processing or viewing the appropriate task is to sort the contents in different fields.

Depending on the method employed, the data collection process may include several stages. Here are a couple such examples:

Data generation is the process of discovering and organizing facts in an orderly manner. This could be a manually generated document or data gathered from a source and easily fed into a computer using a data capture device such as a barcode scanner.

Data preparation is the process of converting data from a source document to a machine-readable format. This may not apply to all input devices. Data obtained by devices that take data directly in digital form do not require transcription.

Data transmission will determine whether or not data must be delivered to the central server using communication means.

Manual labor is time-consuming and dull, especially when doing repetitive tasks. Mechanical devices were developed to help in the automation of manual tasks. Typewriters, printing presses, and weaving looms are examples of mechanical devices. Initially, these devices were devoid of electronic intelligence.

Scientists have spent a long time investigating methods to build devices or technologies that would stimulate some type of human intellect during information and data processing. This was made feasible in part by the development of electronic programmable devices such as computers.

The development of microprocessor technology substantially boosted the efficiency and capability of data processing. Examples include computers, cellular (mobile) phones, calculators, petroleum pumps, modern television sets, washing machines, and other microprocessor-controlled devices.

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If the base length of the triangle is 10 units. Then the area of the triangle will be 35 square units.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The region of a right triangle is straightforwardly relative to the foundation of the triangle. The region of a triangle is 42 square units for a base length of 12 units.

The proportionality is given below.

A ∝ b

A = kb

Where A is the area, b is the base length, and k is the constant.

The ratio of Area to base length remains constant.

If the base length of the triangle is 10 units. Then the equation is given as,

A / 10 = 42 / 12

Simplify the equation, then we have

A / 10 = 42 / 12

A = 35 square units

If the base length of the triangle is 10 units. Then the area of the triangle will be 35 square units.

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one cyclist travels faster than the other. Therefore, the rate of the faster cyclist is (distance between towns) / (2 * hours) and the rate of the slower cyclist is also (distance between towns) / (2 * hours).

Let x = the rate of the faster cyclist, and y = the rate of the slower cyclist.

We can set up the equation:

x + y = (distance between towns) / (time they met)

x + y = (distance between towns) / (hours)

We can solve for x and y:

x = (distance between towns) / (2 * hours)

y = (distance between towns) / (2 * hours)

Therefore, the rate of the faster cyclist is (distance between towns) / (2 * hours) and the rate of the slower cyclist is also (distance between towns) / (2 * hours).

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Answer:

48 and 32

Step-by-step explanation:

both numbers get rounded by 8 going up and down rounding it to 40

Answer:

all of them are true except the last one ( no. e)

Answer:

The annual interest rate is 0.018, or 1.8%.

Step-by-step explanation:

Let r be the annual interest rate, t be the number of years the money was in the account, and I be the amount of interest earned. Since the interest is simple interest, the amount of interest earned is given by the formula I = Prt, where P is the principal, or initial amount deposited. In this case, we know that P = $3000, t = 3.5 years, and I = $262.50. Substituting these values into the formula, we get:

262.50 = 3000r * 3.5

r = 0.018

Thus, the annual interest rate is 0.018, or 1.8%.

The value of y is 9 in the graph where y is 3x.

We must use the equation y = 3x.

To locate the point on the graph that represents the price of three pounds of meat

As a result, when x = 3,

y = 3 × 3

i.e. y = 9

So, the price of 3 pounds of meat is represented by the following point on the graph is point B

The graph in the question is attached below.

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Step-by-step explanation:

a)Perimeter of a Rectangle = [tex]2 (l+w)=2(24+15)=78[/tex]

Circumference of a circle = [tex]\frac{\pi d}{2}[/tex]

= [tex]\frac{3.14X24}{2} \\= \frac{75.36}{2} \\= 37.68[/tex]

Perimeter of the whole figure = [tex]15 + 15 + 24 + 37.68= 91.68cm[/tex]

b) Area of the rectangle =[tex]wl=15X24=360[/tex]

Area of a semi circle = [tex]\frac{\pi }{2} Xr^{2}[/tex]

= [tex]1.57[/tex] x [tex]12X12[/tex]

=[tex]226.08[/tex]

Area of the whole figure = [tex]360 + 226.08[/tex]

= [tex]586.08[/tex][tex]cm^{2}[/tex]

Hope it helps

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The graph of x = 3et cos(t), y = 3et sin(t), 0 ≤ t ≤ π is shown below.

In this question we have been given two curves  x = 3e^t cos(t), y = 3e^t sin(t), 0 ≤ t ≤ π

We need to graph the given curves.

First we find find few coordinates.

For t = 0,

x = 3e^0 cos(0)

x = 3 * 1 * 1

x = 3

and y = 3 * e^0 * sin(0)

y = 3 * 1 * 0

y = 0

For t = π,

x = 3 * e^π * cos(π)

x = 3 * 23.14 * (-1)

x = -69.42

and y = 3 * e^π * sin(π)

y = 3 * 23.14 * 0

y = 0

For x = π/2

x = 3 * e^π/2 * cos(π/2)

x = 3 * 4.81 * 0

x = 0

and y = 3 * e^π/2 * sin(π/2)

y = 3 * 4.81 * 1

y = 14.43

So, we have the coordinates (3, 0), (-69.42, 0) and (0, 14.43)

The graph of x = 3et cos(t), y = 3et sin(t) is as shown below.

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Yes, the starting position of these players form a perpendicular line.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Using Trigonometry

sin [tex]\theta[/tex] = 33.33/100

sin [tex]\theta[/tex] = 0.3333

[tex]\theta[/tex] = [tex]sin^{-1}[/tex] (0.3333)

[tex]\theta[/tex] = 19.469

cos 19.469 = B/ 100

0.9428 = B/ 100

B= 94.28

tan  [tex]\theta[/tex] = P/B

tan  [tex]\theta[/tex] = 94.28/ 33.33

[tex]\theta[/tex] = 70.5

Using Angle Sum property

< 3= 180 - (70.5 + 19.5)

<3 = 180 - 90

<3 = 90

Hence, they form perpendicular line.

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The 95% confidence interval for the true proportion of people who favor candidate is (0.419,0.481).

A random sample of 1000 people was condidered for testing.

Number of people in sample favoured candidate

= 450

So, sample proportion, p = 450/1000 = 0.45

Confidence level= 95% i.e, alpha = 1 - 0.95=0.05, From standard normal Z- table, the value of Z( 0.025) is equals to 1.96..

Confidence interval formula,

CL = p ± Z× √(p×(1-p)/n)

Lower bound of interval is ,

=0.45 - 1.96× √(0.45× (1-0.45)/1000)

= 0.45 - 1.96× √(0.45× 0.55/1000)

= 0.45 - 1.96× √(0.0002475)

=0.419165~ 0.419

So the Upper bound is

= p + Z×√(p×(1-p)/n)

= 0.45 + 1.96× √(0.45× (1-0.45)/1000)

= 0.45 + 1.96× √(0.0002475)

= 0.480835 ~0.481

Hence, the required confidence interval is (0.419,0.481).

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