Samuel does not live closer to school than Amy. Amy does not live closer to school than Dave. Samuel lives farther from school than Dave but closer to school than Grayson. Who lives the farthest from school?

Answer:

A . Isosceles

Step-by-step explanation:

An isosceles triangle has both two equal sides and two equal .

The number of  hours must you skate for the cost of renting and buying to be the same is 20 hours

Let x represent the number of hours

Hence:

40+1.50x=3.50x

Subtract 1.50x from both side

2x=40

Divide both side by 2

x=40/2

x=20

Inconclu sion The number of  hours must you skate for the cost of renting and buying to be the same is 20 hours

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1) The common-difference is -1.2.

2) The 15th term is 40.4.

3)The sum of the first 292 terms is 35,553.6.

1. The first term of an arithmetic sequence is 9, and the sixth term is 3. We need to find the common difference.

Using the formula for the nth term of an arithmetic sequence:

Tn = a + (n - 1)d

We can plug in the values:

T1 = 9

T6 = 3

n = 6

3 = 9 + (6 - 1)d

3 = 9 + 5d

-6 = 5d

d = -6/5

d = -1.2

The common difference is -1.2.

2.The 32nd term of an arithmetic sequence is 14.9, and the common difference is -1.5. We need to find the 15th term.

Using the formula for the nth term of an arithmetic sequence:

Tn = a + (n - 1)d

We can plug in the values:

T32 = 14.9

n = 32

d = -1.5

T32 = a + (32 - 1)(-1.5)

14.9 = a + 31(-1.5)

14.9 = a - 46.5

a = 14.9 + 46.5

a = 61.4

Now we can find the 15th term:

T15 = 61.4 + (15 - 1)(-1.5)

T15 = 61.4 + 14(-1.5)

T15 = 61.4 - 21

T15 = 40.4

The 15th term is 40.4.

3.The first term of an arithmetic sequence is 5, and the common difference is 0.8. We need to find the sum of the first 292 terms.

Using the formula for the sum of an arithmetic sequence:

Sn = (n/2)(2a + (n - 1)d)

We can plug in the values:

a = 5

n = 292

d = 0.8

Sn = (292/2)(2(5) + (292 - 1)(0.8))

Sn = 146(10 + 233.6)

Sn = 146(243.6)

Sn = 35,553.6

The sum of the first 292 terms is 35,553.6.

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1) The common difference in the arithmetic sequence is -1.2.

2) The 15th term of the arithmetic sequence is 40.4.

3) The sum of the first 292 terms of the arithmetic sequence is 28626.4.

4) The balance in the account after 5 years will be $13,760.

5) The balance in the account after 30 months will be $8,474.4.

6) The monthly payment amount will be $137.90

7) The simple annual interest rate charged by The Saver is 415%

Exp:

Question 1:

To find the common difference in an arithmetic sequence, we can use the formula:

common difference = (sixth term - first term) / (6 - 1)

In this case, the first term is 9 and the sixth term is 3. Plugging these values into the formula:

common difference = (3 - 9) / (6 - 1)

common difference = -6 / 5

common difference = -1.2

Therefore, the common difference in the arithmetic sequence is -1.2.

Question 2:

To find the 15th term of an arithmetic sequence, we can use the formula:

nth term = first term + (n - 1) * common difference

In this case, the 32nd term is given as 14.9, and the common difference is -1.5. Plugging these values into the formula:

14.9 = first term + (32 - 1) * (-1.5)

14.9 = first term + 31 * (-1.5)

14.9 = first term - 46.5

first term = 14.9 + 46.5

first term = 61.4

Now we can find the 15th term using the first term and the common difference:

15th term = first term + (15 - 1) * common difference

15th term = 61.4 + 14 * (-1.5)

15th term = 61.4 - 21

15th term = 40.4

Therefore, the 15th term of the arithmetic sequence is 40.4.

Question 3:

To find the sum of the first n terms of an arithmetic sequence, we can use the formula:

sum = (n/2) * (2 * first term + (n - 1) * common difference)

In this case, the first term is 5 and the common difference is 0.8. Plugging these values into the formula:

sum = (292/2) * (2 * 5 + (292 - 1) * 0.8)

sum = 146 * (10 + 233 * 0.8)

sum = 146 * (10 + 186.4)

sum = 146 * 196.4

sum = 28626.4

Therefore, the sum of the first 292 terms of the arithmetic sequence is 28626.4.

Question 4:

To calculate the balance in the account after a certain number of years with monthly interest payments, we can use the formula:

balance = principal * (1 + (interest rate / 100) * (number of months / 12))

In this case, the principal is $8,600, the interest rate is 12% (0.12 as a decimal), and the time is 5 years. Plugging these values into the formula:

balance = 8600 * (1 + (0.12 / 100) * (5 * 12 / 12))

balance = 8600 * (1 + 0.12 * 5)

balance = 8600 * (1 + 0.6)

balance = 8600 * 1.6

balance = 13760

Therefore, the balance in the account after 5 years will be $13,760.

Question 5:

To calculate the balance in the account after a certain number of months with monthly interest payments, we can use the formula:

balance = principal * (1 + (interest rate / 100) * (number of months / 12))

In this case, the principal is $6,284, the interest rate is

14% (0.14 as a decimal), and the time is 30 months. Plugging these values into the formula:

balance = 6284 * (1 + (0.14 / 100) * (30 / 12))

balance = 6284 * (1 + 0.14 * 2.5)

balance = 6284 * (1 + 0.35)

balance = 6284 * 1.35

balance = 8474.4

Therefore, the balance in the account after 30 months will be $8,474.4.

Question 6:

To calculate the monthly payment amount for a loan with a given principal, interest rate, and number of equal monthly payments, we can use the formula:

monthly payment = (principal + (principal * (interest rate / 100) * (number of months))) / number of months

In this case, the principal is $1,709, the interest rate is 182% (1.82 as a decimal), and the number of equal monthly payments is 16. Plugging these values into the formula:

monthly payment = (1709 + (1709 * (1.82 / 100) * 16)) / 16

monthly payment = (1709 + (1709 * 0.0182 * 16)) / 16

monthly payment = (1709 + (1709 * 0.2912)) / 16

monthly payment = (1709 + 497.3848) / 16

monthly payment = 2206.3848 / 16

monthly payment = 137.8993

Therefore, the monthly payment amount will be $137.90 (rounded to two decimal places).

Question 7:

To calculate the simple annual interest rate for a loan with a given principal, monthly payment amount, and number of months, we can use the formula:

interest rate = ((monthly payment * number of months) / principal - 1) * 100

In this case, the principal is $1,000, the monthly payment amount is $859, and the number of months is 6. Plugging these values into the formula:

interest rate = ((859 * 6) / 1000 - 1) * 100

interest rate = (5154 / 1000 - 1) * 100

interest rate = (5.154 - 1) * 100

interest rate = 4.154 * 100

interest rate = 415.4

Therefore, the simple annual interest rate charged by The Saver is 415% (rounded to the nearest whole number).

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To find out when John, Maria, and Bruce will all go to the clinic on the same day, we need to find the least common multiple (LCM) of the numbers 6, 8, and 12, which represents the number of days that will pass before they all meet at the clinic again.

First, we can list the multiples of each number until we find a common multiple:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, ...

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, ...

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

From these lists, we can see that the LCM of 6, 8, and 12 is 24. Therefore, John, Maria, and Bruce will all go to the clinic on the same day again in 24 days from February 17th, 2020.

To find out the exact date, we can add 24 days to February 17th, 2020:

February 17th + 24 days = March 12th, 2020

Therefore, John, Maria, and Bruce will all go to the clinic together again on March 12th, 2020.

Answer:

We can find the next time that John, Maria, and Bruce will all go to the clinic together by finding the least common multiple (LCM) of their visit frequencies.

The visit frequency of John is 6 days, Maria is 8 days, and Bruce is 12 days. To find the LCM, we can list out the multiples of each number until we find a common multiple:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120...

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120...

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120...

From the lists above, we can see that the next time they will all go to the clinic together is on the 24th day, which is the least common multiple of 6, 8, and 12. Therefore, John, Maria, and Bruce will all go to the clinic together again on March 12th, 2020 (since February only has 29 days in a leap year).

Step-by-step explanation:

Answer:

The length of the hypotenuse is  √113 units

Step-by-step explanation:

To find the length of the hypotenuse, we will simply use the distance formula

|d| = √  (x₂ - x₁)²   +   (y₂ -y₁)²

from the diagram, the points on the vertices of the hypotenuse are

(-4, -2)      and    (4,5)

x₁ =-4      y₁= -2         x₂  = 4        y₂ = 5

we can now proceed and insert the values into the formula

|d| = √  (x₂ - x₁)²   +   (y₂ -y₁)²

    = √  (4 + 4)²   +   (5 +2)²

   = √  (8)² + (7)²

  = √ 64+49

  = √113    units

Therefore, the length of the hypotenuse is  √113 units

The equations of nonlinear functions from the options are y = x² + 3 and y = 3/x - 10

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

The list of options

As a general rule:

Using the above as a guide, we have the following as nonlinear functions

y = x² + 3

y = 3/x - 10

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The magnitude of a number is the absolute value of the the number .Therefore, the magnitude of - 5.8 can be express below

The answer is B.

(a) The doubling time of the population is approximately 13.86 years., (b) It takes approximately 23.10 years for the population to triple in size, (c) It takes approximately 27.72 years for the population to quadruple in size.

To calculate the doubling time of the population, we need to find the time it takes for the population to double from its initial value. In this case, the initial population is 9 million.

(a) Doubling Time:

Let's set up an equation to find the doubling time. We know that when the population doubles, it will be 2 times the initial population.

2P(0) = P(t)

Substituting P(t) = 9e^(0.05t), we have:

2 * 9 = 9e^(0.05t)

Dividing both sides by 9:

2 = e^(0.05t)

To solve for t, we take the natural logarithm (ln) of both sides:

ln(2) = 0.05t

Now, we can isolate t by dividing both sides by 0.05:

t = ln(2) / 0.05

Using a calculator, we find:

t ≈ 13.86

Therefore, the doubling time of the population is approximately 13.86 years.

(b) Time to Triple the Population:

Similar to the doubling time, we need to find the time it takes for the population to triple from its initial value.

3P(0) = P(t)

3 * 9 = 9e^(0.05t)

Dividing both sides by 9:

3 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(3) = 0.05t

Isolating t:

t = ln(3) / 0.05

Using a calculator, we find:

t ≈ 23.10

Therefore, it takes approximately 23.10 years for the population to triple in size.

(c) Time to Quadruple the Population:

Similarly, we need to find the time it takes for the population to quadruple from its initial value.

4P(0) = P(t)

4 * 9 = 9e^(0.05t)

Dividing both sides by 9:

4 = e^(0.05t)

Taking the natural logarithm of both sides:

ln(4) = 0.05t

Isolating t:

t = ln(4) / 0.05

Using a calculator, we find:

t ≈ 27.72

Therefore, it takes approximately 27.72 years for the population to quadruple in size.

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Answer:

Y= 2x-28

Step-by-step explanation:

The volume of water in the cylindrical tank, we need to use the formula for the volume of a cylinder, which is V = πr^2h2h, Therefore  the volume of water in the tank is 78.54 cubic feet.

To calculate the volume of water in the cylindrical tank, we need to use the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

Since the tank is lying on its side, the radius is the same as the height. Therefore, we can use r for both values.

The depth of the water, which we'll call d, is the distance from the bottom of the tank to the surface of the water.

To find the volume of water in the tank, we need to find the height of the water in the tank, which is equal to the radius minus the depth: h = r - d.

Now we can substitute these values into the formula for the volume of a cylinder:

V = πr^2h
V = πr^2(r - d)
V = πr^3 - πr^2d

So the volume of water in the tank is equal to the volume of the cylinder minus the volume of the empty space above the water.

We don't have a specific value for the radius or the depth, so we can't calculate the volume exactly. But we can use the given values in the problem to write the formula in terms of those values:

V = π(radius)^3 - π(radius)^2(depth)

For example, if the radius of the tank is 5 feet and the depth of the water is 2 feet, then the volume of water in the tank is:

V = π(5)^3 - π(5)^2(2)
V = π(125) - π(50)
V = 78.54 cubic feet

Therefore, the volume of water in the tank is 78.54 cubic feet.

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Answer:

A is the best buy.

Step-by-step explanation:

A

All trees 42 dollars.

B

1 foot   6

7 1/2 feet = x

x = 7 1/2 * 6

x = 45

C

First 4 feet = 22

3 1/2 feet * 6 = 21

Total = 43

Answer:

It is A.

Step-by-step explanation:

Hope this helped have an amazing day!

We want to get the expected value for the given experiment, we will see that it is equal to -1/6 points, so the correct option is "negative one-sixth"

For an experiment with events {x₁, x₂, ..., xₙ}, each one with probability {p₁, p₂, ..., pₙ}, the expected value is given by:

EV = x₁*p₁ + ... + xₙ*pₙ

Here we have two events:

Let's find the probabilities of each one of these.

She gets 9 points if the sum of the two dice is equal to 8 or 12.

Each dice has 6 outcomes.

Then a combination of two dice has a total of 6*6 = 36 outcomes.

The outcomes that add to 8 or 12 are:

dice 1   dice 2  sum

2           6            8

3           5            8

4           4            8

5          6             8

6           2            8

6           6            12

So 6 out of the 36 outcomes, then the probability of this event is:

p₁ = 6/36 = 1/6

And the other event is for all the other outcomes, so the probability is just:

p₂ = 5/6

Then the expected value is:

EV = (+ 9 points)*(1/6) + (-2 points)*(5/6)  = -1/6 points.

So the correct option is negative one-sixth.

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Answer:

-1/6

Step-by-step explanation:

The number of different sets of officers possible is 1716 sets.

The number of sets of officers possible is the number of ways people can be chosen for the given posts.

Since there are 13 people available for the post of president,

The choice can be made in

13 ways.

For the post of the Vice-President, there are 12 likely candidates. Hence, the choice can be made in

12 ways

Similarly for the post of treasurer, there are 11 likely candidates available. Hence, the choice can be made in 11 different ways.

Hence, the total number of sets of officers possible are

13 X 12 X 11

= 1716 sets.

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Answer:

The temperature is -20 degrees.

Step-by-step explanation:

-10 + 30 = 20

20 - 40 = -20

Hope this helps!

The model's fit to the data is weak, indicated by a correlation coefficient of -0.34. There is a weak negative relationship between the variables, with the model's predictions being imprecise and scattered around the line of fit.

A relationship coefficient of - 0.34 shows a frail negative connection between's the factors in the information. This intends that as one variable expands, the other variable will, in general, diminish, however, the relationship isn't a serious area of strength for exceptionally.

The line of fit for the information recommends that there is a general pattern or example, however, it doesn't fit the information focuses intently. The scatterplot of the information would show focuses spread around the line, for certain focuses straying a considerable amount from it.

The model's capacity to foresee the specific upsides of the reliant variable in light of the free variable(s) is restricted. In outline, the attack of the model to the information isn't an area of strength for extremely, there is a frail negative connection between the factors.

The model's forecasts may not be profoundly precise, and there may be different elements or factors not caught by the model that impact the information.

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Answer:

Im pretty sure it's A because Z and AZ are collinear

Answer:

statement 1, 3 and 4

Step-by-step explanation:

Statements 1 and 4 are true because points Z, A, and X lie on the same line . Also, points W, A, and Y are collinear with A in between points W and Y. So, and  are opposite rays.

Answer:

A.

Step-by-step explanation:

Answer: A

Step-by-step explanation:

The value of the given expression is approximately 71.31.

\($$75 - 12(20 ÷ 2.5) ÷ 26$$\)

The Order of Operations states that the sequence of steps in which we carry out the operations of a given problem.

So, we follow the Order of Operations to solve this expression.

Firstly, we will evaluate the parentheses:

\($$20 ÷ 2.5 = 8$$\)

Now, the given expression becomes:

\($$75 - 12 × 8 ÷ 26$$\)

Then, we will evaluate multiplication and division in order from left to right.

12 × 8 = 96

So, the given expression becomes:

\($$75 - 96 ÷ 26$$\)

Evaluating division, we get:

\($$75 - 3.6923$$\)

Now, we will add and subtract from left to right.

\(75 − 3.6923 ≈ 71.31\)

Therefore, the value of the given expression is approximately 71.31.

So, the required  is approximately 71.31.

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Answer:

skewed to the left

Step-by-step explanation:

A histogram is used to represent data graphically. the histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval. the frequency is usually on the vertical axis while the class interval is usually on the horizontal axis.

If the mean is greater than the median, the histogram would be skewed to the right

If the mean is less than the median, the histogram would be skewed to the left.

The mean in this question is $46,200 while the median is $54,500. So, the histogram would be skewed to the left

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

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

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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Answer:

No Solution

Step-by-step explanation:

X can not equal more than its self.

Answer:

The answer is -285

Step-by-step explanation:

Answer:

The length of the parallelogram is 18 meters

The width of the parallelogram is 16 meters

Step-by-step explanation:

The perimeter of a parallelogram is 68 meters

LEt x be the length of the parallelogram

Width is 2 meters less than its length

Width =x-2

Perimeter of parallelogram = 2(length + width)

Perimeter of parallelogram =

=

Add 2 on both sides

Divide by 4 on both sides

x=18

The length of the parallelogram is 18 meters

The width of the parallelogram is 18-2= 16 meters

For the given signal \(x(t) = 4\sin(40\pi t) + 2\sin(100\pi t) + \sin(200\pi t)\), we are asked to plot the time-domain signal \(x(t)\) and the magnitude spectrum of its Fourier transform \(X(\omega)\).

To plot the time-domain signal \(x(t)\), we can calculate the values of the signal for different time instances and plot them on a graph. Since the signal is a sum of sinusoidal components with different frequencies, the plot will show the variations of the signal over time. The amplitude of each sinusoidal component determines the height of the corresponding waveform in the plot.

To plot the magnitude spectrum of the Fourier transform \(X(\omega)\), we need to calculate the Fourier transform of \(x(t)\). The Fourier transform will provide us with the frequency content of the signal. The magnitude spectrum plot will show the amplitude of each frequency component present in the signal. The height of each peak in the plot corresponds to the magnitude of the corresponding frequency component.

By plotting both \(x(t)\) and the magnitude spectrum of \(X(\omega)\), we can visually analyze the signal in both the time domain and the frequency domain. The time-domain plot represents the signal's behavior over time, while the magnitude spectrum plot reveals the frequency components and their amplitudes. This allows us to understand the signal's characteristics and frequency content.

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Critical values of the function f(θ) = 2cos(θ) +(sin(θ))² on the interval 0≤ θ < 2π is 0 and π.

Therefore, the answer is 0 and π.

f(θ) = 2cos(θ) +(sin(θ))²

f'(θ) = -2sin(θ) +2sin(θ)cos(θ)

Critical values of f are points at which f' is zero or not defined.

For all values of θ, we can find that f'(θ) is defined.

f'(θ) = 0

-2sin(θ) +2sin(θ)cos(θ) = 0

cos(θ) - 1 = 0 or sin(θ) = 0

cos(θ) = 1

θ = nπ, n = 0, 1, 2, ...

sin(θ) = 0

θ = nπ, n = 0, 1, 2, ...

Therefore in the interval 0 ≤ θ < 2π, critical values are 0 and π.

2π is not there as it is not included in the interval.

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Answer:

Yes because the total is 6 pieces and can be used for each to find the answer!

Explanation: My teacher said this was right :)

Based on the relationship between the number of orders served by Mary, Joe, and Deandre, the number of orders they each served was:

Assuming that the number of orders served by Mary was x, the formula for the total orders served would be:

Deandre's orders + Mary's orders + Joe's orders = 95
3x + x + (x - 10) = 95

Solving for Mary's orders gives:

3x + x + x - 10 = 95

5x - 10 = 95

5x = 95 + 10

x = 105 / 5

x = 21

Number of orders by Deandre:

= 21 x 3

= 63 orders

Orders by Joe:

= 21 - 10

= 11 orders

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important to know the size of the freshman classes in relation to the population size before using z-procedures in this situation, so the answer will be option C

In statistical inference, when using z-procedures such as hypothesis testing or constructing confidence intervals, one of the assumptions is that the samples are independent. In this scenario, knowing that the university had 6000 or more entering freshmen is important to ensure that the sample size is less than 10% of the population size.

The 10% condition is necessary to maintain the independence of samples. When the sample size is small relative to the population size, each sample observation has a greater impact on the population proportion, potentially violating the assumption of independence.

By ensuring that the sample size is less than 10% of the population size, we can reasonably assume that each sample observation is independent of each other. This allows us to use z-procedures and rely on the properties of the normal distribution for inference.

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