What is the area of this triangle in the coordinate plane?

6 units²

8 units²

24 units²

48 units²

If Pamela has registered for the first time, it will remain on the Do Not Call list permanently. If she has re-registered, it will remain on the list for an additional five years from the date of re-registration.

The length of time that Pamela's phone number will remain on the National Do Not Call Registry depends on whether she registered her number on the Do Not Call Registry for the first time or if she has re-registered her number after it has already been on the list for a while.

If Pamela registered her phone number for the first time, it will be added to the Do Not Call Registry within 31 days of her registration date. Her phone number will remain on the list permanently, unless she requests to remove it or the number is disconnected.

If Pamela has re-registered her phone number after it has already been on the list for a while, her number's registration will be extended for another five years from the date she re-registered it.

Therefore, if Pamela registered her phone number for the first time, it will remain on the list permanently. If she has re-registered her number, it will remain on the list for an additional five years from the date of re-registration.

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(−2,4) , (4,−4)

Use the midpoint formula to find the midpoint of the line segment.

(x1+x2 /2 , y1+y2 /2)

Substitute in the values for

(x1,y1) and (x2,y2).

((−2+4)/2, (4−4)/2)

Cancel the common factor of

−2+4 and 2.

Tap for more steps...

(−1+2, (4−4)/2)

Add −1 and 2.

(1,4−4/2)

Cancel the common factor of 4−4  and 2.

Tap for more steps...

(1,2−2)

Subtract 2 from 2.

(1,0)

Answer:

6

Step-by-step explanation:

x(4) - 7 = 17

4x - 7 = 17

4x = 17 + 7

4x = 24......... divide both sides by 4

x = 6

2x + 2y = 4xy is wrong

2x + 2y = 2(x+y) is correct

3x+4= 7x wrong

4x²+5x = 9x² wrong

3x²+3x²+4x = 6x² + 4x = 2x(3x + 2)

sorry I don't understand this one.....

-4(3x-5) = -12x + 20

Answer:

120

12 10

4 2 5 2

2 2

The probability that the students will be arranged in order from shortest to tallest is 1/(8!) or 1/40320.

Student is an individual who is enrolled in an educational institution such as a university, college, or a trade school. A student typically takes courses in order to further their knowledge and skills, to prepare for further education or training, or to receive credentials necessary to pursue a job or career. Students can include both full-time and part-time learners. Depending on the institution, a student may also be referred to as a pupil, student-athlete, or scholar. Students can also take part in a variety of student-led activities and organizations, both on-campus and off-campus.

This is because there are 8! (8 factorial) ways in which the students can be arranged in order from shortest to tallest.
Therefore, the probability of any one arrangement is 1/8!  
Thus, the probability of the students being arranged in order from shortest to tallest is 1/8! or 1/40320.

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Answer:

at least 115 feet (35m)

Step-by-step explanation:

Answer:

The answer is X=6

The expression of the inequality of John profit as per given details is given by  $80,000 ≤ $x ≤ $250,000.

Let us consider the John profit represented by $x.

As per first statement we have,

At least amount of $80,000 John must make to pay bills.

This implies ,

$80,000 is less than or equal to John’s profit.

⇒ $80,000 ≤ John  profit

⇒ $80,000 ≤ $x __(1)

Now, John’s profit is less than or equal to $250,000.

⇒John profit ≤ $250,000

⇒ $x ≤ $250,000 ___(2)

Combine (1) and (2) we get the inequality ,

$80,000 ≤ $x ≤ $250,000

Therefore, the expression used to represents the inequality of John profit is equal to  $80,000 ≤ $x ≤ $250,000.

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The given question is incomplete, I answer the question in general according to my knowledge:

John must make at least $80,000 to pay bills. That can be rephrased as $80,000 is less than or equal to John’s profit. You also know that John’s profit is less than or equal to $250,000 . Write the expression to represents the inequality.

The 99% confidence interval is, ( 314 , 358 )

Given that,

sample mean =  x = 334

sample standard deviation = s = 33

sample size = n = 16

Degrees of freedom = df = n - 1 = 16-1 = 15

At 99% confidence level the t is ,

α = 1 - 99% = 1 - 0.99 = 0.01

α / 2 = 0.01 / 2 = 0.005

t_α /2,df = t0.005,15 = 2.9467

Margin of error = E = t_α/2,df * (s /√n)

                              = 2.9467 * (33 / √16)

Margin of error = E = 24

The 99% confidence interval estimate of the population mean is,

x - E <u< x + E

334 - 24 < u < 334 + 24

310 < u < 358

so, we get,

The 99% confidence interval is,

( 314 , 358 )

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The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.

To find the maximum value of f(x), we can take the limit as x approaches infinity:

Answer:

in picture

Step-by-step explanation:

please like my answer

76.74 milligrams will remain after 32 hours.

N(t) = N₀e^(-kt)

where:

N(t) is the amount of substance remaining after time t

N₀ is the initial amount of substance

k is the decay constant

To solve for the decay constant, use the information given in the problem:

100 = 200e^(-22k)

Dividing both sides by 200, we get:

0.5 = e^(-22k)

Taking the natural logarithm of both sides, we get:

ln(0.5) = -22k

Solving for k, we get:

k = ln(0.5)/(-22) = 0.0316

Use this value of k to find the amount of substance remaining after 32 hours:

N(32) = 200e^(-0.0316*32) = 76.74 mg

Therefore, approximately 76.74 milligrams of the substance will remain after 32 hours.

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76.4 milligrams will remain after 32 hours.

Exponential refers to a mathematical function in which a constant base is raised to a variable exponent. The value of the function increases or decreases rapidly as the exponent increases, depending on whether the base is greater than 1 or between 0 and 1. Exponential functions are commonly used to model situations where a quantity grows or decays at a constant percentage rate over time.

Decay is the natural process of deterioration or rotting of a substance over time. It can occur in both organic and inorganic materials and is often caused by the activity of microorganisms, exposure to oxygen or other environmental factors.

To determine the amount of radioactive substance that remains after 32 hours, we can use the formula A = A₀ ×[tex]e^{-kt}[/tex], where A is the amount remaining, A₀ is the initial amount, k is the decay constant, and t is the time elapsed.

we can use the same formula for exponential decay to find the value of k:

100 = 200 × [tex]e^{(-k*22)}[/tex]

0.5 = [tex]e^{(-k*22)}[/tex]

ln(0.5) = -k×22

k = ln(2)/(22)

Now we can use this value of k to find the amount of substance remaining after 32 hours:

N(32) = 200 [tex]e^{(-k*32)}[/tex]

N(32) = 200 [tex]e^{(-(ln(2)/(22))32)}[/tex]

N(32) ≈ 76.4 mg

Therefore, approximately 76.4 milligrams of the substance will remain after 32 hours.

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y = 6 sin [(π/10)t] + 8; equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.

A sinusoidal function is a mathematical function that oscillates or fluctuates in a periodic manner, following a sine or cosine curve.

If the wave approaches a dock in Carmel where the normal depth is 8 meters and varies sinusoidal with time, then we can use the equation for a sinusoidal function:

y = A sin (ωt + φ) + C

where: A is the amplitude of the wave, which is given as 12 meters

ω is the angular frequency, which can be calculated as 2π / T, where T is the period of the wave (20 minutes in this case)

t is the time elapsed since the wave started passing the dock

φ is the phase angle, which we can assume to be 0 since we are not given any information about it

C is the vertical displacement of the wave from the normal depth, which is 8 meters in this case

putting the given values into the equation,

y = 12 sin [(2π/20)t] + 8

Simplifying this equation,

y = 6 sin [(π/10)t] + 8

This equation gives us the depth of the water at the dock as a function of time elapsed since the wave started passing the dock.

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The difference between these two amounts is $619.68

The monthly payment for a loan can be calculated using the formula:

monthly payment = [tex]\frac{(P * r * (1 + r)^n) }{((1 + r)^n - 1)}[/tex]

where P is the principal (the amount borrowed), r is the monthly interest rate, and n is the total number of months in the loan term.

For Miles' loan,

P = $5,000,

r = 0.0775/12,

and n = 4 * 12 = 48.

Plugging these values into the formula, we get:

monthly payment = [tex]\frac{(5000 * 0.0775/12 * (1 + 0.0775/12)^{48})}{ ((1 + 0.0775/12)^{48} - 1) }[/tex]

= $123.37

For Nick's loan,

P = $5,000,

r = 0.1310/12,

and n = 4 * 12 = 48.

Plugging these values into the formula, we get:

monthly payment =[tex]\frac{ (5000 * 0.1310/12 * (1 + 0.1310/12)^{48})}{((1 + 0.1310/12)^{48} - 1) }[/tex]

= $143.34

To find out how much more Nick will have paid than Miles over the four-year period, we can subtract Miles' total payments from Nick's total payments.

Miles will make 48 payments of $123.37, for a total of:

$123.37 * 48 = $5,920.76

Nick will make 48 payments of $143.34, for a total of:

$143.34 * 48 = $6,540.32

The difference between these two amounts is:

[tex]6,540.32 - 5,920.76 = 619.56[/tex]

Rounding this to the nearest cent, we get $619.68. Therefore, the answer is (a) $619.68.

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Answer:200.734

Step-by-step explanation:

150(1+0.06)^t

t=number of years

150(1.060)^5

200.73383664

round

200.734

The balance of this account after 5 years is $200.73

Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by

Amount = [tex]P(1+r/n)^n^t[/tex] where P = Principal, r = annual rate of interest, n = number of times interest is compounded per year, & t = time in years.

The given principal is $150 for 5 years & annual interest rate is 6%.

To find the amount compunded annualy at 6% for 5 years substituting the given values in the above formula i.e.

Amount =  [tex]P(1+r/n)^n^t[/tex]

Amount = $[tex]150(1+0.06)^5[/tex]

Amount = $200.73

Hence, the total amount accumulated for 5 years will be $200.73

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As this is a contradiction, the system cannot be solved. The parallel lines of the two equations do not intersect.

A mathematical expression called and equation demonstrates the parity of two factors or values. It typically includes exponents, parameters, constants, and mathematical like addition, subtraction, multiplication, and division. Finding an unknown variable's value or expressing a correlation between a number of variables is the goal of an equation. To simulate real-world occurrences and address issues, equations are utilised in many mathematical areas, science, and engineering. Systems of equations, linear equations, and quadratic equations are a few types of equations.

given

We can multiply the first equation by two and then add the second equation to the system to find the solution via elimination. This results in:

[tex]2(x - 3y = 7) = 2x - 6y = 14\\2x - 6y = 12[/tex]

To remove x, we may now subtract the second equation from the first equation:

[tex](2x - 6y = 14) - (2x - 6y = 12) = 0[/tex]

That amounts to:

0 = 2

As this is a contradiction, the system cannot be solved. The parallel lines of the two equations do not intersect.

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The numerical measure of linear association is b. correlation coefficient.

The correlation coefficient is a statistical measure that represents the degree of linear relationship between two variables. It takes values between -1 and 1, where -1 represents a perfect negative linear correlation, 0 represents no linear correlation, and 1 represents a perfect positive linear correlation.

A positive correlation means that when one variable increases, the other variable also tends to increase, while a negative correlation means that when one variable increases, the other variable tends to decrease.

The correlation coefficient is calculated using the formula:

[tex]r = (nΣxy - ΣxΣy) / sqrt[(nΣx^2 - (Σx)^2)(nΣy^2 - (Σy)^2)][/tex]

where r is the correlation coefficient, n is the sample size, Σxy is the sum of the products of the corresponding values of x and y, Σx and Σy are the sums of x and y respectively, and Σx^2 and Σy^2 are the sums of the squares of x and y respectively.

In summary, the correlation coefficient is a measure of the strength and direction of the linear association between two variables.

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Below is the correct matching of the questions to the right answers

The statistical measures listed in the previous question are often used to describe and analyze statistical variables.

For instance, the range of a data set is a measure of the spread of values in a variable, while the quartiles and interquartile range provide information about the distribution of the variable. Mean average deviation is a measure of the variability of the variable around its mean value.

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1. Mean average deviation - The average deviation of the data from the mean.

2. Range of a data set - The difference between the highest value and the lowest value in a numerical data set.

3. First quartile - The median in the upper half of the rank-ordered data.

4. Second quartile - The median value in the data set.

5. Third quartile - The median in the lower half of the rank-ordered data.

6. Interquartile range - he distance between the first and third quartiles of the data set.

The statistical measures are often used to describe and analyze statistical variables. For instance, the range of a data set is a measure of the spread of values in a variable, while the quartiles and interquartile range provide information about the distribution of the variable. Mean average deviation is a measure of the variability of the variable around its mean value.

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Answer:

D. y ≥ x² - 4x - 5

Step-by-step explanation:

We can observe two characteristics of this graphed inequality:

1. its shading is above it, therefore the inequality sign must be greater than

2. its boundary line is continuous, not dotted, so the inequality sign must include or equal to

From these two observations, we can assert that D. x² - 4x - 5 is the correct answer because it is the only one which has a greater than or equal to sign.

____________

Note:

We can also check that the equation for the inequality is correct by converting it to vertex form by completing the square, then graphing it ourselves:

[tex]y \ge (x-2)^2 - 9[/tex]

Answer:

The answer is y≥ x²-4x-5

Step-by-step explanation:

x=a,x=b

where a,b are roots of the equation

a= -1 b=5

x= -1,x=5

x+1=0,x-5=0

(x+1)(x-5)=0

x²-5x+x-5=0

x²-4x-5=0

Answer: 9m

Step-by-step explanation:

there is one “m” in each and there is a 9 in both number. (9*2=18), (9*3=27)

Assuming that the marbles are either green or not green and that the probability of picking a green marble is constant on every trial, we can use probability to make a prediction.

Let p be the probability of picking a non-green marble on one trial, then the probability of picking a green marble is 1 - p.

Since we pick marbles with replacement, each trial is independent of the others, and the probability of picking a non-green marble is the same for every trial.

The number of times we pick a non-green marble in 42 trials follows a binomial distribution with parameters n = 42 and p.

The expected value (or mean) of a binomial distribution is given by np, so in this case, the best prediction for the number of times we will pick a non-green marble is:

42 * p

We don't know the value of p, but if we assume that the probability of picking a non-green marble is 1/2 (i.e., the marbles are evenly split between green and non-green), then the best prediction for the number of times we will pick a non-green marble is:

42 * (1/2) = 21

Therefore, the best prediction possible for the number of times you will pick a marble that is not green is 21.

The value of the minimum tension and maximum tension for the interval of [-10,10] in the cable is equal to 40 N and 440529.32N respectively.

Function is equal to,

T = 200 (e^x/10 + e^-x/10).

Simplify it,

⇒T = 20 (e^x + e^-x).

The minimum and maximum of the function T(x) in a given interval [-10,10] for x,

First calculate the derivative of the function T(x) with respect to x and equate it to zero.

⇒ T'(x) = 20 (e^x - e^-x)

⇒20 (e^x - e^-x) =0

⇒20e^-x( e^(2x) - 1 ) = 0

⇒ 20 ≠ 0 , e^-x ≠ 0 for any x

⇒ e^(2x) - 1 =0

⇒e^(2x) = 1

⇒ 2x = log1

⇒ x = 0

Plugin the value of x into the function T, we have

200 (e^0/10 + e^-0/10)

⇒T = 200(1/10 + 1/10)

⇒ T =200(1/5)

⇒T = 40 N  is the minimum tension.

T(x) is symmetric at y-axis.

If x→∞ or x → (-∞) then T(x)→∞.

This implies,

The maximum value of T(x) is at x=±10

T= 200(e^10/10 + e^-10/10)

⇒T = 20 (e^10 + e^-10)

⇒T = 20 × 22026.4658

⇒T = 440529.32N is the maximum tension.

Therefore, minimum and maximum tension if the cable extends from x = 10 to x = -10 meter's is equal to 40 N and 440529.32N respectively.

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Jamal ought to utilize a histogram to display the information regarding the amount of steps he takes each day.

The complete set of people or things that we are interested in investigating is referred to as a population in statistics. We want to examine and draw conclusions from the entire set of facts. For instance, all adult women in a country would represent the population if we were interested in measuring the average height of adult women there.

In contrast, a sample is a smaller portion of the population that is chosen for analysis. When measuring the entire population is neither practicable or practical, this method is utilised.

Jamal ought to utilise a histogram to display the information regarding the amount of steps he takes each day. A histogram is a form of graph that shows how continuous data, such the number of steps, are distributed. It divides the data into intervals or "bins" and displays how frequently data points fall into each bin. Jamal may detect the usual or central trend of his daily step count as well as any fluctuation or outliers in the data by examining the shape of the histogram.

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Answer:

189

Step-by-step explanation:

27,006 / 42

= [tex]\frac{27}{6/42}[/tex]

= [tex]\frac{27}{\frac{1}{7} }[/tex]

= 27 x 7

= 189

So, the answer is 189

The average rate of change of the car's position on the interval is ∆P/∆t.

To find the average rate of change of the car's position on the interval, follow these steps:

Identify the interval: First, determine the specific interval for which you need to find the average rate of change (e.g.,

between times t1 and t2).

Calculate the change in position:

Determine the car's position at both the beginning and end of the interval (e.g., positions P1 and P2).

Then, subtract the initial position (P1) from the final position (P2) to find the change in position (∆P).

Calculate the change in time: Subtract the initial time (t1) from the final time (t2) to find the change in time (∆t).

Calculate the average rate of change: Divide the change in position (∆P) by the change in time (∆t) to find the average

rate of change.

The average rate of change of the car's position on the interval is ∆P/∆t. Include units in your answer (e.g., meters per

second or miles per hour) to indicate the car's rate of change in position.

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Answer:

-3

Step-by-step explanation:

To find the slope (m) of the line that passes through Point A(3, -9) and the origin (0, 0), we can use the formula:m = rise/run = (change in y)/(change in x)We can calculate the change in y and change in x as follows:

Change in y = y2 - y1 = 0 - (-9) = 9

Change in x = x2 - x1 = 0 - 3 = -3

Substituting these values into the formula, we get:

m = rise/run = 9/-3 = -3

Therefore, the slope of the line that passes through Point A(3, -9) and the origin is -3.

45 Distinct handshakes took place when every player shook hands with everyone who played.

To find out how many distinct handshakes took place if every player shook hands with everyone who played, we will

use the concept of combinations.

Identify the number of players involved, which is 10 (you plus 9 friends).

Use the formula for combinations: C(n, k) = n! / [k! × (n-k)!],

where n is the total number of players and k is the number of players in each handshake (which is 2).

Plug in the values: C(10, 2) = 10! / [2! × (10-2)!].

Calculate the factorial values: 10! = 3,628,800, 2! = 2, and 8! = 40,320.

Plug in the factorial values and calculate: C(10, 2) = 3,628,800 / (2 × 40,320) = 3,628,800 / 80,640 = 45.

So, 45 distinct handshakes took place when every player shook hands with everyone who played.

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The perimeter of the window is 102.8cm²

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

First, we will establish that the shape of the window is a semi-circle.

This means we must use the formula for the perimeter of a semi-circle to obtain the perimeter of the window.

The formula for the perimeter of a semi-circle is as follows:

Let the perimeter of a window or semi-circle = P

P = [ 2πr / 2 ] + 2r

Where r = radius of circle or semi-circle

From this, we will simply use the value of the radius given from the diagram in the problem and substitute it into the formula to obtain the perimeter of the window.

P = [ 2πr / 2 ] + 2r

r = 20

So,

P = [ 2π( 20 ) / 2 ] + 2( 20 )

P = 20π + 40

P = 102.83...cm²

P = 102.8cm² ( to the nearest tenth )

Therefore, the perimeter of the window is 102.8cm²

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the simplified  form  of expression is: -(x² + 2x - 2)/((x+2)*(x+4))

what is expression  ?

In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that represents a mathematical quantity or relationship. Expressions can be simple or complex

In the given question,

To evaluate the expression 1/(x+2) - (x+1)/(x+4), we need to find a common denominator for the two terms. The least common multiple of (x+2) and (x+4) is (x+2)(x+4).

So, we can rewrite the expression as:

(1*(x+4) - (x+1)(x+2))/((x+2)(x+4))

Expanding the brackets, we get:

(x+4 - x² - 3x - 2)/((x+2)*(x+4))

Simplifying the numerator, we get:

(-x² - 2x + 2)/((x+2)*(x+4))

Therefore, the simplified expression is:

-(x² + 2x - 2)/((x+2)*(x+4))

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The Don Antonio's profit is 2196.10 - 2196.10 = $35.

The profit that Don Antonio will make from selling his strawberry packages, we need to first calculate how many packages he can make from his two boxes of strawberries.

The first box of strawberries weighs 3.8 kg and the second box weighs 57/2 kg.

The total weight of the strawberries, we need to add these two weights together, which gives us a total of 17.5 kg.

We then need to divide this total weight by 3/4 kg, which is the weight of each package, to get the number of packages that Don Antonio can make.

This gives us a total of 23 packages.

Next, we need to calculate the total cost of the packages.

Since each package costs $95.70, this means that the total cost of the packages is 95.70 x 23 = $2196.10.

Finally, we need to subtract this total cost from the total revenue that Don Antonio will make from selling the packages.

Since each package is sold for $95.70, this means that the total revenue is 95.70 x 23 = $2196.10.

2196.10 - 2196.10 = $35.

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