In 1995, wolves were introduced into Yellowstone Park.



The function `w\left(x\right)=14\cdot1.08^{x}` models the number of wolves, `w`, in the years since 1995, `x`.



Determine the value of `w(25)`.


What does this value say about the wolf population?

Answer:

C. (n+5)(n-5)

Step-by-step explanation:

Select the expression that is equivalent to (n²-25)

Let's check each option. A and B are wrong, so we only check C & D.

C. (n + 5) (n - 5)

n² - 5n + 5n - 25

n² - 25

D. (n - 5)²

(n - 5) (n - 5)

n² - 5n - 5n + 25

n² - 10n + 25

So, the correct answer is C. (n+5)(n-5)

Answer:

-1 - 6x = x - 15

Add 15 to both sides using the addition property of equality.

14 - 6x = x

14 = 7x

2 = x

D) -1 - 6x + 15 = x - 15 + 15

Answer and Step-by-step explanation:

Please refer to the photo for the solution!

Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

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The Math Club raised $400.

To find out how much money the Math Club raised, we need to determine the percentage of the total amount raised that corresponds to the Math Club's portion.

Let's assume the Math Club raised "x" amount of money. The total amount raised by all five clubs is $2000.

According to the incomplete circle graph, the Math Club's percentage is missing, but we know the percentages for the other clubs: Computer Club raised 15%, Gardening Club raised 18%, Art Club raised 30%, and Spanish Club raised 17%.

To find the missing percentage for the Math Club, we subtract the percentages of the other clubs from 100%:

Missing percentage = 100% - (15% + 18% + 30% + 17%) = 100% - 80% = 20%

Now we can set up a proportion to determine the amount raised by the Math Club:

(x / $2000) = 20% / 100%

Cross-multiplying:

x = ($2000 * 20%) / 100%

Simplifying:

x = $400

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The equation of the line parallel to the line passing through (1, -2) and (-4, 3) and passing through the point (-4, -5) is y = -x - 9 in slope-intercept form.

To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use it to construct the equation of the parallel line.

First, let's calculate the slope of the given line passing through points (1, -2) and (-4, 3). The slope, denoted as m, can be found using the slope formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates, we have:

m = (3 - (-2)) / (-4 - 1) = 5 / (-5) = -1

Now that we have the slope, we can use it to construct the equation of the parallel line.

We'll use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line.

We'll use the point (-4, -5) on the parallel line:

y - (-5) = -1(x - (-4))

y + 5 = -1(x + 4)

Simplifying further:

y + 5 = -x - 4

y = -x - 9

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After 300 trials, the experimental probabilities may not align perfectly with the theoretical probabilities. However, with more trials, the experimental probabilities tend to converge towards the theoretical probabilities for closer alignment.

To examine whether experimental probabilities after 300 trials align closely with theoretical probabilities, let's consider an example of flipping a fair coin.

Theoretical probability: When flipping a fair coin, the theoretical probability of obtaining heads or tails is 0.5 each. This assumes that the coin is unbiased and has an equal chance of landing on either side.

Experimental probability: After conducting 300 trials of flipping the coin, we record the outcomes and calculate the experimental probabilities. Let's assume that heads occurred 160 times and tails occurred 140 times.

Experimental probability of heads: 160/300 = 0.5333

Experimental probability of tails: 140/300 = 0.4667

Comparing the experimental probabilities to the theoretical probabilities, we can observe that the experimental probability of heads is slightly higher than the theoretical probability, while the experimental probability of tails is slightly lower.

In this particular example, the experimental probabilities after 300 trials do not align perfectly with the theoretical probabilities. However, it is important to note that these differences can be attributed to sampling variability, as the experimental outcomes are subject to random fluctuations.

To draw a more definitive conclusion about the alignment between experimental and theoretical probabilities, a larger number of trials would need to be conducted. As the number of trials increases, the experimental probabilities tend to converge towards the theoretical probabilities, providing a closer alignment between the two.

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The question probable may be:

Do experimental probabilities after 300 trials tend to align closely with theoretical probabilities? Consider an example scenario and calculate both the theoretical and experimental probabilities to determine if they are close.

Answer:

slope = - [tex]\frac{3}{2}[/tex] , y- intercept = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

3x + 2y = 14 ( subtract 3x from both sides )

2y = - 3x + 14 ( divide through by 2 )

y = - [tex]\frac{3}{2}[/tex] x + 7 ← in slope- intercept form

with slope m = - [tex]\frac{3}{2}[/tex] and y- intercept c = 7

Answer:

Therefore, the correct answer is: x < 23.

Step-by-step explanation:

To solve the inequality x - 5 + 2 < 20, we can simplify it step by step:

x - 5 + 2 < 20

Combine like terms:

x - 3 < 20

Add 3 to both sides of the inequality:

x - 3 + 3 < 20 + 3

Simplify:

x < 23

The solution to the inequality is x < 23.

Therefore, the correct answer is: x < 23.

Answer and Step-by-step explanation:

Please see the photo for the solution :)

Answer:

B

Step-by-step explanation:

Yes, because for each input there is exactly one output. You can have two of the same x values but you cannot have 2 of the same y values. if you have two of the same y values, it is not a function as it doesn't pass the vertical line test.

The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192

The formula for hourly wage can be presented as follows;

Hourly wage  = Total earnings/Total hours worked

The question in the link is presented as follows;

Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid

The amount Jaxon gets paid per hour (his hourly wage) = $6

The number of hours he works each day = 8 hours

The number of days Jaxon works = Four days

The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days

Therefore we get;

Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192

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Answer:

19, 14, 38

Step-by-step explanation:

Let x, y, and z be each number respectively:

[tex]x+y+z=71\\z=2x\\y=x-5\\\\x+y+z=71\\x+(x-5)+2x=71\\2x-5+2x=71\\4x-5=71\\4x=76\\x=19\\\\y=x-5\\y=19-5\\y=14\\\\z=2x\\z=2(19)\\z=38[/tex]

Therefore, the three numbers are 19, 14, and 38.

Answer:

In summary, the faster cyclist cycles at a speed of 18 mi/h since they travel 36 of the 54 miles in 2 hours while cycling twice as fast as the slower cyclist.

Explanationn:

The two cyclists are 54 miles apart and heading toward each other.

One cyclist cycles 2 times as fast as the other. We will call the faster cyclist A and the slower cyclist B.

They meet 2 hours after starting. This means they travel a total distance of 54 miles in 2 hours.

Since cyclist, A cycles 2 times as fast as cyclist B, cyclist A travels 2/3 of the total distance, and cyclist B travels 1/3 of the total distance.

In two hours, cyclist A travels (2/3) * 54 miles = 36 miles.

We need to find the speed of cyclist A in miles per hour.

Speed = Distance / Time

So the speed of cyclist A is:

36 miles / 2 hours = 18 miles per hour

Therefore, the speed of the faster cyclist is 18 mi/h.

a)  the value of the tractor after two years is $10,400.

b)  the value of the tractor after six years is $5,200.

To find the value of the tractor after a certain number of years, we can substitute the value of t into the equation v = -1,300t + 13,000.

a) After two years:

Substituting t = 2 into the equation, we get:

v = -1,300(2) + 13,000

v = -2,600 + 13,000

v = 10,400

Therefore, the value of the tractor after two years is $10,400.

b) After six years:

Substituting t = 6 into the equation, we get:

v = -1,300(6) + 13,000

v = -7,800 + 13,000

v = 5,200

Therefore, the value of the tractor after six years is $5,200.

To find when the tractor will have no value, we need to find the value of t when v = 0. We can set the equation v = -1,300t + 13,000 equal to 0 and solve for t:

-1,300t + 13,000 = 0

-1,300t = -13,000

t = -13,000 / -1,300

t = 10

Therefore, the tractor will have no value after 10 years.

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The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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The output value is feasible. The input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.

Jade decided to rent movies for a movie marathon over the weekend.

The function g(x) represents the amount of money spent in dollars, where x is the number of movies.

The given function is g(x) which represents the amount of money spent in dollars, where x is the number of movies.

The solution given is (6.5, $17.50).

We need to find whether the solution makes sense for the given function or not.

The input is given as 6.5 and the output is given as $17.50.

This means that Jade rented 6.5 movies and spent $17.50 on renting those movies.

To check whether the solution makes sense or not, we need to see if the input and output values are feasible or not.

The input value 6.5 is not a feasible value because it is not possible to rent half a movie.

Jade can rent 6 movies or 7 movies but not 6.5 movies.

Therefore, the input value is not feasible.

On the other hand, the output value $17.50 is a feasible value because it is possible for Jade to spend $17.50 on renting 6 movies.

The output value is feasible.

Since the input value is not feasible, the possible solution of (6.5, $17.50) does not make sense for this function. The correct answer is No. The input is not feasible.

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If Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

To represent the number of bags of pears, b, that Natalie sells at the Saturday market, we can use the following equation:

b = total_number_of_pears / pears_per_bag

In this equation, "total_number_of_pears" represents the total quantity of pears Natalie has, and "pears_per_bag" represents the number of pears she puts in each bag.

Given that Natalie has a total of 48 pears, we can substitute the value into the equation:

b = 48 / pears_per_bag

Now, we need to determine the number of pears she puts in each bag. The information provided states that Natalie sells bags of pears, and each bag is sold for $5. However, the specific number of pears per bag is not given. To proceed, we need this information.

Let's assume that Natalie puts 4 pears in each bag. We can substitute this value into the equation:

b = 48 / 4

Simplifying the equation gives:

b = 12

So, if Natalie puts 4 pears in each bag, she will be able to sell a total of 12 bags of pears at the Saturday market.

It's important to note that the specific value of "pears_per_bag" will affect the final result. If Natalie puts a different number of pears in each bag, the equation will yield a different number of bags sold.

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Answer:

A.

3.25x + 13.50 ≤ 40

Step-by-step explanation:

The statement "1 is NOT in the domain" is true because for the function f(x), the expression x - 7 results in division by zero when x equals 1, which makes 1 not a valid input for the function.

To determine if a value is in the domain of a function, we need to consider any restrictions or limitations on the input values.

For the function f(x) = √(x - 7), the square root function is defined only for non-negative values.

Therefore, the expression (x - 7) inside the square root must be greater than or equal to zero. In other words, x - 7 ≥ 0.

Solving this inequality, we find x ≥ 7.

This means that any value of x that is greater than or equal to 7 is in the domain of f(x).

However, the statement is asking specifically about the value 1.

Since 1 is less than 7, it does not satisfy the inequality x ≥ 7 and is therefore not in the domain of f(x).

Similarly, for the function g(x) = 4x - 8, there are no restrictions on the domain.

Any real number can be substituted into the function, including the value 1.

Therefore, the statement "1 isn't in the domain of f(0) g" is not accurate.

It is true that 1 is not in the domain of f(x), but it is in the domain of g(x).

In summary, the correct statement is that "1 is not in the domain."

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The angle C in the triangle is 34.05 degrees.

The sum of angles in a triangle is 180 degrees. The angle in a triangle can be found using cosine law as follows:

Therefore, let's find the unknown angle in the triangle as follows;

c² = a² + b² - 2ab cos C

Hence,

4² = 5² + 7² - 2 × 7 × 5 cos X

16 = 25 + 49 - 70 cos X

16 = 74 - 70 cos X

16  - 74 = -70 cos X

-58 = -70 cos X

cos X = 58 / 70

X = cos⁻¹ 0.82857142857

X = 34.0478785629

X = 34.05 degrees

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Answer:

y = (-1/6)x represents a proportional relationship.

The radius of the circle is 25 inches. The length of arc with a central angle of 138° is 115π/6 in

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

The length of an arc with a central angle Ф with circle radius (r) is given by:

Length of arc = (Ф/360) * 2πr

Given the length of arc as 115π/6 in and angle of 138°, hence:

Length of arc = (Ф/360) * 2πr

Substituting:

115π/6 = (138/360) * 2πr

r = 25 inches

The radius of the circle is 25 inches.

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a) Heather contributed $135,000 and Lesley contributed $150,000 to their accounts.

b) Heather's investment is approximately $273,714.17, while Lesley's investment is approximately $191,048.18 when they are 65 years old.

c) Heather has more money by approximately $82,665.99 at age 65.

a) To find out how much money Heather and Lesley contributed to their accounts, we need to calculate the total contributions made by each of them.

Heather:

Heather started investing at age 20 and stopped at age 65, contributing $3000 annually. The number of years she contributed is (65 - 20) = 45 years.

Total contributions by Heather = $3000 × 45 = $135,000.

Lesley:

Lesley started investing at age 40 and stopped at age 65, contributing $6000 annually. The number of years she contributed is (65 - 40) = 25 years.

Total contributions by Lesley = $6000 × 25 = $150,000.

Therefore, Heather contributed $135,000 and Lesley contributed $150,000 to their respective accounts.

b) To calculate the value of their investments at age 65, we can use the formula for compound interest:

Future Value = Principal × (1 + interest rate)^number of years

Heather:

Principal (initial investment) = $3000

Interest rate = 7.5% = 0.075 (converted to decimal)

Number of years = 65 - 20 = 45

Future Value of Heather's investment = $3000 × (1 + 0.075)^45

Lesley:

Principal (initial investment) = $6000

Interest rate = 7.5% = 0.075 (converted to decimal)

Number of years = 65 - 40 = 25

Future Value of Lesley's investment = $6000 × (1 + 0.075)^25

Calculating these values:

Future Value of Heather's investment = $3000 × (1.075)^45 ≈ $273,714.17

Future Value of Lesley's investment = $6000 × (1.075)^25 ≈ $191,048.18

c) To determine who has more money at age 65 and by how much, we compare the future values of their investments.

Heather's investment value at age 65 = $273,714.17

Lesley's investment value at age 65 = $191,048.18

Therefore, Heather has more money at age 65, and the difference in their investments is approximately $273,714.17 - $191,048.18 = $82,665.99.

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The value of the quadratic function y = x² - 4x + 3 is determined by substituting the given value of x into the equation and performing the necessary calculations.

1. Start with the quadratic function: y = x² - 4x + 3.

2. Determine the value of x for which you want to find the value of y.

3. Substitute the given value of x into the equation.

4. Perform the necessary calculations to simplify the expression.

5. Evaluate the expression to find the value of y.

For example, let's find the value of y when x = 2:

1. Start with the quadratic function: y = x² - 4x + 3.

2. We want to find the value of y when x = 2.

3. Substitute x = 2 into the equation: y = (2)² - 4(2) + 3.

4. Simplify the expression: y = 4 - 8 + 3.

5. Perform the necessary calculations: y = -1.

6. Therefore, when x = 2, the value of the quadratic function y = x² - 4x + 3 is -1.

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The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).

To determine the vertices of the image N'M'O' after reflecting triangle NMO over the line x = -1, we need to apply the reflection transformation to each vertex.

For a reflection over the line x = -1, we can find the image of a point (x, y) by finding its reflection as (2(-1) - x, y).

Applying this transformation to each vertex of triangle NMO, we get:

N' = (2(-1) - (-5), 2) = (5, 2)

M' = (2(-1) - (-2), 1) = (2, 1)

O' = (2(-1) - (-3), 3) = (3, 3)

The vertices of the image triangle N'M'O' are N'(5, 2), M'(2, 1), and O'(3, 3).

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The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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The probability that a cell phone will fail within 2 years is 0.4866.

The average lifetime of the cell phone is 6 years, so the decay rate is 1 / 6 = 0.1667.

The probability that a phone will fail within 2 years is given by:

[tex]P(x < 2) = 1 - e^{-0.1667 * 2} = 1 - 0.5134 = 0.4866[/tex]

Rounded to four decimal places, the probability is 0.4866.

Therefore, the probability that a cell phone will fail within 2 years is 0.4866.

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Answer:

Step-by-step explanation:

Answer$535.50

Step-by-step explanation:

15% is equal to .15

So, multiply 600.00x .15=90

                   600.00 - 90.0=510.
                   510. 00x .05=25.50

                   510.00+25.50=535.50

                   Your answer is $535.5