The function f(t)=350(1. 2)^{365t}f(t)=350(1. 2)


365t


represents the change in a quantity over t years. What does the constant 1. 2 reveal about the rate of change of the quantity?

Answer:

B, A, C

Step-by-step explanation:

The rate is the another name for the slope.

A:

Change in y over the change in x.  You find the change by subtracting

[tex]\frac{7-3}{5-3}[/tex] = [tex]\frac{4}{2}[/tex] = 2

The rate is 2.

B:

Change in y over the change in x. You find the change by subtracting.

[tex]\frac{0-3}{-5-0}[/tex] = [tex]\frac{-3}{-5}[/tex] = [tex]\frac{3}{5}[/tex]

The rate is [tex]\frac{3}{5}[/tex].

C:

The rate is the number before the x in the equation.

The rate is 3.

Helping in the name of Jesus.

Answer: C. 54cm^2

Step-by-step explanation:

Break the shape into 2 pieces and multiply the sides. ex. 12 by 2 and 8 by 5 and then add the 2 answers to get 54cm

From the function f(x,y)=y⁵ ln(−2x⁴+3y⁵).  The value of  fx = -10x³y⁵ / (-2x⁴ + 3y⁵) and

fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]

To find fx, we differentiate f(x,y) with respect to x, treating y as a constant:

fx = d/dx [y⁵ ln(-2x⁴ + 3y⁵)]

Using the chain rule and the derivative of ln u = 1/u, we have:

fx = y⁵ * 1/(-2x⁴ + 3y⁵) * d/dx [-2x⁴ + 3y⁵]

Simplifying and applying the power rule of differentiation, we get:

fx = -10x³y⁵ / (-2x⁴ + 3y⁵)

Similarly, to find fy, we differentiate f(x,y) with respect to y, treating x as a constant:

fy = d/dy [y⁵ ln(-2x⁴ + 3y⁵)]

Using the chain rule and the derivative of ln u = 1/u, we have:

fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]

Applying the power rule of differentiation and simplifying, we get:

fy = 15y⁴ ln(-2x⁴ + 3y⁵)

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Angela made $350 per week 25 years ago and Walker made $200 per week 25 years ago.

Let's assign variables to represent Angela and Walker's salaries 25 years ago. Let A be Angela's salary 25 years ago and W be Walker's salary 25 years ago.

Using the information given in the problem, we can set up two equations:

A + W = 550 (their total salary 25 years ago)
4A + 3W = 2000 (their total current salary)

To solve for A and W, we can use substitution or elimination. Let's use substitution.

From the first equation, we can rearrange to solve for A:

A = 550 - W

Substitute this into the second equation:

4(550 - W) + 3W = 2000

Distribute the 4:

2200 - 4W + 3W = 2000

Simplify:

W = 800

Now that we know Walker's salary 25 years ago was $800, we can plug that into the first equation to solve for Angela's salary:

A + 800 = 550

A = -250

Uh oh, a negative salary doesn't make sense in this context. We made a mistake somewhere.

Let's go back to our original equations and try elimination instead:

A + W = 550
4A + 3W = 2000

Multiplying the first equation by 4, we get:

4A + 4W = 2200

Subtracting the second equation from this, we get:

W = 200

Now we can plug this into either equation to solve for A:

A + 200 = 550

A = 350

So Angela made $350 per week 25 years ago and Walker made $200 per week 25 years ago.

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Answer:

-----------------------

Given:

(i) We know 60 out of 110 can speak both languages, so as 60 out of 85. The number 60 is counted twice if we add them together.

Find the number of those speak either language:

(ii) Find the number of thise who can talk neither of these languages:

The table of values in a graph for fabian's income in expenses is

n            E(n)

0           825

1            828.25

2           831.5

4          838

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

The expenses E to make n cakes per month is given by the equation

E = 825 + 3.25n

Next, we assume values for n and calculate E

Using the above as a guide, we have the following:

E = 825 + 3.25(0) = 825

E = 825 + 3.25(1) = 828.25

E = 825 + 3.25(2) = 831.5

E = 825 + 3.25(4) = 838

So, we have

n            E(n)

0           825

1            828.25

2           831.5

4          838

This represents the table of values

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The class will use 20 yards of the 50-yard spool, leaving 30 yards of string leftover.

This leftover string could be used for future projects or saved for another occasion.

Lacey's class will use a total of 720 inches (30 inches per student x 24 students) of string for the candy necklaces.

To convert this to yards, we divide by 36 (since there are 36 inches in a yard). 720 inches ÷ 36 = 20 yards

It's important to note that when working with different units of measurement, it's necessary to convert them to the same unit before performing calculations.

In this case, we converted inches to yards in order to determine the amount of string used by the class. By doing so, we were able to determine how much string was leftover in yards, which is a more appropriate unit of measurement for a spool of string.

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Answer:

In triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is triangle. If m∠ABC = 40°, then the triangle is triangle. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC =

Answer:

52 degrees

Step-by-step explanation: because i looked and they looked the same so i put 52 and it was right

Answer:

the diameter is 14 and the perimeter is 43.97

The equation y=−4(5)x y = − 4 ( 5 ) x can be simplified to y = -20x. This equation is a linear function with a slope of -20. As x increases, y decreases at a rate of 20 units for every one unit increase in x. Therefore, the value of y will decrease rapidly as x increases.

The optimization problem has a maximum value of P when x = 13 and y = 6.5. The maximum value of P = 13 * 6.5 = 84.5.

To solve the optimization problem and maximize P = xy with the constraint x + 2y = 26, follow these steps:

1. Express one variable in terms of the other using the constraint: x = 26 - 2y

2. Substitute the expression for x into the objective function P: P = (26 - 2y)y

3. Differentiate P with respect to y to find the critical points: dP/dy = 26 - 4y

4. Set the derivative equal to zero and solve for y: 26 - 4y = 0 => y = 6.5

5. Plug the value of y back into the expression for x: x = 26 - 2(6.5) => x = 13

6. Check the second derivative to confirm it's a maximum: d²P/dy² = -4 (since it's a constant negative, this confirms it's a maximum)

Thus, the optimization problem has a maximum value of P when x = 13 and y = 6.5. The maximum value of P = 13 * 6.5 = 84.5.

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The area of the wheel is approximately 7.07 square feet.

The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. In this case, the diameter of the wheel is given as 3 feet, so the radius is half of that, which is 1.5 feet.

Substituting the value of the radius into the formula, we get A = π(1.5)^2. Simplifying this expression gives us approximately 7.07 square feet. Therefore, the closest answer to the area of the wheel is 7.07 square feet.

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Answer:

Step-by-step explanation:

The triangle area= 1/2 * the perpendicular height * breath

                           = 1/2*2*(3/4)

                          =0.75

The value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.

To evaluate the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex], where E is the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane, we can use cylindrical coordinates. In cylindrical coordinates, the equation of the paraboloid becomes:

[tex]z = 9 - (r^2)[/tex]

The limits of integration are:

0 ≤ r ≤ 3 (since the paraboloid intersects the xy-plane at z = 0 when r = 3)

0 ≤ θ ≤ 2π

0 ≤ z ≤ 9 - (r^2)

The triple integral becomes:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r√(r^2) dz dθ dr[/tex]

Simplifying, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r^2 dz dθ dr[/tex]

Evaluating the innermost integral, we get:

∫[tex]0^(9-r^2) r^2 dz = (9-r^2)r^2[/tex]

Substituting this back into the triple integral, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π (9-r^2)r^2 dθ dr[/tex]

Evaluating the remaining integrals, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 (9r^2 - r^4) dθ[/tex]

= 2π [243/5]

= 486π/5

Therefore, the value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] dV over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.

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The type of statistical study in which the population is influenced by researchers is known as an experimental study.

In an experimental study, researchers manipulate one or more variables to observe the effect on another variable. The population in an experimental study is usually a sample that is randomly selected to represent the larger population.

The researchers intentionally intervene in the study, which can impact the behavior or responses of the participants. This can be seen as a form of bias since the researchers are influencing the population. However, in some cases, this is necessary to determine causality or to test a hypothesis.

To minimize bias, experimental studies often use control groups. The control group is used to provide a baseline for comparison with the group that is exposed to the manipulated variable. This helps to determine if any observed effects are due to the intervention or if they are due to other factors.

In summary, an experimental study is the type of statistical study in which the population is influenced by researchers. While this can introduce bias, the use of control groups and other measures can help to minimize the impact of this bias on the results.

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Let's break down the information given in the problem:

- Jane became a real estate agent in 1990.

- She sold a house 8 years later (in 1998) for $144,000.

- She sold the same house 11 years after that sale (in 2009), which is 19 years after she became an agent, for $245,000.

To write an equation that represents the value of the house (V) related to the number of years (t) since Jane became a real estate agent, we can use the information from the two sales to find the rate of change in the value of the house over time. We can use this rate of change to write an equation in point-slope form:

V - V1 = m(t - t1)

where V1 is the value of the house at time t1, m is the rate of change in the value of the house, and t is the time since Jane became a real estate agent.

Using the two sales, we can find the rate of change in the value of the house as follows:

m = (V2 - V1) / (t2 - t1)

where V2 is the value of the house at the second sale, t2 is the time of the second sale (19 years after Jane became an agent), V1 is the value of the house at the first sale, and t1 is the time of the first sale (8 years after Jane became an agent).

Substituting the given values, we get:

m = ($245,000 - $144,000) / (19 - 8) = $10,100 per year

Now we can use the point-slope form equation to find the value of the house at any time t since Jane became a real estate agent. Let's choose 1990 as our initial time (t1), so V1 = $0:

V - 0 = $10,100 (t - 0)

Simplifying, we get:

V = $10,100t

Therefore, the equation that represents the value of the house (V) related to the number of years (t) since Jane became a real estate agent is V = $10,100t. Note that this equation assumes a constant rate of change in the value of the house over time, which may not be accurate in real life.

We know that the indicated probability is approximately 0.1210.

To use the normal approximation, we need to check if the conditions for a normal approximation are met. In this case, we have:

np = 81 * 0.5 = 40.5 ≥ 10
n(1-p) = 81 * 0.5 = 40.5 ≥ 10

Since both conditions are met, we can use the normal approximation to find the probability.

First, we need to find the mean and standard deviation of the sampling distribution of sample proportions:

mean = np = 81 * 0.5 = 40.5
standard deviation = sqrt(np(1-p)) = sqrt(81 * 0.5 * 0.5) = 4.5

Next, we need to standardize the value of x:

z = (x - mean) / standard deviation
z = (46 - 40.5) / 4.5 = 1.22

Finally, we can use a standard normal table or calculator to find the probability:

P(z ≥ 1.22) = 0.1118

Therefore, the answer is approximately 0.1210.

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a. To find the probability that there are no cars in the system, we need to use the formula for the steady-state probability distribution of the M/M/1 queue:
P(0) = (1 - λ/μ)
where λ is the arrival rate (2 per hour) and μ is the service rate (3 per hour).
P(0) = (1 - 2/3) = 1/3 or 0.3333
Therefore, the probability that there are no cars in the system is 0.3333.

b. To find the average number of cars in the system, we can use Little's Law:
L = λW
where L is the average number of cars in the system, λ is the arrival rate (2 per hour), and W is the average time spent in the system.
We can solve for W by using the formula:
W = 1/(μ - λ)
W = 1/(3 - 2) = 1 hour
Therefore, the average number of cars in the system is:
L = λW = 2 x 1 = 2 cars

c. To find the average time spent in the system, we already calculated W in part b:
W = 1 hour

d. To find the probability that there are exactly two cars in the system, we need to use the formula for the steady-state probability distribution:
P(n) = P(0) * (λ/μ)^n / n!
where n is the number of cars in the system.
P(2) = P(0) * (λ/μ)^2 / 2!
P(2) = 0.3333 * (2/3)^2 / 2
P(2) = 0.1111 or 11.11%
Therefore, the probability that there are exactly two cars in the system is 11.11%.

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It takes about 1.5 seconds for the ball to hit the ground.

To find how long it takes for the ball to hit the ground, we need to find the value of x when h(x) = 0, since the height of the ball is 0 when it hits the ground. We can set -16x²+36 = 0 and solve for x:

-16x²+ 36 = 0

Dividing both sides by -16:

x² - 2.25 = 0

Adding 2.25 to both sides:

x²= 2.25

Taking the square root of both sides (we can ignore the negative root since time cannot be negative):

x = √(2.25) ≈ 1.5

Therefore, it takes about 1.5 seconds for the ball to hit the ground.

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The inverse for each relation:

1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)} - {(-2, 1), (3, 2), (-3, 3), (2, 4)}

2. {(4,2),(5,1),(6,0),(7,‐1)} - {(2, 4), (1, 5), (0, 6), (-1, 7)}

3. Inverse equation: y=(-1/8)x+3/8

4. Inverse equation: y=3/2x+15/2

5. Inverse equation: y=2x-20

6. Inverse equation: y=[tex]x^{(1/2)}+3[/tex]

7. Since fog(x) = gof(x) = x, f and g are inverse functions.

8. Since fog(x) = gof(x) = x, f and g are inverse functions.

1. To find the inverse of the relation, we need to swap the positions of x and y for each point and then solve for y.

{(1, -2), (2, 3), (3, -3), (4, 2)}

Inverse: {(-2, 1), (3, 2), (-3, 3), (2, 4)}

2. Again, we swap x and y and solve for y.

{(4, 2), (5, 1), (6, 0), (7, -1)}

Inverse: {(2, 4), (1, 5), (0, 6), (-1, 7)}

3. To find the inverse equation for y=-8x+3, we swap x and y and solve for y.

x=-8y+3

x-3=-8y

y=(x-3)/-8

Inverse equation: y=(-1/8)x+3/8

4. To find the inverse equation for y=2/3x-5, we swap x and y and solve for y.

x=2/3y-5

x+5=2/3y

y=3/2(x+5)

Inverse equation: y=3/2x+15/2

5. To find the inverse equation for y=1/2x+10, we swap x and y and solve for y.

x=1/2y+10

x-10=1/2y

y=2(x-10)

Inverse equation: y=2x-20

6. To find the inverse equation for y=(x-3)², we swap x and y and solve for y.

x=(y-3)²

[tex]x^{(1/2)}=y-3[/tex]

[tex]y=x^{(1/2)}+3[/tex]

Inverse equation: [tex]y=x^{(1/2)}+3[/tex]

7. To verify that f(x)=5x+2 and g(x)=(x-2)/5 are inverse functions, we need to show that fog(x)=gof(x)=x for all x in the domain of f and g.

fog(x) = f(g(x)) = f((x-2)/5) = 5((x-2)/5) + 2 = x

gof(x) = g(f(x)) = g(5x+2) = ((5x+2)-2)/5 = x/5

Since fog(x) = gof(x) = x, f and g are inverse functions.

8. To verify that f(x)=1/2x-7 and g(x)=2x+14 are inverse functions, we need to show that fog(x)=gof(x)=x for all x in the domain of f and g.

fog(x) = f(g(x)) = f(2x+14) = 1/2(2x+14) - 7 = x

gof(x) = g(f(x)) = g(1/2x-7) = 2(1/2x-7) + 14 = x

Since fog(x) = gof(x) = x, f and g are inverse functions.

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After about 15.7 months, the apartment complex will have 800 occupied units.

Logistic growth is a type of growth in which the growth rate of a population decreases as the population size approaches its maximum value. In this case, the apartment complex has a maximum capacity of 1500 units.

Starting with 15 occupied units and growing at a rate of 10% per month, the number of occupied units can be modeled by a logistic function.

To find the number of months it takes to reach 800 occupied units, we need to solve for the time when the logistic function equals 800.

Let P(t) be the number of occupied units at time t (in months), then we have:

P(t) = 1500 / (1 + 1485[tex]e^{(-0.1t)}[/tex])

We want to find t such that P(t) = 800. Solving for t, we get:

t = -10 ln(1 - 4/37) ≈ 15.7 months

This means that after about 15.7 months, the apartment complex will have 800 occupied units.

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The correct symbol to compare the expressions is < (less than).

7 × (2/10) is equivalent to 1.4, which is less than 7. Therefore, 7 is greater than 1.4, and we can write 7 × (2/10) < 7 as the comparison between the expressions.

To compare the two expressions, we can analyze their values without actually multiplying them. The expressions are:

1. 7 × (2/10)
2. 7

Now let's simplify the first expression without multiplying:

7 × (2/10) = 7 × (1/5) (since 2 and 10 have a common factor of 2)

Now let's compare:

7 × (1/5) ? 7

Since we're multiplying 7 by a fraction that is less than 1 (1/5), the result will be smaller than 7. Therefore, the correct comparison symbol is "<":

7 × (1/5) < 7

The correct expression so formed is 7 × (2/10) < 7.

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Answer:

1.6×10^-12..............

This is the inequality that represents all possible widths, w, in feet of the garden is W^2 + 2W - 120 ≥ 0

The area of a rectangle is given by the formula A = L x W, where A is the area, L is the length, and W is the width. In this problem, we are given that the garden is rectangular and that the length is 2 feet longer than the width, so we can write L = W + 2.

We are also told that the area of the garden is at least 120 square feet, so we can write:
A = L x W ≥ 120
Substituting L = W + 2, we get:
(W + 2) x W ≥ 120

expanding the left side, we get:
W^2 + 2W ≥ 120
Rearranging, we get:
W^2 + 2W - 120 ≥ 0

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Answer: (4)

Step-by-step explanation:

Two lines E and F are same.

5x + 5y = 40

x + y = 8

Deviding both hands of E by 5,

we get F's equation.

So every single point on the line x+y=8

represents the solution of the given system.

The significant increase in the percent of filers between the under-18 group and the 18-26 group can be attributed to various factors, including age, income, and financial independence.

Firstly, individuals under the age of 18 are typically considered minors and are often dependent on their parents or guardians for financial support. As a result, they may not have any significant income that requires them to file taxes, and their income might be included in their parent's or guardian's tax return. This leads to a lower percentage of filers in the under-18 group.

On the other hand, the 18-26 age group marks the transition into adulthood, where individuals begin to gain financial independence. Many start working full-time jobs or attend college, where they may earn income through part-time jobs or internships. This increased income leads to a higher percentage of filers in the 18-26 group, as they are now responsible for filing their own tax returns.

Furthermore, the age range of 18-26 also coincides with the period where individuals are more likely to have various income sources. This includes scholarships, grants, and student loans for those attending college. These additional income sources may also contribute to the increased percentage of filers in this age group.

Lastly, as individuals become more financially independent, they may become more aware of tax benefits and deductions available to them, such as educational credits or deductions for student loan interest. This newfound awareness could encourage more people within the 18-26 age group to file taxes, leading to a higher percentage of filers.

In conclusion, the dramatic jump in the percent of filers between the under-18 group and the 18-26 group can be attributed to factors such as increased financial independence, diverse income sources, and greater awareness of tax benefits and deductions.

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We can use the point-slope form of the equation of a line to find the equation of the tangent line.

To find the equation of the line that is tangent to circle A from point C (2, 8), we need to first find the point of tangency, which is the point where the line intersects the circle.

Point C (2, 8) is outside the circle, so the tangent line will be perpendicular to the line connecting the center of the circle to point C and will pass through point C.

Step 1: Find the center of the circle

The center of the circle A is at (6, 5).

Step 2: Find the slope of the line connecting the center of the circle to point C

The slope of the line connecting the center of the circle (6, 5) and point C (2, 8) is:

m = (8 - 5) / (2 - 6) = -3/4

Step 3: Find the equation of the line perpendicular to the line from Step 2 passing through point C

The slope of the line perpendicular to the line from step 2 is the negative reciprocal of the slope:

m_perp = -1 / (-3/4) = 4/3

Now we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y - 8 = (4/3)(x - 2)

Simplifying, we get:

y = (4/3)x + 4.67

So the equation of the line that is tangent to circle A from point C (2, 8) is y = (4/3)x + 4.67.

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Answer:

The length of one leg of this right triangle is 4/√2 = 2√2 cm.