Choose the correct answer.
-
Let f(x) = x - 4 and g(x) = x2. Find (gof)(-3).
A.1
B.12
C.49
D.-7

The differential equation that models this situation is dx/dt = kx(M - x) (option c).

To determine the differential equation that models the situation, let's analyze the problem statement.

The rate at which a person can memorize a list of M words is proportional to the product of the number of words memorized and the number of words that have not been memorized.

Let's denote the number of words memorized as "a" and the number of words not yet memorized as "M - a" (where M is the total number of words in the list).

The problem states that the rate of memorization is proportional to the product of "a" and "M - a". We can express this mathematically as:

Rate of memorization ∝ a * (M - a)

To convert this proportionality into an equation, we introduce a positive constant k:

Rate of memorization = k * a * (M - a)

The left side of the equation represents the rate of change of the number of words memorized (da/dt), and the right side represents the product of "a" and "M - a" multiplied by the constant k.

Therefore, the differential equation that models this situation is:

da/dt = k * a * (M - a)

Comparing this with the given options, we can see that the correct choice is option C:

dx/dt = k * x * (M - x)

The complete question is:

At any time t > 0 the rate at which a person can memorize a list of M words is proportional to the product of the number of words memorized and the number of words that have not been memorized. If a denotes the number of words memorized at time t, which differential equation models this situation? Assume k is a positive constant.

A. dx/dt = kx

B. dx/dt = kx(x - M)

C. dx/dt = kx(M - x)

D. dx/dt = kt(M - t)

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a. To reach a savings goal of $180,000 by your 18th birthday, assuming starting from your first birthday and earning a 6.5% annual return, your parents would need to save a fixed amount each year.

b. If they adjust their goal to $220,000 and assume a five-year college duration, the annual savings required would change.

a. To calculate the amount your parents would need to save each year to reach the goal of $180,000, we can use the concept of present value. The present value (PV) of the savings should equal the future value (FV) of $180,000, given an annual interest rate of 6.5% and a time period of 17 years (from your first to 18th birthday). By using the formula for calculating present value of an annuity, we can determine the required annual savings amount.

b. If your parents adjust their goal to $220,000 and consider a five-year college duration, the time period would change from 17 years to 16 years (from your first birthday to the year before your 18th birthday). Using the new future value of $220,000 and the same interest rate of 6.5%, the required annual savings amount can be recalculated.

To obtain the specific annual savings amount in both scenarios, the calculations can be done using financial formulas such as the present value of an annuity formula or by utilizing financial calculators or spreadsheets.

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By analyzing the sensitivity report, you can gain insights into the stability and flexibility of the optimal solution without the need for re-solving the LP problem.

To solve a linear programming (LP) problem using Excel Solver, you can follow these steps:
1. Open Excel and enter the LP problem in a spreadsheet. Define the decision variables, objective function, and constraints.
2. Install the Solver add-in if it is not already installed. You can find the Solver add-in in the "Data" tab under "Analysis."
3. Go to the "Data" tab and click on "Solver" to open the Solver dialog box.
4. In the Solver dialog box, set the objective cell to the target cell of your LP problem. Select either "Min" or "Max" depending on whether you want to minimize or maximize the objective.
5. Define the decision variable cells as the changing cells.
6. Add the constraints by clicking on the "Add" button in the Solver dialog box. Specify the constraint cells and their respective relationships (e.g., <=, =, >=).
7. Set any additional Solver options if necessary, such as limiting the solution to integer values.
8. Click "Solve" to find the optimal solution. Excel Solver will adjust the decision variables to optimize the objective function while satisfying the constraints.
Once you have solved the LP problem using Excel Solver, you can use the sensitivity report to analyze the results. The sensitivity report provides information on the impact of changes to the objective function coefficients and constraint coefficients on the optimal solution.
The sensitivity report typically includes the following information:

1. Shadow prices: These represent the rate of change in the objective function value for each unit change in the right-hand side (RHS) of a constraint. A positive shadow price indicates that an increase in the RHS will lead to an increase in the objective function value, while a negative shadow price indicates the opposite.
2. Allowable increase and decrease: These values indicate how much a constraint coefficient can change without affecting the optimal solution. If a constraint has a non-zero allowable increase or decrease, it means the coefficient can change within that range without impacting the optimal solution.
3. Objective coefficient range: This range shows the allowable range for the objective function coefficients without changing the optimal solution. If a coefficient falls within this range, it will not affect the optimal solution.
Using the sensitivity report, you can answer questions related to changes in the LP problem without re-solving it. For example:
1. How would an increase in the RHS of a specific constraint affect the optimal solution? You can refer to the shadow price of that constraint to determine the impact.
2. What is the maximum amount a constraint coefficient can change without affecting the optimal solution? You can check the allowable increase and decrease values for each constraint.
3. What is the range for the objective function coefficients where the optimal solution remains the same? You can refer to the objective coefficient range.
By analyzing the sensitivity report, you can gain insights into the stability and flexibility of the optimal solution without the need for re-solving the LP problem.

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Answer:

3.584 ×\(10^{18}\)

The 99% confidence limit will be option B which is (45, 55)

90% confidence limits for the population mean are (46,54)

mean = 46+54 / 2 = 50.

the margin of error E = 54-46/2 = 4

For 90% Confidence Z- Critical value is = 1.645

But the margin of error

E = ZS/√n

4=(1.645)S/√n

S/√n = 4 / 1.645

= 2.4316

For 95% confidence Z-critical value is 1.96

A 95% confidence interval is = mean ± E

(50 ± 1.96) S/√n = (50 ± 1.96)×2.4316

= 50+ 4.7660

= 45.2340, 54.7660

= (45, 55)

Hence the correct option is B which is (45, 55) as the 99% confidence limit.

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Answer:

160÷3=40

Step-by-step explanation:

that is the answerrrrrrrrrrrrrrrrrrrrrrrrrrr

From the given information provided, the average stopping distance is 316 feet for car travelling at 65mph on dry level pavement.

The average stopping distance of a car traveling at 65 mph on dry, level pavement depends on various factors, such as the condition of the pavement, the condition of the tires, the weight of the car, and the efficiency of the braking system.

However, as a general estimate, the average stopping distance of a car traveling at 65 mph on dry, level pavement is about 316 feet. This includes both the reaction time of the driver and the braking distance of the car. It's important to note that this is an average estimate and actual stopping distance can vary depending on the conditions mentioned above. It's always best to drive at a safe speed and maintain a safe distance from other vehicles to avoid accidents.

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Use the limit comparison test to determine the convergence or divergence.

[infinity]n=2 Σ \(\frac{1}{n^{7/8-1}}\)  =  lim (n→∞) \(1/n^{7/8-1}\)/ (1/n²)

To establish a comparison, we need to find a value of p such that our series is larger than the p-series for all n greater than some value N. We can do this by simplifying the expression \(1/n^{7/8-1}\) to 1/nᵃ, where a = 7/8 - 1 = -1/8.

Now, we want to find a p-series with p > 0 that is smaller than our series. One such series is the p-series Σ 1/n², since p = 2 > 0.

We can then apply the limit comparison test, which states that if the limit of the ratio of the two series is a finite positive number, then both series either converge or diverge. Specifically, we have:

lim (n→∞) \(1/n^{7/8-1}\)/ (1/n²)

= lim (n→∞) \(n^{(2-7/8+1)}\)

= lim (n→∞) \(n^{1/8}\)

In summary, we can use the limit comparison test to compare the series Σ \(1/n^{7/8-1}\) to the p-series Σ 1/n², and find that both series converge. The key concept in this method is the idea of comparing series using limits and established results.

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Based on the corresponding angles theorem, the value of x is: 64°.

When two angles that are formed by a transversal and two parallel lines lie in relative position to each other on each of the parallel lines, they are called corresponding angles. According to the corresponding angles theorem, both angles are congruent to each other.

Angle x and 64 degrees are corresponding angles. They are therefore congruent to each other.

Thus, x = 64° [corresponding angles theorem]

In summary, based on the corresponding angles theorem, the value of x is: 64°.

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The required value of x and y in the given equation are ,

x= 1,

y = -1 .

The algebraic method to solving simultaneous linear equations is known as substitution method. This method, as the name suggests, involves substituting the value of one variable from one equation into the second equation. This makes it much easier to answer a pair of linear equations by combining them into a single linear equation with only one variable.

The given equations are

0.1x - 0.3y = 0.4                             ...(1)

0.3x − 0.2y=0.5                              ....(2)

Multiply both the equations by 10, we get

x - 3y = 4                                           ...(1)

3x − 2y = 5                                        ...(2)

Multiply (1) by 3

3x - 9y = 12

3x − 2y = 5

Subtracting both the equations

-7y = 7

y = -1

From (1):

x - 3(-1) = 4

x + 3 = 4

x = 4 - 3

x = 1

The required value for x and y is,

x= 1,

y = -1

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Answer:The answer is 10!

Step-by-step explanation:

Answer:

greatest common factor 10 and 40 is 10

Step-by-step explanation:

The modification to a research study that will result in a narrower confidence interval is option D is correct choice

The modification to a research study that will result in a narrower confidence interval is option D: decreasing the confidence level and increasing the sample size. By decreasing the confidence level, we are willing to accept a lower level of certainty in our results, which can lead to a narrower interval. Increasing the sample size also leads to a narrower interval as it reduces the variability in our data and increases the precision of our estimates.

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Answer:

The first plant manufactures 2x + 21 more items daily.

Step-by-step explanation:

Given that:

Production level of plant one = 7x + 19

Production level of plant two = 5x -2

To find the number of items first plant manufactures more than second plant, we will find the difference between production levels.

Difference = (7x + 19) - (5x - 2)

Difference = 7x + 19 - 5x + 2

Difference = 2x + 21

Hence,

The first plant manufactures 2x + 21 more items daily.

Answer:

B) 94.2 in³

Step-by-step explanation:

V = (πr²h)/3

= 9π(10)/3 = 90π/3 = 30π ≈ 94.25

Therefore, we have:z = 11/tan(31°)≈ 19.29 Therefore, the values of x, y, and z are 11, 11, and 19.29, respectively.

Given that lines p and q are parallel, solve for the missing variables, x, y, and z, in the figure shown as below:In the above figure, we are given that lines p and q are parallel to each other. Therefore, the alternate interior angles and corresponding angles are congruent.As we can observe, ∠4 is alternate to ∠5 and ∠4 = 112°.

Therefore, ∠5 = 112°.Now, considering the right triangle ABD, we can write: t

an(θ) = AB/BD ⇒ tan(θ) = x/z ⇒ z*tan(θ) = x  ... (1)

Similarly, considering the right triangle BCE, we can write:

tan(θ) = EC/BC ⇒ tan(θ) = y/z ⇒ z*tan(θ) = y ... (2)

We also know that

x + y = 22 ... (3)

Multiplying equations (1) and (2), we get: (z*tan(θ))^2 = xy ... (4)Squaring equation (1), we get

(z*tan(θ))^2 = x^2 ... (5)

Substituting equation (5) in equation (4), we get:

x^2 = xy ⇒ x = y ... (6)

Substituting equation (6) in equation (3), we get:

2x = 22 ⇒ x = 11 y = 11

Squaring equation (2), we get:

(z*tan(θ))^2 = y^2 ⇒ z = y/tan(θ) ⇒ z = 11/tan(31°)  ... (7)

Using a calculator, we can find the value of z.

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Answer:

volume of a cylinder = π r^2 *h

108π=π*r^2*h

108=r^2*h

12=r^2

3.464=r

radius =3.464

Step-by-step explanation:

Brainliest would be appreciated

Ask for questions!

Answer:

The length of the cylinder's radius is 3

Step-by-step explanation:

A cylinders radius is found by the formula, r= √ v/πh

So, 108π/πh.

Because there is pi in both the numerator and denominator, we can cancel them out. This leaves the equation to be : r = √ 108/12.

r = √ 108/12

108/12 is 9.

r = √9

r = 3

Answer:

the answer is 23

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

if you do 230 divided by 10 you get 23, or you can distribute 230 in 10 groups.

Answer:

(x, y) = (3.7, 1.7)

Step-by-step explanation:

5x + 2y = 22

-2x + 6y = 3

use elimination -- multiply equation I by -3 to eliminate the y variable

-3(5x + 2y = 22) → -15x - 6y = - 66

-15x - 6y = -66

-2x + 6y = 3

solve

-17x = -63

divide

x = 63/17

plug in x to equation I to find y

-2x + 6y = 3

-2(63/17) + 6y = 3

-126/17 + 6y = 3

add 126/17 to both sides

6y = 177/17

divide by 6

y = (177/17)(1/6)

y = 177/102 → 59/34

(x,y) = (63/17, 59/34)

(x, y) = (3.7, 1.7)

The factor and levels in the scenario is,

Factor = dip flavor. Levels = strawberry, orange, and banana.

What is popsicles?

A frozen treat on a stick made of liquid is known as an ice pop. An ice pop is "quiescently" frozen, or frozen when at rest, and turns into a solid block of ice, unlike ice cream or sorbet, which are churned while freezing to prevent ice crystal formation. It is held by the stick, which serves as a handle.

There is only one factor (independent variable) involved in above case, i.e. dip flavor is only factor mentioned in given case.

We can see that dip flavor has three categories or levels, i.e. strawberry, orange, and banana

Therefore, we have

factor = dip flavor and levels = strawberry, orange, and banana.

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Answer:

Here is your answer . hope it helps.

Answer:

18.9

Step-by-step explanation:

Start with parentheses.

4/5 + 3/5 = 7/5

Simplify 7/5, 7/5 = 1 2/5

Next numbers.

3.5 x 5 = 17.5

Add.

17.5 + 1 2/5 = 18.9

Answer:

→ 9x^2 - 4x - 3 = [41].

Step-by-step explanation:

Simplify:

9x^2 - 4x -3

=> 9(-2)^2 - 4(-2) - 3 [∵ x = 1 (Given)]

=> 9(4) - 4(-2) - 3

=> 36 + 8 - 3

=> 44 - 3

=> 41 Ans.

The area of an equilateral triangle with sides measuring 20 cm is approximately 173.2  square cm (Option c), rounding to the nearest tenth.

To find the area of an equilateral triangle, we can use the formula (sqrt(3) / 4) * side^2, where "side" represents the length of any side of the triangle.

The formula for the area of an equilateral triangle is derived from dividing the triangle into two congruent right-angled triangles and using the Pythagorean theorem. The (sqrt(3) / 4) term accounts for the relationship between the side length and the height of the equilateral triangle.

In this case, the given side length is 20 cm. Substituting this value into the formula, we have:

Area = (sqrt(3) / 4) * 20^2

= (sqrt(3) / 4) * 400

≈ 0.433 * 400

≈ 173.2 square cm

Rounding the answer to the nearest tenth, the area of the equilateral triangle is approximately 86.6 square cm.

Therefore, the correct answer is option (c) 173.2 square cm.

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The differences in dependent measures between levels are the main effects

The differences in the dependent measure between the levels of one variable within one level of another variable are known as simple main effects. These effects can be tested statistically to determine if they are statistically significant, which would indicate that the difference between the levels of the first variable is meaningful within the context of the second variable.

One independent variable having a certain degree of another independent variable is the simple main effect of a factorial experiment. The levels of the other independent variable are averaged over the primary effect of one independent variable. Results for a straightforward main effect are examined as though every level of the other independent variables had its own experiment.

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Answer:

18

Step-by-step explanation:

1/3n=6

multiply both sides by 3/1 (or 3)

1/3(3)=1

3(6)=18

n=18

The prefrontal cortex is responsible for regulating higher cognitive functioning of the brain.

What is prefrontal cortex?

In the frontal lobe of the brain, there is a structure called the prefrontal cortex. It carries out cognitive functions like memory, attention, planning, flexibility, etc. It is regarded as the region of the brain that develops the least quickly

Prefrontal cortex is located in the frontal lobe.

The prefrontal cortex is responsible for regulating higher cognitive functioning of the brain.

Mid-twenties is when it reaches maturity. This explains why teenagers are more likely to establish harmful behaviours than younger kids and why adults are better at planning and thinking. An attention deficit and trouble remembering details can be brought on by prefrontal cortex (PFC) damage. Moreover, it may result in psychological changes, a diminished capacity for feeling, and bodily impairments associated with daily activities.

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For which population is 636363 wins a legitimate estimate of the average longest streak: Only the top 200200200 longest streaks worldwide in June

Mean = sum of data / Number of data

The 200200200 longest streaks weren't randomly selected from a larger population. They are not representative of all players in the world or Canada, but they are the top 200200200 longest streaks of all players. So,

Only the top 200200200 longest streaks worldwide in June will win.

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Answer:

d. 4x − 5y = 27x + 6y = 10

I hope my answer helps you.

Answer:

372.r2

Step-by-step explanation: