questions are in the images attached below :)

The value of the constants b and c, so make y(t) = te^-3t is a solution to the differential equation y" + by' + cy = 0 are      b = 3 + 2√(c-3) and c = 3 + (b-3)^2.

The differential equation given is: y'' + by' + cy = 0. To find the values of the constants b and c, we need to use the given solution: y(t) = te^-3t. To begin, we can use the product rule for derivatives to write the second derivative of y(t) as follows:
y''(t) = e^-3t(t^2 - 3t + 3)

Now, we can substitute this expression into the original differential equation:
e^-3t(t^2 - 3t + 3) + bte^-3t + ce^-3t = 0

Next, we can rearrange and factor this equation as follows:
e^-3t(t^2 + (b-3)t + (c-3)) = 0

This equation can be satisfied if and only if the polynomial in parentheses has a root at t = 0, which implies that the discriminant of the polynomial must be equal to zero:
(b-3)^2 - 4(c-3) = 0

Finally, we can solve this equation for b and c, giving us:
b = 3 + 2√(c-3)
c = 3 + (b-3)^2

Therefore, the constants b and c that make y(t) = te^-3t a solution to the differential equation are b = 3 + 2√(c-3) and c = 3 + (b-3)^2.

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Hence, in answering the stated question, we may say that equation (3x - 9 - 3x + 6)/9 = 1/9 => -3/9 = 1/9

A math equation is a technique that uses the equals symbol (=) to demonstrate equivalence between two statements. An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. The equal sign separates the integers 3x + 5 and 14 in the equation 3x + 5 = 14. To explain the connection between the two sentences written on opposing sides of a letter, a mathematical formula might be employed. The logo and the software are frequently the same. For instance, 2x - 4 = 2.

To solve this equation, we can start by simplifying the left-hand side using a common denominator:

[tex](x - 3)/3 - (x - 2)/3 = 1/9\\(3(x - 3) - 3(x - 2))/9 = 1/9\\[/tex]

[tex](3x - 9 - 3x + 6)/9 = 1/9\\-3/9 = 1/9[/tex]

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I am almost 99% sure it would be (A). < TRS

Answer:

C

Step-by-step explanation:

Answer:

D. 192

Step-by-step explanation:

192 possible combinations.

[tex]12 * 8 = 192[/tex]

Think of it this way. If you can choose a shirt and pants with colors blue and green for each, You combinations would be blue blue, green green, blue green, and green blue. 2 options and 2 options.

[tex]2 * 2 = 4[/tex]

Another example with ice cream, flavor and topping.

Choose 1 option from each category.

Flavors:  Vanilla, Chocolate, Strawberry

Toppings: Caramel, Sprinkles, M&Ms

All Combinations:

Vanilla, Caramel

Vanilla, Sprinkles

Vanilla, M&Ms

Chocolate (with the three toppings)

Strawberry (with the three toppings)

9 total combinations, [tex]3 * 3 = 9.[/tex]

Multiply the number of options for each category.

The Celsius temperature that has the same value as when converted to a Fahrenheit temperature is -40

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

F = 9/5C + 32

The Celsius temperature that has the same value as F implies that

C = F

Substitute the known values in the above equation, so, we have the following representation

C = 9/5C + 32

So, we have

C - 9/5C = 32

Evaluate the like terms

-4/5C = 32

So, we have

C = -32 * 5/4

Evaluate

C = -40

Hence, the value of C is -40

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The total number of customers is 500. We need to find the number of customers who received each discount.

For a 10% discount, customers received cards labeled 2, 4, 8, or 10. The total number of customers who received one of these cards is:

47 + 47 + 51 + 45 = 190

Therefore, the relative frequency for a 10% discount is:

190 / 500 = 0.38 or 38%

For a 40% discount, customers received cards labeled 7 or 9. The total number of customers who received one of these cards is:

54 + 47 = 101

Therefore, the relative frequency for a 40% discount is:

101 / 500 = 0.202 or 20.2%

For a 25% discount, customers received cards labeled 1, 3, 5, or 6. The total number of customers who received one of these cards is:

52 + 59 + 66 + 32 = 209

Therefore, the relative frequency for a 25% discount is:

209 / 500 = 0.418 or 41.8%

Based on the table, it seems that a large percentage of customers are receiving the 25% discount (41.8%). If the manager of the store wants approximately half of the customers to receive this discount, it may not be appropriate to use this method. However, it is also important to consider other factors, such as the store's profit margins and overall sales volume, when determining the best discount strategy.

Identify the total number of customers, which is given as 500 in the table.

For the 10% discount, add up the number of customers who received cards labeled 2, 4, 8, or 10. In the table, the corresponding counts are given as 47, 47, 51, and 45, respectively. Add these numbers together to get the total number of customers who received a 10% discount:

47 + 47 + 51 + 45 = 190

To find the relative frequency for a 10% discount, divide the number of customers who received a 10% discount (190) by the total number of customers (500):

190 / 500 = 0.38 or 38%

Therefore, the relative frequency for a 10% discount is 38%.

Repeat steps 2 and 3 for the other two discounts. For the 40% discount, add up the number of customers who received cards labeled 7 or 9, which are given as 54 and 47 in the table, respectively:

54 + 47 = 101

Then, find the relative frequency for a 40% discount by dividing the number of customers who received a 40% discount (101) by the total number of customers (500):

101 / 500 = 0.202 or 20.2%

Therefore, the relative frequency for a 40% discount is 20.2%.

Finally, for the 25% discount, add up the number of customers who received cards labeled 1, 3, 5, or 6, which are given as 52, 59, 66, and 32 in the table, respectively:

52 + 59 + 66 + 32 = 209

Then, find the relative frequency for a 25% discount by dividing the number of customers who received a 25% discount (209) by the total number of customers (500):

209 / 500 = 0.418 or 41.8%

Therefore, the relative frequency for a 25% discount is 41.8%.

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Answer:

Point A = (-5,5)

Step-by-step explanation:

Explanation is given in the picture...

Answer:

5 weeks

Step-by-step explanation:

To solve this problem, we can use the idea of proportionality. We know that the number of quizzes Percy takes is directly proportional to the number of weeks he attends school. This means that we can set up a proportion:

12 quizzes / 4 weeks = 15 quizzes / x weeks

We can cross-multiply to get the following:

12x = 60

Then we can solve for x:

x = 60/12 = 5

Therefore, Percy will have to attend 5 weeks of school to take a total of 15 quizzes.

The proportion of cherry tomatoes that are rejected due to being at most 15 mm or at least 30 mm in diameter is approximately 0.0040, or 0.4%.

We need to first determine the z-scores corresponding to these values in order to determine the percentage of cherry tomatoes that are rejected because they are either at most 15 mm or at least 30 mm in diameter. Where x is the diameter, is the mean diameter, and is the standard deviation, we can apply the formula.

The z-score for a 15 mm diameter is z = (15 - 22) / 2.5 = -2.8. The z-score for a 30 mm diameter is z = (30 - 22) / 2.5 = 3.2.

As the tomatoes that go outside the range between these two z-scores are the ones that are rejected, we are interested in learning what percentage of tomatoes do so. The area under the normal curve outside of this range can be calculated using a calculator or a conventional normal distribution table.

Left of z = -2.8 is the area of 0.0033, while right of z = 3.2 is the area of 0.0007. We multiply these two probabilities together to get the total area outside of this range: 0.0033 + 0.0007 = 0.0040.

As a result, 0.4%, or around 0.0040, of cherry tomatoes are rejected because they have a diameter of at least 30 mm and no more than 15 mm.

The option that comes the closest to the correct response is 0.0033. That is not the appropriate answer since it only considers the region to the left of z = -2.8 and excludes the region to the right of z = 3.2.

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A graph of each inequality is shown in the grid below.

A shape which the solution region represent is a rectangle.

In order to graph the solution for the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

0.4r ≤ 120     .....equation 1.

r ≥ 4(360/5)    .....equation 2.

By evaluating the given system of inequalities, we have;

r ≤ 120/0.4

r ≤ 300

r ≥ 4(360/5)

r ≥ 4(72)

r ≥ 288

By combining the system of inequalities, we have:

288 ≤ r ≤ 300

Based on the graph (see attachment), we know that the solution to the given system of inequalities is the shaded region between the solid line, as well as the point of intersection of the lines representing each inequality.

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Answer:

Your question is not fully completed. People can't solve it because it is not fully completed.

Step-by-step explanation:

The function f(x).g(x) = 4x³ - 17x² + 15x + 18 and the domain of this function is (-∞, +∞).

The domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined.

In other words, it is the set of values of x for which the function has a corresponding output value (also known as the dependent variable).

Here we have

f(x) = 4x + 3

g(x) = x² - 5x + 6  

Then f(x) · g(x) can be calculated as follows

=> (4x + 3) [ x² - 5x + 6 ]

Using distributive property, we get:

=> 4x (x² - 5x + 6) + 3(x² - 5x + 6)

=> 4x³ - 20x² + 30x + 3x² - 15x + 18

=> 4x³ - 17x² + 15x + 18  

Hence, f(x).g(x) = 4x³ - 17x² + 15x + 18    

The domain of the function f(x) = 4x³ - 17x² + 15x + 18 is all real numbers since there are no restrictions or conditions that would make the function undefined for any value of x.

Therefore,

The function f(x).g(x) = 4x³ - 17x² + 15x + 18 and the domain of this function is (-∞, +∞).

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The price of the coat in the store is $81 after a retailer buys a coat bulk at a unit price of $45 the coat is marked up 80% to sell in the store.

The retailer buys the coat at a unit price of $45 and marks it up by 80%. To calculate the markup, we need to first find 80% of $45, which is

0.8 x $45 = $36.

We can then add the markup to the cost price to get the selling price:

$45 + $36 = $81.

Therefore, the price of the coat in the store is $81.

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Answer:

If Sharon has 300 channels with her cable service, then her monthly cost is calculated as follows:

300 channels × $0.20 per channel = $60

This means that Sharon's current cable bill is $60 per month. If she switches to Great Vista Satellite, her monthly cost will be $180, which is $120 more than her current bill. This increase in cost can be represented by the equation:

$120 = 300 channels × $0.20 per channel × m

where "m" is the number of months Sharon has to subscribe to the satellite service to break even.

Simplifying the equation, we get:

m = $120 ÷ ($0.20 × 300 channels) = 2

Therefore, Sharon will have to subscribe to the satellite service for 2 months to break even. After that, she will start saving $0.20 per channel per month compared to her cable service.

The expression can be simplified by breaking it down into its individual components. we multiply this by 5 squared, which simplifies to 25 x 5 = 125. Lastly, we subtract 7.3 from 125 to get 117.7, which is the final answer.

First, we can evaluate the expression inside the parentheses, which is -4.5 + 6.87. This evaluates to 2.37. We then divide this by 3 to get 0.79. Next, we multiply this by 5 squared, which gives us 79. Lastly, we subtract 7.3 from 79 to get 71.7, which is the final answer.

The expression can be expanded by breaking it down into its individual parts. First, we have -19, which is already in its expanded form. Next, we can expand the expression inside the parentheses, which is -4.5 + 6.87. This can be expanded to -4 + 0.5 + 6 + 0.87, which simplifies to -4 + 6 + 0.87 = 2.87. We then divide this by 3 to get 0.79. Next, we multiply this by 5 squared, which simplifies to 25 x 5 = 125. Lastly, we subtract 7.3 from 125 to get 117.7, which is the final answer.

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The distance from your eyes to the horizon is approximately 4.7 kilometers (2.92 miles).

The surface refers to the two-dimensional, flat, or curved boundary of a three-dimensional object. For example, the surface of a sphere is a curved two-dimensional boundary that encloses the three-dimensional space inside the sphere.

The distance from your eye to the horizon on the Earth's surface depends on your height above the surface. Assuming that you are standing on a flat surface and your eyes are at an average height of about 1.7 meters (5.6 feet) above the ground, the distance to the horizon.

distance to horizon = √(2Rh + h²)

where R is the radius of the Earth (6,371,000 meters) and h is the height of your eyes above the ground (1.7 meters).

Plugging in the values, we get:

distance to horizon = √(2 x 6,371,000 x 1.7 + 1.7²) = 4,690 meters (approximately 15,387 feet or 2.92 miles)

Therefore, if you are standing on the Earth's surface with your eyes at an average height of 1.7 meters, the distance from your eyes to the horizon is approximately 4.7 kilometers (2.92 miles).

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rate of cooling of the turkey in minutes is 41.13545

The formula for finding the rate of cooling of a roasted turkey is provided in the question. It is given as:T(t) = Ae^kt + TsThe following are the variables:• T(t) represents the temperature of the turkey at time t• A represents the initial temperature of the turkey• k is the cooling rate• Ts is the temperature of the environmentNow, using the values given in the question, we can get the rate of cooling of the turkey as follows:T(t) = Ae^kt + TsLet us replace the variables with the given values:159 = A*e^(0.5k) + 75 => A*e^(0.5k) = 84 => A = 84/e^(0.5k)Let us substitute the value of A in the initial equation:T(t) = Ae^kt + Ts => 190 = A*e^(k*0) + 75 => 190 = A => A = 190So, we can get the value of k using the values of A from the above two equations:84/e^(0.5k) = 190 => e^(0.5k) = 84/190 => e^(0.5k) = 0.4421052631578947 => k = (ln0.4421052631578947) / 0.5 = -0.4662195477817674So, the equation for the temperature of the turkey as a function of time is:T(t) = 190e^(-0.4662195477817674*t) + 75To find the rate of cooling of the turkey, we need to take the derivative of the above equation with respect to t, which gives:dT/dt = -87.75877428502014*e^(-0.4662195477817674*t)This is the rate of cooling of the turkey. To find the rate of cooling in minutes, we substitute t = 0.5 in the above equation and simplify to get:dT/dt = -41.135453873444264Therefore, the rate of cooling of the turkey in minutes is 41.13545 (accurate to at least 5 decimal places).

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If 87¹/₂ percent of milk is water and a gallon consists of 16 cups, the number of cups of water in a gallon of milk is 14 cups.

A value expressed in percentage implies that it is the quotient multiplied by 100.

The quotient is the result of the division operation involving a portion and the whole value.

The number of cups in a gallon of milk = 16

The percentage of the content that is water = 87¹/₂%

87¹/₂% of 16 = 14 cups (16 x 87¹/₂%)

Thus, we can state that out of 16 cups in a gallon of milk, water consists of 14 cups, which is 87¹/₂ per cent.

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Answer:

k=2 when W=50,V=5

W=162 when V=9,k=remains constant

Step-by-step explanation:

W=V²

W=kV²

50=k×5²

50=k×25

50=25k

divide both sides by 25

k=2

k remains constant

W=KV²

W=2×9²

W=2×81

W=162

Answer:

=7542,71

Step-by-step explanation:

13 680.00 x 0.551368

=7542,71424

round off to the second decimal place

=7542,71

Answer: 5.56%

Step-by-step explanation:

Deduct the original price from the price that reflects the increase to get the increment.

R13 28-R 12,58 = R, 70

Place the increase on the original price and multiply by 100%

R, 70/R 12,58 x 100/1

Percentage increase = 5.56%

To check, calculate 5.56%o of 12,58 and add to 12,58, you will get R13,28

The measure of angle B on the straight line is 22 degrees

When two angles lie along a straight line, they form a straight angle which measures 180 degrees.

The statement from the question can be represented as

m∠A = 4(m∠B + 17.5°)

But we know that the sum of the measures of angles A and B is 180 degrees, since they form a straight angle.

m∠A + m∠B = 180°

Substitute the known values in the above equation, so, we have the following representation

4(m∠B + 17.5°) + m∠B = 180°

Simplifying this equation, we get:

5m∠B + 70° = 180°

Subtracting 70 degrees from both sides, we get:

5m∠B = 110°

Dividing both sides by 5, we get:

m∠B = 22°

Therefore, the measure of angle B is 22 degrees.

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In this case, the probability of getting a question wrong is 0.5, and there are 16 questions, so the expected value of incorrect answers is 0.5 x 16 = 8.

The expected value of the number of incorrect answers on a 16-question true or false exam with random guessing is 8. This is because there are an equal number of true and false answers, and the chance of getting each one correct is 50%. Therefore, the expected value of incorrect answers is 8.

To calculate the expected value, you need to multiply the probability of getting a question wrong by the number of questions.

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This tells us that c and k must be related such that ck = -0.03.This differential equation tells us that the rate of change of q with time (dq/dt) is equal to a negative constant, -0.03.

This differential equation tells us that the rate of change of q with time (dq/dt) is equal to a negative constant, -0.03. This means that q is decreasing over time. Therefore, c and k must be related such that ck = -0.03, since this constant is the product of c and k. This tells us that c and k must be related, but does not tell us the exact value of either c or k.

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Answer:

The expression to represent the total area as the sum of the areas of each room would be:

Total area = area of kitchen + area of bathroom + area of remaining space

Total area = 7 x 11 + 4 x 11 + (11 - 7 - 4) x 11

Total area = 77 + 44 + 11

Total area = 132 square feet

The t-value for the year 2025 is t = 10, the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 is $46,166 and the U.S. per capita real disposable income expected to exceed $50,000 is 2030.

Given equation is 1 = 707.6t + 39,090

(a) To find what t-value corresponds to 2025.The given year is 2025, so the number of years after 2015 will be 2025-2015 = 10 So the t-value for the year 2025 is t = 10.

(b) To find the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 Substitute t = 10 in the given equation1 = 707.6t + 39,0901 = 707.6(10) + 39,0901 = 7,076 + 39,0901 = 46,166So, the predicted U.S. per capita real disposable income (to the nearest $10) in 2025 is $46,166.

(c) To find in what year is the U.S. per capita real disposable income expected to exceed $50,000.Substitute 50,000 for 1 in the equation, we get50,000 = 707.6t + 39,09050,000 - 39,090 = 707.6t10,910 = 707.6t10,910/707.6 = t15.41 ≈ 15 years. So, the U.S. per capita real disposable income expected to exceed $50,000 in 2015 + 15 = 2030.

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Alexandra's net pay each month, using mathematical operations, is C. $3,648.60.

The net pay is the difference between the gross pay or earning and the total deductions.

The net pay per month can be computed following these steps:

Gross earnings per year = $59,904.00

Monthly taxes = $998.40

Annual taxes = $11,980.80 ($998.40 x 12)

Monthly medical, dental, and vision insurance = $345.00

Annual medical, dental, and vision insurance = $4,140 ($345 x 12)

Total deductions and taxes = $16,120.80 ($11,980.80 + $4,140)

Annual net pay = $43,783.20 ($59,904.00 - $16,120.80)

Monthly net pay = $3,648.60 ($43,783.20/12)

Thus, monthly, Alexandra will earn a net pay of Option C.

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Answer:

I gotta get you to do a little bit so I can't give you the direct answer -_-

Step-by-step explanation:

Lets start with this question, what is 30% of 250?

We multiply 250*0.3, which gives us an increase of 75 the first day

__________________________________

Second day: 250+75=325 views

325*0.3=97.5

__________________________________

Third day: 422.5

422.5*0.3=126.75

__________________________________

We add the increases, which is 75+97.5+126.75

This gives us 299.25

Now we just have to find the fourth day and average it! (which I trust you know how to do, just helping you get the jist of it)

Hope I helped!

The fraction of pizza that Shroff ate is 2/3 of a pizza.

The Greatest Common Factor (GCF) is the largest number that divides evenly into two or more integers. It is also known as the Greatest Common Divisor (GCD).

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by that number.

The GCD of 52 and 78 is 26 (because 26 is the largest number that divides evenly into both 52 and 78).

So, to simplify the fraction, we divide both the numerator and denominator by 26:

52/78 = (52 ÷ 26) / (78 ÷ 26) = 2/3

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