Which of the following functions (there may be more than one) are solutions of the differential equation y' 4y' + 4y = et ? y = e%t + et Iy = et y = e2t + tet y = te2t +et y = e2t

Answer: The formula is  Monthly Payment = P (r(1+r)^n)/((1+r)^n-1)

Step-by-step explanation:

EMI = [P x R x (1+R)^N]/[(1+R)^N-1], where P stands for the loan amount or principal, R is the interest rate per month [if the interest rate per annum is 11%, then the rate of interest will be 11/(12 x 100)], and N is the number of monthly instalments

Answer: 48

Step-by-step explanation:

The leading coefficient of the polynomial is -2, and the degree of the polynomial is 3.

To identify the leading coefficient and degree of the polynomial, we need to consider the highest power of the variable in the polynomial expression.

In the given polynomial, -2y³ is the term with the highest power of y. The coefficient of this term, which is -2, is the leading coefficient of the polynomial. The degree of a polynomial is determined by the highest power of the variable. In this case, the highest power of y is 3 in the term -2y³. Therefore, the degree of the polynomial is 3.

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Answer:

-1.20

Step-by-step explanation:

You are correct because you just had to subtract 2.50 - 3.75 and you get -1.20.

Answer:

-1.25 feet below surface level.

Answer:

Which essay topic would be best suited to a cause-and-effect text structure?

A. The similarities between public libraries and electronic libraries

B. How to download an electronic book to a computer

C. How the rise of computers has changed teen reading habits

D. The best applications for reading on a computer

The optima of the Lagrangian objective function is minimized at z = 54,000. Also the Lagrange multiplier solution corresponds to a minimum.

The optimal values for the Lagrangian objective function can be determined by solving the given optimization problem using Lagrange multipliers. We have the objective function z = 6x₁² + 12x₂² and the constraint g(x₁, x₂) = 90 = x₁ + x₂.

To find the optimal values, we form the Lagrangian function L(x₁, x₂, λ) = f(x₁, x₂) - λ(g(x₁, x₂) - 90). Here, λ is the Lagrange multiplier.

Taking the partial derivatives with respect to x₁, x₂, and λ, and setting them to zero, we obtain the following equations:

∂L/∂x₁ = 12x₁ - λ = 0

∂L/∂x₂ = 24x₂ - λ = 0

∂L/∂λ = x₁ + x₂ - 90 = 0

Solving these equations simultaneously, we find x₁ = 30, x₂ = 60, and λ = 360. Substituting these values back into the objective function, we get z = 6(30)² + 12(60)² = 54,000.

To determine whether this is a maximum or minimum, we can examine the second partial derivatives of the Lagrangian. Calculating the second partial derivatives, we have:

∂²L/∂x₁² = 12

∂²L/∂x₂² = 24

Since both second partial derivatives are positive, we can conclude that the Lagrange multiplier solution corresponds to a minimum. Therefore, the optima of the Lagrangian objective function is minimized at z = 54,000.

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A. The solution for t in the equation P e^(10t) - Q e^(-8t) = 0 using natural logarithms is t = (1/18) ln(Q/P).

B. To solve the equation P e^(10t) - Q e^(-8t) = 0 using natural logarithms, we can apply logarithmic properties and algebraic manipulation.

1. Start by isolating the exponential terms:

  P e^(10t) = Q e^(-8t)

2. Take the natural logarithm (ln) of both sides of the equation:

  ln(P e^(10t)) = ln(Q e^(-8t))

3. Apply the properties of logarithms:

  ln(P) + ln(e^(10t)) = ln(Q) + ln(e^(-8t))

4. Simplify the natural logarithm of exponential terms:

  ln(P) + 10t = ln(Q) - 8t

5. Move the terms involving t to one side of the equation:

  10t + 8t = ln(Q) - ln(P)

6. Combine like terms:

  18t = ln(Q/P)

7. Solve for t by dividing both sides by 18:

  t = (1/18) ln(Q/P)

Therefore, the exact solution for t in the equation P e^(10t) - Q e^(-8t) = 0 using natural logarithms is t = (1/18) ln(Q/P).

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The question is incomplete:

Lin is shopping for a couch with her dad and hears him ask the salesperson, "How much is your commission?" The salesperson says that her commission is 5.5% of the selling price. How much commission will the salesperson earn by selling a couch for $495?

Answer:

The salesperson will earn $27.22 as comission by selling a couch for $495.

Step-by-step explanation:

From the information given, you know that Lin's comission is 5.5% of the selling price, so in order to find the amount of the commision the salesperson will earn you have to calculate 5.5% of the selling price:

495*5.5%=27.22

According to this, the answer is that the salesperson will earn $27.22 as comission by selling a couch for $495.

The volume of the solid generated by revolving the region enclosed by the triangle about the y-axis is 9π cubic units.

To find the volume of the solid generated by revolving the region enclosed by the given triangle about the y-axis, we can use the washer method.

The first step is to determine the limits of integration.

The triangle is bounded by the vertical lines x = 4, x = 5, and the line connecting the points (4, 1) and (5, 2).

We need to find the y-values that correspond to these x-values on the triangle.

At x = 4, the corresponding y-value on the triangle is 1.

At x = 5, the corresponding y-value on the triangle is 2.

So, the limits of integration for y will be from y = 1 to y = 2.

Now, let's consider an arbitrary y-value between 1 and 2. We need to find the corresponding x-values on the triangle.

The left side of the triangle is a vertical line segment, so for any y-value between 1 and 2, the corresponding x-value is x = 4.

The right side of the triangle is a line connecting the points (4, 2) and (5, 2).

This line has a constant y-value of 2, so for any y-value between 1 and 2, the corresponding x-value is given by the equation of the line: x = 5.

Now, we can set up the integral using the washer method. The volume can be calculated as follows:

V = ∫[1,2] π(\(R^2 - r^2\)) dy,

where R is the outer radius and r is the inner radius.

Since we are revolving the region about the y-axis, the outer radius R is the distance from the y-axis to the right side of the triangle, which is x = 5.

Thus, R = 5.

The inner radius r is the distance from the y-axis to the left side of the triangle, which is x = 4.

Thus, r = 4.

Substituting these values into the integral, we have:

V = ∫[1,2] π(5^2 - 4^2) dy.

Simplifying the integral:

V = ∫[1,2] π(25 - 16) dy

= ∫[1,2] π(9) dy

= 9π ∫[1,2] dy

= 9π [y] [1,2]

= 9π (2 - 1)

= 9π.

Therefore, the volume of the solid generated by revolving the region enclosed by the triangle about the y-axis is 9π cubic units.

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The normalcdf function is a feature on some calculators that is used to calculate the cumulative probability of normal distribution within a certain range, from x1 to x2. It requires four values: the mean, the standard deviation, the lower limit, and the upper limit.

We need to find the probability that an infant's weight will be greater than 4 pounds. The given mean is 5.4 pounds with a standard deviation of 0.9 pounds.Assuming infants' weights follow a normal distribution with this mean and standard deviation, we can solve this problem using the normalcdf function with the following values:Lower limit: 4 poundsUpper limit: infinityMean: 5.4 poundsStandard deviation: 0.9 poundsWe input these values into the normalcdf function as normalcdf(4, infinity, 5.4, 0.9).

In this scenario, a baby boutique wants to introduce a new line of baby clothes, and they want to assure that the clothes fit well by reviewing the standard for infant clothing. The designers can use the weight of infants as a guideline for determining the size of the clothes. The weight of infants varies based on age and sex, and for a baby boutique, it is essential to consider the weight of infants to design clothes that fit comfortably.For assurance in the infant's size, the designers have to review the standard for infant clothing. In 2014, the CDC found a sample mean weight for infants between 0 and 2 months of age to be 5.4 pounds with a standard deviation of 0.9 pounds. To design clothes that fit well for infants, it is essential to know the probability of the weight of an infant falling within a specific range.Assuming infants' weights follow a normal distribution with a mean of 5.4 pounds and a standard deviation of 0.9 pounds, the probability that an infant's weight will be greater than 4 pounds can be found using the normalcdf function. This function is used to calculate the cumulative probability of normal distribution within a certain range, from x1 to x2. It requires four values: the mean, the standard deviation, the lower limit, and the upper limit. In this case, the lower limit is 4 pounds, and the upper limit is infinity. We input these values into the normalcdf function as normalcdf(4, infinity, 5.4, 0.9).The result of this function is the probability that an infant's weight will be greater than 4 pounds. Based on the normal distribution curve, we can say that there is a high probability that an infant's weight will be greater than 4 pounds.

To summarize, the probability that an infant's weight will be greater than 4 pounds is found using the normalcdf function. The input values for this function are the mean, standard deviation, lower limit, and upper limit. The mean and standard deviation are given as 5.4 pounds and 0.9 pounds, respectively. The lower limit is 4 pounds, and the upper limit is infinity. We input these values into the normalcdf function as normalcdf(4, infinity, 5.4, 0.9). The result of this function is the probability that an infant's weight will be greater than 4 pounds. Based on the normal distribution curve, we can say that there is a high probability that an infant's weight will be greater than 4 pounds.

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50% of Susan's trips to class would take more than 50 minutes.Answer: 50%.

Given data: The average time it takes for Susan to get to her class is 50 minutes. And the standard deviation is 5 minutes. We have to find the proportion of Susan's trips to class would take more than 50 minutes.

Solution:To find out the required proportion, we need to calculate the Z-score first.

\(Z-score = (X - μ)/σ\)

where, X = the value of the random variable (Susan's time to get to class)

μ = the population mean (average time)σ = the standard deviation

Here, X = 50 minutes

μ = 50 minutes

σ = 5 minutes

Z-score = (X - μ)/σ

= (50 - 50)/5

= 0

The Z-score table indicates that the area under the standard normal distribution curve for a Z-score of 0 is 0.5. Therefore, 50% of Susan's trips to class would take more than 50 minutes.Answer: 50%.

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T= 250 + 45a.

Since the cost of the medicine costs $250, and there is $45 dollars per appointment then 45 a would represent the 45 dollars for every appointment she chooses to have.

Hope this helps and have a nice day.

-R3TR0 Z3R0

Equivalent ratios are the ratios which are the same when we compare them.

Ratios that can be streamlined or reduced to the same value are said to be equivalent. In other words, if one ratio can be written as a multiple of the other, then they are said to be equivalent.

Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you can determine the equivalent ratio. The procedure is the same as finding equivalent fractions.

The term "proportion" also refers to the equality of two ratios. For example 3/6 and 8/16 are equivalent as they can be reduced to 1/2.

An overview was given as the information is incomplete.

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Answer:

Since there is one value of y for every x in the relation above, yes this relation is a function.

I hope this helped you get to your answer, or at least help you out a bit. Thanks and have a great day of learning!

Answer:

x=35

Step-by-step explanation:

3x+15=2x+50 (opposite angles are equal)

3x=2x+35

x=35

Answer:

your answers are

Step-by-step explanation:

1. \(2x-3=y+3\)

\(2x-3=y+3\\ 2x+y=-3\\divide |by |2\\x+y=-1.5\)

so x + y = -1.5

The ways 3 different novels, 2 different mathematics books, and 1 biology book can be arranged on a bookshelf are as follows: All books are unique.

The total number of books that can be arranged in this case is:

3! x 2! x 1! = 6 x 2 x 1 = 12.

There are 6 possible ways to arrange the 3 novels.There are 2 possible ways to arrange the 2 mathematics books.There is only 1 possible way to arrange the biology book. So, the total number of ways these books can be arranged in this scenario is,

6 x 2 x 1 = 12.

Two of the novels are a set The total number of books that can be arranged in this case is:

2! x 2! x 1! = 2 x 2 x 1 = 4.

There are 2 possible ways to arrange the set of novels (as there are only 2).There are 2 possible ways to arrange the other novel.There are 2 possible ways to arrange the mathematics books.There is only 1 possible way to arrange the biology book. So, the total number of ways these books can be arranged in this scenario is

2 x 2 x 2 x 1 = 8.

I hope this helps!

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70% percentage of the original roland-morris score of 20 was improved to the final score of 6.

Given that,

We have to find what percentage of the original roland-morris score of 20 was improved to the final score of 6.

We know that,

The original roland-morris score of 20 was improved to the final score of 6.

The initial score = 20

Final Score = 6

The improvement is 20 - 6 = 14

So,

The percent improvement is (14/20)* 100 = 70%

Therefore, 70% percentage of the original roland-morris score of 20 was improved to the final score of 6.

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The smallest value within the class is the lower class limit, and the largest value within the class is the upper class limit.

A class limit is a set of boundary values in the form of a range that describes the lowest and highest data values that a class can contain. The lower class limit refers to the smallest data value in a class, whereas the upper class limit refers to the largest data value in a class. The width of a class is determined by the difference between the upper and lower class limits. Here are a few examples to give you a better understanding of how this works:

Class:              5-9 5 9

Lower Limit:    10-14 10 14

Upper Limit:    15-19 15 19

This shows class limits for three different classes.

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The missing values of the proportion are;

a. 18

b. 19.5

c. 45%

d. 180

The percentage of a number can be defined as the fraction of a number and hundred.

It is represented with the symbol, %.

From the information given, we have that'

1. 6% of 30

This is represented as;

60 /100 × 30

Multiply the values

18

2. 65% of 30

This is represented as

65/100 × 30

Multiply the values

1950/100

19.5

3. 18/40 × 100

Multiply the values

1800/40

45%

4. 81 = 45/100x

cross multiply the values

x = 180

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Answer:

-7 and 1 multiply to 7 and add up to -6

Step-by-step explanation:

-7 and 1 multiply to 7 and add up to -6

Answer:the 2nd choice

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

______horizontal_________lines only intersect the y axis; ______vertical_________ only intersect the x axis

Vertical lines only intersect the y axis; horizontal lines only intersect the x axis.

A vertical line is a line parallel to the Y-axis in a coordinate plane. The x-coordinate for any point along this line will be the same. The coordinate points of vertical lines are, for example, represented as (5, 0), (1, 0), (- 4, 0), and so on.

Vertical lines run parallel to the y-axis, so their slope isn’t defined. As a result, the equation of the vertical line crossing the x-axis at any point ‘a’ is: x = a

Where, x is the coordinate of a point on the line and a is the point at which the line crosses the x-intercept.

A horizontal line is a straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system. In other words, the straight line that does not make any intercept on the X-axis and it can have an intercept on Y-axis is called horizontal line.

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Answer:

15cm

Step-by-step explanation:

Theorem: All tangents to a circle from the same point are equal.

Sine E, F, G and H are points of Tangency, by the theorem above:

The diameter line EC divides the Isosceles Trapezoid into two equal parts.

Therefore:

We then have by the equality above that:

BC=BF+FC

=5+10

=15cm

Answer:  sqrt(x+1)+4

This is the same as writing \(\sqrt{x+1}+4\)

The +4 is not under the square root

==========================================================

Explanation:

g(x) is the same as y, since they're both outputs of a function

So we have the starting equation y = (x-4)^2 - 1

Swap x and y and solve for y to get the inverse.

y = (x-4)^2 - 1

x = (y-4)^2 - 1

x+1 = (y-4)^2

(y-4)^2 = x+1

y-4 = sqrt(x+1) ... see note below

y = sqrt(x+1)+4

Note: Recall that \(x \ge 4\) and we swapped x and y. This ultimately means \(y \ge 4\) and this only occurs if we picked the positive version of the square root (ignoring the negative version).

Answer:

We had this question last week let me check my book real quick.

Answer:

Cafe A - 54

Cafe B - 56

Step-by-step explanation:

Answer:

$ 6.50

Step-by-step explanation:

Based on the given conditions, formulate 3+2 × 1.75

calculate the first two terms 3+3.5

calculate the first two terms 6.5

Answer: 6.5