Okay I put -646/15 but it’s wrong can someone help me

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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Thus, the total surface area of the given triangular prism is found to be:

A = 232  ft².

A prism is a solid form that is enclosed by plane faces on all of its sides. A prism has two different kinds of faces. Bases refer to the identical top and bottom faces.

The name "prism" refers to the form of these bases. For instance, a prism is referred to be a triangular prism if its base is triangular.

The dimension of the prism is shown:

Perimeter =  sum of bases

P = 7 + 5 +5 = 17

P = 17 ft

Curved surface area = perimeter x height

                               = 17 × 8

                              = 136 ft²

Base area shown triangular prism = 1/2 *h (b1 + b2)

= 1/2 * (5 + 7)

= 48 ft²

Now,

Total surface area of shown triangular prism:

A = P*h + 2* base area

A = 136 + 2*48

A = 232  ft²                            

Thus, the total surface area of the given triangular prism is found to be:

A = 232  ft².

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Complete question:

Find the total surface area of the prism.

7 ft

8 ft

5 ft

5 ft

The picture is attached:

Because is likely that the first outcome affected the second one, we can conclude that the events are dependent.

Two events are independent if the outcome of one can't affect the outcome of the other.

Here, first, she chooses a blue marker from one box and then a yellow one from another, these are the two events.

Now, these are independent or dependent?.

Well, the fact that she chooses a blue marker first, means that she probably would not want to choose another blue marker for the second one. So yes, the first outcome does affect the second outcome, meaning that the events are dependent.

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Answer:

There are 336 ways to have 8 horses place for 1st, 2nd, and 3rd place

Step-by-step explanation:

Answer:

g(x) = 3 ln(x)

Step-by-step explanation:

The sequence of transformations that maps DOG to D'O'G' is a rotation of about 90 degrees of the origin, followed by a translation of 5 units right.

Rotation is a physical phenomenon where an object spins around an axis. It is a type of circular motion where an object moves in a circular path around a central point.

To accomplish this transformation, first, the point representing the letter D is rotated 90 degrees clockwise around the origin so that it is now pointing in the same direction as the letter O. After that, the point representing the letter D is translated 5 units to the right, resulting in the final transformation of DOG to D'O'G'.

Thus, the sequence of transformations that maps DOG to D'O'G' is a rotation of about 90 degrees of the origin, followed by a translation of 5 units right.

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Answer:

The missing number is 11.

Step-by-step explanation:

3+2=5; 5+4=9; The pattern is +2, +4.

3 + 2 = 5 ⇒ 5 + 4 = 9 ⇒ 9 + 2 = 11 ⇒ 11 + 4 = 15

\(S_1 = \frac{a+b}{2}h = \frac{7+9}{2}*5=\frac{18*5}{2}= 9 * 5 = 45~m^2\)

\(S_\triangle = \frac{ab}{2} = \frac{5*9}{2} = \frac{45}{2} = 22,5~m^2\)

\(S = S_1 + S_\triangle = 45 + 22,5 = 67,5~m^2\)

Answer: 67,5 m².

Answer:

Rat rat rat rat:)

Step-by-step explanation:

Answer:

2x+4 or 4+2x

Step-by-step explanation:

The process involves finding the complementary solution x_c(t) by solving the homogeneous equation, determining the particular solution x_p(t) using the method of variation of parameters, and combining them to obtain the general solution x(t).

1. The method of variation of parameters can be used to solve the initial value problem x' = axf(t), x(a) = xa, where a and f(t) are given functions. In this case, we have the values a = 4 - 2t and f(t) = 16t^2. We need to find the solution x(t) using the initial condition x(0) = 2.

2. To solve the initial value problem using the method of variation of parameters, we first find the complementary solution x_c(t) by solving the homogeneous equation x' = ax.

3. For the given a = 4 - 2t, the homogeneous equation becomes x' = (4 - 2t)x. By separation of variables and integration, we find the complementary solution x_c(t) = Ce^(2t - t^2).

4. Next, we find the particular solution x_p(t) by assuming a particular solution of the form x_p(t) = u(t)e^(2t - t^2), where u(t) is a function to be determined.

5. Differentiating x_p(t) and substituting it into the original differential equation, we can solve for u'(t) and determine the form of u(t). After finding u(t), we substitute it back into x_p(t).

6. Finally, the general solution is given by x(t) = x_c(t) + x_p(t). By substituting the values and integrating, we can obtain the specific solution x(t) for the given initial condition.

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Answer:

Shown below.

Step-by-step explanation:

Test Marks          Tally          Frequency          Percentage

1                                                    8                   8/60 = 0.133

2                                                   6                   6/60 = 0.100

3                                                   5                   5/60 = 0.083

4                                                   5                   5/60 = 0.083

5                                                   5                   5/60 = 0.083

6                                                   8                   8/60 = 0.133

7                                                   6                   6/60 = 0.100

8                                                   7                   7/60 = 0.116

9                                                   4                   4/60 = 0.066

10                                                 5                   5/60 = 0.083

Total                                            59                 59/60 = 0.983

For the Tally section, I believe you just fill in tally marks corresponding to the frequency. One of the observations in the table is 0, which is not a column in the frequency table.

Answer:

no solutions

Step-by-step explanation:

same slope different y intercepts

Based on the given data, there is not enough evidence to suggest a significant difference in the average number of words spoken per day between male and female students at this university at a significance level of 0.05.

The critical value will be:

= ✓(55)(7520²) + (55)(9108²))/(56 + 56 - 2))

≈ 8285.89

t = (16177 - 16569) / (8285.89 * ✓(1/56 + 1/56))

≈ -0.4704

The critical value for a two-tailed test with α = 0.05 and df = 110 is approximately ±1.983.

Since the absolute value of the test statistic (0.4704) is less than the critical value (1.983), we fail to reject the null hypothesis.

Therefore, based on the given data, there is not enough evidence to suggest a significant difference in the average number of words spoken per day between male and female students at this university at a significance level of 0.05.

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Answer:

Statement A describes all possible solutions where x = 2. April will purchase 2 bottles of orange juice and 4 bottles of apple juice.

A negative correlation means that as the x variable decreases, the y variable tends to decrease as well. In other words, there is an inverse relationship between the two variables.

A negative correlation indicates that when the value of one variable decreases, the value of the other variable also tends to decrease. It implies an inverse relationship between the two variables. For example, if we consider the variables "temperature" and "ice cream sales," a negative correlation would mean that as the temperature decreases, the sales of ice cream also tend to decrease.

To determine the strength of a negative correlation, we can calculate the correlation coefficient, often denoted by "r." The correlation coefficient ranges from -1 to +1, with -1 indicating a perfect negative correlation. The closer the value of "r" is to -1, the stronger the negative correlation between the variables.

In summary, a negative correlation suggests that as the x variable decreases, the y variable tends to decrease as well. It signifies an inverse relationship between the two variables. The strength of the negative correlation can be measured using the correlation coefficient, where values closer to -1 indicate a stronger negative correlation.

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The hypothesis is called the alternative hypothesis test.

According to the statement

We have to explain about the alternative hypothesis.

So, For this purpose, we know that the

The alternative hypothesis is one among ll|one amongst |one in every of} two mutually exclusive hypotheses in a hypothesis test. the choice hypothesis states that a population parameter doesn't equal a specified value.

From the given information:

she randomly selects houses during this neighborhood and compares their estimated market price within the current year to their estimated value within the previous year. suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market price of the previous year from the value of the present year.

Then

the alternative hypothesis test usually suggests that there's an opportunity of variation (difference) within the data observed.

Hence, since we are told the "real real estate agent believes that the values of homes within the neighborhood she works in have increased (the chance of variation) from last year," which "each difference is calculated by subtracting the market price of the previous year from the market price of this year," we are able to reach the conclusion that this can be an example of an alternate hypothesis test.

So, The hypothesis is called the alternative hypothesis test.

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Answer:

A1. The rectangular coordinates for the point (5, 5TT ) are

(5, 5т).

A2. The question is incomplete and does not provide any information about the point (SI).

A3. To find the rectangular coordinates for the point (3,

-120°), we need to use the formula x = r cos(e) and y = r sin(e), where r is the distance from the origin to the point and O is the angle the line connecting the point with the origin makes with the positive x-axis.

A4. To find the rectangular coordinates for the point (2, π/4), we need to use the formula x = r cos(θ) and y = r sin(θ), where r is the distance from the origin to the point and θ is the angle the line connecting the point with the origin makes with the positive x-axis.

We have r = 2 and θ = π/4.

So, x = r cos(θ) = 2 cos(π/4) = √2 and y = r sin(θ) = 2 sin(π/4) = √2.

Therefore, the rectangular coordinates for the point (2, π/4) are (√2, √2).

A5. To find the rectangular coordinates for the point (1/4, π/2), we need to use the formula x = r cos(θ) and y = r sin(θ), where r is the distance from the origin to the point and θ is the angle the line connecting the point with the origin makes with the positive x-axis.

We have r = 1/4 and θ = π/2.

So, x = r cos(θ) = (1/4) cos(π/2) = 0 and y = r sin(θ) = (1/4) sin(π/2) = 1/4.

Therefore, the rectangular coordinates for the point (1/4, π/2) are (0, 1/4).

A6. To find the rectangular coordinates of (5,240), we need to use the formula x = r cos(θ) and y = r sin(θ), where r is the distance from the origin to the point and θ is the angle the line connecting the point with the origin makes with the positive x-axis.

We have r = 5 and θ = 240°. Converting 240° to radians, we get θ = 4π/3.

So, x = r cos(θ) = 5 cos(4π/3) = -2.5 and y = r sin(θ) = 5 sin(4π/3) = -4.330.

Therefore, the rectangular coordinates for the point (5,240) are (-2.5, -4.330).

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Step-by-step explanation:

Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Answer:

What is item 12? Not enough information.

Answer:

The correct answer is D: 5x3 + 11x5 ft

Step-by-step explanation:

Answer:

The correct answer is D: 5x3 + 11x5 ft

Step-by-step explanation:

The equation to determine the price of a pizza for a given number of toppings could be represented as follows: Price = Base Price + (Price per Topping x Number of Toppings)

Let's assume the base price of a medium pizza is $10, and the price per topping is $1. If you order your favorite medium pizza with, let's say, 3 toppings, we can calculate the expected price using the equation: Price = $10 + ($1 x 3) = $10 + $3 = $13. Therefore, you would expect to spend $13 for your favorite medium pizza with 3 toppings.

The equation allows for flexibility in pricing based on the number of toppings chosen. Each additional topping incurs an extra cost, which is added to the base price of the pizza. This pricing model enables customers to customize their pizza according to their preferences and budget, as they can choose the number of toppings they desire while knowing the corresponding price.

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Answer:

Aonnalin, great name  :)  answer as below

Step-by-step explanation:

They tell us to use slope-intercept form.   This is something you will just have to remember  y = mx+b    

It is confusing b/c there is the other one, the point-slope formula too.  but just remember both and know that the point-slope one is to get to the slope-intercept one.    y-y1 = m(x-x1)  

m= slope

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

P1= (0,7)  in the form (x1,y1)

P2 =(8,-2) in the form (x2,y2)

m = -2-7 / 8-0

m = -9 / 8

now that we have the slope, just use either point with the point-slope

y-7 = (-9/8)(x-0)

y-7 = -9x/8

y = -9x/8 + 7

y = \(\frac{-9}{8}\) X + 7

slope-intercept form  :)

The required after 8 years, the investment will be worth approximately $156,753.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Amount = principal[1 + r/n]ⁿᵃ

Principal = P rate= r Time =a  , n = compounding frequency

Here,
To calculate the future value of Joshua's investment after 8 years with an interest rate of 6% compounded daily, we can use the formula:

In this case, P = $97,000, r = 6% = 0.06, n = 365 (since the interest is compounded daily), and t = 8.

So, we have:

\(A = $97,000 \times (1 + 0.06/365)^{365 * 8}\)

A = $195,239.00

Therefore, after 8 years, the investment will be worth approximately $156,753.

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Step-by-step explanation:

you know how functions work ?

the variable (or variables) in the findings expression is a placeholder for actual values.

when we have an actual value, we put that into the place of the variable and then simply calculate.

x = 5

therefore, the functional calculation is

y = 3×5 - 7 = 15 - 7 = 8

keep in mind the priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

therefore, we need to calculate "3×5" before we deal with the "- 7" part.

Answer:

Step-by-step explanation:

y=8

We want to know which of the given expressions will produce an answer with three significant figures. That is, it has an answer with three nonzero numbers.

Let us find the values to know

Answer:

Lin originally had 4 bags * the same amount of apples per bag = 4 * x apples.

After eating 1 apple from each bag, she was left with 4 * x - 4 apples = 28 apples.

Therefore, each bag originally contained x = 28 + 4 = 32 apples.

Answer:

A and C

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4x2+48x+144=52

Step 2: Subtract 52 from both sides.

4x2+48x+144−52=52−52

4x2+48x+92=0

For this equation: a=4, b=48, c=92

4x2+48x+92=0

Step 3: Use quadratic formula with a=4, b=48, c=92.

x=−48±√832/8

x=−6+√13 or x=−6−√13