9. (10 points) Find the inverse Laplace transform of 232 +7s+14 (32+2x+10) (5+1)
8. (10 points) Find the Laplace transform of f(t) = t- cos(3t) +e7+(t - 1)2.

Here is the table with the earnings per share (EPS) for each year, rounded to the nearest cent.

Year Net income Preferred dividends Shares outstanding EPS formula EPS

2020 $100,000 $0 100,000 (n) $1.00

2021 $120,000 $0 100,000 (n) $1.20

2022 $140,000 $0 100,000 (n) $1.40

Formula reference: (n) = (Net income - Preferred dividends) / Weighted average-number of common shares outstanding

Here are the steps on how to calculate the EPS:

The EPS formula is a simple way to measure a company's profitability. It is calculated by dividing the net income after preferred dividends by the weighted average number of common shares outstanding. The higher the EPS, the more profitable the company is.

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The radius of the cone given the diameter is 5 feet.

The area of the base of the cone is 25π square feet

The volume of the cone is 75π cubic feet.

Volume of a cone: V = 1/3Bh

Height of the cone = 9 feet

Diameter of the cone = 10 feet

Radius of the cone = diameter / 2

= 10/2

= 5 feet

Area of the base of the cone = πr²

= π × 5²

= π × 25

= 25π squared feet

Volume of a cone: V = 1/3Bh

= 1/3 × 25π × 9

= 225π/3

= 75π cubic feet

Hence, the volume of the cone is 75π cubic feet

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Answer:

5, 25, 75

Proof:

Answer:

36

Step-by-step explanation:

9     4

18    8

27   12

36*  16

      20

      24

       28

       32

       36*

36 is the least common denominator.

9 x 4 = 36

1/4 = 9/36

5/9 = 20/36

The correct statement is c. The Adjusted R-squared is a measure used in multiple regression analysis that is between 0 and 1. It is different from the R-squared value in simple linear regression.

The Adjusted R-squared can decrease if the addition of another X regressor does not sufficiently lower the sum of squared residuals (SSR) relative to the impact of increasing the number of predictors (k). It measures the proportion of the variance explained by the predictors, adjusted for the number of predictors and the sample size, rather than the ratio of the sum of squared residuals to the total sum of squares. It provides a measure of how well the regression model fits the data, and it ranges between 0 and 1. A value closer to 1 indicates that a higher proportion of the variance in the dependent variable is explained by the predictors.

Adding another X regressor to the multiple regression model can impact the Adjusted R-squared. If the additional regressor does not significantly contribute to reducing the sum of squared residuals (SSR) relative to the increase in the number of predictors (k), the Adjusted R-squared can decrease. This means that the added regressor does not improve the model's ability to explain the variance in the dependent variable adequately.

However, the Adjusted R-squared does not directly measure the ratio of the sum of squared residuals to the total sum of squares. Instead, it represents the proportion of the variance explained by the predictors, adjusted for the number of predictors and the sample size. It penalizes models with a large number of predictors that may overfit the data, thereby providing a more reliable measure of the model's goodness of fit.

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9514 1404 393

Answer:

  g(x) decreasing: (-4, 0)

  f(x) ≤ g(x) on [-4, -2] U [2, 3]

Step-by-step explanation:

I agree with most of your answers.

Any point where there is a horizontal tangent will not be in that interval. That excludes x=-4 and x=0. The "decreasing" interval of g(x) is (-4, 0), with round brackets.

The domain of g is only [-4, 3], so functions f and g can only be compared on their joint domain. f(x) ≤ g(x) on the intervals [-4, -2] U [2, 3].

Answer:

I helped you with a previous question. So I got your pass.

Step-by-step explanation:

bla bla bla bla

have a great day!

Answer:

880

Step-by-step explanation:

Answer:

Rs. 3,960 is the cost of carpeting.

Answer:

x=65

Step-by-step explanation:

90 degree angle

90-25= 65

It is a straight line with angle measures of 90°, x° and 25° opposite to the angle marked 180°.

Hence, their sum is 180°.

➛\(90 \degree + x + 25 \degree = 180 \degree\)

➛\(115 \degree + x = 180 \degree\)

Then,

➛\( x = 180 \degree - 115 \degree\)

➛\(x = 65 \degree\)

The measure of the angle will be 65° (Ans)

~\( \large{ \blue{ \sf{FadedElla}}}\)

Answer:

30.67

Step-by-step explanation:

Given the following

Opposite side = x

Adjacent = 17

Angle = 61degrees

Using the SOH  CAH TOA identity

tan theta = opp/adj

tan 61 = x/17

x = 17tan61

x = 17(1.8040)

x = 30.67

Hence the value of x is 30.67

Answer:

13. 3

Step-by-step explanation:

Given Points:

(x1= 4, y1 = 11), (x2= - 9, y2 = 8)

Distance Formula:

d² = (x2 -x1)² + (y2 -y1)²

Substitute and Calculate:

d² = ( -9 -4)² + ( 8 -11)²

d² = (-13)² + (-3)²

d = √(169+9)

d = √178

d = 13.34166406 round to the nearest tenth

d = 13. 3

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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The final cost of an item with an original price of $23, after a 15% discount, can be calculated using the expression p - 0.15p. The final cost is $19.55.

To calculate the final cost of an item with an original price of $23 after a 15% discount, we can use the expression p - 0.15p. In this expression, p represents the original price of the item.

Substituting the given value of $23 into the expression, we have:

Final cost = $23 - 0.15($23)

Final cost = $23 - $3.45

Final cost = $19.55

Therefore, the final cost of an item with an original price of $23, after a 15% discount, is $19.55.

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The value of the z-score for the value of sample 48 will be negative 0.4.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The mean is 50 and the standard deviation is 5.

Then the value of the z-score for the value of sample 48 will be

z = (x - mean) / (standard deviation)

Then we have

z = (48 - 50) / (5)

z = -2 / 5

z = -0.4

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We can make use of a slope field to sketch the two approximate solutions of the differential equation. The slope field for the differential equation is dy/dx.

a) We will now mark the point (0,4) on the slope field as shown in the image below.

Solution 1: We will begin at the point (0, 4) and move along the slope lines to obtain the first solution. This first solution is shown in blue in the image below,

Solution 2: For the second solution, we will begin at the point (0,4) and move along the slope lines in the opposite direction to obtain the second solution. This second solution is shown in red in the image below.

Substituting x = 0 and y = 4, we get: 4 = sin(0) + C4 = 0 + CC = 4

Therefore, the particular solution is: y = sin(x) + 4

Below is the graph of the solution: Graph of y = sin(x) + 4

We can compare this graph of the particular solution with the sketches in part (a).

The graph of the solution matches the first solution in blue.

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(a)i. Evaluating the constant:

\($$\int_{-1}^{1} c(1+x)(1-2x) dx = 1$$$$\implies c = \frac{3}{4}$$\)

Therefore, the probability density function is:

\($$f(x) = \frac{3}{4} (1+x)(1-2x), -1< x < 1$$\) ii. Plotting the probability density function:

From the graph, it is observed that the density function is skewed to the left.

(b)i. The mean:

\($$E(X) = \int_{-1}^{1} x f(x) dx$$$$E(X) = \int_{-1}^{1} x \frac{3}{4} (1+x)(1-2x) dx$$$$E(X) = 0$$\)

ii. The second moment about the origin:

\($$E(X^2) = \int_{-1}^{1} x^2 f(x) dx$$$$E(X^2) = \int_{-1}^{1} x^2 \frac{3}{4} (1+x)(1-2x) dx$$$$E(X^2) = \frac{1}{5}$$\)

Therefore, the variance is:

\($$\sigma^2 = E(X^2) - E(X)^2$$$$\implies \sigma^2 = \frac{1}{5}$$\)

iii. The standard deviation:

$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{5}} = \frac{\sqrt{5}}{5}$$(c)

i. The cumulative distribution function:

\($$F(x) = \int_{-1}^{x} f(t) dt$$$$F(x) = \int_{-1}^{x} \frac{3}{4} (1+t)(1-2t) dt$$\)

ii. The probability density function can be obtained by differentiating the cumulative distribution function:

\($$f(x) = F'(x) = \frac{3}{4} (1+x)(1-2x)$$\)

iii. Evaluating\(P(-0.2 < X <0.2):$$P(-0.2 < X <0.2) = F(0.2) - F(-0.2)$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} f(x) dx$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} \frac{3}{4} (1+x)(1-2x) dx$$$$P(-0.2 < X <0.2) = 0.0576$$\)

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please see both picture for answer

Answer:

the number is -7.6

Step-by-step explanation:

Important terms

Applying this vocabulary to the phrase "five times a the sum of a number and 15 is 37" , we can convert it into a mathematical expression

We have 5 times the sum of a number and 15 is 37 ( it's important to know that 5 is being multiplied by (unknown number + 15) rather than it being multiplied just by the unknown number)

Let unknown number = x

We get 5(x + 15) = 37

We now want to solve for x algebraically

5(x + 15) = 37

==> divide both sides by 5

x + 15 = 7.4

==> subtract 15 from both sides

x = -7.6

The unknown number is -7.6

Given the speeds of each runner : Liz runs 10 feet per second, Will runs 264 feet in 33 seconds, Jake runs 1 mile in 384 seconds, Zach runs 875 feet in 1 minute. We need to convert the speeds of each runner into the same unit  that is feet per second in order to compare them.

Liz runs 10 feet per second.

Will runs 264 feet in 33 seconds, which is (264/33) ≈ 8 feet per second.

Jake runs 1 mile in 384 seconds, which is (1 mile = 5280 feet) (5280/384) ≈ 13.75 feet per second.

Zach runs 875 feet in 1 minute, which is (875/60) ≈ 14.58 feet per second.

Comparing the speeds, we can see that Zach runs the fastest at approximately 14.58 feet per second.

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Answer:

good night :))))))))))))

Answer:

umm this question is from a wile ago hehe but anyways i got points hehehe

Step-by-step explanation:

Answer:

Where is that question you're talking about please

Answer:

the set of possible values of the independent variable or variables of a function.

Step-by-step explanation:

Answer:

All the x-values in the ordered pairs together make up the domain

Step-by-step explanation:

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

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Answer:

c

Step-by-step explanation:

The work done by the gas during the isothermal expansion is 331.32 J.

Isothermal Expansion refers to a process in which the temperature of a system stays constant while the volume increases. In this process, an ideal gas expands from 1.1 m³ to 1.8 m³, and the gas constant is R = 8.314 J/(mol K).

The work done by the gas during the isothermal expansion can be calculated as follows:Answer:During an isothermal process, the change in internal energy of the system is zero since the temperature remains constant.

Therefore,ΔU = 0The first law of thermodynamics is given by:ΔU = q + w

where q is the heat absorbed by the system, and w is the work done on the system.Since ΔU = 0 for an isothermal process, the above equation reduces to:w = -q

During an isothermal process, the heat absorbed by the system is given by the equation:q = nRTln(V₂/V₁)Where, n is the number of moles, R is the gas constant, T is the temperature, V₁ is the initial volume, and V₂ is the final volume.

Substituting the given values, we have:q = (1 mol) × (8.314 J/(mol K)) × (293 K) × ln(1.8 m³ / 1.1 m³)q = 331.32 J

Therefore, the work done by the gas during the isothermal expansion is given by:w = -qw = -(-331.32 J)w = 331.32 J

Thus, the work done by the gas during the isothermal expansion is 331.32 J.

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The population mean, or average score for the population on a certain variable, is symbolised as follows:μ = ( Σ Xi ) / N.

The mean of a data set is the sum of all values ​​divided by the total number of values, often called the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean", it is the most commonly used measure of central tendency. This result is obtained by dividing the total number of values ​​in the data set by the sum of all those values. Both raw data and data combined into frequency tables can be used in calculations. Mean refers to the average of a number. The calculation is simple: divide by the number of numbers when you added all the numbers. the total divided by the number.

The population mean or population mean score for  a given variable is symbolized as follows:μ = ( Σ Xi ) / N. The symbol 'μ' represents the population mean.

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Answer: To find the value of k, we can use the fact that the product of two numbers is equal to the product of their sum and difference. In this case, we have:

(n + 4)(n + k) = n^2 - n - 20

The product of their sum and difference is:

(n + 4 + n + k)(n + 4 - n - k) = (2n + 4 + k)(-k)

Multiplying out the factors, we get:

2n^2 + 4n + 4k - k^2 = n^2 - n - 20

Combining like terms, we get:

n^2 + 3n + 4k - k^2 = -20

This equation can be rewritten as:

k^2 - 3n - 4k + 20 = 0

To complete the square, we need to add and subtract ((3/2)^2 = (9/4)) from both sides:

k^2 - 3n - 4k + 9/4 + 20 - 9/4 = 0

This simplifies to:

(k - 3/2)^2 = 25/4

Taking the square root of both sides, we get:

k - 3/2 = sqrt(25/4)

Adding 3/2 to both sides, we get:

k = 3/2 + sqrt(25/4)

The value of k is therefore 3/2 + sqrt(25/4).

The value of k is -5.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given an expression,

n² - n - 20

This can be factored as (n + 4)(n + k).

We have to find the value of k.

Equating,

n² - n - 20 = (n + 4)(n + k)

n² - n - 20 = n² + 4n + kn + 4k

n² - n - 20 = n² + (4 + k)n + 4k

Equating,

4 + k = -1

k = -5

Hence the value of k is -5.

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Answer:

4

Step-by-step explanation:

Answer:

this don't make any sense bro

Step-by-step explanation:

what is the number in between 2 3

21 + 15 can be written as the product 3 x 12, where 3 is the GCF of 21 and 15.

What are factors?

In mathematics, factors are numbers that can be multiplied together to obtain another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these numbers can be multiplied in different combinations to produce 12.

The greatest common factor (GCF) of 21 and 15 is 3. To write 21 + 15 as a product using the GCF as one of the factors, we can first factor out the GCF from each term:

21 + 15 = 3 x 7 + 3 x 5

Now, we can use the distributive property of multiplication over addition to factor out the GCF:

21 + 15 = 3 x (7 + 5)

Simplifying the expression inside the parentheses, we get:

21 + 15 = 3 x 12

Therefore, 21 + 15 can be written as the product 3 x 12, where 3 is the GCF of 21 and 15.

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Answer: