Use appropriate algebra and theorem 7. 2. 1 to find the given inverse laplace transform. (write your answer as a function of t. ) ℒ−1 (s 1)3 s5

Answer:

6x-1

Step-by-step explanation:

I dont know  how to explain but it is correct

Answer:

6x – 1

Step-by-step explanation:

The simplification of the trigonometric equation gives:

\(cos^2(x) + cot^2(x)\)

Here we have the following expression:

\(\frac{1 - sin^2(x)}{cot^2(x)}\)

Remember that:

\(cot^2(x) = \frac{cos^2(x)}{sin^2(x)}\)

Then we can rewrite our expression as follows:

\(\frac{1 - sin^2(x)}{cot^2(x)} = (1 - sin^2(x))*\frac{cos^2(x)}{sin^2(x)}\)

We can expand that to get:

\((1 - sin^2(x))*\frac{cos^2(x)}{sin^2(x)} = \frac{cos^2(x)}{sin^2(x)} - \frac{cos^2(x)}{sin^2(x)} *sin^2(x) = \frac{cos^2(x)}{sin^2(x)} + cos^2(x) = cot^2(x) + cos^2(x)\)

That is the expression simplfiied.

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From the given information provided, the number of people having brown eyes in town is 180.

If the probability that a person in the town has brown eyes is 2/5, then we can expect that 2 out of every 5 people have brown eyes.

To find the number of people in the survey who would be expected to have brown eyes, we can use the following proportion:

(2/5) = (x/450)

where x is the number of people expected to have brown eyes.

Solving for x, we can cross-multiply:

5x = 2 × 450

5x = 900

x = 180

Therefore, the expected number of people in the survey who would have brown eyes is 180.

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Answer:

-5 = Contraction

-(1/4) = Contraction

3.5 = Expansion

(6/7) = Expansion

Step-by-step explanation:

Contraction means decreasing and expansion means increasing. So the numbers containing negative signs are contraction and the numbers containing positive signs are expansion.

Hope this will help and if so, please mark me brainliest.

Answer:

a

Step-by-step explanation:

Assuming the randomly throw is equally distributed along the rectangle area, the probability of hitting the square is the fraction of the area of the square with respect to the total are of the rectangle.

The area of the square is the square of its side:

And the area of the rectangle is the product of its lengths by its height:

So, the probability is the area of the square divided by the area of the rectangle:

The probability if 9%.

The equation -2x=3/8 is not a literal equation.

A literal equation can be defined as an equation which primarily of letters.

It is an equation  made up of several variables or letters.

Examples of literal equations are;

We can see from the examples shown that the equations or formulas have several variables or letters that could be written in terms of other variables.

Given the equation;

-2x=3/8

We can see that there is only one variable to be worked out and hence, is not a literal equation.

Thus, the equation -2x=3/8 is not a literal equation.

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The equation of the line that passes though (-2, 0 and have a slope of 1 is y = x + 2.

The equation of a line can be represented in slope in intercept form as follows:

y = mx + b

where

Therefore, the slope of a line is the change in the dependent variable with respect to the change in the independent variables.

Hence,

slope = 1 and the line passes through(-2, 0).

Therefore,

y = x + b

let's find b using (-2, 0)

0 = -2 + b

b = 2

Therefore, the equation is y = x + 2.

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Answer:

0.075 is less

Step-by-step explanation:

It is 0.075 because 0.96 is closer to 1 and so is greater

Answer:

  (d)  x = 4

Step-by-step explanation:

You want the solution to the system of equations using the given graph.

The solution to the equation f(x) = g(x) is the x-coordinate of the point(s) on their graphs where the curves intersect.

The graph shows the point of intersection of the two functions is (4, 1). This is the solution you have marked in the supplied image.

  x = 4

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A. For model log(y) only:

Answer: 23.5325

B. For model log(x) only:

Answer: 0.9592

C. For model log(y) and log(x):

Answer: 3.2000

A more detailed explanation of the answer.

For the given question, suppose a slope of 3.2 is obtained for a model fitted to log-transformed data. The task is to calculate the back-transformed slope for each of the following models.

A. For model log(y) only:
Backtransformed slope = exp(3.2) - 1
1. Calculate exp(3.2) = 24.53253
2. Subtract 1: 24.53253 - 1 = 23.53253
Answer: 23.5325 (rounded to 4 decimal places)

B. For model log(x) only:
Backtransformed slope = 1 - exp(-3.2)
1. Calculate exp(-3.2) = 0.04076
2. Subtract from 1: 1 - 0.04076 = 0.95924
Answer: 0.9592 (rounded to 4 decimal places)

C. For model log(y) and log(x):
Backtransformed slope = 3.2
Answer: 3.2000 (rounded to 4 decimal places)

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The probability of obtaining at least 1 false positive if the number of employees is 500 is 0.5

Probability

In the statistics concept, the probability refers the possible number of way of happening the particular event.

Given,

A test for a certain drug has a 0.1% probability of producing a false positive.

Here we need to find  the probability of obtaining at least 1 false positive if  a company hired 500 drug-free employees.

In the given question, we have the following values,

=> number of employees = 500

=> Probability of false positive = 0.1%

So, the probability of obtaining at least 1 false positive is calculated as,

=> 500 x 0.1/100

=> 5 x 0.1

=> 0.5

Therefore, the probability of obtaining at least 1 false positive is 0.5.

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Explicación paso a paso:

Dado

an = n + 3

bn = 5n-1

a) an-bn = n + 3- (5n-1)

= n + 3-5n + 1

= n-5n + 3 + 1

= -4n + 4

an-bn = 4-4n

b) an + 3bn = (n + 3) +3 (5n-1)

= n + 3 + 3 (5n) +3 (-1)

= n + 3 + 15n-3

= n + 15n + 3-3

= 16n + 0

= 16n

an + 3bn = 16n

3) Dado a1 = 1, a2 = 1

an = an-1 + an-2

Debemos escribir los primeros ocho términos de la secuencia.

a3 = a3-1 + a3-2

a3 = a2 + a1

a3 = 1 + 1

a3 = 2

a4 = a3 + a2

a4 = 2 + 1

a4 = 3

a5 = a4 + a3

a5 = 3 + 2

a5 = 5

a6 = a5 + a4

a6 = 5 + 3

a6 = 8

a7 = a6-a5

a7 = 8 + 5

a7 = 13

a8 = a7 + a6

a8 = 13 + 8

a8 = 21

Por tanto, los primeros ocho términos de la secuencia son 1, 1, 2, 3, 5, 8, 13 y 21

As y varies directly as (x−2)² and y = 5/3 when x = 4, then the equation for y in terms of x is y = (5/12)(x - 2)²

If the values of y varies directly as does of x, then there is a constant say "k" that is true for them, else y does not vary directly as x.

For y = 5/3 when = 4, we can solve for the constant k as follows:

5/3 = k(4 - 2)² {we simplify the expression in the bracket}

5/3 = k2²

5/3 = k4

k = 5/(3 × 4) {cross multiplication}

k = 5/12

Therefore, as y varies directly as (x−2)² and y = 5/3 when x = 4, the equation for y in terms of x is y = (5/12)(x - 2)²

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Answer:

ok, here is your answer

Step-by-step explanation:

The answer is (d) 258.000 g and 2.58×10^-2g.Both numbers have the same number of significant figures, which is six.The first number, 258.000 g, has three significant figures after the decimal point, and three before the decimal point. The zeros after the decimal point are significant because they are part of a measured quantity.The second number, 2.58×10^-2g, is written in scientific notation. It also has six significant figures because the number 2.58 has three significant figures, and the exponent -2 has two significant figures.-

Answer:

1. 4.2 x 10^-7

2. 2.9 x 10^-6

3. 7.1 x 10^-2

4. 2.56 x 10^5

Answer:

least to greatest

4.2 * 10^-7

2.9*10^-6

7.1 * 10^-2

2.56 * 10^5

Step-by-step explanation:

2.56 * 10^5 =256000

4.2 * 10^-7 =0.00000042

7.1 * 10^-2 =0.071

2.9*10^-6 = 0.0000029

Answer:

32 feet

Step-by-step explanation:

See attached worksheet

The sequence of Transformations involved to form ∆A′B′C′ is a reflection over the y-axis, followed by a translation to the right 6 units.

The graph shows two triangles plotted on a coordinate plane.

One triangle is at A (minus 4, 2), B (minus 6, 2), and C (minus 2, 6).

Another triangle is at A prime (2, 2), B prime (4, 2), and C prime (0, 6). ∆ABC goes through a sequence of transformations to form ∆A′B′C′.

The sequence of transformations involved is a reflection over the y-axis, followed by a translation to the right 6 units. The steps to get from ∆ABC to ∆A′B′C′ are as follows:

Step 1: Reflection over y-axis: This transformation can be done by replacing the x-coordinates of each point with their opposites, or by drawing perpendiculars from each point to the y-axis and reflecting them across the y-axis. In either case, the new points are A(-(-4),2) = A(4,2), B(-(-6),2) = B(6,2), and C(-(-2),6) = C(2,6).

Step 2: Translation to the right 6 units: This transformation involves adding 6 units to each of the x-coordinates of the reflected triangle. The new points are A'(2+6,2) = A'(8,2), B'(4+6,2) = B'(10,2), and C'(0+6,6) = C'(6,6).

Therefore, the sequence of transformations involved to form ∆A′B′C′ is a reflection over the y-axis, followed by a translation to the right 6 units.

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Answer:

180⁰

Step-by-step explanation:

Since the angle of straight line is 180⁰

Answer:

A and B = 180 degrees

Step-by-step explanation:

this is because a circle is 360 and a line wich would be cutting the line in half is 180. so the two andles must add up to 180 degrees.

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 7 ) and (x₂, y₂ ) = (3, 19 )

m = \(\frac{19-7}{3-0}\) = \(\frac{12}{3}\) = 4

The line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = 4x + 7 → A

Answer: 24

Step-by-step explanation:

The price to earnings ratio (PE ratio) is used to know if the price of stock of a particular company is either overvalued or undervalued.

The price to earnings ratio is calculated as:

= Price per share/Earnings per share

where Price per share = $60

Earnings per share = $2.50

PE Ratio = $60/$2.50

= 24

Therefore, the PE ratio is 24.

If A and B are independent events, the probability of their intersection (A ∩ B) is 0.2.

If A and B are independent events, the probability of their intersection (A ∩ B) can be calculated using the formula:

P(A ∩ B) = P(A) × P(B)

Given that P(A) = 0.5 (or 5/10) and P(B) = 0.4 (or 4/10).

we can substitute these values into the formula:

P(A ∩ B) = (5/10) × (4/10)

= 20/100

= 0.2

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Step-by-step explanation:

\(\large\underline{\sf{Solution-}}\)

\(\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)\)

Let assume that

\(\rm :\longmapsto\:y = {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)\)

We know,

\(\boxed{\tt{ {cosec}^{ - 1}x = {sin}^{ - 1}\bigg( \dfrac{1}{x} \bigg)}}\)

So, using this, we get

\(\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2x}{1 + {x}^{2} } \bigg)\)

Now, we use Method of Substitution, So we substitute

\( \red{\rm :\longmapsto\:x = tanz \: \rm\implies \:z = {tan}^{ - 1}x}\)

So, above expression can be rewritten as

\(\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2tanz}{1 + {tan}^{2} z} \bigg)\)

\(\rm :\longmapsto\:y = sin^{ - 1} \bigg( sin2z \bigg)\)

\(\rm\implies \:y = 2z\)

\(\bf\implies \:y = 2 {tan}^{ - 1}x\)

So,

\(\bf\implies \: {cosec}^{ - 1}\bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = 2 {tan}^{ - 1}x\)

Thus,

\(\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)\)

\(\rm \:  =  \: \dfrac{d}{dx}(2 {tan}^{ - 1}x)\)

\(\rm \:  =  \: 2 \: \dfrac{d}{dx}( {tan}^{ - 1}x)\)

\(\rm \:  =  \: 2 \times \dfrac{1}{1 + {x}^{2} } \)

\(\rm \:  =  \: \dfrac{2}{1 + {x}^{2} } \)

Hence,

\( \purple{\rm :\longmapsto\:\boxed{\tt{ \dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = \frac{2}{1 + {x}^{2} }}}}\)

Hence, Option (d) is correct.

\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

Looking at the triangles, the information needed to prove that ABC∼△DEF is AC = 10

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

AB and DE, BC and FE, then AC and DF

The solution is worked out using sides BC and FE, then AC and DF

BC / AC = FE / DF

8 / AC = 16 / 20

reducing the fraction 16/20 gives

8 / AC = 8 / 10

hence  AC = 10

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102,566,767, 1,9044828e-10, and 297,060 are the answers to the questions.

The questions above use addition and multiplication to solve the problem.

101,455,348 + 1,111,419 = 102,566,767

0.000000612 x 0.00031119 = 1,9044828e-10

297,060 + 0.0004839 = 297,060

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The equation m = 20d correctly represents the total number of minutes Marie plays the piano in d days.

The equation that shows the total number of minutes, m, Marie plays the piano in d days is:

m = 20d

The equation represents the relationship between the number of days, d, and the total minutes Marie spends playing the piano, m. In this case, since Marie spends 20 minutes playing the piano every day, the total minutes played can be calculated by multiplying the number of days, d, by 20.

The equation m = 20d states that the total minutes played (m) is equal to 20 times the number of days (d). For example, if Marie plays the piano for 3 days, substituting d = 3 into the equation would give m = 20 × 3 = 60 minutes.

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Answer:

x = 114

Step-by-step explanation:

114 and x are vertical angles, therefore they are congruent.

Answer:

Vertical Angles are equal so 114

Step-by-step explanation:

A reason not to use a chi-square test of homogeneity to analyze a set of data is if the assumptions of the test are not met. These assumptions include:

1. The data must be categorical, meaning it consists of counts or frequencies in different categories.

2. The sample size must be large enough, with an expected frequency of at least 5 in each cell of the contingency table.

3. The observations must be independent, meaning each data point should not influence the others.

If any of these assumptions are not met, it may not be appropriate to use a chi-square test of homogeneity to analyze the data. Instead, you may need to consider alternative statistical methods that better suit your data and research question.

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