Solve for x:
(2x/3) + 10 = (x/5) + (36/5)

The inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

To find the inverse Laplace transform of each function, we need to express them in terms of known Laplace transforms. Here are the solutions for each function:

a)

\(F(s) = \large{\frac{2e^{-0.5s}}{s^2-6s+9}}\)

To find the inverse Laplace transform, we first need to factor the denominator of F(s). The denominator factors as (s - 3)². Therefore, we can rewrite F(s) as:

\(F(s) = \large{\frac{2e^{-0.5s}}{(s-3)^2}}\)

Now, we know that the Laplace transform of eᵃᵗ is 1/(s - a). Therefore, the inverse Laplace transform of

\(e^(-0.5s) \: is \: e^(0.5t).\)

Applying this, we get:

\(f(t) = 2e^(0.5t) * t \\

b) F(s) = \large{\frac{s-1}{s^2-3s+2}}\)

We can factor the denominator of F(s) as (s - 1)(s - 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{s-1}{(s-1)(s-2)}}\)

Simplifying, we have:

\(F(s) = \large{\frac{1}{s-2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(2t) \\

c) F(s) = \large{\frac{s-1}{s^2+s-2}}

\)

We factor the denominator of F(s) as (s - 1)(s + 2). The expression becomes:

\(F(s) = \large{\frac{s-1}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{1}{s+2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-2t) \\

d) F(s) = \large{\frac{e^{-s}(s-1)}{s^2+s-2}}\)

We can factor the denominator of F(s) as (s - 1)(s + 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{e^{-s}(s-1)}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{e^{-s}}{s+2}}\)

The Laplace transform of

\(e^(-s) \: is \: 1/(s + 1).\)

Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

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multiply Start Fraction 5 Over 7 End Fraction by 3.

What do math fractions mean?

An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.

                                Whether it is in the numerator or denominator, a complex fraction contains a fraction.

                             The numerator and denominator of a correct fraction are opposite each other.

What is basic fraction theory?

Every fraction has two components: the numerator, which is the actual number of parts, and the denominator, which is the total number of parts.

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Answer:

c is the answer i took the test

Step-by-step explanation:

Answer:

slope is 5

Step-by-step explanation:

Answer: 5

Step-by-step explanation:

(4,3) (2,-7)

Put it in the equation of y2 - y1 over x2 - x1

-7-3 = -10 and 2 - 4 = -2 that will give you the fraction of -10/-2

Reduce the fraction and that will give you the answer of 5, slope = 5

In slope-intercept form it would be y - 3 = 5 (x - 4)

Hope this helps! ^^

Answer:

RP is the correct amswer.

Step-by-step explanation:

please mark me as a brainlist...

Answer: A, B, D

it can’t be “C” because that would be equal to 40%

Answer:

{x | x ≠ -1, 2, 4}

Step-by-step explanation:

Domain: input values (x-values)

Asymptote: a line which the curve gets infinitely close to, but never touches.

Hole: a point on the graph where the function is not defined.

From inspection of the graph:

As vertical asymptotes and holes restrict the domain of a rational function, the domain is  {x | x ≠ -1, 2, 4}

Answer:

$77429.824

Step-by-step explanation:

Let the total college cost for one year = x

43% of x was paid with scholarship fee

Percentage left = 100% - 43% = 57%

57% is equivalent to 11,033.75

57/100x= 11,033.75

0.57x = 11033.75

x = 11033.75 / 0.57

x =19357.456 ; this is Jacinta's college fee for a year ;

Hence

College fee for 4 years :

19357.456 * 4 = $77429.824

Given that in the above rectangle, m∠4 = 35°:

To understand how the above were arrived at, you must understand the properties of a rectangle.

A rectangle is a four-sided flat shape with four right angles. Its properties include:

Four sides: A rectangle has four sides, two of which are parallel and of equal length, and the other two sides are also parallel and of equal length but different from the first two.

Four right angles: All four angles of a rectangle are right angles (90 degrees).

Opposite sides are parallel: The two pairs of opposite sides are parallel to each other.

Diagonals are equal: The diagonals of a rectangle bisect each other, which means they cut each other into two equal parts.

Equal opposite sides: The opposite sides of a rectangle are equal in length.

Equal adjacent sides: The adjacent sides of a rectangle are also equal in length.

Symmetry: A rectangle has two lines of symmetry, which means it can be divided into two equal parts by a line that passes through its center.

Area: The area of a rectangle is calculated by multiplying its length and width together.

Perimeter: The perimeter of a rectangle is calculated by adding the length of all four sides together.

So,

Note that ∠ABC = ∠BCD = ∠CDA = ∠DAC = 90°

This means that ∠BCA = 4 + 3 = 90°

Since m∠4 = 35°

m∠3 = 90 - 35°; therefore

m∠3 = 55°

This logic holds true for ∠ABC, and ∠6 where ∠6 =35° - Properties of a diagonal of a rectangle.

Note that m∠4 = m∠1 - Alternate angles thus,

∠1 = 35°

Since ∠4 = ∠6 = 35°

∠5 = 180 - (35 + 35)  -  Sum of Angles in a Triangle.

∠5 = 110°

There are other was to find ∠8 but the easiest is to use sum of angles on a straight line. Since ∠5 and ∠8 are supplementary,

m∠8 = 180 - 110 = 70°

Thus, if ∠8 = 70° and ∠3 = 55; then

m∠7 = 180 - (70 + 55) - Sum of Angles in a Triangle
m∠7 = 55°

Thus, in summary,

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The 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542).,

The formula for the confidence interval of a proportion:

CI = p ± z* (√(p*(1-p)/n))

where:

p is the sample proportion (40/90 = 0.4444)

z* is the critical value of the standard normal distribution at the 95% confidence level (1.96)

n is the sample size (90)

Substituting the  values, we have

CI = 0.4444 ± 1.96 * (√(0.4444*(1-0.4444)/90))

CI = 0.4444 ± 1.96 * (√(0.00245))

CI = 0.4444 ± 1.96 * 0.0495

CI = 0.4444 ± 0.097

Hence, the 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542) when rounded to three decimal places.

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The postfix expression of "7+5-3*2(6*7)/4" is "7 5 + 3 2 * 6 7 * 2 * - 4 /". Evaluating the postfix expression gives the result of the expression. The prefix expression for the given infix expression is "/ - + 7 5 * 3 * 2 ( * 6 7 ) 4".

To convert the infix expression "7+5-3*2(6*7)/4" into postfix expression, we follow the rules of operator precedence and associativity. The postfix expression is obtained by placing operators after their operands.

The postfix expression for the given infix expression is:

"7 5 + 3 2 * 6 7 * 2 * - 4 /"

To evaluate the postfix expression, we use a stack data structure. We scan the postfix expression from left to right and perform the corresponding operations.

Starting with an empty stack, we encounter the operands "7" and "5". We push them onto the stack. Then we encounter the operator "+", so we pop the last two operands from the stack (5 and 7), perform the addition operation (7 + 5 = 12), and push the result back onto the stack.

We continue this process for the remaining operators and operands in the postfix expression. Finally, after evaluating the entire expression, the result left on the stack is the final answer.

To convert the infix expression into prefix expression, we follow similar rules but scan the expression from right to left. The prefix expression is obtained by placing operators before their operands.

The prefix expression for the given infix expression is:

"/ - + 7 5 * 3 * 2 ( * 6 7 ) 4"

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Answer:

A

Step-by-step explanation:

A square has all equal lengths so those shapes cannot be, same with rectangles

Answer:

The common ratio is 1/2

Step-by-step explanation:

To find the common ratio, take the second term and divide by the first term

8/16 = 1/2

We can check by the third term by the second term

4/8 = 1/2

Answer:

1/2 for APX

Step-by-step explanation:

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Answer:

Step-by-step explanation:

From the table you have points (-1, 3) and (2, 9)

general equation

y-y1 = m (x-x1)

the slope m= (y2-y1) / (x2-x1) = 9-3/ 2+1 = 6/3 =2

so the equation shhould be

y+1=2(x-3)

Sydney equation is wrong because her slope is wrong 1/2

Answer:

Angle A: 52.5

Angle B: 68.9

Angle C: 58.6

Step-by-step explanation:

Brainliest?

:)

The samples in the first proposal are independent, while the samples in the second proposal are dependent.

In the first proposal, where the manufacturer randomly samples 10 different dealerships for each set of sales numbers (last year and 15 years ago), the samples are independent. This is because the selection of dealerships for one set of sales numbers does not affect or influence the selection of dealerships for the other set of sales numbers. Each dealership is chosen randomly and independently for each set.

On the other hand, in the second proposal, where the manufacturer randomly samples 10 dealerships for both sets of sales numbers, the samples are dependent. This is because the selection of dealerships for one set of sales numbers is directly tied to the selection of dealerships for the other set of sales numbers. The same 10 dealerships are chosen for both sets, so the samples are not independent.

The choice between independent and dependent samples can have implications for statistical analysis. Independent samples allow for direct comparisons between the two sets of sales numbers, while dependent samples may introduce potential bias or confounding factors due to the shared dealership selection.

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Answer: the standard deviation decreases

Step-by-step explanation:

The final value is 4 (mod5)

Hence, 17^342 ≡ 2^342 ≡ 4 (mod5).

To find 5^903 (mod60), we can use Euler's totient function. Since 60 = 2^2 × 3 × 5, we have φ(60) = 2^1 × 3^1 × 4 = 24. Therefore, we can use Euler's theorem to write:

5^24 ≡ 1 (mod60)

Raising both sides to the power of 37, we get:

5^(24*37) ≡ 1^37 ≡ 1 (mod60)

So 5^888 ≡ 1 (mod60).

Now, we can write:

5^903 = 5^888 * 5^15

Since 5^888 ≡ 1 (mod60), we just need to find 5^15 (mod60).

To do this, we can use the repeated squaring method. Writing 15 in binary form, we have:

15 = 1111 (in binary)

So we can compute:

5^1 ≡ 5 (mod60)

5^2 ≡ 25 (mod60)

5^4 ≡ 25^2 ≡ 25 (mod60)

5^8 ≡ 25^2 ≡ 25 (mod60)

Therefore:

5^15 ≡ 5^8 * 5^4 * 5^2 * 5^1 ≡ 25 * 25 * 25 * 5 ≡ 25 (mod60)

Hence, 5^903 ≡ 5^15 ≡ 25 (mod60).

To find 17^342 (mod5), we can use the fact that 17 ≡ 2 (mod5). Therefore:

17^342 ≡ 2^342 (mod5)

Using the repeated squaring method again, we can compute:

2^1 ≡ 2 (mod5)

2^2 ≡ 4 (mod5)

2^4 ≡ 1 (mod5)

Therefore:

2^342 ≡ 2^2 * (2^4)^85 ≡ 4 * 1^85 ≡ 4 (mod5)

Hence, 17^342 ≡ 2^342 ≡ 4 (mod5).

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Step-by-step explanation:

y= -200 - 72

y= -272

because -a - b = -x

this is a formula

Answer:

155°

Step-by-step explanation:

x and the angle 155° are identical because they are alternate exterior angles of parallel lines intersected by a transversal.

Answer:

Step-by-step explanation:

the value of x is 155 degree because the relation between x and 155 degree is that they are alternate exterior angle and alternate exterior angle are equal.

Using multiplication as a mathematical operator, Kareem will 864 more cards and Nicole will get 24 more cards

Multiplication is a mathematical operation that involves multiplying two or more numbers together. It is one of the four basic operations in mathematics, along with addition, subtraction, and division.

In this problem, we may require the use of some mathematical operators to find the solution to the problem.

1.

He currently has 216 cards, but he needs 15 sets of cards.

1 set of card = 72 cards

Let's calculate the number of sets he currently has.

1 set of card = 72 cards

x set = 216 cards

cross multiply both sides and solve for x.

x * 72 = 216 * 1

x = 216 / 72

x = 3 sets

He currently has 3 sets of cards.

Since he wants 15 sets of cards, we will need 12 more set of cards.

The number of cards can be calculated by multiplying 12 by 72

Number of cards = 12 * 72 = 864

He needs 864 more cards.

2.

1 set of card = $27

1 set = 72 cards

But she's bringing $9 to join, we can calculate the ratio of cards she will get.

1 / 27 = x / 9

x = 9 / 27

x = 1/3

She will get 1/3 of the cards bought which will be

72 * 1/3 = 24 cards

She will get 24 cards

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The elementary matrix E such that EA = B is E = [-1 0 0; 0 1 0; 1 0 1].

To find an elementary matrix E such that EA = B, given A = [1 3 2; 0 1 3; -1 -3 0] and B = [-1 -3 0; 0 1 3; 1 3 2], follow these steps:

Step 1: Identify the operations needed to transform A into B.
- Multiply the first row of A by -1 to obtain the first row of B.
- Keep the second row of A unchanged.
- Add the first row of A to the third row of A to obtain the third row of B.

Step 2: Create the elementary matrix E based on the identified operations.
E = [-1 0 0; 0 1 0; 1 0 1]

Step 3: Verify that EA = B by multiplying E and A.
E * A = [-1 0 0; 0 1 0; 1 0 1] * [1 3 2; 0 1 3; -1 -3 0] = [-1 -3 0; 0 1 3; 1 3 2] = B

So, the elementary matrix E such that EA = B is E = [-1 0 0; 0 1 0; 1 0 1].

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1. Since triangle ABC and DEF are congruent, the value of x is -3

2. length AB = 24

length DE = 24

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE

therefore;

12- 4x = 15-3x

collect like terms

12 -15 = -3x +4x

x = -3

therefore the value of x is -3 and

AB = 12 - 4x

AB = 12 -4( -3)

AB = 12 +12 = 24

DE = 15-3x

= 15-3(-3)

= 15 + 9

= 24

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Answer:

207 cubic cm

Step-by-step explanation:

3x3^2x11/3 = 99

4/3x3x3^3 = 108

108+99=207

A 95% confidence interval for the mean weight level based on a sample is (25.504, 25.67)

We know that, the confidence interval is:

\(\bar{x}\pm z\frac{\sigma}{n}\)

where,

\(\bar{x}\) is the sample mean.

z is the critical value.

n is the sample size.

σ (OR s) is the standard deviation for the population.

In this question, we need to calculate the 95% confidence interval for an experiment that found the sample mean temperature for a certain city in August was 101.82, with a population standard deviation of 1.2

The critical value is z = 1.96

We have been given x¯ = 25.6, σ = 0.6 and n = 150

\(\Rightarrow \bar{x}+ z\frac{\sigma}{\sqrt{n} } \\\\= 25.6+ 1.96\frac{0.6}{\sqrt{150} } \\\\=25.67\)

And

\(\Rightarrow \bar{x}- z\frac{\sigma}{\sqrt{n} } \\\\= 25.6- 1.96\frac{0.6}{\sqrt{150} } \\\\=25.504\)

Required interval is (25.504, 25.67)

Thus, the mean weight level( 25.6 grams) is accurate.

Therefore, a 95% confidence interval for the mean weight level based on a sample is (25.504, 25.67)

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Answer:

You have lived about 64857142.86 lives

Step-by-step explanation:

If you do 4.54 billion (the age of the earth) / 70 (the average life span) you get 64857142.8571. And If we round it to the nearest 100th we get 64857142.86.

The half-angle x/2 lies in the range 90° < x/2 < 135° (Quadrant II) and has a sine value of √(25/34).

Based on the given information, cos(x) = -8/17, and the angle x lies in the range 180° < x < 270°, which places it in Quadrant III. In this quadrant, cosine is negative, which confirms the value of cos(x). Now, we need to find the half-angle (x/2) and determine its range.

Since x is in Quadrant III, the angle x/2 will lie in the range 90° < x/2 < 135°, placing it in Quadrant II. In this quadrant, sine and cosine have opposite signs, so while cos(x) is negative, sin(x/2) will be positive. To find the value of sin(x/2), we can use the half-angle identity:

sin(x/2) = ±√[(1 - cos(x))/2] = √[(1 - (-8/17))/2] = √(25/34)

Since x/2 is in Quadrant II, sin(x/2) must be positive, so we take the positive square root:

sin(x/2) = √(25/34)

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