you draw 5 from a deck of cards. what is the probability that you are dealth with hand where the highest is 7
need answer asap

The inverse Laplace transform of G(s) is:

g(t) = (2/3) \(e^{-t}\) - (1/3) \(e^{-2t}\) - (1/3) \(e^{-3t}\)

The inverse Laplace transform of the function G(s) using the partial fraction expansion coefficients obtained from MATLAB, we need to express G(s) in terms of partial fractions.

G(s) = (2s³ + 5s² + 3s + 6) / (s³ + 6s² + 11s + 6)

The denominator of G(s) can be factored as:

s³ + 6s² + 11s + 6 = (s + 1)(s + 2)(s + 3)

Let's write G(s) in terms of partial fractions as follows:

G(s) = A / (s + 1) + B / (s + 2) + C / (s + 3)

To find the values of A, B, and C, we can multiply both sides of the equation by the denominator and equate the coefficients of like powers of s.

(2s³ + 5s² + 3s + 6) = A(s + 2)(s + 3) + B(s + 1)(s + 3) + C(s + 1)(s + 2)

Expanding the right side and collecting like terms, we have:

2s³ + 5s² + 3s + 6 = (A + B + C)s² + (5A + 4B + 3C)s + (6A + 3B + 2C)

Comparing the coefficients of like powers of s, we get the following equations:

A + B + C = 0

5A + 4B + 3C = 5

6A + 3B + 2C = 3

Solving these equations, we find:

A = 2/3

B = -1/3

C = -1/3

Therefore, the partial fraction expansion of G(s) becomes:

G(s) = (2/3) / (s + 1) - (1/3) / (s + 2) - (1/3) / (s + 3)

Now, we can use the linearity property and known Laplace transforms to find the inverse Laplace transform of each term.

Taking the inverse Laplace transform, we have:

g(t) = (2/3) \(e^{-t}\) - (1/3) \(e^{-2t}\) - (1/3) \(e^{-3t}\)

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

g(t) = (2/3) \(e^{-t}\) - (1/3) \(e^{-2t}\) - (1/3) \(e^{-3t}\)

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Answer:

Sure. How was ur V-day?

Step-by-step explanation:

Answer:

sure

Step-by-step explanation:

Answer:

\(\boxed {cot T = -\frac{5}{12}}\)

Step-by-step explanation:

Finding the missing side :

Taking the cot value :

Answer:

csc T =13/12

(cot T)^2=csc^2T -1

Cot T)^2=(13/12)^2-1

(cot. T )^2=169/144-1

(cot T)^2=169-144/144

(cot T)^2=25/144

cot T =√ 25/144

cot T=5/12

where cot is negative in WE

so Cot T=-5/12

Step-by-step explanation:

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Answer:

\(1a. \: = 20 + 200.( \frac{1}{2})^{ \frac{t}{10} }\)

\(1b. \: = 91^{o} c\)

\(1c. \: = 30 \: minutes\)

Step-by-step explanation:

\(1a. \: t = a + b. {c}^{t}\\ a = 20\)

\(t(0) = a + b = 220 = > b = 200 \\ c = (\frac{1}{2})^{ \frac{1}{10} } \)

\(t = 20 + 200.( \frac{1}{2} )^{ \frac{t}{10} } \)

\(1b.when \: t = 15 \\ t = 20 + 200.( \frac{1}{2})^{ \frac{15}{10} } \\ = 20 + 71 \\ = 91^{o}c\)

\(1c.when \: t \: = 45 \\ 20 + 200. (\frac{1}{2} )^{ \frac{t}{10} \: } = 45 \\200.( \frac{1}{2})^{ \frac{t}{10} } = 25 \\ ( \frac{1}{2} )^{ \frac{t}{10} } = \frac{1}{8} \\ \frac{t}{10} = 3\)

\(t = 30\)

Answer:

The square root of one hundred and eight √108 = 10.392304845413

The square root of one hundred and forty-four √144 = 12

Step-by-step explanation:

Answer: 12i

Step-by-step explanation:

Explanation:

For every 4 blue, we have 12 yellow. This means 4+12 = 16 total.

The ratio of blue to total is 4:16 which reduces to 1:4 when we divide both parts by 4. The order of the values matters since 1:4 is different from 4:1.

Answer:

258.53

Step-by-step explanation:

Hope This Helps!

Plz Mark Brainliest!

Answer:

I believe it is 258.53 ,,,,

To add fractions with different denominators, we need to find a common denominator. By adding the fractions 1/2 and 7/8, we got the final answer is 11/8.

A fraction is part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

First, we can see that 3 and 8 have no common factors, so we can find their least common multiple (LCM), which is 24.

Then we can convert both fractions so that they have a denominator of 24:

1/3 = 8/24

4/8 = 3/6 = 12/24

Now we can add the fractions:

8/24 + 12/24 = 20/24

However, we should simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4 in this case.

So the final answer is 5/6.

First, we can find the least common multiple (LCM) of the denominators, which is 8 in this case.

Then we can convert both fractions so that they have a denominator of 8:

1/2 = 4/8

7/8 = 7/8

Now we can add the fractions:

4/8 + 7/8 = 11/8

However, we should simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case.

So the final answer is 11/8.

similarly,

3/4 + 2/3 = 17/12

7/16 + 9/16 = 1

1/6 + 4/9 = 11/18

1/2 + 1/6 = 2/3

3/10 + 1/2 = 4/5

4/15 + 1/3 = 3/5

3/4 + 7/12 = 4/3

5/6 + 3/10 = 17/15

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Answer:

product means addition. So the product of prime numbers would be all of them added together.

Step-by-step explanation:

Can I have brainliest pls Deku?

*i'm muslim 2 btw ;)

Step-by-step explanation:

the domain of a function is always the interval or set of all valid input values (usually x, but here t).

the range is the interval or set of all valid result values (usually y or f(x), here h(t)).

as the graph shows, the function works only for values of t starting at 0 (at 0 seconds the object has 0 ft height, it is still on the ground and about to launch).

and it ends at t = 7.

obviously the object hits the ground after 7 seconds again after coming back down. so, the height function does not make any sense for values of t after that.

so, again, the domain is

0 <= t <= 7

Answer:

582.1

Step-by-step explanation:

a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

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Answer: C

Step-by-step explanation:

\(\left(2x+3\right)\left(x+5\right)\)

\(\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\)

\(=2xx+2x\cdot \:5+3x+3\cdot \:5\)

\($$Simplify\)

\(=2x^2+13x+15\)

Answer:

(6, -3)

Explanation:

The formula for the midpoint rule is (x,y) =( (x1+x2/2) , (y1+y2/2) )

so here, i did ( (12/2), (-6/2) )

Answer:

Step-by-step explanation:

90% mark from z-score table is:

We have also:

According formula for z-score:

Substitute values and solve for x:

The probability that three numbers are the solution of the equation is 1/27.

The total possible outcome or numbers in the is 27.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27.

total = 27

xyz = 27

(1)(3)(9) = 27

probability of the numbers whose product is 27 is calculated as follows;

p = possible numbers / total outcome

p = 1/27

Thus, the probability that three numbers are the solution of the equation is 1/27.

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The inventory depreciation expense is determined as $9,000.

The inventory depreciation expense is calculated by applying the following formula as follows;

inventory depreciation expense = cost of the inventory x depreciation rate

The given parameters include;

cost of the inventory in month of June = $60,000

depreciation rate = 15%

The inventory depreciation expense is calculated as follows;

inventory depreciation expense = $60,000 x 15/100

inventory depreciation expense = $60,000 x 0.15

inventory depreciation expense = $9,000

Thus, the inventory depreciation expense is determined as $9,000.

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Answer:

32

Step-by-step explanation:

g(x) = 2x^2

g(-4)=2(-4)^2

(-4)^2=16

2*16=32

Answer:

g(- 4) = 32

Step-by-step explanation:

To evaluate g(- 4), substitute x = 4 into g(x) , that is

g(- 4) = 2(- 4)² = 2(16) = 2 × 16 = 32

Answer:

(x,y) = (—2,—5)

Step-by-step explanation:

I attached a picture

The expression -x < 3 is equivalent to x > -3 because division by a negative value changes the inequality sign

From the question, we have the following parameters that can be used in our computation:

-x < 3 is equivalent to x > -3

This is so because

-x < 3 is divided by -1 to get x > -3

As a general rule

A division by a negative value changes the inequality sign

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Answer:

45 miles

Step-by-step explanation:

first divide miles/minutes: 15 / 20 = 0.75

then multiply: 0.75 x 60 = 45

Answer:

Step-by-step explanation:

Remark

The formula for this is

Heat = m * c * Δt

Givens

Heat = unknown

m = 200 grams

c = 4.184 Joules / grams oC

Δt = the change in temperature = 35.7 - 22.3 = 13.4

Solution

Heat = 200 * 4.184 * 13.4

Heat = 11213 Joules

Heat = 11.2 Kj

It's hard to get the correct number of sig digs because the 200 is not qualified in any way.

Part 2.

This can really puzzle you until you know that heat given up = the heat taken on. The heat taken on was 11.2 Kj. The Butane lighter must have given that heat on.

Heat of Combustion = Heat Given Up / Number grams burned.

Heat of Combustion = 11.2 Kj / 0.23 grams

Heat of Combustion = 48.8 Kj / gram

The number A(t) of grams of salt in the tank at time is: \(200 - 180e^{-1/40t}\)

To determine the number of grams of salt in the tank at time t, we would apply the equation of state to have:

dA/dt = R(in) - R(out)

For R(out), we would have:

R(in) = 5g/min

R (out) = A/40 g/min

We would substitute these in the equation and apply a differential limit where A = 20 and t = 0

So,

20 = 200 + C

c = -180

Thus, the equation that expresses the rate = \(200 - 180e ^{-1/40t}\)

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Complete Question:

1. A tank contains 200 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.

A(t) = ____ g

(i) To analyze the linear programming problem using the two-phase simplex method, we need to convert the problem into standard form by introducing slack variables. The problem can be expressed as:

Minimize z = x1 + x2

subject to:

3x1 + x2 + x3 = 1

7x1 + 3x2 - x4 = 4

x1, x2, x3, x4 ≥ 0

The two-phase simplex method involves two phases: the first phase identifies an initial feasible solution, and the second phase optimizes the objective function.

In this case, we start with the artificial variables x3 and x4. In the first phase, we maximize the sum of artificial variables while minimizing the objective function. After the first phase, we check if the optimal solution is feasible (i.e., if the value of the objective function is zero).

Once a feasible solution is obtained, we move to the second phase and proceed with the standard simplex method to optimize the objective function. The optimal solution will be obtained when all artificial variables are eliminated, and the objective function reaches its minimum value.

(ii) Yes, this problem can be solved using the dual simplex method. The dual simplex method is used to solve linear programming problems by analyzing the dual problem. However, to apply the dual simplex method, the problem must satisfy certain conditions, such as having a feasible solution and a bounded feasible region.

In this case, since the problem is a minimization problem and has a feasible solution, the dual simplex method can be applied. It involves analyzing the dual problem, constructing a dual tableau, and performing iterations to improve the objective function value.

By applying the dual simplex method, we can find the optimal solution and determine if any additional iterations are required to reach the minimum value of the objective function while satisfying the constraints.

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Answer:

2(6x)_>10?a._>4b_>6d

Answer:

A

Step-by-step explanation:

The question is actually: 2 \sqrt[3]{x^3} ·\sqrt{16x}

The expression is equivalent to option A, \(\rm 8x \sqrt[6]{x}\).

An expression is a mathematical statement that consists of variables, constants, and mathematical operators.

The expression is \(\rm 2\sqrt[3]{x^2} . \sqrt{16x}\)

The expression can be simplified as

\(\rm = 2 . 4 x^{2/3} x^{1/2}\\\\\=8 x ^{ 7/6}\\\\\\ = 8x x^{1/6}\\\\= 8x \sqrt[6]{x}\)

Therefore, the expression is equivalent to option A, \(\rm 8x \sqrt[6]{x}\).

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Answer:

Step-by-step explanation:

A direct variation is a linear relationship between variables so they have a constant ratio. It is a special case of the slope-intercept form y =mx +b, where b = 0.

Answer:

23% chance

Step-by-step explanation:

There are a total of 26 students in the class, and 6 of them play basketball and 15 of them play baseball. This means that there are 6 + 15 - 9 = 12 students who play either basketball or baseball, and 9 students who play neither.

Of the 12 students who play either basketball or baseball, 6 of them play basketball and 15 of them play baseball, so there are 6 students who play both basketball and baseball. This means that the probability that a student chosen randomly from the class plays both sports is 6 / 26 = 0.23, or 23%.