A teacher selects 4 students from her class of 37 to work together on a project. How many ways are there for her to select the students

Take the Laplace transform of both sides:

L[y'' - 4y' + 8y] = L[δ(t - 1)]

I'll denote the Laplace transform of y = y(t) by Y = Y(s). Solve for Y :

(s²Y - s y(0) - y'(0)) - 4 (sY - y(0)) + 8Y = exp(-s) L[δ(t)]

s²Y - 4sY + 8Y = exp(-s)

(s² - 4s + 8) Y = exp(-s)

Y = exp(-s) / (s² - 4s + 8)

and complete the square in the denominator,

Y = exp(-s) / ((s - 2)^2 + 4)

Recall that

L⁻¹[F(s - c)] = exp(ct) f(t)

In order to apply this property, we multiply Y by exp(2)/exp(2), so that

Y = exp(-2) • exp(-s) exp(2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-s + 2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-(s - 2)) / ((s - 2)² + 4)

Then taking the inverse transform, we have

L⁻¹[Y] = exp(-2) L⁻¹[exp(-(s - 2)) / ((s - 2)² + 4)]

L⁻¹[Y] = exp(-2) exp(2t) L⁻¹[exp(-s) / (s² + 4)]

L⁻¹[Y] = exp(2t - 2) L⁻¹[exp(-s) / (s² + 4)]

Next, we recall another property,

L⁻¹[exp(-cs) F(s)] = u(t - c) f(t - c)

where F is the Laplace transform of f, and u(t) is the unit step function

[tex]u(t) = \begin{cases}1 & \text{if }t \ge 0 \\ 0 & \text{if }t < 0\end{cases}[/tex]

To apply this property, we first identify c = 1 and F(s) = 1/(s² + 4), whose inverse transform is

L⁻¹[F(s)] = 1/2 L⁻¹[2/(s² + 2²)] = 1/2 sin(2t)

Then we find

L⁻¹[Y] = exp(2t - 2) u(t - 1) • 1/2 sin(2 (t - 1))

and so we end up with

y = 1/2 exp(2t - 2) u(t - 1) sin(2t - 2)

The inequality that can be used to represent the information that a number is no less than 48 will be n > 48.

Inequality simply means a mathematical expression that is used in which the sides aren't equal to each other.

It should be noted that the expression that a number is no less than 48 means the number is greater than 48. Therefore, the inequality is n > 48.

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Answer: The correct answer is n≥48

Step-by-step explanation: Give me the brainiest

Answer: Yes

Step-by-step explanation:

A: 12 minutesAnswer to B: 36 minutesAnswer to C:

Answer:

5a+2b+b-2a

5a-2a+2b+b

3a+3b

Answer:

[tex]\boxed{\sf All\: real\: numbers}[/tex]

Step-by-step explanation:

[tex]\star \:\sf Classify\: -4m+21\left(m-1\right)\le \:15m+2\left(m-1\right)\: \star[/tex]

Apply Distribution law:

[tex]\sf -4m+21m-21\le \:15m+2\left(m-1\right)[/tex]

Combine like terms:

** [tex]\sf \hookrightarrow -4m+21m=17m[/tex]

[tex]\longmapsto\sf 17m-21\le \:15m+2\left(m-1\right)[/tex]

[tex]\sf 2(m-1)[/tex]

[tex]\hookrightarrow 2m-2[/tex]

-----------------------------------------

[tex]\longmapsto\sf 17m-21\le \:15m+2m-2[/tex]

Combine like terms:

** [tex]\sf 15m+2m=17m[/tex]

[tex]\longmapsto\sf 17m-21\le \:17m-2[/tex]

Add 21 from both sides:

[tex]\longmapsto\sf 17m-21+21\le \:17m-2+21[/tex]

[tex]\longmapsto\sf 17m\le \:17m+19[/tex]

Subtract 17m from both sides:

[tex]\longmapsto\sf 17m-17m\le \:17m+19-17m[/tex]

[tex]\longmapsto\sf 0\le \:19[/tex]

Therefore, the solution of the inequality: All real numbers

_____________________________________________

Answer:

[tex]18[/tex]

Step-by-step explanation:

[tex] \frac{28}{14} = 2 \\ \frac{36}{x} = 2 \\ x = \frac{36}{2} \\ = 18[/tex]

Reduce the expression, if possible, by cancelling the common factors.

Exact Form: [tex] \:- \frac{3}{10} \\ [/tex]

Decimal form[tex] \: \:- 0.3[/tex]

Answer:

The formula of a sphere is v= 4/3 pi root to the power of 3.

Step-by-step explanation:

The answer is B

Step-by-step explanation:

1.) 7=12 - 5 is true

4.) 6(7) - 2(12) = 22 is not true

Answer:

Step-by-step explanation:

x = 127

y = 5

z = 31

Answer:

D how many months until the total spent is the same for both gyms

Step-by-step explanation:

30m+50 = 10m+100

By setting the cost of gym A equal to gym B we are finding  how many months it is when the cost is the same

Answer:

How many months until the total spent is same for both the gyms

Step-by-step explanation:

Then

We may solve it

option D

[tex]\\ \sf\longmapsto y=mx+b[/tex]

[tex]\\ \sf\longmapsto 3=-25(-5)+b[/tex]

[tex]\\ \sf\longmapsto 3=125+b[/tex]

[tex]\\ \sf\longmapsto b=-122[/tex]

Equation of the line

[tex]\\ \sf\longmapsto y=-25x-122[/tex]

Answer:

Graph 4

Step-by-step explanation:

I have to put more words lol

Answer:

The slope is:

[tex] \binom{1}{2} [/tex]

In slope-intercept form the equation is:

[tex]y = \binom{1}{2} x - 3[/tex]

Answer:

2.25

Step-by-step explanation:

m = 9 / 4 = 2.25

points belong to an increasing, linear function.

Equation: y = 2.25x + 2.75.

BRAINLIEST?

Answer:

Answered is x= 55x

Step-by-step explanation:

13x+10 * 12x+20

soln:

or, 13x+12x+10+20

or, 25x+30

:., therefore, x=55x

Answer:

8. B

9. B

10. B

thats my answer

Answer:

6%

Step-by-step explanation:

15/250=3/50   or 6%

The probability that Sarah would win the prize quilt given the tickets she bought  is 6%.

Probability is how likely it is that a stated event would happen. The probability of the event happening lie between 0 and 1.

The probability that Sarah would win the prize quilt = number of tickets bought / total number of tickets

(15 / 250) x 100 = 6%

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Answer:

rude customers and complaints

Answer:

Ignorant managers.

Step-by-step explanation:

Ignore them

Find somewhere else to move.

Answer: 2/3 (answer in decimal form = 0.6)

Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly. Then do the rest of the operations.

Answer:

Step-by-step explanation:

$760(1.023) = $777.48

Answer:−0.6

Step-by-step explanation:

(-1).3/5=−0.6

Using the partial quotient method, it is found that:

When division is done applying the partial quotient method, consecutive subtractions are done with n groups of the divisor.

Each partial quotient is the number of groups, and the final quotient is the sum of the partial quotients.

In this problem, the divisor is as follows;

19.

The first subtraction is by 5700, which is 5700/19 = 300 groups of 19, hence the first partial quotient is of 300.

The second subtraction is by 1520, which is 1520/19 = 80 groups of 19, hence the second partial quotient is of 80.

The third subtraction is by 57, which is 57/19 = 3 groups of 19, hence the third partial quotient is of 3.

Then the final quotient is given as follows:

300 + 80 + 3 = 383.

The subtractions are given by the image at the end of the answer.

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[tex] \huge \bf༆ Answer ༄[/tex]

The domain of given function is All real numbers

[tex] \sf \: f(x) = { \bigg( \dfrac{1}{4} \bigg) }^{x} [/tex]

For each value of x the function is defined.

Example -

The value is [tex] \sf\frac{1}{4}[/tex]

The value is 4

[tex]꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]

Answer:

c) (6,5)

Step-by-step explanation:

The horizontal axis represents x values

The vertical axis represents y values

Answer:

C

Step-by-step explanation:

Answer:

The answer is 476

Step-by-step explanation:

hope this helps :)

Answer:

y=4x-17

Step-by-step explanation: Distribute the 4(x-5)

4x-20

Then add three to both sides

y=4x-17

Answer:

If the radius is 1, then the answer is pi.

Radius=r=1

Area

Answer:

t = c · (3.5)  

Step-by-step explanation:

The rate of change is 3.5.

So it takes three and a half mins to make one plane

So 3.5 times the number of planes equals the total time it takes to make them.

I really hope this helps!