Terrence took a total of 16 pages of notes during 8 hours of class. In all, how many hours will

PLEASE HELP!!! Use addition to solve the linear system of equations. Include all of your work in your final answer. 2x + y = 5,

Arturiano [62]

I: 2x+y=5
II:3x+2y=4

start by eliminating y

-2*I: -4x-2y=-10
II: 3x+2y=4

add both equations together

-2*I+II: -4x-2y+3x+2y=-10+4
-1x=-6
x=6

insert x=6 into I:
2*6+y=5
y=5-12
y=-7

so the solution is x=6, y=-7

4 0

2 years ago

Here are the records of two different sequences (A,B ) of a coin tossed eight times. A: T H H H H H H H B: H T T H T H H T If yo

ser-zykov [4K]

Answer: Sequence B is more probable than A.

Step-by-step explanation:

This two sequences are not equally probable. Sequence B is more probable than A due to the equal chances of getting head (H) and a tail (T). The probability of getting a head is equal to the probability of getting a tail which is 4/8 i.e 0.5

The sequence A is less probable because the head(H) occur more than tail (T). The probability of head occurring is almost a sure event i.e 1 which is not feasible.

6 0

2 years ago

(10 points) Consider the initial value problem y′+3y=9t,y(0)=7. Take the Laplace transform of both sides of the given differenti

Rashid [163]

Answer:

The solution

$Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3 t}$

Step-by-step explanation:

Explanation:-

Consider the initial value problem y′+3 y=9 t,y(0)=7

Step(i):-

Given differential problem

y′+3 y=9 t

Take the Laplace transform of both sides of the differential equation

L( y′+3 y) = L(9 t)

Using Formula Transform of derivatives

L(y¹(t)) = s y⁻(s)-y(0)

By using Laplace transform formula

$L(t) = \frac{1}{S^{2} }$

Step(ii):-

Given

L( y′(t)) + 3 L (y(t)) = 9 L( t)

$s y^{-} (s) - y(0) + 3y^{-}(s) = \frac{9}{s^{2} }$

$s y^{-} (s) - 7 + 3y^{-}(s) = \frac{9}{s^{2} }$

Taking common y⁻(s) and simplification, we get

$( s + 3)y^{-}(s) = \frac{9}{s^{2} }+7$

$y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}$

Step(iii):-

By using partial fractions , we get

$\frac{9}{s^{2} (s+3} = \frac{A}{s} + \frac{B}{s^{2} } + \frac{C}{s+3}$

$\frac{9}{s^{2} (s+3} = \frac{As(s+3)+B(s+3)+Cs^{2} }{s^{2} (s+3)}$

On simplification we get

9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Put s =0 in equation(i)

9 = B(0+3)

B = 9/3 = 3

Put s = -3 in equation(i)

9 = C(-3)²

C = 1

Given Equation 9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Comparing 'S²' coefficient on both sides, we get

9 = A s²+3 A s +B(s)+3 B +C(s²)

0 = A + C

put C=1 , becomes A = -1

$\frac{9}{s^{2} (s+3} = \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}$

Step(iv):-

$y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}$

$y^{-}(s) =9( \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}) + \frac{7}{s+3}$

Applying inverse Laplace transform on both sides

$L^{-1} (y^{-}(s) ) =L^{-1} (9( \frac{-1}{s}) + L^{-1} (\frac{3}{s^{2} }) + L^{-1} (\frac{1}{s+3}) )+ L^{-1} (\frac{7}{s+3})$

By using inverse Laplace transform

$L^{-1} (\frac{1}{s} ) =1$

$L^{-1} (\frac{1}{s^{2} } ) = \frac{t}{1!}$

$L^{-1} (\frac{1}{s+a} ) =e^{-at}$

Final answer:-

Now the solution , we get

$Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3t}$

5 0

2 years ago

Which statement is true regarding the graphed functions ?

daser333 [38]

will u give me diamond dedo please let

Step-by-step explanation:

opbolte99 I am very sorry for what is ur id number on it n

8 0

2 years ago

X°+(x+30)=180° I need answer

djyliett [7]

Answer:

210 + -1x

Step-by-step explanation:

Simplifying

X + (x + -30) = 180

Reorder the terms:

X + (-30 + x) = 180

Remove parenthesis around (-30 + x)

X + -30 + x = 180

Reorder the terms:

-30 + X + x = 180

Solving

-30 + X + x = 180

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '30' to each side of the equation.

-30 + X + 30 + x = 180 + 30

Reorder the terms:

-30 + 30 + X + x = 180 + 30

Combine like terms: -30 + 30 = 0

0 + X + x = 180 + 30

X + x = 180 + 30

Combine like terms: 180 + 30 = 210

X + x = 210

Add '-1x' to each side of the equation.

X + x + -1x = 210 + -1x

Combine like terms: x + -1x = 0

X + 0 = 210 + -1x

X = 210 + -1x

Simplifying

X = 210 + -1x

7 0

2 years ago