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docker41 [41]
2 years ago
13

Determine whether the distribution is a discrete probability distribution

Mathematics
1 answer:
Elodia [21]2 years ago
7 0

Answer:

A child psychologist is interested in the number of times a newborn baby’s crying wakes its mother after midnight. For a random sample of 50 mothers, the following information was obtained. Let X = the number of times per week a newborn baby’s crying wakes its mother after midnight. For this example, x = 0, 1, 2, 3, 4, 5.

P(x) = probability that X takes on a value x.

x P(x)0 P(x = 0) = 250

1 P(x = 1) = 1150

2 P(x = 2) = 2350

3 P(x = 3) = 950

4 P(x = 4) = 450

5 P(x = 5) = 150

Step-by-step explanation:

pa follow po pls.

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The length of a rectangle is five more than triple the width. If the perimeter is 154 inches, what are the dimensions
Mkey [24]

Answer:

Width = 18 inches

Length = 59 inches

Step-by-step explanation:

The length of a rectangle is five more than triple the width. If the perimeter is 154 inches, what are the dimensions

Perimeter of a rectangle = 2L + 2W

The length of a rectangle is five more than triple the width.

L = Length = 5 + 3W

W = Width

If the perimeter is 154 inches, what are the dimensions

Hence,

154 = 2L + 2W

154 = 2(5 + 3W ) + 2W

154 = 10 + 6W + 2W

Collect like terms

154 - 10 = 8W

144 = 8W

W = 144/8

W = 18 inches

Length = 5 + 3W

Length = 5 + 3(18)

Length = 5 + 54

Length = 59 inches

8 0
2 years ago
Please help!!!i need help
Colt1911 [192]
The answer to this question is d
4 0
3 years ago
Read 2 more answers
Apply the method of undetermined coefficients to find a particular solution to the following system.wing system.
jarptica [38.1K]
  • y''-y'+y=\sin x

The corresponding homogeneous ODE has characteristic equation r^2-r+1=0 with roots at r=\dfrac{1\pm\sqrt3}2, thus admitting the characteristic solution

y_c=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x

For the particular solution, assume one of the form

y_p=a\sin x+b\cos x

{y_p}'=a\cos x-b\sin x

{y_p}''=-a\sin x-b\cos x

Substituting into the ODE gives

(-a\sin x-b\cos x)-(a\cos x-b\sin x)+(a\sin x+b\cos x)=\sin x

-b\cos x+a\sin x=\sin x

\implies a=1,b=0

Then the general solution to this ODE is

\boxed{y(x)=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x+\sin x}

  • y''-3y'+2y=e^x\sin x

\implies r^2-3r+2=(r-1)(r-2)=0\implies r=1,r=2

\implies y_c=C_1e^x+C_2e^{2x}

Assume a solution of the form

y_p=e^x(a\sin x+b\cos x)

{y_p}'=e^x((a+b)\cos x+(a-b)\sin x)

{y_p}''=2e^x(a\cos x-b\sin x)

Substituting into the ODE gives

2e^x(a\cos x-b\sin x)-3e^x((a+b)\cos x+(a-b)\sin x)+2e^x(a\sin x+b\cos x)=e^x\sin x

-e^x((a+b)\cos x+(a-b)\sin x)=e^x\sin x

\implies\begin{cases}-a-b=0\\-a+b=1\end{cases}\implies a=-\dfrac12,b=\dfrac12

so the solution is

\boxed{y(x)=C_1e^x+C_2e^{2x}-\dfrac{e^x}2(\sin x-\cos x)}

  • y''+y=x\cos(2x)

r^2+1=0\implies r=\pm i

\implies y_c=C_1\cos x+C_2\sin x

Assume a solution of the form

y_p=(ax+b)\cos(2x)+(cx+d)\sin(2x)

{y_p}''=-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x)

Substituting into the ODE gives

(-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x))+((ax+b)\cos(2x)+(cx+d)\sin(2x))=x\cos(2x)

-(3ax+3b-4c)\cos(2x)-(3cx+3d+4a)\sin(2x)=x\cos(2x)

\implies\begin{cases}-3a=1\\-3b+4c=0\\-3c=0\\-4a-3d=0\end{cases}\implies a=-\dfrac13,b=c=0,d=\dfrac49

so the solution is

\boxed{y(x)=C_1\cos x+C_2\sin x-\dfrac13x\cos(2x)+\dfrac49\sin(2x)}

7 0
2 years ago
Bob has 8 more dimes than quarters if he has a total of $4 .30, how many of each coin dies he have?
attashe74 [19]
The answer is $5.10
4 0
2 years ago
A certain television is advertised as a 59-inch TV (the diagonal length). If the width of
ArbitrLikvidat [17]

Answer:

32.9 inches

Step-by-step explanation:

this can be solved using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base = 49

c =  hypotenuse = diagonal = 59

l² + 49² = 59²

l² = 59² - 49²

3481 - 2401 = 1080

find the square root

32.9 in

3 0
3 years ago
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