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RSB [31]
3 years ago
15

Suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 7 minutes. De

termine the probability that the child must wait between 6 and 9 minutes on the bus on a given morning.
Mathematics
1 answer:
Gala2k [10]3 years ago
6 0

Answer:

The probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

Step-by-step explanation:

Let the random variable <em>X</em> represent the time a child spends waiting at for the bus as a school bus stop.

The random variable <em>X</em> is exponentially distributed with mean 7 minutes.

Then the parameter of the distribution is,\lambda=\frac{1}{\mu}=\frac{1}{7}.

The probability density function of <em>X</em> is:

f_{X}(x)=\lambda\cdot e^{-\lambda x};\ x>0,\ \lambda>0

Compute the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning as follows:

P(6\leq X\leq 9)=\int\limits^{9}_{6} {\lambda\cdot e^{-\lambda x}} \, dx

                      =\int\limits^{9}_{6} {\frac{1}{7}\cdot e^{-\frac{1}{7} \cdot x}} \, dx \\\\=\frac{1}{7}\cdot \int\limits^{9}_{6} {e^{-\frac{1}{7} \cdot x}} \, dx \\\\=[-e^{-\frac{1}{7} \cdot x}]^{9}_{6}\\\\=e^{-\frac{1}{7} \cdot 6}-e^{-\frac{1}{7} \cdot 9}\\\\=0.424373-0.276453\\\\=0.14792\\\\\approx 0.148

Thus, the probability that the child must wait between 6 and 9 minutes on the bus stop on a given morning is 0.148.

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On a certain hot​ summer's day, 645 people used the public swimming pool. The daily prices are $1.75 for children and $2.50 for
VladimirAG [237]

Answer:

327 children and 318 adults

Step-by-step explanation:

The x be the amount of children and y be the amount of adults that were at the swimming pool. We can use this to set up a system of equations:

x+y=645

1.75x+2.50y=1367.25

Move y to the other side in the first equation to isolate x and solve the system using substitution:

x=645-y

  1.75(645-y)+2.50y=1367.25

Distribute

1128.75-1.75y+2.50y=1367.25

         1128.75+0.75y=1367.25

Subtract 1128.75 from both sides

                        0.75y=238.5

Divide both sides by 0.75

                                y=318

x=645-y

x=645-318

x=327

327 children and 318 adults swam at the pool that day

4 0
2 years ago
Jim is clearing out trees and planting grass to enlarge his backyard. He plans to double both the width and the length of his cu
Ierofanga [76]
U should know the area of rectangle is w*l
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3 years ago
How do you solve x/3&gt;-1
Goryan [66]

x/3>-1

Isolate the x. Multiply 3 to both sides

(x/3)3 > -1(3)

x > -1(3)

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hope this helps

7 0
3 years ago
Select all the pairs of like terms in the expression.25y + 15x – 0.2y – 6 + (–2)
ziro4ka [17]

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What is the area of triangle ABC ? round to the nearest square unit ?
mash [69]

Answer: 33 square units

Step-by-step explanation:

Given: Sides lengths of the triangle : 16 units, 10 units, 8 units.

Heron's formula:-

\text{Area of triangle}=\sqrt{s(s-a)(s-b)(s-c)}, where s is the semiperter and a,b and c are the side-lengths of the triangle.

Let a=16 , b=10 and c=8

Then,

s=\dfrac{a+b+c}{2}=\dfrac{16+10+8}{2}=17

Using Heron's formula:-

\text{Area of triangle}=\sqrt{17(17-16)(17-10)(17-8)}\\\\\Rightarrow\ \text{Area of triangle}=\sqrt{1071}=32.7261363439\approx33\text{ square units}

5 0
3 years ago
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