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3 years ago

The perimeter of a rectangle is 142m. The length is 2m more than the width. Find the dimensions. What is the length?

1 answer:

5 0

You have a rectangle that has a width of w. the length us 2 more than the width, so the lengthis w+2. the perimeter is 142. so 142=w+w+(w+2)+(w+2). because the perimeter is all 4 sides added together 2 of those sides being the length and 2 beingtje width. combine like terms to get 142=4w+4. now you subtract 4 from each side and get 138=4w. divide both sides by 4. you get w=34.5. now, w is the width. the length is 2 more than w, which is 34.5+2, or 36.5

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The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. (a) What is th

Sindrei [870]

Answer:

a) 0.0025

b) 0.9975

c) 23.03 minutes

d) 23.03 minutes

Step-by-step explanation:

Let X be the random variable that measures the time waited for a taxi.

If X is exponentially distributed with a mean of 10 minutes,then the probability that you have to wait more than t minutes is

$\large P(X>t) = e^{-t/10}$

1 hour = 60 minutes, so the probability that you wait longer than one hour is

$\large P(X>60)=e^{-6}=0.0025$

Due to the “memorylessness” of the exponential distribution, the probability that you have to wait 10 or less minutes after you have already waited for one hour, is the same as the probability that you have to wait 10 or less minutes

$\large P(X\leq 10)=1-e^{-6}=0.9975$

We want x so that

P(X>x)=0.1

$\large e^{-x/10}=0.1\rightarrow -x/10=ln(0.1)\rightarrow x=-10ln(0.1)=23.03\;minutes$

We want P(X<x)=0.9

$\large 1-e^{-x/10}=0.9\rightarrow e^{-x/10}=0.1\rightarrow x=-10ln(0.1)=23.03\;minutes$

4 0

3 years ago

Solve the equation 14y+82=6x-20 for x if y is 25

Leni [432]

Answer:

x= 226/3 or 75.33333333333333333333333333333

Step-by-step explanation:

14y+82=6x-20

y=25

Sub y=25 into 14y+82=6x-20

14y+82=6x-20

14(25)+82=6x-20

Calculate as follows:

14(25)+82=6x-20

350+82=6x-20

432=6x-20

Add twenty to both sides:

432+20=6x-20+20

452=6x-0

452=6x

Divide both sides by 6

452=6x

452/6=6x/6

452/6=x

x= 226/3 or 75.33333333333333333333333333333

8 0

2 years ago

In a class of students, the following data table summarizes the gender of the students

sergij07 [2.7K]

Answer:

1/2

Step-by-step explanation:

Has A 4+8=12

All together 12+12=24

Probability to have A 12/24 or 1/2

5 0

2 years ago

The mean survivial time after diagnosis for a certain disease is 15 years with a standard deviation of 5 years. Based on a parti

frutty [35]

Answer:

The time the patient expected to survive after diagnosis is 29 years.

Step-by-step explanation:

It is provided that the mean survival time after diagnosis for a certain disease is 15 years with a standard deviation of 5 years.

That is,

$\mu=15\\\sigma=5$

An individual's predicted survival time is <em>a</em> = 2.8 standard deviations beyond the mean.

Compute the time the patient expected to survive after diagnosis as follows:

$X=\mu+a\sigma$

$=15+(2.8\times 5)\\\\=15+14\\\\=29$

Thus, the time the patient expected to survive after diagnosis is 29 years.

5 0

2 years ago

1. Consider the equation 2 x e x + = . This equation has a solution close to x = 0 .

nadya68 [22]

Answer:

the linear approximation formula is based on the equation of the tangent line of a function at a fixed point. The linear approximation of a function f(x) at a fixed value x = a is given by L(x) = f(a) + f '(a) (x - a).

Step-by-step explanation:

4 0

1 year ago