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Fofino [41]
3 years ago
13

Contestants in a dance-a-thon rest for the same amount of time evey hoir. A couple rests for 25 minutew in 5 hours. How long did

they rest in 8 hours?
Mathematics
1 answer:
Semenov [28]3 years ago
4 0

If each couple rests for k minutes every hour, the time spent resting, r, after h hours is given by

r = kh

We know that a couple spent 25 minutes resting in 5 hour. So, the rate is

25 = 5k \iff k = \dfrac{25}{5}=5

So, every couple rests 5 minutes per hour.

This means that, after 8 hours, the couples rest

r = 5\cdot 8 = 40

minutes.

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Square of a standard normal: Warmup 1.0 point possible (graded, results hidden) What is the mean ????[????2] and variance ??????
LenaWriter [7]

Answer:

E[X^2]= \frac{2!}{2^1 1!}= 1

Var(X^2)= 3-(1)^2 =2

Step-by-step explanation:

For this case we can use the moment generating function for the normal model given by:

\phi(t) = E[e^{tX}]

And this function is very useful when the distribution analyzed have exponentials and we can write the generating moment function can be write like this:

\phi(t) = C \int_{R} e^{tx} e^{-\frac{x^2}{2}} dx = C \int_R e^{-\frac{x^2}{2} +tx} dx = e^{\frac{t^2}{2}} C \int_R e^{-\frac{(x-t)^2}{2}}dx

And we have that the moment generating function can be write like this:

\phi(t) = e^{\frac{t^2}{2}

And we can write this as an infinite series like this:

\phi(t)= 1 +(\frac{t^2}{2})+\frac{1}{2} (\frac{t^2}{2})^2 +....+\frac{1}{k!}(\frac{t^2}{2})^k+ ...

And since this series converges absolutely for all the possible values of tX as converges the series e^2, we can use this to write this expression:

E[e^{tX}]= E[1+ tX +\frac{1}{2} (tX)^2 +....+\frac{1}{n!}(tX)^n +....]

E[e^{tX}]= 1+ E[X]t +\frac{1}{2}E[X^2]t^2 +....+\frac{1}{n1}E[X^n] t^n+...

and we can use the property that the convergent power series can be equal only if they are equal term by term and then we have:

\frac{1}{(2k)!} E[X^{2k}] t^{2k}=\frac{1}{k!} (\frac{t^2}{2})^k =\frac{1}{2^k k!} t^{2k}

And then we have this:

E[X^{2k}]=\frac{(2k)!}{2^k k!}, k=0,1,2,...

And then we can find the E[X^2]

E[X^2]= \frac{2!}{2^1 1!}= 1

And we can find the variance like this :

Var(X^2) = E[X^4]-[E(X^2)]^2

And first we find:

E[X^4]= \frac{4!}{2^2 2!}= 3

And then the variance is given by:

Var(X^2)= 3-(1)^2 =2

7 0
3 years ago
ASHLEY IS GOING ON A TRIP TO LONDON. SHE SAVED $100.00 IN SPENDING MONEY. WHEN SHE ARRIVES IN ENGLAND, SHE GOES TO A BANK TO CHA
Ilya [14]

Answer:

65.93

Step-by-step explanation:

Okay, first lets convert the money.

100 ÷ 1.43 = 69.9300699301 (69.93)

69.93 - 4 = 65.93

Ashley has 65.93 pounds.

Hope this helps! Brainliest would be appreciated. :)

4 0
2 years ago
A jet plane can carry up to 200,000 liters of fuel. It used to 130,000 liters of fuel during a flights. What percentage of the f
LekaFEV [45]
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Step-by-step explanation:
Given: Full capacity= 200000 litres
Amount of fuel used during flight= 130000 litres
Now, finding percentage of fuel used on the flight.
∴ Percentage of fuel used=
Solving it, we will get
∴ 65% of fuel capacity been used in this flight.
7 0
3 years ago
I dont get this ............
Karo-lina-s [1.5K]

Answer:

i think these inequalities shows B

6 0
3 years ago
Alice skated 3.4 miles on Monday and 2.6 miles on Wednesday. How much farther did she skate on Monday ?
dezoksy [38]

Answer:

.8 miles further on Monday

Step-by-step explanation:

Take the miles on Monday and subtract the miles on Wednesday

3.4 - 2.6 =.8 miles

8 0
3 years ago
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