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2 years ago

15

Pat is three times as old as she was 14 years ago. In seven years, she will be four times as old as she was 14 years ago. How ol

d is she now?

1 answer:

vekshin12 years ago

6 0

The answer is 21 Hope this helps

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Solve the inequality 2x+y >1

Wittaler [7]

The answer is y>-2x+1

4 0

3 years ago

You can make chili powder from fresh chilis. If 1 chili makes 1 tablespoon of chili powder, how many chilis should you buy?

Tresset [83]

It depends on how much chili powder you want to make. Probably just like one or two

6 0

3 years ago

Suppose that W1, W2, and W3 are independent uniform random variables with the following distributions: Wi ~ Uni(0,10*i). What is

nadya68 [22]

I'll leave the computation via R to you. The $W_i$ are distributed uniformly on the intervals $[0,10i]$ , so that

$f_{W_i}(w)=\begin{cases}\dfrac1{10i}&\text{for }0\le w\le10i\\\\0&\text{otherwise}\end{cases}$

each with mean/expectation

$E[W_i]=\displaystyle\int_{-\infty}^\infty wf_{W_i}(w)\,\mathrm dw=\int_0^{10i}\frac w{10i}\,\mathrm dw=5i$

and variance

$\mathrm{Var}[W_i]=E[(W_i-E[W_i])^2]=E[{W_i}^2]-E[W_i]^2$

We have

$E[{W_i}^2]=\displaystyle\int_{-\infty}^\infty w^2f_{W_i}(w)\,\mathrm dw=\int_0^{10i}\frac{w^2}{10i}\,\mathrm dw=\frac{100i^2}3$

so that

$\mathrm{Var}[W_i]=\dfrac{25i^2}3$

Now,

$E[W_1+W_2+W_3]=E[W_1]+E[W_2]+E[W_3]=5+10+15=30$

and

$\mathrm{Var}[W_1+W_2+W_3]=E\left[\big((W_1+W_2+W_3)-E[W_1+W_2+W_3]\big)^2\right]$

$\mathrm{Var}[W_1+W_2+W_3]=E[(W_1+W_2+W_3)^2]-E[W_1+W_2+W_3]^2$

We have

$(W_1+W_2+W_3)^2={W_1}^2+{W_2}^2+{W_3}^2+2(W_1W_2+W_1W_3+W_2W_3)$

$E[(W_1+W_2+W_3)^2]$

$=E[{W_1}^2]+E[{W_2}^2]+E[{W_3}^2]+2(E[W_1]E[W_2]+E[W_1]E[W_3]+E[W_2]E[W_3])$

because $W_i$ and $W_j$ are independent when $i\neq j$ , and so

$E[(W_1+W_2+W_3)^2]=\dfrac{100}3+\dfrac{400}3+300+2(50+75+150)=\dfrac{3050}3$

giving a variance of

$\mathrm{Var}[W_1+W_2+W_3]=\dfrac{3050}3-30^2=\dfrac{350}3$

and so the standard deviation is $\sqrt{\dfrac{350}3}\approx\boxed{116.67}$

# # #

A faster way, assuming you know the variance of a linear combination of independent random variables, is to compute

$\mathrm{Var}[W_1+W_2+W_3]$

$=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]+2(\mathrm{Cov}[W_1,W_2]+\mathrm{Cov}[W_1,W_3]+\mathrm{Cov}[W_2,W_3])$

and since the $W_i$ are independent, each covariance is 0. Then

$\mathrm{Var}[W_1+W_2+W_3]=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]$

$\mathrm{Var}[W_1+W_2+W_3]=\dfrac{25}3+\dfrac{100}3+75=\dfrac{350}3$

and take the square root to get the standard deviation.

8 0

3 years ago

A bee flew 840 \text{ cm}840 cm840, space, c, m and landed on a flower to collect some pollen. Then the bee flew another 330 \te

alexdok [17]

Answer:

<em>The bee traveled 11.7 meters.</em>

Step-by-step explanation:

A bee flew 840 cm first to land on a flower to collect some pollen and then flew another 330 cm to get back to her hive.

For <u>finding the total distance traveled, we need to just add</u> 840 cm and 330 cm.

So, $(840+330) cm = 1170 cm$

We know that, 1 meter = 100 cm. That means, <u>for converting 'cm' into 'meter' , we need to divide by 100</u>.

Thus, $1170 cm= \frac{1170}{100} meter = 11.7 meter$

So, the bee traveled 11.7 meters.

5 0

3 years ago

What is the volume of the prism ?

tia_tia [17]

Answer:

150 units squared

Step-by-step explanation:

5 0

2 years ago