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3 years ago

7

Suppose you pick a tile out of a bag containing 26 tiles marked with the letters A through Z. What is the probability of picking

a letter from the name JACK or from the name BEN?

1 answer:

Liula [17]3 years ago

6 0

Given that <span>a bag contains 26 tiles marked with the letters A through Z.

The probability of picking a letter from the name JACK is 4 / 26

The probability of picking a letter from the name BEN is 3 / 26.

Therefore, the probability of picking a letter from the name JACK or from the name BEN iis given by 4 / 26 + 3 / 26 = 7 / 26 </span>

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How do you find the area of a triangle?

guapka [62]

The formula to find the area of a triangle is

$\frac{h_{b}b }{2}$

If you have any more questions let me know!

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3 years ago

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A store is having a 20% off sale on all merchandise If Mai buys one item and save $13 what was the original price of her purchas

katrin [286]

Answer:

Step-by-step explanation:

20% off...and she saves $13

so 20% of what number is 13

0.20x = 13

x = 13/0.20

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2 years ago

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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

2 years ago

I don't know how to find a different angle from this. PLEASE HELP FIND X!!!! THANKS!!!

timama [110]

The intersection of the two red rays forms a set of vertical angle pairs. In such a pair, angles opposite one another have the same measure, so the angle opposite the one labeled 93 degrees also has measure 93 degrees.

The red ray on the right together with the black ray pointing directly to the right form a pair of supplementary angles, whose measures add up to 180 degrees. This means the angle adjacent to the one labeled 128 degrees has measure 180 - 128 degrees.

In any triangle, the interior angles' measures add up to 180 degrees. So we have

? + 93 + (180 - 128) = 180

? + 93 - 128 = 0

? = 128 - 93

? = 35

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3 years ago

Solve for . Round to the nearest tenth, if necessary.

Len [333]

Answer:

x ≈ 8.7

Step-by-step explanation:

Using the sine ratio in the right triangle

sin75° = $\frac{opposite}{hypotenuse}$ = $\frac{RS}{QS}$ = $\frac{x}{9}$ ( multiply both sides by 9 )

9 × sin75° = x , then

x ≈ 8.7 ( to the nearest tenth )

7 0

2 years ago