All categories

3 years ago

Find the length of the third side. If necessary, write in simplest radical form.

Mathematics

1 answer:

eduard3 years ago

8 0

Let the third side be x :

( 3√5 )^2 = 6^2 + x^2

45 = 36 + x^2

x^2 = 45 - 36

x^2 = 9

x = 3

You might be interested in

Hot dogs at a carnival cost $2.99 each plus 7% tax. What is the total cost for one hot dog?

marysya [2.9K]

$2.99 + 7% of $2.99 =

= $2.99 + 7% * $2.99

= $2.99 + 0.07 * $2.99

= $2.99 + $0.21

= $3.20

4 0

3 years ago

Read 2 more answers

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

Which best explains if quadrilateral WXYZ can be a parallelogram?

never [62]

The answer is the first answer choice

8 0

2 years ago

Read 2 more answers

Rob Polanski is a tractor salesman. Last week his total sales amounted to $38,642.00, and he received $2,704.94 in commission. W

pentagon [3]

2704.94 / 38642 = 0.07 = 7%

5 0

3 years ago

Read 2 more answers

Pam needs 3 1/2 cups of sugar to make 50 cupcakes. A 5- pound bag of sugar coats $3.69. There are about 2 cups of sugar in a pou

Lorico [155]

Answer:

The answer to your question is $1.29

Step-by-step explanation:

Data

Total amount of cupcakes = 50

Total amount of sugar = 3 1/2 cups = 3.5 cups

Cost of 5-pound bag = $3.69

2 cups = 1 pound

Total cost = ?

Process

1.- Calculate the amount of pounds needed

2 cups ------------------ 1 pound

3.5 cups --------------- x

x = (3.5 x 1) / 2

x = 3.5 / 2

x = 1.75 pounds

2.- Calculate the price of 1.75 pounds

5 pounds -------------- $3.69

1.75 pounds ---------- x

x = (1.75 x 3.69)/5

x = 6.46/5

x = $1.29

3.- Conclusion

The cost of sugar to prepare 50 cupcakes is $1.29

3 0

3 years ago