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3 years ago

6

The perimeter of a rectangle is 136 ft. The ratio of its length to its width is 9 : 8. What are the dimensions of the rectangle?

40 ft by 28 ft 44 ft by 24 ft 48 ft by 20 ft 36 ft by 32 ft

1 answer:

bezimeni [28]3 years ago

5 0

9: 8 = 9+8 = 17

136/17 = 8

8 * 9 = 72 / 2 = 36

8*8 = 64 / 2 = 32

32 +32 + 36 + 36 = 136

the rectangle is 36 x 32

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H=-16t^2+16t+8 <br> Help pls

Hitman42 [59]

Step-by-step explanation: Your answer is in the photo

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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

Ateacher uses 36 centimeters of tape to hang up 9 student projects. At that rate

Troyanec [42]

The teacher would need 40 centimeters of tape to hang 10 student projects.

Step-by-step explanation:

Given,

Tape used to hang projects = 36 centimeters

Number of projects hanged = 9

We will find unit rate;

9 projects = 36 centimeters

1 project = $\frac{36}{9}\ centimeters$

1 project = 4 centimeters

Therefore,

Tape needed to hang 10 projects = 4*10 = 40 centimeters

The teacher would need 40 centimeters of tape to hang 10 student projects.

Keywords: unit rate, multiplication

Learn more about unit rate at:

#LearnwithBrainly

3 0

3 years ago

Due to nght please help part 2 !

mash [69]

Answer:

t≤ 9

Step-by-step explanation:

3.5+4t≤ 39.5

subtract 3.5 from each side

4t≤ 36

divide each side by 4

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3 years ago

Read 2 more answers

A large emerald with a mass of 378.24 grams was recently discovered in a mine. If the density of the emerald is 2.76grams over c

bogdanovich [222]

Answer:

Volume of emerald = 137.04cm³

Step-by-step explanation:

Given that:

Mass of emerald = 378.24grams

Density of emerald = 2.76grams/cm³

Volume = ?

The equation for this relationship is ρ = m / V in which ρ is density, m is mass (kg or g) and V is volume (cm³ or m³) making the density unit kg/m³ or g/cm³.

Therefore

Density = mass/volume

Volume = Mass/density

i.e

Volume of emerald = Mass of emerald / Density of emerald

Volume of emerald = 378.24grams / 2.76grams/cm³

Volume of emerald = 137.043cm³ ~137.04cm³

Volume of emerald =137.04cm³

6 0

3 years ago