A vacant city lot is being turned in to a garden. the neighbors want to fence in a triangular section of the lot and plant flowers there. the longest side of the triangular sec is 8 feet shorter than twice the shortest side. the third side is 4 feet longer than the shortest side. the perimeter is 56 feet. how long is each side?

Answers

Answer 1

Answer: Hi there,
First of all, we see what are looking for.
We want to find the length of each side
What do we know?
Perimeter is 56
We are also given relation of between all the sides
But first we make some suggestions to the problem
Say that x is the shortest side
That means the longest is 2x-8
and the thirst side is x+4
Now we the desired information.
Perimeter=56=x+2x-8+x+4
we solve for x
combining like terms we get
4x-4=56
subtract 4 from both side
4x-4+4=56+4
4x=60
divide by 4 both side
4x/4=60/4
x=15

Shortest side is 15
longest side is 2(15)-8=30-8=22
3rd side is 15+4=19
if we add them up
15+22+19=56

Answer 2

Answer: inside plus outside inside plus outside from middle to lenth out from first.

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Write true or false.
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Factor the difference of cubes. Select prime if the polynomial cannot be factored

Answers

Answer:

(m-(1/3))(m^2+(1/3)m+(1/9)

Step-by-step explanation:

Just use the difference of cubes

Solve
.................
-m/20=-2

Answers

Answer:

$\boxed{m = 40}$

Step-by-step explanation:

$-(m)/(20)=\ -2$

Step 1: Simplify both sides of the equation.

$(-1)/(20)m = -2$

Step 2: Multiply both sides by 20/(-1).

$((20)/(-1)) * ((-1)/(20m) = ((20)/(-1) ) * (-2)$

Hope this helped you!

Tanya enters a raffle at the local fair, and is wondering what her chances of winning are. If her probability of winning can be modeled by a beta distribution with α = 5 and β = 2, what is the probability that she has at most a 10% chance of winning?

Answers

Answer:

$P(X<0.1)= 5.5x10^(-5)$

Step-by-step explanation:

Previous concepts

Beta distribution is defined as "a continuous density function defined on the interval [0, 1] and present two parameters positive, denoted by α and β, both parameters control the shape. "

The probability function for the beta distribution is given by:

$P(X)= (x^(\alpha-1) (1-x)^(\beta -1))/(B(\alpha,\beta))$

Where B represent the beta function defined as:

$B(\alpha,\beta)= (\Gamma(\alpha)\Gamma(\beta))/(\Gamma(\alpha+\beta))$

Solution to the problem

For our case our random variable is given by:

$X \sim \beta (\alpha=5, \beta =2)$

We can use the following R code to plot the distribution for this case:

> x=seq(0,1,0.01)

> plot(x,dbeta(x,5,2),main = "Beta distribution a=5, b=2",ylab = "Probability")

And we got as the result the figure attached.

And for this case we want this probability, since we want the probability that she has at most 10% or 0.1 change of winning:

$P(X<0.1)$

And we can find this probability with the following R code:

> pbeta(0.1,5,2)

[1] 5.5e-05

And we got then this : $P(X<0.1)= 5.5x10^(-5)$

What is the common difference of the arithmetic sequence 5 8 11 14

Answers

Answer:

Step-by-step explanation:

The gap between every single number of this sequence is 3.

14 - 11 = 3

8 - 5 = 3

This gap is called the common difference. You can find it by subtracting values in the sequence that are next to each other.

The answer is for sure 3

How would I do this?

Answers

Answer:

14 to the 10th power

Step-by-step explanation:

If two exponents have the same base, you can subtract them if they're being divided.

In your case:

14 to the 15th power/14 to the 5th power

We can subtract:

15 - 5 = 10

So our final answer would be:

14 to the 10th power

(the fourth answer)

Hope this helps!

Answer:

14¹⁰

Step-by-step explanation:

14¹⁵ divided by 14⁵ equals 14¹⁰

Multiply the polynomials 3(x+7) (show work pls)

Answers

Answer:

3x + 21

Step-by-step explanation:

(3)(x+7)

Now, we distribute the 3 in each term of (x+7)

So, 3*x = 3x and 3*7 = 21.

So our resulting term would be 3x+21.

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