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2 years ago

9. You are installing a swimming pool. Write a polynomial that represents the area of the walkway

Mathematics

1 answer:

Anastasy [175]2 years ago

6 0

Answer:

(10x² +12x +32) ft²

Step-by-step explanation:

The area of the walkway around the pool is the difference between the area of the entire rectangle, and the area of the pool. The area of each rectangle is found by multiplying its length and width.

Overall area:

((2x +6) ft) × (10x) ft = (10x² +60x) ft²

Pool area:

((6x -4) ft) × (8 ft) = (48x -32) ft²

Walkway area:

overall area - pool area = ((10x² +60x) ft²) -((48x -32) ft²)

= (10x² +12x +32) ft²

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Please help thank you

Dvinal [7]

the tale-tell fellow is the number inside the parentheses.

if that number, the so-called "growth or decay factor", is less than 1, then is Decay, if it's more than 1, is Growth.

$\bf f(x)=0.001(1.77)^x\qquad \leftarrow \qquad \textit{1.77 is greater than 1, Growth} \\\\[-0.35em] ~\dotfill\\\\ f(x)=2(1.5)^{\frac{x}{2}}\qquad \leftarrow \qquad \textit{1.5 is greater than 1, Growth} \\\\[-0.35em] ~\dotfill\\\\ f(x)=5(0.5)^{-x}\implies f(x)=5\left( \cfrac{05}{10} \right)^{-x}\implies f(x)=5\left( \cfrac{1}{2} \right)^{-x} \\\\\\ f(x)=5\left( \cfrac{2}{1} \right)^{x}\implies f(x)=5(2)^x\qquad \leftarrow \qquad \textit{Growth} \\\\[-0.35em] ~\dotfill$

$\bf f(t)=5e^{-t}\implies f(t)=5\left( \cfrac{e}{1} \right)^{-t}\implies f(t)=5\left( \cfrac{1}{e} \right)^t \\\\\\ \cfrac{1}{e}\qquad \leftarrow \qquad \textit{that's a fraction less than 1, Decay}$

now, let's take a peek at the second set.

$\bf f(x)=3(1.7)^{x-2}\qquad \leftarrow \qquad \begin{array}{llll} \textit{the x-2 is simply a horizontal shift}\\\\ \textit{1.7 is more than 1, Growth} \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)=3(1.7)^{-2x}\implies f(x)=3\left(\cfrac{17}{10}\right)^{-2x}\implies f(x)=3\left(\cfrac{10}{17}\right)^{2x} \\\\\\ \textit{that fraction is less than 1, Decay} \\\\[-0.35em] ~\dotfill$

$\bf f(x)=3^5\left( \cfrac{1}{3} \right)^x\qquad \leftarrow \qquad \textit{that fraction is less than 1, Decay} \\\\[-0.35em] ~\dotfill\\\\ f(x)=3^5(2)^{-x}\implies f(x)=3^5\left( \cfrac{2}{1} \right)^{-x}\implies f(x)=3^5\left( \cfrac{1}{2} \right)^x \\\\\\ \textit{that fraction in the parentheses is less than 1, Decay}$

6 0

4 years ago

Juanita and Nina are bowling together. The probability of Juanita getting a strike next game is 24%. The probability of Nina get

ASHA 777 [7]

Answer:

(Choice A)

Juanita gets a strike next game.'

Step-by-step explanation:

Your question is obviously incomplete.

Complete question is:

Juanita and Nina are bowling together. The probability of Juanita getting a strike next game is 24%. The probability of Nina getting a strike next game is 0.17. Which of these events is more likely?

(Choice A)

Juanita gets a strike next game.'

(Choice B)

Nina gets a strike next game.

(Choice C)

Neither. Both events are equally likely.

Answer:

Probability of Juanita : P(J)= 24% => 0.24

probability of Nina getting a strike next game: P(N) = 0.17

As you can see 0.24 > 0.17 ----> P(J)>P(N)

Thus it can be concluded that Juanita gets a strike next game is more likely.

so, choice A

4 0

3 years ago

Read 2 more answers

In your own words what would the steps be to solve by elimination.

Tanya [424]

Answer:

Enter the equations.

Multiply each equation by a number to get the lowest common multiple for one of the variables.

Add or subtract the two equations to eliminate that variable .

Substitute that variable into one of the equations and solve for the other variable.

7 0

2 years ago

Software filters rely heavily on ""blacklists"" (lists of known ""phishing"" URLs) to detect fraudulent e-mails. But such filter

crimeas [40]

Answer:

a) $X \sim Binom(n=16, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The expected value is given by this formula:

$E(X) = np=16*0.2=3.2$

b) $P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Part a

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=16, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The expected value is given by this formula:

$E(X) = np=16*0.2=3.2$

Part b

For this case we want this probability:

$P(X=0)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And using this function we got:

$P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815$

6 0

3 years ago

I need some more help

Andrew [12]

Answer:

slope: 2/3 intercept is -3

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers