If there are two Sarahs in a class, would you know who will answer when i say "Sarah"? Is this a function? Explain

Part A) x cannot be 1 or 0, because that would lead do division by 0. If x=1, 1-1=0. If x=0, then we have straight division by 0.

Part B) x=2 or x=1.

Together they could clean the house in 3.75 hours.

Explanation:

Part A is explained with the answer.
Part B)
$\frac{1}{x-1}+\frac{2}{x}=\frac{x}{x-1}$
We will first multiply each term by (x-1) to cancel those denominators:
$\frac{1}{x-1} \times \frac{x-1}{1}+\frac{2}{x} \times \frac{x-1}{1}=\frac{x}{x-1} \times \frac{x-1}{1}
\\
\\ \frac{x-1}{x-1}+\frac{2(x-1)}{x}=\frac{x(x-1)}{x-1}
\\
\\ 1+\frac{2(x-1)}{x}=x$

Now we multiply everything by x to cancel that denominator:
$1(x)+\frac{2(x-1)(x)}{x}=x(x)
\\
\\x+2(x-1)=x^2
\\
\\x+2*x-2*1=x^2
\\x+2x-2=x^2
\\3x-2=x^2$

We want all of the variables to be on the same side of the equation, so subtract 3x from both sides:
3x-2-3x=x²-3x
-2=x²-3x

To solve quadratics, we set them equal to 0. Add 2 to both sides to make this happen:
-2+2=x²-3x+2
0=x²-3x+2

To solve this by factoring, we want factors of 2 that sum to -3. -2(-1)=2 and -2+-1=-3:
0=(x-2)(x-1)

The zero product property tells us that either x-2=0 or x-1=0; therefore x=2 or x=1.

Max cleans 1/10 of the house in an hour, since it takes him 10 hours to clean the whole house. Maggie cleans 1/6 of the house in an hour, since it takes her 6 hours to clean the whole house. Our equation is then:

1/10x+1/6x=1 (one whole, since it is one house; x is the number of hours)

Find a common denominator. 60 is the first thing that 10 and 6 both evenly divide into:
6/60x+10/60x=1
16/60x = 1

Divide both sides by 16/60:

16/60x ÷ 16/60 = 1 ÷ 16/60
x = 1/1 ÷ 16/60
x = 1/1 ×60/16
x = 60/16 = 3.75.

5 0

3 years ago

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An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and it is replaced in the

iragen [17]

Answer:

A. P("Select 2 black balls and then select 2 white balls")=35/768

Step-by-step explanation:

A. First, we have to get an idea of what our experiment talks about:

If I take a black ball, then we note its color and put it back to the urn with 2 more balls of the same color.

So, every time that we take a ball the quantity of balls in the urn changes with the probability that we had before replacing. The first case (that the first ball you select is black) would go like this:

P("Select a black ball first try") = 7 (number of black balls)/12 (total of balls in the urn)

P(B₁)=7/12

Then, the amount of balls in the urn rise to 14 (12 + 2 balls added) and now the quantity of black balls it´s 9 (7 + 2 added). The urn currently has 9 black balls and 5 white balls, of course:

P("Select black ball second try after getting a black ball before") = 9 (number of black balls)/ 14 (total of balls in the urn)

P(B₁B₂)=9/14

<u>Notice that while we keep taking black balls, the quantity of white ball keeps constant</u> and, for the probability that we take a white ball, we just consider the change in the number of balls in the urn

P(B₁B₂W₃)=5/16

And now, we consider the new white balls that are put in the urn (2 white balls, for a total of 18 and 7 white balls):

P(B₁B₂W₃W₄)=7/18

Because all these probabilities are chained and everything comes from the first ball we choose <u>(if you use a tree diagram, they will be in the same branch</u>), we multiply the probabilities to find the probability that all happens in the same experiment:

P(B₁)*P(B₁B₂)*P(B₁B₂W₃)*P(B₁B₂W₃W₄) = 7/12 * 9/14 * 5/16 * 7/18 = 2205/48384

P(B₁)*P(B₁B₂)*P(B₁B₂W₃)*P(B₁B₂W₃W₄)=35/768

And this is the final answer

7 0

3 years ago

What us the name of the period that has the digits 486.in 751,486?

nexus9112 [7]

Hundreds period, since the 6 is in the ones, 8 is in the tens, and 4 is in the hundreds.

4 0

4 years ago

A candle on pauline’s dresser is 10 inches tall and burns at a rate of 0.75 inches per hour. how many hours will it take for the

Natalija [7]

Using a linear function, it is found that it will take 13 hours for the candle to burn down to a height of .25 inches.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

Considering the situation described, the y-intercept is of 10 while the slope is of -0.75, hence the height of the candle after t hours is given by:

h(t) = 10 - 0.75t

The height will be of 0.25 inches when h(t) = 0.25, hence:

0.25 = 10 - 0.75t

0.75t = 9.75

t = 9.75/0.75

t = 13 hours.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

6 0

2 years ago

I NEED ANSWERS TO A AND B ASAP THIS TEST ENDS IN 2 HRS

Nostrana [21]

Answer:

200.3 cm

210 cm

Step-by-step explanation:

to find the mean add all the numbers up and then divide it by the total number sampled

so we have

(198+199*3+200*2+201*5+202*2)/13

which gives you around 200.3

To find the height of the new player we have the following equation

let x be the height of the new player

$\frac{(198+199*3+200*2+201*5+202*2)+x}{14}=201$

solve for x and get

210 cm

8 0

3 years ago

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