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2 years ago

Y= 2x 2x + y=8 Does anyone know the answer

Mathematics

1 answer:

katrin2010 [14]2 years ago

5 0

Answer:

x is 2, y is 4

Step-by-step explanation:

${ \tt{y = 2x - - - (a)}} \\ { \tt{2x + y = 8 - - - (b)}}$

» Substitute for y in equation (b) with that in equation (a)

${ \tt{2x + 2x = 8}} \\ { \tt{4x = 8}} \\ { \tt{x = 2}}$

» Find y

${ \tt{y = 2 \times 2}} \\ { \tt{y = 4}}$

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A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.047.0 and

alisha [4.7K]

Answer:

0.025 = 2.5% probability that a given class period runs between 51.5 and 51.75 minutes.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is between c and d is given by the following formula

$P(c \leq X \leq d) = \frac{d - c}{b-a}$

For this problem, we have that:

$a = 47, b = 57, c = 51.5, d = 51.75$ . So

$P(c \leq X \leq d) = \frac{d - c}{b-a}$

$P(51.5 \leq X \leq 51.75) = \frac{51.75 - 51.5}{57 - 47} = 0.025$

0.025 = 2.5% probability that a given class period runs between 51.5 and 51.75 minutes.

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3 years ago

Answer the following questions about the function whose derivative is f primef′(x)equals=x Superscript negative three fifths Ba

Elden [556K]

Answer:

(a) The critical points of f are x=0 and x=3.

(b)f is decreasing on $(0,3)$ and f is decreasing on $(3,\infty)$ .

(c) Therefore the local minimum of f is at x=3

Step-by-step explanation:

Given function is

$f'(x)= x^{-\frac35}(x-3)$

(a)

To find the critical point set f'(x)=0

$\therefore x^{-\frac35}(x-3)=0$

$\Rightarrow x=0,3$

The critical points of f are 0,3.

(b)

The interval are $(0,3)$ and $(3,\infty)$ .

To find the increasing or decreasing, taking two points one point from the interval (0,3) and another point $(3,\infty)$ .

Assume 1 and 4.

Now $f'(1)=(1)^{-\frac35}(1-3)$

and $f'(4)=(4)^{-\frac35}(4-3)>0$

Since 1∈ $(0,3)$ , f'(x)<0 and 4∈ $(3,\infty)$ , f'(x)>0

∴f is decreasing on $(0,3)$ and f is decreasing on $(3,\infty)$ .

(c)

$f'(x)= x^{-\frac35}(x-3)$

Differentiating with respect to x

$f''(x)=-\frac35x^{-\frac 85}(x-3)+x^{-\frac35}$

Now

$f''(0)=-\frac35(0)^{-\frac 85}(0-3)+(0)^{-\frac35}=0$

and

$f''(3)=-\frac35(3)^{-\frac 85}(3-3)+3^{-\frac35}$

$=0.517>0$

Since f''(x)>0 at x=3

Therefore the local minimum of f is at x=3

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3 years ago

What is the best estimate for this sum?

Pavlova-9 [17]

Answer:

The sum is close to 1/2

Step-by-step explanation:

1/4 = 7/28
2/7 = 8/28
7/28 + 8/28 = 15/28

14/28 = 1/2 and 15/28 is close to 14/28

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2 years ago

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Andrea can clean a house 4 times as fast as Denise. When they work together, Andrea and Denise can clean a large house in 8 hour

steposvetlana [31]

Answer:

8 hours

Step-by-step explanation:

A&D can clean a house in 8 hours together.

Proportionally, Denise works at x. Andrea works at 4x. There is a total of 5x.

Out of the 5x, Denise accounts for x.

x/5x = 1/5 of the work over 8 hours.

1/5 ( Denise's time for cleaning the whole house) = 8 hours.

Multiply both sides by 5:

5(1/5)(Denise's time for cleaning the whole house) = 5*8

Denise's time for cleaning the whole house = 40 hours

I like this method better...

That means in ONE hour, they get 1/8 of the job done.

Let's say Denise takes x hours to clean the house.

In one hour, she would do 1/x of the job (x can't be 0 hours).

Since Andrea does the house 4 times as fast as Denise, who takes x hours to do the job, Andrea takes x/4 hours.

In one hour, Andrea does 4/x of the job.

In one hour the part of the job Andrea does, plus the part of the job Denise does, must total 1/8.

(4/x) + (1/x) = 1/8

5/x = 1/8

Cross multiply:

x = 40

So it would take Denise 40 hours to clean the house by herself. (She's not really that efficient, or the house was REALLY dirty.

Andrea takes x/4 hours or 40/4 = 10 hours to clean the house by herself.

So with a little help from Denise, Andrea decreases her time to clean the house from the 10 hours it would take by herself to 8 hours.

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3 years ago

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