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3 years ago

Help me please thanks

Mathematics

1 answer:

Brut [27]3 years ago

3 0

Forget about the negative sign. First you have to find a least common denominator. This would be 63. Since we had to multiply 9 by 7 to get 63 we have to multiply the numerator (4) by 7. This gives us a new fraction of 36/63. Since we ha e to multiply 21 by 3 to get 63 we have to multiply 19 by 3. This gives us 57. So now we have 36/63 and 57/63. Then we add the negative sign back in making 57/63 -57/63. Now we add them together. Because one has a negative sign and one is positive the number has to be closer to zero. So the answer is -21/63.

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Ruby wanted to get an iPod for 350$ she already had 52$ saved and if she worked for 8 hours a week for 9$ an hour how many weeks

WARRIOR [948]

Answer:

I believe that the answer is 4.13 weeks

Step-by-step explanation:

Since she already has $52 you can automatically start by doing:

$350 - $52 = $298

Since she works 8 hours a week and earns $9 per hour:

8 hours x $9 = $72

Then, take $298 ÷ $72 = 4.13 or about 4 weeks

I divide 298 by 72 because $72 is how much she will earn per week, and by dividing this number by the total amount that she has left to pay narrows it down to about how long she has to save for.

Hope this helps!!

4 0

3 years ago

Two standard number cubes are thrown. Find the probability that the sum of the numbers showing is ten given that the first numbe

Sergio [31]

Given that the first number shows up as four. The second number should be six so that the sum would be ten. Therefore, its probability should be 1/6.

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

3 0

3 years ago

If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.

Ad libitum [116K]

Answer:

The maximum value of f(x) occurs at:

$\displaystyle x = \frac{2a}{a+b}$

And is given by:

$\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b$

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given the function:

$\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0$

And we want to find the maximum value of f(x) on the interval [0, 2].

First, let's evaluate the endpoints of the interval:

$\displaystyle f(0) = (0)^a(2-(0))^b = 0$

And:

$\displaystyle f(2) = (2)^a(2-(2))^b = 0$

Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:

$\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right]$

By the Product Rule:

$\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}$

Set the derivative equal to zero and solve for x:

$\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right]$

By the Zero Product Property:

$\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0$

The solutions to the first equation are x = 0 and x = 2.

First, for the second equation, note that it is undefined when x = 0 and x = 2.

To solve for x, we can multiply both sides by the denominators.

$\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))$

Simplify:

$\displaystyle a(2-x) - b(x) = 0$

And solve for x:

$\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}$

So, our critical points are:

$\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}$

We already know that f(0) = f(2) = 0.

For the third point, we can see that:

$\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b$

This can be simplified to:

$\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b$

Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.

To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:

$\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)$

The critical point will be at:

$\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8$

Testing x = 0.5 and x = 1 yields that:

$\displaystyle f'(0.5) >0\text{ and } f'(1)$

Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.

Therefore, the maximum value of f(x) occurs at:

$\displaystyle x = \frac{2a}{a+b}$

And is given by:

$\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b$

5 0

3 years ago

A department store buys 300 shirts at a cost of $2,400 and sells them at a selling price of $10 each. Find the percent markup.

Solnce55 [7]

Answer:

67%

Step-by-step explanation:

Given : A department store buys 300 shirts at a cost of $1800 .

Then By unitary method , the cost of one shirt = Cost of 300 shirts divided by 300

= $1800 ÷ 300 = $6

i.e. cost of one shirt = $6

Also, Selling price of one shirt = $10

Price mark up = Selling price - Cost price

= $10-$6 = $4

The percent mark up=

(rounded to the nearest percent)

Hence, the percent markup = 67%

4 0

2 years ago

In 2010, the national debt of the United States was about 14 trillion dollars. In 2003 it was about 7 x 10 to the 12 dollars. Ab

maxonik [38]

Okay. 10^12 is 1 trillion. 1 trillion * 7 is 7 trillion. 14 trillion / 7 trillion is 2. The national debt in 2010 is two times larger than in 2003. So that basically means that the national debt doubled from 2003 to 2010.

7 0

3 years ago

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