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2 years ago

PLEASE HELP!

Mathematics

2 answers:

Diano4ka-milaya [45]2 years ago

8 0

14, B. I hope that helps! :)

anygoal [31]2 years ago

6 0

B. 14, from the histogram of the cantaloupes, we see that no cantaloupes weigh more than 8 pounds. When we look at the watermelon histogram, we see that there are 14 watermelons that weigh over 8 pounds.

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A pretzel manufacturer has two production lines. Line A produces a variety of pretzel that is sold for $2.40 per bag. Line A typ

nydimaria [60]

Answer:

f(x)=19x - 7x

Step-by-step explanation:

I am a high schooler as well and was working on this problem as well. I can't say I'm right or wrong because I didn't have a grade on it yet. I believe the answer is f(x)=19x - 7x. The Lines don't have a given value, so I chose the values 12 for Line A and 7 for Line B. I believe the answer is this because Line A would produce 12 bags each day and 3 of them would not be useable, leaving you with 9. Line B would produce 7 and 4 of them would be unusable, leaving you with 3. Line A produces 9 per day while Line B produces 3, and that would check off the part that says, "Line A produces 3 times as many bags as Line B each day." Throughout the problem, it talks about how many bags can each line produces each day, and the sentence talks about that specifically as well. So, the function must be about the amount of bags produced per day. x would represent the number of days that the Lines have been working. 19 is the total amount of bags that was produced in a day. 7 represents the total amount of bags that are unusable. Though I may be wrong, I hope this might help you come to a conculsion of your own.

7 0

3 years ago

A fish tank is a cube. Its side length is 4 1/2 feet. The volume of water needed to completely fill the fish tank is ___ cubic f

GalinKa [24]

The equation for the volume of a cube is V=s^3, where V is volume and s is side length. Plug in and solve:

V=4.5^3

V=4.5*4.5*4.5

V=91.125ft^3

Hope this helps!!

6 0

2 years ago

Fred earns dollars. Chad earns 45% more than Fred which expression represents the amount of money in dollars that chad earns

Genrish500 [490]

Answer:

$0.45x

Step-by-step explanation:

Fred earns dollars. Let Fred earns $x.

Chad earns 45% more than Fred.

We need to find the expression for Chad.

Chad amount = 45% of x

$=\dfrac{45}{100}x\\\\=0.45x$

So, Chad earns $0.45x.

7 0

2 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

2 years ago

Write the Equation of the line in slope intercept form (0, -3), (7.5,0)

makkiz [27]

Answer:

Step-by-step explanation:

First, start off by solving for the slope using this formula:

$\frac{y_{2} -y_{1} }{x_{2}-x_{1} }$

Then, plug in the values: $\frac{0-(-3)}{7.5-0}$

Solve the equation: $\frac{3}{7.5}$

That's your slope.

Then plug in one of the coordinates given in the problem for x and y and solve this equation:

y= $\frac{3}{7.5}$ x+b

Hope that helped!!! :)

7 0

2 years ago