Of Composite Shapes P5

Janice needs 3 gallons of lemonade for a party. She has 4 quarts, 6 pints, and 4 cups of lemonade already made. How much more le

Allisa [31]

4 quarts is 1 gallon
6 pints is 0.75 gallons
4 cups is 0.25 gallons
if you add all of those you would get 2 gallons
so she would need 1 more gallon of lemonade

7 0

3 years ago

Determine the required value of the missing probability to make the distribution a discrete probability distribution. x p(x) 3

Alisiya [41]

To get the required value of the missing probability to make the series complete is to deduct all the probability given to 1 because we know that the discrete probability distribution must be equal to 1. So doing what I have said, this will be:

P(4) = 1 - P(3) - P(5) - P(6)

= 1 – 0.3 – 0.18 – 0.21

<span>= 0.31 is the answer.</span>

3 0

3 years ago

Consider the equation below. f(x) = 2x3 + 3x2 − 336x (a) Find the interval on which f is increasing. (Enter your answer in inter

Vaselesa [24]

We have been given a function $f(x)=2x^3+3x^2-336x$ . We are asked to find the interval on which function is increasing and decreasing.

(a). First of all, we will find the critical points of function by equating derivative with 0.

$f'(x)=2(3)x^{2}+3(2)x^1-336$

$f'(x)=6x^{2}+6x-336$

$6x^{2}+6x-336=0$

$x^{2}+x-56=0$

$x^{2}+8x-7x-56=0$

$(x+8)-7(x+8)=0$

$(x+8)(x-7)=0$

$x=-8,x=7$

So $x=-8,7$ are critical points and these will divide our function in 3 intervals $(-\infty,-8)U(-8,7)U(7,\infty)$ .

Now we will find derivative over each interval as:

$f'(x)=(x+8)(x-7)$

$f'(-9)=(-9+8)(-9-7)=(-1)(-16)=16$

Since $f'(9)>0$ , therefore, function is increasing on interval $(-\infty,-8)$ .

$f'(x)=(x+8)(x-7)$

$f'(1)=(1+8)(1-7)=(9)(-6)=-54$

Since $f'(1)$ , therefore, function is decreasing on interval $(-8,7)$ .

Let us check for the derivative at $x=8$ .

$f'(x)=(x+8)(x-7)$

$f'(8)=(8+8)(8-7)=(16)(1)=16$

Since $f'(8)>0$ , therefore, function is increasing on interval $(7,\infty)$ .

(b) Since $x=-8,7$ are critical points, so these will be either a maximum or minimum.

Let us find values of f(x) on these two points.

$f(-8)=2(-8)^3+3(-8)^2-336(-8)$

$f(-8)=1856$

$f(7)=2(7)^3+3(7)^2-336(7)$

$f(7)=-1519$

Therefore, $(-8,1856)$ is a local maximum and $(7,-1519)$ is a local minimum.

(c) To find inflection points, we need to check where 2nd derivative is equal to 0.

Let us find 2nd derivative.

$f''(x)=6(2)x^{1}+6$

$f''(x)=12x+6$

$12x+6=0$

$12x=-6$

$\frac{12x}{12}=-\frac{6}{12}$

$x=-\frac{1}{2}$

Therefore, $x=-\frac{1}{2}$ is an inflection point of given function.

3 0

3 years ago

A math quiz has 10 questions and is scored out of 100. Each question is worth the same. The function S(q) represents the quiz sc

zysi [14]

Answer: S(q) represents a quantity that changes at a constant rate per unit interval is true and S(q) represents a linear function is true. The rest is false. Hope this helps

Step-by-step explanation:

8 0

2 years ago

Can you help me in this question?

Xelga [282]

Answer:

100+150DHS

Step-by-step explanation:

100 base and 150 is the rate per a day

3 0

2 years ago