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3 years ago

6

Melanie and brad each drink 10 cups of water every day. Lara drinks 3 quarts of water every day. How many gallons of water do th

e three of them drink altogether each week?

1 answer:

Tanzania [10]3 years ago

3 0

That is 23 gallon a day

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Trevor thinks that left-handed pitchers in a baseball league are more likely to strike out batters than right-handed pitchers ar

Scilla [17]

Answer:

C. H0: PL - PR = 0

Ha: PL - PR > 0

The null hypothesis for this case is that left-handed pitchers in a baseball league are not more likely to strike out batters than right-handed pitchers are. That is the proportion of at-bats resulting in a strikeout is significantly equal for both left-handed and right-handed pitchers.

H0: PL - PR = 0

The alternative hypothesis is that the proportion of at-bats resulting in a strikeout is significantly higher for left-handed pitchers

Ha: PL - PR > 0

PL - proportion of at-bats resulting in a strikeout for left-handed pitchers

PR - proportion of at-bats resulting in a strikeout for right-handed pitchers

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

The null hypothesis for this case is that left-handed pitchers in a baseball league are not more likely to strike out batters than right-handed pitchers are. That is the proportion of at-bats resulting in a strikeout is significantly equal for both left-handed and right-handed pitchers.

H0: PL - PR = 0

The alternative hypothesis is that the proportion of at-bats resulting in a strikeout is significantly higher for left-handed pitchers

Ha: PL - PR > 0

PL - proportion of at-bats resulting in a strikeout for left-handed pitchers

PR - proportion of at-bats resulting in a strikeout for right-handed pitchers

8 0

3 years ago

Consider the equation below. (If you need to use -[infinity] or [infinity], enter -INFINITY or INFINITY.)f(x) = 2x3 + 3x2 − 180x

soldier1979 [14.2K]

Answer:

(a) The function is increasing $\left(-\infty, -6\right) \cup \left(5, \infty\right)$ and decreasing $\left(-6, 5\right)$

(b) The local minimum is x = 5 and the maximum is x = -6

(c) The inflection point is $x = -\frac{1}{2}$

(d) The function is concave upward on $\left(- \frac{1}{2}, \infty\right)$ and concave downward on $\left(-\infty, - \frac{1}{2}\right)$

Step-by-step explanation:

(a) To find the intervals where $f(x) = 2x^3 + 3x^2 -180x$ is increasing or decreasing you must:

1. Differentiate the function

$\frac{d}{dx}f(x) =\frac{d}{dx}(2x^3 + 3x^2 -180x) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\f'(x)=\frac{d}{dx}\left(2x^3\right)+\frac{d}{dx}\left(3x^2\right)-\frac{d}{dx}\left(180x\right)\\\\f'(x) =6x^2+6x-180$

2. Now we want to find the intervals where f'(x) is positive or negative. This is done using critical points, which are the points where f'(x) is either 0 or undefined.

$f'(x) =6x^2+6x-180 =0\\\\6x^2+6x-180 = 6\left(x-5\right)\left(x+6\right)=0\\\\x=5,\:x=-6$

These points divide the number line into three intervals:

$(-\infty,-6)$ , $(-6,5)$ , and $(5, \infty)$

Evaluate f'(x) at each interval to see if it's positive or negative on that interval.

$\left\begin{array}{cccc}Interval&x-value&f'(x)&Verdict\\(-\infty,-6)&-7&72&Increasing\\(-6,5)&0&-180&Decreasing\\(5, \infty)&6&72&Increasing\end{array}\right$

Therefore f(x) is increasing $\left(-\infty, -6\right) \cup \left(5, \infty\right)$ and decreasing $\left(-6, 5\right)$

(b) Now that we know the intervals where f(x) increases or decreases, we can find its extremum points. An extremum point would be a point where f(x) is defined and f'(x) changes signs.

We know that:

f(x) increases before x = -6, decreases after it, and is defined at x = -6. So f(x) has a relative maximum point at x = -6.

f(x) decreases before x = 5, increases after it, and is defined at x = 5. So f(x) has a relative minimum point at x = 5.

(c)-(d) An Inflection Point is where a curve changes from Concave upward to Concave downward (or vice versa).

Concave upward is when the slope increases and concave downward is when the slope decreases.

To find the inflection points of f(x), we need to use the f''(x)

$f''(x)=\frac{d}{dx}\left(6x^2+6x-180\right)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\f''(x)=\frac{d}{dx}\left(6x^2\right)+\frac{d}{dx}\left(6x\right)-\frac{d}{dx}\left(180\right)\\\\f''(x) =12x+6$

We set f''(x) = 0

$f''(x) =12x+6 =0\\\\x=-\frac{1}{2}$

Analyzing concavity, we get

$\left\begin{array}{cccc}Interval&x-value&f''(x)\\(-\infty,-1/2)&-2&-18\\(-1/2,\infty)&0&6\\\end{array}\right$

The function is concave upward on $(-1/2,\infty)$ because the f''(x) > 0 and concave downward on $(-\infty,-1/2)$ because the f''(x) < 0.

f(x) is concave down before $x = -\frac{1}{2}$ , concave up after it. So f(x) has an inflection point at $x = -\frac{1}{2}$ .

7 0

3 years ago

Final questions I'm asking if you've been keeping up. Thanks in advance.

GaryK [48]

Question 3 is D and question 4 is c for what I tell of the pictire

5 0

3 years ago

Of the 800 participants in a marathon 220 are running to raise money for a cause. How many participants out of 100 are running f

nadezda [96]

Answer:

27.5 /100 are running for a cause

Step-by-step explanation:

We know that 220/800 are running for a cause

Divide the top and bottom by 8 to get the fraction out of 100

220 /8 =27.5

800/8 = 100

27.5 /100 are running for a cause

7 0

3 years ago

The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. Find the nu

inessss [21]

The numbers are 4,8, and 14 because 4+8+14=26 an 4x2=8 and 8+6=14

7 0

3 years ago