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3 years ago

7

What is true of the data in the dot plot? Check all that apply. Number of Minutes for Each Commercial Break A dot plot going fro

m 1 to 5. 1 has 3 dots, 2 has 0 dots, 3 has 8 dots, 4 has 0 dots, and 5 has 3 dots. The center is 3. The peak is 5. There are no gaps. It is symmetric. It is skewed right. The spread is from 1 to 5. There were 14 commercial breaks.

1 answer:

Natasha2012 [34]3 years ago

5 0

Answer:

The center is 3

The peak is 5

The spread is from 1 to 5.

There were 14 commercial breaks.

Step-by-step explanation:

Edg

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**Spam answers will not be tolerated**

Morgarella [4.7K]

Answer:

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

Step-by-step explanation:

So we have the function:

$f(x)=\frac{4}{\sqrt x}$

And we want to find the derivative using the limit process.

The definition of a derivative as a limit is:

$\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Therefore, our derivative would be:

$\lim_{h \to 0}\frac{\frac{4}{\sqrt{x+h}}-\frac{4}{\sqrt x}}{h}$

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

$=\lim_{h \to 0}\frac{4(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x})}{h}$

Place the 4 in front:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}$

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x})$

Distribute:

$=4\lim_{h \to 0}\frac{({\sqrt{x+h}\sqrt x})\frac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\frac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}$

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

$=4 \lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }$

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

$= 4\lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }(\frac{\sqrt x +\sqrt{x+h})}{\sqrt x +\sqrt{x+h})}$

The numerator will use the difference of two squares. Thus:

$=4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Simplify the numerator:

$=4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Both the numerator and denominator have a h. Cancel them:

$=4 \lim_{h \to 0} \frac{-1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Now, substitute 0 for h. So:

$=4 ( \frac{-1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})})$

Simplify:

$=4( \frac{-1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})})$

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

$=4( \frac{-1}{(x)(2\sqrt{x})})$

Multiply across:

$= \frac{-4}{(2x\sqrt{x})}$

Reduce. Change √x to x^(1/2). So:

$=-\frac{2}{x(x^{\frac{1}{2}})}$

Add the exponents:

$=-\frac{2}{x^\frac{3}{2}}$

And we're done!

$f(x)=\frac{4}{\sqrt x}\\f'(x)=-\frac{2}{x^\frac{3}{2}}$

5 0

2 years ago

How do addition facts help you subtract

Lena [83]

A number fact is made up of three numbers. These three numbers can be used to make up other number facts. Knowing one fact can help children with other facts. Look at the number facts we can make with the numbers 3, 4, and 7.

<span><span>Addition FactsSubtraction Facts</span><span>3 + 4 = 77 – 3 = 4</span><span>4 + 3 = 7<span>7 – 4 = 3</span></span></span>

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2 years ago

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Consider the exponential function f(x) = 2(3x) and its graph.

AveGali [126]

Answer:

The initial value of the function is <u>2</u>

The base of the function is <u>3</u>

The function shows exponential <u>growth</u>

Step-by-step explanation:

f(x) = 2(3^x)

Exponential functions are those with the following equation:

y = a*b^x

where a ≠ 0, b > 0 and b ≠ 1 and x is a real number.

<em>a</em> is the y-intercept and <em>b </em>is the base.

The initial value of the function is the same as the y-intercept

If <em>a</em> is positive, the function growth. If <em>a</em> is negative, the function decay

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3 years ago

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Okay so this is a weird one... if I take a medication twice a day for 9 months how many days have I taken that medication??? I h

Delvig [45]

Answer: 273 days i believe

Step-by-step explanation:

jan: 31 days

feb: 28 Days

mar: 31

apr: 30

may: 31

june: 30

july: 31

aug: 31

sept: 30

add all the days together to get 273

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2 years ago

What does x+7=2 what does x mean

Ksenya-84 [330]

Answer:-5

Step-by-step explanation:

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2 years ago