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2 years ago

Use the given graph to determine the limit, if it exists. (4 points)

Mathematics

1 answer:

skelet666 [1.2K]2 years ago

8 0

<h3>Answer: 3</h3>

Explanation:

Refer to the graph below. It should be similar to what your teacher gave you, based off the description.

Since we're approaching 3 from the right side, this means we'll be working with the horizontal line portion. We could start at something like x = 3.2 and move closer to 3 by getting to x = 3.1 then x = 3.01 then x = 3.001 and so on. We never actually get to 3 itself.

As x gets closer to 3 from this direction, the y values are approaching 3 since every point on this horizontal line has the same y coordinate. Technically the y value is already at 3, but it's the same idea.

In terms of notation, we can write $\displaystyle \lim_{x\to3^{+}}f(x) = 3$

The portion $x \to 3^{+}$ means we're approaching 3 from the positive side, aka the right hand side on the number line.

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How do I convert 12mi/hr = ? Ft/hr

Blizzard [7]

One mile equals 5,280 feet, therefore you would multiply 12 x 5,280 which is 63360 feet per hour.

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2 years ago

Joe heard from a reliable source that only 22% of people actually sleep 8 hours or more per night. You do a survey and find 58 o

Juliette [100K]

Answer:

95% Confidence interval: (31.32%,47.04%)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 148

Number of people who sleep for 8 hours or longer, x = 58

$\hat{p} = \dfrac{x}{n} = \dfrac{58}{148} = 0.3918$

95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting the values, we get:

$0.3918\pm 1.96(\sqrt{\dfrac{0.3918(1-0.3918)}{148}})\\\\ = 0.3918\pm 0.0786\\\\=(0.3132,0.4704)=(31.32\%,47.04\%)$

(31.32%,47.04%) is the required 95% confidence interval.

8 0

3 years ago

A survey of 70 students from a high school is conducted. From this sample, it is found that 58 students have sent a text message

Irina-Kira [14]

Number of students who have sent a text message only is given by the difference between those that have sent a text message and those that have done both.
i.e. Number of students who has sent a text message only = 58 - 12 = 46

Number of students who have uploaded a selfie only is given by the difference between those that have uploaded a selfie and those that have done both.
i.e. Number of students who have uploaded a selfie only = 21 - 12 = 9

The total number of students surveyed is 70.
Let the number of students who have neither sent a text message nor taken a selfie today be x, then
46 + 9 + 12 + x = 70
67 + x = 70
x = 70 - 67 = 3

Therefore, 3 students neither sent a text message nor taken a selfie today.

The number of students that have sent a text message or have taken a selfie today is given by the sum of the number of students that have sent a text message and the number of students that have taken a selfie less the number of people that have done both.
i.e. number of students that have sent a text message or have taken a selfie today = 58 + 21 - 12 = 67.

7 0

3 years ago

What is the definition of marginal utility? A. The average utility from consuming a good or service multiplied by the number of

Ilya [14]

Answer: Option 'E' is correct.

Step-by-step explanation:

Marginal utility is the addition utility derived from each successive unit of a particular good.

so, marginal utility is the change in utility from consuming an addition unit of a good or service.

Mathematically, it is expressed as

$MU=\dfrac{\Delta TU}{\Delta Q}$