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3 years ago

13

A dentist selected 16 patients at random from a population of more than 1000 patients and asked them how many times the patient

flosses per week. The dentist made a line plot of the results.
What is the estimated mode of the number of times all patients floss per week?

5

5.5

6

7

1 answer:

tankabanditka [31]3 years ago

6 0

The mode is the number that apppers the most on any graph.

0 appears twice
1 doesn't appear at all
2 appears once
3 appears once
4 doesn't appear at all
5 appears four times
6 appears three times
7 appears five times
8, 9, or 10 do not appear on the graph at all

So to find the mode we find the number that appears on the graph the most, the number that appears on the graph the most is 7, it appears 5 times, so 7 is the mode of this graph.

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Answer: Each shape has 12 edges

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3 years ago

The altitude a (in feet) of a plane t minutes after liftoff is given by a = 3400t + 600. How many minutes after liftoff is the p

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Answer:

6

Step-by-step explanation:

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Answered by Gauthmath

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3 years ago

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3 years ago

Read 2 more answers

Which of these expressions is not equivalent to the others?

just olya [345]

Normally You would need to simplify all of them, to see what their values are like.

Already from the start, however, we can see that 9n + 3 + 2 and 9n + 11 isnt the same value. Based on this, we should only need to simplify one of the other, to get either 9n + 5 or 9n + 11.

Lets pick the upper one.

(4n + 3) + 5n + 8 - 6
4n + 3 +5n + 2
9n + 5.

This indicated that 9n+11 is the odd one.

To make sure, we can solve the next one:
(4n + 5n) + (3 + 8 - 6)
9n + 5
Which indicated the same thing.

9n+11 is the "outsider", which means:

9n + 11 is the correct answer for this task.

4 0

3 years ago

Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified l

Sloan [31]

Answer:

The integral of the volume is:

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

The result is: $V = 78.97731$

Step-by-step explanation:

Given

Curve: $x^2 + 4y^2 = 4$

About line $x = 2$ --- Missing information

Required

Set up an integral for the volume

$x^2 + 4y^2 = 4$

Make x^2 the subject

$x^2 = 4 - 4y^2$

Square both sides

$x = \sqrt{(4 - 4y^2)$

Factor out 4

$x = \sqrt{4(1 - y^2)$

Split

$x = \sqrt{4} * \sqrt{(1 - y^2)$

$x = \±2 * \sqrt{(1 - y^2)$

$x = \±2 \sqrt{(1 - y^2)$

Split

$x_1 = -2 \sqrt{(1 - y^2)}\ and\ x_2 = 2 \sqrt{(1 - y^2)}$

Rotate about x = 2 implies that:

$r = 2 - x$

So:

$r_1 = 2 - (-2 \sqrt{(1 - y^2)})$

$r_1 = 2 +2 \sqrt{(1 - y^2)}$

$r_2 = 2 - 2 \sqrt{(1 - y^2)}$

Using washer method along the y-axis i.e. integral from 0 to 1.

We have:

$V = 2\pi\int\limits^1_0 {(r_1^2 - r_2^2)} \, dy$

Substitute values for r1 and r2

$V = 2\pi\int\limits^1_0 {(( 2 +2 \sqrt{(1 - y^2)})^2 - ( 2 -2 \sqrt{(1 - y^2)})^2)} \, dy$

Evaluate the squares

$V = 2\pi\int\limits^1_0 {(4 +8 \sqrt{(1 - y^2)} + 4(1 - y^2)) - (4 -8 \sqrt{(1 - y^2)} + 4(1 - y^2))} \, dy$

Remove brackets and collect like terms

$V = 2\pi\int\limits^1_0 {4 - 4 + 8\sqrt{(1 - y^2)} +8 \sqrt{(1 - y^2)}+ 4(1 - y^2) - 4(1 - y^2)} \, dy$

$V = 2\pi\int\limits^1_0 { 16\sqrt{(1 - y^2)} \, dy$

Rewrite as:

$V = 16* 2\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

Using the calculator:

$\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy = \frac{\pi}{4}$

So:

$V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy$

$V = 32\pi * \frac{\pi}{4}$

$V =\frac{32\pi^2}{4}$

$V =8\pi^2$

Take:

$\pi = 3.142$

$V = 8* 3.142^2$

$V = 78.97731$ --- approximated

3 0

3 years ago