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1 year ago

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What is the slope of a line perpendicular to the line whose equation is 4x+5y=354x+5y=35. Fully simplify your answer.

1 answer:

IrinaK [193]1 year ago

5 0

The perpendicular slope is expressed as the negative reciprocal of the slope or − 1 m. In this scenario, the slope, or m, is −4 so the slope of the perpendicular line is − 1 −4 which simplifies to 1 4

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The image shows three tennis balls enclosed in a cylindrical can. Choose all that are correct. The volume of a single tennis bal

Fynjy0 [20]

Answer:

The volume of a single tennis ball is $14.14\ in^{3}$

The volume of three tennis balls is $42.42\ in^{3}$

Step-by-step explanation:

Step 1

Find the volume of a single tennis ball

we know that

The volume of a sphere is equal to

$V=\frac{4}{3}\pi r^{3}$

where r is the radius of the sphere

In this problem

$r=3/2=1.5\ in$

substitute

$V=\frac{4}{3}\pi (1.5)^{3}$

$V=14.14\ in^{3}$

Step 2

Find the volume of the can

we know that

the volume of the cylinder is equal to

$V=\pi r^{2} h$

where r is the radius of the cylinder

h is the height of the cylinder

in this problem we have

$r=3/2=1.5\ in$

$h=8.4\ in$

substitute

$V=\pi (1.5)^{2}(8.4)$

$V=59.38\ in^{3}$

Statement

<u>case A)</u> The volume of a single tennis ball is $14.14\ in^{3}$

The statement is true

See the procedure in Step 1

<u>case B)</u> The volume of the can is $56.55\ in^{3}$

The statement is false

The volume of the can is $59.38\ in^{3}$ --> see the procedure Step 2

<u>case C)</u> The empty space inside the can is $14.13\ in^{3}$

The statement is false

To find the empty space subtract the volume of three tennis ball from the volume of the can

$59.38\ in^{3}-3*14.14\ in^{3}=16.96\ in^{3}$

<u>case D)</u> The volume of three tennis balls is $42.42\ in^{3}$

The statement is true

To find the volume of three tennis balls multiply the volume of a single tennis ball by three

$14.14*3=42.42\ in^{3}$

8 0

3 years ago

In a sample of n = 6 scores, 5 of the scores are each above the mean by one point. Where is the 6th score located relative to th

den301095 [7]

The mean of a dataset is the sum of all data elements divided by the count of the elements.

The location of the 6th score relative to the mean is 5 points below the mean

Let:

$\bar x \to$ <em> Mean</em>

$a \to$ <em> 5 scores</em>

$b \to$ <em> 6th scores</em>

Given that:

$n = 6$

The 5 scores that are 1 above the mean implies that:

$a = \bar x + 1$

The mean of a dataset is calculated using:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x =\frac{5a + b}{6}$

$\bar x =\frac{5(\bar x + 1) + b}{6}$

Open brackets

$\bar x =\frac{5\bar x + 5 + b}{6}$

Multiply both sides by 6

$6\bar x =5\bar x + 5 + b$

Make b the subject

$b = 6\bar x -5\bar x - 5$

$b = \bar x - 5$

This means that the 6th score is 5 points below the mean

Read more about mean at:

brainly.com/question/17060266

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2 years ago

Select all that have a value of 0.<br> -cos pi/2<br> -cos 0<br> -sin 0<br> -sin 3pi/2<br> -tan pi

Lapatulllka [165]

Sin 0 sin 3pi/2 and tan pi

cos pi/2 is -.5
cos 0 is 1

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kykrilka [37]

Answer:

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