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2 years ago

12

Fran is training for a cycle race. In the first week, she cycles 195 miles. In the second week, she manages 243 miles. To the ne

arest tenths, What is the percent increase in distance?

1 answer:

AleksAgata [21]2 years ago

4 0

Answer:

24.6%

Step-by-step explanation:

243-195=48

48/195=x/100

48 × 100

4800/195= 24.6%

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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 21m. what is the volume of the sphere.

Goshia [24]

Answer:

The volume of the sphere is 14m³

Step-by-step explanation:

Given

Volume of the cylinder = $21m^3$

Required

Volume of the sphere

Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;

<em>Using the volume formula of a cylinder</em>

The formula goes thus

$V = \pi r^2h$

Substitute 21 for V; this gives

$21 = \pi r^2h$

Divide both sides by h

$\frac{21}{h} = \frac{\pi r^2h}{h}$

$\frac{21}{h} = \pi r^2$

The next step is to solve for the volume of the sphere using the following formula;

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

Divide both sides by r

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

Expand Expression

$\frac{V}{r} = \frac{4}{3}\pi r^2$

Substitute $\frac{21}{h} = \pi r^2$

$\frac{V}{r} = \frac{4}{3} * \frac{21}{h}$

$\frac{V}{r} = \frac{84}{3h}$

$\frac{V}{r} = \frac{28}{h}$

Multiply both sided by r

$r * \frac{V}{r} = \frac{28}{h} * r$

$V = \frac{28r}{h}$ ------ equation 1

From the question, we were given that the height of the cylinder and the sphere have equal value;

This implies that the height of the cylinder equals the diameter of the sphere. In other words

$h = D$ , where D represents diameter of the sphere

Recall that $D = 2r$

So, $h = D = 2r$

$h = 2r$

Substitute 2r for h in equation 1

$V = \frac{28r}{2r}$

$V = \frac{28}{2}$

$V = 14$

Hence, the volume of the sphere is 14m³

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3 years ago

Read 2 more answers

A coordinate plane with a line passing through (0, negative 3), (2, 0), and (4, 3).

adell [148]

Answer:

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

Step-by-step explanation:

The given line passes through: (0,-3), (2,0), and (4,3).

We first of all find the slope using $m=\frac{y_2-y_1}{x_2-x_1}$

Using $(x_1=0,y_1=-3),and\:(x_2=2,y_2=0)$ we find the slope to be

$m=\frac{0--3}{2-0}=\frac{3}{2}$

The equation is given by $y=mx+c$ , where $m=\frac{3}{2}$ is the slope and c=-3 is the y-intercept.

Therefore the equation is $y=\frac{3}{2}x-3$

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3 years ago

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What are the three angle measures in the triangle shown below

sergeinik [125]

B. 31°, 43°, 106°
since all angles of a triangle add up to 180°, you combine all of the equations to equal 180 and solve for X. the equation you would get it 3x+1+11x-4+5x-7=180. this simplifies to 19x-10=180. then you solve for x, and it is 10. then, you plug 10 into all of the equations separately to find the angles. therefore, the answer is B

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3 years ago

Sam was given a bag of 100 red and blue marbles. He believes

Rashid [163]

Answer:

(D) There are probably more blue marbles than red marbles in the bag.

Step-by-step explanation:

There are a total of 100 marbles in the bag.

In the experiment of 50 trials, Sam had the following outcome:

Blue=35

Red=15

Relative Frequency of Blue Marbles =35/50=0.7

Relative Frequency of Red Marbles =15/50=0.3

Since the relative frequency of blue marbles is greater than the relative frequency of red marbles, <u>there are probably more blue marbles than red marbles in the bag.</u>

The correct option is D.

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3 years ago

Milly has 636 shopkins arranged in 12 rows how many shopkins are in each row

kodGreya [7K]

Divide 636 / 12 which equals 53 ?

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3 years ago

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