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3 years ago

15

16y=14+9y please answer 23 points

1 answer:

NeTakaya3 years ago

4 0

Answer:

<h2>y = 2</h2>

Step-by-step explanation:

$16y=14+9y\qquad\text{subtract}\ 9y\ \text{from both sides}\\\\16y-9y=14+9y-9y\\\\7y=14\qquad\text{divide both sides by 7}\\\\\dfrac{7y}{7}=\dfrac{14}{7}\\\\y=2$

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A cone and a cylinder have the same height and their bases are congruent circles

Anettt [7]

Answer:

$30cm^3$

Step-by-step explanation:

the volume of a cylinder is given by:

$v_{cylinder}=\pi r^2 h$

and the volume of a cone is given by:

$v_{cone}=\frac{\pi r^2 h}{3}$

since both have the same height and radius, we can solve each equation for $r^2h$ (because this quantity is the same in both figures) and then match the expressions we find:

from the cylinder's volume formula:

$r^2h=\frac{v_{cylinder}}{\pi}$

and from the cone's volume formula:

$r^2h=\frac{3 v_{cone}}{\pi}$

matching the two previous expressions:

$\frac{v_{cylinder}}{\pi} =\frac{3v_{cone}}{\pi}$

we solve for the volume of a cone $v_{cone}$ :

$v_{cone}=\frac{\pi v_{cylinder}}{3\pi} \\\\v_{cone}=\frac{v_{cylinder}}{3}$

substituting the value of the cylinder's volume $v_{cylinder}=90cm^3$

$v_{cone}=\frac{90cm^3}{3} \\\\v_{cone}=30cm^3$

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the numbers 2-12 are written on cards and placed in the bag.what is the probability of picking an even number then replacing it

lorasvet [3.4K]

We have the cards numbered as 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.

Sample number is, n(S)=11.

We pick a card and want to get even number like 2, 4, 6, 8, 10, and 12.

Probability of picking an even number would be :-

P(even numbers) = $\frac{6}{11}$

Now we replace the card and want to get a 7 in second attempt.

Probability of picking a 7 would be :-

P(number 7) = $\frac{1}{11}$

Now Probability of this event = P(even numbers) × P(number 7)

Probability = $(\frac{6}{11} )(\frac{1}{11} ) = \frac{6}{121}$

So final answer is $\frac{6}{121}$ .

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3 years ago