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3 years ago

Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.

Mathematics

1 answer:

d1i1m1o1n [39]3 years ago

4 0

Answer:

Use the fact that sin(x) = opp/hyp and tan(x) = opp/adj

where opp=opposite, hyp=hypotenuse, adj=adjacent and recall sin(30)=1/2 and tan(30) = 1/sqrt(3)

sin(30) = 1/2 = 17/y

y = 17(2) = 34

tan(30) = 1/sqrt(3) = 17/x

x = 17sqrt(3)

So the answer is (d)

Note that you could have also use the Pythagorean theorem to find x instead of using tan(30).

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(Lesson 31) The population of Jacksonville, Florida, was 736,000 in 2000 and was increasing at a rate of 1.49% each year. At

damaskus [11]

Answer:

Step-by-step explanation:

Population t years after 2000 = 736,000 × 1.0149^t

736,000 × 1.0149^t = 1,000,000

1.0149^t = 1,000,000/736,000 = 125/92

Take log base 1.0149 of both sides

t ≈ 20.7

Population exceeds a million in 2021

7 0

3 years ago

You choose a tile at random from a bag containing 4 A’s, 3 B’s, and 5 C’s. You replace the first tile in the bad and then choose

shtirl [24]

Answer:

P(B and B) = 1/9

Step-by-step explanation:

There are 4+3+5 = 12 tiles in total

The probability of selecting a B would be 4/12=1/3

When you are replacing a B tile, planning to pick a B tile again, the total tile count doesn't change. Therefore, because the two events are independent, their probabilities are multiplied and so P(B and B) = P(B) * P(B) = 1/3 * 1/3 = 1/9

3 0

3 years ago

A conical vessels with base radius 5 cm and height 24cm is full of water this water is emptied into a cylindrical vessel of base

Aliun [14]

Answer:

$2\ cm$

Step-by-step explanation:

$We\ are\ given\ that,\\Radius\ of\ the\ conical\ vessel=5\ cm\\Height\ of\ the\ conical\ vessel=24\ cm\\Hence,\\As\ we\ know\ that,\\Volume\ of\ a\ cone=\frac{1}{3}\pi r^2h\\Hence,\\The\ volume\ of\ the\ conical\ vessel=\frac{1}{3}\pi (5)^224= \frac{1}{3}\pi 25*24=200\pi \\Hence,\\The\ volume\ of\ the\ conical\ vessel=The\ amount\ of\ water\ filled\ in\ it\\Hence,\\The\ amount\ of\ water\ filled\ in\ the\ conical\ vessel=200\pi\\Lets\ consider\ the\ cylindrical\ vessel:\\Volume\ of\ a\ cylinder=\pi r^2h$

$As\ we\ are\ not\ said\ that\ the\ cylindrical\ vessel\ was\ empty,\ let\ its\ initial\\ height\ be\ h_1\\Radius\ of\ the\ Cylindrical\ vessel=10\ cm\\Initial\ height\ of\ the\ cylindrical\ vessel=h_1\\Initial\ volume\ of\ the\ cylindrical\ vessel=\pi *10^2*h_1=100h_1\pi \\Initial\ amount\ of\ water\ in\ the\ cylindrical\ vessel=100h_1\pi \\Hence,\\Final\ amount\ of\ water\ in\ the\ cylindrical\ vessel=Final\ amount\ of\ water\\ in\ the\ cylindrical\ vessel +Amount\ of\ water\ in\ conical\ vessel$

$Hence,\\Final\ amount\ of\ water\ in\ the\ cylindrical\ vessel=100h_1\pi +200\pi \\Now,\\Let\ the\ final\ height\ be\ h_2\\Hence,\\Final\ amount\ of\ water\ in\ the\ cylindrical\ vessel=\pi *10^2*h_2=100h_2\pi \\Hence,\\100h_2\pi =100h_1\pi +200\pi \\Hence,\\100h_2=100h_1+200\\100h_2-100h_1=200\\100(h_2-h_1)=200\\h_2-h_1=2\\Hence,\\As\ the\ rise\ in\ level\ is\ the\ difference\ between\ the\ initial\ and\ final\\ heights:\\The\ rise\ in\ level\ of\ water=2\ cm$

8 0

3 years ago

I need help please

Zina [86]

Answer:

Its out of A and C srry couldn't help much

8 0

3 years ago

A store sells two different fruit baskets with mangos and kiwis. The first basket has 2 mangos and 3 kiwis for $9.00. The second

Oliga [24]

Answer:

kiwis = $1.5

mangoes = $2.25

Step-by-step explanation:

Two equations can be derived from the question

2m + 3k = 9 equation 1

5m + 2k = 14.25 equation 2

m = mangoes

k = kiwis

multiply equation 1 by 5 and 2 by 2

10m + 15k = 45 equation 3

10m +4k = 28.5 equation 4

Subtract equation 4 from 3

11k = 16.5

k = 1.5

Substitute for k in equation 1

2m + 3(1.5) = 9

2m + 4.5 = 9

2m = 4.5

m = 2.25

3 0

3 years ago