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2 years ago

5

In a volcano, erupting lava flows continuously through a tube system about 15 kilometers to the sea. Assume a lava flow speed o

f 0.5 kilometer per hour and calculate how long it takes to reach the sea.

1 answer:

koban [17]2 years ago

5 0

9514 1404 393

Answer:

30 hours

Step-by-step explanation:

The relation between time, speed, and distance is ...

time = distance/speed

time = (15 km)/(0.5 km/h) = 30 h

It takes 30 hours for the lava to reach the sea.

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Given sin(−θ)=−1/6 and tanθ=−√35/35 What is the value of cosθ?

murzikaleks [220]

Answer:

$cos(\theta)=-\frac{\sqrt{35} }{6}$

Step-by-step explanation:

Recall the negative angle identity for the sine function:

$sin(- \theta)=-sin(\theta)$

Then, we can find the value of $sin(\theta)$ :

$sin(\theta)=-sin(-\theta)\\sin(\theta) =-(-\frac{1}{6} )\\sin(\theta)= \frac{1}{6}$

Now recall the definition of the tangent function:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

Therefore, now that we know the value of $sin(\theta)$ , we can solve in this equation for $cos(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\-\frac{\sqrt{35} }{35} =\frac{1/6}{cos(\theta)} \\cos(\theta)=-\frac{\frac{1}{6} }{\frac{\sqrt{35} }{35} } \\cos(\theta)=-\frac{35}{6\,\sqrt{35} } \\cos(\theta)=-\frac{\sqrt{35} }{6}$

5 0

2 years ago

A cylinder has a base diameter of 8ft and a height of 20ft. What is its volume in cubic ft, to the nearest tenths place?

jenyasd209 [6]

Answer:

$4022.9$

Step-by-step explanation:

Volume of a cylinder is given by cross sectional area multiplied by height hence

V=Ah

Since the cross sectional area of

$A=\pi r^{2}$

Substituting the formula for A into formula for volume then

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

Substituting 8ft for r and 20 ft for h then

$V=Ah=\pi 8^{2}\times 20=4022.8571428571\ ft^{3}\approx 4022.9\ ft^{3}$

Rounded off to the nearest tenths, the volume is equivalent to

$4022.9$

5 0

3 years ago

Probability of a standard six side dice landing on a four in the first three rolls?

Illusion [34]

Answer:

91/216

Step-by-step explanation:

The probability of getting a 4 in the first three rolls is 1 minus the probability of not getting a 4 on any of the rolls.

P(at least one 4) = 1 − P(no 4s)

P(at least one 4) = 1 − (5/6)³

P(at least one 4) = 91/216

Alternatively, you can calculate it this way.

The probability of getting a 4 on the first roll is 1/6.

The probability of getting a 4 on the second roll is (5/6) (1/6) = 5/36.

The probability of getting a 4 on the third roll is (5/6) (5/6) (1/6) = 25/216.

The probability of any of the three events is 1/6 + 5/36 + 25/216 = 91/216.

6 0

2 years ago

The lengths, in minutes, of the movies currently showing at a movie theater are shown in the data set. Create a histogram

alexdok [17]

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the required lengths are not given.

I will use the following data set to answer the question.

$Dataset: 35, 51, 39, 42, 68, 62, 32, 59$

First, is to determine the range of the dataset

$Range = Highest - Least$

$Range = 68 - 32$

$Range = 36$

Next, we will make use of 4 classes. So, we divide range by 10 to get the number of class. 10 represents the interval

$Class= Range/10$

$Class = 36/10$

$Class = 3.6$

$Class \approx 4$

<em>So, we use 4 classes</em>

Plot the frequency distribution table as follows:

$\begin{array}{ccc}{Intervals} & {Observations} & {Frequency} & {31-40} & {32,35,39} & {3} & {41-50} & {42} & {1} & {51-60} & {51,59} & {2} & {61-70} & {62,68} & {2}\ \end{array}$

<em>See attachment for histogram</em>

5 0

2 years ago

Jason has already read 27 pages of a book. He plans to read 3 pages of the book every day. If f(n) represents the total number o

Brut [27]

The fourth choice is correct.
27 would be the Y intercept, and 3n would be the slope.
f(n) = 3n + 27

4 0

2 years ago

Read 2 more answers