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MAXImum [283]
3 years ago
5

A scientist measures the water temperature in the Gulf at Gulfport on the fifteenth of each month. Her data is shown in the tabl

e. What is the average rate of change between March 15 and June 15?
A. 2.6°F per month
B. 3.9°F per month
C. 5.2°F per month
D. 7.8°F per month
Please explain!

Mathematics
2 answers:
andrew-mc [135]3 years ago
6 0
The average rate of change between March 15 and June 15 will be given by:
(82.4-66.8)/(6-3)
=15.6/3
=5.2° F per month

Answer: C
Zina [86]3 years ago
3 0

Answer:

<h2>C. 5.2°F per month</h2>

Step-by-step explanation:

The average rate of change refers to the relation between these variables.

Specifically, this problem can be modeled by a linear function, where the slope is the average rate of change.

So, such rate can be defined as

r=\frac{y_{2}-y_{1}  }{x_{2} -x_{1} }

Where (x_{1} ,y_{1} ) is the first pair and (x_{2} ,y_{2} ) is the second one.

In this case, the first pair is (3,66.8) and the second pair is (6,82.4). Replacing these coordinates, we have

r=\frac{y_{2}-y_{1}  }{x_{2} -x_{1} }=\frac{82.4-66.8}{6-3}=\frac{15.6}{3}=5.2

Which is expressed in Fahrenheit.

Therefore, the average rate of change is 5.2 °F.

This can be interpreted as "The temperature changes +5.2 °F each month between March 15 and June 15".

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1 ton is 2,000 lbs

9 x 2,000 = 18,000

So, 18,000 is equal to 9 tons.

Hope this helps. :)

5 0
3 years ago
Carolyn is building a pen for a dog. The PERIMETER of the pen is 52 ft. The material is sold by the yard. It is 10.99 dollars pe
Mazyrski [523]
     We know that the fence is 52 <em>feet</em> long, but since it's sold in yards, we need to somehow convert feet to yards.
     First, we need to find a little something called a conversion factor. Basically, we need to see what we can do to get from <em>one foot</em> to <em>one yard</em>. 
Well, how many feet are there in a yard? <em><u>3.</u></em><u /><u /> So now we know that <em><u>one foot is 1/3 of a yard.</u>
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So to convert 52ft to yards, we need to divide by 3. What's 52 divided by 3? 
17.33.
Now we just need to multiply that by 10.99 so that we can find out the cost.
We get 190.45. That's your answer!

It all cost <em>$190.45
</em>
<em>Don't forget to rate this answer the Brainliest!</em><em>

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8 0
3 years ago
Which number comes next in this series: 2, 3, 4, 8, 9, 10, 20, 21, 22,?
Mekhanik [1.2K]
44

The pattern is +1,+1,x2
3 0
3 years ago
I'd appreciate it if anyone could help ASAP. I'm giving Brainliest!
n200080 [17]

Answer:

(1, 0.25)

Step-by-step explanation:

To find when f(x)=g(x), then look for a value that is the same for both functions in the table. 0.25 occurs twice for the same x value. This is when they are equal. The solution is (1, 0.25).

7 0
3 years ago
Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co
jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If \sum a_n is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho

If \rho < 1, the series converges absolutely

If \rho > 1, the series diverges

If \rho = 1, the test fails.

Given the series \sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}

To test for convergence or divergence using ratio test, we will use the condition above.

a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}

\frac{a_n_+_1}{a_n} =  \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\

\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\

aₙ₊₁/aₙ =

\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\

note that any constant dividing infinity is equal to zero

|\frac{1+2/\infty+1/\infty^2}{5}|\\\\

\frac{1+0+0}{5}\\ = 1/5

\rho = 1/5

Since The limit of the sequence given is less than 1, hence the series converges.

5 0
3 years ago
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