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viva [34]
3 years ago
14

In the last​ year, a total of 2727 earthquakes occurred in the country. Of​ these, 85.3 % were minor tremors with magnitudes of

3.9 or less on the Richter scale. How many minor earthquakes occurred in the country in the last​ year? Round to the nearest whole number.
Mathematics
1 answer:
Komok [63]3 years ago
3 0

Answer:

Minor earthquakes occurred in the country in the last​ year were<u> 2326</u>.

Step-by-step explanation:

Given:

In the last​ year, a total of 2727 earthquakes occurred in the country.

Of​ these, 85.3 % were minor tremors with magnitudes of 3.9 or less on the Richter scale.

Now, to find the minor earthquakes occured in the country last year.

<em>Total earthquakes occurred in the country = 2727.</em>

<em>The percent of minor earthquakes = 85.3%</em>.

Now, to get the number of minor earthquakes:

85.3% of 2727.

=\frac{85.3}{100} \times 2727.

=\frac{232613.1}{100}

=2326.131

<em>The number of minor earthquakes nearest whole number = 2326.</em>

Therefore, minor earthquakes occurred in the country in the last​ year were 2326.

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These box plots show the prices for two different brands of shoes.
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Answer: Choice C

The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $20.

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Explanation:

Let's go through the answer choices one by one to see which is true and which is false. Also, we'll see which is helpful when it comes to the spread.

----------------------

Choice A

The IQR is found by subtracting the values of Q1 and Q3, which are the left and right edges of the box in that order.

For boxplot A, we have an IQR = Q3-Q1 = 80-70 = 10.

So we can immediately rule out choice A because the IQR for boxplot A is not 20, but instead it's 10.

----------------------

Choice B

The statement made in choice B is true, since the center vertical lines represent the median, but it's not useful to determine the spread. The median only tells us the center of the distribution. It doesn't tell us how spread out the distribution is.

Imagine you didn't have access to the graph. Now if you're told that the median for brand A is larger than brand B's median, then you'd probably think boxplot A is more spread out; however, the boxplot diagram shows the opposite is the case.

So again the median isn't used here. We can rule out choice B.

----------------------

Choice C

This statement is true. We subtract the box edge values to get the IQR values for each boxplot

For brand A we have IQR = Q3-Q1 = 80-70 = 10

For brand B we have IQR = Q3-Q1 = 70-50 = 20

This is the answer we're after.

The IQR is one tool we can use to measure the spread. The range is another option. We could also use the variance or the standard deviation (two slightly similar ideas) to measure the spread.

As you can see from the diagram, the larger the IQR, the more spread out the data will be.

----------------------

Choice D

This is false because earlier we've shown 10 is the IQR for brand A.

7 0
3 years ago
How do I solve for n<br>r=5n+5w
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3 years ago
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5 0
3 years ago
A business has two loans totaling $50,000. One loan has a rate of 8% and the other has a rate of 12%. This year, the business ex
Debora [2.8K]

Answer:

the 8% loan has a principal of $37500

the 12% loan has a principal of $12500

Step-by-step explanation:

Let's start by writing the general  equation for the interest hwre I is the interest, P is the principal (in our case would be loan amounts), "r" is the interest rate in decimal form (in our case one would be 0.12, and the other one 0.08), and t is the time in years (in our case 1 year).

I=P*r*t

Then we write the interest equation coming from each loan at the end of this year (we call I1 the interest coming from the 12% loan and I2 the interest coming from the 8% one). Since we don't know the loan amounts (in fact those are what we need to find) we will name one "x" and the other "y":

I=P*r*t\\I1=x * 0.12*1\\I2=y*0.08*1

Next, we add these last two equations term by term, and replace the addition of both interests by $4500 as given in the information:

I1=x * 0.12*1\\I2=y*0.08*1\\I1+I2 = 0.12x+0.08y\\4500=0.12x+0.08y

This is our first equation in the variables x and y which are our unknowns.

Now we generate the second equation on x and y by writing in agebraic terms the other piece of information we have: "the total of the two loans is $50000. That is the addition of the principals x and y should equal $50000:

x+y=50000

We solve for y in this last equation and replace its form in terms of x in the equation of the interest, and solve for the unknown x:

y=50000-x\\4500 = 0.12x +0.08 y\\4500=0.12x+0.08(50000-x)\\4500=0.12x+4000-0.08x\\4500=0.12x-0.08x+4000\\4500=0.04x+4000\\4500-4000=0.04x\\500=0.04x\\x=\frac{500}{0.04} =12500

Therefore the amount of the loan at 12% is $12500

Now to find the amount of the second loan "y" we use the equation for the totals of the loans:

x+y=50000\\12500+y=50000\\y=50000-12500=37500

Therefore, the loan at 8% is $37500

5 0
3 years ago
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