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devlian [24]
3 years ago
15

What percent of 2b is: 0.04b; 0.2b; 0.56b; 1.8b; 2.5b; 3b; By what percent are they each larger or smaller than 2b?

Mathematics
1 answer:
Marina86 [1]3 years ago
6 0

Answer:

1. 0.04b. <u>0.04b is 2% of 2b. It is smaller than 2b by 98%.</u>

2. 0.2b. <u>0.2b is 10% of 2b. It is smaller than 2b by 90%.</u>

3. 0.56b. <u>0.56b is 28% of 2b. It is smaller than 2b by 72%.</u>

<u>4. </u>1.8b. <u>1.8b is 90% of 2b. It is smaller than 2b by 10%.</u>

<u>5. </u>2.5b. <u>2.5b is 125% of 2b. It is larger than 2b by 25%.</u>

<u>6. 3b. 3b is 150% of 2b. It is larger than 2b by 50%.</u>

Step-by-step explanation:

1. 0.04b

<u>For all the cases, we will use Rule of Three, this way.</u>

Percentage * 2 = 100 * 0.04

Percentage = (100 * 0.04)/2 (Dividing by 2 at both sides)

Percentage = 4/2 = 2%

<u>0.04b is 2% of 2b. It is 98% smaller than 2b.</u>

<u>For all cases, we will use (100 - x) for calculating how smaller or larger the expression is related to 2b, where x is the percentage of the expression itself). In this case, 100 - 2 = 98.</u>

2. 0.2b

Again, we will use Rule of Three, this way:

Percentage * 2 = 100 * 0.2

Percentage = (100 * 0.2)/2 (Dividing by 2 at both sides)

Percentage = 20/2 = 10%

<u>0.2b is 10% of 2b. It is 90% smaller than 2b.</u>

3. 0.56b

Again, we will use Rule of Three, this way:

Percentage * 2 = 100 * 0.56

Percentage = (100 * 0.56)/2 (Dividing by 2 at both sides)

Percentage = 56/2 = 28%

<u>0.56b is 28% of 2b. It is 72% smaller than 2b.</u>

<u>4. </u>1.8b

Again, we will use Rule of Three, this way:

Percentage * 2 = 100 * 1.8

Percentage = (100 * 1.8)/2 (Dividing by 2 at both sides)

Percentage = 180/2 = 90%

<u>1.8b is 90% of 2b. It is 10% smaller than 2b.</u>

5. 2.5b

Again, we will use Rule of Three, this way:

Percentage * 2 = 100 * 2.5

Percentage = (100 * 2.5)/2 (Dividing by 2 at both sides)

Percentage = 250/2 = 125%

<u>2.5b is 125% of 2b. It is 25% larger than 2b.</u>

<u>In this case, 100 - 125 = -25. It means the second expression is larger than 2b by 25%.</u>

<u>6. </u>3b.

Again, we will use Rule of Three, this way:

Percentage * 2 = 100 * 3

Percentage = (100 * 3)/2 (Dividing by 2 at both sides)

Percentage = 300/2 = 150%

<u>3b is 150% of 2b. It is 50% larger than 2b.</u>

<u>In this case, 100 - 150 = -505. It means the second expression is larger than 2b by 50%.</u>

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Each year for 4 years, a farmer increased the number of trees in a certain orchard by of the number of trees in the orchard the
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Answer:

The number of trees at the begging of the 4-year period was 2560.

Step-by-step explanation:

Let’s say that x is number of trees at the begging of the first year, we know that for four years the number of trees were incised by 1/4 of the number of trees of the preceding year, so at the end of the first year the number of trees wasx+\frac{1}{4} x=\frac{5}{4} x, and for the next three years we have that

                             Start                                          End

Second year     \frac{5}{4}x --------------   \frac{5}{4}x+\frac{1}{4}(\frac{5}{4}x) =\frac{5}{4}x+ \frac{5}{16}x=\frac{25}{16}x=(\frac{5}{4} )^{2}x

Third year    (\frac{5}{4} )^{2}x-------------(\frac{5}{4})^{2}x+\frac{1}{4}((\frac{5}{4})^{2}x) =(\frac{5}{4})^{2}x+\frac{5^{2} }{4^{3} } x=(\frac{5}{4})^{3}x

Fourth year (\frac{5}{4})^{3}x--------------(\frac{5}{4})^{3}x+\frac{1}{4}((\frac{5}{4})^{3}x) =(\frac{5}{4})^{3}x+\frac{5^{3} }{4^{4} } x=(\frac{5}{4})^{4}x.

So  the formula to calculate the number of trees in the fourth year  is  

(\frac{5}{4} )^{4} x, we know that all of the trees thrived and there were 6250 at the end of 4 year period, then  

6250=(\frac{5}{4} )^{4}x⇒x=\frac{6250*4^{4} }{5^{4} }= \frac{10*5^{4}*4^{4} }{5^{4} }=2560.

Therefore the number of trees at the begging of the 4-year period was 2560.  

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Answer:

D. \frac{27\pi}{2} inches.

Step-by-step explanation:

We have been given that the circle with center O has a minor arc BSA with a length of 3\pi^{2} inches. The central angle is 40°.

To find the circumference of circle we will use formula:

\frac{\text{Central angle}}{2\pi}=\frac{\text{Arc length}}{2\pi r}, where 2\pi= measure of 360 degrees in radians and 2\pi r= circumference of circle.  

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Upon substituting our given value in the formula we will get,        

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Cross multiplying we will get,      

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Hence, the radius of our circle is 27/4 inches.  

Since the circumference of circle is 2\pi r. Upon substituting  r=\frac{27}{4} we will get,

2\pi r=2\pi* \frac{27}{4}=\frac{27\pi}{2}

Therefore, circumference of our given circle will be \frac{27\pi}{2} inches and option D is the correct choice.

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