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Reika [66]
3 years ago
13

the library at a certain University reported the journal prices had increased by 150% over a period of 10 years The report concl

uded that this representing a price increase of 15% each year if journal prices had indeed increase by 15% each year what percentage increase would that give the over 10 years Ron your answer as a percentage to the nearest whole number
Mathematics
2 answers:
natima [27]3 years ago
7 0
1.15¹⁰=4.0456, the growth rate, so the increase is 3.0456 or 305%.
tatyana61 [14]3 years ago
6 0

Answer:

Over 10 years, increasing 15% each year, the prices would have increased 305%.

Step-by-step explanation:

If journal prices had a constant rate of increase, it's prices could be modeled by the following equation:

P(t) = P(0)(1+r)^{t}

In which P(t) is the price after t years, P(0) is the initial price and r is the rate of increase.

If it increased 15% each year.

We would have r = 0.15. So

P(t) = P(0)(1.15)^{t}

Over 10 years

P(10) = P(0)(1.15)^{10}

P(t) = 4.05P(0)

The initial price is 100%

4.05P(0) - P(0) = 3.05P(0)

Over 10 years, increasing 15% each year, the prices would have increased 305%.

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6/16 or 3/8 because if there are 6 blue out of 16 that it obvious. Please press thank you cuz I hope it helps.
7 0
3 years ago
What is the area of the shaded region in the figure below ? Leave answer in terms of pi and in simplest radical form
ser-zykov [4K]

Answer:

Step-by-step explanation:

That shaded area is called a segment. To find the area of a segment within a circle, you first have to find the area of the pizza-shaped portion (called the sector), then subtract from it the area of the triangle (the sector without the shaded area forms a triangle as you can see). This difference will be the area of the segment.

The formula for the area of a sector of a circle is:

A_s=\frac{\theta}{360}*\pi r^2 where our theta is the central angle of the circle (60 degrees) and r is the radius (the square root of 3).

Filling in:

A_s=\frac{60}{360}*\pi (\sqrt{3})^2 which simplifies a bit to

A_s=\frac{1}{6}*\pi(3) which simplifies a bit further to

A_s=\frac{1}{2}\pi which of course is the same as

A_s=\frac{\pi}{2}

Now for tricky part...the area of the triangle.

We see that the central angle is 60 degrees. We also know, by the definition of a radius of a circle, that 2 of the sides of the triangle (formed by 2 radii of the circle) measure √3. If we pull that triangle out and set it to the side to work on it with the central angle at the top, we have an equilateral triangle. This is because of the Isosceles Triangle Theorem that says that if 2 sides of a triangle are congruent then the angles opposite those sides are also congruent. If the vertex angle (the angle at the top) is 60, then by the Triangle Angle-Sum theorem,

180 - 60 = 120, AND since the 2 other angles in the triangle are congruent by the Isosceles Triangle Theorem, they have to split that 120 evenly in order to be congruent. 120 / 2 = 60. This is a 60-60-60 triangle.

If we take that extracted equilateral triangle and split it straight down the middle from the vertex angle, we get a right triangle with the vertex angle half of what it was. It was 60, now it's 30. The base angles are now 90 and 60. The hypotenuse of this right triangle is the same as the radius of the circle, and the base of this right triangle is \frac{\sqrt{3} }{2}. Remember that when we split that 60-60-60 triangle down the center we split the vertex angle in half but we also split the base in half.

Using Pythagorean's Theorem we can find the height of the triangle to fill in the area formula for a triangle which is

A=\frac{1}{2}bh. There are other triangle area formulas but this is the only one that gives us the correct notation of the area so it matches one of your choices.

Finding the height value using Pythagorean's Theorem:

(\sqrt{3})^2=h^2+(\frac{\sqrt{3} }{2})^2 which simplifies to

3=h^2+\frac{3}{4} and

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Therefore, the area in terms of pi for that little segment is

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8 0
3 years ago
What is 1/2 + 3/4???
Papessa [141]
1/2 + 3/4 = 

1/2 = 2/4

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Answer = 1 1/4

Hope this helped☺☺
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