Answer:
10
Step-by-step explanation:
Given that Sasha has won 0 games in the 40 games she has played.
Let she needs to win x game in a row, so
Total game she played = 40 + x
The number of the game she won is x, which is 20% of the total game she played, so
x = 20% of (40+x)

Hence, she needs to win 10 games in a row.
Answer:
27.76 grams will be present in 500 years
Step-by-step explanation:
The given formula is
, where A is the value of the substance in t years, and
is the initial value
∵ The half-life is a substance is 375 years
- Substitute A by
and t by 375 to find the value of k
∴ 
- Divide both sides by
∴ 
- Insert ㏑ in both sides
∴ ㏑(
) = ㏑ (
)
- Remember ㏑ (
) = n
∵ ㏑ (
) = 375 k
∴ ㏑(
) = 375 k
- Divide both sides by 375
∴ k ≈ -0.00185
∴ 
∵ 70 grams is present now
- That means the initial value is 70 grams
∴
= 70
∵ The time is 500 years
∴ t = 500
- Substitute the values of
and t in the formula
∵ 
∴ A = 27.76
∴ 27.76 grams will be present in 500 years
Answer:
The equation for the nth term of the given arithmetic sequence is: 
Step-by-step explanation:
We need to write an equation for the nth term of the arithmetic sequence:
15,28,41 ....
The equation for arithmetic sequence is: 
Where
is the nth term,
is first term and d is common difference
In the given sequence we have:
a₁ = 15
a₂ = 28
We can find common difference using the formula:

So, the common difference d is 13
Now, equation for nth term will be:

So, the equation for the nth term of the given arithmetic sequence is: 
where n=1,2,3..
Total surface area of a triangular prism = width x height +(sum of sides + width) x length
475 = (width x 10) + (5 + 5 + width) x 15
475 = (10 x width) + (10 + width) x 15
475 = (10 x width) + 150 + (15 x width)
475 - 150 = 25 x width
325 = 25 x width
width = 325/25 = 13 feet
<span>12.3
Volume function: v(x) = ((18-x)(x-1)^2)/(4pi)
Since the perimeter of the piece of sheet metal is 36, the height of the tube created will be 36/2 - x = 18-x.
The volume of the tube will be the area of the cross section multiplied by the height. The area of the cross section will be pi r^2 and r will be (x-1)/(2pi). So the volume of the tube is
v(x) = (18-x)pi((x-1)/(2pi))^2
v(x) = (18-x)pi((x-1)^2/(4pi^2))
v(x) = ((18-x)(x-1)^2)/(4pi)
The maximum volume will happen when the value of the first derivative is zero. So calculate the first derivative:
v'(x) = (x-1)(3x - 37) / (4pi)
Convert to quadratic equation.
(3x^2 - 40x + 37)/(4pi) = 0
3/(4pi)x^2 - (10/pi)x + 37/(4pi) = 0
Now calculate the roots using the quadratic formula with a = 3/(4pi), b = -10/pi, and c = 37/(4pi)
The roots occur at x = 1 and x = 12 1/3. There are the points where the slope of the volume equation is zero. The root of 1 happens just as the volume of the tube is 0. So the root of 12 1/3 is the value you want where the volume of the tube is maximized. So the answer to the nearest tenth is 12.3</span>