Answer:
10
Step-by-step explanation:
The number of tiles in the design is 1 + 2 + 3 + ...
We can model this as an arithmetic series, where the first term is 1 and the common difference is 1. The sum of the first n terms of an arithmetic series is:
S = n/2 (2a₁ + d (n − 1))
Given that a₁ = 1 and d = 1:
S = n/2 (2(1) + n − 1)
S = n/2 (n + 1)
Since S ≤ 60:
n/2 (n + 1) ≤ 60
n (n + 1) ≤ 120
n must be an integer, so from trial and error:
n ≤ 10
Mr. Tong should use 10 tiles in the final row to use the most tiles possible.
Answer:
22.38 g of silicone-32 will be present in 300 years.
Step-by-step explanation:
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by
where,
= quantity of the substance remaining
= initial quantity of the substance
= time elapsed
= half life of the substance
From the information given we know:
- The initial quantity of silicone-32 is 30 g.
- The time elapsed is 300 years.
- The half life of silicone-32 is 710 years.
So, to find the quantity of silicone-32 remaining we apply the above equation
22.38 g of silicone-32 will be present in 300 years.
The value of x is 60, as you wrote. The sum of all angles in a triangle is 180°.
The sum of all angles on a straight line is also 180°. So to find y, solve for the third angle of the triangle on the left.
50 + 60 = 110. 180-110 = 70°.
Now we know 2 of the 3 angles along the line (70° and x, 60°)
70 + 60 + y = 180
130 + y = 180
y = 50
Hope this helps. LMK if you have questions.
Answer:
the value has to be 54.6 and up
Step-by-step explanation:
Answer:
Mia and her family went to dinner, and the bill, including tax, came to $54.65. Mia suggested giving the server a gratuity of about 20 percent of the bill.
If they give a gratuity of 20 percent, what would be the tip rounded to the nearest dollar?
✔ $11
If they give a gratuity of 20 percent, rounded to the nearest dollar, what is the total cost of the dinner, including the tip?
✔ $65.65
Step-by-step explanation:
