Answer:
120 grams will be left after 180 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 that:
- The initial quantity is 480 g,
- The half-life is 90 years,
- 180 years is the time elapsed.
And we want to find how much will be left. For this we use the above formula.
120 grams will be left after 180 years.
Answer:
-24
Step-by-step explanation:
Given expression:
3z (2y - 4)²
z = -2 and y = 3
To solve this problem, simply substitute:
3z (2y - 4)² = 3(-2){2(3) - 4}²
= -6(6-4)²
= -6 (2)²
= -6 x 4
= -24
Answers:
- The lengths of sides PQ and RS are <u> 13 </u>
- The lengths of sides QR and SP are <u> </u><u>20 </u>
This is a 13 by 20 rectangle.
============================================================
Explanation:
Refer to the drawing below.
Let x be the length of side SP. Since we're dealing with a rectangle, the opposite side is the same length. Side QR is also x units long.
We're told that RS = SP - 7 which is the same as saying RS = x-7
We also know that PQ = x-7 as well because PQ is opposite side RS.
In short, we have these four sides in terms of x
- PQ = x-7
- QR = x
- RS = x-7
- SP = x
as shown in the drawing. The four sides add up to the perimeter of 66.
PQ+QR+RS+SP = perimeter
PQ+QR+RS+SP = 66
(x-7)+x+(x-7)+x = 66
4x-14 = 66
4x = 66+14
4x = 80
x = 80/4
x = 20
Use this x value to find the unknown side lengths.
- PQ = x-7 = 20-7 = 13
- QR = x = 20
- RS = x-7 = 20-7 = 13
- SP = x = 20
In short, this is a 13 by 20 rectangle.
-----------------
Check:
perimeter = side1+side2+side3+side4
perimeter = PQ+QR+RS+SP
perimeter = 13+20+13+20
perimeter = 33+33
perimeter = 66
The answer is confirmed.
Answer:
Step-by-step explanation:
a)
the sum of all angles in a quadrilateral must be 360º
y+88+25+35 = 360
y = 360=88-25-35
y = 212º
b)
the sum of all angles in an octagon must be 1080º
45+45+140+140+6y = 1080
6y = 1080-90-280
6y = 710
y = 710/6
y=~ 118,3º
Answer:
a) 5%
b) 24%
Step-by-step explanation:
a) You buy a game for $40, and the sales tax is $2. What percent of the game price are you paying in sales tax?
Percentage you are paying in sales tax
= Sales tax / Sale price of the game × 100
= $2/$40 × 100
= 5%
b) Your doctor told you to eat 25 grams of fiber each day. You had 6 grams of fiber for breakfast. What percent of the 25 grams of fiber have you eaten so far?
The percent of 25 grams of fiber you have eaten so far =
6 grams/25 grams × 100
= 24%
