<span>When creating a subset of 5 elements from 7 elements, order should not matter. Therefore, we use the combination formula over the permutation formula.
The combination formula given n elements total and r elements used is n! / [r!*(n-r)!]. Substituting 7 for n and 5 for r, we get:
7! / (5!*2!) = 7*6 / 2 = 21
21 subsets can be created</span>
The capacity of the tank in gallons is 24 gallons.
<h3>What is an Equation ?</h3>
An equation is a mathematical statement formed when two algebraic expressions are equated by an equal sign.
It is given in the question that
When four gallons are added to a tank that is one-third full
the tank is then one-half full.
Let the capacity of the tank is x gallons
The equation can be formed for the capacity of the tank as
(1/3)x +4 = (1/2)x
(1/3)x -(1/2)x = -4
(1/6)x = 4
x = 24 gallons.
Therefore the capacity of the tank in gallons is 24 gallons.
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Answer: 233 people per thousand
Step-by-step explanation:
Using extrapolation method,
if 150/k in 1950,
200/k in 1990,
275/k in 2020,
2003 lies in between 1990 and 2020. So, you extrapolate the values of 200/k and 275/k for the years respectively.
Therefore,
(2003 - 1990)/(2020 - 2003) = (x - 200)/(275 - x)
Where x is the number of retirees per thousand for 2003
Making x the subject of relation in the above equation.
Cross multiply the equation above;
(2003 - 1990)(275-x) = (2020 - 2003)(x - 200)
13(275 - x) = 17(x-200)
3575 - 13x = 17x - 3400
Collect the like terms
3575+3400 = 17x + 13x
30x = 6975
x = 6975/30
x = 232.5
x = 233 people per thousand to the nearest integer
120% that would be the percentage of 12/10.
12 divided by 10 = 1.2
1.2 times 100 = 120
That is equal to 120%
Answer:
A circle is shown. Secants P N and L N intersect at point N outside of the circle. Secant P N intersects the circle at point Q and secant L N intersects the circle at point M. The length of P N is 32, the length of Q N is x, the length of L M is 22, and the length of M N is 14.
In the diagram, the length of the external portion of the secant segment PN is <u>X</u>
The length of the entire secant segment LN is <u>36</u>.
The value of x is <u>15.74</u>
Step-by-step explanation:
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