Nick is now seven times as old as harry. In 6 years , nick will be five times as old as harry. How old will harry be in 6 years?
Answers
Answer:
18 years
Step-by-step explanation:
Let Nick age is x years and Harry's age is y years.
Hence, we have the equation
x = 7y ......(1)
After six years, Nick's age is (x+6) and Harry's age is (y+6)
Hence, we have
Plugging x = 7y, we get
Hence, from equation (1)
x = 7(12)
x =84
In 6 years, Harry will be of 12 + 6 =18 years.
Nick's age is 7x
In 6 years Harry is 7x+6, and Nick is 5(x+6)
7x+6=5x+30
2x+6=30
2x = 24
x = 12
Harry = 12 years old and in 6 years Harry will be 18.
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of the 9 volunteers? Is this a combination or a
permutation? Explain.
Answer choices:
a. 84; combination because the order does
not matter
b. 504; combination because the order
does not matter
C. 84; permutation because the winners
are chosen one at a time
d. 504; permutation because the winners
are chosen one at a time
Answers
Answer:
c
Step-by-step explanation:
Final answer:
The $5 gift cards can be given to 3 of the 9 volunteers in 84 different ways.
Explanation:
This is a combination problem because the order in which the gift cards are given does not matter.
To find the number of ways the gift cards can be given to 3 of the 9 volunteers, we can use the combination formula:
C(n,r) = n! / (r!(n-r)!)
In this case, n = 9 (the number of volunteers) and r = 3 (the number of gift cards to be given).
Plugging in the values, we get:
C(9,3) = 9! / (3!(9-3)!) = 84
Therefore, there are 84 ways to give the $5 gift cards to 3 of the 9 volunteers.
Learn more about Combination here:
#SPJ5
b) y>-2/7x+8/7
c) y <7/2x-4
d) y <-2/7x-4/7
(whats a Inequality? )
Answers
Answers
Answers
x = 1
Step-by-step explanation:
Expand:
Simplify:Addvalues
Collect like terms and simplify
Divide both sides of the equation by12
Simplify
Answer:
x = 1
Step-by-step explanation:
Original Equation:
3(4x - 3) = -4 + 7
Use the distributive property.
3 x 4x = 12x
3 x -3 = -9
Equation:
12x - 9 = -4 + 7
Add 4 to both sides.
12x - 5 = 7
Add 5 to both sides.
12x = 12
Divide both sides by 12
x = 1
Hope I helped :)
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Answers
6 x + 12 = - 18
6 x = - 18 - 12
6 x = - 30
x = - 30 / 6
x = -5
only 1 solution
hope this helps!
B. The range is y > 3.
C. The initial value is 3.
D. The initial value is 9.
E. The simplified base is √2.
F. The simplified base is 3√2.
Answers
Option B is incorrect: the range is not y > 3, because, for negative values of x, f(x) < 3, e.g. for x = -1, f(x) = 3 * sqrt(18^(-1)) = 3*sqrt(1/18) = 3*0.2357 = 0.7071 < 3.
Option C is correct: f(0) = 3*sqrt(18^0) = 3*sqrt(1) = 3 * 1 = 3
Option D is incorrest: (see working for option C)
A) The domain is all real numbers;
C) The initial value is 3; and
F) The simplified base is 3√2.
Explanation:
A) The domain is the set of numbers that can be use for x. In this function, there are no domain restrictions; this means there are no values for x that will not give you a value for y. This means that all numbers work, which we say is "the set of all real numbers."
C) To find the initial value (starting point), substitute 0 for x:
f(x) = 3(√18)ˣ
f(0) = 3(√18)⁰
f(0) = 3(1) = 3
Thus the initial value is 3.
F) The base of the current function is √18; this is because that is what is raised to a power. If we simplify this, we find the prime factorization of 18, looking for pairs of factors to take out.
The prime factorization of 18:
18 = 2*9
9 = 3*3
This means 18 = 2*3*3; it gives us √18 = √(2*3*3). We have a pair of 3's under the radical, so we take a 3 out; this leaves a 2 under the radical:
√18 = √(2*3*3) = 3√2.