Answer:
41235
Step-by-step explanation:
There are 120 five-digit numbers that can be made from the digits 1, 2, 3, 4, 5 if each digit is used once in the number,
The total number of times where each number will occur or be at first place is calculated as:
4! = 4 × 3 × 2 × 1
= 24
Hence,
24th number = The last number where 1 is at first place
We can write this out as:
12345
12354
12435
12453
12534
12543
13245
13254
13425
13452
13524
13542 e.t.c.
48th number = The last number where 2 is at first place
72nd place = The last number where 3 is at first place.
This means, the 73rd number is the first number where 4 is at first place.
Therefore, the 73rd number based on pattern is 41235
Allen's work is not written properly so I have rearranged it as shown below:
Original problem) –8.3 + 9.2 – 4.4 + 3.7.
Step 1) −8.3 + 9.2 + 4.4 + 3.7 Additive inverse
Step 2) −8.3 + 4.4 + 9.2 + 3.7 Commutative property
Step 3) −8.3 + (4.4 + 9.2 + 3.7) Associative property
Step 4) −8.3 + 17.3
We can see that in step 1), Allen changed -4.4 into +4.4 using additive inverse. Notice that we are simplifying not eliminating -4.4 as we do in solving some equation. Hence using additive inverse is the wrong step.
Alen should have collect negative numbers together and positive numbers together.
Add the respective numbers then proceed to get the answer.
–8.3 + 9.2 – 4.4 + 3.7
= –8.3 – 4.4 + 9.2 + 3.7
= -12.7 + 12.9
= 0.2
Membership is discounted $2 for first month
c=cost of one month
d=discount=$2
x=# of months
xc - 2= total cost
x for 1 month is 1, c is always 12, -2 is constant
1 x(12) - 2=10 for first month
8 months
8c -2=total cost for 8 months
8 x 12 - 2= 94 for 8 months
If f(x) = √x and g(x) = 7x + b, then
f(g(x)) = f(7x + b) = √(7x + b)
If the plot of f(g(x)) passes through (4, 6), then
f(g(4)) = √(7•4 + b) = √(28 + b) = 6
Solve for b :
√(28 + b) = 6
(√(28 + b))² = 6²
28 + b = 36
b = 36 - 28
b = 8
