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Sergio [31]
3 years ago
8

There is a state soccer tournament with 128 teams competing for 1st place. Each week, half of the teams get eliminated. How many

teams remain after 6 weeks?
A.
16
B.
8
C.
4
D.
2
Mathematics
2 answers:
Margarita [4]3 years ago
8 0
\text{Let A denote the number of teams after n weeks}

A_0 = 128
A_1 = A_0(0.5) = 128(0.5)
A_2 = A_1(0.5) = 128(0.5)^{2}
A_3 = A_2(0.5) = 128(0.5)^{3}

A_n = 128(0.5)^{n}
A_6 = 128(0.5)^{6} = 2

Thus, after 6 weeks, there will only be 2 teams left.
V125BC [204]3 years ago
7 0
The answer is D.
Week 0 (start; initial): 128 TEAMS
Week 1: 64 teams
Week 2: 32 teams
Week 3: 16 teams
Week 4: 8 teams
Week 5: 4 teams
Week 6: 2 teams

You can also solve for this using a common ratio.
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Answer:

6,3

Step-by-step explanation:

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The profits in a business are to be shared by the three partners in the ratio of 3 to 2 to 5, in that order. The profit for the
jeka94

Answer:

The first partner will receive $52950, the second partner will receive $35300, the third partner will receive $88250.

Step-by-step explanation:

The profits in the business are to be shared by the three partners in the ratio of 3 to 2 to 5, in that order.

That is:

3 : 2 : 5

The profit for the year was $176,500.

To find the number of dollars that each partner, we have to first find the total ratio and then divide each of the ratios by the total ratio and multiply by the profit.

The total ratio is:

3 + 2 + 5 = 10

The first partner will receive 3/10 of the profits:

\frac{3}{10} * 176500 = $52950

The second partner will receive 2/10 of the profits:

\frac{2}{10} * 176500 = $35300

The third partner will receive 5/10 of the profits:

\frac{5}{10} * 176500 = $88250

The first partner will receive $52950, the second partner will receive $35300, the third partner will receive $88250.

7 0
3 years ago
|9x-7|=|6x+3| Solve the inequality
dexar [7]

Answer:

x = 4/15 and x= 10/3

Step-by-step explanation:

|9x-7|=|6x+3|

There are two solutions, one positive and one negative.

(9x-7)=6x+3                   - (9x-7)=6x+3

We will take the positive one first

(9x-7)=6x+3

Subtract 6x from each side

(9x-6x-7)=6x-6x+3

3x -7=3

Add 7 to each side

3x-7+7 = 3+7

3x = 10

Divide by 3x/3 = 10/3

x = 10/3


Now we will take the negative solution

- (9x-7)=6x+3

Distribute the negative sign

-9x+7 = 6x+3

Add 9x to each side

-9x+9x+7 = 6x+9x+3

7 = 15x+3

Subtract 3 from each side

7-3 = 15x +3-3

4 = 15x

Divide by 15 on each side

4/15 =15x/15

4/15 =x

8 0
3 years ago
What is the slop of the line?
miskamm [114]
The slope of the line is 2. Why? Well, see below for an explanation!

The slope of a line is found by using the formula rise/run (rise over run). This means that by starting at the initial value of the y-intercept, 3, we would count how many units away we are from the next complete point. We do so by counting from left to right, and in this case, going up and then to the right. To get from the point (0, 3) to the point (1, 5), we would move two spaces vertically along the y-axis and one space horizontally along the x-axis. Because the slope of the line is found using the formula m = rise over run, the slope would be 2/1 because we went up 2 points and to the right one. When simplifying, we will find that 2 divided by 1 equals 2. Hence, our slope is 2.

Your final answer: The slope of the line is 2/1 or 2. If you need extra help, let me know and I will gladly assist you.
8 0
1 year ago
The GCD(a, b) = 9, the LCM(a, b)=378. Find the least possible value of a+b.
denis-greek [22]
\mathrm{gcd}(a,b)=9\implies9\mid a\text{ and }9\mid b\implies9\mid a+b

which means there is some integer k for which a+b=9k.


Because 9\mid a and 9\mid b, there are integers n_1,n_2 such that a=9n_1 and b=9n_2, and


\mathrm{lcm}(a,b)=\mathrm{lcm}(9n_1,9n_2)=9\mathrm{lcm}(n_1,n_2)=378\implies\mathrm{lcm}(n_1,n_2)=42

We have 42=2\cdot3\cdot7, which means there are four possible choices of n_1,n_2:

1, 42
2, 21
3, 14
6, 7

which is to say there are also four corresponding choices for a,b:

9, 378
18, 189
27, 126
54, 63

whose sums are:

387
207
153
117

So the least possible value of a+b is 117.
6 0
3 years ago
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