Answer: The loser's card shows 6.
Explanation: Let's start by naming the first student A and the second student B.
Since the product of A and B are either 12, 15, or 18, let's list every single possibility, the first number being A's number and the second number being B's number.
1 12
1 15
1 18
2 6
2 9
3 4
3 5
3 6
4 3
5 3
6 2
6 3
9 2
12 1
15 1
18 1
Now, the information says that A doesn't know what B has, so we can immediately cross off all of the combinations that have the integer appearing once and once ONLY off, because if it happened once only, A would know of it straight away. Now, our sample space becomes much smaller.
1 12
1 15
1 18
2 6
2 9
3 4
3 5
3 6
6 2
6 3
Using this same logic, we know that we can cross off all of the digits that occur only once in B's column.
2 6
3 6
Now, A definitely knows what number B has because there is only one number left in B. Hence, we can conclude that the loser, B, has the integer 6.
Step-by-step explanation:
140/70=2 Therefore, 1 apple equals 2 percent
The remaining 30 percent times 2 equals 60
60 apples plus 140 apples equals 200 apples
Answer B
Answer:
Step-by-step explanation:
Let x represent the number of hours that that he spent washing cars.
Let y represent the number of hours that that he spent landscaping.
In a week, he can work no more than 19 total hours. This means that
x + y ≤ 19- - - - - - - - - - - -1
Jacob is working two summer jobs, making $10 per hour washing cars and making $8 per hour landscaping. He must earn at least $170. This means that
10x + 8y ≥ 170 - - - - - - - - - -2
If Jacob worked 4 hours landscaping, it means that
x + 4 ≤ 19
x ≤ 19 - 4
x ≤ 15
Also,
10x + 8 × 4 ≥ 170
10x + 32 ≥ 170
10x ≥ 170 - 32
10x ≥ 138
10x ≥ 138/10
x ≥ 13.8
The minimum number of hours is 14
9514 1404 393
Answer:
9. ±1, ±2, ±3, ±6
11. ±1, ±2, ±3, ±4, ±6, ±12
Step-by-step explanation:
The possible rational roots are (plus or minus) the divisors of the constant term, divided by the divisors of the leading coefficient.
Here, the leading coefficient is 1 in each case, so the possible rational roots are plus or minus a divisor of the constant term.
__
9. The constant is -6. Divisors of 6 are 1, 2, 3, 6. The possible rational roots are ...
±{1, 2, 3, 6}
__
11. The constant is 12. Divisors of 12 are 1, 2, 3, 4, 6, 12. The possible rational roots are ...
±{1, 2, 3, 4, 6, 12}
_____
A graphing calculator is useful for seeing if any of these values actually are roots of the equation. (The 4th-degree equation will have 2 complex roots.)
The true statements are:
2 - we can tell this by looking at the far right of the graph, as the slope is going downwards, therefore the leading coefficient must be negative
3 - this is a cubic, meaning its degree is 3
6 - by looking at the graph, we can see that there are 3 points where it cuts the x axis, hence 3 real zeros
7 - even multiplicity is where the curve "bounces off" the x axis and does not cross it. This curve have no zeros with even multiplicity
Hope this helped!
