A softball player has a batting average of exactly .300 and no more than 60 times at bat. Suppose this player gets 5 hits in her
1 answer:
Answer:
The highest possible average is 348
Step-by-step explanation:
we know that
No more than 60 means -----> maximum 60 ( less than or equal to 60)
To find the possible average using proportion
Remember that the average is the number of hits in 1,000 times at bat
If the average is 300 with maximum 60 times at bat
then
The number of hits is 60*300/1,000=18 hits
If the player gets 5 hits in her next 6 times at bat
then
In 66 times at bat the number of hits is 18+5=23 hits
Find out the average
Let
x ----> the average
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Answer:
The number is -9
Look at the attachment
Answers:
- System 1: x = 3 and y = -5
- System 2: x = 1 and y = 2
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Explanation:
For now, let's focus on system 1.
We have identical copies of "2y" in each equation, which means that if we were to subtract the equations straight down, then the y terms cancel out. That allows us to solve for x.
- The x terms subtract to 7x-x = 6x
- The y terms subtract to 0 and go away
- The right hand sides subtract to 11 minus (-7) = 11-(-7) = 11+7 = 18
After doing those subtractions, we have the new equation 6x = 18 which solves to x = 3. Divide both sides by 6 to isolate x.
Once we know x, we can find out y.
7x+2y = 11
7(3)+2y = 11
21+2y = 11
2y = 11-21
2y = -10
y = -10/2
y = -5
or we can say
x+2y = -7
3+2y = -7
2y = -7-3
2y = -10
y = -10/2
y = -5
We should lead to the same y value either way. This helps confirm we have the correct x value.
Overall, the solution to system 1 is (x,y) = (3, -5)
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Now onto system 2.
Unfortunately, we don't have identical y terms this time. But what we can do is double everything in the second equation to go from -x+y = 1 to -2x+2y = 2.
The new equivalent system is
Now we have the same situation as before: Subtract straight down, solve for x.
- The x terms subtract to 7x-(-2x) = 7x+2x = 9x
- The y terms go away when subtracting
- The right hand sides subtract to 11-2 = 9
So we have 9x = 9 and that solves to x = 1.
We'll use this x to find the y value.
7x+2y = 11
7(1)+2y = 11
7+2y = 11
2y = 11-7
2y = 4
y = 4/2
y = 2
Or you could pick on the second equation
-x+y = 1
-1+y = 1
y = 1+1
y = 2