sue and 4 friends buy a box of 362 base ball cards at a yard sale. If they share the cards equally,how many cards will each pers
1 answer:
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Answer:
C: I and III only.
Step-by-step explanation:
We have two numbers x and y such that:
And we want to determine which of the following conditions must be true.
First, let's examine the third condition. We have:
To see if this is true, let's try a negative value for y. So, let's use -7. This will give:
Simplify:
This is saying we need a number less than -7 and greater than 7.
This is impossible. So, y <em>must be</em> greater than 0.
Therefore, Condition III must be true.
Next, let's see this compound inequality visually.
Picture the following number-line:
<----------(-y)----------0----------y---------->
Whatever y is, -y is just y on the negative side.
Now, since our condition is that -y<x<y, this means that our x can be anywhere between -y and y. Namely:
<----------(-y)----------0----------y---------->
To determine our correct condition, let's picture x anywhere on the bolded lines. I'm just going to put x here...
<----------(-y)-------(x)--0----------y---------->
Now, remember the alternative definition for absolute value. Namely, the absolute value of x is also the <em>distance</em> from 0 to x. And this distance is always positive.
Since our x is between -y and y, our distance from 0 to x will always be less than the distance from 0 to either y.
Therefore, Condition I is also true.
Let's try an example. Let's let y = 9. So, -y=-9. And let's let x be between 9 and -9, say, -2. So:
<---(-9)-----(-2)--0--------(9)------>
We can see that:
Also, this example counters Condition II, as our x can indeed be negative if we desire it.
Algebraically, if we have a negative x such that:
We can divide everything by -1 to obtain:
We can flip this to get:
Which is our original inequality. So, Condition II does not need to be true.
So, the two conditions that <em>must</em> be true is I and III.
So, our answer is C.
Answer:
Step-by-step explanation:
The table can be computed as:
Advertising Expenses ($ million) Number of companies
25 up to 35 4
35 up to 45 19
45 up to 55 27
55 up to 65 16
65 up to 75 9
TOTAL 75
Let's find the probabilities first:
For 35 up to 45
For 45 up to 55
For 55 up to 65
For 65 up to 75
Chi-Square Table can be computed as follows:
Expense No of Probabilities(P) Expe
compa cted E (n*p)
nies (O)
25-35 4 0.0612 75*0.0612 = 4.59 0.3481 0.0758
35-45 19 0.2218 75*0.2218 = 16.635 5.5932 0.3362
45-55 27 0.3568 75*0.3568 = 26.76 0.0576 0.021
55-65 16 0.2552 75*0.2552 = 19.14 9.8596 0.5151
65-75 9 0.0839 75*0.0839 = 6.2925 7.331 1.1650
Using the Chi-square formula:
Null hypothesis:
Alternative hypothesis:
Assume that:
degree of freedom:
= n-1
= 5 -1
= 4
Critical value from
Decision rule: To reject test statistics is greater than
tabulated.
Conclusion: Since is less than critical value 11.667. Then we fail to reject