Answer:
12
Step-by-step explanation:
A 2 - sided counter ; (red, yellow)
A spinner (1,2,3,4,5,6)
Number of trials = 80
P(red and number > 3) :
P(red) = 1/2 ;
P(number >3) : numbers greater Than 3 = (4, 5, 6)
Hence, P(number <3) = 3 /6 = 1/2
Theoretical probability = 1/2 *1/2 = 1/4
Expected number of outcomes :
1/4 * number of trials
1/4 * 80 = 20
Experimental outcome :
Relative frequency = number of outcomes / number of trials
Relative frequency = 2/5
Hence,
2/5 = number of outcomes / 80
Cross multiply :
160 = number of outcomes * 5
Number of outcomes = 160 /5 = 32
Actual outcomes = 32
Difference between actual and expected :
32 - 20 = 12
<h3>
Answer:</h3>
4/5+5/6
Step-by-step explanation:
4/5+5/6=1 19/30
not
- 49/16+49/14
- 24/17+25/13
- 98/45+98/15
hope this helps u
Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
We need to equalize f' to 0
- k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
- 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
- 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
- ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
- 1/x = e^(1/2)
- x = 1/e^(1/2) = 1/√e ≅ 0.607
Thus, the value of x that gives the maximum transmission is 1/√e.
Answer:
x = 7 and y = −2
(7, -2)
Step-by-step explanation:
x = 1 - 3y
3x + 3y = 15
Substitute −3y + 1 for x in 3x + 3y = 15:
3(1 - 3y) + 3y = 15
3 - 9y + 3y = 15
3 - 6y = 15
-3 -3
-6y = 12
/-6 /-6
y = -2
Now we solve for x. Substitute −2 for y in x = −3y + 1:
x = 1 - 3y
x = 1 + (-3)(-2)
x = 1 + 6
x = 7
Now we check our solution.
x = 1 - 3y
7 = 1 + (-3)(-2)
7 = 7 ✅
3x + 3y = 15
3(7) + 3(-2) = 15
21 - 6 = 15
15 = 15 ✅
17. On average, Nestor works 7.5 hours of overtime in 4 weeks, so works an average of 7.5/4 = 1.875 overtime hours per week.
On average, each week Nestor gets paid for 7.5×5 + 2×1.875 = 41.25 hours, so is paid*
... (41.25 h)×($7.42/h) = $306.075
Each week Rita gets paid for 8×5 + 1.5×3 = 44.5 hours, so is paid
... (44.5 h)×($7.64/h) = $339.98
Their combined earning for a week are $306.075 + 339.98 = $646.055, so over a period of 12 weeks, they are paid a total of
... (12 weeks)×($646.055/week) = $7,752.66
18. Assuming Robin is paid time and a half for overtime, she was paid for
... 40 + 1.5×6 = 49 . . . hours
Then her hourly pay was ($392/week)/(49 hours/week) = $8.00 per hour
___
* The half-cent that shows up in Nestor's average weekly pay does not actually show up in Nestor's paycheck. Here, it is an artifact of dividing his monthly hour total by 4 to get a weekly average. Nestor's total pay for any given week is whole number of cents.
