Answer:
x = (-1)/23
Step-by-step explanation:
Solve for x:
-3 x - 4 (x - 1) = 5 (2 x + 1) + 6 x
-4 (x - 1) = 4 - 4 x:
4 - 4 x - 3 x = 5 (2 x + 1) + 6 x
Grouping like terms, -3 x - 4 x + 4 = 4 + (-3 x - 4 x):
4 + (-3 x - 4 x) = 5 (2 x + 1) + 6 x
-3 x - 4 x = -7 x:
-7 x + 4 = 5 (2 x + 1) + 6 x
5 (2 x + 1) = 10 x + 5:
4 - 7 x = 10 x + 5 + 6 x
Grouping like terms, 10 x + 6 x + 5 = (10 x + 6 x) + 5:
4 - 7 x = (10 x + 6 x) + 5
10 x + 6 x = 16 x:
4 - 7 x = 16 x + 5
Subtract 16 x from both sides:
4 + (-7 x - 16 x) = (16 x - 16 x) + 5
-7 x - 16 x = -23 x:
-23 x + 4 = (16 x - 16 x) + 5
16 x - 16 x = 0:
4 - 23 x = 5
Subtract 4 from both sides:
(4 - 4) - 23 x = 5 - 4
4 - 4 = 0:
-23 x = 5 - 4
5 - 4 = 1:
-23 x = 1
Divide both sides by -23:
Answer: x = (-1)/23
Answer:
The experimental probability is 1/6, and the theoretical probability is 1/4. The theoretical probability is greater than the experimental probability in this trial.
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Explanation:
Theoretical probability is the mathematically calculated probability of the circumstances occurring.
There is a 1/2 chance of rolling an even number, and a 1/2 chance of flipping a coin on heads.
Since the question asks for the possibility of both happening, multiply those together to find the probability:

The theoretical probability of rolling an even number and then flipping a head is
1/4.
Now we'll focus on Taka's trials.
Experimental probability is the probability that is taken from results of a trial.
Take the results, and see if they match the criteria of rolling an even number and flipping heads.
The results that are bolded fit the criteria:
<span>1 H, 4 T, 1 H, 5 T,
2 H, 3 T, 6 T,
2 H, 3 T, 5 T, 3 H, 4 T
</span>
Taka managed to roll and flip the coin to fit the criteria 2 times out of 12. Converted into a fraction, it is 2/12. Simplified, the experimental probability is
1/6.
Answer:
Step-by-step explanation:
Given piecewise function is,
f(x) = -5x + 2 If x < 2
2x - 2 If x ≥ 2
For f(x) = -5x + 2 If x < 2,
Graph of this piece will be a straight line with slope = -5 and y-intercept = 2
For f(x) = 2x - 2 If x ≥ 2,
Similarly, Graph of the second piece of the function will be a straight line with slope = 2 and y-intercept = -2.
By using the graphing tool we can draw the graph of the piecewise function given.
Answer:
Step-by-step explanation:
z(lower) = (15-15)/4 = 0
z(upper) = (19-15)/4= 1
z at 0 = .5
z at 1 = 0.841344746
(look these up in a Z table)
probability "between" = 0.841344746 - .5 = 0.3841344746