When the initial input is equal to 15 and the final output is -6, the machines should be stacked in this order:
When the initial input is equal to 8 and the final output is 2, the machines should be stacked in this order:
From the information provided, we know that the initial input is equal to 15 and the final output is -6. Thus, we would solve the puzzle as follows:
For the fourth machine, we have;
y₄ = -2x + 34
y₄ = -2(15) + 34
y₄ = -30 + 34
y₄ = 4.
Therefore, the output is equal to 4.
For the second machine, we have:
y₂ = (x - 2)²
y₂ = (4 - 2)²
y₂ = 2²
y₂ = 4
Therefore, the output is equal to 4.
For the first machine, we have:
y₁ = -|3x|
y₁ = -|3 × 4|
y₁ = -12.
Therefore, the output is equal to -12.
For the third machine, we have:
y₃ = -x/3 - 10
y₃ = -(-12)/3 - 10
y₃ = 12/3 -10
y₃ = 4 - 10
y₃ = -6
Therefore, the output is equal to -6.
In conclusion, we can logically deduce that the machines should be stacked in this order:
When the initial input is equal to 8 and the final output is 2. Thus, we would solve the puzzle as follows:
y₁ = -|3x|
y₁ = -|3 × 8|
y₁ = -24.
For the third machine, we have:
y₃ = -x/3 - 10
y₃ = -(-24)/3 - 10
y₃ = 24/3 -10
y₃ = 8 - 10
y₃ = -2.
For the second machine, we have:
y₂ = (x - 2)²
y₂ = (-2 - 2)²
y₂ = 4²
y₂ = 16
For the fourth machine, we have;
y₄ = -2x + 34
y₄ = -2(16) + 34
y₄ = -32 + 34
y₄ = 2.
When the initial input is equal to 8 and the final output is 2, the machines should be stacked in this order:
Read more on final outputs here: brainly.com/question/17670171
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Complete Question:
1. In what order should you stack the machines so that when 15 is dropped into the first machine, and all four machines have had their effect, the last machine’s output is -6?
2. When the initial input is 8 in what order should the machines be arranged so that the final output is 2?
Answer: t = 6 s
Step-by-step explanation:
When Rose hit the water, the height of the jump is 0, so: h(t) = 0.
Resolving it, we have:
-16t² + 16t + 480 = 0
To simplify the second degree equation, divided it by 16:
-t² + t + 30 = 0
Now, solve the equation using Bhaskara:
Δ = 1² - 4. (-1) . 30
Δ = 1 + 120
Δ = 121
t =
t₁ = = - 5
t₂ = = 6
Since time can be negative, it took t = 6s for Rose to hit the water.
Answer:
a) 0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.
b) 369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.
c) Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
A result is considered significantly high if it is more than 2.5 standard deviations above the mean.
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
Assume that 24.5% of people have sleepwalked.
This means that
Sample of 1478 adults:
This means that
Mean and standard deviation:
a. Assuming that the rate of 24.5% is correct, find the probability that 369 or more of the 1478 adults have sleepwalked.
Using continuity correction, this is , which is 1 subtracted by the p-value of Z when X = 368.5.
has a p-value of 0.6517
1 - 0.6517 = 0.3483
0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.
b. Is that result of 369 or more significantly high?
362.11 + 2.5*16.5346 = 403.4
369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.
c. What does the result suggest about the rate of 24.5%?
Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.