So lets try to prove it,
So let's consider the function f(x) = x^2.
Since f(x) is a polynomial, then it is continuous on the interval (- infinity, + infinity).
Using the Intermediate Value Theorem,
it would be enough to show that at some point a f(x) is less than 2 and at some point b f(x) is greater than 2. For example, let a = 0 and b = 3.
Therefore, f(0) = 0, which is less than 2, and f(3) = 9, which is greater than 2. Applying IVT to f(x) = x^2 on the interval [0,3}.
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If Deliah does jumping jacks at a constant rate, this means that she does them at the same pace or you could say that she does the same amount of jumping jacks in a specified amount of time, ie. if you counted how many jumping jacks she did in one minute, it would be same as how many she would complete in the next minute, and the next, and so on.
Now given that she does 184 jumping jacks in four minutes, and she has kept a constant pace throughout, to find out how many she does each minute, we simply need to divide the number of jumping jacks she does in 4 minutes by 4. Thus:
Jumping jacks in 1 minute = Jumping jacks in 4 minutes / 4
= 184 / 4
= 46
Thus, Deliah can do 46 jumping jacks per minute.
Answer:
A. (1, -2)
B. the lines intersect at the solution point: (1, -2).
Step-by-step explanation:
A. The equations can be solve by substitution by using the y-expression provided by one of them to substitute for y in the other.
This gives ...
3x -5 = 6x -8
Adding 8-3x to both sides, we get ...
3 = 3x
Dividing both sides by 3 gives ...
1 = x
Substituting this value into the first equation, we can find y:
y = 3(1) -5 = -2
The solution is (x, y) = (1, -2).
__
B. The lines intersect at the solution point, the point that satisfies both equations simultaneously. That point is (1, -2).
Step-by-step explanation:
The total probability that the DeLorean makes the trip is:
P = P(engine) × P(at least 1 time circuit) × P(at least 2 capacitors)
P = P(engine) × (1 − P(0 time circuits)) × P(at least 2 capacitors)
P = 0.94 × (1 − ₄C₀ 0.75⁰ 0.25⁴) × (₃C₂ 0.8² 0.2¹ + ₃C₃ 0.8³ 0.2⁰)
P = 0.94 × (1 − 0.25⁴) × (0.384 + 0.512)
P = 0.83895
The reliability of the DeLorean is approximately 83.9%.
Using the z-distribution, it is found that:
- The 95% confidence interval is of -1.38 to 1.38.
- The value of the sample mean difference is of 1.74, which falls outside the 95% confidence interval.
<h3>What is the z-distribution confidence interval?</h3>
The confidence interval is:
In which:
is the difference between the population means.
In this problem, we have a 95% confidence level, hence
, z is the value of Z that has a p-value of 
, so the critical value is z = 1.96.
The estimate and the standard error are given by:
Hence the bounds of the interval are given by:
1.74 is outside the interval, hence:
- The 95% confidence interval is of -1.38 to 1.38.
- The value of the sample mean difference is of 1.74, which falls outside the 95% confidence interval.
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