George took a nonstop flight from Dallas to
1 answer:
The question provided states that,
George took a direct flight from Dallas to Los Angeles covering 1,233 miles. Initially, the plane was traveling at a speed of 460 miles per hour for the first 75 minutes, then at a speed of 439 miles per hour for the remaining duration.
Let x denote the hours during which the flight flew at 439 miles per hour.
Based on this, we can establish the following:
To convert this into minutes, we must multiply by 60, resulting in
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Response:
Detailed explanation:
Greetings!
You have the variable
X: Area eligible for painting with a can of spray paint (feet²)
This variable is normally distributed with a mean of μ= 25 feet² and a standard deviation of δ= 3 feet²
As this variable has a normal distribution, it needs to be converted into the standard normal form to utilize tabulated cumulative probabilities.
a.
P(X>27)
The first step involves standardizing the X value using Z= (X-μ)/ δ ~N(0;1)
P(Z>(27-25)/3)
P(Z>0.67)
Having determined the Z value, you can find it in the table, but since the table includes probabilities for , the following conversion must be applied:
P(Z>0.67)= 1 - P(Z≤0.67)= 1 - 0.74857= 0.25143
b.
A sample of 20 cans was taken, and you need to ascertain the probability of averaging a coverage area of 540 feet².
The sample mean maintains the same distribution as its source variable, but its variance is influenced by sample size, thus it is normally distributed with parameters:
X[bar]~N(μ;δ²/n)
To cover 540 feet² with 20 cans, the average coverage must be approximately 540/20= 27 feet² per can.
c.
P(X≤27) = P(Z≤(27-25)/(3/√20))= P(Z≤2.98)= 0.999d.No, if the distribution is not normal and skewed, the normal distribution should not be applied for calculating probabilities. While the central limit theorem might approximate the sampling distribution to normal when the sample size is 30 or larger, that isn’t applicable here.
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Answer:
The correct option is:
On the coordinate plane, there is a parabola that opens upwards, passing through the points (2, 10), having its vertex at (5, 1), and intersecting (8, 10).
Step-by-step explanation:
Initially, we must understand the translation rules
1) {f(x) + a} signifies f(x) moved up by (a) units
2) {f(x) – a} means f(x) moved down by (a) units
3) {f(x + a)} represents f(x) moved left by (a) units.
4) {f(x – a)} indicates f(x) moved right by (a) units.
Given information:
f(x) = x²
g(x) = (x-5)² + 1
By comparing the transformation from f(x) to g(x) with the translation rules
It can be concluded that g(x) represents f(x) through a translation of 5 units to the right and 1 unit upwards (rules 1 and 4)
Refer to the attached image, which illustrates the graphs of both f(x) and g(x)
As depicted, g(x) intersects (2, 10), has a vertex at (5, 1), and crosses through (8, 10)
