The train descends at twice the speed compared to its ascent, and it travels at 2/3 of the speed uphill relative to flat terrain.
If its speed downhill is measured at 120 miles per hour, its uphill speed would be 120 divided by 2, equaling 60 miles per hour, and its speed on flat ground would be 60 divided by (2/3), simplified to (60 times 3) divided by 2, resulting in 90 miles per hour.
Consequently, for the train to cover 45 miles on flat terrain, the time required is calculated as 45 divided by 90, which is equal to 0.5 hours, or 30 minutes.
Utilizing the complement rule alongside the standard normal table or Excel, we arrive at the results.
To summarize previous concepts,
the normal distribution represents a symmetrical probability distribution centered around the mean, highlighting that values near the mean occur more frequently than those further away.
The Z-score acts as a statistical measure that indicates a value's relation to the average of a dataset, expressed in standard deviations from the mean.
In addressing the problem:
Let X denote the random variable representing population heights, and we regard the distribution for X as stipulated.
For a sample size of n = 64, since the distribution of X holds normality, so does the distribution of the sample mean.
We aim to determine the following probability, utilizing the Z-score derived via the specified formula.
Answer:
w/2 = 7.5/5
3kg
Here's the detailed explanation:
Remaining question below:
Which proportion could Maddy utilize to solve this issue?
a. w/2 = 7.5/5
b. w/7.5 = 5/2
Solve the proportion to determine the weight of a 2 liter jug.
_____kg
A 5-liter container of sports drink weighs 7.5kg
A 2-liter jug of this drink will weigh x kg
Finding w
Ratio of weight to volume
7.5kg: 5liters translates to 7.5/5
wkg: 2 liters means w/2
Establishing equivalent ratios
7.5 / 5 = w / 2
Cross-multiplying gives
7.5*2=5*w
15=5w
Dividing both sides by 5 results in
w=3
w=3kg
Thus, the weight of the 2-liter sports drink jug is 3kg
To find the original number where 65% equals 1105:
0.65x = 1105
x = 1105 ÷ 0.65
x = 1700... hence, the original number is 1700.
Calculating 82% of 1700:
0.82 * 1700 = 1394 <== this is your answer.
You may either multiply the numbers or the place value, and both methods will yield the same answer.
(2 thousands, 7 tens) multiplied by 10 results in
... (20 thousands, 70 tens)
or
... (2 ten-thousands, 7 hundreds)
