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.
Answer:
Attached is the histogram illustrating the marathon runners’ times.
Step-by-step explanation:
The provided data is as follows;
2.21
2.25
2.76
3.1
3.3
3.5
3.6
3.77
3.8
4.23
4.25
4.25
4.6
4.9
From this data, we can determine;
The count of runners finishing between 0 and 1 hour = 0
The count of runners finishing between 1 and 2 hours = 0
The count of runners finishing between 2 and 3 hours = 3
The count of runners finishing between 3 and 4 hours = 6
The count of runners finishing between 4 and 5 hours = 5
Based on these frequencies across the various time ranges, the histogram for the provided data has been constructed and is attached.
Answer:
Step-by-step explanation:
If you compare numbers based on the hundreds digit, the digits to the left (thousands and ten-thousands) remain the same, while the hundreds digit differs.
This applies for any five-digit numbers structured like:
(3)(5)(not 7)(any digit)(any digit).
Digits to the right of the decimal point, as well as those in the tens and ones places, don't impact this comparison.
The answer
the full question is
If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) create two line segments, and AB ⊥ CD, what condition must be satisfied to establish that AB ⊥ CD?
Let A(x1, y1) and B(x2, y2) represent the first line, while C(x3, y3) and D(x4, y4) represent the second line.
The slope for the first line is given by m = (y2 - y1) / (x2 - x1).
For the second line, the slope is m' = (y4 - y3) / (x4 - x3).
The necessary condition to demonstrate that AB ⊥ CD is
(y2 - y1) * (y4 - y3)
m × m' = --------- × ------------ = -1
(x2 - x1) (y4 - y3)
Answer:
y=4x+7.75; continuous
Step-by-step explanation:
Let’s first establish the equation. Julie requires one segment of yarn measuring 7.75 inches: that's already known.
y = 7.75
Now, for the four pieces of yarn, each will be of equal length x. If she wants them to measure 1 inch, she'd need 4 inches of yarn. Therefore, the calculation would be:
y = 7.75 + 4x
Now, is this graph discrete or continuous? Continuous indicates there's a smooth line without gaps, while discrete has interruptions or spaces. In this scenario, x is continuous, as Julie can cut the yarn to any size for the four pieces. She is not limited to whole numbers; each piece could be, for instance, 2.5 inches or 3.1415 inches.
