Answer:
10s
Explanation:
If it took Beatrice 25 seconds to complete the race
Distance = 100 meter
Beatrice speed = 100/25
= 4m/s
If Alice runs at a constant speed and crosses the finish line $5$ seconds, she must have completed the race in 20s (25 -5).
Her speed where constant
= 100/20
= 5 m/s
It would take Alice
= 50/5
= 10s
It would take Alice 10s to run $50$ meters.
Answer:
See the answer below
Explanation:
A poker that will effectively and safely function to move pieces of coal or logs in a burning fire must be fireproof itself. Hence, to be as safe as possible, such <u>poker should be made from a material that is fireproof</u> and that does not conduct a lot of heat. Otherwise, the poker will catch fire/becomes too hot during the course of usage.
Length of the pipe = 0.39 m
Third harmonic frequency = 1400 Hz
For the third harmonic:
Wavelength = 
The center of the open pipe will host a node and the nearest anti - node from the center will be at the 0.25 × wavelength
Distance from center = 0.25 × wavelength
Distance = 
Plugging the value of the length of the pipe (L) = 0.39 m = 39 cm
Distance = 
Distance from the center to the nearest anti - node = 6.5 cm
Hence, the nearest distance to the anti - node from the center = 6.5 cm
So, option C is correct.
Answer:
The spring constant of the spring is 47.62 N/m
Explanation:
Given that,
Mass that is attached with the spring, m = 29 g = 0.029 kg
The spring makes 20 complete vibrations in 3.1 s. We need to find the spring constant of the spring. We know that the number of oscillations per unit time is called frequency of an object. So,

f = 6.45 Hz
The frequency of oscillator is given by :

k is the spring constant


k = 47.62 N/m
So, the spring constant of the spring is 47.62 N/m. Hence, this is the required solution.
Answer:
18.375
Explanation:
Mean = total of measured values / no of elements of sample
Total = .15 + .89 +1.11+1.46 +2.78 + 3.12 + 4.30 + 4.59 + 4.92 + 6.42 + 7.20+8.04+8.21+12.13+31.86+32.53+33.82+36.60+ 72.99
= 273.03
Mean = 273 .03 / 19
= 14.37
( .15 - 14.37 )² +( 0.89 - 14.37 )²+( 1.11- 14.37 )²+( 1.46 - 14.37 )²+( 2.78 - 14.37 )²+( 3.12 - 14.37 )²+( 4.30 - 14.37 )²+( 4.59 - 14.37 )²+( 4.92 - 14.37 )²+( 6.42 - 14.37 )²+( 7.20 - 14.37 )²+( 8.04 - 14.37 )²+( 8.21 - 14.37 )²+( 12.13 - 14.37 )²+( 31.86 - 14.37 )²+( 32.53 - 14.37 )²+( 33.82 - 14.37 )²+( 36.60 - 14.37 )²+( 72.99 - 14.37 )²
= 202.20 +181.71+ 175.82 + 166.66+ 134.32 + 126.56 + 101.40 +95.64 + 89.30 +63.20 +51.40 +40.06 +37.94+5.01 +305.90 +329.78 +378.30 +494.17 +3436.30
=6415.67
Standard deviation =

= 18.375