Answer:
Danny: y-=.75x+20
Avery: y=1.25x+18
Step-by-step explanation:
To write a system of equations, it usually equals y=mx+b. Since Danny and Avery both earn the set monthly allowance of 20 and 18 dollars respectively, those numbers go on the variable b since it's a set amount and they start off with that amount of money if they weren't nice to their mom at all.
Since we are trying to find the overall amount of money, let y=total money a child earns every month and x=how many times the child is nice to their mother.
The extra .75 cents Danny earns go under the variable m because it is dependent on how many times he is nice to his mom. Along with Avery.
You have two unknown rates, so we need to develop two equations to solve for these unknowns (based on the information given on the problem statement):
5x + 10y = 725
x + y = 100
By substitution, we get:
5x + 10(100 - x) = 725
5x + 1000 - 10x = 725
-5x = 725 - 1000
-5x = -275
x = -275/-5 = 55
100 - 55 = 45
Thus:
The mechanic who worked for 5 hours charged his time at $55/hr, and the mechanic who worked for 10 hours charged his time at $45/hr.
To verify, plug and chug the results back into the original equations:
5(55) + 10(45) = 725
275 + 450 = 725
725 = 725 [OK]
55 + 45 = 100 [OK]
Answer:
Check the explanation
Step-by-step explanation:
Here we have to first of all carry out dependent sample t test. consequently wore goggles first was selected at random for the reason that the reaction time in an emergency taken with goggles would be greater than the amount of reaction time in an emergency taken with not so weakened vision. So that we will get the positive differences d = impaired - normal
b)
To find 95% confidence interval first we need to find sample mean and sample sd for difference d = impaired minus normal.
We can find it using excel that is in the first attached image below,
Therefore sample mean
= 0.98
Sample sd
= 0.3788
To find 95% Confidence interval we can use TI-84 calculator,
Press STAT ----> Scroll to TESTS ---- > Scroll down to 8: T Interval and hit enter.
Kindly check the attached image below.
Therefore we are 95% confident that mean difference in braking time with impaired vision and normal vision is between ( 0.6888 , 1.2712)
Conclusion : As both values in the interval are greater than 0 , mean difference impaired minus normal is not equal to 0
There is significant evidence that there is a difference in braking time with impaired vision and normal vision at 95% confidence level .
The angular velocity is the linear speed divided by the radius.
ω = d/(t*r) = (14.13 ft)/((3 s)*(6 ft))
ω = 0.785 radians/second
There are 180/π degrees per radian, so the angular velocity can also be written as ...
ω = 45 degrees/second