Answer:
5 1/6
Step-by-step explanation:
First you want to get the same denominator on both of the fractions. So you would multiply 1 2/3 or you can change it into a improper fraction which is a fraction greater than 1. So that would be 5/3 times 2/2. Because you want to get the same denominator. That is 10/6. Then you make 3 1/2 a improper fraction which is 7/2 and multiply it by 3/3 to get 21/6. Next you would add them together and get 31/6 but you have to simplify, so you would divide 31 by 6 and get 5 1/6.
I know that's a lot but I hope it helps.
Answer:
176 seconds
Step-by-step explanation:
By using regression line calculator,
Equation of the line of best fit will be,
T = -12.55x + 276.52
Here , T = time taken to cover one lap
x = Age
If the age of Marsha's son is 8 years then expected time taken by her son to cover one lap will be,
T = -12.55(8) + 276.52
T = -100.4 + 276.52
T = 176.12 seconds
Therefore, approximate time taken by Marta's son will be 176 seconds.
Answer:
32.66 units
Step-by-step explanation:
We are given that

Point A=(-2,-4) and point B=(1,20)
Differentiate w.r. t x

We know that length of curve

We have a=-2 and b=1
Using the formula
Length of curve=
Using substitution method
Substitute t=12x+14
Differentiate w.r t. x


Length of curve=
We know that

By using the formula
Length of curve=![s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B1%7D%7B12%7D%5B%5Cfrac%7Bt%7D%7B2%7D%5Csqrt%7B1%2Bt%5E2%7D%2B%5Cfrac%7B1%7D%7B2%7Dln%28t%2B%5Csqrt%7B1%2Bt%5E2%7D%29%5D%5E%7B1%7D_%7B-2%7D)
Length of curve=![s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B1%7D%7B12%7D%5B%5Cfrac%7B12x%2B14%7D%7B2%7D%5Csqrt%7B1%2B%2812x%2B14%29%5E2%7D%2B%5Cfrac%7B1%7D%7B2%7Dln%2812x%2B14%2B%5Csqrt%7B1%2B%2812x%2B14%29%5E2%7D%29%5D%5E%7B1%7D_%7B-2%7D)
Length of curve=
Length of curve=
Length of curve=