We first write the fractions in their decimal forms and find out the ratio.
2 1/4 is equivalent to 2.25, and 1 1/3 is equivalent to 1.33
Ratio will be 2.25 / 1.33 = 1.69 or 1.7 rounded off. Since it cannot be simplified further, then the ratio of mulch to gravel will be 1.7: 1
Quantity of mulch sold → 1.7/2.7 of 172 →0.629 ×172 = 108.2 pounds
Quantity of gravel sold will be 172 -108. 2 = 63 .8 pounds
Step-by-step explanation:
What is 40% of 400?
- Convert the problem to an equation using the percentage formula: P% * X = Y
- P is 40%, X is 400, so the equation is 40% * 400 = Y
- Convert 40% to a decimal by removing the percent sign and dividing by 100:40/100 = 0.4
- Substitute 0.10 for 10% in the equation: 40% * 400 = Y becomes 0.4 * 400 = Y
- Do the math: 0.4 * 400 = 160
- Y = 160
- So 10% of 150 is 160
- Double check your answer with the original question: What is 40% of 400? Multiply 0.4 * 400 = 160
Use a calculator that’s the 100% way to go
Answer:
a) r=-0.719
b) y=10.642-0.976x
c)Predicted y=7.714
Step-by-step explanation:
a)
sumx=1+4+6+7=18
sumy=9+7+8+1=25
sumxy=1*9+4*7+6*8+7*1=92
sumx²=1²+4²+6²+7²=102
sumy²=9²+7²+8²+1²=195
n=number of observation=4
The correlation coefficient is computed by following formula
![r=\frac{nsumxy-(sumx)(sumy)}{\sqrt{[nsumx^{2} -(sumx)^2][nsumy^2-(sumy)^2]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Bnsumxy-%28sumx%29%28sumy%29%7D%7B%5Csqrt%7B%5Bnsumx%5E%7B2%7D%20-%28sumx%29%5E2%5D%5Bnsumy%5E2-%28sumy%29%5E2%5D%7D%7D)
![r=\frac{4(92)-(18)(25)}{\sqrt{[4(102) -(18)^2][4(195)-(25)^2]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B4%2892%29-%2818%29%2825%29%7D%7B%5Csqrt%7B%5B4%28102%29%20-%2818%29%5E2%5D%5B4%28195%29-%2825%29%5E2%5D%7D%7D)
![r=\frac{368-450}{\sqrt{[408 -324][780-625]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B368-450%7D%7B%5Csqrt%7B%5B408%20-324%5D%5B780-625%5D%7D%7D)
![r=\frac{-82}{\sqrt{[84][155]}}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B-82%7D%7B%5Csqrt%7B%5B84%5D%5B155%5D%7D%7D)

By rounding r to 3 decimal places we get r=-0.719.
b)
The regression equation can be written as y=a+bx
We have to find "a" and "b" for regression equation




b=-0.976
xbar=sumx/n
xbar=18/4=4.5
ybar=sumy/n
ybar=25/4=6.25
a=ybar-b(xbar)
a=6.25-(-0.976)4.5
a=6.25+4.392
a=10.642
Thus, the regression equation is
y=a+bx
y=10.642-0.976x
c)
The predicted value of y for x=3 can be computed by putting the value of x in regression equation
y=10.642-0.976(3)
y=10.642-2.928
y=7.714
Hence, the predicted y-value for x=3 is 7.714.