Answer:
The price per serving is $0.315, therefore, it's less than $0.5
Step-by-step explanation:
In order to calculate the price per serving, we can first calculate the price per cup, this is done by dividing the total value of the box by the number of cups it can serve:
![price_{cup} = \frac{3.8}{9} = 0.42](https://tex.z-dn.net/?f=price_%7Bcup%7D%20%3D%20%5Cfrac%7B3.8%7D%7B9%7D%20%3D%200.42)
Since each serving is
of a cup, then it's price has the same proportion and is given by:
![price_{serving} = \frac{3}{4}*0.42 = 0.315](https://tex.z-dn.net/?f=price_%7Bserving%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D%2A0.42%20%3D%200.315)
The price per serving is $0.315, therefore, it's less than $0.5
Answer:
The distance is ![\sqrt{10}](https://tex.z-dn.net/?f=%5Csqrt%7B10%7D)
Step-by-step explanation:
First we need to find the slope of the line and the the its equation, for the slope we use the formula:
![m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{-4-1}{9-(-6)}\\ m=\frac{-5}{9+6}\\ m=\frac{-5}{15}\\m=- \frac{1}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%20m%3D%5Cfrac%7B-4-1%7D%7B9-%28-6%29%7D%5C%5C%20m%3D%5Cfrac%7B-5%7D%7B9%2B6%7D%5C%5C%20m%3D%5Cfrac%7B-5%7D%7B15%7D%5C%5Cm%3D-%20%5Cfrac%7B1%7D%7B3%7D)
Using the line equation we have that:
(1)
Converting the line equation (1) into its general form
![y=- \frac{1}{3} x-1\\3y=-x-3 \\x+3y+3=0](https://tex.z-dn.net/?f=y%3D-%20%5Cfrac%7B1%7D%7B3%7D%20x-1%5C%5C3y%3D-x-3%20%5C%5Cx%2B3y%2B3%3D0)
Finally we use the distance between a line and point formula given by
![d=\frac{Ax+By+C}{ \sqrt{ A^{2} + B^{2} } }](https://tex.z-dn.net/?f=d%3D%5Cfrac%7BAx%2BBy%2BC%7D%7B%20%5Csqrt%7B%20A%5E%7B2%7D%20%2B%20B%5E%7B2%7D%20%7D%20%7D)
where A, B and C are the coefficients of the line and x and y are the coordinates of the point P
![d=\frac{1(4)+3(1)+3}{ \sqrt{ 1^{2}+3^{2} } } \\d=\frac{4+3+3}{ \sqrt{1+9} }\\d=\frac{10}{ \sqrt{10} }\\d=\frac{10 \sqrt{10} }{10}\\d=\sqrt{10}](https://tex.z-dn.net/?f=d%3D%5Cfrac%7B1%284%29%2B3%281%29%2B3%7D%7B%20%5Csqrt%7B%201%5E%7B2%7D%2B3%5E%7B2%7D%20%7D%20%20%7D%20%5C%5Cd%3D%5Cfrac%7B4%2B3%2B3%7D%7B%20%5Csqrt%7B1%2B9%7D%20%20%7D%5C%5Cd%3D%5Cfrac%7B10%7D%7B%20%5Csqrt%7B10%7D%20%20%7D%5C%5Cd%3D%5Cfrac%7B10%20%5Csqrt%7B10%7D%20%7D%7B10%7D%5C%5Cd%3D%5Csqrt%7B10%7D)
Answer:
Upper quartile: 38
Lower quartile: 19
Answer:
10) 8
Step-by-step explanation: