Answer:
8:10 and 12: 15
Step-by-step explanation:
we have to multiply
Answer:
The coordinates for the point on a circle of radius at an angle of are At the radius of the unit circle, 1, serves as the hypotenuse of a 30-60-90 degree right triangle, as shown in (Figure).
Step-by-step explanation:
Answer:
Step-by-step explanation:
The equation Thomas wrote is:
...equation 1
Let us subtract 3x from both sides to get:
We now multiply through by 2 to get:
....equation 2
We can see that equation one and two are equivalent and hence have the same solution.
Therefore Sandra's equation is
Answer:
What is the sample variance of bottle weight 2.33
Step-by-step explanation:
First find the mean. The mean of the bottle weight is obtained by taking the ratio of the sum of ages and total number of ages.
Mean = (4+2+5+4+5+2+6) / 7
= 28 / 7
= 4
Sample Variance = ![\frac{\left[\begin{array}{ccc}(4-4)^{2} +(2-4)^{2} +\\(5-4)^{2} + (4-4)^{2} +\\(5-4)^{2} + (2-4)^{2} +\\(6-4)^{2}\end{array}\right]}{7-1}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%284-4%29%5E%7B2%7D%20%2B%282-4%29%5E%7B2%7D%20%2B%5C%5C%285-4%29%5E%7B2%7D%20%2B%20%284-4%29%5E%7B2%7D%20%2B%5C%5C%285-4%29%5E%7B2%7D%20%2B%20%282-4%29%5E%7B2%7D%20%2B%5C%5C%286-4%29%5E%7B2%7D%5Cend%7Barray%7D%5Cright%5D%7D%7B7-1%7D)
=
= 2.33
5x + 6y = 7 SUBSTITUTION METHOD
2x + 2y = 4
5x + 6y = 7 Solve for either x or y in 1 of the 2 equations.
- 6y - 6y
-----------------------
5x = -6y + 7
----- ------ ----
5 5 5
x = -6/5y + 7/5
2(-6/5y + 7/5) + 2y = 4 Substitute the expression you got for x or y into
-12/5y + 14/5 + 2y = 4 the other equation.
-2/5y + 14/5 = 4
- 14/5 - 14/5
------------------------------
-2/5y = 6/5
-------- --------
- 2/5y - 2/5y
y = -3
5x + 6(-3) = 7 Plug in the value you got for y in step 2 into the
5x - 18 = 7 equation that you didn't use.
+ 18 + 18
------------------
5x = 25
--- -----
5 5
x = 5
(x,y) ⇒ coordinate
(5,-3) ⇒ final answer
