We have been given that Layana’s house is located at
on a map. The store where she works is located at
.
We are asked to find the distance from Layana’s home to the store
We will use distance formula to solve our given problem.
Let us convert our given coordinates in improper fractions.
![2\frac{2}{3}\Rightarrow \frac{8}{3}](https://tex.z-dn.net/?f=2%5Cfrac%7B2%7D%7B3%7D%5CRightarrow%20%5Cfrac%7B8%7D%7B3%7D)
![7\frac{1}{3}\Rightarrow \frac{22}{3}](https://tex.z-dn.net/?f=7%5Cfrac%7B1%7D%7B3%7D%5CRightarrow%20%5Cfrac%7B22%7D%7B3%7D)
![-1\frac{1}{3}\Rightarrow -\frac{4}{3}](https://tex.z-dn.net/?f=-1%5Cfrac%7B1%7D%7B3%7D%5CRightarrow%20-%5Cfrac%7B4%7D%7B3%7D)
Now we will use distance formula to solve our given problem.
![D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Upon substituting coordinates of our given point in above formula, we will get:
![D=\sqrt{(\frac{22}{3}-\frac{22}{3})^2+(\frac{8}{3}-(-\frac{4}{3}))^2}](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B%28%5Cfrac%7B22%7D%7B3%7D-%5Cfrac%7B22%7D%7B3%7D%29%5E2%2B%28%5Cfrac%7B8%7D%7B3%7D-%28-%5Cfrac%7B4%7D%7B3%7D%29%29%5E2%7D)
![D=\sqrt{(0)^2+(\frac{8}{3}+\frac{4}{3})^2}](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B%280%29%5E2%2B%28%5Cfrac%7B8%7D%7B3%7D%2B%5Cfrac%7B4%7D%7B3%7D%29%5E2%7D)
![D=\sqrt{0+(\frac{8+4}{3})^2}](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B0%2B%28%5Cfrac%7B8%2B4%7D%7B3%7D%29%5E2%7D)
![D=\sqrt{(\frac{12}{3})^2}](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B%28%5Cfrac%7B12%7D%7B3%7D%29%5E2%7D)
![D=\sqrt{(4)^2}](https://tex.z-dn.net/?f=D%3D%5Csqrt%7B%284%29%5E2%7D)
![D=4](https://tex.z-dn.net/?f=D%3D4)
Therefore, the distance from Layana's home to the store is 4 units and option A is the correct choice.
Answer:
3
Step-by-step explanation:
Let's say we had a bag of 10 marbles in which 3 are red. The probability of pulling out a red marble is 3/10 = 0.30 = 30%
If we do not replace that red marble, then there are 3-1 = 2 red marbles left and 10-1 = 9 marbles overall leftover. The probabiity of getting another red marble is 2/9 = 0.222 = 22.2% approximately. The probability has changed. The second event probability is dependent on the first event.
If we pulled out a non-red marble on the first selection, then we would have 3 red marbles out of 9 left over so 3/9 = 1/3 = 0.333 = 33.3% is the approximate probability of getting a red marble on the second selection. We see that this is not the same as the 30% we got earlier.
The second event depends entirely on what happens during the first event, so we say the second event is dependent on the first. Or more shortly, "the two events are dependent".
So any time there is the key phrase "no replacement" it means "dependent events".
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Based on what is discussed in the section above, this means that answer choices A and C are NOT independent events.
The other two answer choices do describe independent events. Why? Because the act of flipping a coin does not affect the outcome of the spinner, and vice versa. This is assuming the coin and spinner are kept separate. The probability for one item's outcome remains the same regardless of what happens to the other item's outcome. The same applies to rolling 4 number cubes (aka dice).
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<h3>Final Answers: Choice B and choice D</h3>
Cos 52 = 0.6157
sin 42 = cos 48 = 2/3 (because 42 + 38 = 90 - complementary angles)
if tan 20,5 = 3/8 then tan 69.5 wil = 1 / 3/8 = 8/3
Answer:
The correct answer is option C. 3
Step-by-step explanation:
It is given an expression in variable x
(x² + 3x²)/(x + 1) ÷ (x² - 9)/(3x + 3) * (x - 3)/x
<u>To find the simplified answer</u>
x² + 3x² = x(x + 3)
x² - 9 = (x + 3)(x - 3)
The given expression can be written as,
(x² + 3x²)/(x + 1) ÷ (x² - 9)/(3x + 3) * (x - 3)/x
= x(x + 3)/(x + 1) * 3(x + 1)/(x + 1)(x - 1) * (x -3)/x
=[ x(x +3) * 3(x +1) * (x -3)]/[(x + 1) * (x + 3)(x - 3) *x]
= 3
The correct answer is option C. 3