Answer:
y = 2x + 10
Step-by-step explanation:
We are given the slope of the line and the coordinates of one point on the line. Thus, we use the point-slope formula y - k = m(x - h). Here m = 2, h = -3 and k = 4. Therefore we have:
y - 4 = 2(x + 3)
which can be rewritten as y = 2x + 6 + 4, or y = 2x + 10 (Answer D)
<span>Let us denote the amount of investment in the Fund B with x. We know that Fund B returned 8% and that in Fund A Nicole invested </span>$3000 less than the amount she invested in Fund B, so we can write: x-3000<span>Fund A returned 6%.
Interest = 2060
The percent has been converted by multiplying the equation by 100
8x+6(x-3000)= 2060*100
8x+6x-18000=206000
</span><span>14x=206000+18000
14x=224000
x=16000
Nicole invested in Fund B $16000 and in Fund A </span><span> $16000-3000=13000.</span><span>
</span>
Answer:
2.64
Step-by-step explanation:
The 8 in the thousandths place can round up to .64
Answer:
Step-by-step explanation:
Given
Solving (a):
Find k
To solve for k, we use the definition of joint probability function:
Where
Substitute values for the interval of x and y respectively
So, we have:
Isolate k
Integrate y, leave x:
![k \int\limits^2_{0} y {dx} \, [0,x/2]= 1](https://tex.z-dn.net/?f=k%20%5Cint%5Climits%5E2_%7B0%7D%20y%20%7Bdx%7D%20%5C%2C%20%5B0%2Cx%2F2%5D%3D%201)
Substitute 0 and x/2 for y
Integrate x
![k * \frac{x^2}{2*2} [0,2]= 1](https://tex.z-dn.net/?f=k%20%2A%20%5Cfrac%7Bx%5E2%7D%7B2%2A2%7D%20%5B0%2C2%5D%3D%201)
![k * \frac{x^2}{4} [0,2]= 1](https://tex.z-dn.net/?f=k%20%2A%20%5Cfrac%7Bx%5E2%7D%7B4%7D%20%5B0%2C2%5D%3D%201)
Substitute 0 and 2 for x
![k *[ \frac{2^2}{4} - \frac{0^2}{4} ]= 1](https://tex.z-dn.net/?f=k%20%2A%5B%20%5Cfrac%7B2%5E2%7D%7B4%7D%20-%20%5Cfrac%7B0%5E2%7D%7B4%7D%20%5D%3D%201)
![k *[ \frac{4}{4} - \frac{0}{4} ]= 1](https://tex.z-dn.net/?f=k%20%2A%5B%20%5Cfrac%7B4%7D%7B4%7D%20-%20%5Cfrac%7B0%7D%7B4%7D%20%5D%3D%201)
![k *[ 1-0 ]= 1](https://tex.z-dn.net/?f=k%20%2A%5B%201-0%20%5D%3D%201)
![k *[ 1]= 1](https://tex.z-dn.net/?f=k%20%2A%5B%201%5D%3D%201)
Solving (b): 
We have:
Where
To find , we use:
So, we have:
Integrate x leave y
![P(x > 3y) = \int\limits^2_0 x [0,y/3]dy](https://tex.z-dn.net/?f=P%28x%20%3E%203y%29%20%3D%20%5Cint%5Climits%5E2_0%20%20x%20%5B0%2Cy%2F3%5Ddy)
Substitute 0 and y/3 for x
![P(x > 3y) = \int\limits^2_0 [y/3 - 0]dy](https://tex.z-dn.net/?f=P%28x%20%3E%203y%29%20%3D%20%5Cint%5Climits%5E2_0%20%20%5By%2F3%20-%200%5Ddy)
Integrate
![P(x > 3y) = \frac{y^2}{2*3} [0,2]](https://tex.z-dn.net/?f=P%28x%20%3E%203y%29%20%3D%20%5Cfrac%7By%5E2%7D%7B2%2A3%7D%20%5B0%2C2%5D)
![P(x > 3y) = \frac{y^2}{6} [0,2]\\](https://tex.z-dn.net/?f=P%28x%20%3E%203y%29%20%3D%20%5Cfrac%7By%5E2%7D%7B6%7D%20%5B0%2C2%5D%5C%5C)
Substitute 0 and 2 for y
There is 0.946 liter in 1 quart
3.5/0.946 = 3.6997
~3.7 liters, or C
C is your answer
hope this helps
