This is 2.5 standard deviations from the mean.
We find this by subtracting the mean from our value, and dividing by the standard deviation:
(63-38)/10 = 25/10 = 2.5
Answer:
Rs 17 3/4
Step-by-step explanation:
Cost of 6 1/2 m = 115 3/8
Cost of 1 m = x
- x = 115 3/8 ÷ 6 1/2
- x = (115*8 +3)/8 ÷ 13/2
- x = 923/8 × 2/13
- x = 923/(4*13)
- x = 923/52
- x = 17 39/52
- x = 17 3/4
Cost of 1 meter is Rs 17 3/4
Answer:
The standard form of a hyperbola with vertices and foci on the x-axis:
![\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cdfrac%7B%28x-h%29%5E2%7D%7Ba%5E2%7D-%5Cdfrac%7B%28y-k%29%5E2%7D%7Bb%5E2%7D%3D1)
where:
- center: (h, k)
- vertices: (h+a, k) and (h-a,k)
- Foci: (h+c, k) and (h-c, k) where the value of c is c² = a² + b²
- Slopes of asymptotes:
![\pm\left(\dfrac{b}{a}\right)](https://tex.z-dn.net/?f=%5Cpm%5Cleft%28%5Cdfrac%7Bb%7D%7Ba%7D%5Cright%29)
<h3><u>Part 1</u></h3>
The center of the given hyperbola is (0, 0), therefore:
![\implies \dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bx%5E2%7D%7Ba%5E2%7D-%5Cdfrac%7By%5E2%7D%7Bb%5E2%7D%3D1)
Therefore
are the vertices. From inspection of the graph,
.
<h3><u>Part 2</u></h3>
Choose two points on the asymptote with the positive slope:
(0, 0) and (4, 6)
Use the slope formula to find the slope:
![\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{6-0}{4-0}=\dfrac{3}{2}](https://tex.z-dn.net/?f=%5Csf%20slope%5C%3A%28m%29%3D%5Cdfrac%7Bchange%5C%3Ain%5C%3Ay%7D%7Bchange%5C%3Ain%5C%3Ax%7D%3D%5Cdfrac%7B6-0%7D%7B4-0%7D%3D%5Cdfrac%7B3%7D%7B2%7D)
<h3><u>Part 3</u></h3>
Use the <u>slopes of asymptotes</u> formula, compare with the slope found in part 2:
![\implies \dfrac{b}{a}=\dfrac{3}{2}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bb%7D%7Ba%7D%3D%5Cdfrac%7B3%7D%7B2%7D)
Therefore, ![b=3](https://tex.z-dn.net/?f=b%3D3)
<h3><u>
Part 4</u></h3>
Substitute the found values of
and
into the equation from part 1:
![\implies \dfrac{x^2}{2^2}-\dfrac{y^2}{3^2}=1](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bx%5E2%7D%7B2%5E2%7D-%5Cdfrac%7By%5E2%7D%7B3%5E2%7D%3D1)
![\implies \dfrac{x^2}{4}-\dfrac{y^2}{9}=1](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bx%5E2%7D%7B4%7D-%5Cdfrac%7By%5E2%7D%7B9%7D%3D1)
Answer: 20 liters
<u>Step-by-step explanation:</u>
The mixture is 60 liters. The ratio is 2 : 1 (2 parts to one part)
60 ÷ (2 + 1) = one part
60 ÷ 3 = 20
Therefore, the ratio of 2 : 1 means 2(20) liters milk to 1(20) liters water
If we change it to a ratio of 1 : 2, then we have 1(20) liters milk to 2(20) liters water.
2:1 ratio has 20 liters water
1:2 ratio has 40 liters water
The amount of water added is 40 - 20 = 20 liters