Answer:
1st option: 55 + 19.50m = 250
Step-by-step explanation:
Answer:

Step-by-step explanation:
Consider the selling of the units positive earning and the purchasing of the units negative earning.
<h3>Case-1:</h3>
- Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y
- Mr.A earns Rs6000
So, the equation would be

<h3>Case-2:</h3>
- Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z
- Mr B neither lose nor gain meaning he has made 0₹
hence,

<h3>Case-3:</h3>
- Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z
- Mr.C earns 13000₹
therefore,

Thus our system of equations is

<u>Solving </u><u>the </u><u>system </u><u>of </u><u>equations</u><u>:</u>
we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:

Now solve the equation accordingly:

Solving the equation for x and y yields:

plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,

Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437
Answer:
The standard deviation of the following data set is 32.2
Step-by-step explanation:
step 1
Find the mean
we have
![[56,78,123,34,67,9,20]](https://tex.z-dn.net/?f=%5B56%2C78%2C123%2C34%2C67%2C9%2C20%5D)
Sum the data and divided by the number of elements
![[56+78+123+34+67+91+20]/7=469/7=67](https://tex.z-dn.net/?f=%5B56%2B78%2B123%2B34%2B67%2B91%2B20%5D%2F7%3D469%2F7%3D67)
step 2
For each number: subtract the Mean and square the result
![[(56-67)^{2},(78-67)^{2},(123-67)^{2},(34-67)^{2},(67-67)^{2},(91-67)^{2},(20-67)^{2}]](https://tex.z-dn.net/?f=%5B%2856-67%29%5E%7B2%7D%2C%2878-67%29%5E%7B2%7D%2C%28123-67%29%5E%7B2%7D%2C%2834-67%29%5E%7B2%7D%2C%2867-67%29%5E%7B2%7D%2C%2891-67%29%5E%7B2%7D%2C%2820-67%29%5E%7B2%7D%5D)
![[121,121,3,136,1,089,0,576,2,209]](https://tex.z-dn.net/?f=%5B121%2C121%2C3%2C136%2C1%2C089%2C0%2C576%2C2%2C209%5D)
step 3
Work out the mean of those squared differences
This value is called the "Variance"
step 4
Take the square root of the variance
This seems like a right triangle problem.
So assuming 14 feet is the hypotenuse and 4 feet is a leg of the right triangle, we can use the pythagorean theorem (
) to solve for the height of the house, in which we shall name it x.
So, the equation is
.
Solve for x:
16+x^{2}= 196
x^{2}= 196-16
x^{2}= 180
x = 6√5 feet
Hope this helps!
Answer:
∠1 = 50°
∠2 = ∠3 = 130°
Step-by-step explanation:
In an isosceles trapezoid, such as this one, the angles at either end of a base are congruent:
∠1 ≅ 50°
∠2 ≅ ∠3
The theorems applicable to transversals and parallel lines also apply to the sides joining the parallel bases. In particular, "consecutive interior angles are supplementary." That is, angles 1 and 2 are supplementary, for example.
∠2 = 180° -∠1 = 180° -50° = 130°
We already know angle 3 is congruent to this.
∠1 = 50°
∠2 = ∠3 = 130°
_____
<em>Additional comment</em>
It can be easier to see the congruence of the base angles if you remove the length of the shorter base from both bases. This collapses the figure to an isosceles triangle and makes it obvious that the base angles are congruent.
Alternatively, you can drop an altitude to the longer base from each end of the shorter base. That will create two congruent right triangles at either end of the figure. Those will have congruent corresponding angles.