84 + x + 59 x + 51 =180
2x + 194 = 180
2x + 194 - 194 = 180 - 194 (subtract both sides by 194)
2x = -14
2x/2 = -14/2 (divide both sides by 2)
x = -7
We have the isosceles triangle were y + 12 = 3x - 5,
and the equilateral triangle. Therefore 3x - 5 = 5y - 4.
From the first equation and the second equation we have:
y + 12 = 5y - 4 <em>subtract 12 from both sides</em>
y = 5y - 16 <em>subtract 5y from both sides</em>
-4y = -16 <em>divide both sides by (-4)</em>
<h3>y = 4</h3>
Substitute the value of y to the first equation:
4 + 12 = 3x - 5
16 = 3x - 5 <em>add 5 to both sides</em>
21 = 3x <em>divide both sides by 3</em>
<h3>x = 7</h3>
<h3>Answer: x = 7 and y = 4</h3>
The given equation -2(11 - 12x) = -4(1 - 6x) has infinite solutions
<u><em>Solution:</em></u>
Given that we have to solve the given expression
Given expression is:
-2(11 - 12x) = -4(1- 6x)
We have to use distributive property to solve the given expression
The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.
Which means,
a(b + c) = ab + ac
Apply this in given expression
-2(11 - 12x) = -4(1-6x)
-22 + 24x = -4 + 24x
When both sides of the equation are simplified, the coefficients are the same, then infinite number of solutions occur
If we end up with the same term on both sides of the equal sign, such as 24x = 24x, then we have infinite solutions
DoE studies, for example do not require control group, since they usually involve models in which the number of variables are substantially smaller than the number of experiments. The DoE analysis provides a description model that shows how the responses or output variables depend on the factor settings or input variables. As long as the unknowns are substantially less than the number of equations, there is very minimal risk of over-fitting.
A) Since you need the probability of the person being a freshman and a C grade student, the probability will be 8/45 (number of C grade student who are freshmen divided by the total number of people)
b) You have to add the two probabilities that you are going to find whenever you see an 'or' function.
Student is a sophomore = 22/45
Student made an A = 7/45
Probability = 22/45 + 7/45
= 29/45
c) Whenever you see an 'and' function, you have to multiply up the probability.
Student is a sophomore = 22/45
Student made an A = 7/45
Probability = 22/45 * 7/45
= 154/2025
d) Student made a D = 5/45
Student is a freshman = 23/45
Probability = 5/45 + 23/45
= 28/45
Hopefully, this made sense.