Answer:
±√6
Step-by-step explanation:
is your expression first muiltiply out the 10 to get 15n= 10n+10 3/n next subtract 10 n from both sides to get 5n=10+3/n multiply both sides by n to get 5n^2=13 combine both sides and use the quadratic equation to solve to get your solution of ±√6
Answer:
Option A.
Step-by-step explanation:
The table made by the painter shows the amount of paint required to cover a certain amount of area of the wall.
Amount of paint is directly proportional to the area covered
In other words Amount of paint (y) ∝ Area covered (x)
y ∝ x
As we know when proportionality sign is removed, a constant known as proportionality constant is multiplied with the variable.
So y = k(x) where k is the proportionality constant
Now from the table to cover the area of 64 square feet, 4 pints of paint is required.
Now from the formula
4 = 64x
x =
Now we have to calculate the amount of paint required to cover the area of 256 square feet.
y =
y = 16 pints
Therefore, 16 pints of the paint will be required to cover 256 square feet.
Option A is correct.
Answer:
Step-by-step explanation:
<u>Implicit Differentiation</u>
We use implicit differentiation when it's not possible to find an expression of y as a function of x, or the expression is very hard to differentiate.
The implicit differentiation takes the original equation and differentiates each term, usually applying the product, quotient, power, or other similar rules.
In the course of the differentiation, we'll use f' as the derivative of f.
We'll find y'=dy/dx in the following equation:
Differentiating:
The derivative of a constant is 0, thus:
The first term is a product of variables, so we apply the product rule:
The second term is the power of y. We apply the chain rule:
Operating:
Since x'=1:
Subtracting 3y:
Take y' as a common factor:
Solve for y':
Answer:
a. 3
b. [5,6]
c.
d.Game theory to predict future outcomes based on past results.
Step-by-step explanation:
a. Median is defined as the middlemost data point in a data set of data points arranged in a ranking order.
-Arranging our data points in Ranking order:
0,0,1,1,2,2,3,5,5,5,6,8,8
-Our set has 13 entries. The 7th term is the median Value.
#Hence, the median value of our data set is 3
b. Increasing the median value by 2. And let x and y be the two new scores
-From a above, median is 3:
-The new median value is 5. Adding two data points, makes the 8Th term the median value.
-Given that values of 5 was originally the 8th term, For the median value to be 5,both x and y have to have a value of 5, or one must be a 5 and the next a higher value:
-Hence, [5,6], 5,5] are both possible pairs of x and y
c. From the definition of median in a above,
#If the data points are an odd number of entries, then the median value is (n/2)+1, hence a whole number.
#If the data points are an odd number of entries, then the median value is (n/2), hence a decimal number e.g 2.5:
d. Using game theory, real-world scenarios for such situations asruns in baseball games can be predicted from past outcomes.
-As such, we can predict that the next two games are likely to be in the range of the first 13 scores.