I'd start by writing an equation for each of the right triangles. (Pythagorean theorem)
y² + 9² = z²
x² + z² = (4+9)²
4² + y² = x²
we want to find z so combine the equations by substituting the other variables x,y out.
substitute y² for (x² - 4²) in 1st equation.
(x² - 4²) + 9² = z²
now by rearranging the 2nd equation we can substitute x² for (13² - z²)
(13² - z²) - 4² + 9² = z²
169 - z² - 16 + 81 = z²
234 - z² = z²
234 = 2z²
234/2 = z²
117 = z²
√(117) = z
√(9*13) = z
3√(13) = z
13 goes in the box
Answer:
He use 97 pound of type A coffee
Step-by-step explanation:
Let's call A the pounds of type A coffee that Austin used this month and B the pounds of type B coffee that Austin used this month.
From the sentence: Type A coffee costs bill $5.70 per pound and type B coffee costs $4.65 per pound and the total cost is $943.50, we can formulated the equation 1 as:
5.70*A + 4.65*B=943.50
Because the total cost is the sum of the cost of every type of coffee.
Additionally, from the sentence: This month bill made 181 pounds of the blend, we can formulate the equation 2 as:
A + B = 181
Solving for B, we get:
B = 181 - A
Now, for find the value of A we need to replacing this last equation on equation 1, and solving for A as:
5.70*A + 4.65*B=943.50
5.70*A + 4.65*(181-A)=943.50
5.70*A + 841.65 - 4.65*A = 943.50
5.70*A - 4.65*A = 943.50 - 841.65
1.05*A = 101.85
A = 101.85/1.05
A = 97
So, this month, he use 97 pound of type A coffee.
The answer would be 4.6 x 10^-5
Answer:
130.81
Step-by-step explanation:
We solve this question using z score formula
z = (x-μ)/σ,
where from the question:
x is the raw score = ?
μ is the population mean = 100
σ is the population standard deviation = 15
We are told in the question that:
Mensa is an international society that has one and only one qualification for membership: a score in the top 2% on an IQ test.
The top 2% means a score in the 98th percentile
The z score of the 98th percentile = 2.054
Hence:
2.054 = x - 100/15
Cross Multiply
2.054 × 15 = x - 100
30.81 = x - 100
x = 30.81 + 100
x = 130.81
The IQ score that one should have in order to be eligible for Mensa is the score of 130.81
Well the constant of variation is vital yet if there is a graph, table, or two points provided then you can find the slope. You will have to use different equations and steps of course.
