The digit 7 is in the tens place so 74 will become either 70 or 80 after rounding off to the nearest ten. Draw a number line with 3 numbers on it: 70, 75 and 80. (Both possible rounded off numbers and the number in the middle.
Answer:
f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.
Step-by-step explanation:
The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.
* if x>1, then x-1>0.
* Also since the parabola opens up, then y>5.
So let's solve y=(x-1)^2+5 for x.
Subtract 5 on both sides:
y-5=(x-1)^2
Take square root of both sides:
Plus/minus sqrt(y-5)=x-1
We want x-1>0:
Sqrt(y-5)=x-1
Add 1 on both sides:
Sqrt(y-5)+1=x
Swap x and y:
Sqrt(x-5)+1=y
x>5
y>1
Answer is 2 batches. Because she has five eggs and the plain pasta uses 2 so if she’s trying to do both of them she’ll only have two eggs left and using 8 cups of flour. Making two batches of spinach pasta.
Step-by-step explanation:
To check out how efficient or accurate a model is, we use the akaike information criterion or the Bayesian. If the AIC or BIC are lower, then this model would be better. They are also used to control for model complexity
Akaike information criterion = 2k-2ln where k is the number of parameter. A higher k gives a higher AIC.
In the real world complex models are discouraged and avoided since
1. They cause data to be over fitted and can capture noise and information from this data.
2. They are complex and therefore difficult to interpret
3. They consume a lot of time and computing them has several inefficiencies.
Using these two as measure of performance, we can select optimal choice of independent variable.
With forward/backward regression, we are able to put new variables in the model or remove from it. The best is the one with lowest AIC.
Answer:
B
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 )
Then the discriminant is
Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real irrational roots
• If b² - 4ac > 0 and a perfect square then 2 real rational roots
• If b² - 4ac = 0 then 1 real double root
• If b² - 4ac < 0 then 2 complex roots
Given
x² + 3x - 7 = 0 ← in standard form
with a = 1, b = 3, c = - 7 , then
b² - 4ac
= 3² - (4 × 1 × - 7) = 9 + 28 = 37
Since b² - 4ac > 0 then 2 real irrational roots
