Answer:
0.3101001000......
0.410100100010000....
Step-by-step explanation:
To find irrational number between any two numbers, we first need to understand what a rational and irrational number is.
Rational number is any number that can be expressed in fraction of form 
. Since q can be 1, all numbers that terminate are rational numbers. Example: 1, 12.34, 123.66663
Irrational number on the other hand can't be expressed as a fraction and do not terminate. Also, there is no pattern in numbers i.e. there is no repetition in numbers after the decimal point.
For example: 3.44444..... can be expressed as rational number 3.45.
But 3.414114111.... is an irrational number as there no pattern observed. Also,it does not terminate.
We can find infinite number of irrational numbers in between two rational numbers.
<u>Irrational numbers in between 0.3 and 0.7:</u>
0.3101001000......
0.410100100010000....
0.51010010001.......
0.6101001000....
There are many others. We can choose any two as answers.
Answer:
The solutions are −5 and 1 .
Let
A = event that the student is on the honor roll
B = event that the student has a part-time job
C = event that the student is on the honor roll and has a part-time job
We are given
P(A) = 0.40
P(B) = 0.60
P(C) = 0.22
note: P(C) = P(A and B)
We want to find out P(A|B) which is "the probability of getting event A given that we know event B is true". This is a conditional probability
P(A|B) = [P(A and B)]/P(B)
P(A|B) = P(C)/P(B)
P(A|B) = 0.22/0.6
P(A|B) = 0.3667 which is approximate
Convert this to a percentage to get roughly 36.67% and this rounds to 37%
Final Answer: 37%
We are given the following:
- parabola passes to both (1,0) and (0,1)
<span> - slope at x = 1 is 4 from the equation of the tangent line </span>
<span>First, we figure out the value of c or the y intercept, we use the second point (0, 1) and substitute to the equation of the parabola. W</span><span>hen x = 0, y = 1. So, c should be equal to 1. The</span><span> parabola is y = ax^2 + bx + 1 </span>
<span>Now, we can substitute the point (1,0) into the equation,
</span>0 = a(1)^2 + b(1) + 1
<span>0 = a + b + 1
a + b = -1 </span>
<span>The slope at x = 1 is equal to 4 which is equal to the first derivative of the equation.</span>
<span>We take the derivative of the equation ,
y = ax^2 + bx + 1</span>
<span>y' = 2ax + b
</span>
<span>x = 1, y' = 2
</span>4 = 2a(1) + b
<span>4 = 2a + b </span>
So, we have two equations and two unknowns,<span> </span>
<span>2a + b = 4 </span>
<span>a + b = -1
</span><span>
Solving simultaneously,
a = 5 </span>
<span>b = -6</span>
<span>Therefore, the eqution of the parabola is y = 5x^2 - 6x + 1 .</span>
