Answer: There are no real roots.
Step-by-step explanation:
To find the roots of the function
f(x) = (2^x − 1) - (x2 + 2x − 3) with x ∈ R.
First open the bracket
2^x - 1 - x^2 - 2x + 3 = 0
Rearrange and collect the like terms
2x^2 - x^2 - 2x + 3 - 1= 0
X^2 - 2x + 2 = 0
Factorizing the above equation will be impossible, we can therefore find the root by using completing the square method or the quadratic formula.
X^2 - 2x = - 2
Half of coefficient of x is 1
X^2 - 2x + 1^2 = -2 + 1^2
( x - 1 )^2 = - 1
( x - 1 ) = +/- sqrt(-1)
X = -1 + sqrt (-1) or -1 - sqrt (-1)
The root of the function is therefore
X = -1 + sqrt (-1) or -1 - sqrt (-1)
Since b^2 - 4ac of the function is less than zero, we can therefore conclude that there is no real roots
\left[a _{3}\right] = \left[ \frac{ - b^{2}}{6}+\frac{\frac{ - b^{4}}{3}+\left( \frac{-1}{3}\,i \right) \,\sqrt{3}\,b^{4}}{2^{\frac{2}{3}}\,\sqrt[3]{\left( -1296 - 432\,b^{2} - 16\,b^{6}+\sqrt{\left( 1679616+1119744\,b^{2}+186624\,b^{4}+41472\,b^{6}+13824\,b^{8}\right) }\right) }}+\frac{\frac{ - \sqrt[3]{\left( -1296 - 432\,b^{2} - 16\,b^{6}+\sqrt{\left( 1679616+1119744\,b^{2}+186624\,b^{4}+41472\,b^{6}+13824\,b^{8}\right) }\right) }}{24}+\left( \frac{1}{24}\,i \right) \,\sqrt{3}\,\sqrt[3]{\left( -1296 - 432\,b^{2} - 16\,b^{6}+\sqrt{\left( 1679616+1119744\,b^{2}+186624\,b^{4}+41472\,b^{6}+13824\,b^{8}\right) }\right) }}{\sqrt[3]{2}}\right][a3]=⎣⎢⎢⎢⎢⎡6−b2+2323√(−1296−432b2−16b6+√(1679616+1119744b2+186624b4+41472b6+13824b8))3−b4+(3−1i)√3b4+3√224−3√(−1296−432b2−16b6+√(1679616+1119744b2+186624b4+41472b6+13824b8))+(241i)√33√(−1296−432b2−16b6+√(1679616+1119744b2+186624b4+41472b6+13824b8))⎦⎥⎥⎥⎥⎤
Answer:
0.6154 = 61.54% probability that the student is an undergraduate
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Foreign
Event B: Undergraduate.
There are four times as many undergraduates as graduate students
So 4/5 = 80% are undergraduate students and 1/5 = 20% are graduate students.
Probability the student is foreign:
10% of 80%
25% of 20%. So
Probability that a student is foreign and undergraduate:
10% of 80%. So
What is the probability that the student is an undergraduate?
0.6154 = 61.54% probability that the student is an undergraduate
Answer:yes
Step-by-step explanation:
Answer:
96
Step-by-step explanation:
12.50 + 18.50 + 20 + 20 + 13 + 12 = 96
