Answer:
The conjugate of 2i + 9 = -2i + 9
Product of (2i+9) and (2i+9) is 36i + 77
Step-by-step explanation:
Given - 2i + 9
To find - Find the conjugate and product of the following surds
Proof -
We know that,
The sum and difference of two simple quadratic surds are said to be conjugate surds to each other.
To find a complex conjugate, simply change the sign of the imaginary part (the part with the i ).
So,
The conjugate of 2i + 9 = -2i + 9
Now,
Product of surd (2i+9) is
(2i+9)(2i+9) = 2i(2i) + 2i(9) + 9(2i) + 9(9)
= 4i² + 18i + 18i + 81
= -4 + 36i + 81 { because i² = -1 }
= 77 + 36i
⇒Product of (2i+9) and (2i+9) is 36i + 77
Answer:
-5x
Step-by-step explanation:
The linear term is the term with the variable to the first power. Here, it is -5x.
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<em>Comment on other terms</em>
2x^2 has x to the 2nd power
-12 has x to the 0 power (no variable)
Answer:
1/4
Step-by-step explanation:
2 divided by 8 is .25 which is equal to 1/4
Answer:
212 children, and 265 adults
Step-by-step explanation:
To find the number of children and adults, we can set up a systems of equations.
x= number of children
y= number of adults
Equation 1: Price
1.50x+2.25y=914.25
Equation 2: Total number of people
x+y=477
Now, let's solve the equation using substitution.
Rearrange the second equation to solve for one variable.
x+y=477
x=477-y
Now plug x equals into the first equation, and solve for y.
1.50x+2.25y=914.25
1.50(477-y)+2.25y=914.25
715.5-1.50y+2.25y=914.25
715.5+0.75y=914.25
0.75y=198.75
y=265
We just solved for the number of adults. Now let's plug y equals into the second equation to find the number of children.
x+y=477
x+265=477
x=212
Answer:
a. E(x) = 3.730
b. c = 3.8475
c. 0.4308
Step-by-step explanation:
a.
Given
0 x < 3
F(x) = (x-3)/1.13, 3 < x < 4.13
1 x > 4.13
Calculating E(x)
First, we'll calculate the pdf, f(x).
f(x) is the derivative of F(x)
So, if F(x) = (x-3)/1.13
f(x) = F'(x) = 1/1.13, 3 < x < 4.13
E(x) is the integral of xf(x)
xf(x) = x * 1/1.3 = x/1.3
Integrating x/1.3
E(x) = x²/(2*1.13)
E(x) = x²/2.26 , 3 < x < 4.13
E(x) = (4.13²-3²)/2.16
E(x) = 3.730046296296296
E(x) = 3.730 (approximated)
b.
What is the value c such that P(X < c) = 0.75
First, we'll solve F(c)
F(c) = P(x<c)
F(c) = (c-3)/1.13= 0.75
c - 3 = 1.13 * 0.75
c - 3 = 0.8475
c = 3 + 0.8475
c = 3.8475
c.
What is the probability that X falls within 0.28 minutes of its mean?
Here we'll solve for
P(3.73 - 0.28 < X < 3.73 + 0.28)
= F(3.73 + 0.28) - F(3.73 + 0.28)
= 2*0.28/1.3 = 0.430769
= 0.4308 -- Approximated
