Answer:
a. y = -5x + 4
Step-by-step explanation:
Given the following data;
Slope, m = -5
Intercept, c = 4
Mathematically, the equation of line is given by the formula; y = mx + c
Where;
m is the slope.
x and y are the points
c is the intercept.
Substituting the given parameters, we have;
y = -5x + 4
Answer:
-16 - 30i
Step-by-step explanation:
(3-5i)^2 = (3-5i) * (3-5i)
Applying the "FOIL" method of expanding this expression through multiplication, we get:
9 - 15i - 15i - 25 (since i^2 = -1)
Simplifying this result, we get -16 - 30i
Answer:
a)P=0.42
b) 
Step-by-step explanation:
We have a binomial distribution, since the result of each experiment admits only two categories (success and failure) and the value of both possibilities is constant in all experiments. The probability of getting k successes in n trials is given by:
a) we have k=2, n=10 and p=0.01:
b) We have, 
, Here P is the probability that at least one particle will penetrate the shield, this probabity has to be equal or greater than 0.95. Therefore, this will be equal to subtract from the total probability, the probability that the particles do not penetrate raised to the total number of particles.
Answer:
y = 18 and x = -2
Step-by-step explanation:
y = x^2+bx+c To find the turning point, or vertex, of this parabola, we need to work out the values of the coefficients b and c. We are given two different solutions of the equation. First, (2, 0). Second, (0, -14). So we have a value (-14) for c. We can substitute that into our first equation to find b. We can now plug in our values for b and c into the equation to get its standard form. To find the vertex, we can convert this equation to vertex form by completing the square. Thus, the vertex is (4.5, –6.25). We can confirm the solution graphically Plugging in (2,0) :
y=x2+bx+c
0=(2)^2+b(2)+c
y=4+2b+c
-2b=4+c
b=-2+2c
Plugging in (0,−14) :
y=x2+bx+c
−14=(0)2+b(0)+c
−16=0+b+c
b=16−c
Now that we have two equations isolated for b , we can simply use substitution and solve for c . y=x2+bx+c 16 + 2 = y y = 18 and x = -2
