Answer:
a: 16807
b: 0.0000595
Step-by-step explanation:
(a): We have 7 possibilities of numbers, and we need to choose 5 numbers that can repeat. So, for each of the 5 numbers, we have 7 possibilities. To determine how many codes are possible, we just need to multiply the number of possibilities of each of the 5 numbers, so we have 7x7x7x7x7, or 7^5, which is 16807 possibilities.
(b): to put the correct code in the first try, we need to find the exact combination (just one combination) among these 16807 possibilities, so the probability is 1/16807, which is 0.0000595, or 0.00595%.
Given:
The function, f(x) = -2x^2 + x + 5
Quadratic equation: 0 = -2x^2 + x +5
where a = -2
b = 1
c = 5
The discriminate b^2 - 4ac = 41
To solve for the zeros of the quadratic function, use this formula:
x = ( -b +-√ (b^2 - 4ac) ) / 2a
x = ( 1 + √41 ) / 4 or 1.85
x = ( 1 - √41 ) / 4 or -1.35
Therefore, the zeros of the quadratic equation are 1.85 and -1.35.
Answer:
The max is 85F
The min is 75F
Step-by-step explanation:
For the max 80+5=85F
For the min 80-5=75F
7x^3 is not equivalent to the other varieties of 7x
Answer:
Step-by-step explanation:
First, let us find the gradient of AB:
Gradient of AB = 
= 
We also need to know that The <em>product of gradients which are perpendicular to each other is -1</em>. Using this idea, we can find the gradient of the perpendicular bisector:
(Gradient of perpendicular bisector)( ) = -1
Gradient of perpendicular bisector = 
Now, we need to know at which coordinates the perpendicular bisector intersects AB. <em>A perpendicular bisector bisects a line to two equal parts</em>. Hence the <em>coordinates of the intersection point is the midpoint of AB</em>. Thus,
Coordinates of intersection = ( 
, 
)
= ( 2, 1 )
Now, we can construct our equation. The equation of a line can be formed using the formula 
where 
is the gradient and the line passes through 
. Hence by substituting the values, we get:
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