Here is a sketch of a curve. YA
The equation of the curve is y = x2 + ax + b
where a and b are integers.
The points (0, -7) and (7, 0) lie on the curve.
Find the coordinates of the turning point of the curve.

The turning point of the graph is at (3,-16)

Step-by-step explanation:

The general equation of curve is given as:

y = x² + ax + b

The two point for which the equation satisfies is (0,-7) and (7,0).

Substitute (0,-7) in the general equation:

y = x² + ax + b

-7 = 0² + a(0) + b

b = -7

Substitute (7,0) in the general equation:

y = x² + ax + b

0 = 7² + 7a + b

Where b = -7

0 = 49 + 7a - 7

0 = 42 + 7a

a = -6

The equation of the curve is:

a = -6 and b = -7

y = x² + ax + b

y = x² - 6x - 7

Graph of the equation is attached below.

We can see that the the turning point of the graph is at (3,-16)

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560