Answer:
Randomly selecting a six of diamonds - 1 / 52
Randomly selecting a 7, 8, 9 or 10 - 4 / 13
Step-by-step explanation:
There is only 1 six of diamonds in a standard deck of cards. There are 52 cards in a deck, thus the probability of pulling a six of diamonds is 1 in 52.
There are 4 of each card in a deck. so they are 4 7's, 4 8's. 4 9's and 4 10's. And there are a total of 52 cards in a deck. So the probability of pulling a 7,8,9 or 10 are 4 + 4 + 4 + 4 in 52
4 + 4 + 4 + 4 = 16
16 / 52 simplified is 4 / 13 Therefore the is a 4 in 13 chance of pulling a 7 8 9 or 10
The other ones are correct
Answer:
The equation is 
Step-by-step explanation:
Let the quadratic function be

The point (-4,9) must satisfy this function,


The point (0,-7) must also satisfy this function,


The point (1,-1) must also satisfy this function,


We put equation 2 into equation 1 to get;



We again put equation 2 into equation 3 to get;


We add equation 5 and 6 to get;


We put
into equation 6 to get;



The equation is therefore 
Answer:
63%
Step-by-step explanation:
This is a problem of conditional probability.
The two events that are given are:
- Car stuck in the snow - Let it be event S. P(S) = 70% = 0.70
- Require a tow truck - Let it be event T.
We have to find the probability of being stuck in the snow AND requiring a tow truck which can be given as P(S and T)
We are also given the conditional probability, which is P(T | S) = 90% = 0.90
Using the given formula for our case we can modify the formula as:


Therefore, there is 63% (0.63) chance that you will get stuck in the snow with your car AND require a tow truck to pull you out


Take the derivatives of each to get the tangent vectors:


Take the cross product of the tangent vectors to get a vector that is normal to both lines:

The two given lines intersect when
:

that is, at the point (6, 4, 4).
The line perpendicular to both of the given lines through the origin is obtained by scaling the normal vector found earlier by
; translate this line by adding the vector
to get the line we want,

