D. 1/3
A cube root can be written as an exponent: 1/3
![\sqrt[3]{x} = x^{\frac{1}{3} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D)
Answer:
{GT, GH, BT, BH, RT, RH};
1 /5;
Mutually exclusive ;
Not mutually exclusive.
Step-by-step explanation:
Given :
Green cards, G = 4
Blue cards, B = 4
Red cards, R = 2
For a coin toss :
{H, T}
A card is picked, then a coin is tossed :
Sample space :
{GT, GH, BT, BH, RT, RH}
2.) probability of picking a green card, then probability of landing a head on a coin toss
P(A) = number of required outcome / Total possible outcomes
P(A) = P(green card) * P(Head)
P(A) = (4 / 10) * (1/2)
P(A) = 4 /20
P(A) = 1/5
C.)
Both A and B are mutually exclusive, since both event A and event B cannot occur together, since both red and green cannot be picked during a single pick, this either a red is picked or green is picked, then they are A and B are mutually exclusive.
D.) Event A and C are not mutually exclusive, picking a green card, event A and picking a red or blue card, event B. Both event can happen simultaneously, hence, event A and B are not mutually exclusive.
A) There are a number of ways to compute the determinant of a 3x3 matrix. Since k is on the bottom row, it is convenient to compute the cofactors of the numbers on the bottom row. Then the determinant is ...
1×(2×-1 -3×1) -k×(3×-1 -2×1) +2×(3×3 -2×2) = 5 -5k
bi) Π₁ can be written using r = (x, y, z).
Π₁ ⇒ 3x +2y +z = 4
bii) The cross product of the coefficients of λ and μ will give the normal to the plane. The dot-product of that with the constant vector will give the desired constant.
Π₂ ⇒ ((1, 0, 2)×(1, -1, -1))•(x, y, z) = ((1, 0, 2)×(1, -1, -1))•(1, 2, 3)
Π₂ ⇒ 2x +3y -z = 5
c) If the three planes form a sheath, the ranks of their coefficient matrix and that of the augmented matrix must be 2. That is, the determinant must be zero. The value of k that makes the determinant zero is found in part (a) to be -1.
A common approach to determining the rank of a matrix is to reduce it to row echelon form. Then the number of independent rows becomes obvious. (It is the number of non-zero rows.) This form for k=-1 is shown in the picture.
Answer:
w= 1
Step-by-step explanation:
hope this helps :)
For this case we propose a system of equations:
x: Variable that represents the amount of hours that Olivia's mother drove
y: Variable that represents the amount of hours that Olivia's father drove
So, we have:

From the first equation we have:

Substituting in the second equation:

Thus, Olivia's father drove 3 hours.

Olivia's mother drove 11 hours.
Answer:
