Pendergast

There are 4 friends - 4 choices for the first friend to be picked up. For every choice of the first picked up, there are 3 friends left - 3 choices for the second friend to be picked up. Following the pattern, 2 choices for the third friend, 1 choice for...

13 years ago

Calm down, it's not that difficult. Your child is making valuable use of his last week in school. Think back to your mathematics background - I'm sure you understand this sufficiently to explain it. 86/9 -- 9*9 = 81, so 86/9 = 9 remainder 5. Find the larg...

13 years ago

I don't understand the question. You want to find a and b, yet you state their values.

13 years ago

I assume the the only forces on the rocket after launch are due to gravity. Gravity exerts an acceleration of -32ft/s^2. The height function h(t), derived from acceleration a(t) = -32ft/s^2, is h(t) = (1/2)(-32ft/s^2)*t^2 + v_0*t + h_0. v_0 is the initial...

13 years ago

Sam has 4 chores to complete - he can choose the order. He has 4 choices for the first chore. For each choice of the first, he can choose 1 of the 3 remaining for the second chore. etc. 4*3*2*1 = 24 This is more generally known as the ordering problem --...

13 years ago

The volume of a cone is given by V = (1/3)*pi*r^2*h. We're given V and h, so solve for r. Remember, the diameter is two times the radius.

13 years ago

Correct.

13 years ago

The 3-dimensional box cannot be described by 2 dimensions.

13 years ago

1), 3) check your algebra 4) I'm not sure where you went wrong on this one. However, sqrt(6)-sqrt(2)/4 is greater than 1 (2.0959 in fact) 2), 5) are correct

13 years ago

Correct

13 years ago

There are 7 bronze trophy winners and 7+14+10=31 classmates in total. 7/31

13 years ago

Assuming fair coins, the probability of obtaining heads on one coin is 0.5. Obtaining two heads has probability 0.5*0.5.

13 years ago

f: T->S is a surjection, so a function g: S->T exists. g takes elements of S to t_i, i in N injectively since f exists. Intuitively g can be rewritten to take elements of S to N. Formally, let h:T->N, with h(t_i) = i. Then h(g): S->N.

13 years ago

The probability of drawing an even chip is 2/5, and the probability of drawing an odd chip (which does not change due to replacement) is 3/5. (2/5)*(3/5)

13 years ago

Correct

13 years ago

Correct

13 years ago

Does the second roll depend on the outcome of the first roll? (If so, we call the events "dependent". If not, we call them "independent")

13 years ago

Correct

13 years ago

Correct

13 years ago

The area is A = pi*r^2 We know A = 3.7994ft^2, we know the value for pi. 3.7994ft^2 = pi*r^2 Solve for r.

13 years ago

The cliff makes a right angle with the ocean. The two legs are 50m (the cliff) and 950m (distance on the ocean from the cliff to the ship). Draw the triangle for that, the rest follows.

13 years ago

Use long division.

13 years ago

Break it into two integrals, integral (sec^2(x)tan(x))dx and integral(-tan(x))dx. Both can be solved using u substitution.

13 years ago

C(7,2)*C(8,3) ways of choosing 2 out of 7 men and 3 out of 8 women. C(n,k) = n!/[(k!)(n-k)!] C(15,5) ways of picking 5 committee members out of 15 probability of selecting 2 men and 3 women is good over total -- C(7,2)*C(8,3)/C(15,5)

13 years ago

Probability of getting 0 heads is 1/2^6 Probability of getting at least 1 head is the complement -- 1 - 1/2^6

13 years ago

4/10 chance of rolling 10 3/10 chance of rolling 5 2/10 chance of rolling 25 1/10 chance of rolling 27 Expected value is the sum of the outcomes multiplied by probabilities = (4/10)(10) + (3/10)(5) + (2/10)(25) + (1/10)(27)

13 years ago

duplicate question

13 years ago

sum of first 5 natural numbers = (5)(6)/2 sum of first 21 natural numbers = (21)(22)/2 sum of first 30 natural numbers = 465 = (30)(31)/2 sum of first n natural numbers = (n)(n+1)/2 -- provable by induction

13 years ago

Let b be the number of boys, g be the number of girls. "54 pupils in class" b + g = 54 "3 more boys than girls" b = g+3

13 years ago

87/400

13 years ago

There are 3 terms, so it is a polynomial. The only variable is x. The highest power of x is x^2 - the degree is 2.

13 years ago

The candle has burned up (8hrs)(0.4cm/hr).

13 years ago

Intersections with y=x^2 at x=-2 and x=4 describes two points: (-2, y=(-2)^2) and (4, y=4^2) Find the line between those two points.

13 years ago