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Marco would like to hang a banner over his shoe store. He has two ladders and would like to know high above the ground each ladder will allow him to place the banner.
His 13- foot ladder leans against the building at a point that is 11.3 feet above the ground.
At what height would a 15-foot ladder touch the building if both ladders form the same angle with the ground? Round your answer to the nearest tenth.
____________ feet
A 15-foot ladder leaning up against a wall at the same angle as the 13-foot ladder would touch the wall at _______ feet.
Explain how you determined your answer (explain all work used to determine the answer).
Find the angle that the 15-foot ladder makes with the building. Round your answer to the nearest tenth. ____________ degrees
The 15-foot ladder makes a ________ degree angle with the building.
Explain and show the work you used to solve the problem. Justify the answer you have.
Will the 13-foot ladder make the same angle with the building? Justify your reasoning.
Solve the differential equation:
a) yk - y(k-1) + 2y(k-2) = k² + 5k
b) y(k+2) - 4y(k+1) + yk = 3k +2^k
In LHS yk , y(k-1) and so on is not in multiply but the k part is written in down to y( like yk is not y×k but the k is written in right down of y).
Marco would like to hang a banner over his shoe store. He has two ladders and would like to know high above the ground each ladder will allow him to place the banner.
Question 1
His 13- foot ladder leans against the building at a point that is 11.3 feet above the ground.
At what height would a 15-foot ladder touch the building if both ladders form the same angle with the ground? Round your answer to the nearest tenth.
____________ feet
Question 2
A 15-foot ladder leaning up against a wall at the same angle as the 13-foot ladder would touch the wall at _______ feet.
Explain how you determined your answer (explain all work used to determine the answer). Justify your answer.
Question 3
Find the angle that the 15-foot ladder makes with the building. Round your answer to the nearest tenth.
____________ degrees
Question 4
The 15-foot ladder makes a ________ degree angle with the building.
Explain and show the work you used to solve the problem. Justify the answer you have.
Let X1, X2, X3 be uniform random variables on the interval (0, 1) with Cov(Xi , Xj ) = 1/24 for i, j = 1, 2, 3, i i != j. Calculate the variance of 2X1 + X2 − X3.
At a production process, the produced items are tested for defects. A defective unit is classified as such with probability 0.9, whereas a correct unit is classified as such with probability 0.85. Furthermore, 10% of the produced units are defective. What is the conditional probability that a unit is correct, given that is has been classified as defective?
Consider a box containing 25% white, 50% black and 25% blue balls. Extract with replacement 2 balls. Denote by X and Y the random variables representing the number of white and, respectively, black balls obtained. Find the distribution of XY and calculate ρ(X, Y ).
On the probability field {Ω, K, P}, consider two independent events A and B with P(A) = 1/2, P(B) = 2/5. Calculate the conditional probability that both A and B occur, given that at least one of the events A and B has occurred.
Suppose we roll two dice and let X be the maximum of the two numbers obtained and let Y be their minimum. Write down the distribution tables of X, Y and Z = (X, Y ).
On the probability field {Ω, K, P}, consider two independent events A and B with P(A) = 1/2, P(B) = 2/5. Calculate the conditional probability that both A and B occur, given that at least one of the events A and B has occurred.
The results of a state-wide examination of the reading skills of sixth-grade students were
normally distributed, with a mean score of 104 and a standard deviation of 16. The
students in the top 10% are to receive an award, and those in the bottom 14% will be
required to take a special reading class.
a. What score does a student need in order to receive an award?
b. What is the cut-off score that will be used to determine whether a student will be
required to take the special reading class?
