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At a basketball game, a vender sold a combined total of sodas and hot dogs. The number of sodas sold was more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Identical twins must be the same sex, but the sexes of fraternal twins are independent. Find What is the probability of fraternal twins
compute a 90% confidence interval for the mean serum cholesterol level of teenage males in this city. Assume that the sample was taken from a normal distribution. Round your confidence limits to 2 decimal places.
Let A be a real n x n matrix. Show that a linear subspace E of R^n is A-invariant if and only if E is e^{tA} -invariant for all t in R, where e^{tA} is the exponential matrix associated to A.
A bag contains three red marbles, three green ones, one lavender one, two yellows, and four orange marbles. How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?
How many different 4-card hands are possible? How many different 4-card hands contain a number less than 7?
Find the area of a trapezoid with a height of 8 m and bases of 14 m and 19 m.
An apache helicopter of enemy is flying along the path given by y= x2 +7. Find the nearest distance from where a soldier placed at (3,7) can shoot down the helicopter.
Let E be an open and convex subset of R^n and let f in C^1(E). Show that f satisfies the Lipschitz condition on E if and only if its derivative Df is bounded on E, that is, there exists a constant M => 0 such that the norm of
The natural length of a spring is 10 cm. A force of 25 N stretches it to a length of 20cm. How much work, in units of N-cm, is done in stretching it from a length of 10cm to a length of 15cm?
Given a structure shaped like a pyramid with a square base measuring 9 feet on a side and a height of 8 feet, what is the volume of the tent?
A shop can sell 30 radios at $20 each, per week. For every $1 increase in the price there will be a loss of one sale per week. How much should the shop charge in order to make the maximum profit If the cost to make each radio is $10
Suppose that two of her friends (of the 14 of either gender) do not like each other. If one of the two is invited, the other will not come to the party. How many ways are there to invite 8 people to the party. Explain.
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