Q and R are independent events. Find P( Q and R). P(Q) = ¼, P(R) = (1/5)

A box is filled with several party favors. It contains 12 hats, 15 noisemakers, ten finger traps, and five bags of confetti. Let H = the event of getting a hat. Let N = the event of getting a noisemaker. Let F = the event of getting a finger trap. Let C = the event of getting a bag of confetti. Find P(H).

A rectangular piece of land whose length its twice its width has a diagonal distance of 64 yards. How many yards, to the nearest tenth of a yard, does a person save by walking diagonally across the land instead of walking its length and its width?

Sketch the three basic conic sections in standard position with vertices and foci on the y-axis.

Verify the identity.

$$\frac { \tan x + \tan y } { \cot x + \cot y } = \tan x \tan y$$

Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life in prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino. In this problem, let:

$C$ = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder.

$L$ = Latino Californians. Suppose that one Californian is randomly selected.

Find $P(C|L)$.

Mark each of the following true or false. _____ a.

$$Φ_n(x)$$

is irreducible over every field of characteristic 0. _____ b. Every zero in ℂ of

$$Φ_n(x)$$

is a primitive nth root of unity. _____ c. The group of

$$Φ_n(x) ∈ ℚ[x]$$

over ℚ has order n. _____ d. The group of

$$Φ_n(x) ∈ ℚ[x]$$

over ℚ is abelian. _____ e. The Galois group of the splitting field of

$$Φ_n(x)$$

over ℚ has order φ(n). _____ f. The regular 25-gon is constructible with a straightedge and a compass. _____ g. The regular 17-gon is constructible with a straightedge and a compass. _____ h. For a prime p, the regular p-gon is constructible if and only if p is a Fermat prime. _____ i. All integers of the form

$$2^{(2^k)} + 1$$

for nonnegative integers k are Fermat primes. _____ j. All Fermat primes are numbers of the form

$$2^{(2^k)} + 1$$

for nonnegative integers k.

Vanillin, the dominant flavoring in vanilla, contains C, H, and O. When 1.05 g of this substance is completely combusted, 2.43 g of

$$CO_2$$

and 0.50 g of

$$H_2O$$

are produced. What is the empirical formula of vanillin?

Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form

$$P ( x ) = D ( x ) \cdot Q ( x ) + R ( x )$$

$$P ( x ) = 8 x ^ { 4 } + 4 x ^ { 3 } + 6 x ^ { 2 } , \quad D ( x ) = 2 x ^ { 2 } + 1$$

Consider a file system in which a file can be deleted and its disk space reclaimed while links to that file still exist. What problems may occur if a new file is created in the same storage area or with the same absolute path name? How can these problems be avoided?

What are the major functions of minerals?

Verify Green’s theorem by evaluating both integrals. $\oint_{C} 3 x^{2} y d x+\left(x^{2}-5 y\right) d y=\iint_{R}\left(2 x-3 x^{2}\right) d A$, where C is the rectangle with vertices $(-1,0),(1,0),(1,1),(-1,1)$.

According to the law of comparative advantage, only people with an absolute advantage can benefit from specialization.

What percent of men are shorter than 66.5 inches?