Which phrase best describes the points on this graph?

A number cube numbered 1 - 6 is rolled once. What is the probability that the side facing up shows 4

marshall27 [118]

Answer: $\bold{\dfrac{1}{6}}$

Step-by-step explanation:

There is 1 four out of 6 possible numbers = $\dfrac{1}{6}$

7 0

3 years ago

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find the probability of being delt 5 clubs and 3 cards with one of each remaining suit in 8 card poker

kumpel [21]

Answer: 0.003757(approx).

Step-by-step explanation:

Total number of combinations of selecting r things out of n things is given by:-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

Total cards in a deck = 52

Total number of ways of choosing 8 cards out of 52 = $^{52}C_8$

Total number of ways to choose 5 clubs and 3 cards with one of each remaining suit = $^{13}C_5\times^{13}C_1\times^{13}C_1\times^{13}C_1$ [since 1 suit has 13 cards]

The required probability = $=\dfrac{^{13}C_5\times^{13}C_1\times^{13}C_1\times^{13}C_1}{^{52}C_8}$

$=\dfrac{\dfrac{13!}{5!8!}\times13\times13\times13}{\dfrac{52!}{8!44!}}\\\\=\dfrac{24167}{6431950}\\\\\approx0.003757$

Hence, the required probability is 0.003757 (approx).

5 0

3 years ago

Find a polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4, for which f(-2)=-24

Zanzabum

We want to find a polynomial

f(x) = a x³ + b x² + c x + d

such that the roots of f are x = -3, x = -1, and x = 4, and f(x) takes on a value of -24 when x = -2.

The factor theorem for polynomials tells us that we can factorize f(x) as

a x³ + b x² + c x + d = a (x + 3) (x + 1) (x - 4)

Expand the right side:

(x + 3) (x + 1) (x - 4) = x³ - 13x - 12

So we have

a x³ + b x² + c x + d = a x³ - 13a x - 12a

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

a = a (of course)

b = 0 (there is no x² term on the right)

c = -13a

d = -12a

We also have that f (-2) = -24, which means

f (-2) = a (-2 + 3) (-2 + 1) (-2 - 4)

-24 = 6a

a = -4

which in turn tells us that c = 52 and d = 48.

So we found

f(x) = -4x³ + 52x + 48

4 0

3 years ago

A rectangle has a perimeter of 30 feet and an area of 50 square feet. What are the dimensions of the rectangle.

KiRa [710]

I believe the shorter sides are 5 feet and the longer ones are 10. This is because when you add up the two shorter sides as 10, and the other two as 20, then add them up to 30. That's the perimeter. For the area, you would do 10•5 to get 50 for the area

3 0

3 years ago

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Linda purchase a prepaid phone card for $30. Long distance calls cost $.17 a minute using this card when do use her card. Linda

balandron [24]

Answer: her call lasted for 44 minutes

Step-by-step explanation:

Linda purchase a prepaid phone card for $30. This means that the credit on her card is $30.

Long distance calls cost $0.17 each. Linda use her card only to make a long distance call. Assuming she made a total of x minutes of long distance calls, the cost would be $0.17x. The amount remaining on her card will be

30 - 0.17x

if the remaining credit on her card is $22.52, the number of minutes,x that the call lasted will be

22.52 = 30 - 0.17x

0.17x = 30 - 22.52

0.17x = 7.48

x = 7.48/0.17 = 44

7 0

3 years ago