Answers are (-1,3) (0,2) (1,2) (2,-1) (2,2)

On each round, Ann and Bob each simultaneously toss a fair coin. Let Xn be the number of heads tossed in the 2n flips which occu

CaHeK987 [17]

Answer:

$P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}$

Step-by-step explanation:

In a coin toss the probability of tossing a head is 0.5 (50% head/50% tails)

If n is the number of rounds and 2n the number of coins tossed (one for each player), the probability of having m heads tossed is:

$R=\frac{2n!}{m!*(2n-m)!}$

R is the number of cases (combination of coins tossed) that gives a m number of heads. Each case has a probability of $P_{case}=0.5^{2n}$ so:

$P=\frac{2n!}{m!*(2n-m)!}*0.5^{2n}$

For example, to toss 4 heads in 5 rounds:

n=5
2n=10
m=4

$P=\frac{10!}{4!*(10-4)!}*0.5^{10}$

$P=\frac{10*9*8*7*6!}{4!*6!}*0.5^{10}$

$P=\frac{10*9*8*7}{4!}*0.5^{10}$

$P=\frac{10*9*8*7}{4!}*0.5^{10}=0.205$

8 0

3 years ago

What is the sum of 15 and the opposite of 13?

NemiM [27]

Answer:

2

Step-by-step explanation:

15+-13 = 2

4 0

3 years ago

If LK=MK, LK=7x-10,KN=x+3, MN=9x-11 and KJ=28 find LJ

beks73 [17]

Suppose J, K, L, M, N are points on the same line.

MK = MN + (-KN) = MN - KN = 9x - 11 - x - 3 = 8x - 14

Since LK = MK and LK = 7x - 10, then

7x - 10 = 8x - 14

8x - 7x = -10 + 14

x = 4

LJ = MK + KJ

MK = LK = 7x - 10 = 7(4) - 10 = 28 - 10 = 18

LJ = 18 + 28 = 46

3 0

3 years ago

The owner of a new pet store wishes to display tropical fish in display tanks. The above table shows the species that cannot liv

Pepsi [2]

Answer:

The minimum number of different tanks needed to safely house all the fish is:

3 tanks.

Step-by-step explanation:

To identify the minimum number of different tanks, we're gonna concentrate in a fish species, in this case can be the A: as you see in the table, the A species can live with all the fish excepting the F and G, by their side, the F and G can't live together , by this reason, this three species must live in a different tank, in the next form:

Tank 1: A
Tank 2: F
Tank 3: G

Now the B species, it can live with A, F and G, but for this example we can put in the tank 1 (the tank of the A species). The C especies can live with A, F and G, but how we have A and B together, we're gonna put the C especies in the tank 3 (the tank of the G especies). The D species can live with A and G, we're gonna put in the tank 1 because can live with B species too. The E species can live with A and F, we're gonna put in the tank 2 (the tank of the F species) because the E species can't live with D that is in the in the tank 1. Al last, the H species just can live with A, E, F, and H species, by this reason, the only tank that can be put is the tank 2. In this form, the order is the next:

Tank 1: A, B, D.
Tank 2: F, E, H.
Tank 3: G, C.

And the owner of the pet store must buy three different tanks to display these tropical fish.

5 0

3 years ago

Tests show that the hydrogen ion concentration of a sample of apple juice is 0.0003 and that of ammonia is 3.1 x 10^-9. Find the

scoundrel [369]

PH can be calculated using the following equation
pH = -log [H₃O⁺]
for apple juice the hydronium /hydrogen ion concentration is 0.0003
pH = -log (0.0003)
pH = 3.5
correct answer is C

For ammonia
pH = -log (3.1 x 10⁻⁹)
pH = 8.5
answer should be 8.5

5 0

2 years ago

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