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Leni [432]
2 years ago
10

Suppose that you draw two cards from a deck. After drawing the first card, you do not put the first card back in the deck. What

is the probability (rounded to the nearest ten thousandth) that both cards are diamonds?
(A) 0.0543
(B) 0.0588
(C) 0.0625
(D) 0.0643
(E) None of the above
Mathematics
1 answer:
S_A_V [24]2 years ago
8 0

Answer:

(B) 0.0588

Step-by-step explanation:

The probability is calculated as a division between the number of possibilities that satisfy a condition and the number of total possibilities. Then, the probability that the first card is diamonds is:

P_1=\frac{13}{52}

Because the deck has 52 cards and 13 of them are diamonds.

Then, if the first card was diamonds, the probability that the second card is also diamond is:

P_2=\frac{12}{51}

Because now, we just have 51 cards and 12 of them are diamonds.

Therefore, the probability that both cards are diamonds is calculated as a multiplication between P_1 and P_2. This is:

P=\frac{13}{52}*\frac{12}{51}=\frac{1}{17}=0.0588

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b. From where the shoes spilled (48°N, 161°W) to where they were found on May 22nd 1996 (54°N, 133°W), how many kilometers did t
dsp73

To find kilometers using latitude and longitude:

distlon = lon2 - lon1   = 133-161 = -23

distlat = lat2 - lat1  = 54-48 = 6

a = (sin(distlat/2))^2 + cos(lat1) * cos(lat2) * (sin(distlon/2))^2  

a = (sin(6/2)^2 + cos(48)*cos(54)* sin(-23/2)^2

c = 2 * arctan2( sqroot(a), sqroot(1-a) )  

d = R * c (where R is the radius of the Earth, 6373 km's)

d = 2052 km's

April 30th to May 22nd is 23 days.

23 days x 24 hours per day = 552 hours.

Rate of travel = 2052 / 552 = 3.717 km per hour ( round answer as needed.)

3 0
3 years ago
Is the number of calories you have burned since midnight at any time during the say a function\?
statuscvo [17]
<span>Yes, this would be considered a function of time elapsed. To be a function, there needs to be exactly a one-to-one relationship between the variables. At any one time (elapsed since midnight), there is exactly one value for the number of calories burned.</span>
8 0
3 years ago
Woke out the following giving your answers in their simplest form 3/11÷3/11<br><br><br>​
dedylja [7]

Answer:

mr

Step-by-step explanation:

rm x 3/11 ÷ 3/11

6 0
3 years ago
Four friends went to the movies together. Each ticket cost $8, and then each person also bought a soda for $3.75. Two friends ea
photoshop1234 [79]

Answer:

$37.00

Step-by-step explanation:

Tickets:

4 friends, each ticket costs $8

4*8=32

$32

Sodas:

4 friends, each soda costs $3.75

4*3.75=15

$15

Total:

tickets + sodas

32+15=47

$47

Coupons:

2 friends each had a coupon for $5 off

2*5=10

$10 discount

Grand Total:

total-discount

47-10=37

$37.00

7 0
3 years ago
Please. Answer Fast! Use composition to determine if G(x) or H(x) is the inverse of F(x) for the
s344n2d4d5 [400]

Answer:

A. H(x) is an inverse of F(x)

Step-by-step explanation:

The given functions are:

F(x)=\sqrt{x-2}

G(x)=(x-2)^2

H(x)=x^2+2

We compose F(x) and G(x) to get:

(F\circ G)(x)=F(G(x))

(F\circ G)(x)=F((x-2)^2)

(F\circ G)(x)=\sqrt{(x-2)^2-2}

(F\circ G)(x)=\sqrt{x^2-4x+4-2}

(F\circ G)(x)=\sqrt{x^2-4x+2}

(F\circ G)(x)\ne x

Hence G(x) is not an inverse of F(x).

We now compose H(x) and G(x).

(F\circ H)(x)=F(H(x))

(F\circ H)(x)=F(x^2+2)

(F\circ H)(x)=\sqrt{x^2+2-2}

We simplify to get:

(F\circ H)(x)=\sqrt{x^2}

(F\circ H)(x)=x

Since (F\circ H)(x)=x, H(x) is an inverse of F(x)

3 0
2 years ago
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