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ella [17]
1 year ago
5

Find the probability of each event. A gambler places a bet on a horse race. To win, he must pick the top three finishers in any

order. Eight horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win his bet?
Mathematics
1 answer:
Lina20 [59]1 year ago
3 0

Answer: \dfrac{1}{56}

Step-by-step explanation:

Total horses = 6

Number of ways to choose top 3 finishers in order = 3! = 6

Number ways to select 3 horses out of 8 in order = ^8P_3  [By permutations]

=\dfrac{8!}{(8-3)!}=\dfrac{8!}{5!}=8\times7\times6=336

Now, the probability that the gambler will win his bet =

\dfrac{\text{Number of ways to choose top 3 finishers }}{\text{Number ways to select 3 horses out of 8 in order}}

=\dfrac{6}{336}\\\\=\dfrac{1}{56}

Hence, the required probability =  \dfrac{1}{56}

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Victor fue al mercado para comprar manzanas, naranjas y platanos; las naranjas costaron el doble de lo 1ue pago por las manzanas
Thepotemich [5.8K]

Answer:

El precio de las manzanas = 27 pesos

El precio de las naranjas = 54 pesos

El precio de las bananas = 19 pesos

Step-by-step explanation:

Los parámetros dados son;

El monto total gastado = 100 pesos

Sea el precio de las naranjas = x

Sea el precio de las manzanas = y

Sea el precio de los plátanos = z

La cantidad pagada por las naranjas = 2 · y = x

La cantidad pagada por los plátanos = y - 8 = z

Por lo tanto, tenemos;

La cantidad total gastada = La cantidad pagada por las naranjas + La cantidad pagada por las bananas + La cantidad pagada por las manzanas

∴ El monto total gastado = 100 pesos = 2 · y + y - 8 + y

100 = 4 · años - 8

4 · y = 100 + 8 = 108

y = 108/4 = 27

y = 27

De

z = y - 8 tenemos;

z = 27 - 8 = 19

De 2 · y = x, tenemos;

2 × 27 = x

x = 54

Por lo tanto;

El precio de las naranjas = 54 pesos

El precio de las manzanas = 27 pesos

El precio de los plátanos = 19 pesos.

5 0
1 year ago
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. x+y = 3, x = 4
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The intersection between the curves are
3, 0
0, 3
The volume of the solids is obtained by
V = ∫ π [ (4 - (y-1)²)² - (3 - y)²] dy with limits from 0 to 3
The volume is
V = 108π/5 or 67.86
4 0
1 year ago
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that th
Sergeeva-Olga [200]

Answer:

Step-by-step explanation:

(a)

The bid should be greater than $10,000 to get accepted by the seller. Let bid x be a continuous random variable that is uniformly distributed between

$10,000 and $15,000

The interval of the accepted bidding is [ {\rm{\$ 10,000 , \$ 15,000}], where b = $15000 and a = $10000.

The interval of the provided bidding is [$10,000,$12,000]. The probability is calculated as,

\begin{array}{c}\\P\left( {X{\rm{ < 12,000}}} \right){\rm{ = }}1 - P\left( {X > 12000} \right)\\\\ = 1 - \int\limits_{12000}^{15000} {\frac{1}{{15000 - 10000}}} dx\\\\ = 1 - \int\limits_{12000}^{15000} {\frac{1}{{5000}}} dx\\\\ = 1 - \frac{1}{{5000}}\left[ x \right]_{12000}^{15000}\\\end{array}

=1- \frac{[15000-12000]}{5000}\\\\=1-0.6\\\\=0.4

(b)  The interval of the accepted bidding is [$10,000,$15,000], where b = $15,000 and a =$10,000. The interval of the given bidding is [$10,000,$14,000].

\begin{array}{c}\\P\left( {X{\rm{ < 14,000}}} \right){\rm{ = }}1 - P\left( {X > 14000} \right)\\\\ = 1 - \int\limits_{14000}^{15000} {\frac{1}{{15000 - 10000}}} dx\\\\ = 1 - \int\limits_{14000}^{15000} {\frac{1}{{5000}}} dx\\\\ = 1 - \frac{1}{{5000}}\left[ x \right]_{14000}^{15000}\\\end{array} P(X14000)

=1- \frac{[15000-14000]}{5000}\\\\=1-0.2\\\\=0.8

(c)

The amount that the customer bid to maximize the probability that the customer is getting the property is calculated as,  

The interval of the accepted bidding is [$10,000,$15,000],

where b = $15,000 and a = $10,000. The interval of the given bidding is [$10,000,$15,000].

\begin{array}{c}\\f\left( {X = {\rm{15,000}}} \right){\rm{ = }}\frac{{{\rm{15000}} - {\rm{10000}}}}{{{\rm{15000}} - {\rm{10000}}}}\\\\{\rm{ = }}\frac{{{\rm{5000}}}}{{{\rm{5000}}}}\\\\{\rm{ = 1}}\\\end{array}

(d)  The amount that the customer bid to maximize the probability that the customer is getting the property is $15,000, set by the seller. Another customer is willing to buy the property at $16,000.The bidding less than $16,000 getting considered as the minimum amount to get the property is $10,000.

The bidding amount less than $16,000 considered by the customers as the minimum amount to get the property is $10,000, and greater than $16,000 will depend on how useful the property is for the customer.

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2 years ago
When an apple is dropped from a tower 256 feet high, the function h(t) =-167 +256 models the height of the
DerKrebs [107]

Answer:

around 1.5 sec

Step-by-step explanation:

basically you wanna figure out at what time is the height=0

since h(t) represents height, set it to 0 then solve for t

i believe you might have forgotten the t in the equation so i assumed it was -167t

0=-167t+256

-256=-167t

t=1.53293413174

around 1.5 seconds after it was dropped

alternatively, you could plug the equation into desmos, replacing h(t) with y and t with x and find the x intercept

3 0
1 year ago
central park in new york city is rectangular in shape and measures approximately 1.37 •10 4 feet by 2.64 •10 2 feet if one acre
lara [203]
<span>83.03 acres. To solve this, first calculate how many square feet that central park covers. Just multiply its length and width. So 1.37x10^4 * 2.64x10^2 = 3.6168x10^6 Now divide its area in square feet by the number of square feet in an acre. 3.6168x10^6 / 4.356x10^4 = 8.303x10^1 = 83.03</span>
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2 years ago
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