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bearhunter [10]
3 years ago
13

Priyanka and Ethan were asked to find an explicit formula for the sequence -3,-14,-25,-36,...

Mathematics
1 answer:
irga5000 [103]3 years ago
3 0

Answer:

a_{n} = 8 - 11n

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

a_{n} = a + (n - 1)d

where a is the first term and d the common difference

here a = - 3 and

d = - 14 - (- 3) = - 14 + 3 = -11, thus

a_{n} = - 3 - 11(n - 1)

                        = - 3 - 11n + 11

                        = 8 - 11n

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A store selling newspapers orders only n = 4 of a certain newspaper because the manager does not get many calls for that publica
umka2103 [35]

Answer:

a) The expected value is 2.680642

b) The minimun number of newspapers the manager should order is 6.

Step-by-step explanation:

a) Lets call X the demanded amount of newspapers demanded, and Y the amount of newspapers sold. Note that 4 newspapers are sold when at least four newspaper are demanded, but it can be <em>more</em> than that.

X is a random variable of Poisson distribution with mean \mu = 3 , and Y is a random variable with range {0, 1, 2, 3, 4}, with the following values

  • PY(k) = PX(k) = ε^(-3)*(3^k)/k! for k in {0,1,2,3}
  • PY(4) = 1 -PX(0) - PX(1) - PX(2) - PX (3)

we obtain:

PY(0) = ε^(-3) = 0.04978..

PY(1) = ε^(-3)*3^1/1! = 3*ε^(-3) = 0.14936

PY(2) = ε^(-3)*3^2/2! = 4.5*ε^(-3) = 0.22404

PY(3) = ε^(-3)*3^3/3! = 4.5*ε^(-3) = 0.22404

PY(4) = 1- (ε^(-3)*(1+3+4.5+4.5)) = 0.352768

E(Y) = 0*PY(0)+1*PY(1)+2*PY(2)+3*PY(3)+4*PY(4) =  0.14936 + 2*0.22404 + 3*0.22404+4*0.352768 = 2.680642

The store is <em>expected</em> to sell 2.680642 newspapers

b) The minimun number can be obtained by applying the cummulative distribution function of X until it reaches a value higher than 0.95. If we order that many newspapers, the probability to have a number of requests not higher than that value is more 0.95, therefore the probability to have more than that amount will be less than 0.05

we know that FX(3) = PX(0)+PX(1)+PX(2)+PX(3) = 0.04978+0.14936+0.22404+0.22404 = 0.647231

FX(4) = FX(3) + PX(4) = 0.647231+ε^(-3)*3^4/4! = 0.815262

FX(5) = 0.815262+ε^(-3)*3^5/5! = 0.91608

FX(6) = 0.91608+ε^(-3)*3^6/6! = 0.966489

So, if we ask for 6 newspapers, the probability of receiving at least 6 calls is 0.966489, and the probability to receive more calls than available newspapers will be less than 0.05.

I hope this helped you!

8 0
3 years ago
Find the value of x in each of the given figures.
Kaylis [27]

Answer:

Step-by-step explanation:

1) Given figure is a parallelogram

Area = 144 cm²

base  * altitude = 144

16 * x = 144

x =144/16

x = 9 cm

2)2) Trapezium

Area = \frac{a+b}{2}*h      ; {a and b are parallel sides of trapezium}

( 37 +27 /2) * x  = 480 cm²

64/2 * h = 480

32 *  h = 480

h = 480/32

h = 15 cm

8 0
3 years ago
Help me with this question​
Scrat [10]
In my calculation it’s 4
7 0
3 years ago
Length of a rectangle is 5 cm longer than the width. Four squares are constructed outside the rectangle such that each of the sq
azamat

Answer:

The perimeter of rectangle is 18\ cm

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

x=y+5 ----> equation A

120=xy+2x^{2}+2y^{2} ---> equation B (area of the constructed figure)

substitute the equation A in equation B

120=(y+5)y+2(y+5)^{2}+2y^{2}

120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0

using a graphing calculator -----> solve the quadratic equation

The solution is

y=2\ cm

Find the value of x

x=y+5 ----> x=2+5=7\ cm

Find the perimeter of rectangle

P=2(x+y)=2(7+2)=18\ cm

8 0
3 years ago
D.2<br> Geometry math question no Guessing
AnnyKZ [126]
C. 3

The shape can fit on to itself 3 times before returning to its original position.

Next time try this:

1. Trace and cut out the shape
2. Label the top 'A'
3. Trace the shape one more time. DO NOT CUT THIS ONE OUT
4. Put the cut out shape on the 2nd traced one
5. Put a pen in on the point, like a spinner, and rotate it 90degrees
6. See how many it can fit into itself before 'A' returns to the top.

That will be your answer.

3 0
3 years ago
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