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maw [93]
3 years ago
13

Citrus farmer who grows mandarin oranges finds that the diameters of mandarin oranges harvested on his farm follow a normal dist

ribution with a mean diameter of 5.85 cm and a standard deviation of 0.24 cm. Find the 80th percentile for the diameters of mandarin oranges, round 4 decimal places
Mathematics
1 answer:
SSSSS [86.1K]3 years ago
8 0

Answer:

6.0520

Step-by-step explanation:

Given that:

Mean = 5.85

Standard deviation = 0.24

Let N denote the 80th percentile.

P(X < N) = 0.8

P(Z < \dfrac{(N - 5.85)}{0.24}) = 0.8

Using the Excel formula: = NORM.INV(0.8,5.85,0.24)

The 80th percentile for the diameters of mandarin oranges:

= 6.0520 (to 4 decimal place)

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Solve the following equation. Remember to check for extraneous solutions 1/(x-6) + (x/(x-2)) = (4/(x²-8x+12)).
xxMikexx [17]

Answer:

-1, 2, 6

Step-by-step explanation:

We have to solve the equation as follows: 1/(x-6) + (x/(x-2)) = (4/(x²-8x+12)).

Now, we have, \frac{1}{x-6} +\frac{x}{x-2} = \frac{4}{x^{2}-8x+12 }

⇒\frac{(x-2)+x(x-6)}{(x-2)(x-6)} = \frac{4}{x^{2}-8x+12 }

⇒\frac{x-2+x^{2}-6x }{(x-2)(x-6)} =\frac{4}{(x-2)(x-6)}

⇒\frac{(x-2)(x-6)}{x^{2}-5x-2 }=\frac{(x-2)(x-6)}{4}

⇒(x-2)(x-6)[\frac{1}{x^{2} -5x-2} -\frac{1}{4} ]=0

⇒ (x-2)(x-6) =0 or, [\frac{1}{x^{2} -5x-2} -\frac{1}{4} ]=0

If, (x-2)(x-6) =0, then x=2 or x=6

If, [\frac{1}{x^{2} -5x-2} -\frac{1}{4} ]=0, then x^{2} -5x-2=4

and (x-6)(x+1) =0

Therefore, x=6 or -1

So the solutions for x are -1, 2 6. (Answer)

4 0
3 years ago
Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, -5). Write the equati
amid [387]
In this we know all three zeros and one point from which the graph pass.
So we will let specific cubic polynomial function of the form
f(x) = a(x - x_1)(x-x_2)(x-x_3)

As we know zeros are that point where we will get value of function equal to zero. So it is basically in form (x_n , 0)

SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say x_1 = 2 , x_2 = 3 , x_3 = 5

So required equation is
f(x) = a (x-2)(x-3)(x-5)
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              = a[(x^2 - 5x+6)(x-5)]
              = a(x^3 - 5x^2 + 6x- 5x^2 + 25x - 30)
              = a(x^3 - 10x^2+31x-30)
Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
-5= a (0-0+0 - 30)
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f(x) =  \frac{1}{6}(x^3 -10x^2+31x-30)

For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.
4 0
3 years ago
Read 2 more answers
Solve the equation 2p/3-12=-2
-BARSIC- [3]
Hey there! 

\frac{2p}{3} - 12 = -2

Firstly, we are going add 12 on each of the sides that we're working with. like ↓ 

p - 12 + 12 \\ \\ = -2 + 12

This gives us \frac{2}{3}p = 10 (if you are wondering how we got the out come of 10 it is because I added -2 + 12 = 10

Now multiply \frac{3}{2} on each of your sides 

\frac{3}{2} ( \frac{2}{3}p)  \\ \\  =  \frac{3}{2} (10)

Cancel the first set and you will find the value of p

p = 15

Good luck on your assignment and enjoy your day 

~LoveYourselfFirst:)
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