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sesenic [268]
3 years ago
7

Suppose 3/4 is a root of a polynomial equation. what does this tell us about the leading coefficient and the constant term in th

e equation
Mathematics
1 answer:
snow_tiger [21]3 years ago
5 0

Answer:

Nothing new about leading coefficient. Definition says it can't be zero. It can always be made equal to one by dividing through.

Constant term cannot be zero unless a root is zero.


Step-by-step explanation:

x-3/4 = 0 has root 3/4 constant term -3/4


(x-3/4)(x-b) = 0 has roots 3/4 and b, constant term 3b/4 which is zero only if b is zero.


(x-3/4)(x-b)(x-c) = 0 has roots 3/4, b, c, constant term -3bc/4 which is zero only if b or c is zero.


Etc. ...

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The reliability of a piece of equipment is frequently defined to be the probability, P, that the equipment performs its intended
Sergio [31]

Answer:

a. y=1

b. Mean= 0.5; variance=0.5

c. In the first instance, the probability that p > 0.95 would mean that we are looking for the area of the rectangle with a height of 1 between 0.95 and 1, which implies it has length 0.05.

Therefore, the area is length × height, which is 0.05 ×1 = 0.05.

Second case, the probability that p is less than 0.95 would then be one minus the probability that p is greater than 0.95, so 1 - 0.05 = 0.95

D. a horizontal line at 20 between 0.90 and 0.95, and will be zero outside of this range.

Step-by-step explanation:

With the use of probability distribution, the probability that the equipment performs has a uniform distribution with minimum 0 and maximum 1.

a) The graph of the probability distribution will be 0 outside of the range of 0 to 1, so therefore y = 0. Inside the interval from 0 to 1, it will be constant (which is a horizontal line) with height 1÷(1-0) = 1, therefore y = 1.

b) The mean of the uniform is (maximum+minimum)/2.

Therefore, (1+0)/2 = 1/2 or 0.5.

The variance of the uniform is

(maximum-minimum)^2/12,

so (1-0)^2/12 = 1/12.

c) Since the probability distribution is rectangular, you can find probabilities by recalling the area of a rectangle which is: area = length × breadth.

In the first instance, the probability that p > 0.95 would mean that we are looking for the area of the rectangle with a height of 1 between 0.95 and 1, which implies it has length 0.05.

Therefore, the area is length × breadth, which is 0.05 ×1 = 0.05.

In the second case, the probability that p is less than 0.95 would then be one minus the probability that p is greater than 0.95, so 1 - 0.05 = 0.95.

d) If it is known that p is between 0.90 and 0.95, without the value, then we would assume that p has a uniform distribution between 0.90 and 0.95 since p originally had a uniform distribution.

In this case,

f(p) =

1/(0.95-0.90) = 20, 0.90 < p < 0.95,

0, otherwise.

In a nutshell, this function will have a horizontal line at 20 between 0.90 and 0.95, and will be zero outside of this range.

6 0
4 years ago
To divide 572 divide 4, Stanley estimated to place the first digit of the quotient. In which place is the first digit of the quo
andreyandreev [35.5K]
It would go over the five, so im guessing the hundreds

6 0
3 years ago
It has long been reported that human body temperature follows a normal distribution with a mean of 98.6 degrees Fahrenheit. Ther
Kay [80]

Solution :

The normal body temperature of any human body is considered to be 98.6$^\circ \ F$. But there is a constant debate about the body temperature of a long held standard to the body temperature.

It is given that :

Null hypothesis and alternate hypothesis :

$H_0 : \mu = 98.6$

And $H_A : \mu > 98.6$

n is given as = 180

Test statistics = 3.64

Prove = 0.018 < α = 0.05 (let reject null hypothesis for α = 0.05 )

Therefore, their results are statistically significant and the result is unlikely due to chance alone.

7 0
3 years ago
In the Ardmore Hotel, 20 percent of the guests (the historical percentage) pay by American Express credit card. (a) What is the
xxMikexx [17]

Answer:

(a) The expected number of guests until the next one pays by American Express credit card is 4.

(b) The probability that the first guest to use an American Express is within the first 10 to checkout is 0.0215.

Step-by-step explanation:

The random variable <em>X</em> can be defined as the number of guests until the next one pays by American Express credit card

The probability that a guest paying by American Express credit card is, <em>p</em> = 0.20.

The random variable <em>X</em> follows a Geometric distribution since it is defined as the number of trials before the first success.

The probability mass function of <em>X</em> is:

P(X=x)=(1-p)^{x}p;\ x=0,1,2,3...,\ 0

(a)

The expected value of a Geometric distribution is:

E(X)=\frac{1-p}{p}

Compute the expected number of guests until the next one pays by American Express credit card as follows:

E(X)=\frac{1-p}{p}

         =\frac{1-0.20}{0.20}

         =4

Thus, the expected number of guests until the next one pays by American Express credit card is 4.

(b)

Compute the probability that the first guest to use an American Express is within the first 10 to checkout as follows:

P(X=10)=(1-0.20)^{10}\times0.20

                 =0.1073741824\times 0.20\\=0.02147483648\\\approx0.0215

Thus, the probability that the first guest to use an American Express is within the first 10 to checkout is 0.0215.

3 0
3 years ago
The candy of a lolipop is in the shape of a sphere with a diameter of 4 cm. The
Sever21 [200]
So so so so 0.5cm? Like
3 0
3 years ago
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