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Airida [17]
3 years ago
6

A new antibiotic is effective for 85% of infections. The antibiotic is given to 40 patients. a) Verify that this is a binomial s

etting and write it in notation. b) Describe what P(X=35) means in context. c) What is the probability that the antibiotic will work in at least 35 of the 40 patients? d) What is the probability that the antibiotic will work in less than half of the patients?
Mathematics
1 answer:
Charra [1.4K]3 years ago
4 0
(a)
The binomial distribution can be used because the current situation satisfies all of the following:
1. The probability of success (p=85%) is known and remains constant during the whole experiment
2. The number of trials (n=40) is known and constant.
3. Each trial is a bernoulli trial (success or failure only)
4. All trials are (assumed) independent of each other.
The probability of x successes is therefore
P(X=x)=C(n,x)(p^x)(1-p)^(n-x)

(b) P(X=35) means the probability of 35 successes out of 40 trials at p=0.85
and
P(X=35)=C(40,35)*0.85^35*0.15^5=658008*0.003386*0.00007594
=0.16918

(c) P(X>=35)=∑ P(X=i) for i=35 to 40
=0.16918+0.13315+0.08157+0.03649+0.01060+0.00150
=0.4325

(d) P(X<20)=&sum; P(X=i) for i=0 to 19
=0.00000003513   (individual probabilities are very small).
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One non-negative number is the reciprocal of another number. The sum of the two numbers is a minimum. What are the two numbers
Troyanec [42]

The two numbers are 1 and 1.

Let the non-negative number be x and its reciprocal be y = 1/x

The sum of the two numbers is f(x,y) = x + y

= x + 1/x

= f(x)

For f(x) to be minimum, we differentiate it with respect to x and equate it to zero to find the value of x at which irt is minimum.

So, df(x)/dx = d(x + 1/x)/dx

= dx/dx + d(1/x)/dx

= 1 - 1/x²

Equating it to zero, we have

1 - 1/x² = 0

1 = 1/x²

x² = 1

Taking square-root of both sides, we have

x = ±√1

x = ±1

Since x is non-negative x = + 1

We differentiate f(x) again to determine if this value gives a minimum for f(x).

So, d²f(x)/dx² = d(1 - 1/x²)/dx

= d1/dx - d(1/x²)/dx

= 0 - × (-2/x³)

= 2/x³

Substituting x = 1 into the equation,

d²f(x)/dx² = 2/x³

= 2/1³

= 2 > 0.

So x = 1 is a minimum point for f(x)

Since x = 1 and y = 1/x, y = 1/1 = 1

So, the two numbers are 1 and 1.

Learn more about sum of two numbers here:

brainly.com/question/13854139

5 0
2 years ago
An item is originally priced at $68.89. It is on sale for 42 percent of the original price. Which is an estimate of the sale pri
Fittoniya [83]

Answer:

The answer is $28.93.

Step-by-step explanation:

Using the butterfly method I got $28.93 as my answer.

$68.89 x 42%= $2,893.38

$2,893.38÷100%= $28.9338

$28.9338 rounded to the nearest hundredth is $28.93. I hope this helps.

3 0
2 years ago
<img src="https://tex.z-dn.net/?f=%5Chuge%5Cbold%5Cred%7B%7BHELP%7D%7D" id="TexFormula1" title="\huge\bold\red{{HELP}}" alt="\hu
FromTheMoon [43]

9514 1404 393

Answer:

  1. (f×g)(x) = 2x^2 +2x
  2. (f×g)(x) = 6y^2 -11y -35

Step-by-step explanation:

The distributive property applies.

1. (fg)(x) = f(x)·g(x) = (2x)·(x +1)

  (f×g)(x) = 2x^2 +2x

__

2. (fg)(x) = f(x)·g(x) = (2y -7)·(3y +5) = 2y(3y +5) -7(3y +5)

  (f×g)(x) = 6y^2 -11y -35

_____

<em>Additional comment</em>

Please note in problem 2 that the function argument is x and the variable in the given expressions is y. This means the function value is exactly and only <em>6y^2 -11y -35 for any value of x</em>. It does not change when x changes. (We suspect a typo.)

7 0
3 years ago
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Nezavi [6.7K]
In Quadrant I, both the x and y-coordinates are positive
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Solve the formula for the specific variable <br> Z=x-y/3<br> Y=____
defon

Answer:

-3(z-x) = y

Step-by-step explanation:

Z=x-y/3

Solve for y

Subtract x from each side

z-x = x- y/3 -x

z-x = -y/3

Multiply each side by -3

-3(z-x) = -y/3 * -3

-3(z-x) = y

7 0
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