What is 3 over 6 with a negative exponent of 1

"6. A brand name has a 40% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small s

statuscvo [17]

Answer:

(a) The probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.

(b) The probability that all of the selected consumers recognize the brand name is 0.0041.

(c) The probability that at least 5 of the selected consumers recognize the brand name is 0.041.

(d) The events of 5 customers recognizing the brand name is unusual.

Step-by-step explanation:

Let X = number of consumer's who recognize the brand.

The probability of the random variable X is, P (X) = p = 0.40.

A random sample of size, n = 6 consumers are selected.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

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

(a)

Compute the value of P (X = 5) as follows:

$P(X=5)={6\choose 5}0.40^{5}(1-0.40)^{6-5}\\=6\times0.01024\times0.60\\=0.036864\\\approx0.0369$

Thus, the probability that exactly 5 of the 6 consumers recognize the brand name is 0.0369.

(b)

Compute the value of P (X = 6) as follows:

$P(X=6)={6\choose 6}0.40^{6}(1-0.40)^{6-6}\\=1\times 0.004096\times1\\=0.004096\\\approx0.0041$

Thus, the probability that all of the selected consumers recognize the brand name is 0.0041.

(c)

Compute the value of P (X ≥ 5) as follows:

P (X ≥ 5) = P (X = 5) + P (X = 6)

= 0.0369 + 0.0041

= 0.041

Thus, the probability that at least 5 of the selected consumers recognize the brand name is 0.041.

(d)

An event is considered unusual if the probability of its occurrence is less than 0.05.

The probability of 5 customers recognizing the brand name is 0.0369.

This probability value is less than 0.05.

Thus, the events of 5 customers recognizing the brand name is unusual.

8 0

3 years ago

Write the equation of a line in slope-intercept form that is perpendicular to the line y = 3/5 = 1 and passes through the point

4vir4ik [10]

The slope of the line $y=\frac{3}{5} x-1$ is $m=\frac{3}{5}$ .

The line perpendicular to the above line has slope $-\frac{1}{m} =-\frac{5}{3}$

Its equation is $y=-\frac{5}{3} x+c$ . Since this line passes through, $(-9,4)$ ,

$4=-\frac{5}{3} )(-9)+c\\ c=-11$

Thus the equation of the line in slope intercept form is $y=-\frac{5}{3} x-11$

4 0

3 years ago

This is my last question I need help with.

Viktor [21]

Answer:

Option 1

Step-by-step explanation:

The formula of constant porpotionality is

$y = kx$

or

$y = \frac{k}{x}$

where k is the constant of porpotionality.

This equation is direct variation so we will use

$y = kx$

The equation is in the form

$y = 1.5x$

1.5 is in k place so the constant of porpotionality is 1.5

3 0

3 years ago

Complete the missing value in the solution to the equation. y = 3x -7 (1, ?,)

Luda [366]

Answer: -4

Step-by-step explanation:

So, for y=3x-7, substitute the x with 1 (from (1,?) ) which gives you y=3(1)-7. Lastly, when you solve the equation, it would give you y=-4.

5 0

3 years ago

Help with trig homework please Get Brainiest

kicyunya [14]

Answer:9

Step-by-step explanation:

I"m pretty sure your trying to find height so your base(1.5) times 6 which will be 9 .

6 0

3 years ago