D is the correct option since it represents a combination where neither p nor a equals zero.
Part A
To identify the values of x that make 2x−1 positive
⇒ 2x - 1 > 0
⇒ 2x > 1
⇒ x > 
As a result, for any x greater than
, the expression 2x-1 is positive
Part B
To find values of y making 21−37 negative
⇒ 21-3y < 0
⇒ 21 < 3y
⇒ 7 < y
Thus, for all y values exceeding 7, the expression 21-3y is negative
Part C
To identify values of c that digit 5−3c greater than 80
⇒ 5-3c > 80
⇒ -3c > 75
⇒ -c > 25
⇒ c < -25
Therefore, for values of c less than -25, the expression 5-3c surpasses 80
Answer:
We have the following details:
Confidence level = 99%. Hence, the critical value at a 0.01 significance level is provided below:
The margin of error is mentioned in the question as:
Since we lack information about the previous proportion, we need to assume 
.
Therefore, the required sample size is:
Thus, it requires 664 sample observations.
Answer:
a) 0.00019923%
b) 47.28%
Step-by-step explanation:
a) To determine the likelihood that all sockets in the sample are defective, we can use the following approach:
The first socket is among a group that has 5 defective out of 38, leading to a probability of 5/38.
The second socket is then taken from a group of 4 defective out of 37, following the selection of the first defective socket, resulting in a probability of 4/37.
Extending this logic, the chance of having all 5 defective sockets is computed as: (5/38)*(4/37)*(3/36)*(2/35)*(1/34) = 0.0000019923 = 0.00019923%.
b) Using similar reasoning as in part a, the first socket has a probability of 33/38 of not being defective as it's chosen from a set where 33 sockets are functionally sound. The next socket has a proportion of 32/37, and this continues onward.
The overall probability calculates to (33/38)*(32/37)*(31/36)*(30/35)*(29/34) = 0.4728 = 47.28%.
Answer:
The area calculates to 83.905 cm^3
Step-by-step explanation:
The overall ratio is 9 + 7 + 6 = 22
Thus, the side lengths are computed as follows;
9/22 * 44 = 18 cm
7/22 * 44 = 14 cm
6/22 * 44 = 12 cm
Heron’s formula allows us to determine the area of the triangle
First, we calculate s
s = (a + b + c)/2 = (18+14+12)/2 = 44/2 = 22
Heron’s formula can be expressed as;
A = √s(s-a)(s-b)(s-c)
where a, b, and c are 18, 14, and 12 respectively
Plugging in the values, we obtain;
A = √22(22-18)(22-14)(22-12)
A = √(22 * 4 * 8 * 10)
A = √(7,040)
A = 83.905 cm^3
