39 problems?
The number of problems solved per hour is proportional to the number of team members solving the problems.
Reasons:
The time it takes 2 members to solve 13 problems = 1 hour
The rate at which each team member solve problems = The same rate
Required:
The number of team membersto solve 39 problems in 1 hour
Solution:
The time it takes 2 members to solve 13 problems = 1 hour
Let x represent the number of team members needed to solve 39 problems in 1 hour.
Using a proportional relationship approach, given that the duration is the same, we have;
Which gives;
2 × 3 = x × 1
6 = x
x = 6
Learn more about proportions here:
Answer:
6 team members
Step-by-step explanation:
Answer
Relative risk= 0.742
Odds ratio= 0.745
Detailed calculation shown in diagram:
Which of the following statements have the same meaning as this conditional statement, which ones are the negations, and which ones are not neither? Justify your answers using logical equivalences or truth tables.
A) If a does not divide b or a does not divide c, then a does not divide bc.
B) If a does not divide b and a does not divide c, then a does not divide bc.
C) If a divides bc and a does not divide c, then a divides b.
D) If a divides bc or a does not divide b, then a divides c. (e) a divides bc, a does not divide b, and a does not divide c.
Step-by-step explanation:
Given that the logical statement is
"If a divides bc, then a divides b or a divides c"
we can see that a must divide one either b or c from the statement above
A) If a does not divide b or a does not divide c, then a does not divide bc.
This is False because a can divide b or c
B) If a does not divide b and a does not divide c, then a does not divide bc.
this is True for a to divide bc it must divide b or c (either b or c)
C) If a divides bc and a does not divide c, then a divides b.
This is True since a can divide bc and it cannot divide c, it must definitely divide b
D) If a divides bc or a does not divide b, then a divides c.
This is True since a can divide bc and it cannot divide b, it must definitely divide c
E) a divides bc, a does not divide b, and a does not divide c.
This is False for a to divide bc it must divide one of b or c
Statement A is not the same as the original statement.
Statement B is the negation of the original statement.
Statement C is the same as the original statement.
Statement D is not the same as the original statement.
Condition E is not a statement, but a set of conditions without any logical implications.
Given that;
The conditional statement:
If a divides bc, then a divides b or a divides c
A) If a does not divide b or a does not divide c, then a does not divide bc.
This statement is not the same as the original conditional statement.
The original statement states that if a divides bc, then a divides b or a divides c.
However, statement A states the opposite - if a does not divide b or a does not divide c, then a does not divide bc.
So, this is not the same as the original statement.
B) If a does not divide b and a does not divide c, then a does not divide bc.
This statement is actually the negation of the original conditional statement.
The original statement states that if a divides bc, then a divides b or a divides c.
The negation of this statement would be that if a does not divide b and a does not divide c, then a does not divide bc.
So, statement B is the negation of the original statement.
C) If a divides bc and a does not divide c, then a divides b.
This statement is the same as the original conditional statement. It states that if a divides bc and a does not divide c, then a divides b.
This is equivalent to the original statement, which states that if a divides bc, then a divides b or a divides c.
D) If a divides bc or a does not divide b, then a divides c.
This statement is not the same as the original conditional statement.
The original statement states that if a divides bc, then a divides b or a divides c.
However, statement D states that if a divides bc or a does not divide b, then a divides c.
This is a different condition altogether, so it is not equivalent to the original statement.
E) a divides bc, a does not divide b, and a does not divide c.
This is not a statement but rather an additional condition specified.
It describes a scenario where a divides bc, a does not divide b, and a does not divide c.
However, it doesn't provide any logical implications or conclusions like the conditional statements we have been discussing.
Therefore, we get;
Statement A is not the same as the original statement.
Statement B is the negation of the original statement.
Statement C is the same as the original statement.
Statement D is not the same as the original statement.
Condition E is not a statement, but a set of conditions without any logical implications.
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The value of the derivative at is the slope of the tangent line at the point .
So the tangent line has equation
Answer:
A. 1.49
D. √2
E. five thirds
G. - 0.59
Step-by-step explanation:
In order to be a probability, a value must be at least zero, or at most 1:
Evaluating each of the given values:
A. 1.49
1.49 is at least zero but it is greater than one, therefore 1.49 cannot be a probability.
B. 1
1 represents a probability of 100%, therefore this value can be a probability
C. three fifths
Can be a probability
D. √2
Cannot be a probability
E. five thirds
Cannot be a probability
F. 0
0 represents a probability of 0%, therefore this value can be a probability
G. - 0.59
Negative values cannot be probabilities.
H. 0.04
Can be a probability
Probabilities are values ranging from 0 to 1, inclusive. With this in mind, values 5/3, √2, -0.59, and 1.49 cannot be probabilities as they're either below 0 or above 1.
In the field of mathematics, specifically in statistics, a probability represents the likelihood of an event occurring and is always a value between 0 and 1, inclusively. The value 0 means that an event will not happen, whilst 1 means the event is certain to happen. Therefore, any value less than 0 or greater than 1 cannot be a probability.
Given the values: 0.04, 5 divided by 3, 1, 0, 3 divided by 5, √2, negative 0.59, and 1.49, the values that cannot be probabilities are:
These numbers do not lie within the range of 0 to 1, and hence, cannot represent probabilities.
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