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A function is a relation in which every input value x has at most one output value y.

Consider all options:

a. Relation {(a, b), (a, c), (a, d), (a, e)} is not a function, because input value a has four different output values b, c, d and e.

b. Relation {(a, b), (b, b), (c, b), (d, b)} is a function, because every input value a, b, c and d have at most one output value b.

c. Relation {(a, b), (c, d), (e, f), (g, h)} is a function, because every input value a,  c, e and g have at most one output value b, d, f and g, respectively.

d. Relation {(a, a), (b, c), (c, c), (d, e)} is a function, because every input value a,  b, c and d have at most one output value a, c, c and e, respectively.

Answer: correct choice is D

The contrapositive of this statement would be: "If x does not equal -4, then 5x + 7 will not equal to -13."

what is contrapositive?

The contrapositive is defined as the inverse and converse of a conditional statement.

X is equal to 4 we know this is because the sign in between the number means greater than or equal to so 3 x 4 equals 12 which makes the equation on right true and on the left x.

So, the contrapositive of this statement would be:

"If x does not equal -4, then 5x + 7 will not equal to -13."

Learn more about contrapositive ;

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Using the normal distribution and the central limit theorem, it is found that:

a) The probability is 0.6395.

b) The probability is 1.

c)

The probability from part​ (a) is more relevant because it shows the proportion of male passengers that will not need to bend.

d)

B. Since men are generally taller than​ women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

• It measures how many standard deviations the measure is from the mean.  
• After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
• By the Central Limit Theorem, for the sampling distribution of samples of size n, the standard deviation is

In this problem:

• Mean of 69 in, thus .
• Standard deviation of 2.8 in, thus .

Item a:

This probability is the p-value of Z when X = 70, thus:

has a p-value of 0.6395.

Thus, the probability is 0.6395.

Item b:

Samples of size 100, thus .

This probability is the p-value of Z when X = 70, thus:

By the Central Limit Theorem:

has a p-value of 1.

The probability is 1.

Item c:

We want don't want many people to have to bend, thus, part a has to be considered.

Item d:

Generally, men are taller, so if the design accommodates the men, it will accommodate the women, and the correct option is:

B. Since men are generally taller than​ women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

A similar problem is given at brainly.com/question/24663213

Answer:

a) 0.6406; b) 1.000; c) C. The probability from part​ (a) is more relevant because it shows the proportion of male passengers that will not need to bend; d) B. Since men are generally taller than​ women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

Step-by-step explanation:

For part a,

We use the formula for the z score of an individual,

Our mean, μ, is 69 and our standard deviation, σ, is 2.8.  To find P(X < 70),

z = (70-69)/2.8 = 1/2.8 = 0.36

Using a z table, we see that the area under the curve to the left of this value is 0.6406.  This is our probability.

For part b,

We use the formula for the z score of a sample,

Our mean is still 69 and our standard deviation is still 2.8.  Our sample size, n, is 100.  To find P(X < 70),

z = (70-69)/(2.8÷√100) = 1/(2.8÷10) = 1/0.28 = 3.57

Using a z table, we see the area under the curve to the left of this is greater than 0.9999.  This means that the probability is 1.000.

For part c,

We want to know the proportion of male passengers that will not need to bend.  This is why the value from part a is more important.

For part d,

Men taller on average than women.  This means if we accommodate for the mean, it follows that the women will fit as well.