Let a, b, and c be integers. Consider the following conditional statement: If a divides bc, then a divides b or a divides c
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.

Answers

Answer 1
Answer:

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

Answer 2
Answer:

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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Calculate the product below and give your answer in scientific notation.
(95) x (3 x 104) = ?

Answers

(95)(3 x 104)
(95)(312)
29,640

2.964 x 10^4

Answer:
2.964 x 10^4

A square is inscribed in a circle . If the area of the square is 9 inch square what is the ratio of the radius of the circle to the side of the square.

Answers

Answer:

  (√2)/2

Step-by-step explanation:

The ratio of the radius of the circle to the side of the inscribed square is the same regardless of the size of the objects.

The radius of the circle is half the length of the diagonal of the square. For simplicity, we can call the side of the square 1, so its diagonal is √(1²+1²) = √2 by the Pythagorean theorem. The radius is half that value, so is (√2)/2. The desired ratio is this value divided by 1.

Scaling up our unit square to one with a side length of 3 inches, we have ...

  radius/side = ((3√2)/2) / 3 = (√2)/2

_____

A square with a side length of 3 inches will have an area of (3 in)² = 9 in².

Raj recorded the scores of six of his classmates in the table.Math Scores
98
76
100
88
82
70

What is the range of their test scores?

Answers

The answer is 30. Range: largest number - smallest number = range

According to the Centers or Disease Control and Prevention, 9.6% of high school students current through (c) below a (a) Determine the null and alternative hypotheses. (Type integers or decimals. Do not round.) (b) If the sample data indicate that the null hypothesis should not be rejected, state the conclusion of the high school counselor. 0 A. There is sufficient evidence to conclude that the proportion of high school students exceeds 0.096 at this counselors high school. O B. There is not sufficient evidence to conclude that the proportion of high school students exceeds 0.096 at this counselor's high school o c There is sufficient evidence to conclude that the proportion of high school students stayed 0.096 at this counselor's high school O D There is not sufficient evidence to conclude that the proportion of high school students stayed 0.096 at this counselors high school.

Answers

Answer:

c There is sufficient evidence to conclude that the proportion of high school students stayed 0.096 at this counselor's high school O

Step-by-step explanation:

Given that according to the Centers or Disease Control and Prevention, 9.6% of high school students current through (c) below a

(a) Determine the null and alternative hypotheses.

H_0: p =0.096\nH_a : p >0.096

(right tailed test for proportion of high school students )

b) If the null hypothesis should not be rejected, state the conclusion of the high school counselor.

c There is sufficient evidence to conclude that the proportion of high school students stayed 0.096 at this counselor's high school O

A cooler contains eleven bottles of sports drink: four lemon-lime flavored and seven orange flavored. you randomly grab a bottle and give it to your friend. then, you randomly grab a bottle for yourself. you and your friend both get lemon-lime.find the probability of this occurring.

Answers

The probability that you will choose a lemon-lime for your friend is the number of lemon-limes divided by the total number of drinks, 4/11.

The probability that you will subsequently choose one for yourself is the same ratio with different numbers (because a lemon-lime has already been selected), 3/10.

The probability of both of these events occurring is the product of their individual probabilities: (4/11)·(3/10) = 6/55

Which recursive formula defines this sequence for n > 1?3, 6, 9, 12, 15, 18, ...


Question 4 options:


an=3an−1


an=an−1+3


an=13an−1


an=an−1−3

Answers

Answer:

(B)a_n=a_(n-1)+3

Step-by-step explanation:

Given the sequence: 3, 6, 9, 12, 15, 18, ...

6=3+3

9=6+3

12=9+3

If we continue in like manner, we notice that the nth term (a_n) is an addition of 3 to the previous term (a_(n-1)).

Therefore (for n>1), the recursive formula which defines the sequence is:

a_n=a_(n-1)+3

The correct option is B