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.

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:

**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.

To learn more about the **divide **visit:

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Given h(x)= -5x+3,solve for x when h(x)=3

What is (0.4) exponential form?

Ten samples of coal from a Northern Appalachian source had an average mercury content of 0.242 ppm with a standard deviation of 0.04 ppm. Find a 95% confidence interval for the mean mercury content of coal from this source. Round the answers to four decimal places.

Suppose you are an elementary school teacher. You want to order a rectangular bulletin board to mount on a classroom wall that has an area of 90 square feet. Suppose fire code requirements allow for no more than 30% of a classroom wall to be covered by a bulletin board. If the length of the board is three times as long as the width, what are the dimensions of the largest bulletin board that meets fire code?

Kevin and Caden were both mowing lawns for extra money. Kevin earned $4 per lawn and Caden earned $8 per lawn. For 5 lawns, Caden earned $40. How many lawns would Kevin have to mow to earn the same?

What is (0.4) exponential form?

Ten samples of coal from a Northern Appalachian source had an average mercury content of 0.242 ppm with a standard deviation of 0.04 ppm. Find a 95% confidence interval for the mean mercury content of coal from this source. Round the answers to four decimal places.

Suppose you are an elementary school teacher. You want to order a rectangular bulletin board to mount on a classroom wall that has an area of 90 square feet. Suppose fire code requirements allow for no more than 30% of a classroom wall to be covered by a bulletin board. If the length of the board is three times as long as the width, what are the dimensions of the largest bulletin board that meets fire code?

Kevin and Caden were both mowing lawns for extra money. Kevin earned $4 per lawn and Caden earned $8 per lawn. For 5 lawns, Caden earned $40. How many lawns would Kevin have to mow to earn the same?

(95) x (3 x 104) = ?

(95)(3 x 104)

(95)(312)

29,640

2.964 x 10^4

Answer:

2.964 x 10^4

(95)(312)

29,640

2.964 x 10^4

Answer:

2.964 x 10^4

**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.

98

76

100

88

82

70

What is the range of their test scores?

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

**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.

(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

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**

Question 4 options:

an=3an−1

an=an−1+3

an=13an−1

an=an−1−3

**Answer:**

(B)

**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 () is an addition of 3 to the previous term ().

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

**The correct option is B**