The sign of the product of two integers with the same sign is positive. What is the sign of three integers with the same sign? Explain your thinking.

Final answer:

To determine the number of different arrangements of four books, we calculate the permutation 4!, which equals 24. Hence, there are 24 different ways to arrange the four books.

Explanation:

The question asks about the number of different ways to arrange four books on a shelf, assuming the order of the books makes a difference. This problem is an example of a permutation, where the arrangement of a set of items is important.

To calculate this, we use the formula for permutations, which is n!, where 'n' is the number of items to arrange. In this case, we have four books, so we calculate 4! (which is shorthand for 4 × 3 × 2 × 1).

Therefore, 4! = 24. There are 24 different ways to arrange the four books on the shelf.

The percentage of student absences that occurred on Tuesday is approximately 24%.

The circle graph represents the distribution of student absences by day of the week. The central angle for the Tuesday slice is given as 86.4°. To find the percentage of absences on Tuesday, we use the formula: (Central Angle / Total Central Angle) * 100%. In this case, (86.4° / 360°) * 100% ≈ 24%. Therefore, approximately 24% of the student absences occurred on Tuesday.

The central angle represents the proportion of the total absences attributed to each day. A circle has a total central angle of 360°, and the central angle for each day is a fraction of this total. Tuesday's central angle of 86.4° indicates that Tuesday's absences make up 24% of the total absences.

This method applies because the circle graph represents a whole, and each sector's central angle corresponds to its share of the total. Consequently, the calculation accurately reflects the percentage of absences on Tuesday in relation to the entire week.

In comparing the rates of pay offered by the shoe store, clothing store, and pet store, Jonathan will make the most money per hour working at the shoe store, which offers $7.85 per hour.

Jonathan is considering three different part-time job offers, each with a different hourly pay rate. The shoe store offers $7.85 per hour, the clothing store offers $7.58 per hour, and the pet store offers $7.65 per hour. To maximize his earnings, Jonathan should choose the job that pays the highest hourly rate. By comparing these rates, we can see that the shoe store, which offers $7.85 per hour, pays the most. Therefore, Jonathan will make the most per hour working at the shoe store.

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Students who use PEMDAS often think that multiplication must come before division but that's not necessarily the case. If division appears before multiplication when your reading the problem from left to right, do your division first and then move on to your multiplication.

Answer:

(C) reflexive property

Step-by-step explanation:

In algebra there are several rules and properties that help us work and discover new things, the reflexive property of algebra states that every single thing is equal to itslef, this means that you can use any term, let´s say "w", and "w" will always be equal to itself. W=W, just as a=a.

The solution of the expression [tex]7\dfrac{1}{5}[/tex]  which is in the mixed fraction as a decimal form is 7.2.

The combination of a whole number and a proper fraction is called as mixed fraction.

The solution of the expression [tex]7\dfrac{1}{5}[/tex]   as a decimal is calculated as:

First, convert the given mixed fraction into the improper fraction.

[tex]7\dfrac{1}{5} =\dfrac{(7 \times 5)+1}{5}[/tex]

On further solving,

[tex]\dfrac{(7 \times 5)+1}{5} = \dfrac{36}{5}[/tex]

The improper fraction is converted into the decimal by dividing 36 by 5,

which results to 7.2.

The solution of the expression [tex]7\dfrac{1}{5}[/tex]  as a decimal, is 7.2.

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All negative numbers are integers whose absolute value is greater than itself for example-3.

Absolute values are the value of any digit without considering the sign.

So all negative values will be considered positive for absolute value.

For example, the absolute value of -2 will be 2 and the absolute value of -7 will be 7.

Absolute value is value without considering sign so all negative values will be considered positive.

For example -3 → | -3 | = 3 and 3 > -3

All positive values will be greater than their negative value.

Hence "All negative numbers are integers whose absolute value is greater than itself".

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Answer with explanation:

1.⇒Area of Parallelogram = Corresponding height × Base

                                        = 2 cm × 18 mm

→1 cm = 10 mm

So,  Area of Parallelogram

                                = 2 cm × 1.8 cm

                                 = 3.6 cm²

Option C: →3.6 cm²

→→→2. A triplet ,that is set of three numbers is called Pythagorean triplet, if it is of the form of : {m²-1, 2 m , m²+1}

That is if you write the Pythagorean rule for Right triangle, having sides , m²-1, 2 m , m²+1

then ,→ Square of Largest side = Sum of squares of two smallest side

Square of Largest Side = (m²+1)²

Sum of squares of two smallest side= (2 m)² + (m²-1)²

                  = 4 m² + (m²)² -2 m²+1

                 = (m²)² +2 m²+1

                  =(m²+1)²

So, we will check out , out of four options which of them are Pythagorean Triplet.

Option 1.

Square of Largest Number = 82²=6724

Sum of squares of two smaller number= 42² + 40²

                      = 1764 +1600

                     = 3364

→Square of Largest Number ≠Sum of squares of two smaller number

6724 ≠ 3364

Not a Pythagorean Triple.

Option 2.

Square of Largest Number = 58²=3364

Sum of squares of two smaller number= 42² + 40²

                      = 1764 +1600

                     = 3364

→Square of Largest Number =Sum of squares of two smaller number

3364= 3364

A Pythagorean Triple.

Option 3.

Square of Largest Number = 58²=3364

Sum of squares of two smaller number= 41² + 41²

                      = 1681 +1681

                     = 3362

→Square of Largest Number ≠Sum of squares of two smaller number

3364 ≠ 3362

Not a Pythagorean Triple.

Option 4.

Square of Largest Number = 57²=3249

Sum of squares of two smaller number= 41² + 40²

                      = 1681 +1600

                     = 3281

→Square of Largest Number ≠Sum of squares of two smaller number

3249 ≠ 3281

Not a Pythagorean Triple.

Option B: (42, 40,58) is a Pythagorean triple.

Answer:

C

Step-by-step explanation:

The number 69 is 75 % or 75 percentage of the number 92

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage be represented as A

Let the first number be n₁ = 92

Let the second number be n₂ = 69

And , the percentage value of 69 of the number 92 is given by

n₂ = ( A / 100 ) x 92

On simplifying , we get

69 = ( A / 100 ) x 92

Multiply by 100 on both sides , we get

6900 = 92A

Divide by 92 on both sides , we get

A = 6900 / 92

A = 75 %

Therefore , the value of A is 75 %

Hence , the percentage value of 69 of the number 92 is 75 %

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