Very small numbers are often written in exponential form using scientific notation to make them easier to multiply or divide. Explain how to apply the laws of exponents when multiplying and dividing numbers written in scientific notation.

Please give a detailed and accurate explanation that demonstrates a full understanding. Thanks for any help. :)

Answer:

This may be perfectly expressed in a Rule of Three as:

If 1 yard is equal to 3 feet

15.4 yards are equal to x feet

1 yard-----3feet

15.4 yards------x

Then:

[tex]x=\frac{(15.4 yards)(3 feet)}{1 yard}[/tex]

[tex]x=46.2 feet[/tex]

Therefore the answer is 46.2 feet

Answer:

The required inequity is: [tex]5x\leq 12[/tex]

The price of a gold fish should be less than or equal to $2.4 so that you can by 5 fish.

Step-by-step explanation:

Consider the provided information.

You have $12 to buy five goldfish for your new fish tank.

Let the cost of a goldfish is $x.

For 5 gold fish you needs to pay $5x.

Thus, the required inequity is:

[tex]5x\leq 12[/tex]

We use less than equal to sign as you can pay $12 but not more than it.

Now simplify the above inequity as shown:

Divide both the sides by 5

[tex]\frac{5x}{5}\leq \frac{12}{5}[/tex]

[tex]x\leq 2.4[/tex]

Thus, the price of a gold fish should be less than or equal to $2.4 so that you can by 5 fish.

The expression | 4/13 | evaluates to 4/13 because the absolute value of a positive number is the number itself.

The student's question asks to evaluate the expression | 4/13 |, which involves the use of absolute value. The absolute value of a number is the distance of that number from 0 on the number line, regardless of the direction. Therefore, the absolute value of any positive or negative number is a positive number, and the absolute value of 0 is 0 itself.

In this case, since 4/13 is a positive number, its absolute value is the same as the number itself. So the evaluation of the expression | 4/13 | is simply 4/13.

Rectangular arrangements are made when the number of items can be arranged into rows and columns to form a rectangle. When comparing the number of these arrangements that can be made with 75 cookies and 60 cupcakes, the table with 60 cupcakes allows for more arrangements.

The subject of this question falls under the topic of mathematics, specifically, it is related to the concept of rectangular arrangements or factoring numbers. In this scenario, we have to determine which number (75 cookies or 60 cupcakes), when all items in a table are displayed, allows for more rectangular arrangements.

A rectangular arrangement can be made when the number of items can be arranged into rows and columns to form a rectangle. For instance, 12 items can form a 3x4 or 2x6 rectangular arrangement.

Now let's figure out how many rectangular arrangements can be made for each table:

So, the table with 60 cupcakes allows for more rectangular arrangements than the one with 75 cookies.

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Answer:

perimeter of rectangle is 9/7 units.

Step-by-step explanation:

The perimeter of a rectangle is given by

Perimeter = 2(length + width)

Given that

[tex]length=\frac{1}{7}\\\\width=\frac{1}{2}[/tex]

Substituting these values in the above formula

[tex]P=2(\frac{1}{7}+\frac{1}{2})[/tex]

Add the fractions. The LCD is 14. So, multiply and divide by 14

[tex]P=\frac{2}{14}(\frac{1}{7}\times14+\frac{1}{2}\times14)\\\\P=\frac{1}{7}(2+7)\\\\P=\frac{9}{7}[/tex]

Thus, perimeter of rectangle is 9/7 units.

The average time for each step in the assembly process is 3.75 minutes per step.

To find the average time for each step in the assembly process, we need to divide the total time taken by the number of steps. In this case, the assembly takes 3/4 hour, which is equivalent to 45 minutes. There are 12 steps in the process. So, to find the average time per step, we divide 45 minutes by 12:

Average time per step = 45 minutes / 12 = 3.75 minutes per step.

When a shape is dilated by a scale factor, all lengths within the shape are multiplied by that factor. So, when the regular pentagon is dilated by a scale factor of 3, the perimeter of the new pentagon is 3 times the original. The correct answer is that the perimeter of the new pentagon is 9/2 the perimeter of the original.

In the subject of Mathematics, particularly with shapes and scaling, when a shape is dilated by a scale factor, all lengths within the shape are multiplied by that factor. So, when your regular pentagon is dilated by a scale factor of 3, this means that each side of the pentagon is multiplied by 3. As the pentagon has 5 sides, the total perimeter will be multiplied by 3 as well.

Therefore, the perimeter of the new pentagon is 3 times the perimeter of the original pentagon. This eliminates options F, H, and J, and we find that the correct answer is:

G. The perimeter of the new pentagon is 9/2 the perimeter of the original.

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90% = 0.90

4732000 x 0.90 = 4,258,800

Final answer:

Zero does not have an opposite because it is the identity element in addition; adding zero to any number yields that number without change. Zero's opposite is itself since 0 + 0 = 0. The concept of an 'opposite' is inapplicable for zero displacement or the null vector in vector algebra due to their lack of direction and magnitude.

Explanation:

The question is asking why zero does not have an opposite. In mathematics, zero is unique because it is the only real number that is neither positive nor negative. When we talk about the opposite of a number, we typically mean a number that, when added to the original number, yields zero. For any non-zero number, its opposite is the number with the same magnitude but a different sign. However, zero is the identity element for addition, which means that when you add zero to any number, you get the same number back without any change. Therefore, zero's opposite is itself, because 0 + 0 = 0.

In the context of displacement and vectors, an opposite might refer to direction rather than a notion of being negative or positive. For instance, a displacement of -100 m represents a movement of 100 m in the direction opposite of the chosen positive direction. However, zero displacement means no movement at all, so there can't be an opposite direction.

To elaborate on the concept, when dealing with vector algebra, the equivalent of zero is the null vector, which has no magnitude or direction. Therefore, it doesn't have an opposite because there is no direction or magnitude to invert or negate. Similarly, for an object making a round trip and returning to its starting point, there's zero displacement because its starting and ending points are the same, despite any distance traveled during its journey. This is another instance where zero's unique properties make the concept of an opposite meaningless.

Answer :- Angle addition postulate is the reason which should appear in the box labeled 1.

Explanation:-

Angle addition postulate states that for a given angle ∠AOC if P is interior of ∠AOC then ∠AOC=∠AOP+∠POC.

In the given figure it can be seen that

C is interior of ∠BAD then by angle addition postulate

∠BAC+∠CAD=∠BAD which in box 1.

Thus the second option is correct . "Angle Addition Postulate"  is the reason which should appear in the box labeled 1.

The number that is 70 percent of the number 70 will be 49.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Let the number be 'x'. Then the equation is given as,

x = 70% of the 70

Simplify the equation, then the value of the number is calculated as,

x = 70% of the 70

x = 0.70 × 70

x = 49

The number is 49.

More about the percentage link is given below.

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