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.

The given number is a rational number.

Given:

The given number is [tex]\dfrac{20}{6}[/tex].

To find:

Whether the given number is rational or irrational.

Explanation:

Rational number: It can be defined in the form of [tex]\dfrac{p}{q}[/tex], where [tex]p,q[/tex] are integers and [tex]q\neq 0[/tex].

Irrational number: It cannot be defined in the form of [tex]\dfrac{p}{q}[/tex], where [tex]p,q[/tex] are integers and [tex]q\neq 0[/tex].

The given number is in the form of [tex]\dfrac{p}{q}[/tex], where [tex]p=20,q=6[/tex] both non zero integers.

Therefore, the given number is a rational number.

Learn more:

https://brainly.com/question/18116115

The total hours worked over the weekend are 44 hours, resulting in gross wages of $880.

To calculate the gross wages for the weekend, we need to multiply the hours worked each day by the hourly pay rate of $20. On Friday and Saturday, the working hours are from 7am to 11pm, which is 16 hours each day. On Sunday, the working hours are from 9am to 9pm, which is 12 hours.

To find the total hours worked over the weekend, we add the hours for each day:

Now we calculate the total hours: 16 + 16 + 12 = 44 hours.

Next, we calculate the total earnings by multiplying the total hours by the hourly rate:

= 44 hours x $20 per hour = $880.

Therefore, the gross wages for the weekend work are $880.

Final answer:

To form an equation with a sum of 34 using three numbers, one possible combination is 10, 12, and 12, resulting in the equation 10 + 12 + 12 = 34.

Explanation:

To find a combination of 3 numbers that equal 34, we can use simple addition. For example, let's choose three numbers such as 10, 12, and 12. Adding these together, we get the equation 10 + 12 + 12 = 34. This is just one of many possible combinations that satisfy the condition.

If we wanted a methodical approach to find different combinations, we could start with the first number and systematically increase it while decreasing one of the other numbers. It's important to test different combinations and remember that you can also use the same number more than once as we did with the number 12.

Remember, an equation must have an equal sign, while an expression is just a group of numbers and operations. In this case, we are looking for an equation since we want to show that the sum of the three numbers we pick is equal to 34.

Answer:

The shorter piece is 5 ft long.

The longer piece is 15 ft long.

Step-by-step explanation:

Let's write this into an equation:

(5+2x)+x=20

5+3x=20

Subtract 5 from both sides

3x=15

x=5

The shorter piece is 5 ft long.

The longer piece is 5 feet longer than 2 times 5 ft (the shorter piece).

5+2*5

5+10

15

The longer piece is 15 feet long.

Hope this helped!

The height of the box will be 5 inches considering the ribbon is wrapping over the perimeter along the height.

Perimeter is the addition of an external measure of sides it will always positive.

A perimeter is a length and has a degree of the unit as one.

For example

Perimeter of square = side + side + side + side

The perimeter of the circle = πd where d is the dia of the circle.

The total length of the ribbon = is 70 inches.

The bow takes 32 inches of ribbon.

So left = 70 - 32 = 38 inches.

Now,

38 inches = Perimeter along the height

2 ( L + 14 ) = 38

L + 14 = 19

L = 5 inches.

Hence "The height of the box will be 5 inches considering the ribbon is wrapping over the perimeter along the height".

To learn more about Perimeter,

https://brainly.com/question/6465134

#SPJ2

Answer:

40 minutes

Step-by-step explanation:

In the red line and the blue line trains just arrived at the station.

The red line arrives every eight minutes.

The Blue Line arrives every 10 minutes.

Next they will arrive at the station at the same time, LCM of 8 minutes and 10 minutes.

Because both train will come at same multiple of 8 and 10.

Factor of 8 : 2 × 2 × 2

Factor of 10 : 2 × 5

LCM : 2 × 2 × 2 × 5 = 40

Hence, After 40 minutes both train will arrive at station at same time.

Answer is b or the second option

Step-by-step explanation:

Answer:

1/5

Step-by-step explanation:

The value of the exponent numerical expression (3.4)² will be 11.56.

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (3.4)²

Simplify the expression, then we have

⇒ (3.4)²

⇒ 3.4 x 3.4

⇒ 11.56

The value of the exponent numerical expression (3.4)² will be 11.56.

More about the value of the expression link is given below.

https://brainly.com/question/23671908

#SPJ5

The 7 pieces of pizza have been cut by drawing the straight line through diameter giving 4 parts and drawing the diagonal dividing into 6 parts. The 7th piece has been received by drawing a straight line through one of the pieces.

The pizza has been circular-shaped structure. The straight lines have been able to divide the pizza into 4 equal parts. The lines will be drawn as the horizontal and the vertical diameter to the circular pizza.

The required amount of the number of pizza pieces has been 7. The 2 straight lines divide it into 4 parts.

To attain the required 3 more parts, the pizza has been cut in a diagonal direction as well with 1 straight line giving a total of 6 pieces. The 1 piece has been attained by drawing a straight line through one of the pieces giving the total count of the 7 pizza slices of different shapes and sizes.

The image attached shows the division of the pizza slices into 7 pieces.

For more information, refer to the link:

https://brainly.com/question/16027171

The coordinates of the mid-point is 5 if the XY has endpoints at -13 and 23 after using the segment bisector formula.

A segment bisector is a line, ray, line segment, or point that divides a line segment into two equal halves at its center.

It is given that:

XY has endpoints at -13 and 23.

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

The coordinate of the mid-point = (-13 + 23)/2

The coordinate of the mid-point = (10)/2

The coordinate of the mid-point = 5

Thus, the coordinate of the mid-point is 5 if the XY has endpoints at -13 and 23 after using the segment bisector formula.

Learn more about the segment bisector here:

brainly.com/question/4137998

#SPJ5

The equations for the transformed function in vertex form and in standard form are as follows: Vertex form: [tex]\( y = -(x - 3)^2 + 2 \)[/tex], Standard form: [tex]\( y = -x^2 + 6x - 7 \)[/tex]

To arrive at these equations, let's go through the transformation steps:

1. The original function is [tex]\( y = x^2 \)[/tex].

2. Reflecting the graph in the x-axis changes the sign of the function, resulting in [tex]\( y = -x^2 \)[/tex].

3. Translating the graph 3 units right means replacing [tex]\( x \)[/tex] with [tex]\( x - 3 \)[/tex], giving us [tex]\( y = -(x - 3)^2 \)[/tex].

4. Finally, translating the graph 2 units up means adding 2 to the function, yielding the vertex form [tex]\( y = -(x - 3)^2 + 2 \)[/tex].

To convert this vertex form into standard form, we expand the vertex form and simplify:

[tex]\( y = -(x - 3)^2 + 2 \)\\ \( y = -(x^2 - 6x + 9) + 2 \)\\ \( y = -x^2 + 6x - 9 + 2 \)\\ \( y = -x^2 + 6x - 7 \)[/tex]

This is the standard form of the transformed quadratic function.

The cost of the pen in terms of b is (2b - 6) dollars.

To write the cost of the pen in terms of b, we need to determine the cost of the pen relative to the cost of the markers.

Let's assign a variable to the cost of the shoulder bag. Since the shoulder bag costs twice as much as the box of markers, we can write the cost of the shoulder bag as 2b dollars.

Now, the pen costs $6 less than the shoulder bag, so the cost of the pen can be written as (2b - 6) dollars. Therefore, the cost of the pen in terms of b is (2b - 6) dollars.

A function assigns the value of each element of one set to the other specific element of another set. The total cost of the sand for this court is $2,324.

A function assigns the value of each element of one set to the other specific element of another set.

The function for the total cost can be written as in the form as shown below,

Total cost = Cost of sand + Cost of delivery

The total cost for x tons of sand can be written as,

Total cost(x) = $11(x) + $3(x)

Since the volleyball court needs 166 tons of sand, therefore, the total cost for 166 tons of sand can be written as,

Total cost(x) = $11(x) + $3(x)

Total cost(166) = $11(166) + $3(166)

Total cost = $1826 + $498

Total cost = $2,324

Hence, the total cost of the sand for this court is $2,324.

Learn more about Function here:

https://brainly.com/question/5245372

#SPJ2

The solution to the quadratic equation is x = 2 ± √3

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

x² + 4x + 1 = 0   be equation (1)

And , roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

On simplifying , we get

x = [ -4 ± √ ( 4 )² - ( 4 ) ( 1 ) ( 1 ) ] / 2

x = [ -4 ± √ ( 16 - 4 ) ] / 2

x = [ -4 ± √12 ] /2

On further simplification , we get

x = [ -4 ± 2√3 ] /2

x = 2 ± √3

Therefore , the value of x is 2 + √3 or 2 - √3

Hence , the roots of the quadratic equations is x = 2 ± √3

To learn more about quadratic equations click :

https://brainly.com/question/25652857

#SPJ2