You are shipping a care package to your sister in college. It costs $0.85 per pound plus a flat-fee of $12 to ship the package. Write and use an algebraic expression to find the total cost of shipping a 7 pound care package.

To express 12.405 as a mixed number in simplest form, the whole number part is 12, and the decimal .405 is equivalent to 405/1000, which simplifies to 81/200, resulting in the mixed number 12 81/200.

To express the decimal 12.405 as a mixed number, we first recognize that the number to the left of the decimal point is the whole number part, which is 12. The decimal part is .405, which we need to convert to a fraction. Since .405 has three decimal places, it is equivalent to 405/1000. However, we must simplify this fraction to its simplest form.

We find the greatest common divisor (GCD) of 405 and 1000, which is 5. Dividing both numerator and denominator by 5, we get 81/200. Thus, the mixed number equivalent of 12.405 in simplest form is 12 81/200.

An important note to consider is that when working with significant figures, the number of decimal places in the original number is maintained in the fractional part of the mixed number. Therefore, in a scientific context, the number of significant figures can influence the final result.

A^2

-3^2 = 9

 the answer is 9

Final answer:

To determine how far off course a ship will be after 5 hours traveling at 18.0 mph and being 2.2° off course, use the formula: Distance off course = 18.0 mph x 5 hours x sin(2.2°). This results in the ship being approximately 3.45 miles off course after 5 hours.

Explanation:

To calculate how far off course the ship will be after 5 hours, we first need to find the distance the ship travels while off course.

Distance off course = 18.0 mph x 5 hours x sin(2.2°).

Distance off course ≈ 3.45 miles.

Final answer:

Explanation of independent and dependent variables in a linear equation

Explanation:

Independent variable: The hours worked by Ethan (x).

Dependent variable: Total amount earned (y).

Y-intercept: $25, this represents the initial charge even if no hours are worked.

Slope: $20, this represents the additional amount earned per hour of work.

The question about Ally working in a shop for $18 per hour relates to wage determination and labor economics within the field of Business. Discussions surrounding hourly wages, annual salaries, and job requirements touch upon various economic principles.

Given

The line equation is        

[tex]y= \frac{4}{9}x-2[/tex]

passes through the line (4,3 )

Find out the equation of the perpendicular line.

To proof

given equation is

 [tex]y= \frac{4}{9}x-2[/tex]

the equation of line is in the form y = mx +c

where m = slope

           c is the intercept on the y axis.

compare this equation to the above equation

we get

[tex]m =\frac{4}{9}[/tex]

In perpendicular line case

The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line.

thus slope of the perpendicular line

= [tex]\frac{-9}{4}[/tex]

Than equation perpendicular line becomes

[tex]y= \frac{-9}{4}x + c[/tex]

as the line passes through the point( 4,3)

put these value in the above equation

we get

[tex]3= \frac{-9}{4}\times 4 + c[/tex]

solving the above equation

3 +9 =c

12 =c

put this value in the above equation

we get

[tex]y= \frac{-9}{4}\times x + 12[/tex]

this is equation of the perpendicular line.

Hence proved

The number composed of 12 ten thousands, 8 thousands, 14 tens, and 7 ones is written in standard form as 128,147.

To write the number consisting of 12 ten thousands, 8 thousands, 14, and 7 ones in standard form, each element must be placed according to its value in our base-ten number system. First, we note that 14 needs to be broken down into 'tens' and 'ones' as well.

12 ten thousands = 12 times 10,000

8 thousands = 8 times 1,000

14 tens = 14 times 10

7 ones = 7 times 1

Next, we translate these values into their numeral counterparts:

12 ten thousands = 120,000

8 thousands = 8,000

14 tens = 140

7 ones = 7

Now we simply add these numbers together:

120,000 + 8,000 + 140 + 7 = 128,147

The number 12 ten thousands, 8 thousands, 14 tens, and 7 ones written in standard form is 128,147.

The question is about predicting Micah's adult height based on his height at the age of 2. Using the formula a=2c-1 where 'c' is the height at age 2, we substitute 'c' with 35 (his height at age 2) and calculate. Thus, Micah's adult height is predicted to be 69 inches.

The question asks about Micah's adult height based on the given equation, a = 2c – 1. In this equation, 'a' represents Micah's adult height and 'c' represents his height at age 2. Given that Micah's height at age 2 ('c') is 35 inches, we can substitute this value into the equation to find Micah's adult height ('a').

So, substituting c=35 into the equation gives us: a = 2*35 - 1. Calculating this results in: a = 70 - 1. Therefore, Micah's adult height is predicted to be 69 inches.

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Final answer:

To simplify the expression, follow the order of operations: first perform the multiplication inside the parentheses, then multiply that result, and finally subtract it from the sum of 2 and 3. The expression simplifies to -75.

Explanation:

To simplify the mathematical expression 2 + 3 - 4 (5 × 4) we must apply the rules of order of operations, commonly remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Multiplication inside the parentheses: 5 × 4 = 20

Multiply 4 by the result of the previous step: 4 × 20 = 80

Subtract this result from the sum of 2 and 3: (2 + 3) - 80 = 5 - 80 = -75

Therefore, the expression simplifies to -75.

Remember that in subtraction, you change the sign of the number being subtracted, and then follow the rules of addition: e.g., 5 - 3 becomes 5 + (-3) = 2. Similarly, when two numbers with opposite signs multiply, the result has a negative sign: e.g., (-3) × 2 = -6.