How is estimating decimals when adding helpful?

4,832 yards

Given:

Question:

How many total yards did he have?

The Process:

During the 2011 season, a quarterback passed for 302 yards per game, and he played 16 games.

To find out how many yards he has in the 2011 season, we must multiply the number of passes per game by the number of games he has played.

[tex]\boxed{ \ 302 \times 16 = \ ? \ }[/tex]

Let us use the following strategy:

[tex]\boxed{ \ 302 = 300 + 2 \rightarrow (300 + 2) \times 16 = \ ? \ }[/tex]

Recall that [tex]\boxed{ \ a \times (b + c) \leftrightharpoons (a \times b) + (a \times c) \ }[/tex]

[tex]\boxed{ \ = (300 + 2) \times 16 \ }[/tex]

[tex]\boxed{ \ = (300 \times 16) + (2 \times 16) \ }[/tex]

[tex]\boxed{ \ = (3 \times 16 \times 100) + (2 \times 16) \ }[/tex]

[tex]\boxed{ \ = (48 \times 100) + (32) \ }[/tex]

[tex]\boxed{ \ = (4,800) + (32) \ }[/tex]

[tex]\boxed{\boxed{ \ 4,832 \ }}[/tex]

Thus, he had 4,832 total yards during the 2011 season.

Keywords: during, the 2011 season, a quarterback passed, for 302 yards, per game, and, he played, 16 games, how many, total, he have, 4,832

Method 1: Each person gets one segment, and the remaining two segments are cut into halves.

Method 2: Each person gets a half segment, and the remaining segments are cut into thirds.

Method 1: Each person gets one segment, and the remaining two segments are cut into halves:

Step 1: Give one segment to each person.

Step 2: Cut the remaining two segments into halves.

Step 3: Distribute the halves evenly among the five people.

So, each person will get one whole segment and one half segment.

In total, each person will get 1.5 segments.

Method 2: Each person gets a half segment, and the remaining segments are cut into thirds:

Step 1: Cut each of the three segments into thirds.

Step 2: Give one-third of each segment to each person.

Step 3: Each person will also get a half segment from the remaining two segments.

So, each person will get 0.5 segments from the three initial segments and 0.5 segments from the two remaining segments.

In total, each person will get 1 segment.

Both methods ensure that each of the 5 people gets an equal share of the 3-segment chewy fruit worm.

Final answer:

The thickness of a nail that is 0.1875 inches can be converted to a fraction by expressing it in terms of eighths of an inch, resulting in a fractional thickness of 3/16 inches.

Explanation:

To convert the thickness of a nail from inches to a fraction, we can express the decimal 0.1875 inches in terms of fractional parts of an inch. Since there are 16 eighths in a whole, we can multiply both the numerator and denominator of the fraction 1875/10000 by a number that gives us a denominator that is a multiple of 8. Multiplying both by 2 gives us 3750/20000, which simplifies to 3/16 when we divide both numerator and denominator by 1250.

Therefore, the thickness of the nail is 3/16 inches as a fraction.

The expression representing the amount Melanie earns each hour from babysitting, based on the expression $4x + $16 and her working for four hours, is represented by the variable $x. To determine the hourly rate, we would divide the total hourly charge by the number of hours, but the specific value of $x is not given.

The given expression representing Melanie's total earnings from babysitting for four hours is $4x + $16. Here, $16 is the upfront charge and $4x represents the additional hourly charge multiplied by the number of hours worked. To find the expression representing the amount she earns each hour, we look at the variable part of the expression, which is $4x.

Since Melanie worked for four hours, this part of the expression ($4x) must account for her earnings per hour times the number of hours worked. To find her earnings per hour, we divide the total hourly charge by the number of hours. Therefore, the expression for the hourly rate is $x.

To determine the specific amount that x represents, we would need additional information, such as the total amount she earned after working the four hours. However, based on the given expression, we can conclude that x is representative of Melanie's earnings per hour.

By dividing 475 pounds of apples by 1,000 tarts, we find that each tart contains 0.475 pounds of apples.

To find out how many pounds of apples are used in each tart, we divide the total amount of apples used by the total number of tarts made. In this case, the bakery used 475 pounds of apples to make 1,000 apple tarts. So, we calculate 475 pounds ÷ 1,000 tarts, which gives us 0.475 pounds of apples per tart.

Final answer:

To find out how many pounds of apples are used in each tart, divide the total amount of apples used by the number of tarts. In this case, each tart contains 0.475 pounds of apples.

Explanation:

To find out how many pounds of apples are used in each tart, we need to divide the total amount of apples used by the number of tarts. In this case, the bakery used 475 pounds of apples to make 1,000 apple tarts. So, to find out how many pounds of apples are used in each tart, we can divide 475 by 1,000:

475 pounds ÷ 1,000 tarts = 0.475 pounds per tart

Therefore, each tart contains 0.475 pounds of apples.

The mystery number is really 32.

An equation represents equality of two or more mathematical expression.

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

The mystery number = M

The sum of the number and 8 = M + 8

Half of that sum =  (1/2)(M + 8)

10 added to that sum = (1/2)(M + 8) + 10

Thus (1/2) (M + 8)  + 10  =  30

Now, subtract 10 from each side:              

(1/2) (M + 8)  =  20

Multiply each side by  2 :        

M + 8   =  40  

Subtract 8 from each side:                                

M  =  32 .

So the mystery number is really 32.

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Answer: 10 feet

Step-by-step explanation:

Let h be the height of lamppost.

Since both the person and the lamppost are standing vertical to the ground,  making similar right triangles.

Because the two triangles are similar, the ratio of their sides is the same.

Therefore, we have

[tex]\frac{\text{height of lamppost}}{\text{distance of lampost from mirror}}=\frac{\text{height of person}}{\text{distance of person from mirror}}\\\\\Rightarrow\frac{h}{6}=\frac{5}{3}\\\\\Rightarrow\ h=\frac{6\times5}{3}\\\\\Rightarrow\ h=10[/tex]

Hence, the height of the lamppost = 10 feet.

Setting up a proportional relationship between mirror and lamppost, the height of the lamppost is 10 feets.

Setting up a proportional relationship :

[tex]\frac{Hp}{Dp} = \frac{Hl}{Dm} [/tex]

[tex]\frac{5}{3} = \frac{Hl}{6} [/tex]

Cross multiply :

Hl × 3 = 6 × 5

3Hl = 30

Hl = (30 ÷ 3)

Hl = 10

Therefore, the height of the lamppost is 10 feets.

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The solution to the equation 6 + 2n = 3 is n = -3/2.

Given is an equation we 6 + 2n = 3, we need to solve for n,

To solve the equation 6 + 2n = 3 for n, we'll isolate the variable n by performing the necessary operations step by step.

Here's the solution:

Start with the given equation: 6 + 2n = 3.

Subtract 6 from both sides of the equation to move the constant term to the right side:

6 + 2n - 6 = 3 - 6.

Simplifying the left side gives: 2n = -3.

Divide both sides of the equation by 2 to solve for n:

(2n) / 2 = -3 / 2.

This simplifies to: n = -3/2.

Therefore, the solution to the equation 6 + 2n = 3 is n = -3/2.

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The value of the variable that is missing a number will be 5.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Let x be the missing number. Then the ratio is given as,

6: 30 = 1: x

Simplify the equation, then the value of the variable 'x' will be given as,

6 / 30 = 1 / x

x = 30 / 6

x = 5

The value of the variable that is missing a number will be 5.

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Five less than 3 times a certain number is equal to the original number plus 7. The original number is 6.

From the above given information, we get

3x-5 = x+7

Adding 5 to both sides of the equation, we get

3x-5+5 = x+7+5

Simplifying the above equation

3x = x+12

Subtract x from both sides

3x-x = x+12-x

Simplify

2x = 12

Divide both sides by 2

[tex]$\frac{2 x}{2}=\frac{12}{2}[/tex]

Simplify

x = 6

Therefore, the original number is 6.

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Final answer:

To solve the student's problem, which is an algebraic expression, we set up an equation (3x - 5 = x + 7) and solve for x to find that the original number is 6.

Explanation:

The equation inspired by the student's question can be represented algebraically. This type of problem is a linear equation and an essential concept in algebra.

First, let's let the variable x represent the certain number. The problem states that five less than three times this number is equal to the number plus seven. The equation based on the problem statement is:

3x - 5 = x + 7

To solve for x, we can simplify and rearrange the equation:

Move all the terms with x to one side of the equation by adding -x to both sides:

3x - x - 5 = x - x + 7 2x - 5 = 7

Add 5 to both sides to isolate the term with x:

2x - 5 + 5 = 7 + 5 2x = 12

Divide both sides by 2 to solve for x:

2x/2 = 12/2 x = 6

Therefore, the original number, represented by x, is 6.

The Perfect poultry mix has a vegetable to bread ratio of 1/2, which is greater than the Gobbler stuffing mix's ratio of 1/3.

To determine which mix has the greater vegetable to bread ratio, we need to compare the ratios of dried vegetables to cubed bread for both Gobbler stuffing mix and Perfect poultry mix.

For the Gobbler stuffing mix, we have 1 cup of dried vegetables to every 3 cups of cubed bread, which gives us a ratio of 1/3 or approximately 0.33.

For the Perfect poultry mix, the ratio is 2 cups of dried vegetables to every 4 cups of cubed bread, which simplifies to 1/2 or 0.5.

Comparing the two ratios, we can see that 0.5 (Perfect poultry mix) is greater than 0.33 (Gobbler stuffing mix), so the Perfect poultry mix has the greater vegetable to bread ratio.

Mr. Hall's car traveled approximately 17.23 miles per gallon of gasoline when he drove a total of 37.9 miles using 2.2 gallons.

To calculate the number of miles Mr. Hall's car traveled per gallon of gasoline, we need to divide the total miles driven by the total gallons of gasoline used. Mr. Hall drove a total of 37.9 miles and used 2.2 gallons of gasoline. Thus, to find the miles per gallon (MPG), the calculation would be:

MPG = Total Miles Driven / Total Gallons of Gasoline Used

MPG = 37.9 miles / 2.2 gallons

MPG = 17.23 miles per gallon

So, for each gallon of gasoline, Mr. Hall's car traveled approximately 17.23 miles.

The greater number between 5/8 and 1/2 is 5/8

From the question, we have the following parameters that can be used in our computation:

5/8 or 1/2

Express them as decimals

so, we have the following representation

5/8 = 0.625

1/2 = 0.50

By comparison

0.625 is greater than 0.50

using the above as a guide, we have the following:

This means that the greater number is 5/8

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