Can someone help me on #5

The equation for pressure at depth is:

P = 14.7 + 0.445*d

The diver is approximately 59.101 feet deep.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

With the given information,

The equation for pressure at depth is:

P = 14.7 + 0.445*d

where P is the pressure in pounds per square inch (psi), d is the depth in feet, and 14.7 is the pressure at sea level.

To find the depth of the diver given a pressure of 41.4 psi, we can rearrange the equation and solve for d:

d = (P - 14.7) / 0.445

Plugging in the given pressure:

d = (41.4 - 14.7) / 0.445

d = 59.101 feet

Therefore,

The diver is approximately 59.101 feet deep.

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Abby and Lauren practiced for a 1 hour and 7 minutes.

To find out how long Abby and Lauren practiced together on Wednesday, we need to add the time they each practiced individually.

1. First, we need to express the times practiced in the same form, preferably as fractions:

Abby's practice time: 11/12 of an hour
Lauren's practice time: 2/3 of an hour
2. Next, we need a common denominator to add these fractions. The least common multiple of 12 and 3 is 12:

2/3 = 8/12

3. Now, add the fractions:

11/12 + 8/12 = 19/12

Therefore, Abby and Lauren practiced for a total of 19/12 hours or 1 hour and 7 minutes on Wednesday.

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

To evaluate expressions using the distributive property, you multiply the term outside the parenthesis by each term inside it separately. This process is carried out for each term, considering the sign rules for multiplication. The result is the sum of these individual products.

When using the distributive property to evaluate each expression, we multiply the outer number by each of the terms inside the parenthesis.

Remember, when multiplying two numbers with similar signs, the result is positive, and when multiplying numbers with opposite signs, the result is negative.

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.

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 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:

(1)The percentage error is 6.897 % .

(2)The total cost of the wallet is $34.35 .

(3)The salesman's commission as a percent of his total monthly sales is 4% .

(4)The interest is $5400 .

Step-by-step explanation:

First part

Formula

[tex]Percentage = \frac{Change\ in\ value\times 100}{Exact\ value}[/tex]

Change in value = |Approx value - Exact value|

As given

Mark estimates that the distance from his house to his school is 15.5 mi. The actual distance is 14.5 mi.

Approx value =  15.5 mi

Exact value = 14.5 mi

Change in value = |15.5 - 14.5|

                           = 1

Put all the values in the formula

[tex]Percentage\ error = \frac{1\times 100}{14.5}[/tex]

[tex]Percentage\ error = \frac{100}{14.5}[/tex]

Percentage error = 6.897 % (Approx)

Thus the percentage error is 6.897 % .

Second part

The price of a wallet is $31.95 and the sales tax is 7.5%.

7.5% is written in the decimal form

[tex]= \frac{7.5}{100}[/tex]

= 0.075

Sales tax price = 0.075 × Price of the wallet

                         = 0.075 × $31.95

                          = $2.4 (Approx)

Total cost of the wallets = Cost of the wallet + Sales tax price

                                        = $31.95 + $2.4

                                        = $34.35

Therefore the total cost of the wallet is $34.35.

Third part

Formula

[tex]Percentage = \frac{Part\ value\times 100}{Total\ value}[/tex]

A sneaker store salesman had $4,125 in total monthly sales last month. He made $165 in commission from those sales.

Part value = $165

Total value = $4125

Put all the values in the formula

[tex]Percentage = \frac{165\times 100}{4125}[/tex]

[tex]Percentage = \frac{16500}{4125}[/tex]

Percentage = 4%

Therefore the salesman's commission as a percent of his total monthly sales is 4% .

Fourth part

Formula

[tex]Simple\ interest = \frac{Principle\times Rate\times Time}{100}[/tex]

Principle = $12000

Rate = 15%

Time = 3 years

Put all the values in the formula

[tex]Simple\ interest = \frac{12000\times 15\times 3}{100}[/tex]

[tex]Simple\ interest = \frac{540000}{100}[/tex]

Simple interest = $5400

Therefore the interest is $5400 .

Answer: Hello there!

Let's analyze the graph.

The first thing you can see is that when x increases, y decreases. This means that our function is decreasing.

Now we need to see if it is linear or nonlinear. You can see that the function starts decreasing slowly and it gets sharper when x grows (in the graph you can see a little curve). A linear function is graphed with a straight line, and we can see that is not this case, then our function is nonlinear.

So the correct answer is Nonlinear decreasing, the fourth option.

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.

Answer:

[tex]\frac{1}{400}[/tex] or 0.0025 0r 0.25%

Step-by-step explanation:

There are three categories that will get a prize

1) First place = 1 person

2) Second place = 5 persons

3) Third place = 20 persons

A total of 26 people will get prizes.

However, we want to determine your chance to win one of the second place prizes

There are 5 prizes in second place

This means out of a total of 2000 people, you could be among the 5

i.e 5 out of 2000

This is [tex]\frac{5}{2000} = \frac{1}{400} = 0.0025[/tex]

This means you have a chance of 1 out of 400

= 0.25%