Jacob is training for a marathon. His plan is to run the same distance for 3 days a week, then increase that distance by the same amount each week of training. During week 6, Jacob runs 14 miles per day, which is 1.5 miles more per day than he ran during week 5. Which equation represents the daily running distance, in miles, as a function of time, t, in weeks?

Answer:

they can stay for 4 weeks

Step-by-step explanation:

The price of the dirt bike after the coupon is used and after applying the Kentucky sales tax is $333.89. The discount amount is $105, and the sales tax amount is $18.90.

To find the price of the dirt bike after the coupon is used, we first need to calculate the amount of the discount. The regular price of the dirt bike is $419.99, and the coupon gives a 25% discount. To find the discount amount, we multiply the regular price by 0.25: $419.99 x 0.25 = $105. Next, subtract the discount from the regular price: $419.99 - $105 = $314.99.

Next, we need to calculate the sales tax. The regular price after the discount is $314.99. The Kentucky tax rate is 6%, which we convert to a decimal by dividing by 100: 6 ÷ 100 = 0.06. To find the amount of sales tax, multiply the regular price after the discount by the sales tax rate: $314.99 x 0.06 = $18.90.

Finally, to find the price of the dirt bike after the coupon and sales tax, add the regular price after the discount and the sales tax: $314.99 + $18.90 = $333.89. Therefore, the price of the dirt bike after the coupon is used and after applying the Kentucky sales tax is $333.89.

Answer:

It's the graph with -5 to 5.

Step-by-step explanation:

The best presentation of the solution set for |x| < 5 will be - 5 < x < 5.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

The absolute function is also known as the mode function. The value of the absolute function is always positive.

The absolute function is given as

f(x) = | x |

The inequality is given below.

|x| < 5

Then the solution set for |x| < 5 will be - 5 < x < 5.

The graph is given below.

More about the function link is given below.

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Answer: 1 28/99

Step-by-step explanation:

Final answer:

The calculation 65 - 32/8 follows the order of operations, starting with division and then subtraction. Dividing 32 by 8 gives 4, and subtracting this from 65 gives a final answer of 61.

Explanation:

To solve the equation 65 - 32/8, you need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Firstly, you handle the division. You divide 32 by 8 to get 4.

Then, you subtract the result from 65. So, 65 minus 4 equals 61.

The answer to the calculation  65-32/8 (/=divided by) is 61.

The numbers that have an absolute value greater than 5/2 are 4 and 5.

In general, ImI > 5/2. Where m is any number.

The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.

Given:

The absolute value is [tex]2\frac{1}{2}[/tex].

[tex]2\frac{1}{2}[/tex] = 5/2

And we have to find the numbers that have the greater absolute value than 5/2.

5/2 = 2.5.

Any number that is greater than 2.5 is the required number.

Let 4 and 5 re the numbers.

Then, 4 > 5/2 and 5 > 5/2.

Therefore, 4 and 5 are the numbers.

To learn more about the absolute value;

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To determine the amounts of two plant foods with different nitrogen percentages to create a desired mixture, we set up and solve a system of equations based on the total volume and total nitrogen content.

A mixture problem that involves combining two solutions with different percentages of nitrogen to achieve a solution with a desired percentage of nitrogen.

Let's denote the amount of the 9% nitrogen plant food as x gallons and the amount of the 25% nitrogen plant food as y gallons.

Given that we want to end up with 10 gallons of a 19% nitrogen mixture, we can form the following two equations based on the problem's requirements:

Equation 1: x + y = 10 (Total volume of the mixture)

Equation 2: 0.09x + 0.25y = 0.19 × 10 (Total amount of nitrogen in the mixture)

By solving this system simultaneously, we can find the values of x and y.

The second equation can also be written as 9x + 25y = 190 to work with whole numbers.

We can multiply the first equation by negative 9 and add it to the second equation to eliminate x and solve for y.

This will give us the amount of 25% nitrogen plant food needed, and by subtraction of y from 10, we can find the amount of 9% nitrogen plant food required.

Based on the results, we may need multiple gallons of the 9% nitrogen plant food and a specific number of gallons of the 25% nitrogen to achieve our desired 19% nitrogen plant food.

Final answer:

To find the number of gallons of a 9% nitrogen plant food to be combined with a 25% nitrogen plant food, we can set up an equation based on the principle of conservation of mass and solve for the variable representing the number of gallons of the 9% nitrogen plant food.

Explanation:

To find out how many gallons of a plant food that is 9% nitrogen must be combined with another plant food that is 25% nitrogen to make 10 gallons of a plant food that is 19% nitrogen, we can set up an equation based on the principle of conservation of mass.

Let x be the number of gallons of the 9% nitrogen plant food.

Then, (10 - x) would be the number of gallons of the 25% nitrogen plant food.

The equation can be set up as follows:

0.09x + 0.25(10 - x) = 0.19(10)

Solving the equation will give us the value of x, which represents the number of gallons of the 9% nitrogen plant food needed to be combined with the 25% nitrogen plant food.

the price for one pound is $1.15

to find the total cost you need to multiply the cost of one pound by the total weight of how much was bought

 they bought 1.3 pounds, so multiply 1.3 by 1.15 for the total cost

1.15 * 1.3 = 1.495 which rounds up to $1.50

the shopper paid $1.50