Find 5/6 of 15. Express your answer in simplest form.

Final answer:

After subtracting the lost string (4 3/12 feet) from the initial length (25 6/12 feet) and simplifying, Dakota is left with 21 1/4 feet of kite string.

Explanation:

To calculate the amount of kite string Dakota has left after losing some, we need to perform a subtraction operation involving mixed numbers. Initially, Dakota had 25 6/12 feet of kite string. When Dakota's kite got stuck, she lost 4 3/12 feet of string.

First, let's simplify the mixed numbers by converting them to improper fractions. To do this, multiply the whole number by the denominator and add the numerator. So, 25 6/12 becomes (25 × 12) + 6 = 300 + 6 = 306/12. Similarly, 4 3/12 becomes (4 × 12) + 3 = 48 + 3 = 51/12.

Now subtract the lost string from the initial length: 306/12 - 51/12 = 255/12. Finally, we convert this back to a mixed number by dividing the numerator by the denominator: 255 ÷ 12 = 21 with a remainder of 3, which gives us 21 3/12 feet of string, or 21 1/4 feet when simplified.

Therefore, Dakota now has 21 1/4 feet of kite string left.

Final answer:

The formula to calculate the sale price of items on sale is s = r - (r × discount rate), where 's' is the sale price, 'r' is the regular price, and the discount rate is expressed as a decimal. An example illustrates the process for a $100 item with a 20% discount, resulting in a sale price of $80.

Explanation:

Generally, the sale price can be calculated by subtracting the discount amount from the regular price. The discount amount itself is often a percentage of the regular price. Therefore, if the discount rate is given as a percentage, the formula to find the sale price could be expressed as s = r - (r × discount rate). This is a simplification and assumes that the discount rate needs to be converted from a percentage to a decimal form before applying.

For example, if an item's regular price is $100, and there is a 20% discount, the calculation would be: s = 100 - (100 × 0.20) = $80. Hence, the sale price is $80. This formula is crucial for both customers and businesses to understand how much they save or earn respectively on sale items.

The simplified ratio of 36 to 45 is 4 to 5.

To simplify the ratio 36 to 45,

First, find the greatest common divisor (GCD) of 36 and 45 as

36 = 1, 2, 3, 4, 6, 9, 12

45 = 1, 3, 5, 9, 15 .

So, the GCD of 36 and 45 is 9.

Now, simplifying the ratio

= 36/48

= (9 x 4)/ (9 x 5)

= 4/5

Therefore, the simplified ratio of 36 to 45 is 4 to 5.

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For the third set, they had 9 songs, but one was saved for an encore, so they had 8 songs remaining.

If Lilah's band had practiced 24 songs and they played 7 songs in their first set and 8 songs in their second set,

find out how many songs they had for their third set by subtracting the songs played in the first two sets from the total number of songs they practiced.

Total songs practiced = 24

Songs played in the first set = 7

Songs played in the second set = 8

Total songs played in the first two sets = 7 + 8 = 15

Now, to find the number of songs they had for their third set, subtract the songs played in the first two sets from the total songs practiced:

Number of songs for the third set = Total songs practiced - Total songs played in the first two sets

Number of songs for the third set = 24 - 15

Number of songs for the third set = 9

However, they had to save one song for an encore.

Therefore,  they had 9 songs for their third set, but they played one for the encore, leaving them with 8 songs for the third set.

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In the given scenario, the independent variable is 'm miles', which is the controlled variable that dictates how much tread an automobile tire will lose, represented as 't milliliters'.

In the situation described, an automobile tire loses t milliliters of tread traveling m miles. When analyzing this scenario, it's clear that the amount of tread lost depends on the distance traveled. Thus, the independent variable is the variable that you have control over or can set prior to the start of the experiment or observation, which in this case is m miles. The dependent variable, which changes in response to the independent variable, would be t milliliters of tread lost. As the car travels more miles, the amount of tread lost would likely increase, which shows a dependency of t milliliters on m miles.

Jax's sister has 3 times as many marbles as Jax. By using multiplication, we calculate that if Jax has 6 marbles, his sister, therefore, would have 18 marbles.

In this problem, Jax's sister has 3 times as many marbles as Jax. If Jax has 6 marbles, we get the number of marbles that his sister has by multiplying 6 with 3. That's because we're given that she has 3 times the amount of marbles that Jax has.

So, the calculation would be 6 * 3 = 18. Therefore, Jax's sister has 18 marbles. The principle used here is multiplication in basic arithmetic. It's a method of scaling quantities based on given ratios or proportions. In this case, the ratio given was '3 times as many'.

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The number of co.ck.roaches that one can buy is given as: 95
It is to be noted that this was solved using the knowledge of Algebraic Equations.

An algebraic equation is one where two mathematical statements are equated to one another. See how we arrive at the answer using algebra statements below.

Let us set the

Note that the total money required for the snake's food is thus given as:

X + Y + Z = 100.................................A

5X + Y + 0.05Z = 100  .......................B

To remove the decimals in B, we multiply same both sides of the equation by 20 to get:

100X + 20Y + Z = 2,000   ........................C

Recall that  the number of each animal purchased must ≥ 1

Since we are looking at the number of co.ck.roaches, let us set

X = 1
Z = 1

This gives us:

100 + 20Y + 1 = 2,000

Thus

20Y = 2,000-100-1
Y =  1899/20

Y = 94.95

Hence the answer is approximately 95 co.ckroaches.

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The area of a triangle is half the area of a parallelogram with the same base and height because a triangle's area is calculated using half the product of its base and height, while a parallelogram's area is the full product of its base and height.

The areas of a triangle and a parallelogram with the same base and height are related in that the area of the triangle is exactly half the area of the parallelogram. To understand this, recall that the area of a parallelogram is calculated by multiplying its base by its height ( extit{Base x Height}). A triangle sharing the same base and height will have half the area because the area of a triangle is given by half the product of its base and height ( extit{0.5 x Base x Height}).

Let's say we have a parallelogram and a triangle with the same base 'b' and height 'h'. The area of the parallelogram is  extit{b x h}, while the area of the triangle will be  extit{0.5 x b x h}. This relationship can be visualized by drawing a diagonal across the parallelogram, which cuts it into two equal triangles, each having the same area as the original triangle we're comparing it to.

Answer:

The cost per gallon of gasoline, rounded to the nearest hundredth is $2.73.

Step-by-step explanation:

The cost of 16.1 gallons of gasoline = $43.95

So, the cost of 1 gallon of gasoline is given by = [tex]\frac{43.95}{16.1}[/tex]

= $2.7298 rounded $2.73.

Therefore, the cost per gallon of gasoline, rounded to the nearest hundredth is $2.73.