A recipe for lemonade calls for 1 cup of sugar and 5 cups of water. How much sugar is used per cup of water?

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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Answer: 75%

Step-by-step explanation: The other guy was right.

If 400 reduced by 2 times your age is 244, you will be 78 years old. This conclusion was reached by solving the equation 400 - 2x = 244, where x represents the unknown age.

To solve the problem given, you need to work with the equation provided: 400 decreased by 2 times your age is 244. In mathematical terms, this can be written as 400 - 2x = 244, where 'x' represents your age.

Next, you need to solve for 'x'. The first step is to isolate 'x' by moving terms around. Add 2x to both sides to get 400 = 244 + 2x and then subtract 244 from both sides to get 156 = 2x. You finish the process by dividing both sides by 2, which gives you x = 78. Therefore, if 400 reduced by 2 times your age is 244, you are 78 years old.

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Answer:

it's A or D

Step-by-step explanation:

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.

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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Answer:

i might be wrong but the answer is A

Step-by-step explanation:

Final answer:

The total cost of attending the fair with an access fee and a per-ride charge is represented by the equation C = 3 + 1 × x, where x is the number of rides taken.

Explanation:

To calculate the total cost of attending the county fair which includes an access fee and a per-ride charge, we can write an equation where x represents the number of rides a person takes. The access fee is a fixed cost of $3.00, and the per-ride cost is $1.00. Therefore, if a person takes x rides, the total cost C can be represented by the equation:

C = 3 + 1 × x

For example, if the person takes 5 rides, we would calculate the total cost as 3 + 1 × 5 = $8.00.

To calculate how long a bag of food will last for a cat eating 2/3 cup of food each day, divide the total cups in the bag by the daily consumption amount, resulting in 24 days.

A bag of 16 cups of food will last for 24 days if a cat eats 2/3 cup of food each day. To find the number of days the food will last, you need to divide the total number of cups in the bag by the amount consumed per day: 16 cups ÷ (2/3 cup/day) = 24 days.

Final answer:

The area of the circle, given its circumference of 65π, is calculated as 1056.25π, using the formulas for circumference and area of the circle in terms of the radius.

Explanation:

The circumference of a circle is given by the formula 2πr where r is the radius of the circle. Given that the circumference is 65π, we can find the radius by rearranging the formula: r = circumference / (2π) = 65π / (2π) = 32.5. Next, we use the formula for the area of a circle, which is A = πr², substituting the value we found for r:

A = π(32.5)² = π(1056.25) = 1056.25π.

Therefore, in terms of π, the area of the circle is 1056.25π, which corresponds to choice D of the provided options.

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.