Landon and Keira are preparing refreshments for a party. To make fruit punch, they will mix 2 gallons of grape juice with 1 cup of lemonade and 6 ounces of pineapple juice. How many ounces of punch will they make?

[tex] p\%=\dfrac{p}{100}\\\\225\%=\dfrac{225}{100}=2\dfrac{25}{100}=2.25=2\dfrac{1}{4}\\\\550\%=\dfrac{550}{100}=\dfrac{55}{10}=5\dfrac{5}{10}=5.5=5\dfrac{1}{2}\\\\0.8\%=\dfrac{0.8}{100}=\dfrac{0.8\cdot10}{100\cdot10}=\dfrac{8}{1,000}=0.008=\dfrac{1}{125}\\\\0.06\%=\dfrac{0.06}{100}=\dfrac{0.06\cdot100}{100\cdot100}=\dfrac{6}{10,000}=0.0006=\dfrac{3}{5,000}[/tex]

The points A, B, C cannot be both collinear and form an equilateral triangle simultaneously. This is proven by applying the Pythagorean theorem and trigonometry laws for triangles, which show that the distances and angles do not match the requirements for an equilateral triangle if the points are collinear (on a straight line).

Given that points A,B,C are collinear and you've stated a variety of scenarios about the positioning of these points. Combining all these restrictions, however, leads to a contradiction. An equilateral triangle's points cannot all be collinear as you've mentioned in your last point. A collinear set of points exists on the same straight line. The points of an equilateral triangle do not fall on the same line. Therefore, it's impossible for points A,B,C to be collinear and also form an equilateral triangle ABC.

Applying the Pythagorean theorem to the positions of these points, we see that the distances on the sides of the triangle will not be equivalent if they are positioned in a straight line. Similarly, with the use of trigonometry laws for triangles, such as the ones for vector equations, the same result is found. The vector equations for collinear points lack the trigonometric components found in equilateral triangles.

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Answer:

(B) 6h; $180

Step-by-step explanation:

Let h represents the number of hour.

Given,

Payment for an hour = $ 6,

So, the payment for h hours = 6h dollars,

Where, h is a variable.

Thus, the required variable representation is 6h.

If h = 30,

Thus, the total payment for 30 hours

= 6 ( 30 )

= $ 180

Hence, option B is correct.

There are 360 smokers in group of 400 smokers began smoking before they reached their 21st birthday.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

Approximately 9 out of 10 smokers began smoking before the age of 21.

Now,

Let number of smokers in group of 400 = x

Since, approximately 9 out of 10 smokers began smoking before the age of 21.

Hence, Number of smokers in group of 400 is,

⇒ 9 / 10 = x / 400

Solve for x as;

⇒ 9 × 400 / 10 = x

⇒ 9 × 40 = x

⇒ x = 360

Thus, There are 360 smokers started before they reached their 21st birthday.

Learn more about the proportion visit:

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Hello!

When you flip the coordinates and move them 6 units to the left your coordinates would be: (-4, 8) (0, 8) (5, 1) (1, 3)

The final sales price of the dress is a fraction 12/25 of the original price after successive discounts of 20% and 40%.

To determine the final sales price of the dress after multiple discounts, we can apply each discount successively. Let's assume the original price of the dress is $10, as mentioned in the premise, although this might be a typo or an example figure since a dress would typically cost more.

First discount: 20% off the original price, which is 0.20 x 10 = $2. So the new price after the first discount is $10 - $2 = $8.

Second discount: An additional 40% off on the already reduced price of $8. The additional discount is 0.40 x 8 = $3.20. Therefore, the final sales price after the second discount is $8 - $3.20 = $4.80.

To find the fraction of the original price that the final sales price represents, we divide the final price by the original price: $4.80 / $10 = 0.48. Thus, the fraction of the original price is [tex]\frac{48}{100}[/tex] or 24/50 after simplification, which further simplifies to  12/25

Answer:

[tex]1\frac{17}{25} \\[/tex] bags

Step-by-step explanation:

Number of bags used by Jared for his garden

[tex]= 1\frac{2}{5} \\= \frac{7}{5}\\[/tex]-------------------------- Eq (A)

Number of bags of soil required for new garden

[tex]= \frac{1}{5} * \frac{7}{5} \\= \frac{7}{25} \\[/tex]-------------------------- Eq (B)

Total number of bags that will be used

[tex]= Eq (A) + Eq (B)\\= \frac{7}{5} + \frac{7}{25} \\= \frac{42}{25} \\= 1 \frac{17}{25}[/tex]

Final answer:

The expanded form of the number 0.249 is the sum of each digit multiplied by its place value, which is 0.2 + 0.04 + 0.009.

Explanation:

The question asks to write the number 0.249 in expanded form. The expanded form of a number is the sum of each digit multiplied by its place value. For the number 0.249, the expanded form is:

2/10 + 4/100 + 9/1000

This can also be written as:

0.2 + 0.04 + 0.009

Breaking down the number 0.249 into its decimal place values helps one understand how each digit contributes to the overall value of the number.

Answer:

Package 10−pack of 2.3 ounce bars has the better price per bar

Step-by-step explanation:

Case 1) Package 10−pack of 2.3 ounce bars Cost ($) 17.35

Cost of Package 10−pack of 2.3 ounce bars = 17.35

Cost of Package 1−pack of 1 ounce bars = [tex]\frac{17.35}{10 \times 2.3}[/tex]

                                                                   = [tex]0.7543[/tex]

2)  12−pack of 1.6 ounce bars Cost ($)16.97

Cost of Package 12−pack of 1.6 ounce bars = 16.97

Cost of Package 1−pack of 1 ounce bars = [tex]\frac{16.97}{12 \times 1.6}[/tex]

                                                                   = [tex]0.8838[/tex]

Hence  Package 10−pack of 2.3 ounce bars has the better price per bar

The answer to the question 5258 divided by 47 is approximately 111.87. This is solved using the mathematical operation of division.

To solve the question 5258 divided by 47, we need to use the division operation. Division is one of the four basic operations in mathematics, along with addition, subtraction, and multiplication. In this case, we are dividing 5258 (the dividend) by 47 (the divisor).

Step 1: Start by placing 5258 under the division bar and 47 outside to the left.

Step 2: Divide 5258 by 47. This may be done manually, or by using a calculator. The answer you get is approximately 111.87 when rounded off to the nearest hundredth.

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