A punch recipe says to mix 4 cups pineapple juice, 8 cups orange juice, and 12 cups seltzer in order to make 18 servings of punch.a. How many cups of each ingredient do you need to make 108 cups of punch?
b. how many servings can be made from 108 cups of punch?
c. For every cup of seltzer you use, how much orange juice do you use?

Answers

Answer 1

Answer: a. We know the amounts needed for 18 serving, so we can use proportions to scale this up to 108 cups. It is easy once you realize that 4 cups + 8 cups + 12 cups = 18 servings, and 18 * 6= 108, therefore you will need 6 times the amount of ingredients equally proportionated to each of the juices/seltezer. Therefore, we would need 24, 48, 72 cups of pineapple juice, orange juice, and seltzer.

b. Adding 4, 8, and 12 together, we get 24. 108 cups/24 cups of ingredients = 4.5 servings.

c. Using ratios, we see that we use 8 cups of orange juice for every 12 cups of seltzer. Dividing each side by 12, we get that we use 2/3 cups of orange juice for each cup of seltzer.

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Are all horizontal lines parallel

Answers

By definition, lines are parallel if they have the same gradient (slope). Any horizontal line has a gradient of 0, so it is parallel to any other horizontal line

A rectangle's length is three times its width. Let w denote the rectangle's width. What polynomial represents the rectangle's area?

Answers

Hello,

w=width
3w=the length
Area=3*w*w=3w²

A square pyramid is shown:A square pyramid is shown. The sides of the square base are labeled 0.5 foot. The height of one of the triangular sides is labeled 9 feet.

What is the surface area of the pyramid?

2.5 square feet
5.25 square feet
9.25 square feet
1.5 square feet

Answers

The surface area of the square pyramid is 9.25 square feet.

What is square pyramid?

"A three-dimensional geometric shape that has a square base and four triangular sides that are joined at a vertex."

What is the surface area of square pyramid?

"It is the sum of all the surfaces of the pyramid."

For given question,

We have been given a square pyramid.

The sides of the square base are labeled 0.5 foot.

So, the area of the square base would be,

$\Rightarrow A_1=(0.5)^2\n\n\Rightarrow A_1=0.25$

The height of one of the triangular sides is labeled 9 feet.

And the base of the triangular side is the side of square.

So, the length of the triangular base is 0.5 ft.

So, the area of the four triangular bases would be,

$\Rightarrow A_2=4* ((1)/(2)* 9* 0.5 )\n\n\Rightarrow A_2=4* 2.25\n\n\Rightarrow A_2=9$

The surface area of the square pyramid is the sum of the square base and four triangular bases.

So, the surface area of the square pyramid would be,

$A=A_1+A_2\n\nA=0.25+9\n\nA=9.25$ square feet

Therefore, the surface area of the square pyramid is 9.25 square feet.

Learn more about the surface area of the square pyramid here:

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area of triangles:
0.5x9=4.5
4.5x2=9 (i divided 4 (the amount of triangles) by 2 instead of dividing 4.5 by 2)

area of square:
0.5x0.5=0.25

surface area of whole thing:
9+0.25=9.25

so the answer is 9.25

hope this helps :)

Formulate the quadratic function that contains the points (-1,2), (0,-1) and (2,5). F(x) = 2x2 - x - 1 f(x) = 2x2 x 1 f(x) = 2x2 - x 2 f(x) = 2x2 - x - 2.

Answers

Answer:

(a) F(x) = 2x^2 - x - 1

Step-by-step explanation:

The quadratic regression function of a graphing calculator does this nicely.

The one attached shows the function to be ...

F(x) = 2x^2 -x -1

Additional comments

The supplied point (0, -1) tells you the y-intercept is -1. That means the constant in the function's equation will be -1. Only one answer choice has that.

F(x) = 2x^2 -x -1

As always, the first step in problem solving should be to look at the problem, and look at the available solution choices. Understanding these things will generally allow you to throw out answer choices that don't provide a sensible answer to the question. Here, that leaves you with only one answer choice, which is all you need.

Which figure is the image produced by applying the composition t 0,3 r 0,90 to figure R?A.

figure H

B.

figure I

C.

figure J

D.

figure R

Answers

Answer:

Option A is correct

The only figure after composition of $t_(0 , 3) (r_(0,90^(\circ)))$ to figure R is Figure H

Step-by-step explanation:

From the given figure in R;

The coordinates in Figure R ;

(1 , -1) , (2, -2) ,(4, -2) ( 0, -4)

Composite function defined as when one function is substituted into another function.

To Apply the composition $t_(0 , 3) (r_(0,90^(\circ)))$ to figure R;

First apply the Reflection $r_(0, 90^(\circ))$ in Figure R;

The rule of reflection is given by:

$(x,y) \rightarrow (-y,x)$

By applying the rule of reflection in Figure R ,

then, the coordinates becomes;

(1 , -1) $\rightarrow$ (1, 1)

(2 , -2) $\rightarrow$ (2, 2)

(4 , -2) $\rightarrow$ (2, 4)

(0, -4) $\rightarrow$ (4, 0)

Now, apply the translation $t_(0,3)$

Translation : It is a type of transformation that moves each point in a figure the same distance in the same direction.

then,

the rule of translation is:

$(x,y) \rightarrow (x+0,y+3)$

Apply the rule of translation on coordinates (1,1) , (2,2), (2,4) and (4,0)

then

(1 , 1) $\rightarrow$ (1+0 1+3) =(1,4)

(2, 2) $\rightarrow$ (2+0 2+3) =(2, 5)

(2, 4) $\rightarrow$ (2+0 4+3) =(2 ,7) and

(4, 0) $\rightarrow$ (4+0 0+3) =(4 ,3)

Then, the only figure after composition of $t_(0 , 3) (r_(0,90^(\circ)))$ to figure R is Figure H

Answer:

The correct answer is choice A) Figure H

Saturn’s rings span up to about (7.5 · 10-1) of the distance between the Earth and its moons. If Saturn’s rings span up to (2.82 · 105 kilometers, what is the distance between Earth and its moons. 3.76 · 105 km
21,150 km
21.15 · 104 km
2.115 · 105 km

Answers

The distance between Earth and its moons is 2.115 · 10⁵ km. Then the correct option is D.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Saturn’s rings span up to about (7.5 · 10⁻¹) of the distance between the Earth and its moons. If Saturn’s rings span up to (2.82 · 10⁵ kilometers).

The distance between Earth and its moons is calculated as,

⇒ 7.5 · 10⁻¹ x 2.82 · 10⁵

⇒ 0.75 x 2.82 · 10⁵

⇒ 2.115 · 10⁵ km

Thus, the correct option is D.

More about the Algebra link is given below.

brainly.com/question/953809

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2.82 × 10^5 = (7.5×10^-1) × Length between the earth and the moon
Length between the earth and the moon = (2.82×10^5)÷(7.5×10^-1) = 376000 = 3.76×10^5
i think this is correct hope it helps.

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