Look at the table showing prices of orange juice.

Prices of Orange Juice
Pint (16 oz)
Quart (32 oz)
Half-Gallon (64 oz)
Gallon (128 oz)
$1.28
$1.92
$4.48
$11.52

Which is the best value for buying orange juice?
pint
quart
half-gallon
gallon

Answer:  see proof below

Step-by-step explanation:

Use the following Power Reducing Identities:

[tex]\cos^2 A = \dfrac{1}{2}(1 + \cos 2A)\\\\\sin^2 A = \dfrac{1}{2}(1 - \cos 2A)[/tex]

Use the following Product to Sum Identity:

[tex]\cos A\cdot \cos B=\dfrac{1}{2}\bigg[\cos(A+B)+\cos(A-B)\bigg][/tex]

Proof LHS → RHS

[tex]\text{LHS:}\qquad \qquad \qquad \cos^2\beta\cdot \sin^4\beta\\.\qquad \qquad \qquad =\cos^2\beta\cdot \sin^2\beta\cdot \sin^2 \beta[/tex]

[tex]\text{Power Reducing:}\qquad \dfrac{1}{2}\bigg(1+\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\\\\\\.\qquad \qquad \qquad \quad =\dfrac{1}{8}(1+\cos 2\beta)(1-\cos 2\beta)(1-\cos 2\beta)[/tex]

[tex]\text{Expand:}\qquad \qquad \dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^3 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^2 2\beta \cdot \cos \2\beta\bigg)[/tex]

[tex]\text{Power Reducing:}\qquad \dfrac{1}{8}\bigg(1-\cos 2\beta -\dfrac{1}{2}(1+\cos 4\beta)+\dfrac{1}{2}(1+\cos 4\beta)\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(2-2\cos 2\beta -1-\cos 4\beta +\cos 2\beta +\cos 4\beta \cdot \cos 2\beta \bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta+\cos 4\beta \cdot \cos 2\beta \bigg)[/tex]

[tex]\text{Product to Sum:}\quad \dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta +\dfrac{1}{2}[\cos(4\beta+2\beta)+\cos (4\beta-2\beta)]\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(2-2\cos 2\beta -2\cos 4\beta +\cos 6\beta +\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]

[tex]\text{LHS=RHS:}\\ \dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)=\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]

Answer:

25/35

Step-by-step explanation:

5 times 7 equals 35 and that means that this is the denominator because that is our total amount.

5 times 5 equals 25 and that makes it the numerator because that is what is being taken out of 5 jars

Hopefully this helps you :)

Answer:

261

I hope this helps!

Answer:

what is the value of q?

Step-by-step explanation:

Answer:

58 miles per hour

Step-by-step explanation:

leave a heart please :D

Answer:

333.15 Kelvin (K)

Step-by-step explanation:

When you convert from Celsius to Kelvin, you add 273.15

60 C + 273.15 = 333.15 K

So, that is the answer. Hope this helps!

Answer:

333.15 Kelvin (333 rounded)

Step-by-step explanation:

You must add 273.15.

60 + 273.15 = 333.15.

The answer is 333.15 (333 rounded.)

Answer:

3.14 is the simplified version (approximate) to π

Answer:

33, 35, 37

Step-by-step explanation:

Consecutive: in a row

Odd: any number not evenly divisible by 2

Integers: Whole numbers

Sum: the answer to an addition problem

So, 100 is close to 30*3, so start there and move on. It has to be a little more, so start at 31, 33, and 35, but it's only 99, so you need something a little more. Check 33, 35, and 37 to be sure, and you've got your answer!

Answer:

Exact form: [tex]-11.06[/tex]

Decimal form: [tex]-11.066667[/tex]

Step-by-step explanation:

[tex]-8+9.2[/tex] ÷ [tex]-3[/tex]

Let's simplify. We will have to change [tex]9.2[/tex] and [tex]-3[/tex] a draction

[tex]-8+\frac{9.2}{-3}[/tex]

This equals

Exact form: [tex]-11.06[/tex]

Decimal form: [tex]-11.066667[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

Area of a triangle is given by

[tex] A = \frac{1}{2} bh[/tex]

where b is the base

h is the height

From the question

A = 48 sq. in

h = 16 in.

Substitute the values into the above formula and solve for the base

That's

[tex]48 = \frac{1}{2} 16b \\ 48 = 8b \\ \frac{8b}{8} = \frac{48}{8} [/tex]

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Perimeter of a polygon = Sum of all sides of the polygon

Perimeter of the given rectangle = 2[(5x - 2) + (3x - 0.5)]

                                                      = 2[8x - 2.5]

                                                      = (16x - 5)

Perimeter of the given triangle = (2x + 3) + (2x + 3) + (10x - 5)

                                                   = 14x + 1

Since perimeter of the rectangle and triangle are same, equation will be

(16x - 5) = (14x + 1)

16x - 14x = 5 + 1

2x = 6

x = 3

Perimeter = (16x - 5)

                 = 48 - 5

                 = 43 units

Answer: 95 units.

Step-by-step explanation:

The cost of making x units is:

C(x) = x^2 + 10*x + 45.

Now, if the cost is $10,020, then we can solve this for x as:

C(x) = 10,020 = x^2 + 10*x + 45

x^2 + 10*x + 45 - 10,020 = 0

x^2 + 10*x - 9,975 = 0

Now, remember that for a quadratic equation:

a*x^2 + b*x + c = 0

the solutions are:

[tex]x = \frac{-b +-\sqrt{b^2 - 4*a*c} }{2*a}[/tex]

In this case the solutions are:

x = [tex]x = \frac{-10 +-\sqrt{10^2 - 4*1*(-9,975)} }{2*1} = \frac{-10 +- 200}{2}[/tex]

Then we have two solutions, one for each sign:

x = (-10 -200)/2 = -110

x = (-10 + 200)/2 = 95

Here we must choose the positive option, as x represents a positive quaintity.

Then the number of units manufactured is 95.

S is the answer

Step-by-step explanation:

Let 3+4+8+9+13+14+18+___ 40 terms=S

Answer:

2.4 miles.

Step-by-step explanation:

10sec = 4 miles.......what abt.....

6 sec =  ??

cross multiply:

6sec × 4miles ÷ 10 sec= 2.4miles

Answer:

length = 20 m

width = 16m

Step-by-step explanation:

Answer:

Ten billion

Step-by-step explanation:

There would around 16×10⁻¹⁰ ants to wrap around the earth.

Circumference is the distance around a circle., basically it is the perimeter of the circle.

Given that, an average sized ant is about 4×10⁻³ meter long the circumference of the earth is about 4×10⁻⁷ meters, we are asked to find the number of ants that would it take to wrap around earth,

To find the same, we will multiply the size of ants to the circumference of the earth,

So, 4×10⁻³ × 4×10⁻⁷

= 16×10⁻¹⁰

Hence, there would around 16×10⁻¹⁰ ants to wrap around the earth.

Learn more about circumference, click;

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Answer:

a²+b²=126

Step-by-step explanation:

(a+b)²=a²+b²+2ab

(12)²=a²+b²+2×9

144=a²+b²+18

a²+b²=144-18=126

Answer:

The answer is 4r² – 9

Denise answer is correct.

Step-by-step explanation:

One of the methods of solving the given equation [(2r – 3)(2r + 3)] is the FOIL method

Using the FOIL method (Used for multiplying binomials)

F stands for first

O stands for outer

I stands for inner

L stands for last

In this method, it means we will first multiply the first terms followed by multiplying the outer term, then multiplying the inner terms and finally, the last terms.

So, for the equation  (2r – 3)(2r + 3)

First : (2r)(2r) = 4r²

Outer : (2r)(+3) = 6r

Inner : (–3)(2r) =  – 6r

Last :  (–3)(+3) =  – 9

Adding the results we get

4r² + 6r – 6r – 9 (+6r and – 6r cancels out)

= 4r² – 9

∴ (2r – 3)(2r + 3) = 4r² – 9

Hence, Denise answer is correct

Answer:

No, it is not a magic square.

Step-by-step explanation:

A magic square is when whatever way you add it from, it is always the same answer (the magic sum). As you can clearly tell, it doesn't add up to the same number.

Answer:

Step-by-step explanation:

2z = 4a/m +3

 -3        -3

2z - 3 = 4a/m

 ×m        ×m

(2z -3)m = 4a

     ÷4      ÷4

[(2z -3)m]/4 = a

a = (2mz - 3m)/4

Answer:

0.5625

Step-by-step explanation:

A constant is any numbers in an equation that don't have any variable connected to it.

-9x^3 and 12p are not constants since they are connected to variables.

6 is a constant because its not connected to any variable.

Best of Luck!

======================================================

The blueprints say that 1 inch represents 10 feet. This means we can form the equation below

1 inch = 10 feet

Of course 10 feet is much larger than 1 inch, so they cannot be actually equal to one another, but it helps tie together the two quantities. And it also allows us to multiply both sides by 3 to get

3 inches = 30 feet

So 3 inches on paper means we have 30 feet in real life.

Similarly,

1 inch = 10 feet

5.5 inches = 55 feet (multiply both sides by 5.5)

The 3 inch by 5.5 inch rectangle on paper corresponds to a 30 feet by 55 feet rectangle in real life.

----------------

In short, you multiply each given dimension by 10

3 inches goes to 3*30 = 30 feet

5.5 inches goes to 5.5*10 = 55 feet

Answer:

Step-by-step explanation:

1. isolate the variable   subtract both sides by 8                   (12x+8-8<116-8)  

2. Divide both sides by twelve                                               (12x/12<116-8/12)                                            

3. Simplify                                                                                 (x<108/12)      

=12x+8−8<116−8

=12x<108

[tex] \frac{12x}{12} < \frac{108}{12} [/tex]

x<9

Answer:

n = 8

Step-by-step explanation:

:)

Answer:

Five days

Step-by-step explanation:

First, we have to find out how much food they ate:

240 - 180 = 60

Now, we have to find out the number of days they would take to eat 60 pounds of food. We can do that by dividing:

60/12 = 5

They took five days to have 180 pounds leftover.

Answer:

I think it's -1, 4. But i'm not a 100% sure.

Step-by-step explanation:

Answer:

To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

Step-by-step explanation:

This is how you solve for Range; I can't view the image on my chromebook.

Answer:

10 times.

Step-by-step explanation:

Since 1 liter = 1000 milliliters, we can say that 600 milliliters is equal to 0.6 liters because 600/1000 = 0.6

Since the gas can holds 6 liters, and the lawn mower holds 0.6 liters, 6/0.6 = 10.

So, he can fill his lawn mower 10 times with the gas can

Mr Green can fill his lawn 10 times

the first step is to convert the milliliters to liters

600 milliliters to liters

= 600/1000

= 0.6 liters

the number of times can be calculated as follows

= 6/0.6

= 10

hence it will take Mr. Green  10 times to fill his lawn mower

please see the link below for more information

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