10. Is it possible for a regular polygon to have 240° as the measure of each of its interior
angles?

Answer: 8/3

You first do 4x2 than you would have to divide by 3. 4x2*3

The number of cups of warm water need for 2/3 cup of soap to make solution is [tex]5\frac{1}{3}[/tex]. Therefore, option C is the correct answer.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, a bubble recipe he found requires 4 cups of warm water for every 1/2 cup of soap.

Let the number of cups of warm water need for 2/3 cup of soap be x.

Now, the proportion is

4:1/2 :: x:2/3

1/2 x=4×2/3

x/2=8/3

x=16/3

x= [tex]5\frac{1}{3}[/tex]

Therefore, option C is the correct answer.

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Profit, revenue and cost are related, and can be calculated from one another.

The cost function is given as:

[tex]\mathbf{C(x) =30x + 150}[/tex]

The revenue function is given as:

[tex]\mathbf{R(x) =-0.5(x -90)^2 + 4050}[/tex]

(a) Calculate the profit function

This is calculated using:

[tex]\mathbf{P(x) = R(x) - C(x)}[/tex]

So, we have:

[tex]\mathbf{P(x) =-0.5(x -90)^2 + 4050 - 30x - 150}[/tex]

Evaluate like terms

[tex]\mathbf{P(x) =-0.5(x -90)^2 - 30x + 3900}[/tex]

(b) The domain of the profit function

When profit is 0 or less, then it becomes no profit.

Hence, the domain of the profit function is x > 0

(c) The profit for 60 and 70 items

Substitute 60 and 70 for x in P(x)

[tex]\mathbf{P(60) =-0.5(60 -90)^2 - 30 \times 60 + 3900}[/tex]

[tex]\mathbf{P(60) =1650}[/tex]

The profit when producing 60 items is 1650

[tex]\mathbf{P(70) =-0.5(70 -90)^2 - 30 \times 70 + 3900}[/tex]

[tex]\mathbf{P(70) = 1500}[/tex]

The profit when producing 70 items is 1600

(d) Why producing 10 more units less profit

When a function reaches the optimal value, the value of the function begins to reduce.

This means that, producing 10 more units takes the profit function beyond its maximum point.

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Answer:

2

Step-by-step explanation:

the formula is y^2-y^1 over x^2-x^1

so the y coordinates here are 5 and -5

5--5=10

the x coordinates are -2 and 3

3--2=5

so we are left with 10/5

the answer is 2

hope this helped

The sum of the given geometric sequence to 2 dp is 936.00

To get the sum of a geometric sequence, we will use the formula for calculating the sum to infinity of the sequence as shown:

[tex]S_\infty=\frac{1}{1-r}[/tex]

a is the first term

r is the common ratio

Given the sequence  S = 0.936 + 0.935 + ... + 0.92 + 0.9 + 1

a = 0.936

r = 0.935/0.936 = 0.998

Substitute into the formula

[tex]S_\infty=\frac{0.936}{1-0.999}\\S_\infty=\frac{0.936}{0.001}\\S_\infty=936[/tex]

Hence the sum of the given geometric sequence to 2 dp is 936.00

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Answer:

-1, -24

Step-by-step explanation:

-9-(-8)

double negative = positive

-9+8=-1

21-45=-24

Answer:

a is -1, -2

b is -1, 2

c is 2, 2

Step-by-step explanation:

i hope i helped

Answer:

f(-8) = 169

Step-by-step explanation:

If the given equation is

[tex]27^{\frac13} = 9^{14} + 3^{x + 1}[/tex]

first simplify the left side using the fact that 27 = 3³:

[tex]27^{\frac13} = (3^3)^{\frac13} = 3^{\frac33} = 3^1 = 3[/tex]

and on the right side, 9 = 3²:

[tex]9^{14} = (3^2)^{14} = 3^{2\times14} = 3^{28}[/tex]

So we have

[tex]3 = 3^{28} + 3^{x + 1}[/tex]

Next,

[tex]3^{x+1} = 3^x \times 3^1 = 3 \times 3^x[/tex]

so that

[tex]3 = 3^{28} + 3 \cdot 3^x[/tex]

and dividing both side by 3 gives

[tex]1 = 3^{27} + 3^x[/tex]

Isolate 3ˣ :

[tex]3^x = 1 - 3^{27}[/tex]

Solve for x by taking the base-3 logarithm of both sides:

[tex]\log_3(3^x) = \log_3(1-3^{27})[/tex]

[tex]x \log_3(3) = \log_3(1-3^{27})[/tex]

[tex]\boxed{x = \log_3(1-3^{27})}[/tex]

Answer:

The answer would be 780 miles

Step-by-step explanation:

The reason that that's the answer because since it says that they will average about 65 miles per hour on a 12 hour trip, you have to multiply 65 time 12, which is 780 miles, so

65 miles x 12 hours = 780 miles   :)

Hope this helped!

Answer:

The minimum is 1

Step-by-step explanation:

1 is the lowest point of the function so that's your answer (:

The minimum of the sinusoidal function is 1.

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

y = 2sin(x + ∅) + 3 is a function

The minimum of the sinusoidal function.

y = 2sin(x + ∅) + 3 is a function is given

For the minimum value of sin(x + ∅) = -1, then

y = 2(-1) + 3

y = -2 + 3

y = 1

Thus the minimum of the sinusoidal function is 1.

More about the function link is given below.

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Answer:

x=16/81

Step-by-step explanation:

3^4x-1=15

81x-1=15

81x=15+1

81x+16

divide both sides by 81

x=16/81

Answer:

60 kilometers per hour.

420 kilometers will be covered

Step-by-step explanation:

speed = distance ÷ time.

so 60kmh = 240km divided by 4 Hours

60km = 1 Hour of distance

240km = 4 Hours of distance

Therefore 60 x 3 hour is 180km added to 240 is 420km. So in 7 hours traveling 60 kilometers per hour the will cover 420kms.

Answer:

100-200     Step-by-step explanation: yes 600 is half the students most of them are going to be in class

well the answer is 107.8823529411764705 (repeating decimal)

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Answer:

$0.46

Step-by-step explanation:

6 apples = $2.82

1 apple = 2.82 / 6

= $0.46

Answer:

The triangles are similar.

Step-by-step explanation:

They share a common angle (∠S) and the ratio of the two sides is the same, i.e. SP/SQ = SR/ST

Answer:

(c) The effect of a larger sample size on the margin of error is that the margin of error will increase.

Step-by-step explanation:

Answer:

45 5+[5(4+2)]?

Step-by-step explanation:

i hope is helped:)

The weight of the boy in the robot costume is 351/8 lb or 43 7/8 lb.

To find the weight of the boy, we need to subtract the weight of the costume from the total weight of the boy in the costume.

Total weight of boy and costume = 50 7/8 lb

Weight of costume = 3 1/2 lb

To find the weight of the boy, we can subtract the weight of the costume from the total weight:

Weight of boy = Total weight - Weight of costume

Convert both the total weight and the weight of the costume to improper fractions:

Total weight = 50 + 7/8 = 400/8 + 7/8 = 407/8 lb

Weight of costume = 3 + 1/2 = 6/2 + 1/2 = 7/2 lb

Now, subtract:

Weight of boy = (407/8) lb - (7/2) lb

To perform subtraction, we need to have a common denominator, which is 8 in this case:

Weight of boy = (407/8) lb - (56/8) lb

Now, subtract the fractions:

Weight of boy = (407 - 56)/8 lb

Weight of boy = 351/8 lb

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Answer:

4          /           6                   or 2/3

pecan           total tree

Answer:

2/3

Step-by-step explanation:

So, Bill planted -

Pecan trees = 4

Apple trees = 2

Total trees = 6

We want the fraction of Pecan trees. Thus,

4/6

Where 4 is Pecan trees, (What we want)

And 6 is the total.

4/6 in its simplest form is 2/3.

I hope it helps.

Answer:

She is incorrect; Paloma's ratio of seconds travelled to feet travelled is 1:10.

Step-by-step explanation:

Her ratio is 1:10 because the first number is the number of seconds, and the second number is the number of feet. So for every 1 second, she travels 10 feet, as indicated in the original problem.

Hope this helps.

Answer:

no, there is no solution

Step-by-step explanation:

put it in desmos, but the slopes are the same, so they are parallel and never touch. So, no solution.

Answer:

3,280/38650 x 100% = 8%

Answer:

-5/6 or 5/6

Step-by-step explanation:

Im assuming you want this equation equal to 0, so (6x-5)(6x+5) would reduce to 36x²-25=0. I would then add 25 to the other since and get

36x²=25, divide the whole thing by 36 to single out x

x²=25/36, which would reduce to x²=5/6.

thus x could be either -5/6 or 5/6

Answer:

its x-5 and 4x-5-3x

Step-by-step explanation:

I took the test

Answer:

1. -64

2.-27

Step-by-step explanation:

Hopes this helps

:)