The graph below shows the amount of water used at a campground based on the number of people staying at the campground.What is the average amount of water used per person?A. 10 gallonsB. 12.5 gallonsC. 20 gallonsD. 22.5 gallons

Answer:

10%

Step-by-step explanation:

Original medication = 40 my

It was increased to 45mg

The increase can be calculated as follows

45-40

= 5

Percent Increase can be calculated as follows

= 4/40 ×100

= 0.1×100

= 10%

Hence the increase is 10%

Answer:

\(\large \boxed{\sf \bf \ \ k=320 \ \ }\)

Step-by-step explanation:

Hello,

The number of weekly social media posts varies directly with the square root of the poster’s age and inversely with the cube root of the poster’s income.

If a 16-year-old person who earns $8,000 makes 64 posts in a week, what is the value of k?

\(64=\dfrac{\sqrt{16}}{\sqrt[3]{8000}}\cdot k=\dfrac{4}{20}\cdot k=\dfrac{1}{5}\cdot k=0.2\cdot k\\\\k=64*5=320\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The percentage of the class that are boys is 48%.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. In simpler term ratio compares two values.

Therefore, the ratio of the number of boys to the number of girls in a class is 12 : 13.

The percentage of the class that are boys can be calculated as follows:

percentage of the class that are boys = 12 / 25 × 100

percentage of the class that are boys =  1200 / 25

percentage of the class that are boys = 48%

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When the unit of labor is 6, the marginal product is 796.

The marginal production function (MP) can be obtained by taking the derivative of the production function with respect to labor (L). In this case, the production function is Q = 4L + 3L² + 7L³. Taking the derivative of this equation with respect to L will give us the marginal production function.

The derivative of the production function with respect to L is MP = 4 + 6L + 21L².

To find the marginal product when the unit of labor is 6, we substitute L = 6 into the marginal production function:

MP = 4 + 6(6) + 21(6)²

  = 4 + 36 + 21(36)

  = 4 + 36 + 756

  = 796.

In summary, the marginal production function is MP = 4 + 6L + 21L², and the marginal product when the unit of labor is 6 is 796. The marginal production function represents the additional output produced when one additional unit of labor is employed.

In this case, the marginal production function is a quadratic function with positive coefficients, indicating increasing returns to scale. The marginal product of labor represents the change in output resulting from a one-unit increase in labor input, given the level of other inputs.

When the unit of labor is 6, the marginal product is found by substituting L = 6 into the marginal production function, resulting in a value of 796. This means that when the firm employs an additional unit of labor (6th unit), the output increases by 796 units.

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By graphing or visualizing the parabolic shape, we can observe where the graph intersects the x-axis, which represents the solutions to the equation. In this case, the solutions are x = -3 and x = 1.

To solve the quadratic equation x^2 + 2x - 3 = 0 by graphing, we can plot the graph of the equation and find the x-values where the graph intersects the x-axis.

First, let's rearrange the equation to the standard form: x^2 + 2x - 3 = 0.

We can create a graph by plotting points for different values of x and then connecting them. However, I can describe the process and the key points on the graph.

1. Find the x-intercepts: These are the points where the graph intersects the x-axis. To find them, set y (the equation) equal to zero and solve for x:

  0 = x^2 + 2x - 3.

  This quadratic equation can be factored as (x + 3)(x - 1) = 0.

  Therefore, x = -3 or x = 1.

2. Plot the points: Plot the points (-3, 0) and (1, 0) on the graph. These are the x-intercepts.

3. Draw the graph: The graph of the equation x^2 + 2x - 3 = 0 is a parabola that opens upward. It will pass through the x-intercepts (-3, 0) and (1, 0).

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Answer:

C.

Step-by-step explanation:

Hi there!

We know that \(x^0\) is equal to 1 because any number raised to the zero is always going to be 1.

With that out of the way, we are left with \(x^-^3/1\), which is equivalent to \(x^-^3\)

Using negative exponent rules,

The expression is flipped and the -3 becomes a positive 3.

It will look like this

\(\frac{1}{x^3}\)

Your answer is C.

I hope this helps!

The dot plot that displays the data distribution is the dot plot on the lower left corner of the options with

Two dots at 0

One dot at 2

Two dots at 3

Four dots each at 4, 5, and 6

One dot at 7

A dot plot is a graphical presentation of data, on a number line, with the number of points of dot representing the frequency of data at each value on the number line.

The data can be presented as follows;

2, 6, 4, 3, 0, 3, 4, 6, 5, 0, 4, 5, 7, 5, 6, 4, 5, 6

The above data can be arranged in increasing order as follows; 0, 0, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7
Therefore, the frequencies of 0s is two, the frequencies of 4s, 5s and 6s are four each, and the frequency of 7 is one, which corresponds to the third graph or the graph in the bottom left corner of the figure.

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Answer:

x = 5

Step-by-step explanation:

We know that BD = 2x - 1 and BC + CD = BD.  Thus, we can set the sum of (x- 3) and 7 equal to 2x - 1 to find x:

BC + CD = BD

x - 3 + 7 = 2x - 1

x + 4 = 2x - 1

x + 5 = 2x

5 = x

Thus, x = 5

Checking the validity of our answer:

We can check that our answer is correct by plugging in 5 for x in x - 3 and 2x - 1 and checking that we get the same answer on both sides of the equation:

5 - 3 + 7 = 2(5) - 1

2 + 7 = 10 - 1

9 = 9

Thus, our answer is correct.

Answer:

30,000

Step-by-step explanation:

26,490 becomes 30,000

The value of y is 18

Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.

Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.

Therefore;

14/21 = 12/y

14y = 21 × 12

14y = 252

divide both sides by 14

y = 252/14

y = 18

Therefore the value of y is 18.

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Answer:

Step-by-step explanation:

14.75 - 8.85 = 5.9

5.9/2

The area of the base of the trapezoid prism is 2.5 in²

An equation is an expression that shows the relationship between two or more numbers and variables. Types of equation are linear, quadratic, cubic and so on.

Area is the amount of space occupied by a two dimensional shape. The area of a trapezoid is the sum of the parallel sides multiplied by half of the height. It is given by:

Area = 1/2(sum of parallel sides) * height

The base of the prism shown is a trapezoid with parallel sides 2 in and 3 in, and height of 1 in. Hence:

Area = 1/2(sum of parallel sides) * height

Substituting:

Area = (1/2)(2 + 3) * 1

Area = 2.5 in²

The area is 2.5 in²

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Answer:

12

Step-by-step explanation:

Answer:

5 2/3

Step-by-step explanation:

Answer:

three

Step-by-step explanation:

stem. is the tens place and the leaf is the. ones place

so you want to find 68 so you look in the stem column and look for six

in the row there are 6 numbers which mean:

60, 61, 67, 68, 68, 68

as you can see there is three 68 there for the answer ths 3

Let us first calculate the slope of the function. We need 2 points (0,2.5) and (100,37.5)

so the slope is

So the equation is

A. By substituting the given point.

In this case y=4 and x=3, so we have

which is an absurd. This imply that this point doesnt belong to the line.

Now, we will make the graph:

where we can see that this point is not into the line

Step-by-step explanation:

this is crazy but fun and easy

The value is 1024

Given that (x.x^2.x^3.....x^15)/(x^2+x^4+x^6...x^20)

How to Multiply Exponents With same Bases?

The bases of the equation stay the same, and the values of the exponents get added together

(x^1+2+3+4+5+6+7+8+9+10+11+12+13+14+15)/(x^2+4+6+8+10+12+14+16+18+20)

(x^120)/(x^110)

(x^10)

Now =2

2^10=1024

Therefore  (x.x^2.x^3.....x^15)/(x^2+x^4+x^6...x^20)=1024 when x =2

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Answer:

Step-by-step explanation:

3.6*

It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2

For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.

We get

36 = s^2

Now, we need to get the square root of both sides, which gives us

s = √36 s = 6 cm

Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.

Therefore, the perimeter of the square is 24 cm.

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Answer:

Regal Theatre makes 1.6 times more than Player Productions when they have 0.25 hours longer productions

Step-by-step explanation:

Given

\(h(t) \to\) player production theatre

\(g(t) \to\) regal theatre

Where:

\(g(t) = 1.6h(t + 0.25)\)

Required

Compare both functions

We start from the bracket

\(t + 0.25\)

The + in \(t + 0.25\) means longer hours of production

So:

\(t + 0.25\) means 0.25 hours longer that player productions

\(g(t) = 1.6h(t + 0.25)\)  can be rewritten as:

\(g(t) = 1.6 * h(t + 0.25)\)

The above means 1.6 times player production when they have 0.25 longer hours.

The percent of the bags of chips weigh less than 176 grams is b 16%

From the question, we have the following parameters that can be used in our computation:

Mean = 180

Standard deviation = 4

Bags of chips weigh less than 176 grams

This means that

x = 176

So, the z-score is

z = (176 - 180)/4

Evaluate

z = -1

The percent of the bags of chips weigh less than 176 grams is represented as

P = P(z < -1)

Using a graphing calculator, we have

Percentage = 0.15866

So, we have

Percentage = 16%

Hence , the percentage is 16%

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The key features of the dashed graph are

A graph is a pictorial representation of a function

To describe the key features of the dashed graph, we proceed as follows.

So, the key features of the dashed graph are

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Answer:

B

Step-by-step explanation:

The dashed lines are problem asymptotes, where the denominator is 0. It's showing those at x = 0 and x = 4. Plug in 0 to answer B and you get

(0)(0-4) and that equals 0

Plugging in 4, you get

(4)(4-4) = 4(0) and that also equals 0

0 is what creates that space in the function and disconnects it

Answer:

x = 0 , x = 2

Step-by-step explanation:

3x² = 6x ( subtract 6x from both sides )

3x² - 6x = 0 ← factor out 3x from each term

3x(x - 2) = 0

equate each factor to zero and solve for x

3x = 0 ⇒ x = 0

x - 2 = 0 ( add 2 to both sides )

x = 2

solutions are x = 0 , x = 2

Answer:

x= 2,180

x= number of adult tickets sold

Step-by-step explanation:

First, we need to establish the system of equations:

x= number of adult tickets sold

y= number of children tickets sold

5.5x + 3.5y = 22,210

x + y = 5,100

Now, we isolate one variable in a formula and substitute its value in the other:

x= 5,100 - y

5.5*(5,100 - y) + 3.5y= 22,210

28,050 - 5.5y +3.5y = 22,210

2y= 5,840

y= 2,920

x= 5,100 - 2,920

x= 2,180

Answer:

i

Step-by-step explanation:

Answer:

12 feet

Step-by-step explanation:

use the pythagorean theorem to figure out what the hypotenuse is

3.5^2+3.5^2=x^2

12.25+12.25=x^2

25=x^2

x=5

now that you know the hypotenuse, you can find the perimeter by adding up all the sides

3.5+3.5+5=12

Answer:

the probability that A is the overall winner is 5/14 or 0.35714

Step-by-step explanation:

Given the data in the question;

probability that A is the overall winner P[A is the overall winner]

⇒ \(P_{A}\)\(P_{A}\) + \(P_{A}\)\(P_{C}\)\(P_{B}\)\(P_{A}\)\(P_{A}\) + \(P_{A}\)\(P_{C}\)\(P_{B}\)\(P_{A}\)\(P_{C}\)\(P_{B}\)\(P_{A}\) \(P_{A}\)  + ................

= \(P_{B}\)\(P_{C}\)\(P_{A}\)\(P_{A}\) + \(P_{B}\)\(P_{C}\)\(P_{A}\)\(P_{B}\)\(P_{C}\)\(P_{A}\)\(P_{A}\) + \(P_{B}\)\(P_{C}\)\(P_{A}\)\(P_{B}\)\(P_{C}\)\(P_{B}\)\(P_{C}\)\(P_{A}\) + ........

P(A) = \(\frac{1}{2}\) = \(P_{B}\) = \(P_{C}\)             ∴{ they are evenly matched player}

so P(A is overall winner) will be;

= (\(\frac{1}{2}\))² + (\(\frac{1}{2}\))⁵ + (\(\frac{1}{2}\))⁸ + ..........+ (\(\frac{1}{2}\))⁴ + (\(\frac{1}{2}\))⁷ + (\(\frac{1}{2}\))¹⁰ + .............

= (\(\frac{1}{2}\))² [1 + (\(\frac{1}{2}\))³ + (\(\frac{1}{2}\))⁶ + .........] + (\(\frac{1}{2}\))⁴[1 + (\(\frac{1}{2}\))³ + (\(\frac{1}{2}\))⁶ + .........]

= [ (\(\frac{1}{2}\))² + (\(\frac{1}{2}\))⁴ ] [ 1 / 1 - (\(\frac{1}{2}\))³ ]

= [ (\(\frac{1}{4}\)) + (\(\frac{1}{16}\)) ] [ \(\frac{8}{7}\) ]

= \(\frac{5}{16}\) × \(\frac{8}{7}\)

= 5/14 or 0.35714

Therefore, the probability that A is the overall winner is 5/14 or 0.35714

The probability that A is the overall winner is; 5/14

Now, if the player loses, then it means that two games in a row are won by the same player, and then the tournament will be over. Thus; \(P_{L}\) = 0

       \(P_{WLX}\) = ¹/₈

Furthermore from that above, he will have another chance to win twice in a row which gives a probability in form of a geometric series as;

¹/₄ + (¹/₄ × ¹/₈ ) + (¹/₄ × ¹/₈² ) +  (¹/₄ × ¹/₈³ ) + ........

Now, for that series, as n approaches infinity, the sum of the series would give us;

∑ = ¹/₄(1/(1 - ¹/₈ ))

⇒ ¹/₄(⁸/₇)

⇒ ²/₇

Since player C's first game would already be against another game's winner, then it means that P is also the chance player C will win the tournament but the probability that player A will win is same as probability that player B will win which is;

[1 - (²/₇)]/2

⇒ ⁵/₇ × ¹/₂

P(A) = P(B) = ⁵/₁₄

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Answer:

Associative

Step-by-step explanation:

The associate property for multiplication states that \(a\times(b\times c)=(a\times b)\times c\), thus, \((2\times 6)\times 4 = 2\times (6\times 4)\). The way factors are grouped does not change the product, essentially.