The function g(x) is the height of a football x seconds after it is thrown in the air. The football reaches its maximum height of 28 feet in 6 seconds, and hits the ground at 12 seconds.

What is the practical domain for the function f(x)?

Type your answer in interval notation.

Answer:

[tex]100\pi \text{ in}^3[/tex]

Step-by-step explanation:

Volume of a Cone Equation:

[tex]v = \frac{1}{3}\times \pi \times r^2 \times h[/tex]

1) Find h

Use the Pythagorean Theorem to find h

[tex]a^2 \times b^2 = c^2[/tex]

Change diameter to radius. (10 in ---> 5in)

a = 5

[tex]1) 5^2 + b^2 = 13^2\\\\2) 25 + b^2 = 169\\\\3) b^2 =144\\\\4) 12[/tex]

Step 2) Subtract 25 on both sides so [tex]b^2[/tex] is alone

Step 3) Square root both sides

Step 4) h = 12

2) Plug in known variables:

h = 12 in

r = 5 in;

Equation now:

[tex]v = \frac{1}{3} \times \pi \times 5^2 \times 12[/tex]

3) Solve:

[tex]1) \frac{1}{3} \times \pi \times 5^2 \times 12\\\\2) \frac{\pi}{3} \times 5^2 \times 12\\\\3) \frac{\pi}{3} \times 25 \times 12 \\\\4) \frac{\pi}{3} \times 300\\\\5) \frac{300\pi}{3} \\\\\text{Simplify:}\\100\pi[/tex]

The profit function for a furniture company introducing a new line of lounge chairs is P(x) =[tex]-8.32x^2 + 1,248x - 36,400[/tex], where x represents the number of chairs to be manufactured and sold.

The problem provides the revenue function and cost function for a furniture company introducing a new line of lounge chairs. To find the profit function, we need to subtract the cost function from the revenue function.

The revenue function R(x) is given as 1,248x - [tex]8.32x^2[/tex], where x represents the number of chairs manufactured and sold. This function calculates the total revenue obtained by the company by multiplying the number of chairs sold (x) by the price of each chair (1,248 - 8.32x).

The cost function C(x) is given as 36,400 - 83.2x. This function calculates the total cost incurred by the company to manufacture x chairs, which includes both fixed and variable costs.

To find the profit function for the furniture company, we need to subtract the cost function C(x) from the revenue function R(x):

P(x) = R(x) - C(x) = (1,248x - [tex]8.32x^2[/tex]) - (36,400 - 83.2x)

Simplifying this expression, we get:

P(x) =[tex]-8.32x^2[/tex] + 1,248x - 36,400

Therefore, the profit function for the furniture company is P(x) = [tex]-8.32x^2[/tex] [tex]+ 1,248x - 36,400[/tex].

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Step-by-step explanation:

To solve for x, we need to isolate the variable on one side of the equation. We can start by subtracting 65 from both sides of the equation:

$12715 - 65 = x^2 - 5x

Simplifying:

$12650 = x^2 - 5x

Next, we can move all terms to one side of the equation:

x^2 - 5x - 12650 = 0

Now, we can use the quadratic formula to solve for x:

x = [-(-5) ± sqrt((-5)^2 - 4(1)(-12650))]/(2(1))

Simplifying:

x = [5 ± sqrt(63225)]/2

x = [5 ± 251]/2

So the solutions are:

x = (5 + 251)/2 = 128

x = (5 - 251)/2 = -123

Therefore, x can be either 128 or -123.

Answer:

The solution for problem a is cross multiplication

5×500=2500 and 15×x=15× so 15×=2500

divide both sides by the coefficient 15. 15x ÷15=×

divide 2500 by 15=500

x=500/3= approximately 166.7

Solution for b:

This one's easy!!

10/20=x/500

cross multiply

10×500=5000

20×X=20x

now we have the equation. 20x=5000

stay with me. I hope this makes sense ^_^

divide both sides by the coefficient 20

20x÷20=x

5000÷20=250

x=250

a is true

i hope this helps ;)

Mathematics is a field that involves primarily abstract reasoning and mental calculations, but there are still several types of equipment that mathematicians may use to aid in their work.

What are different equipments use in mathematics?

1.) Calculator: A calculator is an electronic device that performs arithmetic operations quickly and accurately. It is often used by mathematicians to check their calculations, solve equations, and perform more complex calculations.

2.) Protractor: A protractor is a tool used to measure and draw angles. It is commonly used in geometry and trigonometry to draw and measure angles of various shapes.

3.) Compass: A compass is a tool used to draw circles and arcs. It is commonly used in geometry to draw circles, bisect angles, and construct various geometric shapes.

4.) Ruler: A ruler is a straightedge tool used to measure lengths and draw straight lines. It is commonly used in geometry and algebra to draw graphs, construct figures, and measure distances.

5.) Graph paper: Graph paper is a type of paper that has a grid of small squares printed on it. It is often used in algebra and geometry to draw graphs, plot data, and make calculations.

The question doesn't contain any table and is incomplete, below is the complete question -

Fill in the table with equipment measurements.

Equipment Code: The required field for the primary key.

Standard for equipment: The kind of equipment. confirmed by the listing of equipment standards.

Use of Equipment: Describe how the piece of equipment is used in this field.

categorization: Select a categorization for this piece of equipment using the field provided. The Condition Assessment programme organises and categorises your data using this classification.

Equipment state: To characterise the equipment's condition, select one of the values from the list box: new, good, fair, or poor.

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Answer:

50

Step-by-step explanation:

25+25 whcih mdans this must be added to get 50 becuase 25 + 35 is 50

Answer:

The formula gives the circumference of a circle:

C = πd

Where d is the diameter of the circle.

Substituting the given values, we get:

C = (22/7) x 21 cm

C = 66 cm (approx)

Therefore, the circle's circumference with a diameter of 21 cm, approximated using π equals 22/7, is 66 cm.

So, the correct option is (C) 66 cm.

Answer:

$43.96

Step-by-step explanation:

We first need to find the area of the patio which is 12-foot by 14-foot

12 ft * 14 ft = 168 sq ft

next, we need to know how many quarts are needed to cover the entire area of the patio, and we know a quart cover 53 square feet, so we divide the total area of the patio by 53:

168 sq ft ÷ 53 sq ft/quart ≈ 3.17 quarts

We'll need to buy 4 quarts of paint to cover the entire patio.
The cost of 1 quart of paint is $10.99, so the total cost of 4 quarts will be:

4 quarts x $10.99/quart = $43.96

Therefore, the estimated cost of painting the concrete patio will be around $43.96.

The total weight of the dog toys that weighed 1/8 of a pound or 3/8 of a pound is 1 3/8 pounds.

A line plot is a graphical representation of data that involves placing X's or other symbols above a number line to show the frequency of each value in a data set.

Each X represents one occurrence of the data value on the number line. Line plots are useful for quickly visualizing the distribution of a data set, especially when there are only a few unique values in the data set.

Based on the line plot, we can see that there are 2 dog toys that weigh 1/8 of a pound and 3 dog toys that weigh 3/8 of a pound.

To find the total weight of the dog toys that weigh 1/8 of a pound or 3/8 of a pound, we need to add the weights of these toys.

The total weight of the dog toys that weigh 1/8 of a pound is 2/8 of a pound, which simplifies to 1/4 of a pound.

The total weight of the dog toys that weigh 3/8 of a pound is 3 x 3/8 = 9/8 of a pound.

Adding these weights together, we get:

1/4 + 9/8 = 11/8 of a pound

This simplifies to 1 3/8 pounds.

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Answer:

9

Step-by-step explanation:

[tex]2 + ( - 5) + 15 + ( - 3)[/tex]

[tex]2 - 5 + 15 - 3[/tex]

Add the negative and the positive numbers seperately:

[tex]17 - 8 = 9[/tex]

Answer:

The length of the flower bed is 11.4 feet.

Step-by-step explanation:

If the ratio of width to length of the flower bed is 10:19, this means that for every 10 units of width, there are 19 units of length.

Let's call the width of the flower bed "W" and the length "L". We know that W is 6 feet, so we can write:

W:L = 10:19

Substituting the value of W, we get:

6:L = 10:19

To solve for L, we can cross-multiply to get:

10L = 6 x 19

10L = 114

L = 11.4

Therefore, the length of the flower bed is 11.4 feet.

(a) All values at which g has a local minimum: -2, 3

(b) All local minimum values of g: g(-2) ≈ -2.5, g(3) ≈ -1.5

What is the Graph?

The graph is a visual representation of the function g, which shows how the output of the function varies with the input. It plots the values of g(x) on the vertical axis against the values of x on the horizontal axis.

(a) All values at which g has a local minimum:

From the graph, it appears that there are two values at which g has a local minimum:

x = -2

x = 3

(b) All local minimum values of g:

From the graph, the local minimum value at x = -2 appears to be approximately -2.5, and the local minimum value at x = 3 appears to be approximately -1.5. So, the local minimum values of g are:

g(-2) ≈ -2.5

g(3) ≈ -1.5

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Answer:331

Step-by-step explanation:

7360.3097-7029.415≈330.8947

Santiago could have $81 more than Ella after 18 years.

To calculate the amount of money each person can have after 18 years, we are able to use the formulation for compound interest:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Wherein:

For Ella's investment:

P = $4,800

r = 2.28125% = 0.0228125

n = 4

t = 18

[tex]A = 4800(1 + 0.0228125/4)^{(4*18)[/tex]

A = $8,481.48

For Santiago's investment:

P = $4,800

r = 2.28333% = 0.0228333

n = 365 (compounded daily)

t = 18

A = 4800(1 + 0.0228333/365)^(365*18)

A = $8,562.02

The distinction of their final amounts is:

$8,562.02 - $8,481.48 = $80.54

Therefore, Santiago could have $81 more than Ella after 18 years.

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Answer:

Step-by-step explanation:

Convert 3% to a decimal by doing 3/100. You should get 0.03.

Now multiply 0.03 and 44.50, you will get 1.335.

Add 1.335 to 44.50 and you will get 45.835.

The new price of the item after it was marked up is $45.835

I think the correct answer is 326

The mean is 49 and the standard deviation is 5.33.

What is mean?

The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.

We can use the empirical rule to solve these problems. According to the empirical rule:

About 68% of the data falls within one standard deviation of the mean.

About 95% of the data falls within two standard deviations of the mean.

About 99.7% of the data falls within three standard deviations of the mean.

a) To find the mean (u) and standard deviation (sigma) for each problem, we can use the following formulas:

u = (a + b) / 2

sigma = (b - a) / 6

where a and b are the lower and upper bounds for the data, respectively.

b) For each problem, we can use the given information to set up an equation and solve for either the mean or standard deviation.

If 68 percent of the data is between 42 and 58:

a) H: We are not given enough information to solve for the mean or standard deviation.

b) To find one of the missing values, we can use the formulas above and the given information. Since we are given that 68% of the data falls within one standard deviation of the mean, we know that:

(58 - u) / sigma = 1

Simplifying this equation, we get:

58 - u = sigma

We can also use the fact that the range of the data is 16 (from 42 to 58):

b - a = 16

58 - u - (42 - u) = 16

16 = 16u/16

Solving for the mean, we get:

u = (42 + 58) / 2

u = 50

Using the equation 58 - u = sigma, we can solve for the standard deviation:

sigma = 58 - u

sigma = 8

Therefore, the mean is 50 and the standard deviation is 8.

If 95 percent of the data is between 34 and 64:

a) u: We can find the mean using the formula:

u = (a + b) / 2

u = (34 + 64) / 2

u = 49

b) To find the standard deviation, we can use the formula:

sigma = (b - a) / 6

sigma = (64 - 34) / 6

sigma = 5.33

Therefore, the mean is 49 and the standard deviation is 5.33.

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The distance between Toby and Meg are approximately 95 feet apart.

We can solve this problem using the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

The distance between Toby and Meg is the hypotenuse of a right triangle with legs 57 feet and 76 feet.

So we can use the Pythagorean theorem to find this distance:

distance^2 = 57^2 + 76^2

distance^2 = 3249 + 5776

distance^2 = 9025

distance = sqrt(9025)

distance = 95

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The company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find the point at which the company starts to turn a profit, we need to find the value of x for which the revenue is greater than the cost of production.

The revenue function is R(x) = 7x, and the cost of production is C(x) = 13x + 132.

So, we need to solve the inequality:

R(x) > C(x)

7x > 13x + 132

Subtracting 13x from both sides, we get:

-6x > 132

Dividing both sides by -6 (and flipping the inequality because we're dividing by a negative number), we get:

x < -22

Therefore, the company will start to turn a profit when x is greater than -22. In other words, the company will start to turn a profit when they sell more than 22 units of their product.

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Answer:

0.7

Step-by-step explanation:

[tex]\frac{7}{10}=\frac{70}{100}=0.70[/tex]

The number that must row 2 in the matrix be multiplied for the matrix to be changed to B. -2.

What are row operations?

Row operations are mathematical operations that can be performed on the rows of a matrix to manipulate its properties or solve systems of linear equations.

To solve this problem, we need to perform row operations on the matrix until row 2 is transformed into the desired row. Each row operation involves multiplying a row by a scalar, adding or subtracting one row from another, or swapping two rows.

Starting with the given matrix:

20 -2

1 1 1 1 1 6 -14

We can perform the following row operations:

Subtract row 1 from row 2:

20 -2

1 1 1 -19 -19 4 -6

Multiply row 2 by -3:

20 -2

-3 -3 -3 57 57 -12 18

Subtract 2 times row 2 from row 1:

26 4

-3 -3 -3 57 57 -12 18

Divide row 1 by 13:

2 4/13

-3 -3 -3 57 57 -12 18

Therefore, we see that row 2 in the matrix must be multiplied by -3 to transform it into the desired row.

So the answer is: B. -2

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If each shape is 1 whole and the circle is divided in half and shaded on both sides, then the fraction of the shaded part would be [tex]\frac{1}{2}[/tex].

In standard form, the fraction [tex]\frac{1}{2}[/tex] is already in its simplest form, as both the numerator and denominator have no common factors other than 1. In word form, the fraction [tex]\frac{1}{2}[/tex] can be expressed as "one-half," which indicates that one of the two equal parts of the circle is shaded. In numerical-word form, the fraction [tex]\frac{1}{2}[/tex] can be written as "0.5" or "zero point five," which represents the decimal equivalent of the fraction. This form is useful when working with measurements and calculations that involve fractions.

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The complete question is:

Each shape is 1 whole. Write a fraction in standard form, word form, and numerical-word form for the parts that are shaded

Answer:

its on quizzes

Step-by-step explanation:

The total change in value is $45,000 - $12,000 = $33,000. The annual rate of change is 0.0495. Converting the rate of change to a percentage is 4.95%. Assuming the car value continues to drop by the same percentage, the value of the car in 2003 is $10,850.

A percentage is a way of expressing a number as a fraction of 100. Percentages are typically expressed using the symbol "%".

In the given question,

A) The total change in value is $45,000 - $12,000 = $33,000. The time period is 9 years (2000 - 1991). Therefore, the annual rate of change is:

r = [tex](Change in value / Initial value) ^ (1/Time period)[/tex] - 1

r = [tex]($33,000 / $45,000) ^ (1/9)[/tex] - 1

r = 0.0495

Rounding this to 4 decimal places, the annual rate of change is 0.0495.

B) Converting the rate of change to a percentage:

r = 0.0495 * 100

r = 4.95%

Therefore, the answer to part A in percentage form is 4.95%.

C) Assuming the car value continues to drop by the same percentage, we need to calculate the value of the car in the year 2003. The time period from 2000 to 2003 is 3 years. Therefore, the value of the car in 2003 can be calculated as follows:

Value in 2003 = $12,000 * [tex](1 - r) ^ 3[/tex]

Value in 2003 = $12,000 * [tex](1 - 0.0495) ^ 3[/tex]

Value in 2003 = $10,840.09

Rounding this to the nearest 50 dollars, the value of the car in 2003 is $10,850.

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Answer:  Therefore, at the start of the game, Peter had 80 marbles and Jack had 80 marbles.

Step-by-step explanation:

To solve this problem, we can start by noticing that each round cuts the number of teams in half. Therefore, we can create a table to see how many teams are left after each round:

Round Number of Teams

1 32

2 16

3 8

4 4

5 2

6 1

We can see that there are 6 rounds in total, and that the number of games in each round is half the number of teams. So we can calculate the number of games for each round and add them up to get the total number of games:

Round Number of Teams Number of Games

1 32 16

2 16 8

3 8 4

4 4 2

5 2 1

6 1 0

Adding up the number of games for each round, we get:

16 + 8 + 4 + 2 + 1 + 0 = 31

Therefore, a total of 31 games were played in the tournament.

The x intercept of the function f(x) = x√(x + 4) is at

(-4, 0) and (0, 0)

The x-intercept is the point where a graph or a line crosses the x-axis. In other words, it is the point where the value of the dependent variable (usually represented on the y-axis) is zero.

In an equation, the x-intercept is the value of x when y is equal to zero. It is often denoted by the point (x, 0) on a graph.

The plotted graph shows that the x intercept is at

(-4, 0) and (0, 0)

Graph is attached

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The equation of the line L is y = -8x + 35.

What is the slope?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

To find the equation of the line L that passes through the points (5,-5) and (4,3), we need to use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the given points.

First, we need to find the slope of the line L:

m = (y2 - y1) / (x2 - x1)

m = (3 - (-5)) / (4 - 5)

m = 8 / (-1)

m = -8

Now we can use either point to write the equation of the line. Let's use (5, -5):

y - (-5) = -8(x - 5)

y + 5 = -8x + 40

y = -8x + 35

Therefore, the equation of the line L is y = -8x + 35.

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Answer: D. The ecosystem's carrying capacity is higher, so more rabbits have been born and fewer have died.

Explanation: Carrying capacity refers to the maximum number of individuals that an ecosystem can support without causing significant harm to the environment.  In this case, the grassland ecosystem experienced an especially rainy year, which likely led to favorable conditions for both the rabbits and their food sources.

With more rainfall, there would be an abundance of vegetation in the grassland ecosystem.  This increase in food availability would provide ample resources for the rabbits to thrive and reproduce.  As a result, more rabbits would be born during this year.

Additionally, the favorable conditions provided by the rainy year may have also reduced the mortality rate of the rabbits.  With plentiful food and water, the rabbits would be less likely to face resource scarcity and increased competition, leading to fewer deaths.

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