A farmer earns $___ for each orange she sells. She had to pay $___ for fertilizer. Part A: Rewrite the description by filling in the blanks with values of your choice to show the amount of money the farmer could earn selling any number of oranges, n. Make sure the values you choose make sense for this situation. (6 points) Part B: Write an algebraic expression from your written description used in Part A. Let n stand for the number of oranges. (6 points)

Answer:

Step-by-step explanation:

n=30

r=12

Plug into formula

you get:

1.7 in²

The measure of the interior angle at vertex F is 72 degrees.

A hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.

The angle of the hexagon is given in terms of x,

The sum of the angle is equal to 720 degrees

[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]

[tex]20\text{x} = 720[/tex]

[tex]\text{x} = 36[/tex]

[tex]\bold{2x = 72^\circ}[/tex]

Therefore, the measure of interior angle at vertex F is equal to 72 degrees.

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Answer:

Relative maximum at x=0; Relative minimum at x=8/3

Step-by-step explanation:

To find the relative maximums and the relative minimums, you must first find the first derivative of the function. The first derivative of this function is 6x^2-16x. Simply it and you get 2x(3x-8). X would be equal to 0 and 8/3. Next, make a number line where you put 0 and 8/3 have a value of zero.

        +                           -                                 +      

-------------------0----------------------------8/3-----------------------

Plug in a value of x<0 to get the region left of 0. Say we use -1, we get -2(-3-8), which is positive, meaning that it is increasing there. From 0 to 8/3, if we use 1, we get 2(3-8), which is decreasing. If we use 3, we get 6(9-8), which is increasing. From this, we can see that when x=0, the graph has a relative maximum. When x=8/3, the graph has a relative minimum.

Answer:

[tex]m = \frac{35 - 15}{4 - 0} = \frac{20}{4} = 5[/tex]

[tex]y = 5x + 15[/tex]

Answer:

x = - 5 , x = 2

Step-by-step explanation:

f(x) = x² + 3x - 10

to find the zeros let f(x) = 0 , that is

x² + 3x - 10 = 0

consider the factors of the constant term (- 10) which sum to give the coefficient of the x- term (+ 3)

the factors are + 5 and - 2 , since

5 × - 2 = - 10 and 5 - 2 = + 3 , then

(x + 5)(x - 2) = 0 ← in factored form

equate each factor to zero and solve for x

x + 5 = 0 ( subtract 5 from both sides )

x = - 5

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

x = 2

the zeros are x = - 5 , x = 2

Answer:

when substituting x = -0.5, 0, and 1 into the equation, we get the results -8, -7, and -5, respectively.

Step-by-step explanation:

Part A:

To solve the equation 5 + x - 12 = 2x - 7, follow these steps:

Combine like terms on each side of the equation:

-7 + 5 + x - 12 = 2x - 7

-14 + x = 2x - 7

Simplify the equation by moving all terms containing x to one side:

x - 2x = -7 + 14

-x = 7

To isolate x, multiply both sides of the equation by -1:

(-1)(-x) = (-1)(7)

x = -7

Therefore, the solution to the equation is x = -7.

Part B:

Now let's substitute the given values of x and evaluate the equation:

For x = -0.5:

5 + (-0.5) - 12 = 2(-0.5) - 7

4.5 = -1 - 7

4.5 = -8

For x = 0:

5 + 0 - 12 = 2(0) - 7

-7 = -7

For x = 1:

5 + 1 - 12 = 2(1) - 7

-6 = -5

Remember to use the appropriate units for measurements when calculating surface area.

To find the surface area of an object, you need to calculate the total area of all its exposed surfaces. The method for finding the surface area will vary depending on the shape of the object. Here are some common shapes and their respective formulas:

1. Cube: The surface area of a cube can be found by multiplying the length of one side by itself and then multiplying by 6 since a cube has six equal faces. The formula is: SA = 6s^2, where s is the length of a side.

2. Rectangular Prism: A rectangular prism has six faces, each of which is a rectangle. To find the surface area, calculate the area of each face and add them up. The formula is: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.

3. Cylinder: The surface area of a cylinder includes the area of two circular bases and the area of the curved side. The formula is: SA = 2πr^2 + 2πrh, where r is the radius and h is the height.

4. Sphere: The surface area of a sphere can be found using the formula: SA = 4πr^2, where r is the radius.

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The linear equation from the given table is expressed as:

y =  -1500x + 8350

The general form for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

The formula for the equation of a line through two coordinates is:

(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)

We will take the two coordinates (1, 6850) and (2, 5350)

Thus:

(y - 6850)/(x - 1) = (5350 - 6850)/(2 - 1)

(y - 6850)/(x - 1) = -1500

y - 6850 = -1500x + 1500

y = -1500x + 1500 + 6850

y =  -1500x + 8350

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The triangles DEF and SRQ are not similar triangles

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

The triangles in this figure are

DEF and SRQ

These triangles are not similar

This is because:

The corresponding angles in the triangles are not equal

For DEF, the angles are

50, 90 and 40

For SRQ, the angles are

51, 90 and 39

This means that they are not similar by any similarity statement

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Answer:

Percent error is calculated using the formula:

   Percent Error = ( |Predicted Value - Actual Value| / Actual Value ) * 100%

Plugging in Brianna's prediction and the actual number of puppies sold:

   Percent Error = ( |16 - 9| / 9 ) * 100%

The absolute value of (16 - 9) is 7, so the calculation becomes:

   Percent Error = ( 7 / 9 ) * 100%

This is approximately 77.78%, which is Brianna's percent error in her prediction.

The functions y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions because they are linearly independent and satisfy the given homogeneous linear differential equation, allowing for the formation of the general solution.

To show that y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) are a fundamental set of solutions, we need to demonstrate two things: linear independence and satisfaction of the given homogeneous linear differential equation.

First, let's consider linear independence. We can prove it by showing that there is no constant c₁ and c₂, not both zero, such that c₁y₁(t) + c₂y₂(t) = 0 for all t.

Now, let's verify that y₁(t) and y₂(t) satisfy the homogeneous linear differential equation. If the given differential equation is of the form ay''(t) + by'(t) + cy(t) = 0, we can substitute y₁(t) and y₂(t) into the equation and verify that it holds true.

Once we have established linear independence and satisfaction of the differential equation, we can state that the general solution to the homogeneous linear differential equation is given by y(t) = c₁y₁(t) + c₂y₂(t), where c₁ and c₂ are arbitrary constants. This general solution represents the linear combination of the fundamental set of solutions.

In summary, y₁(t) = e^ãt cos(μt) and y₂(t) = e^ãt sin(μt) form a fundamental set of solutions for the given differential equation, and the general solution is given by y(t) = c₁y₁(t) + c₂y₂(t).

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a. There are 15,600 ways to select a president, a vice president, and a secretary from a class of 26 members.

b. There are 14,950 ways to form a 4-person committee from a class of 26 members.

a. To select a president, a vice president, and a secretary from a class of 26 members, we can use the concept of permutations.

For the president position, we have 26 choices. After selecting the president, we have 25 choices remaining for the vice president position. Finally, for the secretary position, we have 24 choices left.

The total number of ways to select a president, a vice president, and a secretary is obtained by multiplying the number of choices for each position:

Number of ways = 26 * 25 * 24 = 15,600

Therefore, there are 15,600 ways to select a president, a vice president, and a secretary from a class of 26 members.

b. To form a 4-person committee from a class of 26 members, we can use the concept of combinations.

The number of ways to choose a committee of 4 people can be calculated using the formula for combinations:

Number of ways = C(n, r) = n! / (r!(n-r)!)

where n is the total number of members (26 in this case) and r is the number of people in the committee (4 in this case).

Plugging in the values, we have:

Number of ways = C(26, 4) = 26! / (4!(26-4)!)

Calculating this expression, we get:

Number of ways = 26! / (4! * 22!)

Using factorials, we simplify further:

Number of ways = (26 * 25 * 24 * 23) / (4 * 3 * 2 * 1) = 14,950

Therefore, there are 14,950 ways to form a 4-person committee from a class of 26 members.

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Third option is correct.The midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b) is (0, b/2).

To find the midpoint of segment WZ, we need to average the x-coordinates and the y-coordinates of the endpoints.

The coordinates of point W are (0, 0), and the coordinates of point Z are (0, b).

To find the x-coordinate of the midpoint, we average the x-coordinates of W and Z:

(x-coordinate of W + x-coordinate of Z) / 2 = (0 + 0) / 2 = 0 / 2 = 0

To find the y-coordinate of the midpoint, we average the y-coordinates of W and Z:

(y-coordinate of W + y-coordinate of Z) / 2 = (0 + b) / 2 = b / 2

Therefore, the midpoint of segment WZ is (0, b/2).

So, the correct answer is (0, b/2).

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Answer:

Step-by-step explanation:

A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres

20 * 10 * 10 = 2000cm^3

1000 cm^3 = 1 Litres

​2000 cm^3 = 2 Litres

There are 70 ways a person can order a two-course meal from the given restaurant.

To determine the number of ways a person can order a two-course meal from a restaurant that offers 10 appetizers and 7 main courses, we can use the concept of combinations.

First, we need to select one appetizer from the 10 available options.

This can be done in 10 different ways.

Next, we need to select one main course from the 7 available options. This can be done in 7 different ways.

Since the two courses are independent choices, we can multiply the number of options for each course to find the total number of combinations.

Therefore, the number of ways a person can order a two-course meal is 10 [tex]\times[/tex] 7 = 70.

So, there are 70 ways a person can order a two-course meal from the given restaurant.

It's important to note that this calculation assumes that a person can choose any combination of appetizer and main course.

If there are any restrictions or limitations on the choices, the number of combinations may vary.

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(a) Using Newton's method, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279.

(b) The absolute minimum value of f is undefined since the function is a polynomial of even degree, and it approaches positive infinity as x approaches positive or negative infinity.

(a) To find the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex]  we can use Newton's method by finding the derivative of the function and solving for the values of x where the derivative is equal to zero.

First, let's find the derivative of f(x):

f[tex]'(x) = 6x^5 - 4x^3 + 12x^2 - 2[/tex]

Now, let's apply Newton's method to find the critical numbers. We start with an initial guess, x_0, and use the formula:

[tex]x_{(n+1)} = x_n - (f(x_n) / f'(x_n))[/tex]

Iterating this process, we can approximate the values of x where f'(x) = 0.

Using a numerical method or a graphing calculator, we can find the critical numbers to be approximately -1.084, -0.581, -0.214, 0.580, and 1.279.

Therefore, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279,

(b) To find the absolute minimum value of f(x), we need to analyze the behavior of the function at the critical numbers and the endpoints of the interval.

Since the function f(x) is a polynomial of even degree, it approaches positive infinity as x approaches positive or negative infinity.

Therefore, there is no absolute minimum value for the function.

Hence, the absolute minimum value of f is undefined.

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The total petty cash expenditures would be =$130.84

To calculate the petty cash expenditures, the following is added up as follows;

The cost for stamp = $12.50

The cost for coffee supplies = $25.19

The cost for pizza delivery = $15.50

The cost for white board markers = $20.00

The cost for sympathy greeting card= $5.78

The cost of flowers for Jean's retirement farewell = $39.87

The cost of courier = $12.00

Therefore the total petty cash expenditures would be= 12.50+25.19+15.50+20+5.78+39.87+12= $130.84

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i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is [tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex]. Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =[tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex].

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Answer: The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.

Answer:

The function given here is a quadratic function of the form f(t) = at^2 + bt + c, where a is -2, b is 8, and c is 300. The maximum value of a quadratic function occurs at its vertex. For a function in the form f(t) = at^2 + bt + c, the t-coordinate of the vertex is given by -b/(2a). We can use this to find the time at which the firework reaches its maximum height.

Given a = -2 and b = 8, we can calculate t = -b/(2a):

t = -8/(2*-2) = 2

We can then substitute this value back into the height equation to find the maximum height:

h(2) = -2(2)^2 + 8*2 + 300

h(2) = -8 + 16 + 300

h(2) = 308

So, the greatest height the fireworks reach is 308 feet.

I agree with both Priya's and Han's equations.

To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.

For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:

2 - 2 = (1/3)(1 - 1)

0 = 0

The equation holds true, so Priya's equation is correct.

For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:

3(2) - 1 = 5

6 - 1 = 5

5 = 5

The equation also holds true, so Han's equation is correct.

Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.

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Answer:

First, the graph is overall decreasing with two local maximums and two local minimums.

Second, it has 5 zeros, since there is one intersection and two touching points with the x-axis.

Considering the above observations we can state that:

Answer:

12

Step-by-step explanation:

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

We are looking at the denominators of 4, 2 and 3.  We are looking for the least common multiple.  If we listed out the multiples of the 3 numbers, we are looking for the lowest number that is in all three lists.

4,8,12

2,4,6,8,10,12

3,6,9,12

the lowest number that we see on all three lists is 12.

Part 1- The lower class boundary for the first class is 100.

Part 2- Approximately 75% of students take exactly two courses.

Part 1:

To find the lower class boundary for the first class, we need to consider the given class intervals. The lower class boundary is the smallest value within each class interval.

Given the class intervals:

100 - 104

105 - 109

110 - 114

115 - 119

120 - 124

125 - 129

130 - 134

The lower class boundary for the first class interval (100 - 104) would be 100.

So, the lower class boundary for the first class is 100.

Part 2:

To determine the percentage of students who take exactly two courses, we need to calculate the relative frequency for that particular category.

Given the data:

of Courses Frequency Relative Frequency Cumulative Frequency

1 23 0.4423 23

2 - 39

3 13 0.25 -

We can see that the cumulative frequency for the second class (2 courses) is 39. To find the relative frequency for this class, we need to divide the frequency by the total number of students surveyed, which is 52.

Relative Frequency = Frequency / Total Number of Students

Relative Frequency for 2 courses = 39 / 52 ≈ 0.75 (rounded to 4 decimal places)

To convert this to a percentage, we multiply the relative frequency by 100.

Percentage of students taking exactly two courses = 0.75 * 100 ≈ 75%

Therefore, approximately 75% of students take exactly two courses.

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Question

Part 1.

Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below.

Lengths (mm) Frequency

100 - 104 1

105 - 109 16

110 - 114 71

115 - 119 108

120 - 124 83

125 - 129 18

130 - 134 3

What is the lower class boundary for the first class?

class boundary =

Part 2

In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

Please round your answer to 4 decimal places for the Relative Frequency if possible.

# of Courses Frequency Relative Frequency Cumulative Frequency

1 23 0.4423 23

2   39

3 13 0.25

What percent of students take exactly two courses? %

The Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.

Let's assume that the Peterson family used their sprinkler for a certain number of hours, which we'll denote as x, and the Stewart family used their sprinkler for the remaining hours, which would be 45 - x.

The water output rate for the Peterson family's sprinkler is given as 35 L per hour. Therefore, the total water output for the Peterson family can be calculated by multiplying the water output rate (35 L/h) by the number of hours they used the sprinkler (x): 35x.

Similarly, for the Stewart family, with a water output rate of 40 L per hour, the total water output for their sprinkler is given by 40(45 - x).

According to the problem, the combined total water output for both families is 1,650 L. Therefore, we can write the equation:

35x + 40(45 - x) = 1,650.

Simplifying the equation, we get:

35x + 1,800 - 40x = 1,650,

-5x = 1,650 - 1,800,

-5x = -150.

Dividing both sides of the equation by -5, we find:

x = -150 / -5 = 30.

So, the Peterson family used their sprinkler for 30 hours, and the Stewart family used theirs for 45 - 30 = 15 hours.

Therefore, the Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.

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The angular velocity of the object is 31.25 radians/second.

Angular velocity is defined as the change in angular displacement per unit of time. In this case, the object rotates a total of 25 radians in 0.8 seconds. Therefore, the angular velocity can be calculated by dividing the total angular displacement by the time taken.

Angular velocity (ω) = Total angular displacement / Time taken

Given that the object rotates 25 radians and the time taken is 0.8 seconds, we can substitute these values into the formula:

ω = 25 radians / 0.8 seconds

Simplifying the equation gives:

ω = 31.25 radians/second

So, the angular velocity of the object is 31.25 radians/second.

Angular velocity measures how fast an object is rotating and is typically expressed in radians per second. It represents the rate at which the object's angular position changes with respect to time.

In this case, the object completes a rotation of 25 radians in 0.8 seconds, resulting in an angular velocity of 31.25 radians per second. This means that the object rotates at a rate of 31.25 radians for every second of time.

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Note the translated question is:

An object that is rotated moves 25 radians in 0.8 seconds. what is the angular velocity of said object?

Answer:

Step-by-step explanation:

To determine the remaining sides of triangle THE given that sin(E) = 4 and TE = 4, we can use the sine ratio.

The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.

In this case, sin(E) = 4/TE, which means the side opposite angle E is 4 and the hypotenuse TE is 4.

Using the Pythagorean theorem, we can find the length of the remaining side TH:

TH^2 = TE^2 - HE^2

TH^2 = 4^2 - 4^2

TH^2 = 16 - 16

TH^2 = 0

TH = 0

Therefore, the length of side TH is 0.