Write an essay on how a surveyor may use trigonometric functions. Use key vocabulary words that have been presented in the Unit throughout your essay. Provide at least 3 detailed examples when writing.

Let [tex]x[/tex] be one of the numbers. Then the other one is [tex]10-x[/tex].

Therefore, the sum of their cubes is:

[tex]x^3+(10-x)^3=x^3+1000-300x+30x^2-x^3=30x^2-300x+1000[/tex]

Now we need to find the minimum value of the resulting function.

[tex](30x^2-300x+1000)'=60x-300[/tex]

[tex]60x-300=0\\60x=300\\x=5[/tex]

The derivative is negative to the left of [tex]5[/tex] and positive to the right of it, therefore, at [tex]5[/tex] there exists the minimum.

[tex]5^3+(10-5)^3=125+125=250[/tex]

Therefore, the minimum value is 250.

A table that best represent the equation include the following: H. table H.

In order to determine the table that best represent the equation, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = 1 in table F, the linear function is given by;

y = x - 12

y = 1 - 12

y = -11 (False).

When the value of x = 0 in table G, the linear function is given by;

y = x - 12

y = 0 - 12

y = -12 (True).

When the value of x = 2 in table G, the linear function is given by;

y = x - 12

y = 2 - 12

y = -10 (False).

When the value of x = 0 in table H, the linear function is given by;

y = x - 12

y = 2 - 12

y = -10 (True).

When the value of x = 4 in table H, the linear function is given by;

y = x - 12

y = 4 - 12

y = -8 (True).

When the value of x = 6 in table H, the linear function is given by;

y = x - 12

y = 6 - 12

y = -6 (True).

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The correct statement would be: An ice cream would need more than 9 votes from the first-place line in the preference schedule.

To determine the number of votes an ice cream would need to accumulate in order to be the majority winner, we should analyze the preference schedule provided.

Looking at the preference schedule, we can see that there are four ice cream flavors:

Chocolate (C), vanilla (V), strawberry (S), and pistachio (P).

Each row represents the rankings given by Janice's friends.

To be the majority winner, an ice cream flavor would need to accumulate more votes than any other flavor.

In this case, we can determine the highest number of votes an ice cream flavor can receive by considering the first-place line in the preference schedule.

From the first-place line, we can see that the maximum number of votes any flavor has received is 9.

Therefore, an ice cream flavor would need more than 9 votes from the first-place line to be the majority winner.

Based on the given options, the correct statement would be: An ice cream would need more than 9 votes from the first-place line in the preference schedule.

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Answer:

s(x) = 0.23x + 400

Step-by-step explanation:

Let x = cost of merchandise sold

We start by finding the slope which is the percent of commission Alysse receives.

Let's start with doing 607 - 515. This is because we are subtracting the commissions, which also can be y2 - y1. Then, we do 900-500=400 (x2-x1). This is how to find the slope of the function. [tex]\frac{y2-y1}{x2-x1}=\frac{92}{400} =0.23[/tex], 0.23 being the slope.

s(x) = b+0.23x, now substitute values making the money received as s(x).

515 = b+0.23(500)

515=b+115

-115   -115

400 = b

607 = 400+0.23(900)

607 = 400 + 207

607 = 607

So, s(x) = 0.23x + 400

Answer:

Solution is in the attached photo.

Step-by-step explanation:

This question tests on the concept of shapes, this shape can be separated into 2 basic shapes, triangle and rectangle.

The area of the triangle is 25061.6 cm²

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

The area of a triangle is expressed as;

A = 1/2bh where b is the base a d h is the height. This formula only works for right angled triangle.

Another formula for area of triangle is 1/2 absinC

a = 180cm

b = 280cm

C = 84°

A = 1/2 × 180 × 280 × sin84

A = 50123.9/2

A = 25061.6 cm²

Therefore the area of triangle OPQ is 25061.6 cm².

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When A plug is removed from a trough to drain the water, The appropriate form of the expression is 10(x - 1)² - 3. Option D

The appropriate form of the expression that would reveal the time, in minutes, when the trough is empty is: 10(x - 1)² - 3.

This expression represents the volume of the trough after the plug is removed, with x representing the time in minutes. When the volume of the trough is equal to zero, it means the trough is empty.

Therefore, setting the expression equal to zero and solving for x will give us the time when the trough is empty.

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The caluclated values are:

N = 500:

SEM = 9 * √[(500 - 48) / (500 - 1)] / √(48)

= 1.24 (rounded to 2 decimals)

N = 5000:

SEM = 9 * √t[(5000 - 48) / (5000 - 1)] / √(48)

= 1.30 (rounded to 2 decimals)

N = 50000:

SEM = 9 * √[(50000 - 48) / (50000 - 1)] / √(48)

= 1.30 (rounded to 2 decimals)

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Answer:

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

Use formula:

We are given:

Substitute given and solve for x:

So, 70 people speak both German and Italian.

The calculated value of x in the circle is 7

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

The circle

From the circle, we have

Center = H

Also, we have

LIne GH bisects the chord FD

Using the above as a guide, we have the following:

DG = FG

So, we have

5x + 2 = 7x - 12

This gives

2x = 14

So, we have

x = 7

Hence, the value of x is 7

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The way to correct the entry on the calculator without deleting what is already there is by multiplying by 2.

Consider the scenario at hand, where an inadvertent error was committed during a calculator operation. The initial intention was to multiply by 100, yet the input mistakenly resulted in a multiplication by 50.

Seeing as this is multiplication, and the number that was to be multiplied is larger than the number given, you can find the quotient of the larger number from the smaller number to be :

= 100 / 50

= 2

Then multiply the entry by 2 as this would then lead to the correct result of 3, 500.

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The coordinates of the hole of the rational function are (-3, -3).

Here we have the following rational function:

[tex]f(x) = \frac{x^2 + 3x}{x + 3}[/tex]

The hole is when the denominator becomes zero, that is at x = -3

Now, we can rewrite the numerator as:

x² + 3x = x*(x + 3)

Then we can rewrite the function as:

[tex]f(x) = \frac{x^2 + 3x}{x + 3} = \frac{x*(x + 3)}{x + 3} = x[/tex]

Evaluating that in x = -3 we get f(x) = -3, then the coordinates of the hole aer (-3, -3).

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The value of x is 40 degree.

We have,

Far Arc = 130 degree

Near Arc = 50 degree

According to "Angle-Arc Theorem." It states that the angle formed by the intersection of two tangents, two secants, or one tangent and one secant outside a circle is equal to half the difference of the intercepted arcs.

In other words, The angle formed outside of the circle is always equal to the the far arc minus the near arc divided by 2.

Using Angle = (Far Arc - Near Arc) /2

So, x= (130- 50)/2

x = 80/2

x= 40

Thus, the value of x is 40 degree.

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Answer:

6.6, 22/73,

Step-by-step explanation:

Alright, here we go.
A: The mean is all of the values divided by the number of values, which is equal to 1,927.5 or:
0.5 * 5 + 1 * 16 + 2 * 28 + 3 * 22 + 4 * 17 + 5 * 98 + 8 * 13 + 10 * 73 + 12 * 5 + 15 * 2 + 20 * 4 + 25 * 9.

There are 292 or 5 + 16 + 28 + 22 + 17 + 98 + 13 + 73 + 5 + 2 + 4 + 9 packages. 1,927.5 / 292 = 6.6
B: The packages that weigh less than five pounds are 5 + 16 + 28 + 22 + 17 or 88 / 292 = 22 / 73
C and D: Manager original mean result not given.

Answer:

d. Certain

Andres will always roll a number greater than or equal to 1 since 1 is the lowest number on the die. Therefore, the probability of rolling a number greater than or equal to 1 is certain.

Step-by-step explanation:

Let's denote the number of hours Nathan works delivering pizzas as "x" and the number of hours he works babysitting as "y." We can set up the following system of inequalities:

Nathan's total earnings should be at least $40:

10x + 5y ≥ 40

Nathan's total working hours should be less than six hours a week:

x + y < 6

These two inequalities represent the given conditions that Nathan wants to make at least $40 and work for less than six hours a week.

Answer:

15

Step-by-step explanation:

2 x 1 and 7/8 = 3 and 6/8 miles

= 3.75 miles

Since there are park benches every 1/4 mile on the trail, we can find the number of benches by dividing the total length of the trail by the distance between the benches:

Number of benches = (3.75 miles) / (1/4 mile per bench)

Number of benches = 15

Answer:

C

Step-by-step explanation:

using the sine ratio in the right triangle

sin P = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{QR}{PQ}[/tex] = [tex]\frac{12}{13}[/tex] , then

∠ P = [tex]sin^{-1}[/tex] ( [tex]\frac{12}{13}[/tex] ) ≈ 67° ( to the nearest degree )

To answer the given questions, let's use conditional probability based on the information provided:

a. To find the probability that the selected student does not get a scholarship, given that they cannot get a job within 2 months after graduation, we can use Bayes' theorem. Let's denote the events as follows:

A: Not getting a scholarship

B: Not getting a job within 2 months after graduation

We want to find P(A|B), which is the probability of not getting a scholarship given that the student cannot get a job within 2 months. According to the given information, 25% of students who cannot get a job within 2 months get at least one university scholarship.

Using Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

P(B|A) is the probability of not getting a job within 2 months given that the student does not get a scholarship. Since this information is not provided, we cannot determine this probability.

b. To find the probability that the selected student gets no university scholarship, we can use the law of total probability. Let's denote the events as follows:

A: Not getting a scholarship

B: Getting a job within 2 months after graduation

C: Not getting a job within 2 months after graduation

We want to find P(A), the probability of not getting a university scholarship. According to the given information, 60% of students get a job within 2 months after graduation, and among those students, 70% get at least one university scholarship. For students who cannot get a job within 2 months, 25% get at least one university scholarship.

Using the law of total probability:

P(A) = P(A|B) * P(B) + P(A|C) * P(C)

We don't have the values for P(A|B) or P(B) and P(A|C) or P(C), so we cannot calculate the exact probability of not getting a university scholarship.

Therefore, without additional information or values for conditional probabilities, we cannot provide specific numerical answers to these questions.

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The median and the range for the data-set are given as follows:

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

The ordered data-set is given as follows:

3, 6, 12, 15, 17, 19, 21.

The middle value is of 15, hence it represents the median of the data-set.

The range of a data-set is defined as the difference between the largest and the smallest value in the data-set, hence:

21 - 3 = 18.

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With the unit price of $5 per pound, the 25-pound shipment would cost $125.

We have,

To determine the cost of a 25-pound shipment of jelly beans, you would need the unit price per pound of jelly beans.

Without that information, it's not possible to calculate the total cost accurately.

Once you have the unit price per pound, you can simply multiply it by the weight of the shipment.

For example, if the unit price per pound is $5, then the cost of a 25-pound shipment would be:

Cost = Unit Price per Pound × Weight of Shipment

= $5/pound × 25 pounds

= $125

Thus,

With the unit price of $5 per pound, the 25-pound shipment would cost $125.

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Answer: For Area A, 60

For Area B, 16

For Area C, 16

For the entire shape, 92

Step-by-step explanation:

If you look at the top of the entire shape, it says the width is 10 cm, that means 10 cm's for the entire width and not just shape A.

If you look at shape B, it says the width is 4 cm, that means 4 out of those 10 cm's are for B and not A but we dont need the width of shape B, so we subtract that 4 bc it isnt necessary since its not in shape A

if you look at the left of shape A, it says 10 cm for the height, when finding area for a rectangle, always do width x height. We have both the width and the height so now we just multiply them, 10 x  6 = 60

Answer:

A = 60cm^2

Step-by-step explanation:

Given:

Length of figure: A = 10cm

Width of figure: B = 10 - 4 = 6cm

Figure A is rectangular in nature.

So, the Area of the figure: A = 1 x b = 10 x 6 = 60cm^2

The value of ascending order of numbers are,

⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|

We have to given that,

All the numbers are,

⇒ 5⁰

⇒ |2|

⇒ (- 1/2)²

⇒ 5/8

⇒ 30%

Now, We can simplify each as,

⇒ 5⁰

⇒ 1

⇒ |2|

⇒ 2

⇒ (- 1/2)²

⇒ 1/4

⇒ 0.25

⇒ 5/8

⇒ 0.625

⇒ 30%

⇒ 30/100

⇒ 0.3

Hence, Ascending order is,

0.25, 0.3, 0.625, 1 , 2

Or,

⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|

Thus, The value of ascending order of numbers are,

⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|

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The mean, median, mode and range of the data are 68.58, 68, 68 and 17 respectively.

A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.

1. The mean of the data is;

mean = 62 + 63 + 65 + 66 + 68 + 68 + 68 + 70 +  70 + 72 + 72 + 79 / 12

mean = 68.58

2. The median of the data = 68

3. The mode of the data = 68

4. The range of the data = 17

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The total mass of the four packages is given as follows:

37.67 kg.

The total mass of the four packages is obtained adding the masses of each package given on the table for this problem.

From the table given in this problem, the mass for each package is given as follows:

Hence, adding these amounts, the total mass of the package is obtained as follows:

3.94 + 14.81 + 11.27 + 7.65 = 37.67 kg.

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Answer: 0.16

Step-by-step explanation: