Your friend Alex has won a scholarship to study abroad. Alex has
only 8 weeks to earn enough money to buy a plane ticket, and he wants to work at an
amusement park over the summer to achieve this goal.
Tech internship
Part-time(20
hours/week)
S11.50/hour

Amusement park
attendant
Full-time (40 hours/week)
S9/hour + $100 bonus

Airplane ticket
8 weeks to buy the ticket
Cost $2200

3. How much time does Alex have? For each job, calculate the number of hours Alex could work before he has to buy his plane ticket.
4. For each job, write an inequality that represents the number of hours Alex could
work before the trip.
5. Write an inequality that represents the amount of money Alex needs to earn.
6. On a graph, sketch your equation from question 2 that represents the money Alex could earn at the job at the amusement park.

In order to improve my grades, i am going to prioritize consistent studying next year to improve my grades.

The consistent studying is the main key to academic success. By dedicating regular time to review and learn material, students are better able to retain information and recall it during exams.

When we create a study schedule and sticking to it, this can help us students stay on track and avoid cramming before exams which often leads to stress and poor performance. This type of studying also allows for a deeper understanding of complex concepts and improves critical thinking skills.

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The speed of the object is 12121 m per week.

What does it mean to do speed?

The object is moving at a speed of 2 centimeters every 7 seconds.

We need to find the speed in m per week.

2 cm = 0.02 m

1 week = 604800 s

7 s =  \(1.65 * 10^{-6} week\)

Speed = distance/time

So,

\(v = \frac{0.02 m}{1.65 * 10^{-6 } week}\)

\(v = 12121.21 m/ week\)

or v = 12121 m/ week

So, the speed of the object is 12121 m per week.

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After divide, the solution of the expression is,

⇒ x (x + 2y) / 5

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The expression is,

⇒ (x² - 4y²) ÷ (5x - 10y) / x

Now, We an simplify as;

⇒ (x² - 4y²) ÷ (5x - 10y) / x

⇒ (x² - (2y)²) ÷ (5x - 10y) / x

⇒ (x - 2y) (x + 2y) ÷ 5(x - 2y) / x

⇒ (x - 2y) (x + 2y) × x/ 5 (x - 2y)

⇒ x (x + 2y) / 5

Thus, The solution of the expression is,

⇒ x (x + 2y) / 5

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Answer:

Add 5 to both sides.

Step-by-step explanation:

3.7 = x + (-5)

3.7 + 5 = x + ( -5) + 5

5 cancels on the right

8.7 = x

The correct step to solve an equation is add 5 to both sides. Therefore, option B is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 3.7=x+(-5).

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 3.7=x-5

Add 5 to both sides of an equation, we get

3.7+5=x-5+5

x=8.7

The correct step to solve an equation is add 5 to both sides. Therefore, option B is the correct answer.

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Answer:

$6.80

Step-by-step explanation:

1.79 x 3.8 = 6.802

So $6.80

The theoretical probability that the coin lands on tails and you roll a 5 is equals to the 1 over 12, i.e., 1/12.

Probability is calculated by ratio of the number of ways it could happen the total number of possible outcomes. We have, a cube with six sided and each side is labeled with numbers 1, 2, 3, 4, 5, and 6. So, total possible outcomes on rolling six sided cube = 6 = { 1,2,3,4,5,6 }

Total number of outcomes when a coin is fillped = 2 = { H, T}

A coin is flipped and a cube is rolled.

Favourable outcomes to result a 5 on rolling cube = 1

So, probability of occurrence 5 on rolling = 1/6

Similarly, favourable outcomes for lands tail on flipping a coin = 1.

That is probability of landing tails on filpping= 1/2.

Since these are independent events, the collective probability is equals to multiplication the results of each event. The probability of rolling a 5 and flipping tails = 1/2 x 1/6 = 1/12. Therefore, The required probability is 1/12.

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Answer:

3,3,4,6,6

4,4,5,6,7

5,5,6,6,8

Step-by-step explanation:

mode = n

median= n+1

mean = n+2

Range = n+3

let sets:

a,b,c,d,e

mode = n, at least two of them are the same and equal to n

n,n,c,d,e

median belong to the set, in ascending order:

n,n,n+1,d,e

which means d,e ≥ n+1, d≠e

mean is n+2

5(n+2)=n+n+n+1+d+e

2n+9=d+e

Assume e is the maximum:

Range is n+3:

e-n=n+3

e=2n+3

d=6≥n+1

n≤5,

Set is n,n,n+1,6,n+3

n+1≤6≤n+3

3≤n≤5

3,3,4,6,6 bimodal

4,4,5,6,7

5,5,6,6,8 bimodal

Answer:

8494.87 m^2

Step-by-step explanation:

A=TTr^2

Tri-County will have to charge approximately $83.1 per MWh to break even.

To calculate the break-even price that Tri-County will have to charge to cover its costs, we need to consider both the fixed costs and the variable costs. The fixed costs are given as $80.1 million per year.

The variable costs are calculated by multiplying the quantity of electrical power sold (150,000 MWh per year to Boulder) by the variable cost per MWh ($20). Therefore, the variable costs amount to 150,000 MWh/year * $20/MWh = $3 million per year.

To cover both fixed and variable costs, Tri-County needs to charge a total amount that equals the sum of these costs. The total cost is $80.1 million + $3 million = $83.1 million per year.

Now, let's calculate the break-even price per MWh. Since Tri-County has a demand of 1,000,000 MWh from its customers (other than Boulder), we can divide the total cost by this quantity to find the break-even price.

Break-even price = Total cost / Quantity of electrical power demanded
Break-even price = $83.1 million / 1,000,000 MWh = $83.1/MWh

Therefore, Tri-County will have to charge approximately $83.1 per MWh to break even.

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The measure of the angle in degrees is approximately 713 degrees. Note that this result is greater than 360 degrees because the angle is not a standard angle in a plane but a measure in three-dimensional space.

Since 1/360th of the circumference of the circle is 0.5 cm long, the circumference of the circle is 360 times longer, or 180 cm long.

The arc subtended by the angle is 79 cm long, which is a fraction of the entire circumference. To find the angle in degrees, we need to convert the arc length to an angle measure using the formula:

angle measure = (arc length / circumference) x 360 degrees

Substituting the values we know, we get:

angle measure = (79 cm / 180 cm) x 360 degrees

Simplifying the fraction, we get:

angle measure = 1.9833 x 360 degrees

Rounding to the nearest degree, we get:

angle measure ≈ 713 degrees

Therefore, the measure of the angle in degrees is approximately 713 degrees. Note that this result is greater than 360 degrees because the angle is not a standard angle in a plane but a measure in three-dimensional space.

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∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx equals approximately 1932.5

To evaluate the given integrals, let's first identify the functions f(x) and g(x) and their respective intervals.

f(x) = 4x^2 - 3x + 2

g(x) = 2x^3 - 5x + 1

Interval: [3, 8]

Now, let's evaluate the integrals step by step.

∫[3, 8] f(x) dx:

We integrate the function f(x) over the interval [3, 8].

∫[3, 8] (4x^2 - 3x + 2) dx

To find the integral, we can use the power rule for integration. For each term, we increase the exponent by 1 and divide by the new exponent.

= [4 * (x^3/3) - 3 * (x^2/2) + 2x] evaluated from 3 to 8

Now we substitute the upper and lower limits into the integral expression:

= [(4 * (8^3/3) - 3 * (8^2/2) + 2 * 8) - (4 * (3^3/3) - 3 * (3^2/2) + 2 * 3)]

Simplifying further:

= [(4 * 512/3) - (3 * 16/2) + 16 - (4 * 27/3) + (3 * 9/2) + 6]

= [(1706.67) - (24) + 16 - (36) + (13.5) + 6]

= 1683.17

Therefore, ∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx:

We integrate the function g(x) over the interval [3, 8].

∫[3, 8] (2x^3 - 5x + 1) dx

Using the power rule for integration:

= [(2 * (x^4/4)) - (5 * (x^2/2)) + x] evaluated from 3 to 8

Substituting the upper and lower limits:

= [(2 * (8^4/4)) - (5 * (8^2/2)) + 8 - (2 * (3^4/4)) + (5 * (3^2/2)) + 3]

Simplifying further:

= [(2 * 4096/4) - (5 * 64/2) + 8 - (2 * 81/4) + (5 * 9/2) + 3]

= [(2048) - (160) + 8 - (162/2) + (45/2) + 3]

= 1932.5

Therefore, ∫[3, 8] g(x) dx equals approximately 1932.5

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The value of x  for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.

Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.

From the given diagram, the expression below is true:

2(5x - 1) = 21 + 27

Expand

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

10x.10 = 50/10

x = 5

Hence the value of x is 5

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The argument against the conjecture The area of a rectangle with a perimeter of 40 units must be at least one square unit. A rectangle with dimensions of 19.99 units long and 0.1 units wide has a 40 unit perimeter and an area of 0.1999 square units.

acc to our question-

The goal of the inquiry is to illustrate any potential connections between a rectangle's perimeter and area.

The counterexample presented dimensions that revealed the perimeter, which is 40, but omitted to provide the area, which is 1 square unit.

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The length of the rivet should be 3/8 inch to pass through the two sheets of metal.

We must take into account the shank length as well as the thickness of the two metal sheets.

Assumed:

The thickness of the two metal sheets and the shank length must be added to determine the overall length of the rivet:

Total length = 2 * (Thickness of sheet metal) + Shank length

Substituting the values:

Total length = 2 * (1/16 inch) + 1/4 inch

Calculating the values:

Total length = 1/8 inch + 1/4 inch

Total length = 1/8 inch + 2/8 inch

Total length = 3/8 inch

So, the length of the rivet should be 3/8 inch to pass through the two sheets of metal.

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Given that cot(0) = 4/3 and theta is in Quadrant I, what is sin(theta)?

we have that

If angle theta is in quadrant I , then the value of sin(theta) is positive

Remember that

tan(theta)=1/cot(theta)

so

tan(theta)=3/4

substitute in the expression above

is positive because is quadrant I

remember that

sec(theta)=1/cos(theta)

so

cos(theta)=4/5

tan(theta)=3/4

tan(theta)=sin(theta)/cos(theta)

substitute given values

3/4=sin(theta)/(4/5)

sin(theta)=(3/4)*(4/5)=3/5

the answer is

Answer:

How to solve your problem

2 ( 5 + 8 )

Simplify

Step-by-step explanation:

Distribute

2 ( 5 + 8 )

1 0 + 1 6

solution:

1 0 + 1 6

there you go

The number of students that leave by bus or car is given as follows:

5801 students.

The union and intersection sets of multiple sets are defined as follows:

The or operation is equivalent to the union operation, meaning that we add the number of students that leave by bus to the number of students that leave by car.

Hence the number of students that leave by bus or car is given as follows:

3232 + 2549 = 5801 students.

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The hypothesis is called the alternative hypothesis test.

According to the statement

We have to explain about the alternative hypothesis.

So, For this purpose, we know that the

The alternative hypothesis is one among ll|one amongst |one in every of} two mutually exclusive hypotheses in a hypothesis test. the choice hypothesis states that a population parameter doesn't equal a specified value.

From the given information:

she randomly selects houses during this neighborhood and compares their estimated market price within the current year to their estimated value within the previous year. suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market price of the previous year from the value of the present year.

Then

the alternative hypothesis test usually suggests that there's an opportunity of variation (difference) within the data observed.

Hence, since we are told the "real real estate agent believes that the values of homes within the neighborhood she works in have increased (the chance of variation) from last year," which "each difference is calculated by subtracting the market price of the previous year from the market price of this year," we are able to reach the conclusion that this can be an example of an alternate hypothesis test.

So, The hypothesis is called the alternative hypothesis test.

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Looks like it could be answer three from the looks of it.

The equation of a circle centered at the point (-7,-1) and passes through the point (8,7) is (x+7)² +(y+1)² = 289

The standard equation of a circle is expressed as shown

(x-a)^2 + (y-b)^2 = r^2

where:

(a, b) is the centre

r is the radius

Given the following

Centre = (-7, -1)

Determine the radius

r = √(8+7)² +(7+1)²

r² = 15² + 8²

r² = 225 + 64

r² = 289

Substitute the centre and radius

(x-(-7))^2 + (y-(-1))^2 = 289
(x+7)² +(y+1)² = 289

Hence the equation of a circle centered at the point (-7,-1) and passes through the point (8,7) is (x+7)² +(y+1)² = 289

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Answer:

edge lines

Step-by-step explanation:

Step-by-step explanation:

use the formula a+(n-1)d

a=(first value in sequence)=1

n=100(the term you are finding)

d=(difference)(it is increasing by 10

substitute the value in the formula

1+(100-1)10

100th term=991

The fractional part of the integer is represented by the place value after the decimal. The number 0.56, for example, is made up of 5 tenths and 6 hundredths.

This can also be written as 0.56 = 0.5 + 0.06. In other words, it means, 0.56 = 5/10 + 6/100.

To add decimals, align the decimal points such that all the digits are aligned according to their place values. Add like you would full numbers, starting on the right and working your way to the left. In the sum, align the decimal point with the decimal points in the values being added.

Decimals are one of the forms of numbers in Algebra that have a whole integer and a fractional part separated by a decimal point. The decimal point is the dot that appears between the full number and the fractions section. 34.5, for example, is a decimal number.

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3.1. The data table depicts a collection of organized data. 3.2. The sections of the table represent column headers, row headers, data cells, totals/summary rows and columns, and footnotes/references.

3.1. This table depicts a collection of data organized into different sections.

3.2. Each section of the table represents specific information or categories related to the data being presented. Here are five points explaining what each section stands for:

Column Headers: The column headers provide the names or labels for each column in the table. They identify the type of information or variables being presented in each column.

Row Headers: The row headers provide the names or labels for each row in the table. They often represent different entities or categories associated with the data.

Data Cells: The data cells contain the actual values or measurements for each intersection of a row and column. They represent the specific data points or observations related to the corresponding row and column.

Totals/Summary Rows and Columns: These rows or columns are typically located at the bottom or rightmost side of the table. They display the aggregated values or summaries of the data in the corresponding column or row.

Footnotes/References: The footnotes or references section may appear below the table and provide additional information or explanations related to the data presented in the table. They can clarify any specific details, sources, or assumptions made in the table.

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\(\cot^4 A - \cot^2 A = 1\\\\\cot^4 A = 1 + \cot^2 A\\\\\frac{\cos^4 A}{\sin^4 A} = 1 + \frac{\cos^2 A}{\sin^2 A}\\\\\frac{\cos^4 A}{\sin^4 A} = \frac{\sin^2 A}{\sin^2 A}+\frac{\cos^2 A}{\sin^2 A}\\\\\frac{\cos^4 A}{\sin^4 A} = \frac{\sin^2 A+\cos^2 A}{\sin^2 A}\\\\\frac{\cos^4 A}{\sin^4 A} = \frac{1}{\sin^2 A}\\\\\cos^4 A = \frac{\sin^4 A}{\sin^2 A}\\\\\cos^4 A = \sin^2 A\\\\\)

This then means,

\(\cos^4 A + \cos^2 A = 1\\\\\sin^2 A + \cos^2 A = 1\\\\\)

which is the pythagorean trig identity. This concludes the proof.

Therefore, if \(\cot^4 A - \cot^2 A = 1\), then \(\cos^4 A + \cos^2 A = 1\)

d = 300 - 48t, In this equation, 300 represents the initial distance between you and the car (300 feet), and 48t represents the distance covered by the car as it moves toward you at a speed of 48 feet per second for t seconds.

The situation described involves a car initially positioned 300 feet away from you and moving towards you. The car passes by you at a constant speed of 48 feet per second.

To understand the equation representing the distance of the car from you after t seconds, we need to consider the car's initial position and its movement over time.

Let's assume that the car is moving directly towards you along a straight line. Since the car is approaching you, the distance between you and the car decreases over time.

We can define the initial distance between you and the car as d₀ = 300 feet.

Now, let's consider the car's movement. The car passes by you at a speed of 48 feet per second. This means that for each second that passes, the car covers a distance of 48 feet towards you.

To determine the distance of the car from you after t seconds, we need to subtract the distance covered by the car during that time from the initial distance.

Since the car is moving towards you, the distance covered by the car can be expressed as the product of its speed and the time t: 48t.

Therefore, the equation representing the distance, d, of the car from you after t seconds is given by:

d = d₀ - 48t

Substituting d₀ = 300 into the equation, we get:

d = 300 - 48t

This equation allows us to calculate the distance between you and the car at any given time t, considering the initial distance of 300 feet and the car's constant speed of 48 feet per second.

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Answer:

9.44444

Step-by-step explanation:

Answer: No, your friend is not correct. If the problem was addition, then yes it would equal the same answer, but with subtraction, the answers will be different.

Step-by-step explanation:

a. The appropriate amount of safety stock is 92 kg. b. The item should be reordered when the inventory level reaches approximately 692 kg.

To determine the amount of safety stock and the reorder point (ROP), we need to consider the expected demand during the lead time, the standard deviation of demand during the lead time, and the acceptable stockout risk.

a. Amount of safety stock:

Safety stock is the additional inventory kept to mitigate the risk of stockouts. It acts as a buffer to account for unexpected fluctuations in demand. The formula to calculate safety stock is:

Safety stock = (Z * Standard deviation of demand during lead time)

Where Z is the z-score corresponding to the acceptable stockout risk. Since the acceptable stockout risk is 5 percent, we need to find the corresponding z-score.

Looking up the z-values table for a 5 percent risk (two-tailed test), the z-score is approximately 1.645.

Substituting the values into the formula:

Safety stock = (1.645 * 56)

≈ 92.12 kg

b. Reorder point (ROP):

The reorder point is the level of inventory at which an item should be reordered to ensure that it arrives before the stock runs out during the lead time. It can be calculated using the formula:

ROP = Expected demand during lead time + Safety stock

Substituting the given values:

ROP = 600 + 92

≈ 692 kg

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Ans:

I guess 10 cm

Explanation:

In isosceles triangle, 2 angles and sides are equal.