Show that the triangle and square have the same area

a) To find the average life of the ten batteries, we need to calculate the mean, which is the sum of all the values divided by the number of values.Sum of all values = 10.8 + 10.6 + 11.4 + 8.9 + 10.1 + 10.6 + 9.9 + 12.6 + 10.5 + 11.9 = 106.2

Number of values = 10

Average life = Sum of all values / Number of values = 106.3 / 10 ≈ 10.63

Therefore, the average life of the ten batteries, rounded to the nearest tenth of an hour, is approximately 10.6 hours.

b) Comparing the two advertisements:

i) The first advertisement claims that Atlas batteries are guaranteed to last 10 hours. This means that all Atlas batteries are expected to last at least 10 hours. However, based on the data provided, we can see that the average life of the batteries is approximately 10.6 hours, which is higher than the guaranteed 10-hour minimum

ii) The second advertisement claims that Atlas batteries have an average life of over 10 hours. This statement aligns with the data we have, as the average life of the batteries is indeed over 10 hours.

Based on the information provided, the second advertisement claiming that Atlas batteries have an average life of over 10 hours is more accurate, as the average life calculated from the given data is 10.6 hours.

In summary, the average life of the ten batteries is approximately 10.6 hours, and the second advertisement stating an average life of over 10 hours is more accurate based on the data provided.

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The correct equation that could be used to determine the degree measure of one of the congruent angles is 2x + 43 = 180.

In a triangle, the sum of the interior angles is always 180 degrees.

Given that one interior angle of the triangle is 43 degrees, and the other two angles are congruent, we can represent the measure of one of the congruent angles with the variable x.

To determine the degree measure of one of the congruent angles, we can set up an equation using the fact that the sum of all three interior angles of a triangle is 180 degrees.

The equation that represents the situation is:

2x + 43 = 180

This equation accounts for the 43 degrees angle given and represents the sum of the two congruent angles (2x) plus the 43-degree angle equaling 180 degrees.

Solving this equation will allow us to find the value of x, which represents the degree measure of one of the congruent angles.

Once we find the value of x, we can substitute it back into the equation to find the actual degree measure of the congruent angle.

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Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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Have a GREAT day!!!

Answer:

A

Step-by-step explanation:

MODE is the number that appears most often

 there are TWO 4's

The mode is:

4

Work/explanation:

To find the mode, we need to find the number that happens the most in the set.

4 is that number; 8, 10, and 12 don't occur in the set, while 4 occurs two times.

Given statement solution is :- Interpreting the steady matrix:

The value 0.6 in the top left cell represents the proportion of customers who turn in tickets this week and will turn in tickets again next week.

The value 0.3 in the top right cell represents the proportion of customers who turn in tickets this week but will not turn in tickets next week.

The steady matrix provides a snapshot of the probabilities of transitioning between the two states (turning in tickets or not turning in tickets) in the long run, assuming these probabilities remain constant over time.

To analyze the steady matrix for this situation, let's consider the two groups of customers: those who turn in tickets and those who do not turn in tickets.

Let's denote the proportion of customers who turn in tickets as X and the proportion of customers who do not turn in tickets as Y.

According to the given information:

40% of the customers who turn in tickets do not turn in tickets the following week. This means that 60% of the customers who turn in tickets will turn in tickets again the following week.

30% of the customers who do not turn in tickets will turn in tickets the following week. This means that 70% of the customers who do not turn in tickets will continue not turning in tickets the following week.

Based on these percentages, we can construct the steady matrix:

java

Copy code

     |  Customers turning in tickets (X) | Customers not turning in tickets (Y) |

----------|----------------------------------|--------------------------------------|

Next week 0.6 0.3

This week 0.4 0.7

Interpreting the steady matrix:

The value 0.6 in the top left cell represents the proportion of customers who turn in tickets this week and will turn in tickets again next week.

The value 0.3 in the top right cell represents the proportion of customers who turn in tickets this week but will not turn in tickets next week.

The value 0.4 in the bottom left cell represents the proportion of customers who do not turn in tickets this week but will turn in tickets next week.

The value 0.7 in the bottom right cell represents the proportion of customers who do not turn in tickets this week and will continue not turning in tickets next week.

These values describe the transition probabilities between the two customer groups. For example, if there are 100 customers in total, 60 of them will turn in tickets next week, and 40 of them will not. Similarly, 30 customers who turn in tickets this week will not do so next week, while 70 customers who do not turn in tickets this week will continue to not turn them in next week.

The steady matrix provides a snapshot of the probabilities of transitioning between the two states (turning in tickets or not turning in tickets) in the long run, assuming these probabilities remain constant over time.

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a) To maximize profits, 10 units should be sold in market 1 and 5 units in market 2.

b) The corresponding prices are $180 in market 1 and $160 in market 2.

c) If it becomes illegal to discriminate, the profit loss is $50.

d) The imposition of a tax of $5 per unit sold in market 1 would likely decrease the monopolist's profit and potentially lead to adjustments in prices and quantities sold in both markets.

a) To maximize profits, the monopolist should set marginal revenue equal to marginal cost in each market.

In this case, marginal revenue is equal to the derivative of the demand function with respect to quantity, and it can be calculated as MR = dP/dQ.

For market 1:

MR₁ = dP₁/dQ₁ = -2

For market 2:

MR₂ = dP₂/dQ₂ = -4

Setting MR equal to marginal cost, which is the derivative of the cost function with respect to quantity, gives:

MR₁ = -2 = dC/dQ₁ = 20

MR₂ = -4 = dC/dQ₂ = 20

Solving these equations, we find:

Q₁ = 10

Q₂ = 5

Therefore, the monopolist should sell 10 units in market 1 and 5 units in market 2 to maximize profits.

b) To determine the corresponding prices, we substitute the quantities obtained in part (a) into the demand functions:

For market 1:

P₁ = 200 - 2Q₁ = 200 - 2(10) = 180

For market 2:

P₂ = 180 - 4Q₂ = 180 - 4(5) = 160

Therefore, the corresponding prices are $180 in market 1 and $160 in market 2.

c) To calculate the profit lost if it becomes illegal to discriminate, we need to compare the profits under discrimination with the profits under non-discrimination.

Under discrimination, the monopolist charges different prices in each market, while under non-discrimination, the same price is charged in both markets.

Under discrimination:

Profit = Total revenue - Total cost

For market 1:

Total revenue₁ = P₁ [tex]\times[/tex] Q₁ = 180 [tex]\times[/tex] 10 = $1

For market 2:

Total revenue₂ = P₂ [tex]\times[/tex] Q₂ = 160 [tex]\times[/tex] 5 = $800

Total revenue = Total revenue₁ + Total revenue₂ = $1800 + $800 = $2600

Total cost = C = 20(Q₁ + Q₂) = 20(10 + 5) = $300

Profit = Total revenue - Total cost = $2600 - $300 = $2300

Under non-discrimination:

Since the same price is charged in both markets, we take the average price:

Average price = (P₁ + P₂) / 2 = (180 + 160) / 2 = $170

Total revenue = Average price [tex]\times[/tex] (Q₁ + Q₂) = $170 [tex]\times[/tex] (10 + 5) = $2550

Total cost remains the same at $300.

Profit = Total revenue - Total cost = $2550 - $300 = $2250

Therefore, the profit lost if discrimination becomes illegal is $2300 - $2250 = $50.

d) The imposition of a tax of $5 per unit sold in market 1 would increase the cost per unit for the monopolist.

This would affect the profit-maximizing quantity in market 1 and potentially lead to a change in prices.

The monopolist would compare the new marginal cost, which includes the tax, with the marginal revenue to determine the new profit-maximizing quantities and prices.

The tax would likely reduce the monopolist's profits and could potentially result in adjustments in production and pricing strategies.

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To determine the best course grade your friend can earn, we need to calculate the weighted average of the scores obtained so far and the score on the final exam.

Given that the final exam counts for 15% of the course grade, we can calculate the weighted average using the formula:

Weighted average = (Weighted score on assessments) + (Weighted score on the final exam)

The weighted score on assessments is equal to (100% - 15%) = 85%, as it constitutes 85% of the course grade. We can calculate the weighted average as follows:

Weighted average = (0.85 * 84%) + (0.15 * Final exam score)

To find the best course grade your friend can earn, we need to maximize the final exam score. Since the maximum grade is 100%, the best course grade your friend can earn is when the final exam score is 100%. Substituting this value into the equation:

Weighted average = (0.85 * 84%) + (0.15 * 100%)

               = 0.714 + 0.15

               = 0.864

To express the result as a percentage, we multiply by 100:

Weighted average = 0.864 * 100

               = 86.4%

Therefore, the best course grade your friend can earn is 86.4%.

To determine the minimum score your friend would need on the final exam to earn a 75% for the course, we set up the following equation:

Weighted average = (0.85 * 84%) + (0.15 * Final exam score) = 75%

Simplifying the equation: (0.85 * 84%) + (0.15 * Final exam score) = 75%

0.714 + (0.15 * Final exam score) = 75%

0.15 * Final exam score = 75% - 0.714

0.15 * Final exam score = 74.286%

To find the minimum score, we divide both sides by 0.15:

Final exam score = 74.286% / 0.15

               = 495.24%

Therefore, your friend would need a minimum score of 495.24% on the final exam to earn a 75% for the course. However, it's important to note that scores are typically capped at 100%, so achieving a score above 100% may not be possible in this context.

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The x-coordinate of point C is -70.

To find the y-intercept and equation of the line passing through points A(14, -1) and B(2, 1), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.

First, let's find the slope (m) using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - (-1)) / (2 - 14) = 2 / (-12) = -1/6

Next, we can substitute the coordinates of point A and the slope into the slope-intercept form:

-1 = (-1/6)(14) + b

Solving for b:

-1 = -7/3 + b

b = -1 + 7/3

b = -3/3 + 7/3

b = 4/3

Therefore, the equation of the line passing through points A and B is:

y = (-1/6)x + 4/3

Now, let's find the x-coordinate of point C when its y-coordinate is 13.

We can substitute the y-coordinate into the equation and solve for x:

13 = (-1/6)x + 4/3

Multiplying the equation by 6 to eliminate the fraction:

78 = -x + 8

Subtracting 8 from both sides:

70 = -x

Dividing by -1:

x = -70.

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Answer:   THIRD OPTION (C):              X          Y

       Y  =  KX  +  B

        Now (3  =  K  +  b  ---->   ( K  =  3

        (6  =  2K  +  6  ----> ( B  =  0

          X =  3

          Y  =  3  *  3  

              =   9   ≠  12   Now, This is NOT a LINEAR FUNCTION

        Y  =  KX  +  B

Now (2  =  K + B  ---->  (K  = 3

        (5  =  2K + B  ---> (B  =  - 1

Then, Y  =  3X  -  1

          X = 3

           Y =  3  *  3  -  1

              =  8  ≠  9 Now, This is NOT a LINEAR FUNCTION

       Y  =  KX  +  B

      Now (-3  =  K  + B ---->  (K  =  - 2

        (-5  =  2K + B -----> (B  =  - 1

      Then,  Y  =  - 2X  -  1

           X   =   3

            Y  =  - 2 *  3  -  1

                 =   - 7  

                 =  - 7

        Now:  X  =  4

          Y  =  -2  *  4  -  1

               =  - 9

               =  - 9, Now, This is a LINEAR FUNCTION

        ( - 4  =  2K  + B  ----->  ( B  =  0

        Now: Y  =   - 2x

        Then:  X  = 3

         Y  =  - 6   ≠    - 2,  Now This is NOT A LINEAR FUNCTION

Answer:  THIRD OPTION (C):              X          Y

I hope this helps you!

1) The lower limit of the confidence Interval is: 1489.77.

The upper limit of the confidence Interval is: 1530.23

2) The lower limit of the confidence Interval is: 1478.32

The upper limit of the confidence Interval is: 15411.68

The formula to find the confidence interval is:

CI = x' ± z(σ/√n)

where:

CI is confidence interval

x' is sample mean

z is z-score at confidence level

σ is standard deviation

n is sample size

1) The parameters are:

σ = $234

x' = $1510

n = 362

z at 90% CL = 1.645

Thus:

CI = 1510 ± 1.645((234/√362)

CI = 1510 ± 20.23

CI = (1489.77, 1530.23)

2) The parameters are:

σ = $234

x' = $1510

n = 362

z at 99% CL = 2.576

Thus:

CI = 1510 ± 2.576((234/√362)

CI = 1510 ± 31.68

CI = (1478.32, 15411.68)

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If (x-2) is a factor of [tex]f(x) = x^3 + x^2 - 16x + k.[/tex] then f(x) is divisible by (x-2) when k = 20.

If (x-2) is a factor of [tex]f(x) = x^3 + x^2 - 16x + k,[/tex] then it means that when we divide f(x) by (x-2), the remainder is zero.

To verify this, we can perform the division using polynomial long division or synthetic division.

Using synthetic division, the divisor (x-2) corresponds to the root 2:

2 | 1 1 -16 k

  2    6    -20+k

For the remainder to be zero, the last term in the synthetic division must be zero: -20 + k = 0.

Solving this equation, we find:

k = 20

Therefore, if (x-2) is a factor of [tex]f(x) = x^3 + x^2 - 16x + k,[/tex] then f(x) is divisible by (x-2) when k = 20.

In summary, if (x-2) is a factor of[tex]f(x) = x^3 + x^2 - 16x + k,[/tex]  then f(x) is divisible by (x-2) when k = 20.

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The relative Frequencies of the data in the first row are 0.25 for Group 1 and 0.75 for Group 2.

Given two-way table.Category 1Group 1 - 30Group 2 - 90Category 2Group 1 - 14Group 2- 32To find the relative frequency of the data in the first row, we need to first calculate the sum of the numbers in the first row.

Then we need to divide each of the individual numbers in the first row by the sum of the numbers in the first row to get the relative frequency of each group. Let's begin by calculating the sum of the numbers in the first row.Sum of the numbers in the first row = 30 + 90 = 120

Relative frequency of Group 1 in the first row = (Number of Group 1 in the first row) / (Sum of the numbers in the first row) = 30/120 = 0.25 (rounded to the nearest hundredth)Relative frequency of Group 2 in the first row = (Number of Group 2 in the first row) / (Sum of the numbers in the first row) = 90/120 = 0.75 (rounded to the nearest hundredth)We can complete the table with the above calculated relative frequencies. Group 1 0.25Group 2 0.75

Therefore, the relative frequencies of the data in the first row are 0.25 for Group 1 and 0.75 for Group 2.

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The value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.

The given expression ♾️. n-1 Σ 1/4(-1/3) represents a summation of the term 1/4(-1/3) over a range of values from 1 to n-1, where n is an unknown value. We need to find the value of S4, which represents the sum of this expression when n is equal to 4.

To find the value of S4, we substitute n = 4 into the expression and evaluate it.

♾️. n-1 Σ 1/4(-1/3) = ♾️. 4-1 Σ 1/4(-1/3)

Simplifying, we get:

♾️. 3 Σ 1/4(-1/3)

Since the term 1/4(-1/3) is constant, we can pull it out of the summation:

1/4(-1/3) ♾️. 3

Now, ♾️. 3 represents the sum of 3 terms. Multiplying 1/4(-1/3) by 3 gives:

1/4(-1/3) * 3 = -1/4 * 1/3 * 3 = -1/12

Therefore, the value of S4 for the given expression ♾️. n-1 Σ 1/4(-1/3) is -1/12.

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The probable question could be:

What is the value of s4 for expression ♾️. n-1 Σ 1/4(-1/3) ?

A) 1/9

B) 7/54

C) 5/27

D) 10/27

Answer:

A) Part Whole

Step-by-step explanation:

This is an Addition Problem, 5+3=8 then you can either count up from 8.

Or Subtract 10 by 8 and Get 2 Fruit Snacks Bought

Answer:

To solve the given simultaneous equations: 2x + y = 5 ------------(1) 2x^2 + y^2 = 11 ------------(2)

We can use the method of substitution to solve the equations.

Substituting y = 5 - 2x from equation (1) into equation (2), we get: 2x^2 + (5 - 2x)^2 = 112x^2 + 25 - 20x + 4x^2 = 112x^2 + 4x^2 - 20x + 25 - 11 =

simplifying, we get: 6x^2 - 20x + 14 = 0

Dividing by 2, we get: 3x^2 - 10x + 7 = 0

Factorizing, we get: (3x - 7)(x - 1) = 0

Solving for x, we get: x = 1 or x = 7/3

Now substituting x = 1 in equation (1), we get:2(1) + y = 5y = 5 - 2y = 3 Therefore, one solution is x = 1 and y = 3

Substituting x = 7/3 in equation (1), we get: 2(7/3) + y = 5y = 5 - 14/3y = 1/3

Therefore, the other solution is x = 7/3 and y = 1/3

Hence, the solutions of the given simultaneous equations are x = 1 and y = 3 or x = 7/3 and y = 1/3.

Step-by-step explanation:

Hope this helped!! Have a great day/night!!

Answer:

Step-by-step explanation:

The coordinate that exists on the line y = 2x - 4 is (2, -4).

To determine which of the given coordinates exists on the line y = 2x - 4, we need to substitute the x and y values of each coordinate into the equation and check if the equation holds true.

Let's go through each option:

A. (-1, 2):

Substituting x = -1 and y = 2 into the equation, we get:

2 = 2(-1) - 4

2 = -2 - 4

2 = -6

This is not true, so (-1, 2) does not lie on the line.

B. (2, -4):

Substituting x = 2 and y = -4 into the equation, we get:

-4 = 2(2) - 4

-4 = 4 - 4

-4 = 0

This is not true, so (2, -4) does not lie on the line.

C. (3, -5):

Substituting x = 3 and y = -5 into the equation, we get:

-5 = 2(3) - 4

-5 = 6 - 4

-5 = 2

This is not true, so (3, -5) does not lie on the line.

D. (1, -2):

Substituting x = 1 and y = -2 into the equation, we get:

-2 = 2(1) - 4

-2 = 2 - 4

-2 = -2

This is true, so (1, -2) lies on the line.

Therefore, the coordinate that exists on the line y = 2x - 4 is (1, -2).

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Applying the sine ratio, the trigonometric ratio of sin C, as a simplified fraction is: sin C = 9/41.

The sine ratio in trigonometry 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 mathematical notation, the sine ratio is given by sin(∅) = opposite/hypotenuse.

We are given the following:

Reference angle (∅) = C

length of the hypotenuse = 82

length of the opposite side = AB = √(82² - 80²) = 18 [Pythagorean theorem]

Plug in the values:

sin C = 18/82

Simplify:

sin C = 9/41

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The trend appears to be linear. Assuming the trend continues, the number of unemployed will first reach 43 in the year 2022.

To determine whether the trend appears linear, we can plot the data points on a graph and check for a consistent pattern. Let's create a scatter plot with the years on the x-axis and the number of unemployed on the y-axis.

Year     |  Number Unemployed

1990     |  750

1992     |  670

1994     |  650

1996     |  605

1998     |  550

2000     |  510

2002     |  460

2004     |  420

2006     |  380

2008     |  320

When we plot these points, we can see that there is a consistent downward trend in the number of unemployed over the years.

Next, we can try to fit a line to the data points to see if it follows a linear pattern. Using a linear regression model or by visual inspection, we can determine that the data points approximately follow a straight line.

Assuming this linear trend continues, we can extrapolate to find the year when the number of unemployed first reaches 43. By extending the line beyond the given data points, we can estimate that it will intersect the y-axis (number of unemployed) at approximately 43.

Therefore, the year when the number of unemployed first reaches 43 would be around 2022.

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The coordinates in the solution to the systems of inequalities graphically is in the shaded region

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

x + y ≤ 3

x + y > - 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

This means that all coordinates in the shaded region are the solutions to the system

One of the coordinates in the solution to the systems of inequalities graphically is (0, 0)

The graph is attached

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Question

Graph the solution of this system of linear inequalities.

x + y ≤ 3

x + y > - 2

The value of x is approximately 8.4.To find the value of x, we can use the fact that CD is parallel to BE to establish a relationship between the corresponding sides of the two triangles formed.

Based on the given information, we have:

DC = 4x - 11

BE = 6

AD = 15

ED = 4

Using the corresponding sides in the triangles, we can set up a proportion:

AD/ED = CD/BE

Substituting the known values:

15/4 = (4x - 11)/6

Now we can cross-multiply to solve for x:

6 * 15 = 4 * (4x - 11)

90 = 16x - 44

Adding 44 to both sides:

134 = 16x

Dividing both sides by 16:

x = 8.375

Rounded to the nearest tenth, x ≈ 8.4.

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The tugboat is approximately 588.235 feet away from the top of the lighthouse.

To find the distance between the tugboat and the top of the lighthouse, we can use trigonometry and the concept of tangent.

Let's denote the distance between the tugboat and the top of the lighthouse as x.

We know that the angle of elevation is 12° and the height of the lighthouse is 125 feet.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In this case, the tangent of the angle of elevation is equal to the height of the lighthouse divided by the distance between the tugboat and the lighthouse:

tan(12°) = 125 / x

To find x, we need to isolate it on one side of the equation.

We can do this by taking the inverse tangent (arctan) of both sides:

x = 125 / tan(12°)

Using a calculator, we can calculate the value of the tangent of 12°:

tan(12°) ≈ 0.212556

Now, we can substitute this value into the equation to find x:

x = 125 / 0.212556 ≈ 588.235

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Answer:

A=-1

Step-by-step explanation:

       Therefore,   The Speed of the plane is:   X   =  130 mph

        520 / x   =  160 / x  -  90

        520/x   =  160/x - 90

         x   ≠   90

         x  ≠  0  and   x  -  90  ≠  0

        520x   -   46800  =   x  *  160

        520/x  =  160/x - 90

        520(x  -  90)  =  160x

        520x  -   46800  = 160x

        520x  -  160x   =  46800

        360x     =    46800

               x     =    46800/360

               x     =    130

        Therefore, The Speed of the plane is:   X   =  130 mph

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Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

Inequalities are mathematical statements that describe a relationship between two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are used to compare quantities and express their relative sizes or order.

The most common symbols used in inequalities are:

">" (greater than): indicates that the value on the left side is larger than the value on the right side.

"<" (less than): indicates that the value on the left side is smaller than the value on the right side.

"≥" (greater than or equal to): indicates that the value on the left side is greater than or equal to the value on the right side.

"≤" (less than or equal to): indicates that the value on the left side is less than or equal to the value on the right side.

"≠" (not equal to): indicates that the values on both sides are not equal.

Inequalities can be represented using variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Solutions to inequalities are often expressed as intervals or sets of values that satisfy the given inequality.

Inequalities are used in various branches of mathematics, as well as in real-world applications such as economics, physics, and social sciences, to describe relationships, make comparisons, and analyze data.

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The probability that a random point on AK will be on DF is 0.4 or 40%.

The given line segments have coordinates on a coordinate plane. To find the probability that a random point on AK will be on DF, we have to determine the length of AK and DF.

Firstly, we need to find the coordinates of D and F, which can be determined from the given coordinates. The coordinates of D are (-4, 8) and the coordinates of F are (4, 8).

Therefore, the length of DF can be found by applying the distance formula as shown below: DF = √((4-(-4))² + (8-8)²)DF = √(8² + 0²)DF = √64DF = 8  Similarly, we can find the coordinates of A and K as well.

The coordinates of A are (-10, 6) and the coordinates of K are (10, 6).Therefore, the length of AK can be found by applying the distance formula as shown below: AK = √((10-(-10))² + (6-6)²)AK = √(20² + 0²)AK = √400AK = 20.

Therefore, we can find the probability that a random point on AK will be on DF by using the formula: P = Length of DF / Length of AKSubstituting the values, we get P = 8/20P = 0.4 or 40%

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Answer:

1. Potatoes are grown all over the world and are related to tomatoes and eggplants.

Step-by-step explanation:

In number 2, the eggplants are grown all over the world, not the potatoes.

In numbers 3 and 4, potatoes, tomatoes AND eggplants are grown all over the world.

The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.

To write the equation for calculating the yearly interest earned on an investment, we can use the formula:

Interest = Principal * Rate

Where:

- Principal is the initial investment amount.

- Rate is the interest rate expressed as a decimal.

In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:

Rate = 16% = 16/100 = 0.16

Substituting the values into the equation:

Interest = $750 * 0.16

To calculate the interest, we multiply the principal by the interest rate:

Interest = $750 * 0.16 = $120

Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:

Interest = $750 * 0.16

Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.

Year | Initial Investment | Interest Earned | Total Value

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

 1        $750                 $120              $870

 2        $870                 $139.20          $1009.20

 3        $1009.20            $161.47          $1170.67

 4        $1170.67            $187.31          $1357.98

 5        $1357.98            $217.28          $1575.26

In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.

The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.

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a) The equation for the amount of money in the investment account is as follows:

Simple interest = [tex]Amount = P + (PRT)[/tex]

Compound interest = [tex]A =[/tex]  [tex]P(1+R)^x[/tex]

b) The completion of the table showing the amount in the account at the end of each period is as follows:

Year                            Money

            Simple Interest     Compound Interest

0               $750                           $750

1                $870                           $870

2               $990                         $1,170.67

3               $1,110                        $1,827.29

The initial investment = $750

Interest rate per year = 16%

[tex]Amount = P + (PRT)[/tex]

Where P = Principal, R = Rate, and T = Time

[tex]A =[/tex]  [tex]P(1+R)^x[/tex]

Where A = Final Amount, P = Principal, R = Rate, and x = Time

Year       Money

            Simple Interest                               Compound Interest

0           $750                                                 $750

1            $870 ($750 + ($750 x 16% x 1)       $870 [$750 x (1 + 0.16)¹]

2          $990 ($750 + ($750 x 16% x 2)      $1,170.67 [$870 x (1 + 0.16)²]

3         $1,110 ($750 + ($750 x 16% x 3)    $1,827.29 [$1,170.67 x (1 + 0.16)³]

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Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

The next term of the sequence is predicted to be 155.

To construct a difference table, we find the differences between consecutive terms in the sequence. Let's begin:

Sequence: 6, 2, 5, 24, 68, 146, ...

First differences:

2 - 6 = -4

5 - 2 = 3

24 - 5 = 19

68 - 24 = 44

146 - 68 = 78

...

Second differences:

3 - (-4) = 7

19 - 3 = 16

44 - 19 = 25

78 - 44 = 34

...

Third differences:

16 - 7 = 9

25 - 16 = 9

34 - 25 = 9

...

Since the third differences are constant and equal to 9, we can conclude that the given sequence is a polynomial sequence of degree 3.

Now, to predict the next term of the sequence, we need to continue the difference pattern until we reach a constant difference.

Fourth differences:

9 - 9 = 0

Fifth differences:

0

Since the fifth differences are zero, we can deduce that the polynomial sequence has a degree of 3.

Now, to predict the next term, we start with the last term of the given sequence (146) and add the final difference we obtained (9).

146 + 9 = 155

Therefore, the next term of the sequence is predicted to be 155.

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