Determine the equation of the midline of the following graph.

The solution (X = 8, Y = 16) represents a minimum because the second partial derivatives are both positive.

The quadratic equation's roots 32

+6x+8=0 utilises the quadratic formula to determine. x = is the quadratic formula.

where the quadratic equation's coefficients are a, b, and c. Here, an equals 1, b equals 6, and c equals 8. We obtain the quadratic formula's result by entering these values: x =

x = (-6 ± √(36 - 32)) 2 x = (-6 to 4) 2 x = (-6 to 2) 2 x = (-3 to 1) 1 x = (-2 to 4)

Generally, any quadratic equation of the form may be solved using the quadratic formula to get the roots.

Whereas a, b, and c are real numbers, + bx + c=0. One effective method for tackling a wide range of physics and maths issues is the quadratic formula.

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Step-by-step explanation:

This is similar to the other problem you posted (problem 16).

Again, use the law of cosines. I won't write it out because I wrote it out for the other problem you asked.

Just plugin in a = 8, b = 20, and gamma = 35 into the law of cosines. Then you get your c value, which in this problem is your b variable.

I got around 14.20814

Answer:

sorry

Step-by-step explanation:

We have proven that for all whole values of n, the expression (n-3)(n+2) - (n-3)(n+8) is divisible by 6.

We proved that [far]n-3)(n+2) - (n-3)(n+8) is divisible by 6 for all integer values ​​of n.

[distant]n-3)(n+2) - (n-3)(n+8) is divisible by 6 for all integers in n, simplifying the expression so that it is about 6 Indicates a multiple. .

step 1:

Expand the expression using distribution properties.

[tex](n-3)(n+2) - (n-3)(n+8) = n(n+2) - 3(n+2) - n(n+8) + 3(n+8)[/tex]

Step 2:

Simplify by distributing:

=[tex]n^2 + 2n - 3n - 6 - n^2 - 8n + 3n + 24[/tex]

Step 3:

Combine similar terms:

= [tex]-6 - 8n + 2n + 24[/tex]

= [tex]-6 - 6n + 24[/tex]

= 18 - 6n

Step 4:

Factorization 6:

= 6(3-n)

It turns out that this formula is equal to 6 times the quantity (3 - n).

6 is a multiple of 6, so any number multiplied by 6 is divisible by 6. Therefore (3 - n) is divisible by 6 for all integer values ​​of n.  

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The garden will have the greatest possible area of 80,000 square feet when the shorter side is 400 feet, the longer side is 200 feet, and the garden is bordered by a river on one side.

To find the dimensions that guarantee the garden has the greatest possible area, we can use the concept of optimization.

Let's assume the shorter side of the rectangular garden is x feet.

Since one side of the garden is bordered by a river and doesn't require fencing, we only need to fence three sides of the garden.

The perimeter of the garden is given by the sum of the lengths of the three sides, which is equal to 800 feet.

Thus, we have:

x + 2L = 800

Solving for L (the longer side of the garden) in terms of x:

L = (800 - x)/2

The area of the rectangular garden is given by the product of its length and width, which is:

Area = x [tex]\times[/tex] L

Substituting the expression for L in terms of x:

Area = x [tex]\times[/tex] [(800 - x)/2]

To find the dimensions that guarantee the greatest possible area, we need to find the maximum value of this area.

We can do this by differentiating the area function with respect to x, setting it equal to zero, and solving for x:

d(Area)/dx = (800 - 2x)/2 = 0

800 - 2x = 0

2x = 800

x = 400

So, the shorter side of the garden should be 400 feet.

Substituting this value back into the expression for L:

L = (800 - 400)/2 = 200

Therefore, the longer side of the garden should be 200 feet.

Finally, to find the greatest possible area, we can substitute the values of x and L into the area formula:

Area = 400 [tex]\times[/tex] 200 = 80,000 square feet.

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The estimated raw material Inventory balance at the end of July is $27,750.

The estimated raw material inventory balance at the end of July, we need to follow the given information and calculations:

a. Each unit of finished goods requires 5 pounds of raw materials. Therefore, the total raw materials needed for production in August can be calculated as follows:

23,000 units (budgeted unit sales for September) × 5 pounds/unit = 115,000 pounds

b. The ending raw materials inventory equals 10% of the following month's raw materials production. Based on the information provided, the estimated raw materials needed to meet production in August is 111,000 pounds.

111,000 pounds × 0.10 (10%) = 11,100 pounds

This means that the ending raw materials inventory for July should be 11,100 pounds.

c. The cost of raw materials is $2.50 per pound. To find the value of the raw material inventory at the end of July, we multiply the pounds by the cost per pound:

11,100 pounds × $2.50/pound = $27,750

Therefore, the estimated raw material inventory balance at the end of July is $27,750.

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(1) In diagram 1, the method used is proportional height method.

(2) In diagram 2, the method used is angle of depression method.

(3) In diagram 3, the method used for the indirect measurement  is the angle of elevation method.

The method of measurement of the height of the tree is determined as follows;

(1) In diagram 1, the method used to estimate the height of the tree is proportional height method.

(2) In diagram 2, the method used for the indirect measurement  of the height of the tree is angle of depression method, as indicated in the position of the observer.

(3) In diagram 3, the method used for the indirect measurement  of the height of the tree is the angle of elevation method, as  indicated in the position of the observer.

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It would take 15 people approximately 3.6 hours to complete the same task.

To solve this problem, we can use the concept of the work done. Work is defined as the product of the number of people and the time taken to complete a task.

Let's assume that the amount of work required to complete the task is represented by W. We know that 25 people can do the task in 6 hours, so the work done by 25 people in 6 hours is 25 * 6 = 150 person-hours.

Now, we need to find out how long it would take 15 people to do the same task. Let's represent the time taken by 15 people to complete the task as T.

Since the amount of work required to complete the task is the same, we can set up a proportion:

25 people / 6 hours = 15 people / T hours

Cross-multiplying, we get:

25 * T = 15 * 6

Simplifying, we find:

25T = 90

Dividing both sides by 25, we obtain:

T = 90 / 25 = 3.6 hours

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The graph that best represents the inequality, -3 < n, is determined as the graph in option 3.

The inequality, -3 < n, simply means the possible values n are greater than -3, because -3 is less than any of the possible values of n.

Therefore, the correct graph representing the inequality -3 < n is a number line with an open circle at -3 and the line extending to the right. This indicates that n is greater than -3 but does not include -3 itself.

Thus, the graph in option 3 represents -3 < n.

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The simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

The given expression is simplified as follows;

The given expression is written as;

ab³/a⁴b  +  (c²)³

To simplify the expression given above, we will divide the fraction with the common factor as follows;

From the numerator; ab³, we will factor out "ab"

From denominator; a⁴b, we will factor out "ab"

The resulting expression becomes;

ab³/a⁴b  +  (c²)³

= b²/a³  +  c⁶

Note: for the power of c, we simplify by multiplying 2 and 3 = 6

Thus, the simplification of the expression ab³/a⁴b  +  (c²)³ is determined as b²/a³  +  c⁶.

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The domain and the range of the graph are

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

The graph

The above graph can be represented as a list of ordered pairs

The rule of a graph is that

From the graph, we can see that

This means that the domain and range can take any real value for x and y

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

Domain = All set of real values

Range = All set of real values

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The required fraction of non-fiction hardback books sold is 13/40.

Given the table shows the number of different books sold by a shop. What fraction of the books sold were non-fiction, hardback books? We need to find out what fraction of the books sold were non-fiction, hardback books.

The table is: Fiction  Non-fiction eBook 7   5  Hardback 6  13  Paperback 8  1The number of non-fiction hardback books is 13.

Now, the total number of books sold is: 7 + 5 + 6 + 13 + 8 + 1 = 40The fraction of non-fiction hardback books sold = (number of non-fiction hardback books sold) / (total number of books sold)= 13/40The fraction cannot be simplified further.

Therefore, the required fraction of non-fiction hardback books sold is 13/40.

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The algebraic expression for √(4+x)(10-x), which is 121.

To find the value of √(4+x)(10-x) algebraically, we start by simplifying the given equation:

√(4+x) + √(10-x) = 6

To eliminate the square roots, we can square both sides of the equation:

(√(4+x) + √(10-x)[tex])^2 = 6^2[/tex]

Expanding the left side using the binomial formula, we get:

(4+x) + 2√[(4+x)(10-x)] + (10-x) = 36

Simplifying further:

14 + 2√[(4+x)(10-x)] = 36

Subtracting 14 from both sides:

2√[(4+x)(10-x)] = 22

Dividing both sides by 2:

√[(4+x)(10-x)] = 11

Now we can square both sides again to get rid of the square root:

[(4+x)(10-x)] = [tex]11^2[/tex]

Simplifying further:

(4+x)(10-x) = 121

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Step-by-step explanation:

2pi/3 is the same thing as 2pi/3 * 180/pi = 120 degrees

From your choices, we know that it is either c or d.

sin(120) is in the 2nd quadrant, so the x is negative and the y is positive. Remember that sin corresponds to the y value, so it is positive. Therefore option (d) is not true.

A construction of the line plot for the amount of time spent on homework on Monday night is shown in the image attached below.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would make use of an online graphing calculator (tool) to graphically represent the amount of time spent on homework on Monday night on a line plot as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 2 because it has the highest frequency of 3.

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Missing information:

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

Given statement solution is :-

1) Gather your electricity bills from the period before the summer break.

2) Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

3) Research or locate the power consumption information for each appliance.

4) Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

5) After the summer break, collect your electricity bill for the corresponding period.

6) Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

To conduct a comparative study of consecutive electric bills and analyze the impact of a reduction plan, you can follow the steps below:

Examine your electricity bills of pre-summer break:

Gather your electricity bills from the period before the summer break.

Look for details such as total energy consumption (in kilowatt-hours or kWh), billing period, and the cost per unit of electricity.

List the various electrical appliances used in your home:

Create a comprehensive list of all the electrical appliances used in your home.

Include major appliances like air conditioners, refrigerators, washing machines, and smaller devices like televisions, computers, and lights.

Find out the power consumption and duration for each device in use:

Research or locate the power consumption information for each appliance.

This information is typically provided on the appliance itself or in the user manual.

Note down the power rating of each device in watts (W) or kilowatts (kW).

Estimate the average duration each device is used daily in hours (e.g., 2 hours for a television, 8 hours for a refrigerator).

Calculate the estimated electricity consumption and cost:

Multiply the power rating (in kW) of each device by its average daily usage (in hours) to find the daily energy consumption (in kWh).

Multiply the daily energy consumption by the number of days in the billing period to get the total energy consumption for that period.

Multiply the total energy consumption by the cost per unit of electricity to calculate the estimated cost for each appliance.

Sum up the estimated costs for all appliances to get the total estimated electricity bill.

Make an energy reduction plan and determine implementation:

Identify areas where energy consumption can be reduced, such as:

Turning off lights when not in use.

Setting air conditioner temperatures at an optimal level.

Using energy-efficient appliances.

Unplugging devices when not in use.

Determine the feasibility of implementing these energy reduction measures in your home.

Re-examine your electricity bill of post-summer break:

After the summer break, collect your electricity bill for the corresponding period.

Calculate the actual energy consumption and cost using the same method as in step 4.

Compare the actual post-summer break bill with the estimated pre-summer break bill.

Note any changes in energy consumption and cost, and analyze the effectiveness of your energy reduction plan.

Document your reduction plan and changes in the bill:

Write a report summarizing your findings and observations.

Include details about your energy reduction plan, the changes implemented, and the resulting impact on energy consumption and cost.

Provide recommendations for further improvements or adjustments to achieve even greater sustainability.

By following these steps, you can conduct a comparative study of consecutive electric bills, analyze the effectiveness of your energy reduction plan, and track changes in energy consumption and costs.

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Answer:

The volume of the whole figure is:
8,847 ft^3 + 26,542 ft^3 =  35,389 cubic feet

Step-by-step explanation:

The volume of the rectangle lower part is :
38.4ft*24ft * 28.8ft =26,542.08 cubic foot

to the nearest  whole number 26,542 cubic feet

The area of the right  side of the triangle face on the top is  (Base * height) / 2 :
(19.2ft * (38.4ft /2) / 2   =184.32 square feet

As both side of that triangle on top have the same length of hypothenuse. The area of the whole triangle face:
184.32 *2 = 368.64 square feet

The volume of the triangle top:
368.64 ft^2 * 24ft = 8,847.36 cubic feet .

To the nearest whole number 8847 cubic feet

The volume of the whole figure is:
8,847 ft^3+26,542 ft^3 =  35,389 cubic feet

Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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No, Mr. Morake's statement is not true.

The basic charge is included in the water usage bill. The basic charge is a fixed fee that is charged to all customers, regardless of their water usage. It helps to cover the costs of maintaining the water infrastructure, such as the water mains and pipes. The basic charge for Mr. Morake's property is R150.00. This means that the total amount of his water bill should be R216.27, not R201.27.

Here is a breakdown of Mr. Morake's water bill:

* Basic charge: R150.00

* Water usage: R51.27

* Total: R201.27

It is possible that Mr. Morake is confused about the difference between the basic charge and the water usage charge. The basic charge is always included in the water bill, while the water usage charge is only charged if you use more than a certain amount of water. In Mr. Morake's case, he used more than the amount of water that is exempt from the water usage charge, so he was charged the full water usage amount.

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Answer:

Least common multiple = 150

Step-by-step explanation:

The least common multiple is defined as the smallest multiple that two or more numbers have in common.

We can find the least common multiple by listing the multiples of both numbers:

Multiples of 15:

15, 30, 45, 60, 75, 90, 105, 120, 135, 150

Multiples of 50:

50, 100, 150

Thus, 150 is the least common multiple of 15 and 50.

Answer:

[tex]x \leq -4[/tex]

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

[tex]-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4[/tex]

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, [tex]x \leq -4[/tex], -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

The smallest integer that Pearl wrote down is -12.Let's assume the smallest integer that Pearl wrote down is represented by the variable "x."

According to the given information, the sum of the seven consecutive integers is equal to $\frac{21}{4}$ times the largest integer.

The sum of consecutive integers can be expressed as the sum of an arithmetic series. The sum of an arithmetic series can be calculated using the formula:

Sum = (n/2)(first term + last term)

In this case, the first term is x and the last term is x + 6 (since there are seven consecutive integers). Therefore, the sum of the integers can be written as:

Sum = (7/2)(x + (x + 6))

Simplifying the equation:

(7/2)(2x + 6) = (21/4)(x + 6)

Multiplying both sides by 4 to eliminate the fractions:

14x + 42 = 21x + 126

Subtracting 14x from both sides:

42 = 7x + 126

Subtracting 126 from both sides:

-84 = 7x

Dividing both sides by 7:

-12 = x.

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Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

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Answer:

1.

a) Slope: 1/3. Y-intercept:-2.

b) y=1/3x-2

2.

a) y=9.50x+15

b) To solve, substitute 12 in for x. y=9.50(12)+15. y=114+15. y=129. It will cost $129 for a full year membership.

The solutions to the equation sin(θ) + 1 = cos(2θ) on the interval 0 ≤ θ ≤ 2π are θ = 0, θ = π, θ = 7π/6, and θ = 11π/6.

To solve the equation sin(θ) + 1 = cos(2θ) on the interval 0 ≤ θ ≤ 2π, we can use trigonometric identities and algebraic manipulations to simplify and find the solutions.

Let's start by using the double-angle identity for cosine:

cos(2θ) [tex]= 1 - 2sin^2(\theta)[/tex]

Substituting this into the equation, we have:

[tex]sin(\theta) + 1 = 1 - 2sin^2(\theta)[/tex]

Rearranging the equation, we get:

[tex]2sin^2(\theta) + sin(\theta) = 0[/tex]

Factoring out sin(θ), we have:

sin(θ)(2sin(θ) + 1) = 0

Now we can set each factor equal to zero and solve for θ:

sin(θ) = 0 or 2sin(θ) + 1 = 0

For sin(θ) = 0, the solutions are θ = 0 and θ = π (since sin(θ) = 0 at these values on the interval 0 ≤ θ ≤ 2π).

For 2sin(θ) + 1 = 0, we can solve for sin(θ):

2sin(θ) + 1 = 0

2sin(θ) = -1

sin(θ) = -1/2

The solutions for sin(θ) = -1/2 on the interval 0 ≤ θ ≤ 2π are θ = 7π/6 and θ = 11π/6.

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The width of the box of tissues is approximately 10.49 cm.

We can use the formula for the volume of a rectangular prism:

Volume = Length × Width × Height

We may rearrange the formula to find the breadth if we know the volume is 1501.5 cm3 and the length is 11 cm:

Width = Volume / (Length × Height)

Substituting the given values:

Width = 1501.5 cm³ / (11 cm × 13 cm)

Width = 1501.5 cm³ / 143 cm²

Calculating the result:

Width ≈ 10.49 cm

So, the width of the box of tissues is approximately 10.49 cm.

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Answer:

  319

Step-by-step explanation:

You want to know the 45th term of the arithmetic sequence that begins -33, -25, -17, ...

The general term of an arithmetic sequence with first term a1 and common difference d is ...

  an = a1 +d(n -1)

For a1 = -33 and d = (-25 -(-33)) = 8, the n-th term is ...

  an = -33 +8(n -1)

Then the 45th term is ...

  a45 = -33 +8(45 -1) = -33 +352 = 319

The 45th term of the sequence is 319.

<95141404393>

The cumulative probability 0.68 from the z-score for the cumulative probability 0.236, we find that 'c' is approximately 0.0686.

To determine the value of 'c' in the expression P(0.68 <= Z <= c) = 0.236, where Z is a standard normal random variable, we need to use the standard normal distribution table.

The standard normal distribution table provides the cumulative probability for values up to a given z-score. In this case, we are given the cumulative probability of 0.236.

To find the value of 'c', we need to look up the corresponding z-score in the table.

Look up the z-score for the cumulative probability 0.68 in the standard normal distribution table. The closest value in the table is 0.7486.

Subtract the z-score for the cumulative probability 0.68 from the z-score for the cumulative probability 0.236:

c = 0.7486 - 0.68 = 0.0686

In summary, to find the value of 'c' in the expression P(0.68 <= Z <= c) = 0.236, we use the standard normal distribution table to find the corresponding z-score. Therefore, the value of 'c' is approximately 0.0686.

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Answer:

Hi

Step-by-step explanation:

Please paste your question so I can solve it

Thanks

Answer:

  (x, y) = (5, 2)

Step-by-step explanation:

You want to use the elimination method to solve these equations:

To solve the equations by the elimination method you want to combine them in such a way that the coefficient of one of the variables is zero.

The coefficients of x are 4 and 3, so we can eliminate the x variable by multiplying the first equation by 3 and the second equation by -4 before we combine (add) them.

The coefficients of y are 2 and -4, so we can eliminate the y variable by multiplying the first equation by 2 before we combine (add) them. This seems simpler.

  2(4x +2y) +(3x -4y) = 2(24) +(7)

  11x = 55 . . . . . . . . simplify

  x = 5 . . . . . . . . divide by 11

  4(5) +2y = 24 . . . . . . substitute for x in the first equation

  2y = 24 -20 . . . . . subtract 20

  y = 2  . . . . . . . . divide by 2

The solution is (x, y) = (5, 2).

<95141404393>