Find value of b and A

Answers

Answer 1

Answer:

Hi

Step-by-step explanation:

Please paste your question so I can solve it

Thanks


Related Questions

Please help me with this i really need help quickly.

Answers

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

How to Determine the Graph of an Inequality?

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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Cuantas permutaciones pueden hacerse con la palabra columna

Answers

There are 720 Permutations that can be made with the word "column."

The number of permutations that can be made with the word "column," we need to consider the arrangement of the letters in the word.

The word "column" has 6 letters. When calculating permutations, we need to consider that the order of the letters matters.

In this case, we have 6 options for the first letter, 5 options for the second letter, 4 options for the third letter, 3 options for the fourth letter, 2 options for the fifth letter, and 1 option for the last letter.

To find the total number of permutations, we multiply the number of options for each letter:

6 * 5 * 4 * 3 * 2 * 1 = 720.

Therefore, there are 720 permutations that can be made with the word "column."

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PLS HELP ME COMPLETE 1 AND 2! 90 points! ​

Answers

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.

A box of tissues is 13cm in height and 11 cm in length. Its volume is 1501.5 cm cubed. What is the width, of the box of tissues?

Answers

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

How to find the width of the box of tissues

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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Which of these lines best fits the data?
y
10
8
6
4-
2
y
10
8
8 10
6
4
2
0 2 4 6 8 10
Y+
10
8-
6-
4
2
0 2 4 6 8 10
10-
8-
6
4
2
0 2 4 6 8 10
X

Answers

The top right line (second line) best fits the data in this problem, as it has the lowest residuals.

What are residuals?

For a data-set, the definition of a residual is that it is the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

For a line of best fit, we have that the residuals are the lowest possible, meaning that the points are the closest to the line.

Hence the top right line best fits the data in this problem, as it has the lowest residuals.

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Urgent please help thank you guys for all the help

Answers

Answer:

$15.00 per day and $0.22 per mile.

Step-by-step explanation:

To determine the daily fee and mileage fee charged by Best Rentals, we can set up a system of equations based on the given information.

Let's assume the daily fee is represented by "d" and the mileage fee is represented by "m."

For Mateo:

3d + 300m = 111.00

For Dara:

5d + 600m = 207.00

Now we can solve this system of equations to find the values of "d" and "m."

Multiplying the first equation by 2 to eliminate "m," we get:

6d + 600m = 222.00

Subtracting the second equation from this equation, we have:

(6d + 600m) - (5d + 600m) = 222.00 - 207.00

d = 15.00

Substituting the value of "d" into the first equation, we can solve for "m":

3(15.00) + 300m = 111.00

45.00 + 300m = 111.00

300m = 111.00 - 45.00

300m = 66.00

m = 0.22

Therefore, Best Rentals charges $15.00 per day and $0.22 per mile.

¿Cuantas permutaciones pueden hacerse con la palabra columna?

Answers

Answer:

Se pueden hacer 5040 permutaciones con la palabra COLUMNA.

Explanation:

La palabara COLUMNA posee 7 letras, por lo que debemos hacer permutación sin repetición.

La formula es:

P_^{n}: n!

Donde n son todos los elementos.

PLEASE HELP! I JUST NEED TO KNOW HOW YOU SOLVE THIS!!! SEE ATTACHED!!! WILL MARK YOU BRAINLIEST!!! Surface Area​

Answers

The surface area of the complex solid is 530 square yards.

How to determine the surface area of a complex solid

In this problem we need to determine the surface area of the complex solid, that is, the sum of the area of all faces of the solid. The area formulas required to find the surface area is:

A = w · h

Where:

A - Area, in square yards.w - Width, in yardsh - Height, in yards.

The surface area of the complex solid is:

A = 2 · (11 yd) · (3 yd) + 2 · (4 yd)² + (12 yd) · (11 yd) + (12 yd) · (3 yd) + (12 yd) · (7 yd) + 2 · (4 yd) · (12 yd) + (12 yd) · (7 yd)

A = 66 yd² + 32 yd² + 132 yd² + 36 yd² + 84 yd² + 96 yd² + 84 yd²

A = 530 yd²

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16) Solve for side AB.
AB-
Round your answer to the nearest hundredth.

A) 5.45
B) 6.45
C) 7.45

Answers

Answer:

AB= 7.45

Anwer C)

Step-by-step explanation:

Cos (angle) = Nearest side / Huypothenuse

Cos(20)      = 7 / AB

Cos(20) * AB = (7 /AB) * AB

Cos (20) * AB = 7

(Cos(20) *AB) / Cos(20) = 7 / Cos(20)

AB = 7 / cos(20)

AB=    7.45

In this triangle, side AB is the hypotenuse.

In order to find the hypotenuse, we can use the trigonometric function “cosine”,
since.

Cosine =
Adjacent side (which is 7) / hypotenuse

Cos(50) = 7 / AB

AB = 7 / Cos(50)

AB = 10.89006678802289

AB ≈ 10.89

Have a good day ^^

If 25 people can do a task in 6 hours, how long would it take 15 people to do the same task?

Answers

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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WEEK 2 Direction: Answer the following problems. 1. Jun wanted to know how much ice cream he got in on scoop. The radius of a scoop is 2 inches. Find the volum Use 3.14 for pi. (SHOW YOUR SOLUTION) a) What is asked in the problem? b) What are the given facts? c) What is the formula to be used? d) Number Sentence e) Final answer. (show your solution pls)​

Answers

We are given the radius of the scoop and asked to find the volume of ice cream in one scoop. By using the formula for the volume of a sphere and substituting the given radius, we can calculate the volume. The final answer is approximately 33.49 cubic inches.

a) The problem asks for the volume of ice cream in one scoop.

b) The given fact is that the radius of the scoop is 2 inches.

c) The formula to be used is the volume of a sphere, which is given by V = (4/3)πr³, where V is the volume and r is the radius.

d) Number Sentence:

  - Given: Radius (r) = 2 inches

  - Formula: V = (4/3)πr³

  - Substituting the value: V = (4/3)π(2)³

  - Simplifying: V = (4/3)π(8)

  - Evaluating: V = (4/3)(3.14)(8)

  - Multiplying: V = 33.49333333 (approx.)

e) Final answer: The volume of ice cream in one scoop is approximately 33.49 cubic inches.

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Help with graph, algebra, just need the answer, A, B, C, or D

Answers

The domain and the range of the graph are

Domain = (a) All real valuesRange = (a) All real values

Calculating the domain and range of the graph

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

The domain is the x valuesThe range is the f(x) values

From the graph, we can see that

There are no holes or discontinuity on the graphThe curve span across the x-axis and the y-axis

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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What is the surface area of the prism in square inches?



A net has 3 rectangular faces and 2 triangular faces. One rectangle has a base of 13 and height of 5. Another has a base of 12 and height of 5. Another has a base of 5 and height of 5. The triangles have a base of 12 and height of 5.


A-60 square inches

B-168 square inches

C-276 square inches

D-304 square inches

Answers

None of the provided options (A, B, C, D) matches the correct surface area of the prism, which is 210 square inches.

To find the surface area of the prism, we need to calculate the area of each face and then sum them up.

Let's calculate the areas of each face:

Rectangle 1: Area = base × height = 13 × 5 = 65 square inches

Rectangle 2: Area = base × height = 12 × 5 = 60 square inches

Rectangle 3: Area = base × height = 5 × 5 = 25 square inches

Triangle 1: Area = (base × height) / 2 = (12 × 5) / 2 = 30 square inches

Triangle 2: Area = (base × height) / 2 = (12 × 5) / 2 = 30 square inches

Step 2: Sum up the areas of all the faces.

Total Surface Area = Area of Rectangle 1 + Area of Rectangle 2 + Area of Rectangle 3 + Area of Triangle 1 + Area of Triangle 2

Total Surface Area = 65 + 60 + 25 + 30 + 30

Total Surface Area = 210 square inches

Therefore, the surface area of the prism is 210 square inches.

Now, let's sum up the areas of all the faces:

Total surface area = 65 + 60 + 25 + 30 + 30 = 210 square inches

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What is the approximate value of this logarithmic expression?
log3 16

Answers

The approximate value of log3 16 is 2.5247. This means that 3 raised to the power of approximately 2.5247 is equal to 16.

The logarithmic-expression[tex]log3 ^1^6[/tex] can be interpreted as "the exponent to which 3 must be raised to obtain 16." In other words, we are looking for a number, let's call it x, such that 3 raised to the power of x equals 16.

To determine the approximate value of[tex]log3^1^6[/tex], we can make use of the change of base formula for logarithms, which states that loga b = logc b / logc a. Applying this formula, we can rewrite log3 ^16 as log10 16 / log10 3.

Using a calculator, we find that log10 16 is approximately 1.2041 and log10 3 is approximately 0.4771. Dividing these two values, we get 1.2041 / 0.4771 ≈ 2.5247.

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= OGRAPHS, FUNCTIONS, AND SEQUENCES Graphically solving a system of linear equations both of the for... Here is a system of equations. y=2x+5 y=x+1 Graph the system. Then write its solution. Note that you can also answer "No solution" or "Infinitely many" solutions. -6 4 6 X Solution: No solution X Infinitely many 0/5 S
how do you graph this and find the answer
[tex]y = 2x + 5[/tex]
[tex]y = x + 1[/tex]

Answers

The solution to the system of equations: y = 2x + 5 and y = x + 1 is x = 1 and y = 2.

Understanding Linear Equation

Linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised to the power of 1. In other words, it represents a straight line when graphed on a coordinate plane.

The general form of a linear equation is:

ax + by + c = 0

Here, "x" and "y" are variables, and "a," "b," and "c" are constants.

For example, the equation y = 2x + 3 is a linear equation with one variable (x) and represents a straight line on a graph. The coefficients 2 and 3 determine the slope and y-intercept of the line, respectively.

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Prove that for all whole values of n the value of the expression (n-3)(n+2)-(n-3)(n+8) is divisible by 6.

Answers

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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A candy bar that originally sold for $.60 undergoes a #% price increase each year. How much would it cost after 13 years

Answers

The candy bar would cost approximately $1.18 after 13 years with a 7% price increase each year.

To calculate the cost of the candy bar after 13 years with a 7% price increase each year, we can use the formula:

Cost after n years = Initial cost × (1 + Percentage increase/100)^n

Given that the initial cost of the candy bar is $0.60 and the percentage increase is 7%, we can substitute these values into the formula:

Cost after 13 years = $0.60 × (1 + 7/100)^13

Now, let's perform the calculations:

Cost after 13 years = $0.60 × (1 + 0.07)^13

Cost after 13 years = $0.60 × (1.07)^13

Cost after 13 years ≈ $0.60 × 1.967151

Cost after 13 years ≈ $1.18

Therefore, the candy bar would cost approximately $1.18 after 13 years with a 7% price increase each year.

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Question

A candy bar that originally sold for $.60 undergoes a 7% price increase each year. How much would it cost after 13 years

Mr.
Morake's municipal bill showed R201,27, for water usage at the end of august 2018 , He stated that the basic charge was not included on the water . is the state true?

Answers

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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Let Z be a standard normal random variable. Use the table, to determine the value of c.
P(0.68 <= Z <= c) = 0.236.
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

Answers

The value of c is given as 1.24

How to solve for the value of c

To find the value of "c" in the equation P(0.68 ≤ Z ≤ c) = 0.236, we need to use the standard normal distribution table. This table provides the cumulative probability for different values of the standard normal random variable Z.

Look up the cumulative probability 0.68 in the table. The closest value we find is 0.6799. Corresponding to this value, we note the associated Z-score, which is approximately 0.50.

Next, look up the cumulative probability 0.236 in the table. The closest value we find is 0.2389. Corresponding to this value, we note the associated Z-score, which is approximately -0.74.

Subtract the Z-score for the lower limit from the Z-score for the upper limit: 0.50 - (-0.74) = 1.24.

The value of "c" that satisfies P(0.68 ≤ Z ≤ c) = 0.236 is approximately 1.24.

Therefore, c ≈ 1.24.

The value of c is given as 1.24

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Rumus suatu fungsi di nyatakan dengan f (x) = 2x + 5. Jika f(a) = 7, nilai a adalah

Answers

Step-by-step explanation:

As my previous answer got deleted for being wrong (in which it was right), I will answer again.

The answer is 1. Why? Just plug it into the equation. F(1) = 2(1) + 5 = 7.

This is proof that it is right, and that there are some corrupt admins on brainly.

How to get to this solution?

Well notice how we are given what f(a) is. It is 2a + 5. So plug this in for f(a).

If we do so, we get 2a + 5 = 7.

Solving this equation, we get a = 1.

Need all answered please

Answers

This has to do with proprotions.

RV is 12

AE/AC = BF/BD

BD/AC = BF/AE

DF/CE = BD/AC

What is proportions?

In mathematics, proportions express the relationship between two ratios.

They compare two equivalent fractions or ratios and state that they are equal, allowing us to solve for unknown values in a proportional relationship.

To solve the equation (24/32) = (RV/16), we can cross-multiply and solve for RV.

Cross-multiplying gives us

24 * 16 = 32 * RV

Simplifying further

384 = 32 * RV

To isolate RV, divide both sides of the equation by 32

384 / 32 = RV

Simplifying the division

12 = RV

Therefore, the value of RV in the equation (24/32) = (RV/16) is 12.

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Need help with top problem. Maybe bottom too

Answers

1) The area of a circle circumscribed about a square is 307.7 cm².

2.a.) The angle ACB is 39 degrees.°.

2b.) The value of x is 5.42.

How to determine the area of a circle?

We shall find the radius to determine the area of a circle.

First,  find the side length of the square:

Since the perimeter of the square = 56 cm, then, each side of the square is 56 cm / 4 = 14 cm.

Next, find the diagonal of the square, using the Pythagorean theorem:

Diagonal = the diameter of the circumscribed circle.

Diagonal² = side length² + side length²

= 14 cm² + 14 cm²

= 196 cm² + 196 cm²

= 392 cm²

Take the square root of both sides:

Diagonal = √392 cm ≈ 19.80 cm (rounded to two decimal places)

Then, the radius of the circle which is half the diagonal:

Radius = Diagonal / 2 ≈ 19.80 cm / 2 ≈ 9.90 cm (rounded to two decimal places)

Finally, compute the area of the circle using the formula:

Area = π * Radius²

Area = 3.14 * (9.90 cm)²

Area ≈ 307.7 cm² (rounded to two decimal places)

Therefore, the area of the circle that is circumscribed about a square with a perimeter of 56 cm is 307.7 cm².

2. a) We use the property of angles in a circle to solve for angle ACB: an angle inscribed in a circle is half the measure of its intercepted arc.

Given that arc AB has a measure of 78°, we can find angle ACB as follows:

Angle ACB = 1/2 * arc AB

= 1/2 * 78°

= 39°

Therefore, the angle ACB is 39 degrees.

2b.) To solve for the value of x, we use the information that the angle ADB =  (3x - 12)⁴.

Given that angle ADB is (3x - 12)⁴, we can equate it to the measure of the intercepted arc AB, which is 78°:

(3x - 12)⁴ = 78

Solve the equation for x, by taking the fourth root of both sides:

∛∛((3x - 12)⁴) = ∛∛78

Simplify,

3x - 12 = ∛(78)

Isolate x by adding 12 to both sides:

3x - 12 + 12 = ∛(78) + 12

3x = ∛(78) + 12

Finally, divide both sides by 3:

x = (∛(78) + 12) / 3

x = (4.27 +12) / 3

x = 5.42

So, x is 5.42

Therefore,

1) The area of the circle is 154 cm².

2a.) Angle ACB is equal to 102°.

2b.) The value of x is 5.42

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please help me with this ​

Answers

The solution to trigonometric equation sin θ + 1 / 2 = 1 is equal to θ = π / 6 + i · 2π or θ = 5π / 6 + i · 2π.

How to solve a trigonometric equation

In this problem we must determine the solution to a trigonometric equation, this can be done both by algebra properties and trigonometric formulas. First, write the entire expression:

sin θ + 1 / 2 = 1

Second, clear the trigonometric function:

sin θ = 1 / 2

Third, use inverse trigonometric functions:

θ = π / 6 + i · 2π or θ = 5π / 6 + i · 2π, where i is a whole number.

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SUSTAINIBILTY COUNTS! ENERGY CHALLENGE WHAT TO DO: COMPARITIVE STUDY OF CONSECUTIVE ELECTRIC BILLS o of post summer break with all calculations.

SUSTAINIBILTY COUNTS! ENERGY CHALLENGE
WHAT TO DO: COMPARITIVE STUDY OF CONSECUTIVE ELECTRIC BILLS HOW TO DO: 1) Examine your electricity bills of pre summer break.
2) List the various electrical appliances used in your home.
3) Find out the power consumption, duration for the device in use.
Do estimate calculation of your bills as per power consumption.
4) Make an energy reduction plan and determine how far you could implement it.
5) Re – examine your electricity bill of post summer break with all calculations.
6) WRITE your reduction plan & change in the bill. ​

Answers

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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Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to $\frac{21}{4}$ times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

Answers

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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Q3. is the universal set and A, B and C are three sets. universal set ={p,q,r,s,t} A = {q.r.s) B = {p.q.t}

given that A cap C = r
(b) write down all the possibilities for set C one of the possibilities for set C is selected at random.

(c) Find the probability that this set C is such that B C = 0​

Answers

b(i) The possibilities for set C can be:

C = {r}

C = {r, p}

C = {r, q}

C = {r, s}

C = {r, t}

C = {r, p, q}

C = {r, p, s}

C = {r, p, t}

C = {r, q, s}

C = {r, q, t}

C = {r, s, t}

C = {r, p, q, s}

C = {r, p, q, t}

C = {r, p, s, t}

C = {r, q, s, t}

C = {r, p, q, s, t}

b(i). The probability of selecting any particular set C from the possibilities listed is 1/16.

c. The probability that B ∩ C = 0 is 1/16.

What are the possibilities for set C?

Given the information:

Universal set: {p, q, r, s, t}

A = {q, r, s}

B = {p, q, t}

A ∩ C = {r}

(b) To find the possibilities for set C, consider the elements that are common to set A and set C, as indicated by A ∩ C = {r}.

The elements in set C can be any subset of the universal set that contains the element "r".

Therefore, the possibilities for set C can be:

C = {r}

C = {r, p}

C = {r, q}

C = {r, s}

C = {r, t}

C = {r, p, q}

C = {r, p, s}

C = {r, p, t}

C = {r, q, s}

C = {r, q, t}

C = {r, s, t}

C = {r, p, q, s}

C = {r, p, q, t}

C = {r, p, s, t}

C = {r, q, s, t}

C = {r, p, q, s, t}

(b) If one of the possibilities for set C is selected at random, there are a ⁴otal of 24 = 16 possible subsets of the universal set. Therefore, the probability of selecting any particular set C from the possibilities listed in part (a) is 1/16.

(c) We need to find the probability that set B ∩ C = 0.

From the possibilities for set C listed above, the only set C that satisfies this condition is C = {r}.

Therefore, the probability that B ∩ C = 0 is 1/16.

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Ringani worked overtime to raise a total amount R30 000.00 to settle his student debt. If he has deposited R8 500.00 yearly into an account earning 7,04% interest per year compounded annually. How long, rounded to one decimal place did it took her to accumulate the total amount? A. 3.0 years B. 2.4 years C. 2.8 years D. 2.0 years​

Answers

It took Ringani 2.8 years  to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate Compounded annually.The correct answer choice is C. 2.8 years.

To determine how long it took Ringani to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into an account with a 7.04% interest rate compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final amount

P is the principal amount (initial deposit)

r is the interest rate (in decimal form)

n is the number of times the interest is compounded per year

t is the time in years

In this case, we have:

P = R8,500.00

A = R30,000.00

r = 7.04% = 0.0704 (in decimal form)

n = 1 (compounded annually)

We want to find the value of t.

Using the formula, we can rearrange it to solve for t:

t = (log(A/P)) / (n * log(1 + r/n))

Substituting the given values, we have:

t = (log(30,000/8,500)) / (1 * log(1 + 0.0704/1))

Calculating this using a calculator, we find that t is approximately 2.8 years.

Therefore, it took Ringani approximately 2.8 years (rounded to one decimal place) to accumulate the total amount of R30,000.00 by depositing R8,500.00 yearly into the account with a 7.04% interest rate compounded annually.

The correct answer choice is C. 2.8 years.

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The population of a town has been growing, following the equation p= 200t+4500
, where t is years after 2010. The number of restaurants in the town has been growing according to the equation R=6t+35
.

Complete an equation for the number of restaurants per capita (per person)

Restaurants per capita:


How many restaurants per capita does this model predict for the year 2016?

Answers

The model predicts that there are approximately 0.012456 (71/5700) restaurants per capita in the year 2016

To determine the number of restaurants per capita, we need to divide the number of restaurants (R) by the population (p). Given that R = 6t + 35 and p = 200t + 4500, we can substitute these values into the equation for restaurants per capita.

Restaurants per capita = R / p

Substituting the given equations, we get:

Restaurants per capita = [tex](6t + 35) / (200t + 4500)[/tex]

To find the number of restaurants per capita for the year 2016, we need to calculate the value of t for that year. Since t represents years after 2010, in 2016, t would be 6 (2016 - 2010 = 6).

Restaurants per capita (2016) = [tex](6 * 6 + 35) / (200 * 6 + 4500)[/tex]

= [tex](36 + 35) / (1200 + 4500)[/tex]

= 71 / 5700

This means that, on average, there is roughly one restaurant for every 80 people in the town. Please note that this prediction is based on the given growth equations and assumes a linear relationship between population and the number of restaurants.

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[The following information applies to the questions displayed below.]
Morganton Company makes one product and it provided the following information to help prepare
a. The budgeted selling price per unit is $60. Budgeted unit sales for June, July, August, and Septe
20,000, 22,000, and 23,000 units, respectively. All sales are on credit.
b. Forty percent of credit sales are collected in the month of the sale and 60% in the following mont
c. The ending finished goods inventory equals 20% of the following month's unit sales.
d. The ending raw materials inventory equals 10% of the following month's raw materials production
finished goods requires 5 pounds of raw materials. The raw materials cost $2.50 per pound.
e. Thirty percent of raw materials purchases are paid for in the month of purchase and 70% in the fo
f. The direct labor wage rate is $13 per hour. Each unit of finished goods requires two direct labor-h
g. The variable selling and administrative expense per unit sold is $1.50. The fixed selling and admin
month is $70,000.
9. If 111,000 pounds of raw materials are needed to meet production in August, what is the estimated raw m
at the end of July?
Raw material inventory balance
$ 257,250

Answers

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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4x+2y=24,3x-4y=7.To find the elimination method

Answers

Answer:

  (x, y) = (5, 2)

Step-by-step explanation:

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

4x +2y = 243x -4y = 7

Elimination method

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).

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