What is the slope-intercept equation of the line that contains the points (0, 3) and (1, 1)?

The required solution is x = (25/11) × log(70/17).

It is required to give exact answers, not decimals.

Therefore, the given equation is 1.7(2.8)⁴ˣ = 7(4.6)ˣ.

This can be simplified as follow

s;1.7 × (2⁹/5)⁴ˣ = 7 × (2⁴⁶/10)⁽ˣ/⁵⁾

1.7 × 2³⁶ˣ/25 = 7 × 2²³ˣ/5

Now, divide both sides of the equation by 2^23x/5;

1.7 × 2⁽³⁶ˣ/²⁵ ⁻ ²³ˣ/⁵⁾= 7

Simplify the left side;

1.7 × 2⁽¹¹ˣ/²⁵⁾ = 7

Now, divide both sides by 1.7;

2⁽¹¹ˣ/²⁵⁾ = 70/17

Take log on both sides;

log(2⁽¹¹ˣ/²⁵⁾)) = log(70/17)11x/25 × log(2) =

log(70/17)x = (25/11) × log(70/17)

Thus, the required solution is x = (25/11) × log(70/17).

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Sales revenue will be recorded at $4,000 and yang Yang would be required to Recognize sales tax liability of $360.

What is  sales revenue?

Sales = $4,000

State sales tax rate = 9%

State sales tax = Sales x State sales tax rate

= 4,000 x 9%

= $360

Sales revenue will be recorded at $4,000 and sales revenue is not affected by the sales tax amount.

Hence, Yang would be required to Recognize sales tax liability of $360.

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a) Speed = distance/time

From the information given,

Distance = 3.75

time = 0.3

Thus, her speed would be

Speed = 3.75/0.3 = 12.5 miles per hour

b) Given that

Distance = 4.5 miles

Speed = 12.5 miles per hour,

Time = distance/speed = 4.5/12.5

Time = 0.36 hours

It will take her 0.36 hours to go 4.5 miles

The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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Answer:

distance = 11.1803 units

midpoint :  (-1.5, 6).

Step-by-step explanation:

To plot the points A(4, 5) and B(-7, 7) on the grid, we locate the points at the coordinates (4, 5) and (-7, 7) respectively.

The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the values for A and B, we get:

d = √((-7 - 4)^2 + (7 - 5)^2)

d = √(11^2 + 2^2)

d = √(121 + 4)

d = √125

d = 11.1803 (rounded to hundredths place)

The midpoint of two points (x1, y1) and (x2, y2) can be calculated as follows:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

The midpoint of A and B is:

x = (4 - 7) / 2 = -1.5

y = (5 + 7) / 2 = 6

So the midpoint of A and B is approximately (-1.5, 6).

Understanding a set’s nature or properties is made easier by its closure property

The set is closed if it has the closure property. This means that any operation performed on an element within a set will provide a result that belongs to that element’s set.

Why Closure Property is important?

Understanding a set’s nature or properties is made easier by its closure property. Mathematical applications of closure are numerous. Any operation that adheres to this condition is said to be “closed” or to have “fulfilled the operation’s closure property.”

Example – The set of even number is closed under subtraction

                   Even – Even = Even

                   6 – 4 = 2

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Answer:

-7,-6,-3.these are the vertices

Answer:

8x + 5y

12(8) + 7(5) =

96 + 35 =

131

$131

Answer:

Angle 2 = 45 degrees

Step-by-step explanation:

Angle 1 = Angle D because they are alternate interior angles.

Angle 3 = Angle A because they are alternate exterior angles.

Angle 1 = 135 degrees

Therefore, Angle D = 135 degrees

180 - Angle D = Angle 2

Angle 2 = 180 - 135

Angle 2 = 45 degrees

Answer:

4

Step-by-step explanation:

Formula for area of hexagon is ((3*square-root 3)/2)*a^2.

Answer:

20 homes

Step-by-step explanation:

Given that :

Total number of homes = 800

Average years at which homes are listed = 8 years

To obtain the annual home listing = total number of Homes / average years

Annual home listing = 800 / 8

Annual home listing = 100 homes

If 20% of the homes are listed on the year in question :

20% of 100 homes

0.2 * 100

= 20 homes

20 homes can be listed that year

Answer: 40 chocolates

Step-by-step explanation:

9514 1404 393

Answer:

  the difference of squares is 24(3n+2), so a multiple of 24

Step-by-step explanation:

The sequence has a first term of 7 and a common difference of 6, so the n-th term is ...

  a[n] = a1 +d(n -1)

  a[n] = 7 + 6(n -1)

  a[n] = 6n +1

Then the (n+1)-th term is ...

  a[n+1] = 6(n+1) +1 = 6n +7

The difference of the squares of these terms is ...

  a[n+1]^2 -a[n]^2 = (6n+7)^2 -(6n+1)^2

  = (36n^2 +84n +49) -(36n^2 +12n +1)

  = 72n +48

  = 24(3n +2) . . . . . always a multiple of 24

The difference of squares of terms n and n+1 is 24(3n+2), a multiple of 24.

_____

Check

The difference between squares for n=1 and n=2 is 13^2 -7^2 = 169 -49 = 120. The formula tells us the difference is 24(3·1 +2) = 24·5 = 120, in agreement.

Answer:

4:55 hrs :)

Step-by-step explanation:

1:30 hours + 40 min + 40 min + 2:05 

1:30 hrs + 1:20 hrs + 2:05 hrs

2:50 hrs + 2:05 hrs

4:55 hrs

Have an amazing day!!

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The endpoints of the major axis of the ellipse ((x-3)^2)/9+(y-6)^2/16=1 are (3,6) and (3,2).

In the given equation, we can see that the x-term is squared and has a denominator of 9, while the y-term is squared and has a denominator of 16. This indicates that the major axis is aligned with the y-axis since the denominator of the y-term (16) is larger than the denominator of the x-term (9), making the y-axis the major axis.

To find the length of the major axis, we need to identify the square root of the larger denominator in the equation. In this case, the square root of 16 is 4. This means that the length of the major axis is 2 times the square root of 16, which is 2 times 4, resulting in a length of 8 units.

To determine the endpoints of the major axis, we look at the center of the ellipse. In the equation, the center is represented as (3, 6), which means that the ellipse is centered at the point (3, 6). Since the major axis is aligned with the y-axis, the endpoints of the major axis will have the same x-coordinate as the center (3) and will differ in their y-coordinates.

To calculate the y-coordinates of the endpoints, we add and subtract half the length of the major axis from the y-coordinate of the center (6). Half the length of the major axis is 8/2 = 4, so we add and subtract 4 from the y-coordinate of the center. This gives us the endpoints of the major axis as (3, 6 + 4) = (3, 10) and (3, 6 - 4) = (3, 2).

Therefore, the endpoints of the major axis are (3, 10) and (3, 2).

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Answer:

41.245

Step-by-step explanation:

36.50*13%. fffbbuyt the gdgdhrbsbeb

Answer:

Step-by-step explanation:

A and B are complementary angles since C is right angle.

The entire trip to the mall took 5 hours, and it was 24 miles away. Cameron biked for 2 hours and walked for 3 hours.

Cameron started biking to the mall at a speed of 9 mph. After some time, the bike got a flat so Cameron walked the rest of the way, traveling at a speed of 2 mph. The distance that Cameron biked to the mall was x, and the distance he walked to the mall was 24 - x.

Cameron traveled at two different speeds, 9 mph and 2 mph, and traveled a total of 24 miles. So the time he spent biking plus the time he spent walking was 5 hours, and we can create an equation:

Time biking + time walking = 5 hours x/9 + (24 - x)/2 = 5 hours

Multiply everything by 18 to remove the denominators:
2x + 9(24 - x) = 90
2x + 216 - 9x = 90-7x = -126x = 18
Time biking = x/9 = 18/9 = 2 hours
Time walking = (24 - x)/2 = (24 - 18)/2 = 3 hours

Therefore, Cameron biked for 2 hours and walked for 3 hours.

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Answer:

The answer is the 3rd quadrant.

Answer:

A. The slope of a line parallel to m is positive.

Step-by-step explanation:

The population of bacteria 1 minute ago was 25 million.

If the population of bacteria is increasing at the rate of 100% every minute, this means that the population is doubling every minute. So, if the population is currently at 50 million, then 1 minute ago it was half that amount.

To find out the population of bacteria 1 minute ago, we can divide the current population by 2:

50 million / 2 = 25 million

This is because if the population is increasing at 100% every minute, this means that every minute the population is doubling. So, if the current population is 50 million, then it must have been half that amount 1 minute ago, since it would have only undergone one doubling period in that time.

It is important to note that this assumption of exponential growth may not hold true for all populations, and that there may be other factors that affect the growth rate of bacteria in real-world scenarios.

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Complete Question : in an experiment, the population of bacteria is increasing at the rate of 100 % every minute. the population is currently at 50 million. how much was the population of bacteria 1 minute ago?

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is 70π/3.

To find the area between the large loop and the small loop of the curve, we need to find the points of intersection of the curve with itself.

Setting the equation of the curve equal to itself, we have:

2 + 4cos(3θ) = 2 + 4cos(3(θ + π))

Simplifying and solving for θ, we get:

cos(3θ) = -cos(3θ + 3π)

cos(3θ) + cos(3θ + 3π) = 0

Using the sum to product formula, we get:

2cos(3θ + 3π/2)cos(3π/2) = 0

cos(3θ + 3π/2) = 0

3θ + 3π/2 = π/2, 3π/2, 5π/2, 7π/2, ...

Solving for θ, we get:

θ = -π/6, -π/18, π/6, π/2, 5π/6, 7π/6, 3π/2, 11π/6

We can see that there are two small loops between θ = -π/6 and π/6, and two large loops between θ = π/6 and π/2, and between θ = 5π/6 and 7π/6.

To find the area between the large loop and the small loop, we need to integrate the area between the curve and the x-axis from θ = -π/6 to π/6, and subtract the area between the curve and the x-axis from θ = π/6 to π/2, and from θ = 5π/6 to 7π/6.

Using the formula for the area enclosed by a polar curve, we have:

A = 1/2 ∫[a,b] (r(θ))^2 dθ

where a and b are the angles of intersection.

For the small loops, we have:

A1 = 1/2 ∫[-π/6,π/6] (2 + 4cos(3θ))^2 dθ

Using trigonometric identities, we can simplify this to:

A1 = 1/2 ∫[-π/6,π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ

Evaluating the integral, we get:

A1 = 10π/3

For the large loops, we have:

A2 = 1/2 (∫[π/6,π/2] (2 + 4cos(3θ))^2 dθ + ∫[5π/6,7π/6] (2 + 4cos(3θ))^2 dθ)

Using the same trigonometric identities, we can simplify this to:

A2 = 1/2 (∫[π/6,π/2] 20 + 16cos(6θ) + 8cos(3θ) dθ + ∫[5π/6,7π/6] 20 + 16cos(6θ) + 8cos(3θ) dθ)

Evaluating the integrals, we get:

A2 = 80π/3

Therefore, the area between the large loop and the small loop of the curve r = 2 + 4cos(3θ) is:

A = A2 - A1 = (80π/3) - (10π/3) = 70π/3

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Answer:

Answer:

Perimeter = 2(l+b)

Perimeter = 116

width = x

length = 3x

116 = 2(3x+ x)

116 = 6x+2x

116 = 8x

x = 116/8

x = 14.5

You can verify answer by inputing value of x to see if perimeter is = 116 :

perimeter = 2(l+b)

116 = 2(3(14.5) + 14.5)

116 = 2(43.5 + 14.5)

116 = 87 + 29

116 = 116

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Answer: 10

Step-by-step explanation:

So since this is all about perimeter you just got to add the values together. So lets use 12 as the denominator for every fraction. 1/4 is equal to 3/12 and 2/3 is equal to 8/12. So in conclusion 3/12 plus 8/12 and 1/12 will equal 1 in total. and then add up all the whole numbers 4 + 2 + 3 + 1 will get you 10. So 10 is your answer.

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1. Objective Function and Constraints:

Maximize 2x1 + 3x2 + 5x3 subject to x1 + x2 + x3 ≤ 1500, x1 + x2 ≤ 1100, x2 ≤ 800, x3 ≤ 400.

2. Using Excel Solver, find the optimal allocation of funds.

3. The maximum value of the objective function is reported by Excel Solver.

We have,

Objective Function and Constraints:

Let:

x1 = amount spent on food

x2 = amount spent on shelter

x3 = amount spent on entertainment

Objective Function:

Maximize: 2x1 + 3x2 + 5x3 (since each dollar spent on food has a satisfaction value of 2, each dollar spent on shelter has a satisfaction value of 3, and each dollar spent on entertainment has a satisfaction value of 5)

Constraints:

Subject to:

x1 + x2 + x3 ≤ $1,500 (maximum disposable income)

x1 + x2 ≤ $1,100 (amount spent on food and shelter combined must not exceed $1,100)

x2 ≤ $800 (amount spent on shelter alone must not exceed $800)

x3 ≤ $400 (entertainment cannot exceed $400)

Using Excel Solver:

In Excel, set up a spreadsheet with the following columns:

Column A: Variable names (x1, x2, x3)

Column B: Objective function coefficients (2, 3, 5)

Column C: Constraints coefficients (1, 1, 1) for the first constraint (maximum disposable income)

Column D: Constraints coefficients (1, 1, 0) for the second constraint (amount spent on food and shelter combined)

Column E: Constraints coefficients (0, 1, 0) for the third constraint (amount spent on shelter alone)

Column F: Constraints coefficients (0, 0, 1) for the fourth constraint (entertainment limit)

Column G: Right-hand side values ($1,500, $1,100, $800, $400)

Apply the Excel Solver tool with the objective function and constraints to find the optimal allocation of funds.

Once the Excel Solver completes, it will report the maximum value of the objective function, which represents the optimal satisfaction value achieved within the given budget constraints.

Thus,

Objective Function and Constraints: Maximize 2x1 + 3x2 + 5x3 subject to x1 + x2 + x3 ≤ 1500, x1 + x2 ≤ 1100, x2 ≤ 800, x3 ≤ 400.

Using Excel Solver, find the optimal allocation of funds.

The maximum value of the objective function is reported by Excel Solver.

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In both the Vendor Compliance at Geoffrey Ryans (A) and Operational Execution at Arrows Electronics cases, there are common problems and challenges. These include issues related to vendor management.

One of the key problems faced by both companies is vendor compliance. This refers to the ability of vendors to meet the requirements and standards set by the company. Both cases highlight instances where vendors fail to meet compliance standards, leading to disruptions in the supply chain and operational inefficiencies. This problem affects the overall performance and profitability of the companies.

Another challenge faced by both companies is operational execution. This encompasses various aspects of operations, including inventory management, order fulfillment, and delivery. In both cases, there are instances where operational execution falls short, leading to delays, errors, and customer dissatisfaction. This challenge requires the companies to streamline their processes, improve communication and coordination, and enhance overall operational efficiency.

Overall, the problems and challenges in both cases revolve around effective vendor management, supply chain optimization, and operational excellence. Addressing these issues is crucial for both companies to improve their performance, meet customer demands, and maintain a competitive edge in the market.

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354 Valencia student tickets and 133 non-student tickets were sold.

Let's use algebra to solve the problem. Let

x be the number of Valencia student tickets sold

y be the number of non-student tickets sold

We know that

x + y = 487 (the total number of tickets sold is 487)

14x + 25y = 8391 (the total receipts from ticket sales is $8391)

We can use the first equation to express one of the variables in terms of the other. For example, we can solve for y

y = 487 - x

Here we have to use the substitution method, we can then substitute this expression for y into the second equation

14x + 25(487 - x) = 8391

Simplifying and solving for x

14x + 12275 - 25x = 8391

-11x = -3884

x = 354

So, 354 Valencia student tickets were sold. We can use the first equation to find y

x + y = 487

354 + y = 487

y = 133

So, 133 non-student tickets were sold.

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