The equation y = 1000x - 5000 represents the monthly profits of a start-up dry cleaning company. Time in months is x and profit in dollars is y. The first date of operation is when time is zero. However, preparation for opening the business began 3 months earlier with the purchase of equipment and supplies. Graph the linear function for x-values from -3 to 8

Answer:

x=5,6

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

the probability that the battery will need to be replaced within its warranty period is 0.5507, which is Option A.

The given type of battery whose life is measured in years is an exponential random variable with a decay parameter of 0.2. This type of battery has a warranty period of 4 years. The question is about finding the probability that a battery will need to be replaced within the warranty period, which is a mathematical concept of probability. The warranty period for the battery is 4 years.

Therefore, the required probability can be calculated as follows:

\($P(X < 4) = 1 - e^{(-\lambda\times4)}$\)

Where λ is the decay parameter = 0.2

Substitute these values in the above formula:

\(P(X < 4) = 1 - e^{(-0.2\times4)}= 1 - e^{(-0.8)}= 1 - 0.4493= 0.5507\)

Hence, within the warranty period the probability of a battery which will need to be replaced is 0.5507. Thus, option A is the correct answer.

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The transformation of C(9, 3) when dilated by a scale factor of 3, using the origin as the centre of dilation is C'(27,9).

The given coordinate is C(9, 3) and a scale factor is 3.

Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.

If any figure is dilated by a scale factor k with the centre of dilation as the origin.

Then the change pr transformation in each of the vertices of the figure is given by (x,y) ⇒ (kx, ky).

Here, k=3.

So, C(9,3) ⇒ C'(9×3,3×3)

= C(9,3) ⇒ C'(27,9)

Therefore, the transformation of C(9, 3) when dilated by a scale factor of 3, using the origin as the centre of dilation is C'(27,9).

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No, 5783 is not divisible by 3; 5783 is not divisible by 4 also and 5783 is also not divisible by 11

Yes, a hole in a function is considered a type of discontinuity. A hole occurs when a point is missing from the graph of a function, which causes the graph to have a break in it.

A discontinuity is a break or jump in the graph of a function. A hole in a function is a type of discontinuity where a point is missing from the graph, causing the graph to have a break in it. This type of discontinuity is usually caused by a function having a denominator that is equal to zero, as this creates an undefined point on the graph. This can also occur when two parts of the function are not connected, causing an open gap in the graph. In both cases, the graph is not continuous and has a discontinuity at the point where the hole is present.

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Yes, the function has a hole in discontinuity.

The term function in math is called as a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.

Here we to identify is a hole in a function a discontinuity.

the term discontinuity is defined as is discontinuous at a point if it becomes undefined or the limit at that point does not exist. And whether this point is known as the point of discontinuity.

While we looking the hole on a graph looks like a hollow circle. And which  represents the fact that the function approaches the point, here it is not actually defined on that precise value. Where the major reason why this function is not defined at is because is not in the domain of the function.

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The function representing the sum of the series for x in the interval (5/8, 7/8) is:
f(x) = 1 / (1 - (8x - 6))

To find all values of x for which the series converges, we consider the given series:

Σ (8x - 6)^n, from n = 0 to ∞

This is a geometric series with the common ratio r = (8x - 6). A geometric series converges if the common ratio r has an absolute value less than 1, i.e., |r| < 1.

So, we need to find all values of x such that:
|8x - 6| < 1

To solve this inequality, we break it into two parts:

1. 8x - 6 < 1
8x < 7
x < 7/8

2. 8x - 6 > -1
8x > 5
x > 5/8

Combining these inequalities, we get the interval for which the series converges:
(5/8, 7/8)

Now, for these values of x, we can write the sum of the series as a function of x using the geometric series formula:
f(x) = a / (1 - r)

Here, a is the first term of the series (when n = 0), which is 1, and r is the common ratio (8x - 6):
f(x) = 1 / (1 - (8x - 6))

So, the function representing the sum of the series for x in the interval (5/8, 7/8) is:
f(x) = 1 / (1 - (8x - 6))

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Answer:

\(6 ^{m} \div 6^{ - 3} = {6}^{6} \)

\(6 ^{m + 3} = {6}^{6} \)

Equating the power , we get

m+3 = 6

m = 6- 3

m = 3

The correct answer is D. Both A and B are correct.

Both a Project Network Diagram and a Gantt Chart are commonly used tools to communicate project status. Each of these tools provides a visual representation of project tasks, their dependencies, and their respective timelines.

A Project Network Diagram, also known as a project schedule network diagram or an activity network diagram, illustrates the sequence and dependencies of project activities. It uses nodes (representing activities) and arrows (representing dependencies) to depict the logical flow of tasks in a project.

A Gantt Chart is a horizontal bar chart that shows project tasks as bars along a timeline. It displays the start and end dates of each task, allowing project managers and stakeholders to visualize the overall project schedule and understand the progress of individual tasks.

Both these tools are effective in communicating project status and can be used together or individually, depending on the project's requirements and preferences of the project team.

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Given

Equation

x tea chart __, 0, 2, __

y tea chart 0,__, __, 3

Procedure

y = 0

12x = 16

x = 16/12

x = 4/3

x = 0

-8y = 16

y = 16/-8

y = -2

x = 2

12(2) - 8y = 16

24 - 8y = 16

-8y = 16-24

-8y = -8

y = 1

y = 3

12x - 8(3) = 16

12x - 24 = 16

12x = 16+24

12x = 40

x = 40/12

x = 20/6

x tea chart 4/3, 0, 2, 20/6

y tea chart 0, -2, 1, 3

Answer:

30.96 \(in^2\)

Step-by-step explanation:

Given that

Side of square = 12 in

Diameter of circle = 12 in

We know that, radius is half of diameter,

So, r = 6 cm

We have to find the area of square which is not covered by the circle.

i.e. Required Area = Area of Square - Area of Circle

Please refer to the attached to have a better understanding of the given situation.

Formula:

Area of square = \((side)^2\)

Area of circle = \(\pi r^2\)

Required Area = \(12^2\) - \(\pi \times 6^{2}\)

\(\Rightarrow 144 - 3.14 \times 36\\\Rightarrow 144 - 113.04\\\Rightarrow 30.96\ in^2\)

So, the answer is 30.96 \(in^2\).

Answer:

The next four multiples of 5/10 are:

1.              ➡️                       1/2

2.             ➡️                       3/4

3.             ➡️                        1

4.             ➡️                      1 1/4

The distance between the opposite sides of the trampoline can be found to be 14. 42 yards

To find the distance between the opposite sides of the trampoline, we are essentially finding the diagonal length. We can use the Pythagorean theorem to do this by dividing the trampoline into two right triangles.

The distance between the opposite sides would then be:

c ² = a ² + b ²

c ² = 8 ² + 12 ²

c ² = 64 + 144

c ² = 208

c = √ 208

c = 14. 42 yards

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The Net Pay for the year for gross annual pay is $19 163. Employment insurance premiums are deducted at a rate of 2 with income taxes at a rate of 17% on all amounts over $8131 is $16,137.03.

To find the net pay for the year, we need to subtract the deductions from the gross pay and then subtract the income tax from the remaining amount.

First, we need to find the total amount deducted for EI and CPP premiums:

EI premium = 2.25% of $19,163 = $431.67

CPP premium = 3.75% of $19,163 = $720.86

Total deductions = $431.67 + $720.86 = $1,152.53

Next, we need to find the taxable income by subtracting the basic personal amount from the gross pay:

Taxable income = $19,163 - $8,131 = $11,032

Then, we need to calculate the income tax on the taxable income:

Income tax = 17% of ($11,032) = $1,873.44

Finally, we can calculate the net pay by subtracting the total deductions and income tax from the gross pay:

Net pay = $19,163 - $1,152.53 - $1,873.44 = $16,137.03

Therefore, the net pay for the year is $16,137.03.

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Answer:

13/14

Step-by-step explanation:

3/7 x 2/2 = 6/14

1/2 x 7/7 = 7/14

6/14 + 7/14 = 13/14

Answer:

1/14

Step-by-step explanation:

Answer:

r = 4

a8 = 114,688

Step-by-step explanation:

a1=7

a11 = 7340032

a11 = a1*r^10

7340032 = 7 * r^10

7340032 = 7r^10

r^10 = 7340032/7

r^10 = 1,048,576

Find the 10th root of both sides

10√r^10 = 10√1,048,576

r = 4

a8 = a1 * r^7

= 7 * 4^7

= 7 * 16,384

= 114,688

a8 = 114,688

There are 50,000 odd five-digit counting numbers that can be formed by choosing digits from the set with repetition allowed.

To determine the number of odd five-digit counting numbers that can be formed by choosing digits from a set (with repetition allowed), we need to consider the restrictions and possibilities for each digit position.

1. The leftmost digit:

2. The remaining four digits:

To find the total number of odd five-digit counting numbers, we multiply the possibilities for each digit position:

Total number = (5 options for the leftmost digit) \(\times\) (10 options for each of the remaining four digits)

Total number = \(5 \times 10^4 = 50,000\)

Therefore, there are 50,000 odd five-digit counting numbers that can be formed by choosing digits from the set when repetition is allowed.

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Answer:

Step-by-step explanation:

x²-b

The amount that Blake should have invested is $28875.38

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

Given here: Interest rate=5.7% compounded daily

Let p be the principal that Blake needs to invest

76000=P(1+5.7%/365)³⁶⁵ ˣ ¹⁷

76000=P(1.000156)⁶²⁰⁵

P=$28875.38

Thus Blake should have invested $28875.38

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Answer:

the answer is C

Step-by-step explanation:

the number line shows the numbers 70/100 - 80/100. the x appears 6 lines after 70/100 which is 0.76

Equivalent expressions are expressions that have the same result.

The expression in this problem is defined as follows:

13 + 4g.

The commutative property is applied in this problem, meaning that the order of the terms is exchanged, hence the equivalent expression is given as follows:

4g + 13.

The numeric values of the expression are given as follows:

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The inequality that represents the values for h (number of hours) is h≥1.5.

It is already known every hour Jordan can burn 250 calories, we can use this number to determine the number of hours he will need to burn 375 calories.

This means he needs at least 1.5 hours to burn at least 375 calories.

We know the number of hours required should be equal, or greater than 1.5 hours, due to this, the best inequality is:

The symbol ≥ represents equal or greater than, which matches the number of hours required.

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The perimeter of the horse corral is 600 feet.

The area of Rectangle is length times of width.

The area of any regular polygon is given by the formula: Area = (a x p)/2, where a is the length of the apothem and

p is the perimeter of the polygon.

Given that area of the horse corral is 3000 ft²

Length of the apothem is 10 ft

We need to find the perimeter.

3000=10p/2

6000=10p

Divide both sides by 10

600=perimeter

Hence, the perimeter of the horse corral is 600 feet.

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On solving the provided question, we can say that The attached table shows some iterations using this formula. To 3 dp, the solution of equation  is x ≈ -2.803.

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

You want to use the iterative formula x = ∛(5x -8) to find a solution to x³ -5x +8 = 0, starting with x₁ = -3.

Iteration

Your iterator appears to be found by solving for x:

 x³ -5x +8 = 0

 x³ = 5x -8

 x = ∛(5x -8)

The attached table shows some iterations using this formula. To 3 dp, the solution is x ≈ -2.803.

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Given that the High Plains Aquifer overlaps so many states, less data is now available to the latter might water use in one state affect water use in another state.

An aquifer is a layer of unconsolidated materials, rock cracks, or water-bearing, porous rock that lies underground. Using a water well, one may draw groundwater from aquifers. The properties of aquifers differ widely.

if a state utilizes excessive amounts of water and is "upstream" from another state. Less data is now available to the latter. Similar to how water is distributed uniformly in a pool, aquifers do the same thing underground; as a result, if one state uses more water than it should, it decreases the levels for all the other states. Due to this, management must now take place at the interstate level with more political entities participating. A resolution is inevitably more difficult the more people involved.

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Answer:

4 avocados

Step-by-step explanation:

$3.74/$0.89 = 4.2, but you can't have 4.2 avocados so you round down to 4

Answer:

Step-by-step explanation:

First factorise 16 and 40

\(\sqrt{16}+\sqrt{40}=\sqrt{4*4}+\sqrt{2*2*2*5}\\\\= 4 +2*\sqrt{2*5}\\\\= 4 +2\sqrt{10}\)