A leaf blower was marked up 150% from an original cost of $80. Last Friday, Lee bought the leaf blower and paid an additional 7. 75% in sales tax. What was his total cost?


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The new pοpulatiοn in a year is estimated tο be 1470.67 snails.

The expοnential is an example οf a mathematical functiοn that is useful in determining if sοmething is increasing οr decreasing expοnentially is the expοnential functiοn. As implied by its name, an expοnential functiοn uses expοnents. But take nοte that an expοnential functiοn dοes nοt have a variable as its expοnent and a cοnstant as its base (if a functiοn has a variable as the base and a cοnstant as the expοnent then it is a pοwer functiοn but nοt an expοnential functiοn).

We can use the formula for exponential growth to find the new population in a year:

\(\rm N(t) = N0 \times e^{(rt)\)

where N(t) is the population after time t, N0 is the initial population, r is the per capita growth rate, and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we have:

\(\rm N(1) = 1400 \times e^{(0.05 \times 1) }= 1470.67\)

Therefore, the new population in a year is estimated to be 1470.67 snails.

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To determine the required sample size for a political poll with a 4% margin of error and a 97.5% confidence level, a formula can be used. For this scenario, the sample size required would be approximately 862 respondents.

To calculate the sample size needed for a political poll with a 4% margin of error and a 97.5% confidence level, the following formula can be used:

n = (Z^2 * p * (1-p)) / E^2

Where:

n is the sample size

Z is the Z-score associated with the desired confidence level (in this case, it is 2.24)

p is the expected proportion of support for the candidate (this value is typically unknown, so a conservative estimate of 0.5 is often used to get the maximum sample size)

E is the margin of error

Plugging in the values for this scenario, we get:

n = (2.24^2 * 0.5 * (1-0.5)) / 0.04^2

n ≈ 862

Therefore, the required sample size for this political poll is approximately 862 respondents. This sample size would provide a margin of error of 4% at a 97.5% confidence level, meaning that there is a 97.5% chance that the true proportion of support for the candidate lies within the range of the survey results plus or minus the margin of error.

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Explanation:

Let's say we started at (0,2) which is the y intercept of this blue line.

Now let's say we wanted to move to (4,0) which is the x intercept.

To do this, we need to do these two things:

This "down 2, right 4" motion directly determines the slope. The "down 2" is the rise, and the "right 4" is the run.

Slope = rise/run = -2/4 = -1/2

Slope = -1/2

The rise is negative because we are going downhill while moving to the right.

Side note: We can use the slope formula as an alternative route.

Answer:

-40

Step-by-step explanation:

2x + 5y = 10

-4(2x + 5y) = -4 * 10

-4(2x + 5y) = -40

An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

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Answer:

\(2(3r-2)(r+3)\)

Step-by-step explanation:

Factor \(6r^2+14r-12\)

\(6r2+14r-12\)

\(=2(3r-2)(r+3)\)

Answer:

\(2(3r-2)(r+3)\)

Step-by-step explanation:

\(6r^2+14r-12\)

Start by factoring out the greatest common factor, \(2\):

\(2(3r^2+7r-6)\)

Factor out the trinomial in the parentheses using the "Reverse FOIL" method (Write 2 parentheses and factor out the trinomial into them):

\(2(3r-2)(r+3)\)

_

To check:

(Multiply First, Outside, Inner, Last):

\(2(3r^2+9r-2r-6)\)

Combine like terms:

\(2(3r^2+7r-6)\)

Distribute the \(2\):

\(6r^2+14r-12\)

The slope and y-intercept of the linear function are -5 and 7 respectively.

Linear functions are those whose graph is a straight line. In other words, a linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to the straight line.

A linear function has one independent variable and one dependent variable.

A linear function has the following form. y = mx + b.

where

Therefore, let's find the slope of the function.

slope = m = Δy / Δx

using (0, 7) and (4, -13)

slope = m = -13 - 7 / 4 - 0

slope = - 20 / 4

slope = -5

Let's find the y-intercept using (0, 7).

y = -5x + b

7 = -5(0) + b

b = y-intercept = 7

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The dog house's dimensions in the drawing are smaller than those of the actual drawing.

A variable in a ratio of two separate measurements is defined by the scale factor.

There are occasions when drawings of huge models are displayed at a scale factor that is smaller.

The sole point that remains constant during a dilation is its center, which is a fixed point in the plane around which all other points expand or shrink.

So, in this instance, point D is the dilation's center.

Hence, The dog house's dimensions in the drawing are smaller than those of the actual drawing.

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Efficient part families grouping can be achieved through systematic analysis and automation, utilizing advanced algorithms and artificial intelligence to optimize production.

Methodical and efficient part families grouping:

Utilize advanced algorithms: Implement computer algorithms and data analysis techniques to automate the grouping process. These algorithms can efficiently analyze large amounts of data and identify similarities among parts.

Apply artificial intelligence (AI): Employ AI techniques, such as machine learning, to train models on historical data and generate accurate predictions for part families grouping. This can help reduce the reliance on manual analysis by trained personnel.

Optimize production parameters: Incorporate additional factors like production capacity, equipment availability, and scheduling constraints to optimize part families grouping. This can maximize production efficiency and minimize downtime.

Continuous improvement: Regularly update and refine the grouping process based on feedback and new data to enhance efficiency and adapt to evolving production requirements.

Principles of material handling - Work:

Efficiency: Design work processes that minimize unnecessary movements, reduce handling time, and optimize the sequence of operations. This can be achieved through proper layout planning and standardization of work methods.

Standardization: Establish standardized procedures and work instructions to ensure consistent and efficient handling of materials. This helps reduce errors, minimize training time, and improve overall productivity.

Workload balancing: Distribute work tasks evenly among workers to avoid excessive strain on any individual and maintain a smooth workflow. This can be achieved by analyzing workloads, considering individual capabilities, and adjusting assignments accordingly.

Principles of material handling - Ergonomics:

Worker safety and well-being: Design workstations and handling equipment that consider ergonomic principles to minimize the risk of injuries and promote the health and comfort of workers. This includes factors like proper equipment height, adjustable controls, and ergonomic tools.

Reduce physical stress: Implement ergonomic strategies such as using lifting aids, providing proper training on lifting techniques, and incorporating ergonomic principles into work processes to minimize physical strain on workers.

Human-machine interaction: Ensure that machinery and equipment are designed to accommodate human operators effectively.

This involves considering factors like reach distances, control placement, and feedback mechanisms to optimize the interaction between humans and machines, enhancing both productivity and worker comfort.

By adopting a systematic and automated approach to part families grouping and incorporating principles of work and ergonomics in material handling, production can be maximized while ensuring efficient and safe operations.

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The value of n in the equation 6=-2(10n+7) is -1.

Given an equation 6=-2(10n+7).

We are required to find the value of n in the given equation.

Equation is the relationship between two or more variables that are expressed in equal to form. The equation of two variables look like ax+by=c. It may be linear equation, quadratic equation, cubic equation and many more depending on the powers of the variable that are present in the equation. In the given equation the variable is n.To find the solution of the equation we need to find the value of variable n.

6=-2(10n+7).

6=-2(10n+7)

6=-20n-14

20n=-14-6

20n=-20

n=-20/20

n=-1.

Hence the value of n in the equation 6=-2(10n+7) is -1.

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Answer:

Solution: Given, the equation is x3 + 6x2 - 9x - 54. We have to find the real zeroes of the given equation. Therefore, the roots of the equation are +3, -3 and -6.

Answer: 0.384 millimeters.

Step-by-step explanation:

Step 1: Area of a rectangle can be found by the formula Area = Length × Width.

Step 2: We have the area of the rectangle to be 48 square millimeters and the length of 8 millimeters.

Step 3: Substitute these values into the formula. Area = Length × Width = 48 × 8 = 384 millimeters.

Step 4: Since the area is given in square millimeters, we will need to divide the result by 1000, to get the width in millimeters.  Width = 384 ÷ 1000 = 0.384 millimeters.

Step 5: Thus, the width of the rectangle is 0.384 millimeters.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form. The value of x for which the given matrix is singular is `19 ± 2√190`.

Given matrix is, A =  [-x  9;  -7  x - 38]

We have to find the value of x for which the given matrix is singular. A matrix is singular if its determinant is zero. Therefore, the determinant of the given matrix must be zero for it to be singular. \(|A| = (-x * (x-38)) - (9 * (-7))|A|\)

\(= -x² + 38x + 63\).

Now, the determinant of the matrix A must be zero as it is a singular matrix. |A| = -x² + 38x + 63

= 0

=> x² - 38x - 63

= 0On solving the quadratic equation, we get; \(x = \frac{38 \pm \sqrt{(-38)^2 - 4(1)(-63)}}{2(1)}\)\(x = 19 \pm 2\sqrt{190}\).

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Focus groups are not appropriate for generating statistics and making scientific generalizations.

The given statement is True.

Focus groups are qualitative research methods used to gather in-depth insights and subjective opinions from a small group of participants.

They typically involve a moderator guiding a discussion among a selected group of individuals to explore their perspectives, attitudes, and experiences on a specific topic.

The main objective of focus groups is to obtain rich, contextual information rather than to produce statistical data.

Focus groups usually consist of a small number of participants, typically ranging from 6 to 12 individuals, which makes it difficult to achieve statistical significance or representativeness.

The participants are not randomly selected, but rather purposively chosen based on specific criteria relevant to the research focus.

While focus groups offer valuable qualitative insights, they are not designed to generate statistically reliable data or make generalizations to a larger population.

The results obtained from focus groups are specific to the participants involved and their unique perspectives.

Therefore, it is not appropriate to use focus group findings as a basis for making scientific generalizations or drawing statistically significant conclusions about a broader population.

To make scientific generalizations and produce statistical data, researchers typically employ quantitative research methods, such as surveys or experiments, with larger and more diverse samples that allow for statistical analysis and inference.

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Answer:

The answer is

Step-by-step explanation:

To solve the fraction reduce the fraction with d

That's we have

Next simplify the expression using the rules of indices to simplify the letters in the fraction

For c

Since they are dividing we subtract the exponents

We have

For e

Substituting them into the expression we have

Reduce the fraction by 3

We have the final answer as

Hope this helps you

In this case, sin(4) and -sin(5) cancel out, sin(8) and -sin(9) cancel out, and so on. Since each pair of terms cancel out, the sum of the series converges to 0.

We want to determine the sum of the series:

\(\sum(_{n=1} ^\ infinity)}(sin(4n) - sin(4n+1))\)

Notice that for each term in the series, we have sin(4n) - sin(4n+1). To find the sum, we can examine the first few terms of the series:

\(Term1: sin(4) - sin(5)\\Term2: sin(8) - sin(9)\\Term3: sin(12) - sin(13)...\)

Now, observe that the series consists of alternating positive and negative sine values, creating a telescoping series. In a telescoping series, the terms cancel each other out, leaving only a finite number of terms remaining.

In this case, sin(4) and -sin(5) cancel out, sin(8) and -sin(9) cancel out, and so on. Since each pair of terms cancel out, the sum of the series converges to 0.

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Answer:

B. 183

Step-by-step explanation:

m<L = (1/2)[m(arc)KN - m(arc)KM)]

35 = (1/2)(177x - 107x)

70 = 70x

x = 1

m(arc)KN = 177x = 177

m(arc)NMK = 360 - m(arc)KN

m(arc)MNK = 360 - 177

m(arc)MNK = 183

According to the probability, we expect approximately 12 or 13 of the 20 cards to have flowers on them.

To calculate the probability of selecting four cards with no flowers on them, we can first determine the number of ways to choose four cards from the 16 non-flower cards in the package. This is:

16C4 = 16! / (4! * (16-4)!) = 1820

Therefore, there are 1,820 different ways to choose four cards with no flowers on them.

To find the probability of selecting four cards with no flowers on them, we can divide the number of ways to choose four non-flower cards by the total number of ways to choose any four cards:

P(4 non-flower cards) = 1,820 / 4,845 = 0.375

So the probability of selecting four cards with no flowers on them is 0.375.

To find the probability of selecting at least one card with flowers on it, we can subtract the probability of selecting four non-flower cards from 1:

P(at least one flower card) = 1 - P(4 non-flower cards) = 1 - 0.375 = 0.625

Therefore, the probability of selecting at least one card with flowers on it is 0.625.

To answer the original question, we can use this probability to estimate how many of the 20 cards we would expect to have flowers on them. We can multiply the probability by the total number of cards in the package:

Expected number of cards with flowers = 0.625 x 20 = 12.5

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0 . 12 + 14 . 6 answer is 14 . 72

Answer:

0.12

+ 14.60

14.72

Step-by-step explanation:

at first place 0.12

and add 14.60

your answer is 14.72

while adding make sure the decimal u place must be in same sequence

Answer: A

Step-by-step explanation:

Answer:

3rd graph from the top.

Step-by-step explanation:

It can't be the top one because the kids shoulder doesn't start at the ground.

It can't be the second or fourth because it shows him not waiting in line.

Therefore it must be the 3rd!

Answer: 3rd option

Step-by-step explanation:

Because the description says that it starts not at 0(from the kid's shoulder), the 1st and 4th options are out.

2nd option is incorrect because the kid had to stand in line so the shoulder height doesn't change(unless he was picking stuff up or something)

That leaves the 3rd option.

Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

If the cost of one paperback book is less than $1, he would receive even more change.

To solve this problem, we need to know the cost of one paperback book. Unfortunately, that information is missing from the question. Without it, we cannot determine the total cost of the 5 paperback books and therefore cannot calculate Prakash's change.

However, we can make an educated guess based on the fact that the question mentions both paperback and hardcover books. Typically, hardcover books are more expensive than paperbacks, so we can assume that the cost of one paperback book is less than the cost of one hardcover book.

Assuming that each hardcover book costs $10, the total cost of 3 hardcover books would be $30. If Prakash gives the clerk $20 bills, he would pay $60 in total. If we subtract the cost of the 3 hardcover books ($30) from the total amount paid ($60), we are left with $30.

This is the maximum amount of change Prakash could receive if each paperback book costs $1.

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For the parabola y = 2x² + 3x + 1,

a. i.  The x-intercepts are x = -1/2 and x = -1

a. ii. The y-intercept is y = 1

b. i. The line of symmetry is at x = -3/4

b. ii. The equation of the line of symmetry is x = -3/4

c.  The vertex is at (-3/4, -1/8)

A parabola is part of a conic section which is a curve.

Given the parabola y = 2x² + 3x + 1, we find the x- intercept when y = 0.

So, y = 2x² + 3x + 1

2x² + 3x + 1 = 0

2x² + 2x + x + 1 = 0

Factorizing, we have

2x(x + 1) + (x + 1) = 0

(2x + 1)(x + 1) = 0

2x + 1 = 0 or x + 1 = 0

2x = -1 or x = -1

x = -1/2 or x = -1

So, the x-intercepts are x = -1/2 and x = -1

Given the parabola y = 2x² + 3x + 1, we find the y- intercept when x = 0.

So, y = 2x² + 3x + 1

So, y = 2(0)² + 3(0) + 1

y = 0 + 0 + 1

y = 1

So, the y-intercept is y = 1

The line of symmetry passes through the vertex of the parabola where dy/dx = 0.

So, y = 2x² + 3x + 1

dy/dx = d(2x² + 3x + 1)/dx

= d(2x²)/dx + d3x/dx + d1/dx

= 4x + 3 + 0

= 4x + 3

So, when dy/dx = 0,we have

4x + 3 = 0

4x = -3

x = -3/4

So, the line of symmetry is at x = -3/4

The equation of the line of symmetry is x = -3/4

Since the vertex of the parabola is a t x = -3/4, substituting this into the equation, we have

y = 2x² + 3x + 1

y = 2(-3/4)² + 3(-3/4) + 1

y = 2(9/16) - 9/4 + 1

y = 9/8 - 9/4 + 1

y = (9 - 18 + 8)/8

y = (17 - 18)/8

y = -1/8

So, the vertex is at (-3/4, -1/8)

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Answer:

put the yes in the second box, fourth box, and fifth box.

Step-by-step explanation:

trust me, your welcome

If the arrival times of Caryl's school bus are distributed on a normal curve, the standard deviation would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.

The standard deviation is a statistic that measures the amount of variation or dispersion from the central tendency of a set of data values. A low standard deviation indicates that the data is tightly clustered around the mean or average, while a high standard deviation indicates that the data is more spread out.

The standard deviation is particularly useful when dealing with normally distributed data, as it allows us to estimate the probability of a certain range of values occurring. In this case, Caryl can use the standard deviation to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.

Hence, option c. standard deviation would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day.

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Answer:

\( \sqrt{ {1}^{2} + {2}^{2} + {( - 2)}^{2} } = \sqrt{1 + 4 + 4} = \sqrt{9} = 3\)

(1, 2, -2) is 3 units away from the origin.

(0, 0, 5) is 5 units away from the origin.

So (0, 0, 5) is farther away from the origin.

Answer: 5x-10

Step-by-step explanation: I graphed this and it worked, also the slope has to be different than the equation or it will be parallel.