PLEASE HELP 15 POINTS
An item costs $420 before tax, and the sales tax is $16.80 .
Find the sales tax rate. Write your answer as a percentage.

The graph of the parametric equations x = -2cos(t) and y = -sin(t) within the range 0 ≤ t < 2π is an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis.

To sketch the graph of the parametric equations x = -2cos(t) and y = -sin(t), where 0 ≤ t < 2π, we need to plot the coordinates (x, y) for each value of t within the given range.

1. Start by choosing values of t within the given range, such as t = 0, π/4, π/2, π, 3π/4, and 2π.

2. Substitute each value of t into the equations to find the corresponding values of x and y. For example, when t = 0, x = -2cos(0) = -2 and y = -sin(0) = 0.

3. Plot the obtained coordinates (x, y) on a graph, using a coordinate system with the x-axis and y-axis. Repeat this step for each value of t.

4. Connect the plotted points with a smooth curve to obtain the graph of the parametric equations.

The graph will be an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis. It will have a vertical compression and a horizontal stretch due to the coefficients -2 and -1 in the equations.

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The maximum number of real zeros in a polynomial will same as its degree thus 3 degrees will have 3 zeros.

The roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.

An n degree of a polynomial can have a maximum of n number of variables.

For example, a quadratic equation ax² + bx + c = 0 is a two-degree equation so it has a maximum of two roots or zeros.

As per the given a polynomial is having 3 degrees so it will have exactly 3 roots.

Hence "A polynomial can have as many real zeros as the number of degrees it has, therefore one with three degrees can have up to three of them.".

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Answer:

y = 3 x−2

Step-by-step explanation:

The half-life of Potassium-42 can be calculated using the following formula:

t1/2 = (ln 2) / λ

where t1/2 is the half-life, ln is the natural logarithm, and λ is the decay rate.

Substituting the values given, we get:

t1/2 = (ln 2) / 0.055

t1/2 ≈ 12.6 hours

Therefore, the original quantity of Potassium-42 will be halved in approximately 12.6 hours.

It will take approximately 13.51 hours for the original quantity of potassium 42 to be halved with a decay rate of 5.5% per hour.

To find the number of hours it takes for potassium 42 to be halved with a decay rate of 5.5% per hour, we can use the formula:

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The required requirement of the density curve is should be equal to 1 and the ordinate should not be zero.

Given that,
Two requirements of a density curve are to be determined.

A density curve is defined as a curve on a graph that represents the distribution of values in a dataset.

Here,

The two requirements of a density curve should be,

a. The area under the density curve should be equal to 1.

b. The ordinate of the curve should not be zero i.e. they should always have the vertical height.

Thus, the required requirement of the density curve is mentioned above.

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The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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the vector equation for the given line is r(t) = (9 + t, -8 + 6t, 5 - (1/3)t).

To find the vector equation of the given line, we use the formula r(t) = r0 + tv, where r0 is the position vector of any point on the line, v is the direction vector of the line, and t is a scalar parameter that determines the position of any other point on the line.

In this case, we are given that r0 = (9, -8, 5) and v = (1, 6, -1/3). Substituting these values into the formula, we get:

r(t) = (9, -8, 5) + t(1, 6, -1/3)

Expanding the expression by multiplying the scalar t with the vector v, we get:

r(t) = (9 + t, -8 + 6t, 5 - (1/3)t)

So the vector equation for the given line is r(t) = (9 + t, -8 + 6t, 5 - (1/3)t).

The vector equation represents all the points on the line as a function of a single parameter t. As t varies, the position vector r(t) traces out the line. The direction of the line is given by the vector v, which is parallel to the line. The point (9, -8, 5) is any point on the line, and we can use it to find the coordinates of other points on the line by adding a scalar multiple of the vector v to it.

Overall, the vector equation of a line in three-dimensional space is a powerful tool for representing lines and their properties, and it is commonly used in geometry, physics, and engineering.

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A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable.

In experimental research, an independent variable is a variable that the researcher manipulates or systematically varies in order to study its effect on the dependent variable. It is called "independent" because it is not influenced by any other variables in the experiment, and its effects on the dependent variable can be observed and measured independently of any other factors.

Only when a possible design confound fluctuates systematically with the independent variable does internal validity come under threat. In other words, it might be challenging to distinguish between the effects seen on the dependent variable and the independent variable if there is a component that fluctuates consistently or predictably with changes in the independent variable. Internal validity is less likely to be threatened by random or unplanned variation.

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A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable. This means that if the confound varies randomly or haphazardly, it is less likely to affect the results of the study.

This means that the confound is consistently related to the independent variable, making it difficult to determine if the observed effects are due to the independent variable or the confound. If the confound varies spontaneously or haphazardly, it is less likely to pose a threat to internal validity, as it would not be consistently associated with the independent variable.

However, if the confound is related to the independent variable in a consistent and predictable way, it can introduce bias and undermine the internal validity of the study. It is important for researchers to carefully control for potential confounds and ensure that any observed effects are truly due to the independent variable and not some other factor.

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\( \bf Question :- \\ \)

what is the value of expression

when g=4 and h=2

\( \bf Solution :- \\ \)

\( \longrightarrow \: \: \frac{1}{4} (16 + g) - h \\ \\ \longrightarrow \: \: \frac{1}{4} (16 + 4) - 2 \\ \\ \longrightarrow \: \: \frac{1}{{ \cancel{4} }} \times( \cancel{ 20)} - 2 \\ \\ \longrightarrow \: \: 1 \times 5 - 2 \\ \\ \longrightarrow \: \: 1 \times 3 \\ \\ \longrightarrow \: \: 3 \\ \)

Henceforth, Option c is the required answer.

Answer:63.75 :)

Step-by-step explanation:

Answer:

$63.75

Step-by-step explanation:

85 x 75/100

85/1 x 3/4

255/4 - > $63.75

- You should already know how to do this yourself as this is very easy and basic question.

Answer:

thursday

Step-by-step explanation:

comparing value

3x+2=-3x-2

6x=-4

x=-4/6Have solution.

y=-2x+10

y=-2x+10

both are equal So no solution.

3rd

y=-x+4

y=-x+4

both are equal So no solution

4th

3x+y=8

3x+y=9

both are equal So no solution

Given:

Required:

Solution:

First, set y = 4 ( 3x - 5), then solve for x in terms of y

Lastly, write the answer using x as a variable

Answer:

The vertical asymptotes for the given function are x = 4 and x = -4.`Therefore, Student A is correct in their approach and final answer.

Given the rational function is `f(x) = (x + 3) / (x² - 16)`.To find the vertical asymptote for the given rational function `f(x) = (x + 3) / (x² - 16)` for four students and to identify who is correct in their approach and final answer, first, we have to find the vertical asymptote of the given function. We know that the vertical asymptotes occur at the zeroes of the denominator when the numerator is not zero. Thus, the denominator must equal zero at `x = -4` and `x = 4`. So, the vertical asymptotes occur at `x = -4` and `x = 4`.Hence, the correct approach and final answer for vertical asymptote of the given rational function is Student A.  Student A: `The vertical asymptotes are the vertical lines that indicate where the function becomes unbounded. These lines occur when the denominator of the rational function is zero and the numerator is not zero.

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The question asks for four students determined the vertical asymptote for this rational function. The correct approach and answer is needed.

Therefore, the correct student's answer is (D) which indicates there are three vertical asymptotes at x = –2,

x = 1, and

x = 4.

Let's find the answer to the question: To find the vertical asymptote of the rational function, we need to find out when the denominator is equal to zero. We can factor the denominator, so we have (x + 2) (x – 1) (x – 4). The denominator will be equal to zero when any of the three factors are equal to zero:

(x + 2) = 0

(x – 1) = 0,

or (x – 4) = 0.

Solving each equation, we find the following values for x:

x = –2,

x = 1,

and x = 4

Therefore, the correct student's answer is (D) which indicates there are three vertical asymptotes at x = –2,

x = 1, and

x = 4.

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Answer:

Step-by-step explanation: Simple plug x in.

x=1

(Square root) 4 -1=1

x=6

(square root) 9 -1=2

x=13

(square root ) 16-1=3

x=1 Y=1

x=6  Y=2

x=13  Y=3

Answer:

h(-8)=9(-8) +27

h(-8)=72-27

h(-8)=45

Step-by-step explanation:

Answer:greengrocer should Dell 17 kg before profit. 500$ profit

Step-by-step explanation:

The three workers can produce 25 thingamajigs if they split their time evenly between producing widgets and thingamajigs.

Step 1: Calculate the production rate of each workerFirstly, calculate the production rate of each worker for both widgets and thingamajigs. In one hour, Karen can make 1 widget or 3 thingamajigs. In one hour, Sue can make 1 widget or 1 thingamajig. Lastly, Peter can make 3 widgets or 1 thingamajig in one hour.Karen's hourly production rate: 1 widget or 3 thingamajigsSue's hourly production rate: 1 widget or 1 thingamajigPeter's hourly production rate: 3 widgets or 1 thingamajig

Step 2: Calculate the total hourly production of the groupSecondly, calculate the hourly production of the entire group. To split their time evenly, they will have to spend 5 hours each producing widgets and thingamajigs.In 5 hours, Karen can produce 5 widgets or 15 thingamajigs (since her hourly production rate is 1 widget or 3 thingamajigs).In 5 hours, Sue can produce 5 widgets or 5 thingamajigs (since her hourly production rate is 1 widget or 1 thingamajig).In 5 hours, Peter can produce 15 widgets or 5 thingamajigs (since his hourly production rate is 3 widgets or 1 thingamajig).Step 3:

Calculate the total number of thingamajigsLastly, add up the total thingamajigs produced by each worker in 5 hours and you'll have the answer:15 (Karen's production) + 5 (Sue's production) + 5 (Peter's production) = 25 thingamajigsIn total, the three workers can produce 25 thingamajigs if they split their time evenly between producing widgets and thingamajigs.

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The width of the river is 1700m

What is the time, distance & speed relation?

Speed is calculated by dividing the distance traveled by the amount of time it took to get there. Divide the distance by the speed to find the passing time. To get the distance, multiply the speed by time.

Let 'x' be the distance from THE far bank where 700 is the distance to the NEAR bank

boat one has travelled 700 (rate = 700/unit time) boat two has travelled   x rate = x / unit time

boat one then travels   x  + 400  more      and boat two travels   700 + (700+x -400) more    when they meet

The time is the same:    

rate x time = distance  

distance/rate = time    

equate the distances divided by the respective rates

(700 + x + 400)/700     =    (  x  +  700     +  (700+x-400) )/x

1100x + x^2 = 1400x + 700000

x^2 - 300x - 700000 = 0                        

quadratic formula yields  x = 1000  

One boat travels 700 the other 1000 when they first meet.....width of the river =   700+ 1000 = 1700 m

Hence, the width of the river is 1700m

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r is increasing on the intervals (-∞, -√3) and (√3, ∞).

The given function is r(x) = 2x⁴ - 12x² - 15.

We need to differentiate the function with respect to x, as follows:

r'(x) = 8x³ - 24x

Now, we need to determine the intervals where r is increasing.

When the derivative r'(x) is greater than zero, the function r(x) is increasing.

Therefore, we need to solve:

r'(x) > 0

⇒ 8x³ - 24x > 0

⇒ 8x(x² - 3) > 0

This inequality holds if the expression is greater than zero or less than zero.

The inequality is equal to zero when:

x = 0 or x = ±√3.

From the above inequality, we can conclude that r(x) is increasing in the intervals (-∞, -√3) and (√3, ∞).

Answer: r is increasing on the intervals (-∞, -√3) and (√3, ∞).

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Answer:

90

Step-by-step explanation:

We can check this by finding 20% of 90 and seeing that it is equal to 18

The point that divides AB into a 3:2 ratio is calculated by (d) for a ratio of 3:2, divide AB into 5 equal parts. Each equal part is 2 units, so the point that divides AB into a 3:2 ratio is 2

The given parameters are:

A = -4

B = 6

Start by calculating the length AB using:

AB = |B - A|

This gives

AB = |6 -(-4)|

Evaluate

AB = 10

Next, the length is divided into 5 parts.

So, the length of each part is:

Length = 10/5

Length = 2

The point on the location 3 : 2 is then calculated as:

Point = A + 3 * Length

This gives

Point = -4 + 3 * 2

Evaluate

Point = 2

The above computation is represented by option (d)

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Answer:

The third one

Step-by-step explanation:

Answer:

Profit percentage” usually (but not always) refers to “gross profit percentage” which, in turn refers to the “gross profit margin” expressed as a percentage. The formula for gross profit margin is “gross profit” divided by “revenue.”

“Revenue” generally refers to gross income or gross receipts. It is the amount received without accounting for any expenses whatsoever. If you sell two widgets at $50 each, it costs you $10 to produce each widget, you get taxed $5 per widget, your revenue will be $100 ($50×2). The costs associated with generating income is ignored.

“Gross profit” generally refers to revenue minus costs-of-goods-sold (COGS). COGS refers to the direct costs of producing goods. If you sell one gizmo, it costs you $20 in materials and $10 in employee wages to produce the gizmo, and $50 for a salesman to sell the gizmo, your COGS is $30 ($20+$10; the cost of the salesman is not included).

Consider this scenario: You sell two gidgets at $100 each, the materials to manufacture each gidget is $4, the per gidget rental costs of the manufacturing facility is $6, and it takes two hours to produce one gidget and you are paying an employee dedicated to gidget making $15 per hour, it costs $5 per gidget to move gidgets from the production facility to the store, renting the store costs $50, and at the store your salesperson is paid $50.

In the above scenario, your revenue is $200 ($100×2). The direct cost for producing one gidget is $40 ($4 in materials plus $6 in allocated manufacturing plant rent plus $15/hr×2hrs in labor). The costs for transport, renting the store, and labor for salesperson are not direct costs of producing the gidgets, and therefore ignored. Thus, your COGS is $80 ($40×2).

If revenue is $200 and COGS is $80, then gross profit is $120 ($200-$80). Thus, your gross profit margin is 0.6 ($120/$200). Hence, your gross profit percentage is 60% (0.6×100).

Answer:

Step-by-step explanation:

\(\frac{-33}{9}+2=\frac{-33}{9}+\frac{2*9}{1*9}\\\\\\=\frac{-33}{9}+\frac{18}{9}\\\\= \frac{-33+18}{9}\\\\=\frac{-15}{9}\)

GCF of 15 and  9 is 3. so divide both numerator and denominator by 3

\(= \frac{-5}{3}\\\\= -1\frac{2}{3}\)

Answer:

whats the question???

Step-by-step explanation:

Answer:

whats the question ?

Step-by-step explanation:

Researchers try to gain insight into the characteristics of a sample population by examining a sample of the population.

A sample is a subset of individuals or units taken from a larger population. Researchers use sampling methods to select a representative group of individuals from the population they are interested in studying. By studying the sample, researchers can make inferences and draw conclusions about the characteristics, behaviors, or trends that may exist within the entire population.

The goal of sampling is to obtain a sample that accurately represents the population in terms of its relevant characteristics. Researchers carefully select their samples to ensure that they are representative and minimize bias. This allows them to generalize the findings from the sample to the larger population with a certain level of confidence.

By examining a sample, researchers can collect data, analyze patterns, and draw conclusions about the population as a whole. This approach is more feasible and practical than attempting to study the entire population, especially when the population is large or geographically dispersed.

Therefore, researchers use samples to gain insight into the characteristics of a population, making option d. "Sample" the correct answer.

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A frequency polygon is a graphical representation of a frequency distribution. Skewness refers to the asymmetry or departure from symmetry in the shape of the distribution. In terms of frequency polygons:

A frequency polygon with a large positive skew will have a long tail on the right side of the distribution, indicating an elongated right tail. This means that there are a few extreme values on the right side pulling the distribution in that direction, resulting in a positive skew.

Conversely, a frequency polygon with a large negative skew will have a long tail on the left side of the distribution, indicating an elongated left tail. This means that there are a few extreme values on the left side pulling the distribution in that direction, resulting in a negative skew.

It is important to note that without specific data or frequency distributions to analyze, it is not possible to determine which specific frequency polygons have large positive or negative skewness. The skewness of a distribution can only be determined by examining the actual data or frequency distribution.

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