8800 = 6870(0.995) + 2500

Answer

• a) Range: (-∞, –1)

• b) Horizontal asymptote when x ≤ 2: y = –3. Vertical asymptote when x > 2: x= 2. Horizontal asymptote when x > 2: y = –1.

• c) When x decreases, it approaches –3, and when x increases, it approaches –1.

Explanation

• Part A: Graph the piecewise function f (x) and determine the range.

Using a graphing tool we can get the following graph:

As the range is all the y-values included in the function, we can see that in this case, the range is:

• Part B: Determine the asymptotes of f (x). Show all necessary calculations.

We have to get the asymptotes from the part where x ≤ 2 and x > 2.

In x ≤ 2 we do not have a vertical asymptote as it is not a rational function, but we do have a horizontal asymptote, which is y = k when we have the function:

Thus, in our case y = –3.

In x > 2, we do have a vertical and horizontal asymptote. We can get the vertical asymptote by setting the denominator of the function to 0:

If we solve the expression by factoring we get two solutions:

Based on our function we can see that the vertical asymptote is x = 2 when x > 2. Then, the horizontal asymptote can be calculated with the limit:

Thus, our horizontal asymptote is y = –1 when x > 2.

• Part C: Describe the end behavior of f (x).

The end behavior of a function is how the function acts when x increases or decreases. Based on our graph we can see that when x decreases, it approaches –3, and when x increases, it approaches –1.

Answer:

1

Step-by-step explanation:

divide the volume value by 16

The probability that a resident in the town uses Social Networking Site 1 is 6/9 or 66.67%.

Probability:

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event or how likely a statement is to be true. The probability of an event is a number between 0 and 1, with 0 representing an impossibility and 1 representing certainty, roughly speaking. The higher the probability of an event, the higher the probability of an event occurring. A simple example is a fair (unbiased) coin toss. Since the coin is fair, both outcomes ("heads" and "tails") are equally likely. The probability of an "eagle" is equal to the probability of a "tail". Since no other outcome is possible, the probability of getting heads or tails is 1/2 (which can also be written as 0).

Given that:

56% of residents use Social Networking Site,

36% use Social Networking Site 2, and

24% use both Social Networking site 1 and 2,

Therefore,

The probability that a resident in the town uses Social Networking Site 1 is 6/9 or 66.67%.

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The top 10% of professors spend above $125.94 each week on entertainment. To find the z-score for the top 10% of professors, we need to find the z-value that corresponds to the 90th percentile.

To find out the amount of money spent by the top 10% of professors on entertainment each week, we need to use the z-score formula and the standard normal distribution table.

The z-score formula is:

z = (x - μ) / σ

where:

x = the amount spent on entertainment

μ = the mean amount spent on entertainment

σ = the standard deviation

To find the z-score for the top 10% of professors, we need to find the z-value that corresponds to the 90th percentile. The 90th percentile can be calculated as follows:

90th percentile = mean + z-score * standard deviation

From the standard normal distribution table, we can find that the z-score corresponding to the 90th percentile is 1.28.

So,

90th percentile = 95.25 + 1.28 * 27.32 = 125.94

Therefore, the top 10% of professors spend above $125.94 each week on entertainment.

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Answer:

Drag and drop 6(2x-1) to 12x-6.

Drag and drop 6(4x-2) to Neither.

Drag and drop 3(8x+4) to 24x+12.

Drag and drop 6(4x+2) to 24x+12.

Drag and drop 2(6x-3) to 12x-6.

Step-by-step explanation:

To check these, use distributive property to solve each one.

6(2x-1) = 12x-6

6(4x-2) = 24x-12

3(8x+4) = 24x+12

6(4x+2) = 24x+12

2(6x-3) = 12x-6

Hope this helps!

Please mark brainliest! Thanks!

Answer:

x≥3

Step-by-step explanation:

Treat the ≥ symbol like it is an equals sign. First, subtract 14x from each side to get 6x+12≥30. Then, Subtract 12 from each side to get 6x≥18. I will let you solve the rest :)

Answer:

\(\huge\boxed{C.\ x\geq3}\)

Step-by-step explanation:

\(20x+12\geq14x+30\qquad\text{subtract 12 from both sides}\\\\20x+12-12\geq14x+30-12\\\\20x\geq14x+18\qquad\text{subtract}\ 14x\ \text{from both sides}\\\\20x-14x\geq14x-14x+18\\\\6x\geq18\qquad\text{divide both sides by 6}\\\\\dfrac{6x}{6}\geq\dfrac{18}{6}\\\\\boxed{x\geq3}\)

The answer is 42 meters squared

Answer:

3

Step-by-step explanation:

2x3=6/2=3

The maximum value of f is 12, which occurs at the point (3, 0). The minimum value of f is -5, which occurs at the point (3, 2). The absolute maximum value is 12, and the absolute minimum value is -5 on the set D.

To find the absolute maximum and minimum values of the function f(x, y) = x² + y² - 4xy + 3 on the set D = {(x, y) | 1 ≤ x ≤ 3, 0 ≤ y ≤ 2}, we can evaluate the function at the critical points and endpoints of the set D.

Critical Points:

To find the critical points, we need to find the values of x and y where the partial derivatives of f with respect to x and y are equal to zero.

∂f/∂x = 2x - 4y = 0

∂f/∂y = 2y - 4x = 0

Solving these equations simultaneously, we get x = y.

Substituting x = y in the equation ∂f/∂x = 2x - 4y = 0, we get 2x - 4x = 0, which gives x = 0.

So, we have a critical point at (0, 0).

Endpoints of D:

The endpoints of D are (1, 0), (3, 0), (1, 2), and (3, 2).

Now, let's evaluate the function at the critical point and the endpoints:

f(0, 0) = (0)² + (0)² - 4(0)(0) + 3 = 3

f(1, 0) = (1)² + (0)² - 4(1)(0) + 3 = 4

f(3, 0) = (3)² + (0)² - 4(3)(0) + 3 = 12

f(1, 2) = (1)² + (2)² - 4(1)(2) + 3 = -2

f(3, 2) = (3)² + (2)² - 4(3)(2) + 3 = -5

Now, we compare these values to find the absolute maximum and minimum:

The maximum value of f is 12, which occurs at the point (3, 0).

The minimum value of f is -5, which occurs at the point (3, 2).

Therefore, the absolute maximum value is 12, and the absolute minimum value is -5 on the set D.

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Answer:

Step-by-step explanation:0.15

Answer:

6120

Step-by-step explanation:

i)

15/100 × 7200

=1080 ( the amount of discount based on the marked prize )

ii) 7200-1080=6120

Answer:

2x - 7

Step-by-step explanation:

Answer: the cost of the sketch notebook is $4.85.

Step-by-step explanation:

Answer:

208 per serving

Step-by-step explanation:

642/3=208

Based on Transformation of functions the transformed equation is  \(y=x^3\) is \(y=\frac{-1}{7}(x+8)^3\).

There are two different translations we can apply to a function graph. In addition, they are scaling. If you count reflections, there are three, but reflections are really a specific instance of the second translation.

Transformations:

Reflecting a function on X-axis  : Change y in function to -y.

Reflecting aa function on Y-axis : Change x in function to -x.

Shifting right by a:  Replace x by (x-a)

Shifting left by a:  Replace x by (x+a).

Shifting up by a: Replace y by (y-a).

Shifting down by a: Replace y by (y+a).

Scaling up by  n times: Multiply n

Step1: Vertical compression by a factor of  \(\frac{1}{7}\), we need to multiply the function by \(\frac{1}{7}\) .

So, we have:

\(y=\frac{1}{7}x^3\);

Step2:Horizontal shift by 8 units to the left, we need to add 8 to x.

So, we have:

\(y=\frac{1}{7}(x+8)^3\);

Step3:Reflection over the x-axis, we need to Replace y by -y.

So, we have:

\(y=-\frac{1}{7}(x+8)^3\)

Based on Transformation of functions the transformed equation is  \(y=x^3\) is \(y=\frac{-1}{7}(x+8)^3\).

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The severe limitation of using the internet for primary research is that a sample universe  composed solely of internet respondents represents a potential bias.

Given options 1)The data on the Internet are usually outdated.

2) The educational qualifications of the respondents of surveys on the Internet cannot be identified accurately.

3) A sample universe composed solely of Internet respondents represents a potential bias.

4)Secondary data cannot be accessed on the Internet for conducting research.

5) Using the Internet for primary research is the most expensive way of conducting primary research.

We have to choose most appropriate option which shows the severe limitation of using internet for primary research.

The most appropriate option is option third which is that a sample universe composed solely of internet respondents a potential bias

There is biasness because on internet people gives their own opinion and reviews and don't think about reality. The data may have been collected for the research according to researcher's priority. The data may be outdated but it is of our choice whether we use that data or not because generally the date is given on the internet. We can also access secondary data on the internet. Using internet in research is not so expensive because some organisation provides study materials to researchers themselves.

Hence the limitation of using the internet for primary research is that a sample universe composed solely of internet respondents a potential. bias.

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Answer:

The graphs are not shown, but I can tell you that x < 3.5

Step-by-step explanation:

\(4x + 2 < 2x + 9\)

\(2x + 2 < 9\)

\(2x < 7\)

\(x < 3.5\)

Answer:28

Step-by-step explanation: 7x4 Equals 28 basketballs

X = 7

Y = 6

Y = 24

X = ?

24/6=4

7x4 = 28

Your answer is 28

Answer:

360

Step-by-step explanation:

It's a simple concept. All you have to do is double the answer! Here's why:

We already know that 12 x 15 is 180. Now we're trying to figure out 24 x 15. 24 is 12 two times, or 12 doubled. Since 12 is doubled, the answer should also be doubled.

Let's take an easier example: 3 x 2.

The answer is 6. What if you doubled the 3 to get 6 x 2? The answer is 12, which is 6 doubled. By doubling the multiplier or multiplicand of the problem, you are also doubling the answer.

It's not just doubling, either. If 3 x 2 is 6. Then 9 x 2 is 18. You tripled the multiplier which is 3, so the answer is also tripled.

Hope this makes some sense lol

Answer:

Question 1: -3 and 6 in that order

Question 3: 3 and y=1/2x+3 in that order

Question 2: 2 and y=2x+4 in that order

Step-by-step explanation:

:)

Answer:

The 95% confidence interval \(0.57 < p <0.63\)

The 90% confidence interval  \(0.5748 < p <0.6252\)

The 90% confidence interval has the smaller margin of error.

This makes sense because the 90% confidence interval is narrower and more precise(i.e a decreased error band  ) than the 95% confidence interval

95% confidence interval is more likely to contain the true percentage

This is because 95% confidence interval signify's a higher confidence  of containing the true percentage than the 90% confidence interval  

Step-by-step explanation:

From the question we are told that

   The sample size is  n =  1019

    The  sample proportion is  \(\r p = 0.60\)

Given from the question that the confidence level is 95% then the level of significance is mathematically represented as

         \(\alpha = (100 - 95)\%\)

        \(\alpha = 0.05\)

Generally the critical value of  \(\frac{\alpha }{2}\) obtained from the normal distribution table is  

    \(Z_{\frac{\alpha }{2} } = 1.96\)

Generally the margin of error is mathematically represented as

         \(E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1 - \r p )}{n} }\)

=>     \(E = 1.96 * \sqrt{\frac{0.60 (1 - 0.60 )}{1019} }\)

=>    \(E = 0.030\)

Generally the 95% confidence interval is mathematically represented as

         \(\r p - E < p < \r p +E\)

        \(0.60 - 0.030 < p <0.60 + 0.030\)

        \(0.57 < p <0.63\)

This interval means that there is 95% chance that the true percentage will be in this interval

Given from the question that the confidence level is 90% then the level of significance is mathematically represented as

         \(\alpha = (100 - 90)\%\)

        \(\alpha = 0.10\)

Generally the critical value of  \(\frac{\alpha }{2}\) obtained from the normal distribution table is  

    \(Z_{\frac{\alpha }{2} } = 1.645\)

Generally the margin of error is mathematically represented as

         \(E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1 - \r p )}{n} }\)

=>     \(E = 1.645 * \sqrt{\frac{0.60 (1 - 0.60 )}{1019} }\)

=>    \(E = 0.0252\)

Generally the 90% confidence interval is mathematically represented as

         \(\r p - E < p < \r p +E\)

        \(0.60 - 0.0252 < p <0.60 + 0.0252\)

        \(0.5748 < p <0.6252\)

This interval means that there is 90% chance that the true percentage will be in this interval

From the calculation the 90% confidence interval has the smaller margin of error.

This makes sense because the 90% confidence interval is narrower and more precise(i.e a decreased error band  ) than the 95% confidence interval

Generally the confidence interval that is more likely to contain the true percentage  of all American adults who have used the Internet to obtain medical information in the past month is the 95% confidence interval ,

This is because it signify's a higher chance of containing the true percentage than the 90% confidence  

Answer:

Step-by-step explanation:

Let the initial amount of yellow paint be x

Then we have x increased by 30% equals 3.9 liters:

Step-by-step explanation:

10x+1=12x-5

1+5=12x-10x

6=2x

6/2=2x/2

3=x

The equation of the parabola is:

(y - 6)² = -12(x +2)

Parabola is the locus of a point such that its distance from a fixed point (called the focus) and a given line (called the directrix) is always the same.

The equation of a parabola is given by:

(y - k)² = 4p(x - h)

Where (h, k) is the vertex, (h + p, k) is the focus

Given the vertex of a parabola is (-2,6), and its focus is (-5,6).

Hence, k = 6, h = -2;

h + p = -5

-2 + p = -5

p = -3

Hence the equation of the parabola is:

(y - 6)² = -12(x +2)

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Answer:

A=87.5

Step-by-step explanation:

Hope im right and this helps you

The correct choice is within your skills and abilities.

Once you get to determine things you are capable of and things you are not capable of, you will be able to concentrate on your strengths more. This will in turn produce big results as compared to if you opted to concentrate on your weaknesses.

It will also result in no or less time wasted in doing what you are less capable of.

Its almost close to impossible to be able to do everything. Each person is gifted in a certain area or skill or capability. We are all different and that's okay.

Its so important to concentrate in the areas you are more comfortable with. This will help you much with improving your skills and abilities.

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Answer:

Step-by-step explanation:

a you just had to say a

The boundary lines are y > -3x + 4: dotted line and  y <= 8x + 1: solid line

From the question, we have the following parameters that can be used in our computation:

y > -3x + 4

y <= 8x + 1

The boundary line for the inequality "<" is a dotted line, which means that the endpoint is not included in the solution set.

The boundary line for the inequality ">=" is a solid line, which means that the endpoint is included in the solution set.

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No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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