the inequality 7-2/3x

The limit does not exist (denoted as DNE). The given limit is lim\((2^(12²-1))^(1/√r-1)\) as r approaches 1.

To evaluate this limit, we can simplify the expression.

In the exponent, 12² - 1 equals 143, and the base is 2. Therefore, we have \((2^143).\)

In the denominator, √r - 1 is a square root expression, and as r approaches 1, the denominator becomes √1 - 1 = 0.

Since we have the form 0^0, which is an indeterminate form, we need to further analyze the expression.

We can rewrite the original expression as \(e^(ln(2^143) / √r-1).\)

Using the properties of logarithms, we can simplify ln\((2^143)\) to 143 * ln(2).

Now, the expression becomes \(e^(143 * ln(2) / √r-1).\)

As r approaches 1, the denominator approaches 0, and the expression becomes \(e^(143 * ln(2) / 0).\)

Since the denominator is approaching 0, we have an indeterminate form of the type ∞/0.

To evaluate this limit, we need additional information or techniques. Without further clarification or specific instructions, we cannot determine the exact value of this limit.

Therefore, the limit does not exist (denoted as DNE).

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Complete question is;

Which of the number(s) below are potential roots of the function? p(x) = x⁴ + 22x² – 16x – 12

A) ±6

B) ±1

C) ±3

D) ±8

Answer:

Options A, B & C: ±6, ±1, ±3

Step-by-step explanation:

We are given the polynomial;

p(x) = x⁴ + 22x² – 16x – 12

Now, the potential roots will be all the rational numbers equivalent of p/q.

Where;

p are the factors of the constant term of the polynomial

q are the factors of the leading coefficient of the polynomial

Now, in the given polynomial, the constant term is seen as -12 while leading coefficient is 1 which is the coefficient of x⁴.

We know that factors of 12 are any of:

±1, ±2, ±3, ±4, ±6 and ±12

While possible factors of 1 is just ±1.

Thus, all the potential roots of the polynomial function are;

±1, ±2, ±3, ±4, ±6 and ±12

From the options given, option A, B & C could be the potential roots.

Answer:

6, 1,3 ACE

Step-by-step explanation:

Answer:

I'm not sure what you mean by opposite, but by all means the opposite of 0.93 would be -0.93 as it's the negative value of that decimal.

Step-by-step explanation:

Answer:

theta = \(\frac{\pi }{4}\) + 2\(\pi\)n, \(\frac{3\pi }{4}\) + 2\(\pi\)n, \(\frac{5\pi }{4}\) + 2\(\pi\)n, \(\frac{7\pi }{4}\) + 2\(\pi\)n

Step-by-step explanation:

sin^2 theta - cos^3 theta = 1

cos^3 theta = 1 - sin^2 theta

sin^2 theta - cos^3 theta = 0

Substitute

sin^2 theta - ( 1 - sin^2 theta ) = 0

Distribute negative

sin^2 theta - 1 + sin^2 theta = 0

Combine same values

2sin^2 theta - 1 = 0

2sin^2 theta = 1

sin^2 theta = \(\frac{1}{2}\)

sin theta = +- \(\frac{1}{\sqrt{2}}\)

Right Triangle:  1 - 1 - \(\sqrt{2}\)

theta = \(\frac{\pi }{4}\) + 2\(\pi\)n, \(\frac{3\pi }{4}\) + 2\(\pi\)n, \(\frac{5\pi }{4}\) + 2\(\pi\)n, \(\frac{7\pi }{4}\) + 2\(\pi\)n

period of Sin function is 2\(\pi\)

Answer:

Nina sold 24 Amazebars  Plz Mark Brainliest

Step-by-step explanation:

  Cost:

80 x 0.40 = 32

180x 0.30 = 54

40 x 0 = 0

Total = 86

Income

80 x 2.25 = 180

180 x 2.25 = 405

X x 2.25 = 2.25x

Total = 585 + 2.25x

How many did she sell:

553 = 585 - 86 + 2.25x

553 = 499 + 2.25x

553 - 499 = 2.25x

54 = 2.25x

54/2.25 = x

24 = x

Answer:

1. $155 ≥ $31.50p + $13.25

2. p ≤ 4

1. The word that describes a pattern in nature that is also exhibited in the external appearances of animals is "symmetry."

Symmetry refers to the balanced arrangement of parts or elements. In nature, many animals display symmetry in their body structure, such as butterflies with their symmetrical wings.

2. The word that describes a pattern exhibited by objects when their similar parts are regularly arranged around a central axis and the pattern looks the same after a certain amount of rotation is "rotational symmetry."

Rotational symmetry occurs when an object can be rotated and still maintain its original appearance. For example, a circle has rotational symmetry because it looks the same after any amount of rotation.

3. The word that describes curved patterns made by a series of circular shapes revolving around a central point is "spiral."

Spirals can be seen in various aspects of nature, like the arrangement of petals in a sunflower or the shape of a seashell.

4. The word that describes a pattern exhibited by objects that do not change their size and shape even if they are moved to another location is "translation symmetry."

Translation symmetry means that an object can be moved without altering its characteristics. For instance, a rectangle has translation symmetry because it remains the same even if it is shifted horizontally or vertically.

5. The word that describes an exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a contour or an axis is "reflection symmetry" or "mirror symmetry."

Reflection symmetry means that an object can be divided into two equal halves, and each half is a mirror image of the other. For example, the letter "A" exhibits reflection symmetry when it is divided vertically down the middle.

Now, moving on to the second part of the question, which involves finding values in the Fibonacci sequence:

1. Fib(8) = 13
2. Fib(19) = 4181
3. Fib(23) = 28,657

1. To find Fib(8), we can use the Fibonacci sequence. Fib(1) = 1, Fib(2) = 1, and each subsequent term is the sum of the previous two terms. So, Fib(3) = Fib(1) + Fib(2) = 1 + 1 = 2.

Similarly, Fib(4) = 2 + 1 = 3, Fib(5) = 3 + 2 = 5, Fib(6) = 5 + 3 = 8, and Fib(7) = 8 + 5 = 13. Therefore, Fib(8) is 13.

2. To find Fib(19), we can continue using the Fibonacci sequence. By applying the same pattern of adding the previous two terms, we find that Fib(19) is 4181.

3. Given that Fib(22) = 17,711 and Fib(24) = 46,368, we can determine Fib(23) by subtracting the known terms

. Since Fib(23) = Fib(24) - Fib(22),

we have Fib(23) = 46,368 - 17,711 = 28,657.

In summary:
1. Fib(8) = 13
2. Fib(19) = 4181
3. Fib(23) = 28,657

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Answer:

6

Step-by-step explanation:

3+6=9 9x7=63

Answer: 6

Step-by-step explanation:

You can set the unknown number as x and then you would add 3 to x and multiply that by 7.

The equation would be 7(x+3)=63

7(x+3)=63

7x+21=63

7x=42

x=6

The answer is 6

When analyzing categorical data, it is often useful to examine the relationship between two variables. Crosstabs, or contingency tables, are commonly used to display the counts of observations in each combination of the two variables. However, these raw counts can be difficult to interpret, especially if the totals for each variable are different.
By transforming the counts into percentages of row or column totals, we can better understand the patterns and relationships in the data. Percentages allow us to compare the proportions of one variable within each category of the other variable, regardless of the total number of observations. This can help us identify any trends or patterns in the data that may not be immediately apparent from the raw counts.

For example, suppose we have a crosstab of gender and favorite color. The raw counts may show that more females than males prefer blue, but it's difficult to know if this difference is meaningful without knowing the total number of males and females in the sample. By transforming the counts to percentages of row totals, we can see that 40% of females prefer blue, while only 30% of males do. This suggests that there may be a relationship between gender and favorite color.

Overall, transforming raw counts into percentages of row or column totals can help us better understand the relationship between two categorical variables, especially when the totals are different.

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Answer:

The answer is 1/6

Step-by-step explanation:

So Think of a half and then divide it into 3 parts for a half it will be 1/3 but for a meter it will be 1/6 because there is 2 half's in 1 whole

Hope this helps!! :D

Please mark  brainliest if this helped you!

Answer:

In each case, translate the words into numbers and operations.

1. 2x - 10

2. 3/4 x

3. 7x

4. 16/x

5. 10n - 12

6. 50n

7. n - 4

8. n/8

9. 2/3 x

10. 5n - 10

Answer:

Step-by-step explanation:

The temperature when the plane reaches an altitude of 5000 ft will be 47.2 F.

Temperature Drop per 1000 ft      :       1.6 F

Temperature Drop for 5000 ft       :       1.6 x (5000/1000)

      :       1.6 x 5 = 8.0

Temperature at 5000 ft                   :      55.2 – 8  = 47.2 F

#1234

The temperature when the plane reaches an altitude of 5000 feet will be 47.2 Fahrenheit.

In the given case, there is a drop of 1.6 Fahrenheit in temperature for every thousand feet that an airplane climbs into the sky.

The temperature on the ground is 55.2 Fahrenheit.

Temperature Drop per 1000 feet = 1.6 Fahrenheit

Temperature Drop for 5000 feet = 1.6 x (5000/1000)

                                                       = 1.6 x 5

                                                       = 8.0 Fahrenheit

To get the temperature when the plane reaches an altitude of 5000 feet,

The temperature at 5000 feet = 55.2 – 8 = 47.2 Fahrenheit

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Here, we want to graph the line y = 2x-3 using slope and the y-intercept

The value of the slope if positive or negative will tell us the direction of the graph whether rising or falling while the y-intercept will tell us the point at which the graph crosses the y-axis

Mathematically, we can have the equation representing a linear function as;

where m represents the slope and b represents the y-intercept

If the slope is positive as in the case with this question (+2), then the graph is a rising graph.

To complete the graph, we need to identify the y-intercept which is -3 in this case

So to graph the line, we locate the point -3 on the y-axis then we draw a rising line through this point

To get a point on the x-axis, we will need the value of the x-axis

The value on the y-axis is 0 at this point

An overview is shown below;

(a) The probability that a randomly selected policyholder lives more than 80 years is approximately 0.3106.  (b) Given that a male policyholder just turned 80, the probability that he will live for at least three more years is approximately 0.6166.

(a) To find the probability that a randomly selected policyholder lives more than 80 years, we need to calculate the cumulative probability of survival beyond 80 for both males and females separately, and then weigh them based on the gender distribution.

For males: Using the normal distribution with mean 75 and standard deviation 8, we find the probability of survival beyond 80 is approximately 0.3446.

For females: Using the normal distribution with mean 78 and standard deviation 6, we find the probability of survival beyond 80 is approximately 0.2847.

The weighted probability for a randomly selected policyholder is (0.60 * 0.3446) + (0.40 * 0.2847) = 0.3106.

(b) Given that a male policyholder just turned 80 years old today, we can use conditional probability to calculate the likelihood of him living for at least three more years.

Using the normal distribution with mean 75 and standard deviation 8, the probability of survival beyond 83 (80 + 3) is approximately 0.8621.

Therefore, the probability that a male policyholder, who just turned 80, will live for at least three more years is 0.8621.

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The equation for the plane consisting of all points that are equidistant from the points (−7, 1, 1) and (3, 3, 5) is 20x + 4y + 8z = -9.

In order to determine the distance of this plane (x, y, z) with the given points, we would use the distance formula.

Mathematically, the distance between three (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

For these points (x, y, z) and (−7, 1, 1), the distance is given by:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Distance = √[(x₂ - (-7))² + (y₂ - 1)² + (z₂ - 1)²]

Distance = √[(x₂ + 7)² + (y₂ - 1)² + (z₂ - 1)²]

By using the algebraic formulas, the expanded expression is given by:

(a - b)² = a² - b² - 2ab

(a + b)² = a² + b² + 2ab

Distance = √[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)]   .......equation 1.

For these points (x, y, z) and (3, 3, 5), the distance is given by:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Distance = √[(x - 3)² + (y - 3)² + (z - 5)²]

Distance = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]    .....equation2.

Since both distances are equidistant, we would equate eqn. 1 and eqn. 2 and then simplify:

√[(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1)] = √[(x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)]

(x² + 14x + 49) + (y² - 2y + 1) + (z² - 2z + 1) = (x² - 6x + 9) + (y² - 6y + 9) + (z² - 10z + 25)

x² + 14x + 49 + y² - 2y + 1 + z² - 2z + 1 = x² - 6x + 9 + y² - 6y + 9 + z² - 10z + 25

14x + 6x - 2y + 6y - 2z + 10z + 52 - 43 = 0

20x + 4y + 8z + 9 = 0

20x + 4y + 8z = -9.

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The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.

Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.

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The breakaway point of the root locus is -0.3930. To find the breakaway points of the root locus, we need to find the values of s at which the real part of the transfer function poles or zeros becomes zero.

This means that we need to find the roots of the equation 4s³ + 15s² + 18s + 5 = 0.

Using numerical methods such as the Routh-Hurwitz criterion or the root locus method, we can determine that there are no real roots of the equation. Therefore, the breakaway points must be complex conjugate pairs.

Using a numerical solver or a quadratic formula, we can find that the complex conjugate roots are -1.6785+ j0.6028 and -1.6785 – j0.6028. However, these roots do not lie on the real axis, so they are not breakaway points.

To find the breakaway point, we need to look for the point on the real axis between the two complex roots where the real part of the transfer function poles or zeros becomes zero. Using a numerical solver or by inspection, we can find that this point is -0.3930. Therefore, the breakaway point of the root locus is -0.3930.

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The uncertainty on the area of the circle, given the radius measurement of 10 mm ± 0.2 mm, is 12.6 mm². The correct option is a.

The formula for the area of a circle is A = πr², where r represents the radius. In this case, the measured radius is 10 mm with an uncertainty of ± 0.2 mm. To determine the uncertainty in the area, we need to calculate the maximum and minimum possible values.

Maximum radius: 10 mm + 0.2 mm = 10.2 mm

Minimum radius: 10 mm - 0.2 mm = 9.8 mm

Using these values, we can calculate the maximum and minimum areas:

Maximum area: A_max = π(10.2 mm)² = 328.32 mm²

Minimum area: A_min = π(9.8 mm)² = 301.56 mm²

The uncertainty is then given by the difference between the maximum and minimum areas:

Uncertainty = A_max - A_min = 328.32 mm² - 301.56 mm² = 26.76 mm²

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Answer:

the answer would be a x^3-11x^2

Step-by-step explanation:

Dividing two polynomials may produce another polynomial only when the divisor has a lower degree than the dividend. Otherwise, it will generally result in a rational function.

No, dividing two polynomials may not result in another polynomial. It can produce a rational function.

A polynomial is an algebraic expression consisting of terms with non-negative integer exponents. When two polynomials are divided, the result is not always a polynomial.

If the degree of the polynomial being divided (dividend) is higher than the degree of the polynomial dividing (divisor), then the result can be a polynomial with a lower degree. However, if the degree of the divisor is equal to or greater than the degree of the dividend, the result will generally be a rational function, which is a ratio of two polynomials.

A rational function has the form P(x)/Q(x), where P(x) and Q(x) are polynomials and Q(x) is not equal to zero. The division can introduce terms with negative or fractional exponents, making the result a rational function rather than a polynomial.

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The answer is yes, (x + 6) is a possible length of a rectangle with area x² + x − 30.

To determine whether (x + 6) is a possible length of a rectangle with area x^² + x − 30, we can use an area model to visualize the situation.

First, we need to find the width of the rectangle.

The area of a rectangle is given by the formula A = lw,

where A is the area, l is the length, and w is the width.

We are given that the area is x² + x − 30, so we can set this equal to lw and solve for w:

x² + x − 30 = (x + 6)w

w = (x² + x − 30)/(x + 6)

The length of a rectangle must be greater than or equal to its width, so we need to check whether (x + 6) is greater than or equal to (x² + x − 30)/(x + 6). This simplifies to:

(x + 6) ≥ x² + x − 30

Expanding the left side and simplifying, we get:

x² + 12x + 36 ≥ x² + x − 30

11x ≥ -66

x ≥ -6

Since x must be a positive number (since we are dealing with lengths), we can conclude that (x + 6) is the possible length of the rectangle. Therefore, the answer is yes, (x + 6) is a possible length of a rectangle with an area x² + x − 30.

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The area of an circle with radius equal to 300 is 90000π (282743.34).

The area of circle can be found from the formula: A=πR², where R is the radius. It is important to know that the radius is equal to two times the value of diameter (D=R/2).

The question gives:

Diameter= 600 therefore the Radius is D/2=600/2=300.

Thus, the area of circle will be:

A=πR²

A=π300²

A=90000π, as π=3.14159.... you can write:

A=90000 * 3.14159

A=282743.34

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Answer:

3014.4ft³

Step-by-step explanation:

V=Πr²h(volume of cylinder)

=(3.14)(8)²(15)

=3014.4ft³

The project is performing well at the end of WEEK 7.

1. The planned value (PV) at the end of WEEK 7 is $30,000.
2. The earned value (EV) at the end of WEEK 7 is $30,000.
3. The actual cost (AC) at the end of WEEK 7 is $30,000.
4. The cost variance (CV) at the end of WEEK 7 is $0.
5. The schedule variance (SV) at the end of WEEK 7 is $0.
6. The cost performance index (CPI) at the end of WEEK 7 is 1.0 (CV/AC).
7. The schedule performance index (SPI) at the end of WEEK 7 is 1.0 (EV/PV).
8. At the end of WEEK 7, this project is performing according to the plan. The CPI and SPI are both equal to 1.0, indicating that the project is on track in terms of cost and schedule. The cost variance (CV) and schedule variance (SV) being zero further support this conclusion, as it means that the project is meeting its planned budget and schedule.

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The maximum percentage cannibalization that can exist before the overall change in contribution dollars becomes negative is 100%. Any cannibalization beyond this point would result in a negative overall change in contribution dollars.

To determine the maximum percentage cannibalization that can exist before the overall change in contribution dollars becomes negative, we need to compare the contribution from the existing Irish Red sales to the contribution lost due to cannibalization.

The contribution per pint for Irish Red can be calculated as follows:

Contribution per pint for Irish Red = Price - Unit Variable Cost

                                  = $5.50 - $2.70

                                  = $2.80

The contribution from Irish Red sales, assuming 1,000 pints per month, can be calculated as:

Contribution from Irish Red = Contribution per pint for Irish Red * Number of pints

                         = $2.80 * 1,000

                         = $2,800

Now, let's calculate the contribution lost due to cannibalization. Assuming a maximum percentage cannibalization of "x%," the number of pints of Irish Red cannibalized by Irish Stout can be calculated as:

Number of pints cannibalized = (x/100) * 1,000

                           = 10x

The contribution lost due to cannibalization can be calculated as:

Contribution lost = Contribution per pint for Irish Red * Number of pints cannibalized

                = $2.80 * 10x

                = $28x

To find the maximum percentage cannibalization where the overall change in contribution dollars becomes negative, we need to equate the contribution lost to the contribution from Irish Red sales:

$28x = $2,800

Dividing both sides of the equation by $28:

x = $2,800 / $28

x = 100

Therefore, the maximum percentage cannibalization that can exist before the overall change in contribution dollars becomes negative is 100%. Any cannibalization beyond this point would result in a negative overall change in contribution dollars.

In summary, if the cannibalization of Irish Red by Irish Stout exceeds 100%, the overall change in contribution dollars will become negative. This means that the Irish Red sales would be negatively impacted to a greater extent than the contribution gained from Irish Stout sales.

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Answer:

 point slope form: y - y1 = m(x - x1)

m = slope, (x1, y1) is a point on the line

y - (-9) = 2(x - 1)

y + 9 = 2(x-1)

Step-by-step explanation:

The first derivatives for the given functions are:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For  \(y = 100200x + 7x,\) the first derivative is dy/dx = 100207.

For \(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

To find the first derivative for each of the given functions, we'll use the power rule, constant rule, and chain rule as needed.

For the function\(y = 3x^2 + 5x + 10:\)

Taking the derivative term by term:

\(d/dx (3x^2) = 6x\)

d/dx (5x) = 5

d/dx (10) = 0

Therefore, the first derivative is:

dy/dx = 6x + 5

For the function y = 100200x + 7x:

Taking the derivative term by term:

d/dx (100200x) = 100200

d/dx (7x) = 7

Therefore, the first derivative is:

dy/dx = 100200 + 7 = 100207

For the function \(y = ln(9x^4):\)

Using the chain rule, the derivative of ln(u) is du/dx divided by u:

dy/dx = (1/u) \(\times\) du/dx

Let's differentiate the function using the chain rule:

\(u = 9x^4\)

\(du/dx = d/dx (9x^4) = 36x^3\)

Now, substitute the values back into the derivative formula:

\(dy/dx = (1/u) \times du/dx = (1/(9x^4)) \times (36x^3) = 36x^3 / (9x^4) = 4/x\)

Therefore, the first derivative is:

dy/dx = 4/x

To summarize:

For \(y = 3x^2 + 5x + 10,\) the first derivative is dy/dx = 6x + 5.

For y = 100200x + 7x, the first derivative is dy/dx = 100207.

For\(y = ln(9x^4),\) the first derivative is dy/dx = 4/x.

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Answer:

\( \frac{9 - 8}{12 } \\ = \frac{1}{12} \\ = 0.8333333...\)