Given that x + 1/2 = 5, what is 2*x^2 - 3x + 6 - 3/x +2/x^2

pls help me soon

Answer:

To solve for r, we can start by simplifying the equation:

1475/2pi = (3/4r^2pi) + (1/4pi*(r-15)^2) + (1/4pi(r-25)^2)

Multiplying both sides by 2*pi:

1475 = 3/4r^2pi2 + 1/4pi*(r-15)^22 + 1/4pi*(r-25)^2*2

1475 = 3/2r^2pi + 1/2pi(r-15)^2 + 1/2pi(r-25)^2

Multiplying both sides by 2:

2950 = 3r^2pi + pi*(r-15)^2 + pi*(r-25)^2

Distributing pi:

2950 = 3r^2pi + pir^2 - 30pir + 225pi + pir^2 - 50pir + 625pi

Combining like terms:

2950 = 5r^2pi - 80pir + 850*pi

Rearranging:

5r^2pi - 80pir + 850*pi - 2950 = 0

Simplifying:

5r^2pi - 80pir + 675*pi = 0

Dividing both sides by 5*pi:

r^2 - 16*r + 135 = 0

This is a quadratic equation, which can be solved using the quadratic formula:

r = (-(-16) ± sqrt((-16)^2 - 4(1)(135))) / (2(1))

r = (16 ± sqrt(256 - 540)) / 2

r = (16 ± sqrt(284)) / 2

r ≈ 1.7321 * 16 or r ≈ 8.2679

Since r represents the distance from the center of the octagon to a vertex, only the larger value of r makes sense in this context.

Therefore, r ≈ 8.2679 feet.

To find the area of the region in which the cow can graze, we can divide the octagon into eight congruent isosceles triangles with base 25 feet and height equal to the distance from the center to a side (which is equal to r).

The area of each triangle is (1/2)bh = (1/2)(25)(8.2679) = 103.3494 square feet.

Multiplying by 8 to account for all eight triangles:

8 * 103.3494 = 826.7952 square feet.

Rounding to the nearest square foot:

The area in which the cow can graze is approximately 827 square feet

Answer: Area: 460.48 ft^2         Perimeter: 90.12 ft

Step-by-step explanation:

The area is 1/2 * 3.14 * (16 / 2)^2 (area of semicircle)

+ 10 * 12 / 2 (area of triangle)

+ 20 * 15 (area of rectangle)

= 460.48

The perimeter is 1/2 * 16 * 3.14 (perimeter of semicircle)

+ 10 (perimeter of triangle)

+ 20 + 15 + 20 (perimeter of rectangle)

= 90.12

The probability of obtaining a reading less than 0.35° C is approximately 35%.

Accοrding tο the prοbability fοrmula, the likelihοοd οf an event οccurring is equal tο the ratiο οf the number οf favοurable οutcοmes tο the tοtal number οf οutcοmes. Prοbability οf an event οccurring P(E) = The number οf favοurable οutcοmes divided by the tοtal number οf οutcοmes.

The readings at freezing οn a set οf thermοmeters are nοrmally distributed, with a mean (x) οf 0°C and a standard deviatiοn (μ) οf 1.00°C. We want tο knοw hοw likely it is that we will get a reading that is less than 0.35°C.

To solve this problem, we must use the z-score formula to standardise the value:

[tex]$Z = \frac{x - \mu}{\sigma}[/tex]

Z = standard score

x = observed value

[tex]\mu[/tex] = mean of the sample

[tex]\sigma[/tex] = standard deviation of the sample

Here

x = 0.35° C

[tex]\mu[/tex] = 0° C

[tex]\sigma[/tex] = 1.00°C

Using the values on the formula:

[tex]$Z = \frac{0.35 - 0}{1}[/tex]

Z = 0.35

The probability of obtaining a reading less than 0.35° C is approximately 35%.

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The Born exponent or interatomic potential energy for Rbl is 11 ( approximately). The correct option is D).

The Born exponent for RbI can be calculated using the relationship between the Born exponent and the interionic distance. The Born exponent is defined as the ratio of the repulsive to attractive contributions to the interatomic potential energy, and it depends on the charges and sizes of the ions.

For Rb+ and I-, the Born exponents are 10 and 12, respectively. This means that the repulsive interaction between Rb+ and I- is weaker than the attractive interaction, as the repulsion is proportional to Rb+^10 and the attraction is proportional to I^-12. Therefore, the attractive interaction dominates.

For RbI, we can use the relationship between the Born exponent and the interionic distance to calculate the Born exponent. This relationship is given by:

B = (1/d) * ln[(l1 + l2)/|l1 - l2|]

where B is the Born exponent, d is the interionic distance, and l1 and l2 are the ionic radii of the cation and anion, respectively.

Assuming the ionic radii of Rb+ and I- are additive, we have:

l1 + l2 = l(RbI) = l(Rb+) + l(I-) = 1.52 + 1.81 = 3.33 Å

|l1 - l2| = |l(Rb+) - l(I-)| = |1.52 - 1.81| = 0.29 Å

Substituting these values into the equation for B, we get:

B = (1/d) * ln[(l1 + l2)/|l1 - l2|] = (1/d) * ln[3.33/0.29] ≈ 11.02

Therefore, the Born exponent for RbI is approximately 11.02.

The correct answer is D).

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Answer: he would be 2 standard deviations above the

Step-by-step explanation:

The probability of obtaining a reading between 0.59°C and 0.88°C is 0.7224 and 0.8106.

The sum of all possible values, weighted by the chance of each value, is equal to the mean of a discrete probability distribution of the random variable X. Each possible number of X must be multiplied by its probability P(x) before being added as a whole to determine the mean. In statistics, the mean is one measure of central trend in addition to the mode and median. The mean is simply the average of the numbers in the specified collection. It suggests that values in a specific data gathering are evenly distributed. In order to find the mean, the total values given in a datasheet must be added, and the result must be divided by the total number of values.

In this question, using the formula,

z-score = (x – μ) / σ

where:

x: individual data value

μ: population mean

σ: population standard deviation

for x=0.59

μ= 0

σ= 1

z-score= 0.59

Probability=0.7224

for x=0.88

z-score= 0.88

Probability=0.8106

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Answer:

From the given information, we know that the area to the left of c under the standard normal distribution curve is 0.0166.

Using a standard normal distribution table or calculator, we can find the corresponding z-score for this area.

A z-score represents the number of standard deviations away from the mean. For a standard normal distribution, the mean is 0 and the standard deviation is 1.

Looking up the area of 0.0166 in the z-table, we find that the corresponding z-score is approximately -2.06.

Therefore, we have:

P(z < c) = 0.0166

P(z < -2.06) = 0.0166

So, c = -2.06.

Answer:

Using a standard normal distribution table, we can find the z-score corresponding to a probability of 0.0166:

z = -2.07

Therefore, c = -2.07.

Step-by-step explanation:

The value of error term E(x,y) = 8x^2 - 8x - 56.

The definition of differentiability states that a function f(x,y) is differentiable at a point (a,b) if there exists a linear function L(x,y) such that:

f(x,y) - f(a,b) = L(x,y) + E(x,y)

where E(x,y) is an error term that approaches 0 as (x,y) approaches (a,b).

In the case of the function f(x,y) = 8x^2 - 8y, we want to find E(x,y) at the point (-1,-7).

First, we need to calculate f(-1,-7):

f(-1,-7) = 8(-1)^2 - 8(-7) = 56

Next, we need to find the linear function L(x,y) that approximates f(x,y) near (-1,-7). To do this, we can use the gradient of f(x,y) at (-1,-7):

∇f(-1,-7) = (16,-8)

The linear function L(x,y) is given by:

L(x,y) = f(-1,-7) + ∇f(-1,-7) · (x+1, y+7)

where · denotes the dot product.

Substituting the values, we get:

L(x,y) = 56 + (16,-8) · (x+1, y+7)

= 56 + 16(x+1) - 8(y+7)

= 8x - 8y

Finally, we can calculate the error term E(x,y) as:

E(x,y) = f(x,y) - L(x,y) - f(-1,-7)

= 8x^2 - 8y - (8x - 8y) - 56

= 8x^2 - 8x - 56

Therefore, the error term E(x,y) for the function f(x,y) = 8x^2 - 8y at the point (-1,-7) is E(x,y) = 8x^2 - 8x - 56.

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The set of ordered pair that does not represent a function is option 1 {(4,0), (8, -8), (4,1), (5,8)}.

A function in mathematics is a relationship between two sets in which every element of the first set (referred to as the domain) is connected to exactly one element of the second set (called the range). A function is typically represented by the symbol f(x), where x is a domain element and f(x) is a corresponding range element.

We know that, a set of ordered pairs represents a function if each input is associated with only one output.

From the given options we observe that, {(4,0), (8, -8), (4,1), (5,8)}, does not represent a function.

Hence, the set of ordered pair that does not represent a function is option 1 {(4,0), (8, -8), (4,1), (5,8)}.

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A = {u + 2v, -3} is the basis for subspace U given that the set A is now linearly independent and that U = span(A).

Since U = span(S), and the set S is linearly independent, let S = {u, v} be the basis of the subspace U.

Now determine whether or not the set A = {u + 2v, -3v} is linearly independent.

A set of vectors must all have linear combinations that add up to zero in order for them to be considered linearly independent. Let a and b represent any scalars so that,

a(u + 2v) + b(-3v) = 0

Simplify the obtained equation.

au + 2av - 3bv = 0

au + v(2a - 3b) = 0

Make 2a - 3b = A.

Rewrite the equation that was found using this.

Now because u and v are linearly independent, a and A must be zero, and as a result, the constant b is also zero.

Set A is hence linearly independent.

Also, au + Av ∈ U, so, U = span(A).

Considering that the set A is now linearly independent and that U = span(A), the basis for subspace U is A = {u + 2v, -3}.

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The complete question is:

If {u, v} is a basis for the subspace U, show that {u + 2v, −3v} is also a basis for U.

The function rule for this graph is  y = -1/2(x) + 2.

In Mathematics, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁) or [tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]

Where:

At data point (0, 2), a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)\\\\y - 2 = \frac{(0- 2)}{(4 -0)}(x -0)[/tex]

y - 2 = -1/2(x)

y = -1/2(x) + 2.

In this context, we can reasonably infer and logically deduce that an equation of the line that represents this graph in slope-intercept form is y = -1/2(x) + 2.

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To solve the equation -12x + 24 = 0, we want to get x by itself on one side of the equation.

First, we can subtract 24 from both sides:

- 12x + 24 - 24 = 0 - 24

This simplifies to:

- 12x = -24

Next, we can divide both sides by -12:

- 12x / -12 = -24 / -12

This simplifies to:

x = 2

Therefore, the solution to the equation -12x + 24 = 0 is x = 2.

There are 500 odd numbers between 1 and 999.

We can solve this problem using the arithmetic sequence formula, which is

an = a1 + (n - 1)d

where

an is the nth term of the sequence

a1 is the first term of the sequence

n is the number of terms in the sequence

d is the common difference between consecutive terms

In this case, a1 = 1, the common difference is 2, and we want to find the value of n such that an = 999. So we have

999 = 1 + (n - 1)2

Simplifying this equation, we get

998 = 2(n - 1)

499 = n - 1

n = 500

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Answer:

Anna had 23 sweets in her bag at the start of the day.

Step-by-step explanation:

Let's use working backwards to find out how many sweets were in the bag at the start of the day.

At the end of lesson 4, Anna had 1 sweet left in her bag. So, before she gave a sweet to her teacher in lesson 4, she had 2 sweets left in her bag.

In lesson 3, she gave out half of the sweets left in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 3, she had 2 x 2 + 1 = 5 sweets in her bag.

In lesson 2, she gave out half of the sweets left in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 2, she had 5 x 2 + 1 = 11 sweets in her bag.

In lesson 1, she gave out half of the sweets in her bag and then gave one to the teacher. So, before she gave a sweet to her teacher in lesson 1, she had 11 x 2 + 1 = 23 sweets in her bag.

Therefore, Anna had 23 sweets in her bag at the start of the day.

Answer:

H= -35/4

Decimal form: -8.75

Explanation:

Answer: it represents half of the students in 1 class

Step-by-step explanation:

1/2 divided by s

Answer:

1/2s would then represent one half (or 50%) of the students in the singular class stated.

Answer:

Step-by-step explanation:

its C

Answer:

True

Step-by-step explanation:

Vertical angles are right angle that is 90°

A supplementary angle is an angle that forms up by 2 angles with the sum of 180°.

It is true because 2 vertical angles form a supplementary angle.

Answer:

The value of the land 20 years after it appreciates at annual rate at 5% is $132676.47.

An asset's value increases over time through a process called appreciation. Depreciation, on the other hand, reduces an asset's value throughout its useful life. The rate at which an asset's value increases is known as the appreciation rate. An increase in the value of financial assets, such as stocks, is referred to as capital appreciation. When a currency appreciates, it means that its value increases when compared to other currencies on the foreign exchange markets.

The annual rate is given as 5%.

The new value after 20 years can be calculated using the formula:

[tex]A = P * (1 + r/n)^{(nt)}[/tex]

Substituting the values we have:

[tex]A = $50,000 * (1 + 0.05/1)^{(1*20)}\\A = $50,000 * 1.05^{20}\\A = $132,676.47[/tex]

Hence, the value of the land 20 years after it appreciates at annual rate at 5% is $132676.47.

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Step-by-step explanation:

(a) Experimental probability of rolling an even number = (number of rolls for 2, 4, and 6) / (total number of rolls) = (4 + 5 + 6) / 40 = 0.375

(b) Theoretical probability of rolling an even number = number of even outcomes / total number of outcomes = 3 / 6 = 0.5

(c) Statement 2 is true: With a small number of rolls, it is not surprising when the experimental probability is much greater than the theoretical probability.

The probability of landing on yellow is 0.2, probability of component is 0.8, and sum of event and complement is 1.

On assuming that the pie is evenly divided into 5 parts,

So, the probability of landing on yellow is = 1/5 = 0.2,

The complement of landing on yellow is the probability of not landing on yellow, which is the probability of landing on any of the other 4 parts of the pie.

So, the probability of the complement is = 4/5 = 0.8,

The sum of the event (landing on yellow) and the complement (not landing on yellow) is equal to the probability of the entire sample space, which is 1.

⇒ P(Yellow) + P(Not Yellow) = 1

⇒ 0.2 + 0.8 = 1

So, the sum of the event and the complement is 1 or 100%.

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The given question is incomplete, the complete question is

A circular pie is divided in 5 parts , Green , Yellow, Blue Black and Red.

Find the probability of landing on yellow, the probability of complement, and the sum of the event and the complement.

The three angles are= angleMCD + angleCMD + angleGMF= 180.

Two lines intersect at a location, creating an angle.

An "angle" is the term used to describe the width of the "opening" between these two rays. The character is used to represent it.

Angles are frequently expressed in degrees and radians, a unit of circularity or rotation.

In geometry, an angle is created by joining two rays at their ends. These rays are referred to as the angle's sides or arms.

An angle has two primary components: the arms and the vertex. T

he two rays' shared vertex serves as their common terminal.

According to our question-

angleM= 127

angleC=27

angleG=26

127+27+26

180

Hence, The three angles are= angleMCD + angleCMD + angleGMF= 180.

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Answer: <MCD, <CMD, and <GMF

Step-by-step explanation:

Answer: 10 is two units from 0 on the number line, so there are six numbers that are 10 units from 0.

Step-by-step explanation:

let me have brainliest real quick

The Monotone Convergence Theorem can be demonstrated by considering the decreasing sequence {a_n} = 1/n, which is bounded below by zero and converges to zero.

Consider the sequence of real numbers {a_n} defined as a_n = 1/n. We want to show that the sequence converges to zero.

First, notice that the sequence is decreasing since a_n+1 = 1/(n+1) < 1/n = a_n for all n ≥ 1. Moreover, the sequence is bounded below by zero since a_n > 0 for all n. Thus, the sequence {a_n} is a decreasing bounded sequence and by the Monotone Convergence Theorem, it must converge to some limit L.

Let's now calculate the limit L. Since the sequence is decreasing and bounded below by zero, its limit L must be greater than or equal to zero. Furthermore, for any ε > 0, there exists an N such that 1/n < ε for all n > N, since the sequence converges to zero. Therefore, we have

|a_n - 0| = |1/n - 0| = 1/n < ε for all n > N.

This shows that the limit of the sequence is zero, i.e., lim (n → ∞) 1/n = 0.

Thus, we have demonstrated that the Monotone Convergence Theorem applies to the sequence {a_n}, which is decreasing and converges to zero.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Give an example to show that the Monotone Convergence Theorem?

The slope-intercept version of the equation for the tangent line to f(x) at the position (-5, -1) is y =  (-1/5)x -2. Thus,

m = -1/5

y =  (-1/5)x -2

A tangent line is a straight line that οnly has οne cοntact with a functiοn. (See earlier.) The instantaneοus rate οf change οf the functiοn at that exact place is shοwn by the tangent line. At each given pοint οn the functiοn, the slοpe οf the tangent line is equal tο the derivative οf the functiοn at that same lοcatiοn.

We must determine the derivative οf the functiοn and evaluate it at x = -5 in οrder tο determine the slοpe οf f(x) = 5/x at the pοint (-5, -1).

f(x) = 5/x

f'(x) = [-5/x²]

When we enter x = -5, we obtain:

f'(-5) = [-5/(-5)²] = -1/5

As a result, the tangent line to f(x) at the point (-5, -1) has a slope of -1/5.

y - y1 = m(x - x1)

y - (-1) = (-1/5)(x - (-5))

y + 1 = (-1/5)(x + 5)

y = (-1/5)x -10/5

y = (-1/5)x -2

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The percentage of students earned a B in the statistics course is 22.5%. So, the correct option is B).

To find the percentage of students who earned a B in the course, we need to determine the total number of students who took the course and the number of students who earned a B.

Using the information given in the bar chart, we can determine that there were a total of 40 students who took the statistics course. The number of students who earned a B is given as 9 in the bar chart. Therefore, the percentage of students who earned a B is (9/40) x 100%, which simplifies to 22.5%.

The total number of students who took the statistics course is:

Y = A + B + C + D + F = 5 + 9 + 11 + 8 + 7 = 40

The percentage of students who earned a B is:

(B/Y) x 100% = (9/40) x 100% = 22.5%

Therefore, the correct answer is (B) 22.5%.

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There is a vertical asymptote at x = 2 and the slope and intercept of the oblique asymptote are 2 and - 1, respectively.

In this problem we find the definition of a rational function:

f(x) = (2 · x² - 5 · x + 3) / (x - 2)

The vertical asympote correspond to the vertical line at the x-value where the function is undefined. And the oblique asymptote is defined by a equation of the form:

y = m · x + b

Where:

And the slope and the intercept of the asymptote can be found by means of the following equation:

Slope

[tex]m = \lim_{x \to \pm \infty} \left[\frac{f(x)}{x}\right][/tex]

Intercept

[tex]b = \lim_{x \to \pm \infty} [f(x) - m \cdot x][/tex]

First, factor and simplify the rational equation to determine whether any zero is evitable:

f(x) = (2 · x² - 5 · x + 3) / (x - 2)

f(x) = (2 · x - 3) · (x - 1) / (x - 2)

The discontinuity at x = 2 is not evitable. Then, the equation for the vertical asymptote is x = 2.

Second, determine the slope and the intercept of the oblique asymptote:

[tex]m = \lim_{x \to \pm \infty} \left[\frac{2\cdot x^{2}-5\cdot x + 3}{x^{2} - 2\cdot x} \right][/tex]

m = 2

[tex]b = \lim_{x \to \pm \infty} \left[\frac{2\cdot x^{2}-5\cdot x + 3}{x - 2} - 2 \cdot x\right][/tex]

[tex]b = \lim_{x \to \pm \infty} \left[\frac{2\cdot x^{2}-5\cdot x + 3-2 \cdot x^{2}+4\cdot x}{x-2}\right][/tex]

[tex]b = \lim_{x \to \pm \infty} \left[\frac{3 - x}{x-2} \right][/tex]

b = - 1

The slope and the intercept of the oblique asymptote are 2 and - 1, respectively.

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Using the correct order of operations, the value is 13

PEDMAS is simply described as a mathematical acronym that represents the different arithmetic operations in order from least to greatest of application.

The alphabets represents;

From the information given, we have;

15-(4-3)2

solve the parentheses first

15 - (1)2

Multiply the values

15 - 2

Subtract the values

13

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The complete question:

Solve using the correct order of

operations of PEMDAS

15 - (4-3)2

Using differentiation, the area of the triangle is decreasing at the given time.

The formula for the area of a triangle is:

A = (1/2)bh

where b is the base and h is the height.

Differentiating both sides of the equation with respect to time t, we get:

[tex]\frac{dA}{dt} = (1/2)[(\frac{db}{dt}) h + b(\frac{dh}{dt}) ][/tex]

Substituting the given values, we get:

[tex]\frac{dA}{dt} = (1/2)[(1)(10) + (5)(-2.5)] = (1/2)(10 - 12.5) = -1.25[/tex]

Since the derivative of the area with respect to time is negative (-1.25), the area of the triangle is decreasing at the given instant.

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Answer:

12/2652

Step-by-step explanation:

First, the probability of drawing a king for the first time is 4/52. The chance of drawing another is 3/51. Multiplying, we get the 3rd answer choice, 12/2652