Which of the following equations would have no solution?

10x + 3 = 3 + 10x
-8+16x = 16x - 8
4(2x-3) = 8x - 12
3(-2x + 4) = -6x - 12

Answer: 18x-12-3y

Step-by-step explanation:

To find which equation has exactly one solution in common with y = 6x - 2, we need to determine the point where they intersect.

Substituting y = 6x - 2 into the equations given, we get:

18x - 3(6x - 2) = 6

Simplifying this equation gives us:

x = 2

Substituting x = 2 into y = 6x - 2, we get:

y = 6(2) - 2 = 10

Therefore, the point where y = 6x - 2 intersects with the other equations is (2, 10).

Now, we can substitute x = 2 and y = 10 into each of the other equations to see which ones have exactly one solution:

(1) 18x - 3y = 6:

18(2) - 3(10) = 6

36 - 30 = 6

This equation does not have exactly one solution at (2, 10).

(2) (1/2)y = 3x - 2:

(1/2)(10) = 3(2) - 2

5 = 4

This equation does not have exactly one solution at (2, 10).

(3) 2y = 4x - 12:

2(10) = 4(2) - 12

20 = 0

This equation does not have exactly one solution at (2, 10).

(4) 18x - 12 - 3y = 0:

18(2) - 12 - 3(10) = 0

36 - 12 - 30 = 0

This equation has exactly one solution at (2, 10).

Therefore, the equation that has exactly one solution in common with y = 6x - 2 is 18x - 12 - 3y = 0.

The square of magnitude of a vector is the sum of the squares of its components. For example, if a vector has components x, y, and z, then its square of magnitude is x2 + y2 + z2.

The magnitude of a vector represents its length or size, which is given by taking the square root of the sum of the squares of its components. For example, for a two-dimensional vector v = [x, y], its magnitude is ||v|| = √(x² + y²).

Now, the square of the magnitude of a vector is obtained by squaring this expression. Therefore, we get:

||v||² = √(x² + y²))² = x² + y²

In other words, the square of the magnitude of a vector is simply the sum of the squares of its components. We can also express this in terms of the dot product of the vector with itself. Recall that the dot product of two vectors u and v is given by:

u · v = u1v1 + u2v2 + ... + unvn

where u1, u2, ..., un and v1, v2, ..., vn are the components of the vectors u and v, respectively.

If we take the dot product of a vector v with itself, we get:

v · v = v² + v2² + ... + vn²

which is precisely the sum of the squares of the components of the vector. Therefore, we can conclude that the square of the magnitude of a vector is given by the dot product of the vector with itself, i.e., ||v||²= v · v.

Learn more about vector at https://brainly.com/question/13916333

#SPJ11

G(t) = 678.97 * 1.0194t, where t is the number of years after 2017. This formula illustrates the exponential growth of GDP in Switzerland, which increases by 1.94% each year.

The gross domestic product (GDP) of Switzerland in 2017 is given as $678.97 billion. If the GDP increases by 1.94% per year, then we can use an exponential growth formula to find the GDP in any year t after 2017.

The exponential growth formula is given by

G(t) = G₀ * (1 + r)ᵗ

Where G₀ is the initial GDP, r is the annual growth rate, and t is the number of years after the initial year.

Plugging in the given values, we get

G(t) = 678.97 * (1 + 0.0194)ᵗ

G(t) = 678.97 * (1.0194)ᵗ

Hence, the formula for the GDP of Switzerland t years after 2017 is G(t) = 678.97 * (1.0194)ᵗ (in billions of dollars).

Learn more about exponential growth here:

brainly.com/question/30140466

#SPJ11

The inflection points of f function is none.

To find the inflection points of a function, we need to take the second derivative of the function and find the values of x where the second derivative changes sign.

Let's apply this concept to the function f(x) = x/4x²+6. To find the second derivative of f(x), we first need to find the first derivative.

f(x) = x/4x²+6

f'(x) = (4x²+6)1 - x(8x) / (4x²+6)²

Simplifying f'(x), we get:

f'(x) = (6 - 8x²) / (4x²+6)²

Now, we take the derivative of f'(x) to find the second derivative:

f''(x) = [(6 - 8x²)'(4x²+6)² - (6 - 8x²)(4x²+6)²'] / (4x²+6)⁴

Simplifying f''(x), we get:

f''(x) = (-48x) / (4x²+6)³

To find the inflection points of f(x), we need to find the values of x where f''(x) changes sign. Since f''(x) is always negative, there are no inflection points for this function.

Therefore, the answer is 'NONE'.

To know more about inflection point here

https://brainly.com/question/30760634

#SPJ4

To determine which songs to play at the school dance, I would use random sampling techniques.

What is random sampling?

Random sampling is a statistical technique used to select a subset of individuals or items from a larger population in a way that each member of the population has an equal chance of being included in the sample.

To determine which songs to play at the school dance, I would use random sampling techniques to select a representative sample of songs that appeal to students in grades 6-8.

First, I would create a list of potential songs, taking into account popular artists and genres that are popular among students. Then, I would use a random number generator or a random selection process to choose a subset of songs from the list.

To ensure that the sample is representative, I would make sure to include a variety of genres and artists, rather than just selecting songs from one or two popular artists. Additionally, I would consider the demographic makeup of the school and try to include songs that are popular among different groups of students.

Finally, I would play the selected songs at the dance and solicit feedback from the students to determine which songs were most popular and whether any adjustments need to be made for future events.

Hence, To determine which songs to play at the school dance, I would use random sampling techniques.

To learn more about random sampling, visit:

https://brainly.com/question/24466382

#SPJ1

Answer:

the ones that are selected are right

Step-by-step explanation:

Answer: -3

Step-by-step explanation: I GOT YOU BRO

The size of θ is 31.354 degree. A degree in mathematics is a professional option for those who are driven by solutions and addressing problems in the real world.

A bachelor's degree, also referred to as a college degree, is an undergraduate degree that you can obtain by enrolling in classes at a university in the topic of your choice. Examples include bachelor of arts (BA), bachelor of science (BSc), and bachelor of music (BMus). A certificate is a record that certifies a certain level of education and professional experience. Compared to degrees, diplomas are often more focused on a particular career, easier to obtain, and offer more practical experience. An educational institution, like a university, would provide a certificate of degree or diploma as proof that the recipient has achieved a degree or successfully completed a particular course of study.

sin(∠LKM)=LM/KM

sin(θ) = 12.8/24.6

θ= 31.354 degree.

Learn more about degree here

https://brainly.com/question/29165823

#SPJ1

Given expression −12x−18 is equivalent to -6(2x + 3).

What exactly are expressions?

An expression in mathematics is a set of numbers, variables, and mathematical operations including addition, subtraction, multiplication, division, and exponentiation.

Expressions can represent a wide variety of mathematical ideas, such as numerical values, algebraic equations, or functions. They can be as simple as a single number or variable, or as complex as a multi-term polynomial or trigonometric expression.

Now,

The expression −12x−18 can be simplified using the distributive property of multiplication as follows:

−12x − 18 = -6(2x + 3)

Therefore,

             the expression is equivalent to -6(2x + 3).

To know more about expressions visit the link

brainly.com/question/13947055

#SPJ1

The five-sided die will give an odd result 30 times out of 50.

A dice (Old French de, from the Latin datum "given or played") is a small faceted object, usually a cube, used to generate random numbers or other symbols.

Consider the information provided.

We have a five-sided die.

So the total number of results is: 1, 2, 3, 4, 5

Now odd = 1, 3, 5

Here the total number of results is 5, the favorable result is 3.

Probability odd = 3/5

Expected = 50 × 3/5

                = 30

So the expected is 30.

So this five-sided die will give an odd result 30 times out of 50.

Learn more about Times:

https://brainly.com/question/28050940

#SPJ4

a) The probability of pregnancies lasting between 265 and 275 days is:P(265 < X < 275) = P(z1 < Z < z2) = P(Z < 0.6111) - P(Z < 0.0556) = 0.7291 - 0.5239 ≈ 0.2052 or 20.52%

b) At least 275 days should the longest 25% of all pregnancies last.

c) The standard deviation of the normal model of the distribution of the sample mean is 2.8449

d) The probability that the mean duration of these patients' pregnancies will be less than 267 days is:P(y < 267) = P(z < 1.4907) = 0.9319 (rounded to four decimal places).

Assuming that the duration of human pregnancies can be described by a normal model with a mean 264 days and a standard deviation of 18 days, we need to find the following percentages.

To find the percentage of pregnancies that last between 265 and 275 days, we have to find the z-scores for the values of 265 and 275.Then we will calculate the probability between these two values using the Z-score table.z1 = (265 - 264) / 18 = 0.0556z2 = (275 - 264) / 18 = 0.6111Now, we can look up the probability associated with each of these z-scores in the Z-table. The probability corresponding to z1 is 0.5239, and the probability corresponding to z2 is 0.7291. Therefore, the probability of pregnancies lasting between 265 and 275 days is:P(265 < X < 275) = P(z1 < Z < z2) = P(Z < 0.6111) - P(Z < 0.0556) = 0.7291 - 0.5239 ≈ 0.2052 or 20.52%

We need to find the value of X such that the probability of a pregnancy lasting more than X is 25%.The Z-score corresponding to the 75th percentile is found using the Z-table, which is 0.67449. So the value of X corresponding to the 75th percentile is:X = µ + zσ = 264 + (0.67449) (18) = 275.14222 ≈ 275 Therefore, at least 275 days should the longest 25% of all pregnancies last.

Suppose a certain obstetrician is currently providing prenatal care to 40 pregnant women. Let y represent the mean length of their pregnancies. According to the central limit theorem, Mean: The sample mean of a population is equal to the population mean. Hence, the mean of the normal model of the distribution of the sample mean is 264.SD(y): The standard deviation of the normal model of the distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size.σy = σ/√nσy = 18/√40σy = 2.8449 Therefore, the standard deviation of the normal model of the distribution of the sample mean is 2.8449

We need to find the probability that the mean duration of these patients' pregnancies will be less than 267 days. Since the sample size is greater than 30, we can use the z-distribution.z = (y - µ) / (σ / √n)z = (267 - 264) / (18 / √40)z = 1.4907 Now, we can look up the probability associated with this z-score in the Z-table. The probability corresponding to z = 1.4907 is 0.9319.Therefore, the probability that the mean duration of these patients' pregnancies will be less than 267 days is:P(y < 267) = P(z < 1.4907) = 0.9319 (rounded to four decimal places).

Learn more about Probability

brainly.com/question/30034780

#SPJ11

a) The probability model for rolling two 4-sided dice can be represented as a table or matrix with 16 equally likely outcomes, each with a probability of 1/16.

b) The probability the sum of the numbers is 5 based on the probability model is 25%

a) The probability model for rolling two 4-sided dice can be represented using a table or a matrix, where the rows and columns represent the possible outcomes of the first and second die, respectively. Since each die has four equally likely outcomes, there are 4 x 4 = 16 possible outcomes in total. We can list these outcomes as ordered pairs (blue, yellow), where blue and yellow represent the numbers on the bottom of the blue and yellow dice, respectively

(1,1) (1,2) (1,3) (1,4)

(2,1) (2,2) (2,3) (2,4)

(3,1) (3,2) (3,3) (3,4)

(4,1) (4,2) (4,3) (4,4)

Each outcome has a probability of 1/16, since each die has four equally likely outcomes.

b) To find the probability that the sum of the numbers is 5, we need to count the number of outcomes where the sum is 5 and divide by the total number of outcomes. There are four outcomes where the sum is 5: (1,4), (2,3), (3,2), and (4,1). Therefore, the probability is

4/16 = 1/4 = 0.25 = 25%

Learn more about probability here

brainly.com/question/11234923

#SPJ4

The  number of arrangements of the letters in mathematics that contain TH but not immediately by an E (not THE).The word 'MATHEMATICS' has 11 letters is 9 * 10! - 8 * 2 * 9! = 4,005,120 arrangements.

We have to find the number of arrangements such that TH appear together but the TH is not immediately followed by an E. That is the number of arrangements where the letters THE appear together is excluded.To begin, we can count the number of ways that we can arrange the letters.

This is 11!Since TH should be kept together, we can count them as a single letter. Then there are ten letters (M, A, T, E, M, A, T, I, C, S) left. So there are 10! ways to arrange these letters.There are 9 positions where the letters TH can be placed, as they can't be placed at the beginning or the end (where there is no letter before or after them).

TH can be placed in any of these positions, and the remaining 9 letters can be placed in any of the 10 positions, i.e., 9 * 10!.This count includes the arrangement THE that we wish to exclude. In each of the 8 positions in which we can place TH so that it is not immediately followed by E, there are two choices for the placement of E:

either before or after the pair. So each arrangement of the remaining 9 letters appears twice in our count. We have to subtract from the count above. So, the number of arrangements of the letters in mathematics in which TH appears together but the TH is not immediately by an E (not THE) is:9 * 10! - 8 * 2 * 9! = 4,005,120 arrangements.

To know more about permutation refer here :

https://brainly.com/question/13715183

#SPJ11

The indefinite integral of x²(x-2)³/2 is (2/7)(x-2)⁷/₂ + (8/5)(x-2)⁵/₂+ (8/3)(x-2)³/₂+ C.

In calculus, a differentiable function F whose derivative is identical to the original function f is known as an antiderivative, inverse derivative, primitive function, primitive integral, or indefinite integral of a function f. F' = f can be used to represent this.

Let's start by making a substitution, let u = x - 2, then du/dx = 1, and dx = du.

We can now rewrite the integral as:

∫(u+2)² u³/₂ du

Expanding the square, we get:

∫u⁵/₂+ 4u³/₂+ 4u¹/₂ du

Integrating term by term, we get:

(2/7)u⁷/₂ + (8/5)u⁵/₂ + (8/3)u³/₂+ C

Substituting back u = x - 2, we get:

(2/7)(x-2)⁷/₂+ (8/5)(x-2)⁵/₂ + (8/3)(x-2)³/₂ + C

Learn more about indefinite integral at https://brainly.com/question/15650147

#SPJ11

Each property will be approximately 24.518 hectares in size.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

To find the size of each property, we need to divide the total area of land by the number of properties:

147.11 hectares / 6 = 24.518333...

Rounding to the nearest thousandth of a hectare, we get:

24.518 hectares (rounded to three decimal places)

Therefore, each property will be approximately 24.518 hectares in size.

To learn more about the area of the rectangle visit:

brainly.com/question/2607596

#SPJ1

The value of the function is f(5)=32.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here the given function is,

a(x)=5[tex]\vert x-10\vert[/tex] +7

Now take a(x) as f(x) then,

=> f(x)=5[tex]\vert x-10\vert[/tex] +7

Put x=5  into f(x) then,

=>  f(5) =5[tex]\vert5-10\vert+7[/tex]

=> f(5) =[tex]5\vert-5\vert+7[/tex]

=> f(5) = 5.5+7

=> f(5)=25+7 =32.

Hence the value of the function is f(5)=32.

To learn more about function refer the below link

https://brainly.com/question/11624077

#SPJ1

The two negative angles are -5π/3 and -11π/3, and the three positive angles are 7π/3, 13π/3, and 19π/3.

To find two negative and three positive angles, expressed in radians, for which the point 1 13 the unit circle that correspond to each angle is (1/2, v3/2), we can use the following steps:

Step 1: Determine the reference angle for the given point. The reference angle is the angle formed by the positive x-axis and the terminal side of the angle. In this case, the reference angle is 60 degrees, or π/3 radians.

Step 2: Find the positive angles by adding or subtracting multiples of 2π to the reference angle. The positive angles are:

π/3 + 2π = 7π/3
π/3 + 4π = 13π/3
π/3 + 6π = 19π/3

Step 3: Find the negative angles by subtracting multiples of 2π from the reference angle. The negative angles are:

π/3 - 2π = -5π/3
π/3 - 4π = -11π/3

Hence, the solutions consist of two negative angles (-5π/3 and -11π/3) and three positive angles (7π/3, 13π/3, and 19π/3).

To know more about negative angles refer here:

https://brainly.com/question/13529952#

#SPJ11

a) As per the demand function, the solution for C is $160, and k is 0.0006

b) The optimal price and quantity that will maximize the revenue for the small business's new product are approximately $48.56 and 414 units, respectively.

To solve for C and k, we need to eliminate one of the variables, either C or k. We can achieve this by taking the ratio of the two equations, which yields:

[tex]$45/40 = (Cek(1000))/(Cek(1200))$[/tex]

Simplifying the equation, we get:

[tex]$1.125 = e^{200k}$[/tex]

Taking the natural logarithm of both sides, we get:

ln(1.125) = 200k

Therefore, k=ln(1.125)/200 = 0.0006

Substituting this value of k in one of the equations, we can solve for C. We can use the first equation:

[tex]$45=Ce^{ln(1.125)*1000/200}$[/tex]

Simplifying, we get:

C=180/1.125 ≈ $160

To find the quantity that maximizes revenue, we need to take the derivative of the revenue function with respect to x and set it equal to zero, and then solve for x.

Taking the derivative of R(x), we get:

[tex]R'(x) = 160e^{(ln(1.125)x/200)} + 160x\times(ln(1.125)/200)\times e^{(ln(1.125)x/200)}[/tex]

Setting R'(x) = 0, we get:

[tex]160e^{(ln(1.125)x/200)} + 160x\times(ln(1.125)/200)\times e^{(ln(1.125)x/200)}=0[/tex]

Simplifying the equation, we get:

[tex]e^{(ln(1.125)x/200)} = -x\times(ln(1.125)/200)[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(e^{(ln(1.125)x/200)}) = ln(-x\times(ln(1.125)/200))[/tex]

x = -200/ln(1.125) ≈ -414.72

The negative value of x is not meaningful in this context, so we can ignore it. Therefore, the quantity that maximizes revenue is approximately 414 units.

To find the corresponding price that yields the maximum revenue, we can substitute x = 414 in the demand function:

p = [tex]160e^{(ln(1.125)*414/200)}[/tex]≈ $48.56

To know more about demand function here

https://brainly.com/question/28198225

#SPJ4

Answer: Right triangle

Triangle ABC is a triangle because it has exactly 3 points connected to each other. It is a right triangle because at Point B, the angle created when connecting the points is 90 degrees.

As per the sample mean, the appropriate inference procedure for analyzing the results is a one-sample t-interval for a population mean. (option d).

In this scenario, a researcher is investigating the design of racing swimsuits for women and has selected a sample. The researcher wants to compare the mean swim times of two groups of women, one wearing a new racing swimsuit and the other wearing a traditional swimsuit.

This option is appropriate when we want to estimate the mean of a population based on a sample. In this scenario, we are interested in comparing the means of two samples, and we don't have any information about the population mean. Therefore, this option is not suitable.

In conclusion, the appropriate inference procedure for analyzing the results in this scenario is a two-sample t-interval for a difference between sample means, as it is used to compare the mean of two independent samples.

To know more about sample mean here

https://brainly.com/question/14127076

#SPJ4

Complete Question:

A researcher in sports equipment is investigating the design of racing swimsuits for women. The researcher selected a sample. The difference in the sample mean swim times will be calculated. Which of the following is the appropriate inference procedure for analyzing the results?

a) A two-sample t-interval for a difference between sample means

b) A two-sample t-interval for a difference between population means

c) A one-sample t-interval for a sample mean

d) A one-sample t-interval for a population mean

e) A matched pairs t-interval for a mean difference

The value of the constant k is 5

Direct variation can be defined a type of variation in mathematics in which there is a simultaneous increase in the value of the variables.

As the value of one of the variable increases, the value of the other variable also increases and as the value of one of the variables decreases, the value of the other variable also decreases.

From the information given, we have that;

y ∝ x

Determine the constant

y/x = k

Where , 'k' is the constant of variation

Substitute the value of x and y, we have;

k = 100/20

divide the values

k = 5

Learn about direct variation at: https://brainly.com/question/6499629

#SPJ1

Answer: x = 5.2136 or x = -1.2136

Step-by-step explanation: Let's first simplify the expression by using the identity:

(a+b)^2 = a^2 + 2ab + b^2

For this problem, let a = sqrt(2) and b = 1, so we get:

(sqrt{2}+1)^2 = 2 + 2sqrt{2} + 1 = 3 + 2sqrt{2}

Now we can rewrite the original equation as:

(sqrt{2}+1)^x + (sqrt{2}-1)^x = 6

[(sqrt{2}+1)^(x/2)]^2 + [(sqrt{2}-1)^(x/2)]^2 + 2(sqrt{2}+1)^(x/2)(sqrt{2}-1)^(x/2) = 6

Let's define a = (sqrt{2}+1)^(x/2) and b = (sqrt{2}-1)^(x/2), then the equation can be rewritten as:

a^2 + b^2 + 2ab = 6

Now we can substitute the value we found earlier for (sqrt{2}+1)^2:

a^2 + b^2 + 2ab = 3 + 2sqrt{2}

We can rewrite this as:

(a+b)^2 = 3 + 2sqrt{2}

Taking the square root of both sides, we get:

a+b = ±√(3 + 2sqrt{2})

Now we can substitute back in the expressions for a and b:

(sqrt{2}+1)^(x/2) + (sqrt{2}-1)^(x/2) = ±√(3 + 2sqrt{2})

We can solve for x/2 by taking the logarithm of both sides:

log[(sqrt{2}+1)^(x/2) + (sqrt{2}-1)^(x/2)] = log[±√(3 + 2sqrt{2})]

x/2 = 2.6068 or -0.6068

Multiplying both sides by 2, we get:

x = 5.2136 or -1.2136

Therefore, the solutions are:

x = 5.2136 or x = -1.2136.

The angle at which the third archer launched arrow C is 30 degrees, based on the fact that the angle between arrows A and C is 150 degrees, and corresponding angles are equal, as well as alternate angles.

Arrow A and arrow  B are parallel to the ground, arrow C crosses arrow  A and arrow B. arrow C crosses arrow  A at an angle of 150⁰°.

So, considering the corresponding angles C crosses B at an angle of 150°. Because correspondent angles are equal. angle 2, 6 are the required correspondent angles.

Therefore, knowing the alternate angles, the third archer launched arrow C at 30°. Here, the alternate angles are 1 and 7. Launching the arrow on the tree, angle 7 will be angle of launch.

To know more about Angle:

https://brainly.com/question/28451077

#SPJ4

_____The given question is incomplete, the complete question is given below:

The arrows shot by the three archers hit a tree as shown below. Arrow A and B are in parallel to the ground and arrow C cuts across the other two arrows. If the longer angle made by arrow A and C is 150°, What is the angle at which the third archer launched arrow C?

There are 75,354,201 lattice paths from (0,0) to (10,12) that pass through (3,5).

To explain, lattice paths are the number of paths between two points in a grid, with each move only moving in one direction. In this case, the two points are (0,0) and (10,12), and (3,5) is the point that must be passed through. The number of possible paths can be calculated using a combination formula.

The number of paths can be calculated using the formula: C_nr = n! / (r! (n-r)!), where n is the total number of spaces to travel, and r is the number of horizontal steps. In this case, n = 22 and r = 10. Therefore, C_2210 = 75,354,201.

This formula can be interpreted as the number of different arrangements of objects in a row, given the constraints of the problem. In this case, the objects are the steps taken in a lattice path. It is the number of ways to arrange 10 steps to the right and 12 steps up, while making sure that one of the steps is from (0,0) to (3,5).

In conclusion, there are 75,354,201 lattice paths from (0,0) to (10,12) that pass through (3,5). This can be calculated by using the combination formula C_nr = n! / (r! (n-r)!), with n = 22 and r = 10.

For more such questions on Lattice paths.

https://brainly.com/question/30904623#

#SPJ11

Answer:

We need at least 100 terms of the series to approximate the sum with an error of less than 0.05.

The 4 terms are required to approximate the sum of the series with an error of less than 0.05.

To determine the number of terms required to approximate the sum of the series with an error of less than 0.05, we need to use the formula for the error of an alternating series:

Error = |a_n+1|

where a_n+1 is the next term in the series.

Since the series is -1^n/2n!, the next term in the series is -1^(n+1)/2(n+1)!.

We need to find the smallest value of n that satisfies the inequality:

|a_n+1| < 0.05

|-1^(n+1)/2(n+1)!| < 0.05

1/2(n+1)! < 0.05

2(n+1)! > 1/0.05

2(n+1)! > 20

Now we can try different values of n to find the smallest one that satisfies the inequality:

n = 1: 2(1+1)! = 2(2)! = 2(2)(1) = 4 (not greater than 20)

n = 2: 2(2+1)! = 2(3)! = 2(3)(2)(1) = 12 (not greater than 20)

n = 3: 2(3+1)! = 2(4)! = 2(4)(3)(2)(1) = 48 (greater than 20)

Therefore, the smallest value of n that satisfies the inequality is n = 3.

So, the number of terms required to approximate the sum of the series with an error of less than 0.05 is n+1 = 3+1 = 4.

4 terms are required to approximate the sum of the series with an error of less than 0.05.

Learn more about Error

brainly.com/question/30524252

#SPJ11

Approximately normal with mean is $206,274 and standard deviation is $3,788 and this can be determined by applying the central limit theorem, option A.

There were 5,317 previously owned homes sold in a western city in the year 2000.

The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881.

Simple random samples of size 100.

According to the central limit theorem the approximately normal mean is $206274.

Now, to determine the approximately normal standard deviation, use the below formula:

[tex]s=\frac{\sigma}{\sqrt{n} }[/tex]

where 's' is the approximately normal standard deviation, 'n' is the sample size, and  is the standard deviation.

Now, put the known values in the equation (1).

s = 37881 / √100

= 3788.1

s ≈ 3788

Therefore, option A is correct that Approximately normal with mean $206,274 and standard deviation $3,788.

Learn more about Standard deviation:

https://brainly.com/question/26682678

#SPJ4

Complete question:

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

(A) Approximately normal with mean $206,274 and standard deviation $3,788

(B) Approximately normal with mean $206,274 and standard deviation $37,881

(C) Approximately normal with mean $206,274 and standard deviation $520

(D) Strongly right-skewed with mean $206,274 and standard deviation $3,788

(E) Strongly right-skewed with mean $206,274 and standard deviation $37,881

The histogram on the right is skewed left, therefore the mean is less than the median. This is true in a skewed distribution.

Skewness is a measure of the asymmetry of the probability distribution. If the distribution is skewed to the right, it is said to have a positive skew. If the distribution is skewed to the left, it is said to have a negative skew. When a histogram is skewed to the left, its tail is longer on the left-hand side than on the right-hand side. This implies that there are more values on the left-hand side of the histogram than on the right-hand side, and thus the mean will be less than the median since the mean is sensitive to outliers that are far from the center of the distribution.

To learn more about histogram refer :

https://brainly.com/question/30664111

#SPJ11

Because perpendicular parking spaces require turning at a  90 degree angle, allow yourself plenty of room by delaying turning until you can see all the way down the stall line.

Perpendicular parking spaces require turning at a 90-degree angle. This means that you will need to make a sharp turn in order to fit into the parking space.

It is important to allow yourself plenty of room by delaying turning until you can see all the way down the stall line. This will help you to avoid hitting any other cars or obstacles that may be in your way. It is also important to make sure that you are lined up with the parking space before you begin turning.

Once you have turned at the 90-degree angle, you can begin to slowly back into the parking space until you are fully parked.

Learn more about angle here:

https://brainly.com/question/24084436

#SPJ11

False. A p-value for correlation that is measurably critical implies that it's far improbable that the found correlation is because of irregular possibility alone.

In various words, a measurably critical p-value demonstrates that there's a genuine affiliation or relationship between the two variables being examined. however, measurable importance doesn't be guaranteed to imply causation or a strong correlation, and it is practical that various components or variables might be contributing to the decided correlation.

It's far crucial to interpret factual importance inside the context of the exploration question and investigate the plan and recollect different factors like impact length, sample length, and capacity confounding variables.

to know more about variables click here:

https://brainly.com/question/28248724

#SPJ4

Answer:

∠DAC=72°

Step-by-step explanation:

Solution Given:

∠AFD=∠BFC Being Vertically opposite angle.

Since their angle are equal so,

∠AFD=49°

again

In traingle ADF

∠ADF+∠AFD+∠DAC=180°  Since the sum of interior angle of a traingle is 180°

substituting value

59°+49°+∠DAC=180°

108°+∠DAC=180°

subtracting 108° in both side we get

∠DAC=180°-108°

Therefore, ∠DAC=72°

Answer:

m∠DAC = 72°

Step-by-step explanation:

Given the information
m∠DFA = m∠BFC since they are vertically opposite angles formed by the intersection of the diagonals

Therefore
m∠DFA = 49°

In triangle AFD, the sum of the three angles must equal 180°

So m∠ADF + m∠DFA + m∠DAC = 180°

We know
m∠ADF = 59° and m∠DFA = 49°

Plugging these values we get

59° + 49° + m∠DAC = 180°

108° + m∠DAC  = 180°

m∠DAC = 180 - 108 = 72°