(1 point) how many terms of the series do we need to add in order to find the sum to the indicated accuracy? ∑n=1[infinity](−1)n−1n2,error≤0.002.
Answers
To determine the number of terms we need to add in order to find the sum of the series with an error less than or equal to 0.002, we can use the concept of the Alternating Series Estimation Theorem.
The Alternating Series Estimation Theorem states that for an alternating series with terms decreasing in absolute value, the error in approximating the sum of the series by the sum of a finite number of terms is less than or equal to the absolute value of the next term.
In the given series, ∑n=1[infinity](−1)n−1n^2, the terms are decreasing in absolute value as n increases, so we can apply the Alternating Series Estimation Theorem.
The next term in the series, which determines the error, is given by (-1)^n * (n+1)^2. To ensure the error is less than or equal to 0.002, we need to find the smallest value of n such that:
|(-1)^n * (n+1)^2| ≤ 0.002
We can solve this inequality by testing values of n until we find the smallest value that satisfies it. Starting with n = 1:
|(-1)^1 * (1+1)^2| = 4 > 0.002
The inequality is not satisfied for n = 1.
Let's continue testing values of n:
|(-1)^2 * (2+1)^2| = 9 > 0.002
|(-1)^3 * (3+1)^2| = 16 > 0.002
|(-1)^4 * (4+1)^2| = 25 > 0.002
|(-1)^5 * (5+1)^2| = 36 > 0.002
|(-1)^6 * (6+1)^2| = 49 > 0.002
...
After testing a few values, we can see that the smallest value of n that satisfies the inequality is n = 9:
|(-1)^9 * (9+1)^2| = 100 > 0.002
Therefore, we need to add at least 9 terms in order to find the sum of the series with an error less than or equal to 0.002.
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Related Questions
A rectangle is placed on the coordinate grid such that one side is on the x-axis and one side is on the
y-axis. What 3-dimensional shape is formed by this rectangle rotating around the y-axis?
cube
O sphere
O cylinder
O rectangular prism
Answers
Answer:
A cylinder
Step-by-step explanation:
Picture a can of lets say beans.
It has two circles on its top and bottom side, as well as a cylinder connecting those two parts.
If you were to disassemble the can, you would be left with two circles and a cylinder.
Now the how dose a rectangle connect to a can? Well, if you were to flatten the cylinder you are left with a rectangle and two circles.
Pertaining to the problem, if you were to take a 2d rectangle on a coordinate plane and spin it around the y-axis you would create, in the 3d perspective, a cylinder.
Additionally if you were looking at it from a 2d perspective a circle.
Answer:
Cylinder
Step-by-step explanation:
Vibrations of harmonic motion can be represented in a vectorial form. Analyze the values of displacement, velocity, and acceleration if the amplitude, A=2+T, angular velocity, ω=4+U rad/s and time, t=1 s. The values of T and U depend on the respective 5th and 6th digits of your matric number. For example, if your matric number is AD201414, it gives the value of T=1 and U=4.
Answers
The values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.
We know that the amplitude, A = 2 + T; the angular velocity, ω = 4 + U rad/s; and time, t = 1s. Here, the value of T = 1 and the value of U = 4 (as mentioned in the question).
Harmonic motion is a motion that repeats itself after a certain period of time.
Harmonic motion is caused by the restoring force that is proportional to the displacement from equilibrium.
The three types of harmonic motions are as follows: Free harmonic motion: When an object is set to oscillate, and there is no external force acting on it, the motion is known as free harmonic motion.
Damped harmonic motion: When an external force is acting on a system, and that force opposes the system's motion, it is called damped harmonic motion.
Forced harmonic motion: When an external periodic force is applied to a system, it is known as forced harmonic motion.Vectorial formVibrations of harmonic motion can be represented in a vectorial form.
A simple harmonic motion is a projection of uniform circular motion in a straight line.
The displacement, velocity, and acceleration of a particle in simple harmonic motion are all vector quantities, and their magnitudes and directions can be determined using a coordinate system.
Let's now calculate the values of displacement, velocity, and acceleration.
Displacement, s = A sin (ωt)
Here, A = 2 + 1 = 3 (since T = 1)and, ω = 4 + 4 = 8 (since U = 4)
So, s = 3 sin (8 x 1) = 2.68 m (approx)
Velocity, v = Aω cos(ωt)
Here, v = 3 x 8 cos (8 x 1) = 2.24 m/s (approx)
Acceleration, a = -Aω2 sin(ωt)
Here, a = -3 x 82 sin(8 x 1) = -18.07 m/s2 (approx)
Thus, the values of displacement, velocity, and acceleration are 2.68 m, 2.24 m/s, and -18.07 m/s2 respectively.
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A rectangle’s length is 6 more than 4 times its width. If the perimeter is 42, how long is the rectangle
Answers
The Length of the rectangle is 18 unit.
What is the Perimeter of a Rectangle?Perimeter of rectangle = 2(length + width)
Given the following:
Let x represent the width of the rectangle
Width of the rectangle = x
Length of the rectangle = 4x + 6
Perimeter of rectangle = 42 units
Therefore, we would write the following equation to find x based on the formula for finding the perimeter of a rectangle:
2(4x + 6 + x) = 42
2(5x + 6) = 42
10x + 12 = 42
10x = 42 - 12
10x = 30
10x/10 = 30/10
x = 3
The width (x) = 3.
Length of the rectangle = 4(3) + 6
Length of the rectangle = 18 unit.
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What is the solution to the inequality |2x – 3| > 5?
A) x < –1 or x > 4
B)x < 0 or x > 8
C)0 < x < 8
D)–1 < x < 4
Answers
The solution to the inequality |2x - 3| > 5 is: x < -1 or x > 4
Therefore, the correct option is A) x < -1 or x > 4.
Given that we need to find the solution to the inequality |2x – 3| > 5
To solve the inequality |2x - 3| > 5, we can break it down into two cases:
Case 1: 2x - 3 > 5
In this case, we have:
2x - 3 > 5
2x > 5 + 3
2x > 8
x > 4
Case 2: -(2x - 3) > 5
In this case, we have:
-(2x - 3) > 5
-2x + 3 > 5
-2x > 5 - 3
-2x > 2
x < -1 (remember to reverse the inequality when multiplying or dividing by a negative number)
Combining the solutions from both cases, we find that the solution to the inequality |2x - 3| > 5 is:
x < -1 or x > 4
Therefore, the correct option is A) x < -1 or x > 4.
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Use elementary row operations to transform the augmented coefficient matrix to echelon form. Then solve the system by back substitution. X₁-4x2 +5x3. = 23 2x₁ + x₂ + x3 = 10 -3x + 2x₂-3x3 = = -23 *** An echelon form for the augmented coefficient matrix is What is the solution to the linear system? Select the correct choice below and, if necessary, fill in the answer box(es) in your choice. OA. There is a unique solution, x₁ = x₂ = x3 - (Simplify your answers.) B. There are infinitely many solutions of the form x₁ = x2-x3-t where t is a real number. (Simplify your answers. Type expressions using t as the variable.) 21 OC. There are infinitely many solutions of the form x, .X₂S, X₁t where s and t are real numbers. (Simplify your answer. Type expression using s and t as the variables.) D. There is no solution.
Answers
The solution to the linear system is unique solution which is x₁ = 1/6, x₂ = 3/2, and x₃ = 17/6.
The correct answer is option A.
To solve the given system of linear equations using elementary row operations and back substitution, let's start by representing the augmented coefficient matrix:
[1 -4 5 | 23]
[2 1 1 | 10]
[-3 2 -3 | -23]
We'll apply row operations to transform this matrix into echelon form:
1. Multiply Row 2 by -2 and add it to Row 1:
[1 -4 5 | 23]
[0 9 -9 | -6]
[-3 2 -3 | -23]
2. Multiply Row 3 by 3 and add it to Row 1:
[1 -4 5 | 23]
[0 9 -9 | -6]
[0 -10 6 | -68]
3. Multiply Row 2 by 10/9:
[1 -4 5 | 23]
[0 1 -1 | -2/3]
[0 -10 6 | -68]
4. Multiply Row 2 by 4 and add it to Row 1:
[1 0 1 | 5/3]
[0 1 -1 | -2/3]
[0 -10 6 | -68]
5. Multiply Row 2 by 10 and add it to Row 3:
[1 0 1 | 5/3]
[0 1 -1 | -2/3]
[0 0 -4 | -34/3]
Now, we have the augmented coefficient matrix in echelon form. Let's solve the system using back substitution:
From Row 3, we can deduce that -4x₃ = -34/3, which simplifies to x₃ = 34/12 = 17/6.
From Row 2, we can substitute the value of x₃ and find that x₂ - x₃ = -2/3, which becomes x₂ - (17/6) = -2/3. Simplifying, we get x₂ = 17/6 - 2/3 = 9/6 = 3/2.
From Row 1, we can substitute the values of x₂ and x₃ and find that x₁ + x₂ = 5/3, which becomes x₁ + 3/2 = 5/3. Simplifying, we get x₁ = 5/3 - 3/2 = 10/6 - 9/6 = 1/6.
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Assume that each year the IRS randomly audits 20% of the tax returns. If a married couple has filed separate returns, answer the following questions. (a) What is the probability that both the husband and the wife will be audited? (b) What is the probability that only one of them will be audited? (c) What is the probability that neither one of them will be audited? (d) What is the probability that at least one of them will be audited?
Answers
This problem concerns probability and assumes that the IRS randomly audits a fraction of tax returns each year. The query is about a married couple that filed separate returns, and it wants to know how likely it is that both will be audited, just one will be audited, neither will be audited, and at least one will be audited. The problem assumes that the percentage of audited tax returns is set at 20%.
(a) The probability that both the husband and wife will be audited is equal to the product of the individual probabilities:
P(both audited) = 0.2 * 0.2 = 0.04
(b) The probability that only one of them will be audited is the sum of the probabilities that the husband is audited and the wife is not, and vice versa:
P(only one audited) = 0.2 * 0.8 + 0.8 * 0.2 = 0.32
(c) The probability that neither one of them will be audited is the complement of the probability that at least one of them will be audited:
P(neither audited) = 1 - P(at least one audited) = 1 - (0.2 * 0.8 + 0.8 * 0.2 + 0.2 * 0.2) = 0.36
(d) The probability that at least one of them will be audited is equal to one minus the probability that neither of them will be audited:
P(at least one audited) = 1 - P(neither audited) = 1 - 0.36 = 0.64
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What is the sum of the measures of the interior angles of a 12-gon ?
A: 1620
B: 1800
C: 1980
D: 2160
Answers
Answer:
B. 1800 degrees.
Step-by-step explanation:
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On 1 July 2005 Neil Chen purchased a block of land (1004 m2) with a 3 bed-room house on it for $820,000. The house was rented out immediately since 1 July 2005 till June 2018. As the relevant information was not available to him, Neil did not claim deductions for capital works under ITAA97 Div 43 for the income years in which the property was used to produce assessable income. Neil also did not obtain a building cost estimate from a quantity surveyor as he did not want to incur the expense. During July 2018, Neil decided to demolish the existing house and the vacant land was subdivided into two equal-sized blocks on 1 November 2018. Construction of two new dwellings was completed on 1 October 2019 at a total cost of $900,000 ( $450,000 for each house). Neil used both dwellings as investment properties and each of them was rented out on 1 October 2019. Neil claimed deductions for capital works under ITAA97 Div 43 for the income years for both dwellings. Due to Covid19, financial difficulties caused him to sell one of the dwellings. On 30 May 2021 he entered into a contract for sale and the tenants were moved out on 30 June 2021. The sale price was $1,050,000 with settlement on 30 June 2021. Selling costs, i.e., agent commission amounted to $12,000. Required Calculate the net capital gain(s). Neil also had $31,500 capital losses from previous years. ($21,500 loss from sale of BHP Shares and $10,000 loss from sale of Stamps).
Answers
The net capital gain is $19,500. To calculate the net capital gain(s) for Neil Chen, we need to consider the relevant transactions and deductions. Neil purchased a block of land with a house in 2005, rented it out until June 2018, and then demolished the house and subdivided the land into two blocks.
He constructed two new dwellings and rented them out starting from October 2019. Neil sold one of the dwellings in May 2021 and incurred selling costs. Additionally, he had capital losses from previous years. Based on these details, we can determine the net capital gain(s) by subtracting the total capital losses and selling costs from the capital gain from the sale.
To calculate the net capital gain(s), we need to consider the following components:
1. Calculate the capital gain from the sale: The capital gain is the difference between the sale price and the cost base. In this case, the sale price is $1,050,000, and the cost base includes the original purchase price ($820,000), construction costs ($450,000), and any other relevant costs associated with the property.
2. Deduct selling costs: Selling costs, such as agent commission, should be subtracted from the capital gain. In this case, the selling costs are $12,000.
3. Consider previous capital losses: Neil had capital losses from previous years totaling $31,500.
To calculate the net capital gain(s), subtract the total capital losses ($31,500) and selling costs ($12,000) from the capital gain from the sale. The resulting amount will represent the net capital gain(s) for Neil that is $19,500
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What are the coordinates of the vertex of the function
Answers
4. (2, 16)
Step-by-step explanation:The vertex of a quadratic is where the function changes directions.
Finding the Vertex
As stated the vertex is where the function changed from increasing to decreasing or vice versa. Since this graph opens downward, the vertex will be where the maximum is. The maximum occurs that (2, 16). Therefore, the vertex is also at (2, 16).
Had the quadratic opened upwards, the vertex would occur at the minimum value.
Writing the Equation
Since we know the vertex, we can find the equation for the quadratic. Quadratic formulas can be written as y = a(x - h)² + k. In this formula, a is a constant that tells us whether the graph opens up or down, h is the x-value of the vertex, and k is the y-value of the vertex. So, to find the equation, we can plug in the values we know for the vertex. Then make the a-value negative because we know the graph opens down.
y = -(x - 2)² + 16PQ= RQ and PS= RS a=?
Answers
The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.
What are interior angles?In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.
Given:
The length of the segment PQ is equal to the length of the segment RQ.The length of the segment PS is equal to the length of the segment RS.The following steps can be used in order to determine the measure of angle a:
Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.
Step 2 - Apply the sum of interior angle property on triangle PQR.
\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)
\(\angle\text{Q}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-60\)
\(\angle\text{R}=60^\circ\)
Step 3 - Now, apply the sum of interior angle property on triangle PSR.
\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)
\(\angle\text{S}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-90\)
\(\angle\text{R}=45^\circ\)
Step 4 - Now, the measure of angle a is calculated as:
\(\angle\text{a}=60-45\)
\(\angle\text{a}=15\)
The measure of angle a is 15 degrees.
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a homeowner measured her rectangle backyard is having a length of 40 yards and a width of 25 yard. Her measurements were accurate to the nearest yard. What is the range of possible values for an eight. The actual area in square yards of her backyard
Answers
Answer:
A. 936 ≤ A < 1066
Step-by-step explanation:
It is given that:
w = width of lawn accurate to nearest yard = 25 yards
L = length of lawn accurate to nearest yard = 40 yards
Now, for the lower bound value of the area (\(A_l\)) can be given as follows:
\(A_l = (L-Uncertainty)(w-Uncertainty)\\A_l = (40\ yards-1\ yard)(25\ yards - 1\ yard)\\A_l = 936\ sq.\ yard\)
Now, for the upper bound value of the area (\(A_u\)) can be given as follows:
\(A_u = (L+Uncertainty)(w+Uncertainty)\\A_u = (40\ yards+1\ yard)(25\ yards + 1\ yard)\\A_u = 1066\ sq.\ yard\)
Therefore, the correct option is:
A. 936 ≤ A < 1066
Which relation is not a function?
Helppppo due now
Answers
Answer:
B.
Step-by-step explanation:
there cannot be two of the same x value's. It would make it a circle on the graph, or something close to that, which isn't a function.
can anyone help me with this
Answers
The volume of the following figure is
240 in² which of the following is the missing side length?
A. 7 in
B. 6 in
C. 8 in
D. 5 in
Answers
Answer:
C. 8 in
Step-by-step explanation:
(5)(6)(x)=240
solve for x
30x=240
x=240/30
x=8
H0: μ1 = μ2Ha: μ1 ≠ μ2The two-sample Hotelling's T-square statistic is 6.012 The F-value is about 0.951 with 6 and 93 degrees of freedom. The p-value is 0.463.Given the evidence (T-square = 6.012; F=0.951; d. f.=6,193; p-value=0.463).QuestionShould we reject the null hypothesis? Since we use Hotelling T-square for our test statistics ,does the T-square and F-value matters in making decision here?Please give thorough explanation.Please send me answer in typed form strictly prohibited handwritten solution. ( without mention any table).
Answers
We should not reject the null hypothesis. Yes, the T-square and F-value matters in making decision here because T-square measures population difference, F-value measures significance.
According to the given information, the null hypothesis (H0) states that the means of two populations (μ1 and μ2) are equal, while the alternative hypothesis (Ha) suggests that the means are not equal.
To determine whether we should reject the null hypothesis, we need to consider the evidence provided, including the two-sample Hotelling's T-square statistic, the F-value, the degrees of freedom, and the p-value.
1. T-square statistic:
The T-square statistic measures the overall difference between the two populations based on the sample data. In this case, the T-square statistic is calculated as 6.012.
2. F-value:
The F-value is used to assess the significance of the T-square statistic. It is calculated using the degrees of freedom associated with the numerator and denominator. Here, the F-value is approximately 0.951, with 6 and 93 degrees of freedom.
3. p-value:
The p-value represents the probability of obtaining the observed T-square statistic (or a more extreme value) under the assumption that the null hypothesis is true. In this case, the p-value is 0.463.
To make a decision regarding the null hypothesis, we typically compare the p-value to a predetermined significance level (α). If the p-value is less than α, we reject the null hypothesis; otherwise, we fail to reject it. The common significance level is 0.05 (5%).
In this case, the p-value (0.463) is greater than the significance level (0.05). Therefore, we do not have sufficient evidence to reject the null hypothesis. This means that we cannot conclude that the means of the two populations are significantly different.
Regarding the T-square and F-value, they are both used in the Hotelling's T-square test. The T-square statistic measures the overall difference between the populations, while the F-value assesses the significance of this difference. In this context, both values are important in understanding the evidence and making a decision about the null hypothesis.
In summary, based on the given evidence (T-square = 6.012, F = 0.951, df = 6, 93, p-value = 0.463), we do not have enough evidence to reject the null hypothesis. Both the T-square and F-value are crucial in evaluating the significance of the observed difference between the populations.
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20 points and brainly please hurry
Answers
Answer:
B
Step-by-step explanation:
Area of a rectangle = Length x width
= 1.3x
26 Mr Hussain buys 13 kg of onions, 3½ kg of potatoes and
7 kg of cabbage. What total mass does he carry home?
Answers
Answer:
23.5kg
Step-by-step explanation:
the total mass of the things he bought is what we are asked to find.
13kg of onions+3.5kg of potatoes+7kg of cabbage is the total mass he carried home.
=23.5kg
In triangle ABC, the right angle is at vertex C, a = 714 cm and the measure of angle A is 78° . To the nearest cm, what is the length of side c?
Answers
Answer:
c = 730 cm
Step-by-step explanation:
To solve this question we just need to use the law of sines:
The ratio between a side in the triangle and its opposite angle is always the same.
So we have that:
\(a / sin(A) = c / sin(C)\)
\(714 / sin(78) = c / sin(90)\)
sin(78) is equal 0.9781 and sin(90) is equal 1, so we have:
\(714 / 0.9781 = c / 1\)
\(c = 714 / 0.9781 = 730\ cm\)
7+2x/3 =5 what’s the answer
Answers
4
Step-by-step explanation:\( \sf \frac{7 + 2x}{3} = 5\)
\( \sf = 7 + 2x = (5 \times 3)\)
\( \sf = 7 + 2x = 15\)
\( \sf = 2x = 15 - 7\)
\( \sf = 2x = 8\)
\( \sf = \: \: \: x = 8 \div 2 \\ \sf x = 4\)
Step-by-step explanation:
\(\begin{aligned}\frac{7+2x}{3}&=5\\7+2x&=5\times 3\\7+2x&=15\\2x&=15-7\\2x&=8\\x&=\frac{8}{2}\\x&=\boxed{4}\end{aligned}\)
Write an equation of the line with a slope of 2/3
and y -intercept of -8
Answers
Answer: y= 2/3 + -8
Step-by-step explanation: Put into slope intercept form
The equation of the line with a slope of 2/3 and y -intercept of -8 is y = 2/3 x -
8
The slope intercept equation is represented as follows:
y = mx + b
where
m = slope
b = y-intercept
Therefore,
The equation of the line has a slope(m) of 2 / 3 and y-intercept of -8.
The equation can be represented as follows:
y = 2/3 x - 8
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Using Cramer's Rule In Exercises 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, and 22, use Cramer's Rule to solve (if possible) the system of linear equations. 13x - 6у = 17 26x -12y = 8
Answers
Using Cramer's Rule, we cannot solve this system of linear equations because the determinant of the coefficient matrix is 0. However, we can conclude that the system has infinitely many solutions.
Using Cramer's Rule, we can solve the system of linear equations 13x - 6у = 17 and 26x -12y = 8 by following these steps:
Step 1: Find the determinant of the coefficient matrix, which is:
| 13 -6 |
| 26 -12 |
= (13)(-12) - (-6)(26)
= -156 - (-156)
= 0
Step 2: Since the determinant of the coefficient matrix is 0, we cannot use Cramer's Rule to solve this system of equations.
Step 3: We can check if the system has no solution or infinitely many solutions by comparing the ratios of the coefficients of x and y in the two equations.
The ratio of the coefficients of x in the two equations is 13/26 = 1/2, and the ratio of the coefficients of y in the two equations is -6/-12 = 1/2. Since these ratios are equal, the system has infinitely many solutions.
Using Cramer's Rule, we cannot solve this system of linear equations because the determinant of the coefficient matrix is 0. However, we can conclude that the system has infinitely many solutions.
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solve for measure angle F
solve for measure angle T
Answers
The measure of angle F and angle T are 109 degrees and 94 degrees respectively.
What is the measure of angle F and angle T?Opposite angle of a quadrilateral inscribed in a circle are supplementary.
From diagram 2.
Angle D is opposite angle F.
Since opposite angle of a quadrilateral inscribed in a circle are supplementary.
Angle D + Angle F = 180
71 + Angle F = 180
Angle F = 180 - 71
Angle F = 109 degrees.
From diagram 3.
Angle V is opposite angle T.
Opposite angle of a quadrilateral inscribed in a circle are supplementary.
Angle V + Angle T = 180
86 + Angle T = 180
Angle T = 180 - 86
Angle T = 94 degrees.
Therefore, Angle F = 109 degrees and Angle T = 94 degrees.
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f(x) = 9x + 3 ; x =-10
Answers
Answer:
f(-10) = -87
Step-by-step explanation:
x = -10
f(x) = 9x + 3
f(-10) = 9(-10) + 3 Replace x with the given number
= -90 + 3 Multiply 9 and -10
f(-10) = -87 Add -90 and 3
The instructions on a carton of chemicals call for mixing 144 fl oz of water, 24 fl oz of chemical No. 1, and 56 fl oz of chemical No. 2. How many quarts are
contained in the final mixture?
Answers
The final mixture contains 7 quarts.
What is Mixture?
A mixture is generated when more than one chemical is mixed. A mixture can be created in a variety of ways, including using a liquid, solid, or gaseous medium.
First, let's add up the amount of the three ingredients to find the total volume of the mixture:
144 fl oz + 24 fl oz + 56 fl oz = 224 fl oz
Now, we can convert fluid ounces to quarts:
1 quart = 32 fluid ounces
So, we can divide the total volume in fluid ounces by 32 to find the total volume in quarts:
224 fl oz / 32 fl oz/quart = 7 quarts
Therefore, The final mixture contains 7 quarts.
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Margarita entrena tres semanas para participar en un maratón. En la segunda semana recorre 1 km más que en la primera y en la tercera semana, corre el doble de km que los corridos en la segunda, ¿cuál es la representación algebraica simplificada de los kilómetros recorridos durante el entrenamiento?
Answers
Queremos encontrar una expresión algebraica que representa la situación dada.
Encontraremos que está es: 4*D + 3
Lo primero que debemos hacer es definir la variable.
Definamos D como la distancia que Margarita recorre en la primer semana.
En la segunda semana, Margarita recorre un kilometro más que en la primera, entonces en la segunda semana Margarita recorre:
D + 1km
En la tercera semana, Margarita recorre el dolbe de km recorridos en la segunda.
En la segunda ella recorrio D + 1km, y el doble de eso es:
2*(D + 1km) = 2*D + 2km
La distancia total recorrida sera la suma de las 3 semanas:
D + (D + 1km) + (2*D + 2km)
Simplificando los km, así solo queda una expresión algebraica, obtenemos:
D + (D + 1) + (2*D + 2)
Podemos simpliicar esto para obtener:
D + D + 1 + 2*D + 2
(D + D + 2*D) + (1 + 2)
4*D + 3
Entonces la representación algebraica simpliicada de los kilómetros recorridos durante el entrenamiento es:
4*D + 3
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how to do this question plz
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Answer:
112 students
Step-by-step explanation:
Please see the attached picture for full solution.
To conduct a test of hypothesis with a small sample, we make an assumption that?
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To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .
What is normal distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
The normal distribution appears as a "bell curve" on a graph.
A probability bell curve is more properly described as the normal distribution.The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.Not all symmetrical distributions are normal, but all normal distributions are symmetrical.Natural occurrences frequently resemble the usual distribution.To know more about normal distribution........
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12
Find the lowest common multiple (LCM) of 28, 42 and 63
Show your working clearly.
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Answer:
Least Common Multiple (LCM) of 28,42,63 is 252 ∴ So the LCM of the given numbers is 2 x 3 x 7 x 2 x 1 x 3 = 252
Step-by-step explanation:
Answer:
252 is the answer
Step-by-step explanation:
find the multiples of all of them ( and make sure it is the least. )
28:
28, 56, 84, 112, 140, 168, 196, 224, 252, 280, 308
42:
42, 84, 126, 168, 210, 252, 294, 336
63:
63, 126, 189, 252, 315, 378
bolded + undurlined is the answer
you see that 252 is the answer
252 is the answer
The organizer of a late night street fair in a popular tourist city wants to analyze the relationship between daily revenue and the following variables: the number of male visitors, the number of female visitors, the number of retail stands, the number of food (and beverage) stands, and the number of performances that take place on a given night. The regression output table is provided below. Based on these results and using a 10% significance level, the organizer thinks he can improve the model. He wants to try removing at least one variable from the analysis to create and compare new models. Which variable or variables would you recommend that he consider removing from the regression model? SELECT ALL THAT APPLY.
Answers
The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.
Based on the regression table provided, we can answer this question. The following is the regression table:Regression output table for night street fair variableNameCoefficientStandard Errort-StatP-ValueConstantb0.340.1402.430.023Number of male visitorsb10.6130.51320.750.462Number of female visitorsb10.9070.57918.830.000Number of retail standsb0.1160.0452.570.016Number of food (and beverage) standsb0.3160.0575.500.000Number of performanceb0.1460.1071.360.184The null hypothesis is rejected if p-value < 0.1; that is, there is a significant difference between the independent and dependent variables. The p-value of the Number of male visitors, the Number of female visitors, the Number of retail stands, the Number of food (and beverage) stands, and the Number of performances variables are 0.462, 0.000, 0.016, 0.000, and 0.184, respectively. As a result, the variables that are significant at the 10% level are the Number of female visitors, the Number of retail stands, and the Number of food (and beverage) stands. Therefore, the organizer should consider removing the Number of male visitors and Number of performance variables from the regression model. The variables that the organizer can consider removing from the regression model are the Number of male visitors and Number of performance.
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If the circumference of a cylinder is 32pie and it’s lateral surface area is 750cm^2 find the height of the cylinder
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The height of the cylinder is approximately 5.97 cm.
Define cylinderA cylinder is a three-dimensional geometric shape that consists of two parallel, congruent circular bases and a curved lateral surface that connects the bases. The bases are perpendicular to the lateral surface, which means that the lateral surface forms a curved rectangle.
Given;
The circumference of the cylinder is 32π.
The lateral surface area of the cylinder is 750 cm².
Lateral surface area of a cylinder = 2πrh
Circumference of a cylinder = 2πr
We can use the circumference formula to find the radius of the cylinder:
2πr = 32π
r = 16
Now we can use the lateral surface area formula to find the height of the cylinder:
750 = 2π(16)(h)
750 = 32πh
h = 750/(32π)
h ≈ 5.97
As a result, the cylinder's height is around 5.97 cm.
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