1 only C) p > 0 D) p < 0 Which of the following conditions are necessary to conclude that the series an converges using the alternating series test? 1. The terms an alternate in sign for all n > N for some positive integer N. II. lim an = 0 III. (antil N for some positive integer N. 1200 A I only B I and II only с II and III only D) I, II, and 111
If your limitation is non-zero and finite, the series conduct similarly so their succession will bear similarly as well. Limit Comparison Test: Let ∞∑n=1an and ∞∑n=1bn be positive-termed series. If limn→∞ an b n=c, where c is limited, and c>0, then either both sequences join or both diverge.
What is meant by limit comparison?You compare two series a (subscript n) and b (subscript n) with a n greater than or equal to 0 and b n greater than 0 in the limit comparison test. When n reaches infinity, c = lim a n/b n follows. Both series will either converge or diverge if c is positive and finite. The original series is divergent, according to the limit comparison test. The limit in question does not exist, hence the limit comparison test does not apply. The original series converges, as demonstrated by the comparison test. It is possible to demonstrate how the original series deviates using the comparison test.To learn more about limit comparison, refer to:
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Find approximate values of the solution of the given initial value problem at T=0.1, 0.2, 0.3, and 0.4 using Euler method with h=0.1y'= 0.5-t+2y ; y(o)=1
A starting value or starting point is what is meant by the term "initial value" (plural "initial value").
What is meant by initial value?The definition of an initial value is accurate: It is a starting value or starting point. When the input value is 0, the initial value of a function is its output. For instance, the starting value would be the amount of money you had on day 0 if your function was to track how much money you made over a specific period of time. A function's initial value is the value it has when x is zero. This corresponds to the y-intercept. The graph reveals that our line crosses the y-axis at the coordinates 0 and 8. When x=0 is entered into an exponential function, the result is the function's initial value. The initial value of the exponential function f(x) = abx f (x) = a b x is a.Given,
[tex]$y_{n+1}=y_n+h\left(x_n-y_n\right)^2$[/tex]
Since
[tex]$x_0=0, y\left(x_0\right)=0.5$[/tex]
[tex]\frac{h}{x} & =0.1 \\ x & =0.3\end{aligned}$[/tex]
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e solid has a triangular base in the x y-plane. the solid has ---select--- in the x z-plane. the solid has ---select--- in the y z-plane. the solid has ---select--- in the plane z
The triangular base in the xy plane can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.
In the xz plane, the solid has a plane defined by the equation z = f(x). This equation can be derived from the equation of the base by substituting the y values with the corresponding mx + b values. Similarly, in the yz plane, the solid has a plane defined by the equation z = g(y). This equation can be derived from the equation of the base by substituting the x values with the corresponding (y - b)/m values. To calculate the area of the solid, we can use the formula A = 1/2h(b1 + b2), where h is the height of the solid and b1 and b2 are the lengths of the two bases. The area of the solid can then be found by substituting the appropriate values into this formula.
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In a randomly generated list of numbers from 0-6, what is the chance that each number will concur
In a randomly generated list of numbers from 0 to 6, each number has an equal chance of occurring. Since there are 7 numbers total (0, 1, 2, 3, 4, 5, and 6), the chance of each number occurring is 1/7 or about 14.3%.
A probability simple definition is what?
A probability is a measure of the likelihood of a particular event occurring. It is a value between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. A probability of 0.5, for example, indicates that the event has an equal chance of occurring or not occurring. A probability can be expressed as a fraction, decimal, or percentage.
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How is a thermometer different than a number line
Answer:
A thermometer is different than a number line because a thermometer goes from the bottom up with a minimum count. As a number line goes both ways with a pointer indicating where the point stands on either side.
Step-by-step explanation:
For this exercise, use the position function s(t) = −4.9t^2 + 160, which gives the height (in meters) of an object that has fallen for t seconds from a height of 160 meters. The velocity at time t = a seconds is given by lim t→a s(a) − s(t) a − t . When will the object hit the ground? At what velocity, v, will the object impact the ground?
Answer:
5
Step-by-step explanation:
u just know
there are four balls in a bag, but it is not known of what colours they are ; one ball is drawn and found to be white : find the chance that all the balls are white.
So the chance of drawing a white ball in the first draw is 1/4 and the chance that all the balls are white is the same.
What is the straightforward meaning of probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
If one ball is drawn and found to be white, and it is not known of what colors the other balls are, the probability that all the balls are white is 1/4 or 25%. This is because there is only one outcome where all the balls are white (all four balls are white) out of the four total possible outcomes (all four balls are white, three are white and one is not, two are white and two are not, one is white and three are not, and none are white). So the chance of drawing a white ball in the first draw is 1/4 and the chance that all the balls are white is the same.
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use the definition of continuity and the properties of limits to show that the function is continuous at the number a
Continuity is the formulation of a function that varies with no breaks or jumps. The concepts of limits and continuity have been used to show that the function is continuous at the number a below.
If a graph has no holes asymptotes or breaks at any point then the function is said to be continuous. Or if we can draw the function without lifting our pen then it is called continuous.
The conditions which it should satisfy are,
1)The limit must exist at that point.
2) The function must be defined at that point, and
3)The limit and the function must have equal values at that point. So,
A function f(x) is said to be continuous at x=a if,
lim f(x) = f(a)
x→a
A function is said to be continuous on the interval [a,b] if it is continuous at each point in the interval.
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three students reported the length of a pencil as 12 cm 12,0 cm and 12,00 cm do all three readings have the same information
yes three readings have the same information for three students reported the length of a pencil as 12 cm 12,0 cm and 12,00 cm
The precision was good while the accuracy was poor. Precision is defined
as how close measurements are with each other.
We were told the data from the measurement was between 12cm-
12cm which shows how close the measurements are hence having a good precision.
The accuracy is defined as how close a measurement is to the theoretical
or actual value. In this case, the actual value is 12cm which is far from the
values gotten from measurements hence signifying the accuracy was poor.
yes three readings have the same information for three students reported the length of a pencil as 12 cm 12,0 cm and 12,00 cm
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The numeric components of the electric field in a region of space can be calculated using the equations E; fzy and Ey (0, Y) and (X,Y) ? Which of the following expressions vields the potentia difference between the points (0,y) and (x,Y)a. -6yb. 6yc. -3x^2yd. 3x^2ye. 3x^2y-6
The potential difference between the points (0, y) and (x, y) is given by the equation V = 3x^2y - 6yx.
e. 3x^2y-6y
The potential difference between two points (x, y) and (0, y) is given by the equation V = -E⋅x. The electric field in the region is given by the equations E; fzy and Ey (0, Y) and (X,Y). Using these equations, the electric field in the region can be calculated as E = 3x^2y - 6y. Therefore, the potential difference between the points (0, y) and (x, y) is given by V = -(3x^2y - 6y)⋅x = 3x^2y - 6yx.
The potential difference between the points (0, y) and (x, y) is given by the equation V = 3x^2y - 6yx.
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which expression is equivalent to 5M-3N when M=3x-2 and N=2x-5
A9x+5
B9x-25
C21x+5
D21x-25
Answer:
A. 9x+5
Step-by-step explanation:
[tex]5(3x-2)-3(2x-5)\\15x-10-6x+15\\9x+5[/tex]
ron ate 2/5 of a pie, carolyn ate 3/10 of the same pie. how much of the pie is left
Answer: 3/10
Hope this helps :)
Step-by-step explanation:
2/5= 4/10
4/10 + 3/10= 7/10
3/10 of the pie is left
Match the following:
Whole Number:
Fraction:
Answer Choices: If the similar figure is smaller than the original then the scale factor is a ______. If the similar figure is larger than the original then the scale factor is a __________
If the similar figure is smaller than the original then the scale factor is a fraction. If the similar figure is larger than the original then the scale factor is a whole number.
How do scale factors work ?The scale factor is a ratio that compares the corresponding side lengths of two similar figures. If the similar figure is smaller than the original, the scale factor is a fraction less than 1, for example, 2/3 or 3/4. This means that the corresponding side lengths of the similar figure are 2/3 or 3/4 of the corresponding side lengths of the original figure.
On the other hand, if the similar figure is larger than the original, the scale factor is a whole number greater than 1, for example, 2 or 3.
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Ishi bought a $6.95 canvas and 8 tubes of paint. She spent a total of $24.95 on the canvas and paints. Determine the cost of each tube of paint.
Answer:
1 tube of paint is $2.25.
Step-by-step explanation:
We can set this as an equation first. Since we know that the canvas is $6.95 and the total is $24.95, those are the values that we will work with to determine the tube price. We can set the tube price as 8x, x being the tube price, and 8 being the number of tubes Ishi plans to buy. Now, we can set an equation:
6.95 + 8x = 24.95
8x = 18
x = 18/8 (simplified is 9/4, or 2.25)
X=4y 4y+X=24 what the answer
x= 12, y= 3 answer for the equation
x= 4y equation 1
4y +x= 24 equation 2
Substituting the value of x in the equation 2
4y +4y = 24
8y= 24
y= 24/8
y= 3
Now putting the derived value of y in equation 1
x=4y
x= 4*3
x= 12
y= 3
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Which of the following is an appropriate statement about Wilt’s free-throw shooting, based on this dotplot?
a) If Wilt were still only a 56% shooter, the probability that he would make at least 34 of his shots is about 0,03.
b) If Wilt were still only a 56% shooter, the probability that he would make at least 34 of his shots is about 0,03.
c) If Wilt is now shooting better than 56%, the probability that he would make at least 34 of his shots is about 0,03.
d) If Wilt is now shooting better than 56%, the probability that he would make at least 34 of his shots is about 0,03.
If Wilt were still only a 56% shooter, the probability that he would make at least 34 of his shots is about 0,03.The correct option is a
To perform this simulation, we can use a computer program to generate a random number between 0 and 1 for each shot.
If the random number is less than or equal to 0.56, then the shot is counted as a make. We can then repeat this process 50 times and count the number of shots that were made.
We can repeat this process many times, and count the proportion of times that 34 or more makes are achieved. This proportion is the estimated probability that a 56% free-throw shooter would make 34 or more in a sample of 50 shots.
Hence a) If Wilt were still only a 56% shooter, the probability that he would make at least 34 of his shots is about 0,03.
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find two nonzero vectors perpendicular to 2 in r3 that are not scalar multiples of each other, 2 looks like. 2
v1 and v2 be two nonzero vectors perpendicular to 2 in R3.
We can calculate the dot product of each vector with 2 to determine if they are perpendicular.
v1•2 = (x1, y1, z1)•(2, 0, 0) = 2x1
v2•2 = (x2, y2, z2)•(2, 0, 0) = 2x2
If 2x1 = 0 and 2x2 = 0, then v1 and v2 are perpendicular to 2. To make sure they are not scalar multiples of each other, we can check that the coordinates of each vector are not all the same. Let's say v1 = (a, b, c) and v2 = (d, e, f). If a≠d, b≠e, and c≠f, then v1 and v2 are not scalar multiples of each other.
For example, let v1 = (1, 2, 3) and v2 = (4, 5, 6). Then v1•2 = 2 and v2•2 = 8, which both equal 0. Therefore, v1 and v2 are perpendicular to 2. Furthermore, since 1≠4, 2≠5, and 3≠6, v1 and v2 are not scalar multiples of each other.
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consider a grid of points. find the number of squares with all their vertices belonging to the points of this grid.
The number of squares that can be formed on a grid with n points on one side is (n² - (n-1)²).
The number of squares that can be formed with all their vertices belonging to the points of a grid can be calculated using the formula:
n² - (n-1)²
where n is the number of points on one side of the grid.
This is because there are n² total points on the grid, and each point can be used as a vertex for n-1 squares (when n>1) in the horizontal and vertical directions. However, each of these squares is counted twice, once for each corner point. So we subtract (n-1)² to account for the overcounting.
For example, if there are 4 points on one side of the grid, the number of squares that can be formed is 4² - (4-1)² = 16 - 9 = 7 squares.
In general, the number of squares that can be formed on a grid with n points on one side is (n² - (n-1)²).
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if y^2-2xy+3x^3=5, then at the point (-1,2) dy/dx =
Answer:
5
Step-by-step explanation:
To find the derivative of a function at a given point, we need to use the concept of limits and the definition of a derivative. In this case, we are trying to find dy/dx at the point (-1,2) for the given function y^2-2xy+3x^3=5
Since the function is equal to 5, we can assume that y^2-2xy+3x^3-5 =0, then we can find the partial derivative with respect to x and y.
∂/∂x (y^2-2xy+3x^3-5) = -2y + 9x^2
∂/∂y (y^2-2xy+3x^3-5) = 2y - 2x
Now we can substitute the point (-1,2) into the equation,
dy/dx = -2(2) + 9(-1)^2 = -4 + 9 = 5
Therefore, dy/dx at the point (-1,2) is equal to 5
It's important to note that this result is valid only for this specific point, it does not mean that it's the slope of the function in general.
Squaroot of p^10 where p>0
Answer:
p^5
Step-by-step explanation:
p^10/2=p^5
the sine of the angle at a is equal to side bc divided by side ab. the sine of angle a is therefore equal to:
sin(a) = bc/ab. is the angle of a is therefore the sine of angle at a is equal to side bc divided by side ab.
this is explained as below as :
The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse. In this case, the angle at "a" is opposite side "bc" and the hypotenuse is side "ab". Therefore, the sine of angle "a" is equal to the ratio of side "bc" divided by side "ab", or sin(a) = bc/ab.
The sine of an angle in a triangle is a trigonometric function that is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The hypotenuse is the side of a right triangle that is opposite the right angle.
In this particular case, the statement "the sine of the angle at a is equal to side bc divided by side ab" is referring to a right triangle where angle "a" is one of the angles, side "bc" is the side opposite angle "a" and side "ab" is the hypotenuse.
This is known as the sine ratio and it is used in trigonometry to calculate the sine of an angle in a right triangle. It is important to note that the sine ratio is only valid for right triangles, and the measure of the angle must be in radians.
It's also worth mentioning that this relationship holds true for any angle in a triangle, not only in right triangles, but in non-right triangles sine, cosine and tangent ratios are defined differently.
So, the sine of angle "a" is calculated as the ratio of side "bc" to side "ab" (bc/ab).
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What is 3(4 + x) + 2 x 3 = ?
which of the following shows a correct side-by-side bar chart with store location on the horizontal axis and side-by-side bars of the percentage of time spent on each task?
The resulting bar chart would show that in Store A, the employees spend 30% of their time on stocking, 40% on cashiering, and 30% on cleaning.
To create a side-by-side bar chart for this data, we would first organize the data into a table with store locations as the rows and tasks as the columns. Each cell in the table would contain the percentage of time spent on that task at that store location.
For example, the table might look like this:
Stocking Cashiering Cleaning
Store A 30% 40% 30%
Store B 25% 35% 40%
Store C 35% 25% 40%
To create the bar chart, we would then place the store locations on the x-axis and use different colors to represent the different tasks. The length of each bar would correspond to the percentage of time spent on that task at that store location.
The resulting bar chart would show that in Store A, the employees spend 30% of their time on stocking, 40% on cashiering, and 30% on cleaning.
Similarly, the chart will provide an easy visual representation of the time spent on each task at each store location.
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The complete question is -
The management of a retail company wants to analyze the time spent by employees on different tasks at different store locations. The data collected shows the percentage of time spent on tasks such as stocking, cashiering, and cleaning at three store locations: Store A, Store B, and Store C. Create a side-by-side bar chart to represent this data and analyze the results.
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WHAT IS THIS?: Evaluate 4+ (m - n)^4 when m = 7 and n =5.
Evaluation of 4+ (m - n)^4 when m = 7 and n =5 is -108
What is Foil method?To combine binomials, utilize the FOIL Method.
An abbreviation is F O I L. First, Outside, Inside, and Last are represented by the letters, denoting the sequence of multiplying terms. For your solution, multiply the first word, an outside term, the inside term, the very last term, and then join like terms.
FOIL specifies the specific terms to multiply and their order.
First - multiply the first terms
Outside - multiply the outside/outer terms
Inside - multiply the inside/inner terms
Last - multiply the last terms
Given;
4+ (m - n)^4
m=7, n=5
Now, the binomial formula of (m - n)^4 by foil method
=m^4-4m^3n+6m^2n^2-4mn^3+n^4
=2401-4(343)(5)+6(49)(25)-4(7)(125)+500
=2401-6860+7350-3500+500
=-109
Therefore, the value of expression by foil method will be -109
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PLEASE SOMEONE EXPLAIN HOW TO DO THIS QUESTION SO CONFUSED AND DUE IN AND HOUR
The minimum number of students is 3.
Average of grouped data:The mean is a value that is used to determine the central tendency of the data and is the average or computed central value of a set of values.
The method of determining the mean of a set of data that are grouped together in several categories is known as the mean of grouped data.
A frequency table must be set across the data's frequencies in order to calculate the mean of grouped data, which makes the calculation simple.
[ Here we need to create a frequency table to solve the problem ]
Here we have
Score 10 20 30 40
No of students 6 7 8 ?
To calculate the average of the score make the table as follows
Let 'x' be the number of students that the class average over 23
Score (x) No of students(f) fx
10 6 60
20 7 140
30 8 240
40 x 40x
∑f = 21 + x ∑fx = 440 + 40x
Average of score = ∑fx/ ∑f = [ 440 + 40x ]/21+x
As we assumed the average score is 23
=> [440 + 40x ]/21+x = 23
=> [440 + 40x ] = [ 21+x ] (23)
=> 440 + 40x = 483 + 23x
=> 40x - 23x = 483 - 440
=> 17x = 43
=> x = 43/17 = 2.53 (approx 3 )
Therefore,
The minimum number of students is 3.
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What are the domain and range of the following function: (3, 5), (-2, 4), (6, 1), (8, 7)?
Congress is debating a proposed law to reduce tax rates. If the current tax rate is r%, then the proposed rate after x years is given by this formula: r/1+1/1+1rRewrite this formula as a simple fraction. Use your formula to calculate the new tax rate after 1 year, 2 years, 5 years, and 15 years. 1 year____2 years____5 years___15 years____
Would tax rates increase or decrease over time? O increase O decrease Congress claims that this law would ultimately cut peoples' tax rates by 75%. Do you believe this claim? Explain.
The simple fraction is [tex]= \frac{x + 1}{2x + 1}r[/tex]
In math, what is a fraction?
A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction.
Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
[tex]= \frac{r}{1 + \frac{1}{\frac{1 + 1/x }{} } }[/tex]
[tex]= 1 + 1/x[/tex]
= x + 1/x we have
= [tex]\frac{1}{x + 1/x}[/tex]
[tex]= \frac{x}{x + 1}[/tex]
[tex]= 1 + \frac{x}{x + 1}[/tex]
[tex]= \frac{ 2x + 1}{x + 1}[/tex]
r%*x+1/(2x+1)
[tex]= \frac{x + 1}{2x + 1}r[/tex]
reduce to the appropriate fraction. The denominator was then brought up and the numerator down as I normalized.
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The complete question is -
Congress is debating a proposed law to reduce tax rates. If the current tax rate is r%, then the proposed rate after x years is given by this formula: r 1 1 1 1 x . Rewrite this formula as a simple fraction.
Four students used the same meter stick to measure an edge of the same wooden cube four times. They obtained the following results
Which student'$ measurements represent the greatest precision? A Student I B Student II C. Student III D Student IV
the standard deviation of 2nd student data is least so the measurement of 2nd student is more precise.
In this problem we have four sample of four students which measure by same meter stick. Average of all student's data is 12.4 which is same. we have to check whose measurement is precision. according to least standard deviation is least which data is more precision.
the standard deviation=[tex]\sqrt{\frac{\sum(xn-x')^2}{n-1} }[/tex] ,where x' is average of data .
by the above formula.
We have standard deviation for first student is 0.40.
2nd student is 0.23, 3rd student is 0.52 and 4th student is 0.36.
after examining the standard deviation of all data 2nd student measurement is more precision.
The complete question is,
Four students used the same meter stick to measure an edge of the same wooden cube four times. They obtained the following results:
Student I II III IV
11.90 cm 11.95 cm 11.90 cm 11.95 cm
12.25 cm 12.35 cm 12.15 cm 12.30 cm
12.70 cm 12.60 cm 12.45 cm 12.55 cm
12.75 cm 12.70 cm 13.10 cm 12.80 cm
Average 12.40 cm 12.40 cm 12.40 cm 12.40 cm
Which student’s measurements represent the
greatest precision?
A. Student I
B. Student II
C. Student III
D. Student IV
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HELP!!!
Ivan must choose a number between 55 and 101 that is a multiple of 4, 10, and 20. Write all the numbers that he could choose. If there is more than one number, separate them with commas.
Answer:
60, 80, 100
Step-by-step explanation:
What you need to do in this case is find animver between 55 and 101 that has a first number as an even number and the second number as zero
Answer:
60,80,100
Step-by-step explanation:
I don't even know
Simplify. Rewrite the expression in the form x^nx n x, start superscript, n, end superscript. \dfrac{x^{5}}{x^2}= x 2 x 5
The rewritten expression in the form of xⁿ is x^3
In math, the expression refers the combination of variables, constants and exponents.
Given,
Here we have the expression x^5 / x^2
Now, we have to rewrite this expression into the form of xⁿ.
As per the law of exponents, we have rewrite the given expression as,
=> x^5*x^-2
Now, as per the law of exponent of multiplication, we can write it as,
=> x^5-2
Now, it can be further simplified as,
=> x^3
expression can be with one variable two variable or any number similar concept for constant also that is it can be any number
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Find the perimeter of the following trapezoid:
Answer:
17 feet
Step-by-step explanation:
perimeter is the measurement of the border of a shape
2.5 + 6 + 8 + 2.5 = 17
