In mathematics, a plane is a two-dimensional surface that can be enlarged indefinitely. In order to make a plane we need at least 3 points.
Why do 3 points make a plane?In order to make a plane we need at least 3 points. Let A, B and C are three points which can be defined by two particular vector AB and AC.
As the two vectors is located on the plane, we can use their cross product to define a normal vector on the plane.
As we see a triangle which is a two-dimensional geometric figure that is developed based on 3 points. Triangle is the smallest polygon. The other polygon needs more point for creation.
Therefore, it is proved that minimum three points is mandatory for plane formation.
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what can you say about the series ∑an in each of the following cases
a) lim |(an+1)/(an)∑|=1
n→[infinity] b) lim nth root(|(an)|=2/3
n→[infinity]
c) lim |(an+1)/(an)|=0.8
n→[infinity]
d) lim |(an+1)/(an)|=3/2
n→[infinity]
e) lim |(an+1)/(an)|=3
n→[infinity]
f) lim nth root(|(an)|=1/2
n→[infinity]
In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.
In case a, since the limit of the ratio of consecutive terms is 1, the series is convergent and its sum is equal to the limit of the sequence of partial sums of the series.In case b, since the limit of the nth root of the absolute value of the terms is 2/3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case c, since the limit of the ratio of consecutive terms is 0.8, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case d, since the limit of the ratio of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case e, since the limit of the ratio of consecutive terms is 3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case f, since the limit of the nth root of the absolute value of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit.Learn more about Convergent here:
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What is the value of 5 + 5.3^4?
810
410
O65
120
Therefore , the solution of the given problem of expression comes out to be 794.0481.
Describe expression.combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.
• 3 x/2 variable is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.
Here,
Given : 5 + [tex](5.3)^{4}[/tex]
=> 5 + (5.3)*(5.3)*(5.3)*(5.3)
=> 789.0481 + 5
=> 794.0481
Therefore , the solution of the given problem of expression comes out to be 794.0481.
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Reduce 22/154
to its lowest form.
22/154=11/77=1/7
1/7 is the lowest form
Fill in the blank question.
Miss Wade's science class of 20 students is going on a field trip to the zoo. Each student will also take a train ride around the zoo. Mr. Sexton's class of 25 students is going on a field trip to the state park and will take a canoe trip. Admission to the zoo is twice that of the state park's entry fee as shown in the table. Each group will spend the same total amount of money.
Answer:
The total cost of the science class trip to the zoo is $1200
Step-by-step explanation:
The cost of the science class trip to the zoo is $1200, and the cost of Mr. Sexton's class trip to the state park is $1000.
What does ∈ mean in math?
This is a symbol in mathematics that represents "to the power of" or "exponent".
It is used to indicate that a number or expression is being multiplied by itself a certain number of times. For example, if the expression 2aˆ3 is written, it means that 2 is being multiplied by itself 3 times, or 2x2x2. In other words, 2aˆ3 = 2x2x2 = 8.
The number to the right of the aˆ symbol is called the "exponent". The number or expression to the left of the aˆ symbol is called the "base". When a number is raised to the power of one, it is equal to itself. Any number to the power of zero is equal to one. The exponent can be a positive, negative, or fractional number.
Exponents are used to simplifying calculations and can be used to represent large numbers in a more concise form.
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Find the length of the third side. If necessary, round to the nearest tenth
Answer:
I'm pretty sure the answer for this is 28 :))
Write the ratio. Explain what the ratio means.
butterflies : caterpillars
For every _
butterfly/butterflies, there is/are _
caterpillar(s).
The ratio is 1:4, which means for every 1 butterfly, there are 4 caterpillars.
This ratio represents the relationship between the number of butterflies and the number of caterpillars. In this case, the ratio is saying that for every 1 butterfly, there are 4 caterpillars. This could mean that for every butterfly that is observed, there are 4 caterpillars that are also present or for every butterfly that is caught, there are 4 caterpillars that are also caught.
This ratio may also indicate that for every butterfly that is born, 4 caterpillars are also born. It could also indicate the population ratio of butterflies to caterpillars in a specific habitat.
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Pepito bought 2 t-shirt at 149.95 each and a pair of pants for php 30.75, if her money was a 200 pesos bill. How much was her change?
If pesos had it would be so pesos have 169.25 dollars left 200-30.75=169.25
Define an exponential function, f(x), which passes through the points (0,125) and (3,8). Enter your answer in the form a*b^x
Answer:
Step-by-step explanation:
put (0, 125) in a*b^x, we get a = 125, then put (3,8) in 125*b^x, we get 125*b^3=8
b^3=8/125
b=2/5
then the answer is 125*(2/5)^x
Interest earned- $25
principal- $500
interest rate -???
time- 2 years
what is the interest rate
The interest rate is 2.5 %.
Simple interest is the form of interest used for short term loans, such as one receives at pawnshops or from loan sharks. It is governed by the formula:
I = Prt
where I is the amount of interest, P is the principal (amount of money borrowed), r is the interest rate (per year), and t is the time (expressed in years).
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
I = $25, P = $500, r = ?, t = 2 years
∴ I = Prt
∴ r = I / Pt
∴ r = 25 / ( 500 * 2)
∴ r = 25 / 1000
∴ r = 0.025
∴ r = 0.025 * 100 %
∴ r = 2.5 %
Therefore, the interest rate is 2.5 %.
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Please help me with my HW
Answer: 4k^7
Step-by-step explanation:
for k(x)=4÷5x-6,determine k^-1(8)
The value of k⁻¹(8) in for k(x) = 4 ÷ 5x - 6 is 2/35.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, k(x) = 4 ÷ 5x - 6.
k(x) = (4/5x) - 6.
Let, y = k(x).
y = (4/5x) - 6.
(4/5x) = y + 6.
1/x = 5(y + 6)/4.
x = 4/{5(y + 6)}.
y = 4/{5(x + 6)}.
k⁻¹(x) = 4/{5(x + 6)}.
k⁻¹(8) = 4/{5(8 + 6)}.
k⁻¹(8) = 4/{5(14)}.
k⁻¹(8) = 4/70.
k⁻¹(8) = 2/35.
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Question
Joshua's goal is to sell more than 20 items at a farmers' market. So far, he has sold 6 items. Each customer buys 2 items.
Let c represent the number of additional customers Joshua must have to meet his goal.
Drag and drop the answer into the box to correctly complete the statement.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Joshua needs to have more than Response area additional customers to meet his goal.
Joshua will need 7 additional customers.
How to determine the number of customers he needs?
The parameters that will help us to determine the number of customers is give as follows:
Joshua's goal is to sell more than 20 items at a farmers' market. So far, he has sold 6 items. Each customer buys 2 items.
Since Joshua's goal is to sell more than 20 items at a farmers' market and he has sold 6 items. and If each of his customers buys 2 items, the number of additional customers needed will be:
= (20 - 6) / 2
This is given as 14 / 2
The the number of customers needed = 7
In conclusion He will need 7 additional customers.
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What is the domain of the following function?
Therefore , the solution of the given problem of equation comes out to be each diagonal measures 8.4 units in length..
Define equation.An equation is a mathematical representation of two equal variables, one on each side of a "equals" sign. Everyday issues can be resolved with equations. We commonly look for pre algebra help to deal with problems in real life. Pre-algebra contains the fundamental concepts of mathematics.
Here,
Given: 16x + 2 = 36x - 6
8 = 20x
x = 8/20,
simplifying to 2/5, or 0.4
You would set the two equations equal to one another and find x because a rectangle's diagonals are congruent.
Re-enter the value of x into a single of the equations.
=>16(0.4) + 2
=>6.4 + 2
=>8.4
To make sure, confirm with the other diagonal.
=>36(0.4) - 6
=>14.4 - 6
=>8.4
Each diagonal measures 8.4 units in length..
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The complete question is "To find the diagonal x value by the given equation 16x + 2 = 36x - 6 "
Hello good morning do anyone think they could help please
Answer:2
Step-by-step explanation:
Solve the proportion below. 7/x = 19/114 x=____
A. 8
B. 4
C. 28
D. 24
Can someone help me please? Picture attached
a = [tex]6\sqrt{5}[/tex] is the right angled triangle's third side when the right angle triangle's opposite sides are 18 and 12, respectively.
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
given
by pythagoras theorem
c2 = a2 + b2
18*18 = a2 + 12*12
324 - 144 = a2
a2 = 180
a = [tex]6\sqrt{5}[/tex]
a = [tex]6\sqrt{5}[/tex] is the right angled triangle's third side when the right angle triangle's opposite sides are 18 and 12, respectively.
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Is polynomial Y⁴+ 4y²+ 5 have zeroes or not?
The polynomial Y⁴+ 4y²+ 5 does not have zeroes.
What is polynomial?Polynomials are an essential component of the "language" of mathematics and algebra. They are used to express numbers as a result of mathematical operations in nearly every field of mathematics. Polynomials can also be used as "building blocks" in other kinds of mathematical expressions, such as rational expressions.
Polynomials can be used to represent a wide range of everyday mathematical processes. A polynomial can be formed by adding the costs of items on a grocery bill. A polynomial can be used to calculate the distance travelled by a vehicle or object. Polynomials can be used to calculate the perimeter, area, and volume of geometric figures. These are just a few of the many uses for polynomials.
We know that, (a +b)² = a² + b² + 2ab
Here given that,
⇒ y⁴ + 4y² + 5 = 0
⇒ y⁴ + 4y² + 4 + 1 = 0
⇒ (y² + 2)² + 1 = 0
Because the first term is a square, the expression (y² + 2)² + 1 will never be zero for any value of y.
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Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently.
Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300.
PLS HELP ME IM ABT TO CRY!!!! 100 PTS
Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn.
Salesman C does not earn any commission. His weekly salary is $900.
If Salesman A has exactly ____ sales, he will reach his maximum weekly commission.
Answer:
Sales = 20
Step-by-step explanation:
Simply make the equation "1300 = 65s" to solve the problem
1300 = 65s
Divide both sides by 65.
1300/65 = 65s/65
Divide 1300 by 65 to get 20.
20=s
Swap sides so that all variable terms are on the left-hand side.
s=20
Deshad runs a river tubing company that serves 300 customers a day during sunny, summer days. He knows that 45% of the customers rent life jackets. Suppose that Deshad calculates the daily proportion p ^ on top of customers who rent life jackets from his sample of 300. We can assume the customers each day represent a random sample
Here acccording to the question,We are examining the conditions under which the sampling distributions of the sample proportions given.
What is sampling distribution?
Sampling distribution is a statistic that determines the probability of an event based on data from a small group within a large population. Its primary purpose is to establish representative results of small samples of a comparatively larger population. Since the population is too large to analyze, you can select a smaller group and repeatedly sample or analyze them. The gathered data, or statistic, is used to calculate the likely occurrence, or probability, of an event.
Sampling distribution According to the given ScenarioWe are examining the conditions under which the sampling distributions of the sample proportions appear uniform, roughly normal, skewed to the left or skewed to the right.
When np10 and n(1p)10, where n is the sample size and p is the sample of proportions, are true, we know that the sampling proportions of the sample distributions will have a normal shape.
Aforementioned that our sample size is 300 people and that p = 0.45, we can use the given data to calculate
Successes anticipated: np= 300(0.45) = 135 10
Failures predicted: n(1p)=300 (10.45)=165 10
Since both of these statements are accurate, sample distribution sampling proportions will have a normal shape.
Because we anticipate each sample to have at least 10 successes and 10 failures, we have a normal sampling distribution.
As a result, the sample distribution has a roughly normal shape.
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When can parallelism make your algorithms run faster when could it make your algorithms run slower?
When an algorithm necessitates extensive sharing of instantaneous results, parallelism slows it down. Because there are multiple independent parallel processes and the right number of threads, parallelism will speed up an algorithm.
What algorithm is parallelizable?The ones with data dependencies are the most challenging. It will be exceedingly challenging, for instance, if you are dealing with a vector and the input for the computation at point n depends on the output at position n-1.
When this occurs, you must comprehend what the original algorithm is doing and take an alternative approach. For the aforementioned case, it might be a difficulty with digital signal processing including a feedback-containing digital filter. These are challenging to parallelize, but that is not the sole solution. Instead, you might use the filter and signal's fast Fourier transforms, multiply them, and then perform the inverse transform. All of these operations can be partially parallelized.
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What is 0.632 as a fraction? Move numbers to the blanks to complete the fraction.
8
79
125
313
457
495
632
999
Answer:
Step-by-step explanation:
Converting 0.632 to a fraction, Step-by-Step
Step 1:
The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:
\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}
1×1000
0.632×1000
=
1000
632
Step 3:
Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:
\frac{632}{1000} = \frac{79}{125}
1000
632
=
125
79
Given the table of values, determine the the constant of proportionality, then write the equation of the proportion.
The constant of proportionality is 9 and equation of the proportion.
is y= 10x.
What is Constant of Proportionality?If the ratio of one variable to the other is constant, then there is a proportional relationship between the two variables. If x and y are in a proportional relationship, then the ratio of y to x is the constant of proportionality.
Given:
As, we know using the Constant of Proportionality
y = kx
or, k = y/x where k is Constant of Proportionality.
Then, from the table we have
k = 90/9
k= 10
Thus, y = kx
or, y= 10x
Hence, the equation of the proportion is y= 10x.
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HELPPP 1. Write an equation of the ellipse with foci (0,14) and co-vertices at (±4,0).
The equation of the ellipse with foci (0,14) and co-vertices at (±4,0) is [tex]x^2/16+y^2/36[/tex].
Define ellipse.An ellipse is a geometric shape that is defined as the set of points such that the sum of the distances between the points and two fixed points (foci) is constant. It is a type of conic section and is defined by the equation:
[tex](x^2/a^2) + (y^2/b^2) = 1[/tex]
Where a and b are the semi-major and semi-minor axes, respectively. An ellipse can also be defined as the shape that results from the intersection of a plane and a cone at an angle that is not perpendicular to the base of the cone.
[tex]c=14, b=4, a²=b²+c²== > a=2√9\\x^2/b^2 + y^2/a^2\\x^2/16+y^2/36[/tex]
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The two expressions below have the same value when rounded to the nearest hundredth
log5b log948
what is the approximate value of logb to the nearest hundredth
0.93
1.23
9.16
65.53
The approximate value of ㏒(b) to the nearest hundredth is 1.23.
Logarithms:The other method to write exponents in mathematics is using logarithms. A number's base-based logarithm is equal to some other number. A logarithm performs exponentiation's exact opposite function.
In Logarithms, ㏒ₐ(b) = ㏒(b)/ ㏒(a)
Given that
The two expressions below have the same value when rounded to the nearest hundredth
=> ㏒₅ (b) = ㏒₉ (48)
As we know ㏒ₐ(b) = ㏒(b)/ ㏒(a)
=> ㏒₅ (b) = ㏒(b)/㏒(5)
=> ㏒(b)/㏒(5) = ㏒₉ (48)
=> ㏒(b) = ㏒₉ (48) ㏒(5)
=> ㏒(b) = (1.7618)(0.6989)
=> ㏒(b) = 1.23132202
=> ㏒(b) = 1.23
Therefore,
The approximate value of ㏒(b) to the nearest hundredth is 1.23.
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Solve the following equation, and check your solution. Show all of your work.
-17+n/5=33
I’ve added my work attached :)
n = 250
What is the answer of 2x^2 4x 6 0?
The answer of the equation "2x^2 - 4x - 6 = 0" is -1 and 3.
The equation is solved using factorization:
2x^2 - 4x - 6 = 0 , given equation
2x^2 - 6x + 2x - 6 = 0 , factorizing
2x(x - 3) + 2 ( x - 3 ) = 0 , taking 2x common from the first two terms and 2 common from the last two terms
(2x + 2) (x - 3) = 0
now solving further
( 2x + 2 ) = 0 & ( x - 3 ) =0
2x = (0 - 2) , x = (0 + 3)
2x = (-2) , x = 3
x = (-2/2)
x = -1
Thus, the equation gives the solution as x = -1 and x = 3.
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Jamal’s test scores are 84, 88, 92, and 94. Natalia’s test scores are 86, 88, 90, 92. Who has the greater test average and who has the most consistent test scores?
Jamal’s test scores are 84, 88, 92, and 94. Natalia’s test scores are 86, 88, 90, 92. Jamal has a greater test average than Natalia. Natalia has more consistent test scores than Jamal.
To find the test average, you add up all the test scores and divide by the number of test scores.
Jamal's average: (84+88+92+94) / 4 = 89.50
Natalia's average: (86+88+90+92) / 4 = 89
Jamal has a greater test average.
To find the consistency of test scores, you can use the range, which is the difference between the highest and lowest scores.
Jamal's range: 94-84=10
Natalia's range: 92-86 = 6
Natalia has the most consistent test scores, as the range of her scores is smaller than Jamal's.
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Based on the following calculator output, determine the population standard
deviation of the dataset, rounding to the nearest 100th if necessary.
1-Var-Stats
-
86.7142857143
Σæ = 607
Σχ2 = 59459
Sx= 33.72296095
o2 = 31.2213950714
n=7
minX = 52
Q₁ = 55
Med=87
Q3 = 110
maxX = 138
Therefore , the solution of the given problem of standard deviation comes out to be 67.15=σx .
Define standard deviation.It tells about how dispersed the data is is indicated by the standard deviation. It expresses the deviation of each observed variable from the mean. Any distribution will have roughly 95% of its values within two standard deviations of the mean.
Here,
We know population SD= Σ(xi-mu)2/n where mu is the population mean and n is the number of observation.
Here
we have n=7 and mu can be taken as x- =310.142
Standard deviation = SD=Σ(xi-mu)2/n
=>(Σxi2/n)-x-2
=>(704883/7)-(310.14)2=67.15=σx
Therefore , the solution of the given problem of standard deviation comes out to be 67.15=σx .
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How do you plot a graph step by step?
Plotting a graph step by step is mentioned below.
Define Graph.In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
What is Bar graph?Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.
There are a few steps to follow when plotting a graph:
Identify the variables in the problem and choose which one to plot on the x-axis and which one to plot on the y-axis.Determine the range of values for each variable. This will help you decide how big to make the scales on the x and y-axis.Choose a scale for each axis. The scale should be such that all the points in the problem can be plotted on the graph. A typical scale is to have equal intervals between each tick mark on the axis.Plot the points on the graph by locating their x-coordinate and y-coordinate on the x-axis and y-axis, respectively, and connecting them with a dot.Draw the x- and y-axes and label them with the appropriate units and ranges. Be sure to include a label on the graph itself so that it's clear what the graph represents.Plot any lines or curves that are also a part of the problem. This could be a line of best fit, a linear regression line, a polynomial function or any other lines or curves that the problem calls for.Once you finished with the line/curve, it is a good practice to give the graph a title and to label the axis with the units used.Lastly, review the graph and ensure that it is accurate and clearly presents the information from the problem.To know more about graph visit:
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