# Recent questions tagged questions

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In a paragraph, What is the difference between neural networks and regression?
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Consider the following quadratic number pattern: $$6 ; 10 ; 18 ; \ldots \ldots$$1. Write down the following two terms of the pattern.2. Determine the equation of the ge...
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What if I need help or have questions about using Acalytica?
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How do we train children's ability to ask curiosity-driven questions?
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Create a quiz with 5 multiple choice questions that assess students' understanding of neural networks. Indicate the correct answer.
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How should AI assistants respond to questions about public figure viewpoints? E.g. Should they be neutral? Should they refuse to answer? Should they provide sources of so...
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how many four-digit numbers contain the digit 5 or 7 (or both) theorem
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Here are the first 5 terms of a sequence. $\begin{array}{lllll}29 & 25 & 21 & 17 & 13\end{array}$Find an expression, in terms of $$n$$, for the $$n$$th term of this seq...
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List 10 multiple of 51
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How can educators use chatGPT to implement the Socratic method of teaching and learning?
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Create a list of the most asked data science interview questions
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Create a list of 8 questions for my interview with the South African Science and Innovation Minister
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Create a list of 8 questions for my interview with a science fiction author:
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What are the central questions an EdTech identity management system (IDM) seeks to answer?
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In summary, what did Angela Duckworth say about grit?
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List the 10 questions in Angela Duckworth's grit scale
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List the 7 questions in Angela Duckworth's grit scale
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What are the 3 most asked questions in mathematics in South Africa?
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What are the metaphysical questions in statistics?
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615
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Why do people visit Acalytica?
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The 3rd and 12th terms of an arithmetic progression are 12 and $$-24$$ respectively. Determine the 49th term.
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The 11th term of an arithmetic sequence is 32 and the sum of the first 11 terms is 187 . Calculate the 21st term.
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$$2 ; x ; y$$ are the first three terms of an arithmetic sequence. If the 2nd term is decreased by 1 , the three terms will form a geometric sequence. Calculate $$x$$ and...
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The 9 th term and the 6 th term of an geometric sequence are 80 and 10 respectively.(a) Find the first term and the constant ratio.(b) Find the number of terms if the las...
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Determine the first three terms of each of the following geometric sequences of which:(a) the 6th term is 28 and 11th term is 896 .(b) the 2 nd term is 3 and the 4 th ter...
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The first term and the last term of an arithmetic series is 5 and 61 respectively while the sum of all the terms is 957 . Determine the number of terms in the series.
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The 13th and 7th terms of an arithmetic sequence are 15 and 51 respectively.(a) Which term is equal to $$-21$$ ?(b) Show that 66 is not a term of the sequence.
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The 15 th and 3rd terms of an arithmetic sequence are 100 and 28 respectively. Determine the 100th term.
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Determine the first three terms of each of the following arithmetic sequences of which:(a) the 3rd term of the sequence is 23 and the 26th term is 230 .(b) the 5 th term ...
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Determine the first three terms of the geometric sequence of which the 7th term is 1458 and the 4th term is 54.
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The sum of the first 12 terms of an arithmetic series is 96 . The 3rd and 6th terms add up to 12 . Determine the first term and the common difference.
371
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Determine the first 3 terms of an arithmetic sequence if the 5 th term of the sequence is 12 and the 14 th term is $$-33$$. Hence determine the 40th term.
444
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Determine $$m$$ in each of the following arithmetic series:(a) $$\quad \sum_{k=1}^m(2)^{8-k}=255 \frac{1}{2}$$(b) $$\quad \sum_{p=1}^m(-8)\left(\frac{1}{2}\right)^{p-1}=-... 413 views 0 answers Calculate the sum of the first 12 terms of the geometric sequence$\frac{1}{4} ;-\frac{1}{2} ; 1 ; \ldots .$ 508 views 1 answers \(t+1 ; 1-t ; 1-5 t ; \ldots$$ are the first three terms of a geometric sequence.(a) Determine the numerical value of $$t$$ where $$t \neq 0$$.(b) Determine the sequence....
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$$x-4 ; x+2 ; 3 x+1 ; \ldots$$ are the first three terms of a geometric sequence. Determine the sequence if $$x$$ is positive.
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Consider the following sequences:sequence $$1: \quad \sqrt{2} ; 2 \sqrt{2} ; 3 \sqrt{2} ; \ldots \ldots . \quad$$ sequence $$2: \sqrt{2} ; 2 ; 2 \sqrt{2} ; \ldots \ldots ... 332 views 0 answers Determine the 9th term for each of the following geometric sequences:(a) \(128 ; 64 ; 32 ; \ldots .$$.(b) 0,$$25 ; 0,5 ; 1 ; \ldots$$.(c) $$\frac{4}{9} ; 1 \frac{1}{3} ; ... 233 views 0 answers Determine the general term for each of the following geometric sequences:(a) \(2 ;-1 ; \frac{1}{2} ; \ldots$$.(b) $$2 ; 8 ; 32 ; \ldots .$$.(c) $$-\frac{2}{3} ; 2 ;-6 ; \... 544 views 1 answers \(k+1 ; k-1 ; 2 k-5$$ are the first three terms of a geometric sequence. Calculate the value of $$k$$ and hence determine the possible sequences.
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$$x+3 ; 2 x+6 ; 3 x+9 ; \ldots$$ are the first three terms of an arithmetic sequence.(a) Determine the 10th term in terms of $$x$$.(b) Determine the $$n$$th term in terms...
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$$p ; 2 p+2 ; 5 p+3 ; \ldots$$ are the first three terms of an arithmetic sequence.(a) Calculate the value of $$p$$.(b) Determine the sequence.(c) Find the 49th term.(d) ...
Given the arithmetic sequence: $$-29 ;-23 ;-17 ; \ldots$$.(a) Determine the 31st term.(b) Determine which term is equal to 31 .
Determine the 38th term for each of the following arithmetic sequences:(a) $$-4 ;-8 ;-12 ; \ldots$$.(b) $$2 ;-1,5 ;-5 ; \ldots$$(c) $$99 ; 88 ; 77 ; \ldots$$.(d) $$6 ; \f... 350 views 0 answers Determine the general term of the following arithmetic sequences:(a) \(\quad-1 ; 3 ; 7 ; \ldots$$.(b) $$4 ;-2 ;-8 ; \ldots \ldots$$(c) $$1 ;-1 ;-3 ; \ldots$$(d) $$99 ; 10... 313 views 1 answers \(x ; 4 x+5 ; 10 x-5$$ are the first three terms of an arithmetic sequence. Determine the value of $$x$$ and hence the sequence.
Consider the following pattern that emerges when you add the terms of a linear number pattern.First the linear number pattern: $$3 ; 7 ; 11 ; 15 ; \ldots$$Line 1: $$\quad... 214 views 0 answers Consider the following number pattern: \(\quad-4 ;-10 ;-18 ;-28 ; \ldots$$(a) Determine the general term and hence the value of the 25 th term.(b) Determine which term wi...