Sequences and Series Examples
1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P. (b) a-k, b-k, c-k a..
1 , A 2 ,.....,A n are called the n arithmetic means between a and b. (vii) The sum of n A.M.s between given numbers a and b is equal to n times the A.M. between a and b. (viii) If a, b, c are in A.P., then for any k: (a) a+k, b+k, c+k are in A.P. (b) a-k, b-k, c-k a..Matrices and Determinants Summary
>If A, B and C are the matrices which can be multiplied then (a) Matrix multiplication is not commutative, i.e., AB BA (always) (b) Associative law holds good for matrix multiplication, i.e., (AB)C = A(BC) (c) Matrix multiplication is distributive with respect to addition A(B + C) = AB + AC or (A +..
>If A, B and C are the matrices which can be multiplied then (a) Matrix multiplication is not commutative, i.e., AB BA (always) (b) Associative law holds good for matrix multiplication, i.e., (AB)C = A(BC) (c) Matrix multiplication is distributive with respect to addition A(B + C) = AB + AC or (A +..Matt is 212 times taller than the center table on which he is standing..
Matt is 2 1 2 times taller than the center table on which he is standing. If the height of the center table is 2 feet, then find Matt's height. => 5 feet or 4 feet or 3 feet or 2 feet..
Evaluate the expression a× 4 for the following values.aa× ..
Evaluate the expression a × 4 for the following values. a a × 4 3 4 5 6 => 34, 44, 54, and 64 or 7, 8, 9, and 10 or 12, 16, 20, and 24 or 24, 20, 16, and 12..
A medical researcher wishes to test the effects of two diets and the t..
A medical researcher wishes to test the effects of two diets and the time of day on the sodium level in a person's blood. Twenty people are randomly selected, and five are randomly assigned to each of the four groups. Find F A × B and analyze the data shown in the tab..
Tom wants to make some kites. It will take 15 minutes to gather all th..
Tom wants to make some kites. It will take 15 minutes to gather all the things required and 5 minutes to make each kite. The table shows the relationship between the number of kites and the time taken to make them. Use the rate of change to identify a linear equation for the dat..
When the given spinner is spun, the theoretical probability of spinnin..
When the given spinner is spun, the theoretical probability of spinning 'A' is 2 6 . Tom spun the spinner four times and recorded the results in the table given below. Find the experimental probability and choose the expression that best compares the theoretical and experimental..
When the given spinner is spun, the theoretical probability of spinnin..
When the given spinner is spun, the theoretical probability of spinning ' A' is 2 6 . Tom spun the spinner four times and recorded the results in the table shown. Find the experimental probability and choose the expression that best compares the theoretical and experimental prob..
Revenues of XYZ Company are shown in the table, where t represents tim..
Revenues of XYZ Company are shown in the table, where t represents time in years since 1997. Find the exponential model for the data. Years since 1997( t ) 0 1 2 3 4 Revenue in billion $ (R) 3 3.18 3.37 3.57 3.79 => R = 3(1.16) t or R = 3(1.06) t or R = 3.18(1.16) t or R = 3.18(..
The theoretical probability of getting an even number when a die is ro..
The theoretical probability of getting an even number when a die is rolled is 3 6 . Jack rolled a die 5 times and recorded the results in the table given below. Find the experimental probability and choose the expression that best compares the theoretical and experimental probab..
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