1) Equations for two lines L1 and L2 are given. Find the angle between L1 and L2.
L1: ? = 7 + 2?, ? = 8 − 4?, ? = −9 + ?
L2: ? = −8 − ?, ? = 3 − 3?, ? = 4 + 3?
2) Find polar form of complex number z :
?) ? = 4√3 − 4?
?) ? = 2√3 − 2i
In: Math
Use the Tornadoes data. Your TASK is to use the months of July and August to predict the tornado activity in October. Answer questions 5 to 7. Choose the best fitting answer. Note: numbers are truncated unless specified.
5. If July had 100 tornadoes and August had 200 tornadoes, what would be your prediction for the number of tornadoes in October?
6. What is the approximate error of this prediction?
7. The intercept here has a value of 5.17. What is the STATISTICAL interpretation of this number?
Tornadoes and Deaths by Year and Month (1950-1994)
Year Total Tornadoes Tornadoes by Month Total Deaths Deaths by Month
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
1950 201 7 20 21 15 61 28 23 13 3 2 4 4 70 1 45 1 12 2 6 0 0 0 0 0 3
1951 260 2 10 6 26 57 76 23 27 9 2 12 10 34 0 1 0 2 7 9 5 0 8 0 1 1
1952 240 12 27 43 37 34 34 27 16 1 0 6 3 230 0 10 209 4 2 2 2 1 0 0 0 0
1953 422 14 16 40 47 94 111 32 24 5 6 12 21 519 0 3 24 36 163 244 0 0 0 0 0 49
1954 550 2 17 62 113 101 107 45 49 21 14 2 17 36 0 2 10 2 9 5 0 1 3 2 0 2
1955 593 3 4 43 99 148 153 49 33 15 23 20 3 129 0 0 5 7 106 2 5 0 2 1 1 0
1956 504 2 47 31 85 79 65 92 42 16 29 7 9 83 0 8 1 67 4 0 1 2 0 0 0 0
1957 858 17 5 38 216 228 147 55 20 17 18 59 38 193 13 0 1 30 87 14 0 0 2 2 25 19
1958 564 11 20 15 76 68 128 121 46 24 9 45 1 67 0 13 0 4 0 43 1 1 1 4 0 0
1959 604 16 20 43 30 226 73 63 38 58 24 11 2 58 3 21 9 1 8 2 0 0 14 0 0 0
1960 616 9 28 28 70 201 125 42 48 21 18 25 1 46 0 0 0 7 34 3 0 1 0 1 0 0
1961 697 1 31 124 74 137 107 77 27 53 14 36 16 52 0 0 7 4 23 2 0 0 15 0 1 0
1962 657 12 25 37 41 200 171 78 51 24 11 5 2 30 1 0 17 2 4 0 0 6 0 0 0 0
1963 463 15 6 48 84 71 90 62 26 33 13 15 0 31 1 0 8 16 1 0 0 2 3 0 0 0
1964 704 14 2 36 157 134 137 63 79 25 22 17 18 73 10 0 6 15 16 0 0 2 0 22 0 2
1965 897 21 32 34 123 273 147 85 61 64 16 34 7 301 0 0 2 268 17 7 0 1 0 1 5 0
1966 585 1 28 12 80 98 126 100 58 22 29 20 11 98 0 0 58 12 0 19 3 0 0 6 0 0
1967 926 39 8 42 149 116 210 90 28 139 36 8 61 114 7 0 3 73 3 6 1 2 5 4 0 10
1968 660 5 7 28 102 145 136 56 66 25 14 44 32 131 0 0 0 40 72 11 2 2 0 0 3 1
1969 608 3 5 8 68 145 137 98 70 20 26 5 23 66 32 0 1 2 4 7 0 19 0 0 0 1
1970 654 9 16 25 117 88 134 82 55 54 50 10 14 73 0 0 2 30 26 6 3 0 0 6 0 0
1971 889 19 83 40 75 166 199 100 50 47 38 16 56 159 1 134 2 11 7 1 1 0 0 0 0 2
1972 741 33 7 69 96 140 114 115 59 49 34 17 8 27 5 0 0 16 0 2 0 2 0 0 2 0
1973 1102 33 10 80 150 250 224 80 51 69 25 81 49 89 1 0 17 10 35 3 1 4 3 0 12 3
1974 945 24 23 36 267 144 194 59 107 25 45 13 8 366 2 0 1 317 10 31 0 0 0 5 0 0
1975 919 52 45 84 108 188 196 79 60 34 12 39 22 60 12 7 12 13 5 6 2 2 0 0 0 1
1976 834 12 36 180 113 155 169 84 38 35 11 0 1 44 0 5 21 1 8 3 2 1 3 0 0 0
1977 852 5 17 64 88 228 132 99 82 65 25 24 23 43 0 2 0 26 4 0 1 6 1 1 0 2
1978 789 23 7 17 107 213 148 143 65 20 7 9 30 53 2 0 0 4 7 17 11 1 6 0 0 5
1979 855 16 4 53 123 112 150 132 126 69 47 21 2 84 0 0 1 58 2 8 1 5 2 7 0 0
1980 866 5 11 41 137 203 217 95 73 37 43 3 1 28 0 0 2 4 8 7 5 0 1 1 0 0
1981 782 2 25 33 84 187 223 98 64 26 32 7 1 24 0 2 1 13 0 8 0 0 0 0 0 0
1982 1047 18 3 60 150 329 196 95 34 38 9 19 96 64 1 0 6 30 14 4 0 0 2 0 0 7
1983 931 13 41 71 65 249 178 99 76 19 13 49 58 34 2 1 0 6 14 2 4 0 0 0 0 5
1984 907 1 27 73 176 169 242 72 47 17 49 30 4 122 0 0 64 33 6 14 0 0 0 4 1 0
1985 684 2 7 38 134 182 82 51 108 40 18 19 3 94 0 0 2 5 78 3 0 3 0 0 3 0
1986 765 0 30 76 84 173 134 88 67 65 26 17 5 15 0 2 6 2 1 0 3 1 0 0 0 0
1987 656 6 19 38 20 126 132 163 63 19 1 55 14 59 0 6 1 1 31 2 0 1 0 0 11 6
1988 702 17 4 28 58 132 63 103 61 76 19 121 20 32 5 0 1 4 3 0 0 3 1 0 14 1
1989 856 14 18 43 82 231 252 59 36 31 30 57 3 50 0 0 1 0 9 5 0 0 0 4 31 0
1990 1133 11 57 86 108 243 329 106 60 45 35 18 35 53 0 1 3 0 5 11 0 29 0 2 0 2
1991 1132 29 11 157 204 335 216 64 46 26 21 20 3 39 1 0 13 21 0 1 1 0 0 0 2 0
1992 1297 15 29 55 53 137 399 213 115 81 34 146 20 39 0 0 5 0 0 1 0 3 0 4 26 0
1993 1173 17 34 48 85 177 313 242 112 65 55 19 6 33 0 3 5 10 2 1 0 6 2 4 0 0
1994 1082 13 9 58 205 161 234 155 120 30 51 42 4 69 0 0 40 12 0 3 3 4 0 0 7 0In: Statistics and Probability
Use the Tornadoes data and your statistical expertise to answer the questions: Is it reasonable to claim that on average there are more than 45, tornado-related deaths in the month of April (per year)?
9. What test/procedure did you perform?
10. What is the P-Value/margin of error?
11. Statistical Interpretation
12. Conclusion
Paste content below in a text document and then open that text document with excel.
Tornadoes and Deaths by Year and Month (1950-1994)
Year Total Tornadoes Tornadoes by Month Total Deaths Deaths by Month
Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec
1950 201 7 20 21 15 61 28 23 13 3 2 4 4 70 1 45 1 12 2 6 0 0 0 0 0 3
1951 260 2 10 6 26 57 76 23 27 9 2 12 10 34 0 1 0 2 7 9 5 0 8 0 1 1
1952 240 12 27 43 37 34 34 27 16 1 0 6 3 230 0 10 209 4 2 2 2 1 0 0 0 0
1953 422 14 16 40 47 94 111 32 24 5 6 12 21 519 0 3 24 36 163 244 0 0 0 0 0 49
1954 550 2 17 62 113 101 107 45 49 21 14 2 17 36 0 2 10 2 9 5 0 1 3 2 0 2
1955 593 3 4 43 99 148 153 49 33 15 23 20 3 129 0 0 5 7 106 2 5 0 2 1 1 0
1956 504 2 47 31 85 79 65 92 42 16 29 7 9 83 0 8 1 67 4 0 1 2 0 0 0 0
1957 858 17 5 38 216 228 147 55 20 17 18 59 38 193 13 0 1 30 87 14 0 0 2 2 25 19
1958 564 11 20 15 76 68 128 121 46 24 9 45 1 67 0 13 0 4 0 43 1 1 1 4 0 0
1959 604 16 20 43 30 226 73 63 38 58 24 11 2 58 3 21 9 1 8 2 0 0 14 0 0 0
1960 616 9 28 28 70 201 125 42 48 21 18 25 1 46 0 0 0 7 34 3 0 1 0 1 0 0
1961 697 1 31 124 74 137 107 77 27 53 14 36 16 52 0 0 7 4 23 2 0 0 15 0 1 0
1962 657 12 25 37 41 200 171 78 51 24 11 5 2 30 1 0 17 2 4 0 0 6 0 0 0 0
1963 463 15 6 48 84 71 90 62 26 33 13 15 0 31 1 0 8 16 1 0 0 2 3 0 0 0
1964 704 14 2 36 157 134 137 63 79 25 22 17 18 73 10 0 6 15 16 0 0 2 0 22 0 2
1965 897 21 32 34 123 273 147 85 61 64 16 34 7 301 0 0 2 268 17 7 0 1 0 1 5 0
1966 585 1 28 12 80 98 126 100 58 22 29 20 11 98 0 0 58 12 0 19 3 0 0 6 0 0
1967 926 39 8 42 149 116 210 90 28 139 36 8 61 114 7 0 3 73 3 6 1 2 5 4 0 10
1968 660 5 7 28 102 145 136 56 66 25 14 44 32 131 0 0 0 40 72 11 2 2 0 0 3 1
1969 608 3 5 8 68 145 137 98 70 20 26 5 23 66 32 0 1 2 4 7 0 19 0 0 0 1
1970 654 9 16 25 117 88 134 82 55 54 50 10 14 73 0 0 2 30 26 6 3 0 0 6 0 0
1971 889 19 83 40 75 166 199 100 50 47 38 16 56 159 1 134 2 11 7 1 1 0 0 0 0 2
1972 741 33 7 69 96 140 114 115 59 49 34 17 8 27 5 0 0 16 0 2 0 2 0 0 2 0
1973 1102 33 10 80 150 250 224 80 51 69 25 81 49 89 1 0 17 10 35 3 1 4 3 0 12 3
1974 945 24 23 36 267 144 194 59 107 25 45 13 8 366 2 0 1 317 10 31 0 0 0 5 0 0
1975 919 52 45 84 108 188 196 79 60 34 12 39 22 60 12 7 12 13 5 6 2 2 0 0 0 1
1976 834 12 36 180 113 155 169 84 38 35 11 0 1 44 0 5 21 1 8 3 2 1 3 0 0 0
1977 852 5 17 64 88 228 132 99 82 65 25 24 23 43 0 2 0 26 4 0 1 6 1 1 0 2
1978 789 23 7 17 107 213 148 143 65 20 7 9 30 53 2 0 0 4 7 17 11 1 6 0 0 5
1979 855 16 4 53 123 112 150 132 126 69 47 21 2 84 0 0 1 58 2 8 1 5 2 7 0 0
1980 866 5 11 41 137 203 217 95 73 37 43 3 1 28 0 0 2 4 8 7 5 0 1 1 0 0
1981 782 2 25 33 84 187 223 98 64 26 32 7 1 24 0 2 1 13 0 8 0 0 0 0 0 0
1982 1047 18 3 60 150 329 196 95 34 38 9 19 96 64 1 0 6 30 14 4 0 0 2 0 0 7
1983 931 13 41 71 65 249 178 99 76 19 13 49 58 34 2 1 0 6 14 2 4 0 0 0 0 5
1984 907 1 27 73 176 169 242 72 47 17 49 30 4 122 0 0 64 33 6 14 0 0 0 4 1 0
1985 684 2 7 38 134 182 82 51 108 40 18 19 3 94 0 0 2 5 78 3 0 3 0 0 3 0
1986 765 0 30 76 84 173 134 88 67 65 26 17 5 15 0 2 6 2 1 0 3 1 0 0 0 0
1987 656 6 19 38 20 126 132 163 63 19 1 55 14 59 0 6 1 1 31 2 0 1 0 0 11 6
1988 702 17 4 28 58 132 63 103 61 76 19 121 20 32 5 0 1 4 3 0 0 3 1 0 14 1
1989 856 14 18 43 82 231 252 59 36 31 30 57 3 50 0 0 1 0 9 5 0 0 0 4 31 0
1990 1133 11 57 86 108 243 329 106 60 45 35 18 35 53 0 1 3 0 5 11 0 29 0 2 0 2
1991 1132 29 11 157 204 335 216 64 46 26 21 20 3 39 1 0 13 21 0 1 1 0 0 0 2 0
1992 1297 15 29 55 53 137 399 213 115 81 34 146 20 39 0 0 5 0 0 1 0 3 0 4 26 0
1993 1173 17 34 48 85 177 313 242 112 65 55 19 6 33 0 3 5 10 2 1 0 6 2 4 0 0
1994 1082 13 9 58 205 161 234 155 120 30 51 42 4 69 0 0 40 12 0 3 3 4 0 0 7 0In: Statistics and Probability
Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.
| Similarities and Differences in a Random Sample of 375 Married Couples | |
| Number of Similar Preferences | Number of Married Couples |
| All four Three Two One None |
34 121 110 68 42 |
Suppose that a married couple is selected at random.
(a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (Enter your answers to 2 decimal places.)
| 0 | 1 | 2 | 3 | 4 |
(b) Do the probabilities add up to 1? Why should they?
Yes, because they do not cover the entire sample space.No, because they do not cover the entire sample space. Yes, because they cover the entire sample space.No, because they cover the entire sample space.
What is the sample space in this problem?
0, 1, 2, 3 personality preferences in common1, 2, 3, 4 personality preferences in common 0, 1, 2, 3, 4, 5 personality preferences in common0, 1, 2, 3, 4 personality preferences in common
In: Statistics and Probability
Which of the following can be excluded from Ellen's gross income?
1. The value of a diamond ring that Ellen received as a gift from David.
2. The value of a mansion that Ellen inherited from her parents.
3. The value of concert tickets that Ellen won in a radio contest.
4. The value of a scholarship for room and board that Ellen received to her state university.
Group of answer choices
c. 1, 2, and 3
a. 1 only
d. 2, 3, and 4.
b. 1 and 2
In: Accounting
1-f(x) =1/8(7x-2), x ≤ 3
a-absolute maximum value b-absolute minimum value c-local maximum value(s) d-local minimum value(s)
2-Show that the equation x3 − 16x + c = 0 has at most one root in the interval [−2, 2].
3-If f(1) = 10 and f '(x) ≥ 3 for 1 ≤ x ≤ 4, how small can f(4) possibly be?
In: Advanced Math
Suzanne's Cleaners is considering two projects with the following cash flow data. Based on payback periods, which project is less risky based on liquidity risk?
PROJECT 1
|
Year |
0 |
1 |
2 |
3 |
4 |
5 |
|
Cash flows |
-$1,100 |
$300 |
$310 |
$320 |
$330 |
$340 |
PROJECT 2
|
Year |
0 |
1 |
2 |
3 |
4 |
5 |
|
Cash flows |
-$850 |
$100 |
$75 |
$500 |
$200 |
$275 |
| A. |
Project 1 |
|
| B. |
Project 2 |
In: Finance
A general reaction written as 2A + 2B → C + 2D is studied and yields the following data.
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[A]0 |
[B]0 |
Initial Δ[C]/Δt |
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0.100 M |
0.100 M |
4.00 × 10–5 mol/L • s |
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0.200 M |
0.100 M |
4.00 × 10–5 mol/L • s |
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0.100 M |
0.200 M |
8.00 × 10–5 mol/L • s |
For the first of the reactions in the table of data, determine –Δ[B]/Δt.
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What is the order of the reaction with respect to B?
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What is the order of the reaction with respect to A?
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What is the overall order of the reaction?
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What are the proper units for the rate constant for the reaction?
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What is the numerical value of the rate constant?
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In: Chemistry
(a) Use a direct proof to show that the product of two odd numbers is odd.
(b) Prove that there are no solutions in integers x and y to the equation 2x2 + 5y2 = 14.
(c) Prove that the square of an even number is an even number using (a) direct proof, (b) an indirect proof, and (c) a proof by contradiction.
Q. 2. Maximum score = 25 (parts (a) 9 points, part (b-i) and (b-ii) 8 points)
(a) Show that 13 + 23 + …. +n3 = [n(n+1)/2]2 whenever n is a positive integer.
(b) Use induction to prove the following for all natural numbers n.
i) -1 + 2 + 5 + 8 +...+ (3n – 4) = (n/2) (3n-5)
ii) ½ + ¼ + 1/8 + … + 1/2n = (2n – 1)/ 2n
Q.3. Maximum score = 25 Prove that 1 + (1/4) + (1/9) +……(1/n2) < 2 - (1/n) for n, a positive integer >1.
Q. 4 Maximum score 25 Determine the formular for an given by the recurrence relation an = an-1 + 6an -2 ; a0 = 1, a1 = 8.
In: Advanced Math
. There are ba (= 14) ways to arrange 1, 2, 3, ..., 8 in two rows of four so that (1) the integers increase in value as each row is read, from left to right, and (2) in any column the smaller integer is on top. Find, as in part (d) of Example 1.43, a) the arrangements that correspond to each of the fol- lowing. 1) 10110010 i) 11001010 lli) 11101000 b) the lists of four l's and four O's that correspond to each of these arrangements of 1, 2, 3, ...,8. 1) 1 345 ii) 1 2 37 fii) 1 2 4 5 2 6 7 8 4 5 6 8 3 6 7 8
In: Statistics and Probability