Answer:
At least 75% of healthy adults have body temperatures within 2 standard deviations of 98.28degreesF.
The minimum possible body temperature that is within 2 standard deviation of the mean is 97.02F and the maximum possible body temperature that is within 2 standard deviations of the mean is 99.54F.
Step-by-step explanation:
Chebyshev's theorem states that, for a normally distributed(bell-shaped )variable:
75% of the measures are within 2 standard deviations of the mean
89% of the measures are within 3 standard deviations of the mean.
Using Chebyshev's theorem, what do we know about the percentage of healthy adults with body temperatures that are within 2 standard deviations of the mean?
At least 75% of healthy adults have body temperatures within 2 standard deviations of 98.28degreesF.
Range:
Mean: 98.28
Standard deviation: 0.63
Minimum = 98.28 - 2*0.63 = 97.02F
Maximum = 98.28 + 2*0.63 = 99.54F
The minimum possible body temperature that is within 2 standard deviation of the mean is 97.02F and the maximum possible body temperature that is within 2 standard deviations of the mean is 99.54F.
x - the shortest side
2x
x + 28
The sum of these must be equal to the perimeter of the flower bed, so
x + 2x + x + 28 = 184
4 x + 28 = 184 Combined like terms
4x = 156 Subtracted 28 from both sides
x = 39 Divided both sides by 4.
So the dimensions are 39 feet, 78 feet, and 67 feet
games won by B: games won by C = 4:3
Team B has won 8 games.
In total, how many games have the three teams won?
Answer:
A = 24
B = 8
C = 6
Step-by-step explanation:
4:3 from B:C
8:6
8 games won by B and 6 games won by C.
3:1 from A:B
24:8
24 by A and 8 by B
Team A won 24 games, Team B won 8 games and Team C won 6 games. So, the total games won by all three teams is 38.
From the problem, we know that the ratio of games won by Team A to Team B is 3:1, and the ratio of games won by Team B to Team C is 4:3. We also know that Team B has won 8 games.
Since the ratio of Team B to Team A is 1:3, Team A must have won 3 times as many games as Team B. Therefore, Team A has won 3 * 8 = 24 games.
The ratio of games won by Team B to Team C is 4:3. This means Team B won 4 games for every 3 games Team C won. Since Team B won 8 games, Team C must have won 3/4 as many games as Team B. Therefore, Team C won 3/4 * 8 = 6 games.
So, in total, the three teams won 24 + 8 + 6 = 38 games.
#SPJ3
8+8i
9514 1404 393
Answer:
45. (8√2)∠π/4
46. (7√2)∠3π/4
Step-by-step explanation:
The polar form of a+bi is ...
a +bi ⇔ (√(a²+b²))∠arctan(b/a)
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45. 8 +8i = (√(8² +8²))∠arctan(8/8) = (8√2)∠π/4
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46. -7 +7i = (√((-7)² +7²))∠arctan(7/-7) = (7√2)∠3π/4
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Additional comment
The arctan function usually returns a value in the range -π/2 to π/2. The quadrant of the desired result can be determined by the signs of the components of the vector. For negative real parts, π needs to be added to the value that is usually returned by the arctan function.
Without the actual numeric data coordinates, it is impossible to compute the true r value. Though we can estimate. The data points are negatively correlated in a fairly strong manner. We can draw a straight line close to all of these points, so the r value is going to be fairly close to -1. The closer r is to -1, the stronger the negative correlation. Having r = -1 exactly means all of the points fall on some single straight line that slopes downward.
Choice B is the next best choice, but its correlation isn't as strong. So that's why I ruled it out. Choices C and D are ruled out immediately since they are positive values.