Answer:
The P-value signifies that the likelihood of obtaining a linear correlation coefficient that is as extreme or more extreme is 3.5%, which is considered significant at α=0.05. Thus, we have sufficient evidence to assert that there exists a linear correlation between the weight of automobiles and their highway fuel consumption.
Step-by-step explanation:
The correlation coefficient demonstrates the relationship between the weights and highway fuel consumption values across seven distinct types of automobiles.
The P-value expresses the significance of this connection. If the p-value is beneath a significance level (e.g., 0.05), it indicates that the relationship is indeed significant.
Answer:
It could either be 455 or 680, based on assumptions.
Step-by-step explanation:
Assuming the three choices are distinct, we can calculate...
15C3 = 15·14·13/(3·2·1) = 35·13 = 455
ways to create the pizza.
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In the case where two or more of the toppings may be identical, this would lead to...
2(15C2) + 15C1 = 2·105 + 15 = 225
additional combinations, resulting in a grand total of...
455 + 225 = 680
unique pizza varieties.
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There is a multiplication factor of 2 for the two-topping selections, since it allows for variations like double anchovies and tomatoes or double tomatoes and anchovies when the topping choices are anchovies and tomatoes.
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nCk = n!/(k!(n-k)!)
Rotational symmetry indicates that an object appears unchanged when rotated.
Upon examining the figures, option B might seem plausible, but observe that the edges vary in length—rotating it will not align perfectly with its original position.
Options C and D are eliminated as they lack any symmetrical characteristics; no matter how they are turned, they appear different.
This leaves option A as the only choice: if you rotate this figure by 180 degrees, its appearance remains unchanged.
Consequently, the figure possessing rotational symmetry is A.
To determine the hypotenuse's length, we apply knowledge of trigonometric functions, specifically sine, which is defined as:
sine (theta) = length of the opposite side / length of the hypotenuse
sine 80 = 4 / hypotenuse
Therefore, Hypotenuse = 4.1 in <--- THAT'S OPTION B
Answer:
Begin by selecting two points from the data. Determine the difference between the second y-coordinate and the first y-coordinate. Next, take that difference divided by the difference between the second x-coordinate and the first x-coordinate.
Step-by-step explanation:
