Answer:
63 tons
Step-by-step explanation:
The problem statement asks for the tons of hay removed from the first pit. It is convenient to let a variable (x) represent that amount. This is said to be 3 times the amount removed from the second pit, so that amount must be x/3.
The amount remaining in the first pit is 90-x.
The amount remaining in the second pit is 75 -x/3.
Since the first pit remaining amount is half the second pit remaining amount, we can write the equation ...
... 90 -x = (1/2)(75 -x/3)
... 180 -2x = 75 -x/3 . . . . multiply by 2
... 105 - 2x = -x/3 . . . . . . subtract 75
... 315 -6x = -x . . . . . . . . multiply by 3
... 315 = 5x . . . . . . . . . . . add 6x
... 63 = x . . . . . . . . . . . . . divide by 5
63 tons of hay were taken from the first pit.
_____
Check
After removing 63 tons from the first pit, there are 27 tons remaining. After removing 63/3 = 21 tons from the second pit, there are 54 tons remaining. 27 is half of 54, so the answer checks OK.
Which of the following could replace the missing ordered pair to make the set not a function?
(−2, 4)
(21, 9)
(−7, 15)
(6, 8)
(13,−15)
The ordered pair that could replace the missing ordered pair to make the set not a function is given as follows:
(−7, 15).
A set of ordered pairs represents a function if every input (first component of the ordered pair) is associated with exactly one output (second component of the ordered pair). In other words, if no two ordered pairs in the set have the same first component but different second components.
Hence the ordered pair (-7,15) would make the relation not a function, as the set already has the ordered pair (-7,-15), in which the input 7 is already mapped to an output of -15, hence it cannot be mapped to an output of 15.
More can be learned about relations and functions at brainly.com/question/12463448
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Answer: 2x^3+5
Step-by-step explanation:
Answer:
y = -3
Step-by-step explanation:
Each side of an equilateral triangle will have a length that is 1/3 the perimeter. This triangle has sides of length 21/3 = 7, so ...
y + 10 = 7
y = 7 - 10
y = -3
This is consistent with the other given side measure ...
y^2 -2 = (-3)^2 -2 = 9 -2 = 7
Which of the following inequalities matches the graph?
Looking at the graph the y values does not change, it stays at zero
The shaded area are the numbers under O
This means the answer is y ≤ 0
Hope it helps
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Answer:
D. No solution
Step-by-step explanation:
Instead of solving everything I just plugged the numbers on equations and saw that for some of them the numbers satisfied one or two equation but not all. Also for some I saw that a number set makes the equation have no solution. For eg, I plugged option B into equation 3 and got 1305=756 which is never true so it is no solution.
Hope you understand :)
Answer:
d. Decrease
Step-by-step explanation:
A Type II error is when we fail to reject a false null hypothesis. Higher values of α make it easier to reject the null hypothesis, so choosing higher values for α can reduce the probability of a Type II error.
The consequence here is that if the null hypothesis is true, increasing α makes it more likely that we commit a Type I error (rejecting a true null hypothesis).
So using lower values of α can increase the probability of a Type II error.
Raising the level of significance in a hypothesis test from .01 to .05 would decrease the probability of making a Type II error. This is because as we become more accepting of risk in making a Type I error, we simultaneously reduce the risk of making a Type II error.
The level of significance in a hypothesis test is the probability that we are willing to accept for incorrectly rejecting the null hypothesis or making a Type I error. If the level of significance is raised, there is a higher chance we incorrectly reject the null hypothesis, increasing the chances of a Type I error. However, this also has an effect on the probability of committing a Type II error, which is to incorrectly accept the null hypothesis.
Specifically, when the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error (option b) will decrease. The reason for this is that increasing the level of significance or alpha means we are more likely to reject the null hypothesis. As we are more accepting of risk in terms of making a Type I error, we are less likely to make a Type II error, as the two error types often move in opposite directions. Thus, the answer to your question is d. The probability of a Type II error will decrease if the significance level is raised from .01 to .05.
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