Carlos has 58 pencils. what is the value of the digit 5 in this number
2 answers:
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Answer:
<em>Answer:</em> <em>A</em>
Step-by-step explanation:
The HL Theorem states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
Triangles TRO and OMT share the hypotenuse, so the first part of the theorem is met.
Both triangles are right because they have an internal angle of 90°, so the second condition is also met.
Since there is no indication of any leg to be congruent to another leg, we need additional information to prove that both triangles are congruent.
One of these two conditions should be met:
Side TM is congruent to side OR, or
Side MO is congruent to side RT.
From the available options, only the first is correct.
Answer: A
Answer:
We conclude that the board's length is equal to 2564.0 millimeters.
Step-by-step explanation:
We are given that a sample of 26 is made, and it is found that they have a mean of 2559.5 millimeters with a standard deviation of 15.0.
Let = <u><em>population mean length of the board</em></u>.
So, Null Hypothesis, :
= 2564.0 millimeters {means that the board's length is equal to 2564.0 millimeters}
Alternate Hypothesis, :
2564.0 millimeters {means that the boards are either too long or too short}
The test statistics that will be used here is <u>One-sample t-test statistics</u> because we don't know about the population standard deviation;
T.S. = ~
where, = sample mean length of boards = 2559.5 millimeters
s = sample standard deviation = 15.0 millimeters
n = sample of boards = 26
So, <em><u>the test statistics</u></em> = ~
= -1.529
The value of t-test statistics is -1.529.
Now, at a 0.05 level of significance, the t table gives a critical value of -2.06 and 2.06 at 25 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so <u><em>we have insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.
Therefore, we conclude that the board's length is equal to 2564.0 millimeters.