Find the area of the quadrilateral in the figure.
1 answer:
<h3>Answer:</h3>
C. 19.64
<h3>Explanation:</h3>The triangle at upper right is a 3-4-5 right triangle, so has an area that is half the product of the leg lengths:
... upper right area = (1/2)(3 units)(4 units) = 6 units²
The triangle at lower left is an isosceles triangle with base length 5 and side length 6. The altitude to the side of length 5 is a bisector of that side and forms right angles at the point of intersection. Hence we can use the Pythagorean theorem to find the triangle's altitude:
... lower left triangle altitude = √(6² - 2.5²) = √29.75 ≈ 5.45436
Then the area of the lower left triangle is half the product of this altitude and the base length of 5 units:
... lower left area = (1/2)(5.45436 units)(5 units) ≈ 13.6359 units²
The quadrilateral's area is the sum of the areas of these triangles, so is ...
... quadrilateral area = upper right area + lower left area
... = 6 units² + 13.6359 units²
... = 19.6359 units² ≈ 19.64 units²
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Confirmed by my geometry program as shown in the attachment.
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Answer:
The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.
Step-by-step explanation:
An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating:
At the null hypothesis, we test if the mean is the same, that is:
At the alternate hypothesis, we test that it is different, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
59.5 is tested at the null hypothesis:
This means that
After testing 250 vans, they found a mean MPG of 59.2. Assume the population standard deviation is known to be 1.9.
This means that
Value of the test statistic:
Pvalue of the test and decision:
The pvalue of the test is the probability of finding a mean that differs from 59.5 by at least 0.3, which is P(|Z|>-2.5), which is 2 multiplied by the pvalue of Z = -2.5.
Looking at the z-table, Z = -2.5 has a pvalue of 0.0062
2*0.0062 = 0.0124
The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.