Solve for x. x³ = 1000
2 answers:
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These are right triangles that will use either sin, cos, or tan, depending upon what you have to work with in regards to the reference angle. The first one has a reference angle of 51 with y being the side opposite it and 12 being the hypotenuse. The sin identity uses the side opposite over the hypotenuse as its formula:
and 12 sin(51) = y and y = 9.325
The second one has the reference angle as the unknown. You could use any of the identities here because you have all the sides of the triangle, but I will use sin again:
and
and
The next one has a referece angle of 13 with 24 being the side adjacent to it and the unknown being the side across from it. You will use the tangent identity here:
and 24 tan(13) = x so x = 5.540
The last one has a reference angle of 20 with the hypotenuse as the unknown x, and the side across from it as 10. Use the sin identity again:
and
and
with x = 29.238
Everything is in regards to the reference angle; you HAVE to be able to identify the reference angle and then how the given sides are related to it.
and 12 sin(51) = y and y = 9.325
The second one has the reference angle as the unknown. You could use any of the identities here because you have all the sides of the triangle, but I will use sin again:
and
and
The next one has a referece angle of 13 with 24 being the side adjacent to it and the unknown being the side across from it. You will use the tangent identity here:
and 24 tan(13) = x so x = 5.540
The last one has a reference angle of 20 with the hypotenuse as the unknown x, and the side across from it as 10. Use the sin identity again:
Everything is in regards to the reference angle; you HAVE to be able to identify the reference angle and then how the given sides are related to it.
Answer:
There is sufficient evidence to support the claim that the new balls have bounce heights with a mean different from 92.8292.82 inches, and it appears that the new baseballs are different
Step-by-step explanation:
Given that in previous tests, baseballs were dropped 24 feet onto a concrete surface, and they bounced an average of 92.82 inches
But new balls showed mean of 92.6 inches with s = 1.72 inches
Sample size = 23
Since sample size is less than 30 and population std deviation is not know we use t test
(Two tailed test at 5% significance level)
Mean difference =
Std error of sample mean = s/sqrt n =
Test statistic t = mean diff/std error = -3.402
df = 23-1 =22
p value = 0.002559
since p value <5% we reject H0
There is sufficient evidence to support the claim that the new balls have bounce heights with a mean different from 92.8292.82 inches, and it appears that the new baseballs are different