You’re given three angle measurements of 30°, 70°, and 80°. How many triangles can you construct using these measurements?
1 answer:
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Answer:
36 objects
Step-by-step explanation:
You want the value of x when t=9, so you're solving ...
9 = 0.007x^2 +0.003x
9 = 0.007(x^2 + 3/7x)
From here, we observe that an approximation is probably sufficient.
9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2
x ≈ 3/√.007 ≈ 35.9 ≈ 36
We can check:
.007(36)(36 3/7) = 9.18
.007(35)(35 3/7) = 8.68
To keep the computer busy for 9 seconds, it needs to sort 36 objects.
Answer:
We conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.
Step-by-step explanation:
We are given that Bottles of a popular cola drink are supposed to contain 300 ml of cola. The distribution of the contents is normal with standard deviation of 3 ml.
A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4, 297.7, 301.0, 298.9, 300.2, 297.0
<u><em>Let </em></u><u><em> = mean contents of cola bottles.</em></u>
SO, Null Hypothesis, :
300 ml {means that the mean contents of cola bottles is more than or equal to the advertised 300 ml}
Alternate Hypothesis, :
< 300 ml {means that the mean contents of cola bottles is less than the advertised 300 ml}
The test statistics that will be used here is <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean contents of cola bottle =
= 299.03 ml
= population standard deviation = 3 ml
n = sample of bottles = 6
So, <em><u>test statistics</u></em> =
= -0.792
<em>Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -0.792 > -1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.</em>
Therefore, we conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.