Solve for “x” to the nearest tenth. (Hint: Find a decimal that, when multiplied by itself, will be approximately 46.)
1 answer:
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Answer:
Length of the shorter diagonal is 8.68 cm.
Step-by-step explanation:
Length of the side AB = 11 cm
Length of side BC = 5 cm
Angle between these sides, m∠ABC = 50°
By cosine rule in ΔABC,
AC² = AB² + BC² - 2AB.BC.cos B
AC² = (11)² + 5² - 2(11)(5)cos50°
AC² = 121 + 25 - 70.71
AC = √(75.29)
AC = 8.68 cm
By the property of parallelogram,
m∠B + m∠C = 180° [Interior consecutive angles]
50° + m∠C = 180°
m∠C = 130°
Similarly, In ΔBCD,
BD² = BC² + CD² - 2BC.CD.cos130°
BD² = (5)² + (11)² - 2(5)(11)cos130°
BD² = 25 + 121 + 70.71
BD² = 216.71
BD = 14.72 cm
Therefore, length of the shorter diagonal will be 14.72 cm.
<h2>Answer with explanation:-</h2>
Let be the population mean .
By observing the given information, we have :-
Since the alternative hypotheses is two tailed so the test is a two-tailed test.
We assume that the life of a large shipment of CFLs is normally distributed.
(a) Given : Sample size : n=81 , since n>30 so we use z-test.
Sample mean :
Standard deviation :
Test statistic for population mean :-
The critical value (two-tailed) corresponds to the given significance level :-
Since the observed value of z (-1.4) is less than the critical value (1.96) , so we do not reject the null hypothesis.
Hence, we conclude that we have enough evidence to accept that the mean life is different from 7450 hours .
(b) The p-value : , it means that the probability that the life of CFLs less than 7240 and greater than 7240 is 0.1615.
(c) The confidence interval for population mean is given by :-
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