Answer: 1.645
Step-by-step explanation:
Given : The quality control manager of a soda manufacturing company wishes to use a significant level of 0.05 to test whether the variabilities in the amount of soda in the company's 16 OZ bottles is more than the variabilities in the company's 12 OZ bottles.
Let
represents the variance for 16 OZ bottles and
represents the variance for 12 OZ bottles.
The Null and Alternative Hypothesis will be :-

, since alternative hypothesis is left-tailed , then the test is left-tailed test.
By using the standard normal distribution table for z, the critical value for this hypothesis:-

The factorization of the numbers is obtained as
(a) 36 = 2² x 3²,
(b) 60 = 2² x 3 x 5,
(c) 84 = 2² x 3 x 7,
(d) 99 = 3² x 11 and
(d) 180 = 2² x 3² x 5
<h3>Factor of the numbers</h3>
To factorize the numbers we use their factors as show below;
<h3>Factors of 36</h3>
36 = 2² x 3²
<h3>Factors of 60</h3>
60 = 2² x 3 x 5
<h3>Factors of 84</h3>
84 = 2² x 3 x 7
<h3>Factors of 99</h3>
99 = 3² x 11
<h3>Factors of 180</h3>
180 = 2² x 3² x 5
Thus, the factorization of the numbers is obtained as 36 = 2² x 3², 60 = 2² x 3 x 5, 84 = 2² x 3 x 7, 99 = 3² x 11 and 180 = 2² x 3² x 5.
Learn more about factorization here: brainly.com/question/25829061
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Answer:
2.2
Step-by-step explanation:
5% of 200 is 10, after six months, so total of $60? not sure though.
Answer:
16. x = 3.0822, -3.0822
17. x = 1.6432, -1.6432
18. x = 1, -1
Step-by-step explanation:
16. log5[(4x²+2)/8] = 1
(4x²+2)/8 = 5¹
4x² + 2 = 40
4x² = 38
x² = 38/4
x² = 19/2
x = +/- sqrt(19/2)
x = 3.0822, -3.0822
17. log7[(2x²-4)(5)] = 1
10x² - 20 = 7¹
10x² = 27
x² = 2.7
x = +/- sqrt(2.7)
x = 1.6432, -1.6432
18. log5[(2x²+8)/2] = 1
x² + 4 = 5¹
x² = 1
x = +/-1