Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is
an important characteristic. A random sample of 10 gears from supplier 1 results in $$\overline{\mbox{x}}_1=290$$ and $$s_1 = 12$$, and another random sample of 16 gears from the second supplier results in $$\overline{\mbox{x}}_2=321$$ and $$s_2 = 22$$.
a. Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use α = 0.05, and assume that both populations are normally distributed but the variances are not equal.
What is the P-value for this test?
b. Do the data support the claim that the mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1? Make the same assumptions as in part (a).
c. Construct a confidence interval estimate for the difference in mean impact strength, and explain how this interval could be used to answer the question posed regarding supplier-to-supplier differences.
a. Is there evidence to support the claim that supplier 2 provides gears with higher mean impact strength? Use α = 0.05, and assume that both populations are normally distributed but the variances are not equal.
What is the P-value for this test?
b. Do the data support the claim that the mean impact strength of gears from supplier 2 is at least 25 foot-pounds higher than that of supplier 1? Make the same assumptions as in part (a).
c. Construct a confidence interval estimate for the difference in mean impact strength, and explain how this interval could be used to answer the question posed regarding supplier-to-supplier differences.
1 answer:
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If the volume of this pyramid is 234 units, the height of the pyramid is equal to 13 units.
<h3>How to calculate the volume of a pyramid.</h3>Mathematically, the volume of a pyramid is given by the formula:
<u>For the </u><u>base area</u><u>:</u>
The area of a right triangle is given by:
A = 54 square units.
<u>Given the following data:</u>
Volume of a pyramid = 234 units.
Side lengths of right triangle = 9 and 12 units.
Now, we can calculate the height of the pyramid:
h = 13 units.
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Answer:
4) is equivalent to
for all
. (Answer: A)
5) is equivalent to
for all
. (Answer: B)
6) is equivalent to
for all
. (Answer: None)
7) is equivalent to
. (Answer: None)
8) is equivalent to
for all
. (Answer: A)
Step-by-step explanation:
We proceed to simplify each expression below:
4)
(i) Given
(ii) Distributive property
(iii) Distributive property
(iv) Existence of multiplicative inverse/Modulative property/Result
Rational functions are undefined when denominator equals 0. That is:
Hence, we conclude that is equivalent to
for all
. (Answer: A)
5)
(i) Given
(ii) Distributive property
(iii) Distributive property
(iv) Commutative property/Existence of multiplicative inverse/Modulative property/Result
Rational functions are undefined when denominator equals 0. That is:
Hence, we conclude that is equivalent to
for all
. (Answer: B)
6)
(i) Given
(ii)
(iii) Commutative and distributive properties.
(iv) Existence of multiplicative inverse/Modulative property/Result
Rational functions are undefined when denominator equals 0. That is:
Hence, we conclude that is equivalent to
for all
. (Answer: None)
7)
(i) Given
(ii)
(iii) Commutative and distributive properties.
(iv) Existence of additive inverse/Modulative property/Result
Polynomic function are defined for all value of .
is equivalent to
. (Answer: None)
8)
(i)
(ii)
/Result
Rational functions are undefined when denominator equals 0. That is:
Hence, is equivalent to
for all
. (Answer: A)