A bag of potatoes weighs 9.42 pounds on a weighing scale. Which of the significant digits in the scale reading is the least reli
2 answers:
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Answer:
We conclude that a compact microwave oven consumes a mean of more than 250 W.
Step-by-step explanation:
We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W with a population standard deviation of 15 W.
They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Let = <u><em>mean power consumption for microwave ovens.</em></u>
So, Null Hypothesis, :
250 W {means that a compact microwave oven consumes a mean of no more than 250 W}
Alternate Hypothesis, :
> 250 W {means that a compact microwave oven consumes a mean of more than 250 W}
The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean power consumption for ovens = 257.3 W
σ = population standard deviation = 15 W
n = sample of microwave ovens = 20
So, <em><u>the test statistics</u></em> =
= 2.176
The value of z test statistics is 2.176.
<u>Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.</u>
Since our test statistic is more than the critical value of t as 2.176 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.
Therefore, we conclude that a compact microwave oven consumes a mean of more than 250 W.
Answer:
∠EGB and ∠AGF are congruent;
Transitive Property of Equality
Step-by-step explanation:
The vertical angles theorem is about the angles that are opposite to each other. These angles are formed when two lines cross each other
Vertical angles are congruent i.e their measures are equal
Look at the attached graph
Given:
AB // CD
E , G , H , F are col-linear
The line which contains points E , G , H , F is a transversal for the parallel lines AB and CD
∵ AB and EF intersected at point G
∴ m∠EGB = m∠AGF ⇒ by the vertical angles theorem
When lines AB and EF intersected at G they formed opposite angles like angles EGB and AGF, then angles EGB and AGF are congruent ( vertical angle theorem)
∵ AB // CD and EF is a transversal
∴ m∠AGF = m∠CHF (corresponding angles theorem)
Transitive Property of Equality: if one angle is equal to two other angles, then the two other angles are equal
Therefore, If a = b and b = c, then a = c
∵ m∠EGB = m∠AGF
∵ m∠AGF = m∠CHF
∴ m∠EGB = m∠CHF (transitive property theorem)
∠EGB and ∠AGF are congruent; Transitive Property of Equality
