8. Marvin has a board that's 15' 3/4" long. He cuts it in half. What is the length of both boards?
1 answer:
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Answer:
a)
b)
Step-by-step explanation:
Data given and notation
represent the mean for Pirates
represent the mean for Splash Mountain
represent the sample standard deviation for the sample Pirates
represent the sample standard deviation for the sample Slpash Mountain
sample size selected for Pirates
sample size selected for Splash Mountain
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
Part a
The confidence interval would be given by:
The degrees of freedom are given by:
Since we want 98% of confidence the significance level is and
, we can find in the t distribution with df =60 a critical value that accumulates 0.01 of the area on each tail and we got:
And replacing we got for the confidence interval:
Part b
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the means are equal, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".
Calculate the statistic
We can replace in formula (1) the info given like this:
Answer:
Answer 1; Angles forming a linear sum to 180°
Answer 2; Substitution
Answer 3; Definition of perpendicular lines
Step-by-step explanation:
The two column proof is presented as follows;
Statement Reason
1. ∠SWT ≅ ∠TWU Given
2. m∠SWT + m∠TWU = 180° Angles forming a linear sum to 180°
3. m∠SWT + m∠SWT = 180° Substitution
4. m∠SWT = 90° Algebra
5. ⊥
Definition of perpendicular lines
Perpendicular lines are defined as lines that are at right angles (90°) to each other, therefore given that the angle formed by the lines and
m∠SWT = 90°, therefore, the lines
and
are perpendicular to each other.