If l is parallel to m, find the value of each missing variable
1 answer:
Answer:
x = 18
y = 5
Step-by-step explanation:
From the figure attached,
'l' and 'm' are the parallel lines and two transversal lines are intersecting these parallel lines at points A, B and C.
Since, m∠ABC + (7x - 23)° = 180° [Supplementary angles]
m∠ABC = 180° - (7x - 23)°
m∠BCA = (11y - 1)° [Vertical angles]
m∠BAC = 49°
In ΔABC,
m∠ABC + m∠BAC + m∠CAB = 180°
180° - (7x - 23)° + 49° + (11y - 1) = 180°
-7x + 11y = -71
7x - 11y = 71 ------(1)
Since, sum of consecutive angles is 180°
Therefore, m(∠ABC) + (3x + 49)° = 180°
180° - (7x - 23)° + (3x + 49)° = 180°
-4x = -72
x = 18
From equation (1),
7(18) - 11y = 71
11y = 55
y = 5
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Answer:
Step-by-step explanation:
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A pilot study was conducted to test if three food rewards are equally appealing to the participants.
Of 60 participants surveyed:
16 preferred cupcakes (CC)
26 preferred candy bars (CB)
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If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3
1.
The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. Where k= number of categories of the variable.
For this example the statistical hypotheses are:
H₀: P(CC)=P(CB)=P(DA)= 1/3
H₁: At least one of the proportions isn't equal to the others.
2.
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3.
The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:
Assuming α: 0.05
The rejection region is then X²₂ ≥ 7.378
4.
I hope this helps!