m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°
Solution:
Line 
intersect at a point W.
Given 
.
<em>Vertical angle theorem:</em>
<em>If two lines intersect at a point then vertically opposite angles are congruent.</em>
<u>To find the measure of all the angles:</u>
∠AWB and ∠DWC are vertically opposite angles.
Therefore, ∠AWB = ∠DWC
⇒ ∠AWB = 138°
Sum of all the angles in a straight line = 180°
⇒ ∠AWD + ∠DWC = 180°
⇒ ∠AWD + 138° = 180°
⇒ ∠AWD = 180° – 138°
⇒ ∠AWD = 42°
Since ∠AWD and ∠BWC are vertically opposite angles.
Therefore, ∠AWD = ∠BWC
⇒ ∠BWC = 42°
Hence the measure of the angles are
m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°.
Answer:
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation for the sample
sample size
represent the value that we want to test
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)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean weight is less than 4 ounces, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and 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 if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
If the value of a is positive, the line slopes upwards.
Answer:
Step-by-step explanation:
The time constant of the isotope is:
The decay of the isotope is described by the following model:
Now, the time is cleared in the equation:
