What is the area of the trapezoid?
Answer:
Area of trapezoid is:
162 cm²
Step-by-step explanation:
Area(A) of trapezoid is given by:
Here, we are given Height=9 cm
One parallel side=6 cm
Other parallel side=(12+6+12) cm
= 30 cm
Sum of parallel side=(6+30) cm
= 36 cm
Area=
= 162 cm²
Hence, Area of trapezoid is:
162 cm²
check the picture below.
Answer:
C) not justified, since people usually swim in the ocean during the day.
(B) what is the estimated average difference in electro-olfactogram readings between the two groups? What is the 95% confidnece limit for the difference between population means?
Answer:
a)
"=T.INV(1-0.025,10)", and we got
Statistical decision
Since our calculated value is higher than our critical value,, we have enough evidence to reject the null hypothesis at 5% of significance.
b)
The degrees of freedom are given:
Step-by-step explanation:
Part a
Data given and notation
represent the mean for scent of pre ovulatory
represent the mean for post ovolatory
represent the sample standard deviation for preovulatory
represent the sample standard deviation for postovulatory
sample size for the group preovulatory
sample size for the group postovulatory
z would represent the statistic (variable of interest)
represent the p value
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the mean's are different, the system of hypothesis would be:
H0:
H1:
If we analyze the size for the samples both are lower than 30, so for this case is better apply a t test to compare means, and the statistic is given by:
(1)
z-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 have all in order to replace in formula (1) like this:
Find the critical value
We find the degrees of freedom:
In order to find the critical value we need to take in count that we are conducting a two tailed test, so we are looking for thwo values on the t distribution with df =10 that accumulates 0.025 of the area on each tail. We can us excel or a table to find it, for example the code in Excel is:
"=T.INV(1-0.025,10)", and we got
Statistical decision
Since our calculated value is higher than our critical value,, we have enough evidence to reject the null hypothesis at 5% of significance.
Part b
For this case the confidence interval is given by:
The degrees of freedom are given:
Answer:
General Formulas and Concepts:
Calculus
Limits
Graphical Limits
Step-by-step explanation:
As we approach 3 from the left according to the graph (follow the left graphed line), we see that we approach -1.
∴
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Answers:
The first blank is 180
The second blank is 60
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The triangle sum theorem basically says that adding up all three angles of any triangle always leads to 180 degrees. So that's why
(angle1)+(angle2)+(angle3) = 180
x+x+x = 180
3x = 180
Divide both sides of that last equation by 3. This is to undo the multiplication of 3 done to x.
3x = 180
3x/3 = 180/3 ... divide both sides by 3
x = 60
Each angle of this equilateral triangle is 60 degrees. In an equilateral triangle, all three sides are the same length. Also in an equilateral triangle, all three angles are the same measure and always 60 degrees.
The Triangle Sum Theorem says that all angles in a triangle add up to 180 degrees. In an equilateral triangle, all angles are equal. Hence, each angle is 60 degrees.
The Triangle Sum Theorem states that the sum of the measures of the angles in a triangle is always 180 degrees. Now, in an equilateral triangle, all angles are equal. Let's denote the measure of each angle with x. According to the theorem, the sum of these measures is x + x + x = 180. Simplifying this gives 3x = 180. Hence, solving for x, which refers to the measure of each angle in the equilateral triangle, we get x = 180 / 3 = 60 degrees. Thus, each angle in an equilateral triangle measures 60 degrees.
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