The measure of angle θ is . The measure of its reference angle is

Find the theoretical probability. Simplify completely.

mart [117]

Answer: 1/2

Explanation:

There are 8 number in the set

And 4 of them are even

We can write it
P(even) = 4/8 = 1/2

6 0

3 years ago

Type the correct answer in each box. Use numerals instead of words. Any non-integer answers in this problem should be entered as

ladessa [460]

Answer:

The interquartile range of the data set is 5

The mean absolute deviation of the data set is 3.6

Step-by-step explanation:

* Lets explain how to find the interquartile range and the mean absolute

deviation (MAD)

- The steps to find the interquartile range is:

1- Arrange the values from the smallest to the largest

∴ The values are 5 , 6 , 10 , 11 , 12 , 13 , 14 , 15 , 18 , 20

2- Find the median

- The median is the middle value after arrange them

* If there are two values in the middle take their average

∵ The values are 10 then the 5th and the 6th are the values

∵ The 5th is 12 and the 6th is 13

∴ The median = $\frac{12+13}{2}=12.5$

∴ The median is 12.5

3- Calculate the median of the lower quartile

- The lower quartile is the median of the first half data values

∵ There are 10 values

∴ The first half is the first five values

∴ The first half values are 5 , 6 , 10 , 11 , 12

∵ The middle value is 10

∴ The median of lower quartile = 10

- Similar find the median of the upper quartile

- The upper quartile is the median of the second half data values

∵ There are 10 numbers

∴ The second half is the last five values

∴ The second half values are 13 , 14 , 15 , 18 , 20

∵ The middle value is 15

∴ The median of upper quartile = 15

4- The interquartile range (IQR) is the difference between the upper

and the lower medians

∴ The interquartile range = 15 - 10 = 5

* The interquartile range of the data set is 5

* Lets talk about the mean absolute deviation

- Mean absolute deviation (MAD) of a data set is the average distance

between each data value and the mean

- To find the mean absolute deviation of the data, start by finding

the mean of the data set.

1- Find the sum of the data values, and divide the sum by the

number of data values.

∵ The data set is 5 , 6 , 10 , 11 , 12 , 13 , 14 , 15 , 18 , 20

∵ Its sum = 5 + 6 + 10 + 11 + 12 + 13 + 14 + 15 + 18 + 20 = 124

∵ The mean = the sum of the data values/the number of the data

∵ The set has 10 numbers

∴ The mean = 124/10 = 12.4

2- Find the absolute value of the difference between each data value

and the mean ⇒ |data value – mean|

# I5 - 12.4I = 7.4

# I6 - 12.4I = 6.4

# I10 - 12.4I = 2.4

# I11 - 12.4I = 1.4

# I12 - 12.4I = 0.4

# I13 - 12.4I = 0.6

# I14 - 12.4I = 1.6

# I15 - 12.4I = 2.6

# I18 - 12.4I = 5.6

# I20 - 12.4I = 7.6

3- Find the sum of the absolute values of the differences.

∵ Their sum = 7.4 + 6.4 + 2.4 + 1.4 + 0.4 + 0.6 + 1.6 + 2.6 + 5.6 + 7.6

∴ Their sum = 36

4- Divide the sum of the absolute values of the differences by the

number of data values to find MAD

∴ MAD = The sum of the absolute values/number of the values

∵ The sum = 36

∵ The data set has 10 values

∴ MAD = 36/10 = 3.6

* The mean absolute deviation of the data set is 3.6

6 0

3 years ago

An isosceles trapezoid has bases of lengths 6 and 8 and a height of 16. Find the area.

11111nata11111 [884]

Answer:

Step-by-step explanation:

In an isosceles trapezoid, the opposite sides are equal.

The formula for determining the area of a trapezoid is expressed as

Area = 1/2(a + b)h

Where

a and b are the length of The bases are the 2 sides of the trapezoid which are parallel with one another.

h represents the height of the trapezoid.

From the information given,

a = 6

b = 8

height = 16

Therefore,

Area of trapezoid = 1/2(6 + 8)16

= 1/2 × 14 × 16 = 112 square units

3 0

3 years ago

Which of the following is NOT true for a hypothesis test for correlation? Choose the correct answer below. A. If |r|less than

pantera1 [17]

Answer:

Answer explained

Step-by-step explanation:

From the information, the true statements for a hypothesis test for correlation is,

If the P-value is less than or equal to the significance level, we should reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.

If |r| less than or equals critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

If the P-value is greater than the significance level, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

Explanation

According to the decision rule of P-value approach, observe that if the P-value is less than or equal to the significance level, then there is evidence to reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.

Similarly, if the P-value is greater than the significance level, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

According to the critical value approach, observe that if the test statistic value is greater than the critical value, then there is evidence to reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation.

- If |r| greater than critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

Explanation

Based on the decision rules of the hypothesis test, the false statement about the test for a correlation is, if |r| less than or equals critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.

3 0

3 years ago

Write an equation for the graph, where y depends on x.

Over [174]

Answer:

y = -3x + 6

Step-by-step explanation:

Equation of straight line is given by,

y = mx + b

m = slope of the line

b = y-intercept

From the graph attached,

m = $\frac{\text{Rise}}{\text{Run}}$

= $\frac{-6}{2}$

= -3

y intercept 'b' = 6

Therefore, equation of the line will be,

y = -3x + 6

5 0

3 years ago