A sociologist was interested in determining if there was a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred. A random sample of 93 adults revealed the following data. Use a Chi-Square independence test to determine if age and type of movie preferred are independent at the 5% level of significance. 18-23 years old 24-29 years old 30-35 years old Totals Drama 8 15 11 34 Science Fiction 12 10 8 30 Comedy 9 8 12 29 Totals 29 33 31 93 Provided the assumptions of the test are satisfied, determine the critical value for the test.
he can buy 4lbs. of live bait and 1lbs of natural bait
step-by-step explanation:
the value of x is 9 ⇒ answer b
step-by-step explanation:
* we can solve this problem using cosine and sine rule
- in δ abc
∵ ab = 36 , bc = 28 , ac = 16
- lets find the measure of angle b using the cosine rule
∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)
∴ cos b = [36² + 28² - 16²]/2(36)(28)
∴ cos b = 19/21
∴ m∠b = cos^-1(19/21) ≅ 25°
- lets find the measure of angle a using the sine rule
∵ sina/bc = sinb/ac = sinc/ab
∴ sina/28 = sin25°/16 ⇒ by using cross multiplication
∴ sina = 28 × sin25°/16
∴ sina = 0.7396
∴ m∠a = sin^-1(0.7396) ≅ 48°
- from the figure m∠abd = m∠dbc
∵ m∠abc = 25°
∴ m∠abd = 25°/2 = 12.5°
- in δabd
∵ m∠a = 48° , m∠abd = 12.5°
∵ the sum of the measures of the interior angles of any δ is 180°
∴ m∠adb = 180° - (48° + 12.5°) = 119.5°
∵ ab = 36
∵ ad = x
- use the sine rule to find x
∵ sin∠adb/ab = sin∠abd/x
∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication
∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9
* the value of x is 9
a. during week 0, the old factory produced p(w)=230(1.1)^0 specialty items.
anything to the 0th power is 1 so 230(1) = 230 specialty items.
the new factory, as shown on the graph, produced 190 specialty items on week 0.
to find how many more were produced at the old factory, do 230 - 190 to get 40 specialty items.
b. the growth rate is given for the old factory p(w)=230(1.1)^0
to find the growth rate of the new factory, you need to plug in points.
we know that at w = 0, f(w) is 190.
p(w) =
to find the value of ? , plug in values for w and p(w).
220 =
220 =
the rate is 22/19
check this by doing it again.
252 =
252/190 = ? ^2
the square root of 252/190 is 22/19, so ? is 22/19.
therefore the equation is p(w) = 190(22/19)^w
when comparing the growth rates, the new factory produces more items in less time.
c. in order to find when the produced items at the new factory exceeds the old factory, we need to graph the old factory's function.
once graphed, it is found that at w=5 the new factory exceeds the weekly number of specialty items produced at the old factory.
the old factory's function is p(w)=230(1.1)^w
at w = 5, p(w)=230(1.1)^5 = 230(1.61051) = 370.4
380 is greater than 370.4 so week 5 is the answer.
well if he bought them at 5 cedis each sold them at 7 cedis each then he would make a profit of 2 cedis of each book. if in total he made 150 cedis profit that means he sold 75 books. he lost 12 books at the start so that means he originally bought a total of 82 books.
step-by-step explanation: