1. given:
csc(x) + sin(x)
2. definition of csc(x) :
1/sin(x) + sin(x)
3. combining fractions with a common denominator:
(1 + sin²(x))/sin(x)
4. expanding 1 = cos²(x) + sin²(x) :
(cos²(x) + sin²(x) + sin²(x))/sin(x)
5. simplifying:
(2 sin²(x) + cos²(x))/sin(x)
6. employing the same identity as in (4) :
(2 (1 - cos²(x)) + cos²(x))/sin(x)
7. expanding 2 (1 - cos²(x)) :
(2 - 2 cos²(x) + cos²(x))/sin(x)
8. simplifying:
(2 - cos²(x))/sin(x)
To estimate the volume, you will use the formula for finding volume of a pyramid.
You will need to convert the height, given in feet, to yards.
(48 x 10)/3= 160 yards
You also need to convert the area of the base to square yards.
571536 ft.²/ 9 ft.² (1 square yd)= 63,504 yd.².
V = 1/3 BH, where B is the area of the base.
V = 1/3 x 63504 x 160
V = 3,386880 cubic yards
The approximate volume of The Great Pyramid is 3,386,880 yd.³.
Let be the number of students who eat cauliflower.
Therefore, .
Let be the total number of students surveyed.
Therefore,
Thus,
Now, for 90% confidence level, from the table we know that .
The formula for the interval range of proportion of students is :
Plugging in the values we get:
Thus, Jane is 90% confident that the population proportion p, for students who eat cauliflower in her campus is between 5.398% and 15.114% (after converting the answer we got to percentage).
Answer:
20 m
Step-by-step explanation:
Given that :
Scale of 1 : 50 is used to make a model
If the model has a height of 40 cm ; the height of the house is:
Then, the actual height of the house is (40 * 50) = 2000 cm
Thus the height of the house in metre is :
100cm = 1 meter
2000 cm = 2000 / 100
2000 cm = 20 meter
Height of house in meter = 20 meter
Square root of 88 is 9.38083152
Square root of 95 is 9.746794345
9.38083152 + 9.746794345 = 19.12762586