Evaluate cos 210° without using a calculator by using ratios in a reference triangle.

Answers

Answer 1
Answer: 210 degrees is a third quadrant degree angle that is in between 180 degrees and 270 degrees. So we expect that the cosine of this angle is equal to a negative value. In this case, the terminal angle of 210 degrees is 30 degrees. Hence, negative cosine  of 30 deg is equal to -sqrt 3/2

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An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airplane in still air. This similar to the current problem as you have to consider the 25 mph tailwind and headwind. Plane on outbound trip of 4 hours with 25 mph tailwind and return trip of 5 hours with 25 mph headwind Let r = the rate or speed of the airplane in still air. Let d = the distance a. Write a system of equations for the airplane. One equation will be for the outbound trip with tailwind of 25 mph. The second equation will be for the return trip with headwind of 25 mph. b. Solve the system of equations for the speed of the airplane in still air.

Keiko spent a total of $60
at the grocery store. Of this amount, she spent
$27
on fruit. What percentage of the total did she spend on fruit?

Answers

she spent 27 out of 60
27/60 = 0.45...multiply by 100 to get the percent 0.45(100) = 45%

In an experiment, the probability that even A occurs is 0.2 and the probability that event B occurs is 0.5. If A and B are independent events, which statement is true?A.
P(A and B) = 0.1

Answers

The probability of event A and event B will be 0.10. Then the correct option is A.

What is probability?

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

In an experiment, the probability that event A occurs is 0.2 and the probability that event B occurs is 0.5.

If A and B are independent events. Then the probability is given as,

P(A and B) = P(A) x P(B)

P(A and B) = 0.2 x 0.5

P(A and B) = 0.10

The probability of event A and event B will be 0.10. Then the correct option is A.

More about the probability link is given below.

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The missing options are given below.

A. P(A and B) = 0.1

B. P(A or B) = 0.1

C. P(A and B) = 0.7

D. P(A or B) = 0.7

Answer:

oop

Step-by-step explanation:

Polynomials
(14x3y2z)4

Answers

With the problem in figures, solving the given polynomials would be based on how it is being situated. If 3,2 and 4 are exponents, you are going to distribute the 3rd exponent which is 4 to the rest of the numbers so the figure goes 14 to the power of 4 then x to the power of 3 multiplied by 4 and y to the power of 2 multiplied by 4. With its polynomial term, the simplified term is 38416 x to the power of 12 y to the power  of 8 and z to the power of 4

Final answer:

The result of raising the polynomial (14x3y2z) to the 4th power is 38416x12y8z4. This is calculated by individually multiplying each part of the polynomial by itself 4 times.

Explanation:

The problem is asking you to calculate the result of raising a polynomial (14x3y2z) to the 4th power.

The operation refers to using the rule of powers which states that any base with an exponent is multiplied by itself the amount of times indicated by the exponent. The result should therefore be calculated as follows:

(14x3y2z)4 = 38416x12y8z4

To find the answer, we raised each part of the polynomial to the 4th power. 144 equals 38416, (x3)4 results in x12 because you multiply the exponents, (y2)4 results in y8 for the same reason and z4 because anything to the power of 4 is itself raised 4 times.

Learn more about Polynomial calculation here:

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What is the volume of a right circular cylinder with a diameter of 19.6 yd and a height of 23.52 yd? Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.

Answers

Answer:

Volume of a right circular cylinder is given by:

V = \pi r^2 h .....[1]  where

V represents the volume of a cylinder.

r represents the radius of a cylinder.

h represents the height of a cylinder.

As per the given statement:

Diameter(D) = 19.6 yd and height(h) = 23.52 yd.

Diameter = 2r where r is the radius of the cylinder.

r = (D)/(2)

r = (19.6)/(2) = 9.8 yd

Substitute these given values in [1] we have;

V = 3.14 * (9.8)^2 * 23.52 cubic yard

V = 3.14 * 96.04 * 23.52

Simplify:

V = 7,092.82291 cubic yard.

Therefore, volume of a circular cylinder to the nearest hundredths is, 7092.82 cubic yard.

Answer: 7092.82

Hope this helps :) !

A theater has 30 seats in the first row, 33 seats in the second row, 36 seats in the third row, and so on in the same increasing pattern. If the theater has 15 rows of seats, how many seats are in the theater?

Answers

there are 495 seats in total.

Twice a number decreased by eight is less than five times the number increased by ten.

Answers

twice a number (2 times x) dcreased by 8 (minus 8) is less than (<) 5 times the number (5 times x) increses by 10 ( plus 10)

2x-8<5x+10
subtract 2x from both sides
-8<3x+10
subtract 10 from both sides
-18<3x
divide both sides by 3
-6<x



the number is any number bigger than -6
x*8-5*x+10 that's the equation...