Verify the identity.
sin (x + y) - sin (x - y) = 2 cos x sin y
Answers
Answer:
Step-by-step explanation:
Related Questions
The following data were given in a study of a group of 1000 subscribers to a certain magazine. In reference to job, marital status, and education, there were
312 professionals,
470 married persons,
525 college graduates,
42 professional college graduates,
147 married college graduates,
86 married professionals,
25 married professional college graduates.
(i) Let a person be picked at random. Determine the probability that the person is married or professional or college graduate.
(ii) Explain why the numbers reported in the study must be incorrect.
Answers
Answer:
[tex](a)[/tex] [tex]P(M\ or\ P\ or\ C) = 1.307[/tex]
(b) See Explanation
Step-by-step explanation:
Given
[tex]P = 312[/tex] ---- Professionals,
[tex]M = 470[/tex] ----- Married persons,
[tex]C = 525[/tex] ---- College graduates,
[tex]PCG = 42[/tex] ----- Professional college graduates,
[tex]MCG = 147[/tex] ----- Married college graduates,
[tex]MP = 86[/tex] ---- Married professionals,
[tex]MPCG = 25[/tex] ---- Married professional college graduates
[tex]Total =1000[/tex]
Solving (a): P(M or P or C)
This is calculated as:
[tex]P(M\ or\ P\ or\ C) = P(M) + P(P) + P(C)[/tex]
[tex]P(M\ or\ P\ or\ C) = \frac{n(M) + n(P) + n(C)}{Total}[/tex]
[tex]P(M\ or\ P\ or\ C) = \frac{470 + 525 + 312}{1000}[/tex]
[tex]P(M\ or\ P\ or\ C) = \frac{1307}{1000}[/tex]
[tex]P(M\ or\ P\ or\ C) = 1.307[/tex]
(b) In probabilities, the probability of an event or collection of events must not exceed 1 and must not go below 0.
In (a) above, the calculated probability exceeds 1.
Because of this single reason, the collected data is incorrect
An animal shelter houses only cats and dogs,
and there are 25% more cats than dogs. If
there are 40 cats, how many dogs are there,
and how many animals are there total?
Answers
Answer:
50
Step-by-step explanation:
PLEASE HELP MEEE
I will give a crown to the right answer
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1) Which of the following cannot be the probability of an event?
A) 0.001
B) 0
C) 1
D)
E) -82
Answers
a sphere has a volume of 36tt in3 find the radius of the sphere
Answers
3•36π=4π • r^3
108 π=4 π • r^3
r^3 =108 π/4 π
r=3 inch
Answer:
r=3 inch
Step-by-step explanation:
find the area of 12m and 8m
Answers
Answer:
Hiya!!
12m * 8m = 96m
Step-by-step explanation:
What is the area of the polygon shown below?
Answers
Answer:
66
Step-by-step explanation:
first you find the area of the rectangle
5*12=60
then you find the area of the triangle
to find the length of the dotted line you need to subtract 9 from 12 which is 3
to find the length of the line adjacent to the dotted line you need to subtract 5 from 9 which is 4
use the triangle area formula 3*4*1/2=6
add the areas of the triangle and the rectangle 60+6=66
In AABC, the measure of C=90°, the measure of ZA=19°, and BC = 5.2 feet. Find the length of CA to the nearest tenth of a foot.
Answers
Answer:
15.1
Step-by-step explanation:
deltamath
Find the area of the shaded region in the image below. Write your answer as a simplified polynomial in standard form.
Answers
Answer:
6x^2+17x+9
Step-by-step explanation:
you have to subtract the area of the white rectangle from the area of the entire rectangle
to find the area of the inner rectangle do (2x-3)*(x+1)=2x^2-3x+2x-3=2x^2-x-3
to find the area of the entire rectangle do (4x+6)*(2x+1)=8x^2+12x+4x+6=8x^2+16x+6
(8x^2+16x+6)-(2x^2-x-3)=8x^2+16x+6-2x^2+x+3=6x^2+17x+9
need help nowww!!!pleaseeeee
Answers
Answer:
x= 68
Step-by-step explanation:
180-44
136 since both sides are equal divide to find angles
68 and since those angles are equal to the second triangles sides its also 68
Sin 14.629 degrees = Cos ___
Answers
Answer:
Step-by-step explanation:
sin(14.629°) = cos(90°-14.629°) = cos(75.371°)
Find the area of the sector and explain please
Answers
Answer:
78.5398
Step-by-step explanation:
Area of a circle:
a=[tex]\pi[/tex]r²
Radius is 10.
a=[tex]\pi[/tex]10²
a=[tex]\pi[/tex]100
a=314.15926
90° is one quarter of the circle, so multiply it by 0.25.
314.15926x0.25=78.5398
I don't know how many places the directions want it rounded to. If it said to use 3.14 for pi, the answer would just be 78.5.
Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether?
Answers
Answer:
3/5
Step-by-step explanation:
1/5 + 2/5 = 3/5
3/5
I'm not sure tho sorry
Find the GCF of each pair of monomials.
1. 20, 45x
2. 15r, 25
3. 8xy, 14x
4. 16mn, 24m
5. 25f, 60g
6. 33c, 55cd
Answers
2. 5
3. 2x
4. 8m
5. 5
6. 11c
True or False:
There are an infinite number of answers for this equation:
63 - X = 34
Answers
Answer: No, the answer is 29, this is false.
Step-by-step explanation: 63-x=34
subtract 63 from both sides
34-63= -29
-x=-29
divide both sides by the negative and you get 29
plug in 29 for x, 63-29=34
Determine the area bounded by the curves f(x) = 4x and g(x) = 3x + 1.
Answers
Answer: 12x^2+4
Step-by-step explanation:
SOMEONE PLZ ANSWER THIS FAST
Kevin can walk 14 miles in 5 hours. How far can he walk in 3 1/2 hours?
Answers
Answer:
9.8 miles
Step-by-step explanation:
14/5= 2.8mph
2.8*3.5= 9.8 miles in 3.5 hours
HELP ASAP
PLZ ITS URGENT
Answers
Answer:
It landed at a height of 14 feet
Step-by-step explanation:
Given
[tex]y = -\frac{1}{8}x^2 +4x[/tex] --- Path of a t-shirt
[tex]3y = 2x - 14[/tex] --- height of bleachers
Required
Height when t-shirts land in bleachers
[tex]3y = 2x - 14[/tex]
Make y the subject
[tex]y = \frac{2}{3}x - \frac{14}{3}[/tex]
Substitute [tex]y = \frac{2}{3}x - \frac{14}{3}[/tex] in [tex]y = -\frac{1}{8}x^2 +4x[/tex]
[tex]\frac{2}{3}x - \frac{14}{3} = -\frac{1}{8}x^2 +4x[/tex]
Multiply through by 24
[tex]16x- 112 = -3x^2 +96x[/tex]
Express as:
[tex]3x^2 + 16x -96x- 112 = 0[/tex]
[tex]3x^2 -80x- 112 = 0[/tex]
Using a calculator:
[tex]x = 28[/tex] or [tex]x = -\frac{4}{3}[/tex]
x can not be negative:
So:
[tex]x = 28[/tex]
Substitute [tex]x = 28[/tex] in [tex]y = -\frac{1}{8}x^2 +4x[/tex] to calculate the height it landed
[tex]y = -\frac{1}{8} * 28^2 + 4 * 28[/tex]
[tex]y = 14[/tex]
if 0 is between 0 and 90 and tan0=7/8 find cos0
Answers
Answer:
0.75
Step-by-step explanation:
o = atan ( 7/8 ) = 41.18
cos ( 41.18 ) = 0.75
Answer:
Step-by-step explanation:
Hh
Select the correct answer.
Four equivalent forms of a quadratic function are given. Which form displays the zeros of function h?
OA. f(x) = -4(x2 - 4)
OB. h() = -4(x - 2)(x + 2)
Och(x) = -47 +16
OD. H(x) = -2(2x - 3)
Answers
Answer:
Step-by-step explanation:
h(x) = -4(x-2)(x+2)
The zeros are 2 and -2.
Answer:
90
Step-by-step explanation:
OA. f(x) = -4(x2 - 4)
OB. h() = -4(x - 2)(x + 2)
Och(x) = -47 +16
OD. H(x) = -2(2x - 3)
write in decimal.
I will mark BRAINLIST.
Answers
Answer:
1.70
8.40
130.200
7.120
6.60
142.30
Step-by-step explanation:
The decimal numeral system is the standard system for denoting integer and non-integer numbers.
Decimal is a point which denotes integer and non-integer numbers (mah own answer)
The hypotenuse is NOT:
Answers
Answer:
NOT found in obtuse triangles
Step-by-step explanation:
you only talk about hypotenuse, adjacent, and opposite in right triangle
What is 5% of 30? Help ASAP plzzzzzzz
Answers
Answer:
1.5
Step-by-step explanation:
The dimensions of a rectangular pool table are: (x + 4)(x + 10), What is the area of the table?
Answers
Answer:
D. x^2 +14x + 40
Step-by-step explanation:
(x+4)(x+10)
x^2+10x+4x+40
x^2+14x+40
Answer:
d) x^2+14x+40
Step-by-step explanation:
You gotta multiply (x + 4)(x + 10)
Kelly flies a distance of 2,100 miles. the trip takes 4 2/3 hours
what is the airplanes unit rate of speed in miles per hour?
at this rate of speed, how many miles the airplane travel in 1 1/2 hours?
Answers
Answer: A=450
Step-by-step explanation:
Help fast please.....
Answers
Answer: 294
7x7=49
49x6=294
Here is a grid of squares.
Write down the ratio of the number of unshaded squares to the number of
shaded squares.
Answers
Answer:
3/10
Step-by-step explanation:
............iam not sure
The required ratio of the unshaded square to the shaded square is 7 : 3.
Given that,
To determine the ratio of the number of unshaded squares to the number of shaded squares.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Number of shaded squares = 3
number of unshaded squares = 7
Required ratio = 7 / 3 = 7 : 3
Thus, the required ratio of the unshaded square to the shaded square is 7 : 3.
Learn more about ratios here:
brainly.com/question/13419413
#SPJ2
the equivalent expression of (7+r)3
Answers
Answer:
21 + 3r
Step-by-step explanation:
(7 + r) 3 =
(7) x 3 + (r x 3) =
21 + 3r
Hope that helps!
PLEASE HELP!!!50 POINTS!!GIVING BRAINIEST!!!Noah is helping his band sell boxes of chocolate to fund a field trip. Each box contains 20 bars and each bar sells for $1.50.
boxes sold (b) money collected (m)
1 $ ?
2 $ ?
3 $ ?
4 $ ?
5 $ ?
6 $ ?
7 $ ?
8 $ ?
b. Write an equation for the amount of money, m, that will be collected if b boxes of chocolate bars are sold.
c. What is the independent variable? (m or b?) What is the dependent variable?(m or b?)
d. Write an equation for the number of boxes, b, that were sold if m dollars were collected. (use / to show division)
e. What is the independent variable?(m or b?)
What is the dependent variable? (m or b?)
Answers
i might have read this problem wrong since i didnt get a clear understanding because of the wording of this problem but i will do the best i can!
step-by-step explanation:
first step is to make a table! and ill just make one on here so you can get a better understanding on this problem :)
----------------------------------
| boxes sold (b) | money collected (m) |
----------------------------------
| 1 | 1.50 |
----------------------------------
| 2 | 3 |
----------------------------------
| 3 | 4.50 |
----------------------------------
| 4 | 6 |
----------------------------------
| 5 | 7.50 |
----------------------------------
| 6 | 9 |
----------------------------------
| 7 | 10.50 |
----------------------------------
| 8 | 12 |
----------------------------------
(b * 1.50) = m
the independent variable = boxes sold (b)
the dependent variable = money collected (m)
hope this helps you and please tell me if i did something wrong or if you need extra help understanding this problem! :)
In ADEF, E = 52°, d = 14, and f = 9. Find e.
Answers
9514 1404 393
Answer:
e ≈ 11.0
Step-by-step explanation:
The law of cosines tells you ...
e² = d² +f² -2df·cos(E)
e² = 196 +81 -252cos(52°) ≈ 121.853
e ≈ √121.853 ≈ 11.04