Answer: [tex]-2+\sqrt{3}[/tex]
=========================================================
Work Shown:
Apply the following trig identity
[tex]\tan(A - B) = \frac{\tan(A)-\tan(B)}{1+\tan(A)*\tan(B)}\\\\\tan(225 - 60) = \frac{\tan(225)-\tan(60)}{1+\tan(225)*\tan(60)}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+1*\sqrt{3}}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\[/tex]
Now let's rationalize the denominator
[tex]\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\\tan(165) = \frac{(1-\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\\tan(165) = \frac{(1-\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{(1)^2-2*1*\sqrt{3}+(\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{1-2\sqrt{3}+3}{1-3}\\\\\tan(165) = \frac{4-2\sqrt{3}}{-2}\\\\\tan(165) = -2+\sqrt{3}\\\\[/tex]
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As confirmation, you can use the idea that if x = y, then x-y = 0. We'll have x = tan(165) and y = -2+sqrt(3). When computing x-y, your calculator should get fairly close to 0, if not get 0 itself.
Or you can note how
[tex]\tan(165) \approx -0.267949\\\\-2+\sqrt{3} \approx -0.267949[/tex]
which helps us see that they are the same thing.
Further confirmation comes from WolframAlpha (see attached image). They decided to write the answer as [tex]\sqrt{3}-2[/tex] but it's the same as above.
A trough has ends shaped like isosceles triangles, with width 2 m and height 5 m, and the trough is 18 m long. Water is being pumped into the trough at a rate of 8 m3/min. At what rate (in m/min) does the height of the water change when the water is 2 m deep
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Answer:
5/9 m/min
Step-by-step explanation:
The depth of the water is 2/5 of the depth of the trough, so the width of the surface will be 2/5 of the width of the trough:
2/5 × 2 m = 4/5 m
Then the surface area of the water is ...
A = LW = (18 m)(4/5 m) = 14.4 m²
The rate of change of height multiplied by the area gives the rate of change of volume:
8 m³/min = (14.4 m²)(h')
h' = (8 m³/min)/(14.4 m²) = 5/9 m/min
Find the slope of the line #67
difference between mutually exclusive
Answer:
A mutually exclusive event is when there are two events that can occur, such as flipping a coin, either it will be a head or a tail. Hence, both the events here are mutually exclusive.
An independent event is termed as an event that occurs without being affected by other events. The happening of one event has nothing to do with the happening of the other and there is no cause-effect between the two.
The wholesale price of 6 oz plastic bottles is 6 cents how many plastic bottles can be purchased for $98.41
Answer:
1640
Step-by-step explanation:
Take the total amount and divide by the amount for one
Make sure to write 6 cent in dollar form (.06)
98.41 / .06
1640.1666
Round down since we need to buy whole bottles
1640
Male Color Blindness When conducting research on color blindness in males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group who have a form of color blindness (based on data from the National Institutes of Health).X Px0 0.6591 0.2872 0.0503 0.0044 0.0015 0+In determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.
Answer:
The sum of the probabilities of all possible outcomes is not 1, which means that a probability distribution is not given.
Step-by-step explanation:
We are given these following probabilities:
[tex]P(X = 0) = 0.6591[/tex]
[tex]P(X = 1) = 0.2872[/tex]
[tex]P(X = 2) = 0.0503[/tex]
[tex]P(X = 3) = 0.0044[/tex]
[tex]P(X = 4) = 0.0015[/tex]
Determine whether a probability distribution is given.
We have to see if the sum of the probabilities of all possible outcomes is 1. So
[tex]0.6591 + 0.2872 + 0.0503 + 0.0044 + 0.0015 = 1.0025[/tex]
The sum of the probabilities of all possible outcomes is not 1, which means that a probability distribution is not given.
Find the medien: 16,12,10,15,7,9,16
Answer:
12
Step-by-step explanation:
arrange the numbers in ascending order and cross out from either side till you have a middle line
FINAL ANSWER:
12
Step-by-step explanation:
Median is the middle number in the data set.
so first of ... we need to arrange the group of numbers from lower to greater.
16, 12, 10, 15, 7, 9, 16 ⇒ 7, 9, 10, 12, 15, 16, 16
Now that we have arranged the numbers from least to greatest all we need to do is to find the middle number of the data set (data set? they are the group of numbers)
Ok, so what you want to do here is to just count the numbers until you get to the middle number of the data set...
7, 9, 10, 12, 15, 16, 16
the median in the given data set is 12.
I hope this helps you!!! Let me know if my answer is incorrect or not...
HAVE A GREAT DAY AND GOD BLESS YOU ;)!!!
Britany wants to read a book. In her room, she has 5 mysteries, 15 historical fictions, 12 modern fantasies, and 7 blographies.
How many different choices are available?
pleaseee
Answer:
39
Step-by-step explanation:
5 + 15 + 12 + 7 = 39
Answer:
39
Step-by-step explanation:
5 + 15 = 20, 12 + 7 = 19, 20 + 19 = 39.
Simplify: 3.5 x 10^-2 + 2.3 x 10^-2
Given:
The given expression is:
[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]
To find:
The simplified form of the given expression.
Solution:
We have,
[tex]3.5\times 10^{-2}+2.3\times 10^{-2}[/tex]
It can be written as:
[tex]=(3.5+2.3)\times 10^{-2}[/tex]
[tex]=5.8\times 10^{-2}[/tex]
Therefore, the simplified form of the given expression is [tex]5.8\times 10^{-2}[/tex].
Michael drove 210 miles in 3 1/2. Jordan drove 330 miles in 6 hours. Which is an accurate comparison of the rates at which the two people drove?
Michael = 210 / 3.5 = 60 miles per hour
Jordan = 330/ 6 =55 miles per hour
Jordan drove 5 miles per hour slower than michael
Find the area of a circle having a radius of 9 cm
Answer:
81 pi cm^2
or approximately 254.34 cm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi (9)^2
A = 81 pi
Using 3.14 as an approximation for pi
A = 81 (3.14)
A =254.34 cm^2
Answer:
81pi cm^2
Step-by-step explanation:
formula : pi*r^2
pi*9^2
pi*81
What is the value of the expression (2x + y) (2x - y) when x = 4 and y = -5?
Answer:
39
Step-by-step explanation:
1. (2(4)-5)(2(4)+5)
2.(3)(13)
3.39
Answer:
Step-by-step explanation:
This is a difference of squares question. You should 64 = 25 = 39 Let's see if that happens.
Difference of squares
(2x - y) ( 2x + y) = 4x^2 - y^2
4(4)^2 - (5)^2
64 - 25 = 39
Now do the question exactly as it is written.
(2*4 - -5)(2*4 + -5)
(8 +5)(8 - 5)
3 * 13
39
They really do give the same answer.
Find the area of athletic field if it's length is 120cm and its width is 28cm .A. 397.6cm B. 3360cm C. 296 cm D. 4592cm E. 3356cm
Answer:
B 3360
Step-by-step explanation:
Area of Rectangle = Length X Width
120 X 28
= 3360 cm
Answered by Gauthmath
Select the correct answer.
Which is the minimum or maximum value of the given function?
dndnsn
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the function is not given. So, I will make an assumption.
A quadratic function is represented as:
[tex]f(x) = ax^2 + bx + c[/tex]
If [tex]a > 0[/tex], then the function has a minimum x value
E.g. [tex]f(x) = 4x^2 - 5x + 8[/tex] ------ [tex]4 > 0[/tex]
Else, then the function has a maximum x value
E.g. [tex]f(x)= -4x^2 -5x + 8[/tex] ---- [tex]-4 < 0[/tex]
The maximum or minimum x value is calculated using:
[tex]x = -\frac{b}{2a}[/tex]
For instance, the maximum of [tex]f(x)= -4x^2 -5x + 8[/tex] is:
[tex]x = -\frac{-5}{2*-4}[/tex]
[tex]x = -\frac{5}{8}[/tex]
So, the maximum of the function is:
[tex]f(x)= -4x^2 -5x + 8[/tex]
[tex]f(-\frac{5}{8}) = -4 * (-\frac{5}{8})^2 - 5 *(-\frac{5}{8}) +8[/tex]
[tex]f(-\frac{5}{8}) = 9.5625[/tex]
Which expression is equal to
(3x – 4)(2x – 5)?
Answer:
6x^2-23x+20
Step-by-step explanation:
i think the expanded form of that equation is equal to it.
(3x-4)(2x-5)
3x(2x-5)-4(2x-5)
6x^2-15x-8x+20
6x^2-23x+20
I hope this helps and sorry if it's wrong
There are 9 members of Collin colleges board of trustees how many different ways can a chairman a vice chairman a secretary and a treasurer be selected
Answer:
Amount of members = 9
then we multiply the different probabilities of the trustess which is 4, so we do 9 x 4= 36
Step-by-step explanation:
So there are 36 different ways
answer: 36 different ways
The line l with equation x - 2y + 2 = 0 crosses the y-axis at the point P. The line
m with equation 3x + y - 15 = 0 crosses the y-axis at the point Q and intersects
l at the point R. Find the area of triangle PQR.
Answer:
Area of ΔPQR is 28 units²
Step-by-step explanation:
-P is the point with coordinates ( 0, y-intercept for line x-2y+2 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point P( 0, b)
x-2y+2 = 0, subtract x and 2 from both sides
-2y = -x-2, divide by -2 both sides
y= (1/2)x +1 so b=1 and P (0, 1)
-Q is the point with coordinates ( 0, y-intercept for line 3x+y -15 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point Q( 0, b)
3x +y -15 =0, subtract 3x and add 15 to both sides
y= -3x +15 so b=15 and Q(0,15)
-R is the intersection of the two lines so is the solution of the system of equations y= (1/2)x +1 and y= -3x +15
(1/2)x +1 = -3x +15, add 3x and subtract1
(1/2) x+3x = 15-1, combine like terms
(7/2)x = 14 , multiply both sides by 2
7x = 28, divide both sides by 7
x= 4
y= (1/2)x +1 = (4/2) +1 =3 so R(4,3)
- the area of ΔPQR is (base *height)/2
base= 15-1= 14
height = 4
A= (14*4)/2 = 14*2 = 28
Which of the following is the point and slope of the equation y + 14 = 7(x - 18)?
Answer:
y = 7x - 140
The slope is 7
The y-intersept is -140
= (7, -140)
Step-by-step explanation:
y + 14 = 7(x - 18)
y + 14 = 7x - 126
y =7x - 126 - 14
y = 7x - 140
Find the range from the ordered pair {(1, 2), (2, 3), (3, 4), (4, 5)}
Answer:
Range { 2,3,4,5}
Step-by-step explanation:
The range is the output values
Range { 2,3,4,5}
If 2 inches is 50 miles then how many miles is 9.2 inches
Answer:
Step-by-step explanation:
Answer:
230
Step-by-step explanation:
50: 2
9.2: x
therefore x = 50*9.2 /2 = 230
i think
57 117find x triangle
Answer:
60
Step-by-step explanation:
x = 180 - [ 57 + ( 180 - 117 ) ]
= 180 - [ 57 + 63 ]
= 180 - 120
x = 60
What is the solution to the inequality -6+|2p+3| > 7
Step-by-step explanation:
you're going to have to set up two expressions since it's an absolute value problem
HELPPP PLEASE ASAP!!! I don’t know how to solve this problem nor where to start? Can some please help me out and explain how you got the answer please. Thank you for your time.
Step-by-step explanation:
Count the number of times you have to move the decimal point to the right until it is to the right of the 1st nonzero number.
a) You have to move the decimal point 11 times until it gets to the right of the 1st nonzero number, which is 7. You then rewrite this number as
[tex]7.2×10^{-11}[/tex]
The exponent of 10 is a negative number because you moved the decimal point to the right.
b) Similarly, you have to move the point 9 times to the right so the answer is
[tex]9.5×10^{-9}[/tex]
Can someone please help me?
you have to read the bottom link for the answer key
HELPPPP
what is this
Answer:
Pls be specific with your question
Find the surface of the figure round your answer to the nearest tenth if necessary
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Answer:
192 cm²
Step-by-step explanation:
The total surface area is the sum of the two triangular base areas and the three rectangular lateral face areas.
SA = 2(1/2)(6 cm)(8 cm) + (6 cm +8 cm +10 cm)(6 cm) = 192 cm²
The surface area of the figure is 192 square centimeters.
Identify the constant of proportionality from the table.
х у
2 18
5 45
7
63
8 72
A. 18
B.
C. 9
0 D. 2
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Find the unlabeled side length
Answer:
hope it helps you.......
Answer:
The unidentified length is 13
Step-by-step explanation:
To solve this we have to use the Pythagorean Theorem
[tex]a^2+b^2=c^2\\5^2+12^2=c^2\\25+144=c^2\\169=c^2\\13=c[/tex]
What is the volume of a calculate the total surface area of a cuboid with the following dimensions (4m by 6m by 8m)
Answer:
V =192 m^3
Step-by-step explanation:
The volume of a cuboid is
V = l*w*h where l is length w is width and h is height
V = 4*6*8
V =192 m^3
PLEASE HELP on this question
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Answer:
(s+r)(x) = 3x² +x +1(s-r)(x) = -3x² +x +1(s·r)(-3) = -54Step-by-step explanation:
a) (s+r)(x) = s(x) +r(x) = (x+1) +3x²
(s+r)(x) = 3x² +x +1
__
b) (s-r)(x) = s(x) -r(x) = (x +1) -(3x²)
(s-r)(x) = -3x² +x +1
__
c) (s·r)(-3) = s(-3)·r(-3) = (-3+1)·(3(-3)²) = (-2)(27)
(s·r)(-3) = -54
At a high school basketball game the Lions and the Eagles are playing. The Lions attempted 16 free throws and made 10, attempted 50 two-point shots and made 25, and attempted 16 three-point shots and made 12. The Eagles attempted 27 free throws and made 10, attempted 44 two-point shots and made 9, and attempted 17 three-point shots and made 12. (Free throws are worth 1 point each, two-point shots worth 2 points each, and three-point shots worth 3 points each)
Required:
a. What is the free throw percentage for the Lions?
b. What is the free throw percentage for the Eagles?
c. What is the field goal percentage (two-point and three-point shots combined) for the Lions?
d. What is the field goal percentage (two-point and three-point shots combined) for the Eagles?
e. How many points did the Lions score?
f. How many points did the Eagles score?
g. Which team won the basketball game?
Answer:
a. The free throw percentage for the Lions is of 62.5%.
b. The free throw percentage for the Eagles was of 37.04%.
c. The field goal percentage for the Lions was of 56.01%.
d. The field goal percentage for the Eagles was of 34.43%.
e. The Lions scored 96 points.
f. The Eagles scored 64 points.
g. Lions
Step-by-step explanation:
a. What is the free throw percentage for the Lions?
10 out of 16, so:
10*100%/16 = 62.5%.
The free throw percentage for the Lions is of 62.5%.
b. What is the free throw percentage for the Eagles?
10 out of 27, so:
10*100%/27 = 37.04%
The free throw percentage for the Eagles was of 37.04%.
c. What is the field goal percentage (two-point and three-point shots combined) for the Lions?
25 + 12 = 37 out of 50 + 16 = 66. So
37*100%/66 = 56.01%.
The field goal percentage for the Lions was of 56.01%.
d. What is the field goal percentage (two-point and three-point shots combined) for the Eagles?
9 + 12 = 21 out of 44 + 17 = 61. So
21*100%/61 = 34.43%
The field goal percentage for the Eagles was of 34.43%.
e. How many points did the Lions score?
10 free throws, 25 two's and 12 three's. So
[tex]10 + 25*2 + 12*3 = 96[/tex]
The Lions scored 96 points.
f. How many points did the Eagles score?
10 free throws, 9 two's and 12 three's. So
[tex]10 + 9*2 + 12*3 = 64[/tex]
The Eagles scored 64 points.
g. Which team won the basketball game?
The Lions scored more points, so they won.
Answer:
avaavavavavav
Step-by-step explanation:
