Answer:
y=¼x-6
Step-by-step explanation:
y=mx+c
y=¼x+-6
y=¼x-6
1. Find the exact value of sin( a−B), given that sin a=−4/5 and cos B=12/13, with a in quadrant III and B in quadrant IV.
2. Find all real numbers in the interval [0,2pi) that satisfy the equation.
3sec^2 x tan x =4tan x
3. Simplify the following trigonometric expressions, using identities as needed:
sin(x)/1−cos(x) + 1−cos(x)/sin(x)
(1) Recall that
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
sin²(x) + cos²(x) = 1
Given that α lies in the third quadrant, and β lies in the fourth quadrant, we expect to have
• sin(α) < 0 and cos(α) < 0
• sin(β) < 0 and cos(β) > 0
Solve for cos(α) and sin(β) :
cos(α) = -√(1 - sin²(α)) = -3/5
sin(β) = -√(1 - cos²(β)) = -5/13
Then
sin(α - β) = sin(α) cos(β) - cos(α) sin(β) = (-4/5) (12/13) - (-3/5) (-5/13)
==> sin(α - β) = -63/65
(2) In the second identity listed above, multiplying through both sides by 1/cos²(x) gives another identity,
sin²(x)/cos²(x) + cos²(x)/cos²(x) = 1/cos²(x)
==> tan²(x) + 1 = sec²(x)
Rewrite the equation as
3 sec²(x) tan(x) = 4 tan(x)
3 (tan²(x) + 1) tan(x) = 4 tan(x)
3 tan³(x) + 3 tan(x) = 4 tan(x)
3 tan³(x) - tan(x) = 0
tan(x) (3 tan²(x) - 1) = 0
Solve for x :
tan(x) = 0 or 3 tan²(x) - 1 = 0
tan(x) = 0 or tan²(x) = 1/3
tan(x) = 0 or tan(x) = ±√(1/3)
x = arctan(0) + nπ or x = arctan(1/√3) + nπ or x = arctan(-1/√3) + nπ
x = nπ or x = π/6 + nπ or x = -π/6 + nπ
where n is any integer. In the interval [0, 2π), we get the solutions
x = 0, π/6, 5π/6, π, 7π/6, 11π/6
(3) You only need to rewrite the first term:
[tex]\dfrac{\sin(x)}{1-\cos(x)} \times \dfrac{1+\cos(x)}{1+\cos(x)} = \dfrac{\sin(x)(1+\cos(x))}{1-\cos^2(x)} = \dfrac{\sin(x)(1+\cos(x)}{\sin^2(x)} = \dfrac{1+\cos(x)}{\sin(x)}[/tex]
Then
[tex]\dfrac{\sin(x)}{1-\cos(x)}+\dfrac{1-\cos(x)}{\sin(x)} = \dfrac{1+\cos(x)+1-\cos(x)}{\sin(x)}=\dfrac2{\sin(x)}[/tex]
HELP ASAP. I can’t miss anymore please help
[tex]4\pi[/tex]
Step-by-step explanation:
[tex]C = 2\pi r,\:\:\:\:r = 4[/tex]
The circumference of the circle of radius 4 is [tex]8\pi[/tex]. Since we are dealing with only half of the circle, the arc length is then half the circumference or [tex]4\pi[/tex].
Matthew participates in a study that is looking at how confident students at SUNY Albany are. The mean score on the scale is 50. The distribution has a standard deviation of 10 and is normally distributed. Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale
Answer:
The percentage of people that could be expected to score the same as Matthew or higher on this scale is:
= 93.3%.
Step-by-step explanation:
a) Data and Calculations:
Mean score on the scale, μ = 50
Distribution's standard deviation, σ = 10
Matthew scores, x = 65
Calculating the Z-score:
Z-score = (x – μ) / σ
= (65-50)/10
= 1.5
The probability based on a Z-score of 1.5 is 0.93319
Therefore, the percentage of people that could be expected to score the same as Matthew or higher on this scale is 93.3%.
Determine how much simple interest you would earn on the following investment:
$13,400 invested at a 6/2 % interest rate for 4 years.
Answer:
How do you mean 6/2%? Clarify it for assistance
Answer:
Simple interest = $ 3,484.00
Step-by-step explanation:
I= P×R×T ÷ 100
The rate is 6 1/2 and I will use the decimal form 6.5,to change that to a whole number we simply move the decimal point one place behind.
Since we moved the decimal point in the numerator we need to do the same for the denominator.Therefore 100 becomes 1000.
13400 × 65 × 4 = $ 3,484.00
1000
Merci de m'aider rapidement !
Answer:
I will answer in English.
We can prove that the angle APS is a triangle rectangle.
Remember that for a triangle rectangle of catheti A and B, and hypotenuse H, the Pythagorean's theorem says that:
A^2 + B^2 = H^2
In this case, we can assume that the hypotenuse is the longer side, AS, and the other two sides are the catheti.
Then we have:
H = 5x + 10
A = 3x + 6
B = 4x + 8
Now let's write the equation from the theorem, and let's see if its true.
A^2 + B^2 = H^2
( 3x + 6 )^2 + (4x + 8)^2 = (5x + 10)^2
So we can start with:
( 3x + 6 )^2 + (4x + 8)^2
And try to "transform" this into:
(5x + 10)^2
First, let's expand it:
((3x)^2 + 2*(3x)*6 + 6^2) + ( (4x)^2 + 2*(4x)*8 + 8^2)
9x^2 + 24x + 36 + 16x^2 + 64x + 64
25x^2 + 40x + 100
Now we can complete squares on the left side, by writing:
(5x)^2 + 2*10*(5x) + 10^2
(5x + 10)^2
Then we saw that the equation is true for every value of x, then we just prove that the triangle fulfills the theorem, thus, the triangle is a triangle rectangle.
A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest, the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 120 students from this university was collected and the size of their CD collections recorded. These particular 120 students had a mean CD collection size of 80 CDs. Select the correct description of the population in this study.
Complete Question
A few years ago, people tended to have relatively large CD collections. For students at a large university in the midwest, the mean number of CDs owned was 78 with a standard deviation of 90. To confirm these numbers, a random sample of 120 students from this university was collected and the size of their CD collections recorded. These particular 120 students had a mean CD collection size of 80 CDs. What is the numerical value of the sample mean?
Answer:
Sample Mean [tex]\=x=80[/tex]
Step-by-step explanation:
From the question we are told that:
Population Mean [tex]\mu=78[/tex]
Standard deviation [tex]\sigma=90[/tex]
Sample size [tex]n=120[/tex]
Sample Mean [tex]\=x=80[/tex]
Therefore
The numerical value of the sample mean is
Sample Mean [tex]\=x=80[/tex]
A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation.
Y
p(x,y) 0 1 2
x 0 0.10 0.04 0.02
1 0.08 0.20 0.06
2 0.06 0.14 0.30
a. What is P(X = 1 and Y = 1)?
b. Compute P(X ≤ 1 and Y ≤ 1).
c. Give a word description of the event {X ≠ 0 and Y ≠ 0}, and compute the probability of this event.
d. Compute the marginal pmf of X and of Y. Using pX(x), what is P(X ≤ 1)?
e. Are X and Y independent rv’s? Explain.
Answer:
a. 0.2
b. 0.42
c. 0.7
d. the solution is in the explanation
e. x and y are not independent
Step-by-step explanation:
a. from the joint probability mass function table,
p(x=1) and p(Y= 1)
= p(1,1) = 0.2
b. prob(0,0)+prob(0,1)+prob(1,0)+prob(1,1)
= 0.10 + 0.04 + 0.08 + 0.20
= 0.42
P(X ≤ 1 and Y ≤ 1) = 0.42
c. prob {X ≠ 0 and Y ≠ 0}
= prob(1,1) + prob(1,2) + prob(2,1) + prob(2,2)
= 0.20 + 0.06 + 0.14 + 0.30
= 0.7
d. we have to calculate the marginal pmf of x and y here.
we have the x values as 0,1,2
prob(x=0) = 0.1 + 0.04 + 0.02
= 0.16
prob(x=1) = 0.08 + 0.2 + 0.06
= 0.34
prob(x=2) = 0.06+0.14+0.3
= 0.50
we have y values as 0,1,2
prob(y=0) = .1+.08+.06
= 0.24
prob(y=1) = .04+.2+.14
= 0.38
prob(y = 2) = 0.02+0.06+0.3
= 0.38
P(X ≤ 1) = prob(x=0)+prob(x=1)
= 0.34+0.16
= 0.50
e. from the joint table we have this,
prob(1,1) = 0.2
prob(x=1) = 0.34
prob(y=1) = 0.38
then prob(x=1)*prob(y=1)
= 0.34*0.38
= 0.1292
therefore prob(1,1) is not equal to prob(x=1)*prob(y=1)
0.2≠0.1292
x and y are not independent
Put -3.0-3.45, -15, and -3.15 in order from least to greatest.
Answer:
-15 -3.45 -3.15 -3.0
Step-by-step explanation:
stuck on this problem
Answer:
B
Step-by-step explanation:
When we reflect something across the y axis, the y axis stays the same but the x values change by a factor of -1.
B is the Answer
Answer:
c. switch the x-values and y-values in the table
Step-by-step explanation:
For any table or graph reflection over the line y=x
The rule is (x,y) ----> (y,x)
f(x) is reflected over the line y=x, so the coordinates of f(x) becomes
(-2,-31) becomes (-31,-2)
(-1,0) becomes (0,-1)
(1,2) becomes (2,1)
(2,33) becomes (33,2)
As per the rule, we switch the x-values and y-values in the table
For reflection over the line y=x , the coordinate becomes
(-31,-2)
(0,-1)
(2,1)
(33,2)
Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the trunk at a height of 20 ft. Find the length of a wire.
14 ft
15 ft
20 ft
29 ft
Based on the height that the wires attach, and the base length of the stakes, the length of the wire is 29 ft.
How long are the wires?This can be solved with the Pythagorean theorem because the height can be treated as the height of a right-angled triangle. The base as the base of the triangle.
The length of the wire is the hypothenuse.
Length:
c² = a² + b²
c² = 21² + 20²
c² = 841
c = √841
= 29 ft
Find out more on the Pythagorean theorem at https://brainly.com/question/343682.
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prove that
[tex]2 \tan30 \div 1 + tan ^{2} 30 = sin60[/tex]
prove that
.
Step-by-step explanation:
2tan 30° / 1 + tan² 30° =
2(⅓√3) /1 + (⅓√3)² =
⅔√3 / 1+ ⅓ =
⅔√3 / 4/3 =
2/4 √3 =
½√3 = sin 60° (proven)
Find domain of (x^2+3)+[tex]\sqrt{x} 3x-1[/tex]
Answer:
= x^2 + 3 + √3x^2 - 1
Step-by-step explanation:
Remove parentheses: (a) = a
= x^2 + 3 + √x . 3x - 1
x . 3x = 3x^2
= x^2 + 3 + √3x^2 - 1
Solve the following inequality.
- 202-16
Which graph shows the correct solution?
Find m angle QSRIf m angle TSQ=15x , m angle TSR=173^ , and m angle QSR=10x-2
[tex]{\color{red}{\huge{\underbrace{\overbrace{\mathfrak{\:\:\:\:\:\:\:꧁"Answer"꧂\:\:\: }}}}}}[/tex]
[tex]\small\color{blak}{{\underline{\bold{ Find \:a X } } } }[/tex]
[tex]\small\color{black}{{\underline{\bold{173°=15z+10x-2 } } } } \\ = 173 = 25x - 2 \\ = - 25x = - 2 - 173 \\ = - 25x - 175 \\ = \small\color{blue}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: x=7\:\:\:\: }}}}[/tex]
[tex]\small\color{blak}{{\underline{\bold{ Find\:a\:m<QSR } } } }[/tex]
[tex]\small\color{blak}{{\underline{\bold{ 10(7)-2 } } } }\\=70-2\\=\small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: m<QSR=68°\:\:\:\: }}}}[/tex]
[tex]\Large\color{red}{{\underline{\mathfrak {{꧁"Carry\:on\: learning"꧂ }}}}}[/tex]
The measure of angle QSR is 68 degrees.
What is substitution?Substitution means putting numbers in place of letters to calculate the value of an expression.
According to the given question.
m ∠TSQ = 15x
m ∠TSR = 173 degrees
m ∠QSR = 10x -2
Since,
m ∠TSR = m ∠TSQ + ∠QSR
Substitute the value of m ∠TSR, m ∠TSQ and m ∠QSR in the above expression.
⇒ [tex]173 = 15x + 10x - 2[/tex]
⇒ [tex]173 = 25x - 2[/tex]
⇒ [tex]175 = 25x[/tex]
⇒ [tex]x = \frac{175}{25}[/tex]
⇒ [tex]x = 7[/tex]
Again, for finding the value of angle QSR substitute the value of x in 10x - 2.
Therefore,
m ∠QSR = 10(7) - 2
⇒ m ∠QSR = 70 - 2
⇒ m ∠QSR = 68 degrees
Hence, the measure of angle QSR is 68 degrees.
Fid out more information about substitution here:
brainly.com/question/27810586
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Name some real-life situations where graphing could be useful. Discuss your ideas. Name some real-life situations where finding the coordinates of the midpoint of a line segment could be useful.
Answer:
mapping an area
Step-by-step explanation:
One situation and probably the most common is mapping an area. Graphs are great for dividing a geographical location into various sections and creating a model representation of the area. The graph itself allows for specific directions to be shared using the x and y coordinates on the graph. The same applies for finding the midpoint of a line segment. For example, this is useful if you were trying to find a place to meetup with a friend that is an equal distance from where you are and from where your friend is currently located. Therefore, allowing you to meetup at the midpoint.
Consider the equations y = VI and y
32 – 1.
The system of equations is equal at approximately
Answer:
[tex]x = 2.62[/tex] and [tex]x = 0.381[/tex]
Step-by-step explanation:
[tex]y = \sqrt x\\[/tex]
[tex]y = x - 1[/tex]
Required
y, when they are equal.
To do this, we set them to another
[tex]\sqrt{x} = x - 1[/tex]
Square both sides
[tex]x = (x - 1)^2[/tex]
Expand
[tex]x = x^2 - 2x + 1[/tex]
Collect like terms
[tex]x^2 -x-2x+1 = 0[/tex]
[tex]x^2 - 3x + 1 = 0[/tex]
Using quadratic formula
[tex]x = 2.62[/tex] and [tex]x = 0.381[/tex]
Can someone help me please! Thanks
Answer:
hello again.. I think you have a problem about figures
Step-by-step explanation:
please be brave when you try to solve..try to draw new lines to get angle and then look at the overall of shape.. the photo helps you good bye
Which expression gives the best estimate of 30 percent of 61?
The answers are below:
Hurry, please!
Answer:
it would be 1/4(60)
Step-by-step explanation:
30 percent of 61 is 18.3 and 1/4 of 60 is 15 which is closest to 18.3
Help Me! Fake Answers will be reported.
How many triangles are there in this picture?
Im sorry if you get this wrong but im going with 14 only because i did this question with my class in school and a boy said 14 and got it right.
Answer:
28
Step-by-step explanation:
there are bigger triangles in the triangles pls dont remove
Let T be the event that an adult admits to texting while driving and N be the event an adult does not admit to texting while driving. We previously determined
P(T) = 0.61
and
P(N) = 0.39.
Since three adults are chosen randomly, we have the following simple events.
TTT TTN TNT NTT TNN NTN NNT NNN
The adults were randomly selected, indicating these can be seen as independent events. Therefore, the multiplication rule can be used. Recall the multiplication rule states that for independent events, the probability that they all occur is the product of their respective probabilities. Let x be the number of adults who admit to texting while driving. Since three adults are randomly selected, then x can take on the values 0, 1, 2, or 3.
When x = 0, then no adult in the group of three admits to texting while driving. This corresponds to the simple event NNN whose probability is calculated as below.
P(x = 0) = P(NNN)
= P(N)P(N)P(N)
= 0.39(0.39)(0.39)
=
When x = 1, then only one adult in the group admits to texting while driving. This corresponds to the simple events TNN, NTN, and NNT. First, calculate the probability of each simple event by multiplying the individual probabilities. Then sum the three simple events to find
P(x = 1).
Calculate
P(x = 1).
P(x = 1) = P(TNN) + P(NTN) + P(NNT)
= P(T)P(N)P(N) + P(N)P(T)P(N) + P(N)P(N)P(T)
= 0.61(0.39)(0.39) + 0.39(0.61)(0.39) + 0.39(0.39)(0.61)
=
Find the remaining probabilities
P(x = 2)
and
P(x = 3).
P(x = 2) = P(TTN) + P(TNT) + P(NTT)
= P(T)P(T)P(N) + P(T)P(N)P(T) + P(N)P(T)P(T)
= 0.61(0.61)(0.39) + 0.61(0.39)(0.61) + 0.39(0.61)(0.61)
=
P(x = 3) = P(TTT)
= P(T)P(T)P(T)
= 0.61(0.61)(0.61)
=
Answer:
Step-by-step explanation:
X P(X=x)
0 0.39*0.39*0.39 = 0.059319
1 3*0.61*0.39*0.39 = 0.278343
2 3*0.61*0.61*0.39 = 0.435357
3 0.61*0.61*0.61 = 0.226981
Find the value of x in each case:
Answer:
36
Step-by-step explanation:
2x is an exterior angle
Exterior angles = the sum of the two remote (unconnected - non supplementary interior angles).
Put symbolically
<LEG = <EGF + <EFG
<EFG = 180 - 4x In this case you need to find the supplemtnt
<LEG = x + 180 - 4x
2x = 180 - 3x Add 3x to both sides
5x = 180 Divide by 5
x = 36
What is 5.071 in words?
Answer:
Step-by-step explanation:
The number 5.071 written in english words is "five and seventy-one thousandths
Help me pls
I put the picture in the attach file below
(Sorry i'm in secondary school but i have a problem with my settings)
Step-by-step explanation:
0 is the ans my guy
dngjdjvkdkckgkdkgkskfkfkv
Write a rational function that meets the following criteria:
Vertical asymptote at x = 1
Horizontal asymptote at y = 2
and a hole at x = 3
Gloria received a 4 percent raise and is now making $24,960 a year, what was her salary before the raise?
She gets a 4% raise so her new pay is 100% + 4% of her previous pay.
104% = 1.04 as a decimal.
Divide her new pay by 1.04:
24,960 / 1.04 = 24,000
Her previous pay was $24,000
Tim Hortons is hiring and offers $200 every week plus $5 per hour. McDonalds offers $300 every week plus $2 per hour. State the conditions under which Tim Hortons is the better employer
Answer:
Assuming you want better payment each week, any number of hours above 33.333 or 33 hours and 20 minutes per week
Step-by-step explanation:
There are several ways we could do this. We could say we want to have Tim Hortons be the better employer on the first week, or after so many weeks by adjusting the hours. I am going to assume we are saying we want it to be a better employer on the first week, so the profit will be the amount made every week plus the money made per hour times the number of hours.
Let's say number of hours is H
So Tim Hortons winds up as 200 + 5H for one week and Mcdonalds will be 300 + 2H.
If you set the two expressions equal to each other you will find where they intersect, which means at that number of hours they will give the same amount of money while any amount before one of the companies will give more and after that many hours the other will. Let's go ahead and solve.
200 + 5H = 300 + 2H
3H = 100
H = 100/3
So H is about 33.333. let's check.
200 + 5(33.333) = 366.665 which rounds to 366.67 dollars
300 + 2(33.333) = 366.666 which also rounds to 366.67 dollars
So at 33.333 hours both give 366.67 dollars. Let's look at a value below it, say 32.
200 + 5(32) = 360
300 + 2(32) = 364
So you can see here Tim Hortons pays less. Now we will try 34 as a value above 33.333
200 + 5(32) = 370
300 + 2(32) = 368
Here Mcdonalds pays less. This was to show that values below 33.333 make Tim Hortonspay less and values above 33.333 make Mcdonalds pay less. In other words any value above 33.333 hours will have Tim Hortons be the better employer. And this is per week
I want to repeat, you can expand this to be multiple weeks and see which of the two becomes better in that epriod of time. This was, I think, the simplest way to answer though.
So the conditions where Tim Horton pays more isif you work more than 33.333 hours per week. This will make them pay more every single week.
Side CA of the right triangle CAT is 3cm long. The hypotenuse is 5cm long. How many
square centimeters is the area of CAT?
Answer:
8
Step-by-step explanation:
By taking the number "3" and plus together with the number 5
Helppp more points 20 math
Answer:
root(250)
answer choice C
Step-by-step explanation:
explanation in the pic above.
2.7.2 : Checkup - Practice Problems
Determine the measure of the interior angle at vertex C.
Answer:
The ANSWER is 18*3= 54
Step-by-step explanation:
total angle inside pentagon = 540 degrees so 3(8x)+2(3x)=540 and that is 30x=540
Answer:
C = 144
Step-by-step explanation:
A 5 sided figure has the interior angle sum of 540 degrees
8x+8x+8x+3x+3x = 540
Combine like terms
30x= 540
30x/30 = 540/30
x = 18
<C = 8*18 = 144
