0.1/0.5 is the same as 1/5
1/5 = X/10
we times both sides by 10 to get x on its own
1/5 x 10 = 10/5 = 2 ( which equals X/10 x 10)
X/10 x 10 = X
2 = X
Write each expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression and all functions are of x only.
[tex]\frac{csc^2 (-x)-1}{1-cos^2 (-x)}[/tex]
[tex]\stackrel{\textit{reciprocal ident.}}{csc(\theta)=\cfrac{1}{sin(\theta)}} ~\hfill \stackrel{\textit{symmetry ident.}}{sin(-\theta )=-sin(\theta)}~\hfill \begin{array}{llll} \stackrel{\textit{pythagorean ident.}}{sin^2(\theta)+cos^2(\theta)=1}\\ sin^2(\theta)=1-cos^2(\theta)\\ cos^2(\theta)=1-sin^2(\theta) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\cfrac{csc^2(-x)-1}{1-cos^2(-x)}\implies \cfrac{~~\frac{1}{sin^2(-x)}-1~~}{sin^2(-x)}\implies \cfrac{~~ \frac{1-sin^2(-x)}{sin^2(-x)}~~}{\frac{sin^2(-x)}{1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{keeping in mind that}~\hfill }{sin^2(-x)\implies [sin(-x)]^2\implies [-sin(x)]^2\implies [sin(x)]^2\implies sin^2(x)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{~~ \frac{1-sin^2(x)}{sin^2(x)}~~}{\frac{sin^2(x)}{1}}\implies \cfrac{1-sin^2(x)}{sin^2(x)}\cdot \cfrac{1}{sin^2(x)}\implies \cfrac{cos^2(x)}{sin^2(x)}\cdot \cfrac{1}{sin^2(x)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cot^2(x)csc^2(x)~\hfill[/tex]
2. Scholarships The probability that Samantha will be accepted by the college of her choice and
obtain a scholarship is 0.35. if the probability that she is accepted by the college is 0.65.
Find the probability that she will obtain a scholarship given that she is accepted by the college.
(4 pts)
The probability that she will obtain a scholarship given that she is accepted by the college is 0.54.
Given that the probability that Samantha will be accepted by the college of her choice and obtain a scholarship is 0.35, to determine, if the probability that she is accepted by the college is 0.65, the probability that she will obtain a scholarship given that she is accepted by the college, the following calculation must be performed:
0.65X = 0.35 X = 0.35 / 0.65 X = 0.538
Therefore, the probability that she will obtain a scholarship given that she is accepted by the college is 0.54.
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Please help ASAP!!! Will give 10 pts!!
Mary has some chocolates. If she shares them equally among 4 friends or 5 friends, there are always 2 extra chocolates left. What is the possible number of chocolates Mary could have?
Answer:
22 chocolates
Step-by-step explanation:
First, let x represent the number of chocolates Mary has. Since she always has 2 extra chocolates, the number of chocolates distributed to her friends would be x - 2. And x - 2 is the least common multiple of 4 and 5 because x - 2 chocolates are evenly distributed among 4 and 5 friends. The LCM of 4 and 5 is 20, so x - 2 is 20. Mary has 22 chocolates.
An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/ unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use α = .05. Use both p-Value and Critical-Value approaches. Type of Ride Roller Coaster Screaming DemonLog FlumeMethod 1 41 52 50 43 44 46 49 46 48Method 2 49 50 48 51 46 44 47 48 46
1. Set up the ANOVA table (to 1 decimal, if necessary).2. The p-value for Factor A is ___________.3. What is your conclusion with respect to Factor A?4. The p-value for Factor B is_________. 5. What is your conclusion with respect to Factor B?6. The p-value for the interaction of factors A and B is ____________.7. What is your conclusion with respect to the interaction of Factors A and B?8. What is your recommendation to the amusement park?
Answer:
An amusement park studied methods
Step-by-step explanation:
how can 26n-7m+4(10n-6m)
Answer:
66n-31m
Step-by-step explanation:
26n-7m+4(10n-6m)
26n-7m+40n-24m
66n-31m
Jordan has a part-time job which pays $75 a week. He has already saved $55 toward the purchase of a $400
could use to find the minimum number of weeks Jordan must work to have enough money to buy the iPhone
Answer:
5 weeks
Step-by-step explanation:
The amount of money he has to earn in order to buy the phone is: 400-55 = 345( dollars)
He gets 345 dollars in: 345÷75= 4 weeks and remains 45 dollars
So he needs to work for 1 more week to have enough money to buy the phone
So he needs to work at least 5 weeks
Suppose a group of 100 women aged 60-64 got a new flu vaccine in 2004, and 5 of them died the following year. Is this event unusual? Specifically, how likely is it that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year? Know the chance of dying of a woman aged 60-64 getting a new flu vaccine in the next five years is 0.009.
Therefore, the probability that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year is 0.0000000059049%, making the event absolutely unusual.
Given that a group of 100 women aged 60-64 got a new flu vaccine in 2004, and 5 of them died the following year, to determine if this event is unusual, and specifically, how likely is it that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year knowing that the chance of dying of a woman aged 60-64 getting a new flu vaccine in the next five years is 0.009, the following calculation must be performed:
0.009 x 0.009 x 0.009 x 0.009 x 0.009 = X 0.000000000059049 = X 0.000000000059049 x 100 = X 0.0000000059049% = X
Therefore, the probability that at least 5 out of 100 women aged 60 to 64 who get the flu vaccine will die within the next year is 0.0000000059049%, making the event absolutely unusual.
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40x^-4 y^-6/(over)10x^-5 y^5
Answer:
4x/y¹¹
Step-by-step explanation:
1) take out constants
40/10 * x⁻⁴y⁻⁶/x⁻⁵y⁵
2) simplify 40/10 to 4
4 * x⁻⁴y⁻⁶/x⁻⁵y⁵
3) Use Quotient Rule: xᵃ/xᵇ=xᵃ⁻ᵇ
4x⁻⁴⁺⁵y⁻⁶⁻⁵
4) Simplify -4 + 5 to 1
4x¹y⁻⁶⁻⁵
5) simplify -6-5 to -11
4x¹y⁻¹¹
6) use rule of one: ₓ¹=ₓ
4xy⁻¹¹
7) use negative power rule: x⁻ᵃ=1/xᵃ
4x * 1/y¹¹
8) simplify
4x/y¹¹
The point (3, 3) is in what quadrant? 2,1,3,4
Answer:
1
Step-by-step explanation:
(3,3) has a positive x value and a positive y value which means it is in the first quadrant
Find the sum. 2/5(d-10)-2/3(d+6)
Answer:
-4d
Step-by-step explanation:
L.c.m=15
15×2/5(d-10)-2/3×15(d+6)
3×2(d-10)-2×5(d+6)
6(d-10)-10(d+6)
6d-60-10d-60
6d-10d-60-60
-4d-0
-4d
280 is 72% of what number?
Answer:
389
Step-by-step explanation:
MARK BRAINLIEST PLEASE
Use the following table to answer the questions below. Give your probabilities as DECIMALS rounded to the hundredths place.
Fair Hair
Dark Hair
Blue Eyes
8
5
Other
7
10
Jamie investigated hair and eye color.
One of the people is chosen. Calculate the probability of choosing
a. Someone with Blue eyes
b. Someone with fair hair and blue eyes
A person with dark hair is chosen. Calculate the probability of
1. them having blue eyes.
2. them not having blue eyes
Answer: 1 =.43, 2=.26, 3=.16 4=.33
Step-by-step explanation: So to find all these answers we have to know the total number of people in the chart 30. Then we have to find what info we need from the chart and divide it by the total number of people. I hope this helped I tried to make it simple.
Solve this plz question plz
We have: [tex](-\frac{15}{18})[/tex] ÷ [tex](-\frac{20}{24})[/tex] = [tex]\frac{-15}{18} .\frac{-24}{20} = \frac{(-3)(5).(-4)(6)}{(3)(6).(4)(5)} = 1[/tex]
ANSWER: 1
ok done. Thank to me :>
Answer:
1
Step-by-step explanation:
[tex]( - \frac{15}{18} ) \div ( - \frac{20}{24} ) \\ now \: you \: have \: fraction \: divided \: by \: fraction \: then \: do \: reciprocal \: \\ ( - \frac{15}{18} ) \times ( - \frac{24}{20} ) \\ = 1[/tex]
My answer is 8, but I'm not completely sure, if I'm wrong could someone please explain how to find the length.
By knowing that S is bisected by the line shown, we will conclude that PD = 8
So here we know that PC = 8, we also can see that:
PCS is a right trianglePDS is a right triangle.Notice that because the blue line bisects S, the angle at "S" on both of these right triangles is the same, and because both of these are right triangles, both must have a 90° angle.
Finally, if two angles are equal, then the 3 angles must be equal between these two triangles.
And notice that both of these triangles share one side, then:
Triangles we know for sure that triangles PCS and PDS have the same angles and one equal side.
This implies that the triangles are congruent, thus, the measures of the corresponding sides must be the same.
Then the length of the shorter side of both triangles must be the same, in triangle PCS the short leg measures 8 units, then in triangle PDS the short leg, PD, also must measure 8 units.
So you are correct.
If you want to learn more about congruent triangles, you can read:
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which statement is true
Two parallel lines are cut by a transversal, as shown below. Solve for b. Then explain your reasoning.
Answer:
b = 14
Step-by-step explanation:
Since both angles are diagonal each other, they are equal to each other.
5b = b + 56
-b -b (subtract b from both sides)
4b = 56
4 4 (divide both sides by 4 to solve for b)
b = 14
can someone please help me with this I don’t wanna fail math
Answer: y = mx + b is the slope intercept form of writing the equation of a straight line
Step-by-step explanation:
Answer:
Step-by-step explanation:
, y=mx+b, of linear equations, emphasizes the slope and the y-intercept of the line.
Molly went to play miniature golf on Monday, when it cost $7 to rent the club and ball, plus $1 per game. Sharon went Thursday, paying $2 per game, plus rental fees of $4. By coincidence, they played the same number of games for the same total cost. How much did each one spend?
Answer:
Molly played 4 games
PLEASE HELP IM BEING TIMED!
Ivan is making cookies for a party. He has 5 cups of flour. The recipe calls for 2 cups of flour. Ivan wants to double the recipe.
Which statement about the amount of flour for the doubled recipe is true?
O A. Ivan has 1 cups of flour more than he needs.
B. Ivan has
5
cup of flour more than he needs.
O c Ivan has exactly enough flour.
D. Ivan needs
cup more flour than he has.
OE. Ivan needs 1
cups more flour than he has.
The recipe calls for 2 cups of flour. The double of this amount is :
[tex]\mathfrak{2*2} [/tex]
[tex]\underline{\mathfrak{=4}} [/tex]
If Ivan has 5 cups, then :
[tex]\mathfrak{5-4} [/tex]
[tex]\underline{\mathfrak{=1}} [/tex]
So, O A. Ivan has 1 cup of flour more than he needs.
[tex]\mathbb{MIREU} [/tex]
write an expression to represent admission to a zoo of $10.00 and the cost of special exhibits s at $4 each. Evaluate you expression when s=2
Answer:
10.00 +4s .
u wanted expression , not answer.?
Step-by-step explanation:
For f(x) = 2(6)*, find y when x=2.
f(2)=
Answer:
I believe it is f(2) = 12
Step-by-step explanation:
I don't know if the * symbol is supposed to be an x but if it is, it would be 12x instead of 12.
You go to a restaurant and get a bill for $95. You need to tip the waitress. The service was good so you decide on tipping the waitress 20%. What is the tip that the waitress will receive
Answer:
19 dollars.
Step-by-step explanation:
0.20 x $95.00=$19.00.
need help solving this
Answer:
x ≈ 41.6°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan x = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{JK}{KL}[/tex] = [tex]\frac{80}{90}[/tex] = [tex]\frac{8}{9}[/tex] , then
x = [tex]tan^{-1}[/tex] ( [tex]\frac{8}{9}[/tex] ) ≈ 41.6° ( to the nearest tenth )
can anyone find out what this is?
Answer:
Expression D
Step-by-step explanation:
all other answers are above 15! hope this helps :D
Sue has 100 dimes and quarters. If the total value of the coins is &21.40, how many of each kind of coin does she have?
Answer:
Let x be the number of dimes and y the number of quarters
x +y = 100
a dime is $0.10 and a quarter is $0.25
0.1x + 0.25y = 21.40 multiply by 100 to remove the decimals
10x + 25y = 2140, From the first equation y = 100 - x and plug it in to the second equation.
10x + 25(100 -x) = 2140
10x + 2500 - 25x =2140
2500 - 15x = 2140
360 = 15x x = 24 and y = 76
There are 24 dimes and 76 quarters
Answer:
76 Quarters = $19.00
24 Dimes = $2.40
$19.00 + $2.40 = $21.40
Step-by-step explanation:
Yaga
How do you multiply a fraction and a whole number? Please explain step by step to get marked as brainliest!
Answer: 1 1/2 x 4 4/7
= 3/2 x 32/7
= 96/14
Step-by-step explanation:
1. Write the whole number as a fraction with a denominator of 1.
2. Multiply the numerators.
3. Multiply the denominators
4. Simplify. If needed, if your answer is greater than 1, you may want to write your answer as a mixed number.
What system the system that is made up of the heart,blood, and blood vessels is called the ____ this is for sceince but i cant find sceince
Answer:
Cardiovascular system
Step-by-step explanation:
If xy + xb + ya + ab = 32 and x + a = 4 , then x + b =
and i will give BRAINLIEST
Answer:
Step-by-step explanation:
If you're actually looking for y + b rather than x + b
Then
xy + xb + ya + ab = (x + a)(y + b) = 32
4(y + b) = 32
y + b = 8
otherwise we have a situation with only two equations and four unknowns. This cannot be resolved without further information.
Pure acid is to be added to a 10% acid solution to obtain 90L of 81% solution. What amounts of each should be used?
How many liters of 100% pure acid should be used to make the solution?
Answer:
Step-by-step explanation:
let X be the quantity of 100% acid
let Y be the quantity of 10% acid
X + Y = 90
Y = 90 - X
X(100) + Y(10) = 90(81)
X(100) + (90 - X)(10) = 90(81)
100X + 900 - 10X = 7290
90X = 6390
X = 71 L