Answer:
32P6
Step-by-step explanation:
nPr
n=32
r=6
Simplify. v80
A. 16v5
B. 5v4
C. 4v5
D. 20v4
Hi!
√80 = √(16 • 5) = √(4² • 5) = 4√5
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]
PLZ PLZ HELP
Mark is investing $47,000 in an account paying 5.26% interest compounded continuously.
What will Mark's account balance be in 17 years?
O $114,932.80
$114,925.39
$114,921.47
$114.925.46
===============================================
Work Shown:
A = P*e^(r*t)
A = 47000*e^(0.0526*17)
A = 114,932.799077198
A = 114,932.80
Notes:
P = 47,000 is the principal or amount depositedr = 0.0526 is the decimal form of 5.26%The "e" refers to the special constant e = 2.718... which is similar to pi = 3.14... I would let your calculator handle this constant. There should be a button labeled "e".Mark's account balance after 17 years would be $114,932.8
What is the formula for the continuous compounding?[tex]A=Pe^{rt}[/tex]
where,
A = Accrued amount
P = Principal amount
r = interest rate as a decimal
R = interest rate as a percent
r = R/100
t = time in years
For given question,
P = $47000, t = 17 years
R = 5.26%
[tex]\Rightarrow r =\frac{5.26}{100}\\\\\Rightarrow r = 0.0526[/tex]
Using the Continuous Compounding Formula,
[tex]\Rightarrow A=Pe^{rt}\\\\\Rightarrow A=47000\times e^{0.0526\times 17}\\\\\Rightarrow A=114932.8[/tex]
Therefore, Mark's account balance after 17 years would be $114,932.8
Learn more about the Continuous Compounding here:
https://brainly.com/question/24246899
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evaluate the expression when b= -6 and c=3
-4c+b
Answer:
-18
Step-by-step explanation:
b = -6
c = 3
-4c + b = ?
Plug in the value of each variable into the equation
-4c + b = ?
= -4(3) + (-6)
= -12 - 6
= -18
i need help solving this .
Answer:b
Step-by-step explanation:
Answer:
just be smart trust me u dont need us to give u the answer ur super smart
Step-by-step explanation:
make me brainliest to help people be encourage
Use the parametric equations of an ellipse, x=acosθ, y=bsinθ, 0≤θ≤2π , to find the area that it encloses.
Answer:
Area of ellipse=[tex]\pi ab[/tex]
Step-by-step explanation:
We are given that
[tex]x=acos\theta[/tex]
[tex]y=bsin\theta[/tex]
[tex]0\leq\theta\leq 2\pi[/tex]
We have to find the area enclose by it.
[tex]x/a=cos\theta, y/b=sin\theta[/tex]
[tex]sin^2\theta+cos^2\theta=x^2/a^2+y^2/b^2[/tex]
Using the formula
[tex]sin^2x+cos^2x=1[/tex]
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]
This is the equation of ellipse.
Area of ellipse
=[tex]4\int_{0}^{a}\frac{b}{a}\sqrt{a^2-x^2}dx[/tex]
When x=0,[tex]\theta=\pi/2[/tex]
When x=a, [tex]\theta=0[/tex]
Using the formula
Area of ellipse
=[tex]\frac{4b}{a}\int_{\pi/2}^{0}\sqrt{a^2-a^2cos^2\theta}(-asin\theta)d\theta[/tex]
Area of ellipse=[tex]-4ba\int_{\pi/2}^{0}\sqrt{1-cos^2\theta}(sin\theta)d\theta[/tex]
Area of ellipse=[tex]-4ba\int_{\pi/2}^{0} sin^2\theta d\theta[/tex]
Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(2sin^2\theta)d\theta[/tex]
Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(1-cos2\theta)d\theta[/tex]
Using the formula
[tex]1-cos2\theta=2sin^2\theta[/tex]
Area of ellipse=[tex]-2ba[\theta-1/2sin(2\theta)]^{0}_{\pi/2}[/tex]
Area of ellipse[tex]=-2ba(-\pi/2-0)[/tex]
Area of ellipse=[tex]\pi ab[/tex]
A driver must decide whether to buy a new car for $24,000 or lease the same car over a four-year period. Under the terms of the lease, she can make a down payment
of $3000 and have monthly payments of $150. At the end of the four years, the leased car has a residual value (the amount she pays if she chooses to buy the car at
the end of the lease period) of $11,000. Assume she can sell the new car at the end of the four years at the same residual value. Is it less expensive to buy or
to lease?
Answer:
3000 is the answer this question.
A statistician calculates that 7% of Americans are vegetarians. If the statistician is correct, what is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%
Answer:
0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A statistician calculates that 7% of Americans are vegetarians.
This means that [tex]p = 0.07[/tex]
Sample of 403 Americans
This means that [tex]n = 403[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.07[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.07*0.93}{403}} = 0.0127[/tex]
What is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%?
Proportion below 7 - 3 = 4% or above 7 + 3 = 10%. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them, and multiply by 2.
Probability the proportion is below 4%
p-value of Z when X = 0.04.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.04 - 0.07}{0.0127}[/tex]
[tex]Z = -2.36[/tex]
[tex]Z = -2.36[/tex] has a p-value of 0.0091
2*0.0091 = 0.0182
0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.
Find f(6), f(0), and f(-1)
f(x)=-7X
Answer:
f(6)=-42
f(0)=0
f(-1)=7
Step-by-step explanation:
since f(x) =-7x
it implies that f(6),f(0) and f(-1) are all equal to f(x)
which is equal to -7x .
so wherever you find x you out it in the
function
Cuanto es 91972×898972819
Answer:
82,680,328,109,068
Step-by-step explanation:
Use the on-line Big Number calculator
1) What is the opposite of adding 5?
2) What is the opposite of subtracting 20?
3) What is the opposite of multiplying by 1/2?
4) What is the opposite of dividing by 10?
I need help pleasereee
Answer:
1. subtracting 5
2. adding 20
3. dividing by 1/2
4. multiplying by 10
What is the coefficient of x2 in the expansion of (x + 2)??
O A.
2
OB.
3
O C.
4
OD.
6
x+2 in expansion of (x+2) ?
A
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 60 mm?
Answer:
22608 mm³/s
Step-by-step explanation:
Applying chain rule,
dV/dt = (dV/dr)(dr/dt)............... Equation 1
Where dV/dr = rate at which the volume is increasing
But,
V = 4πr³/3
Therefore,
dV/dr = 4πr²............... Equation 2
Substitute equation 2 into equation 1
dV/dt = 4πr²(dr/dt).............. Equation 3
From the question,
Given: dr/dt = 2 mm/s, r = 60/2 = 30 mm
Consatant: π = 3.14
Substitute these values into equation 3
dV/dt = 4×3.14×30²×2
dV/dt = 22608 mm³/s
Assume that there is a 8% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive?
Answer:
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
Step-by-step explanation:
For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Assume that there is a 8% rate of disk drive failure in a year.
So 100 - 8 = 92% probability of working, which means that [tex]p = 0.92[/tex]
Two disks are used:
This means that [tex]n = 2[/tex]
What is the probability that during a year, you can avoid catastrophe with at least one working drive?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0064 = 0.9936[/tex]
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. What is the percent of wolves that are female but do not hunt in medium-sized packs?
Probabilityyyyyyyyyyyyyyy
Answer:
Reduce if needed, asked or necessary
Step-by-step explanation:
1. 4/10
2. 2/6
3. 4/10
4. more likely
Answer:
Since Probability Is Usually Written In Fraction Form OR Ratios
(Although It Really Doesn't Matter):
1. 4/10 (2/5)
2. 2/6 (1/3)
3. 6/10 (3/5)
(All Fraction Form)
Last Question:
I can't really see the bottom but probably its 'More likely' since you can already see a bunch of red marbles.
Step-by-step explanation:
This is the basic fraction form : ____ / ____
Based on what they ask, like the probability of picking out a black marble, count the number of black marbles in the particular bag and put that number as the numerator. The denominator is the total amount of marbles in that particular bag. Hope this helps!
the average of two number is xy.if one number is x the other i
Answer:
z = (2xy-x)
Step-by-step explanation:
Let the first number be x and the other number is z.
According to question,
The average of two number is xy i.e.
[tex]\dfrac{x+z}{2}=xy\\\\x+z=2xy\\\\z=2xy-x[/tex]
So, the value of z is (2xy-x) i.e. the other number is (2xy-x).
In which quadrant do the points have negative x-coordinates and negative y-coordinates?
Hi there!
»»————- ★ ————-««
I believe your answer is:
Quadrant III
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
The plane is split into four quadrants. Quadrant III houses all the points with negative signs for both X and Y values.⸻⸻⸻⸻
See the attached picture for reference.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
help me please i am struggle with this
The awnser for this question
1 Find the value of C to that the function probability density function defined as follow, also calculate the man and variance /4
X -1 0 1
f(x) 3c 3c 6c
Answer:
[tex]c = \frac{1}{12}[/tex]
The mean of the distribution is 0.25.
The variance of the distribution is of 0.6875.
Step-by-step explanation:
Probability density function:
For it to be a probability function, the sum of the probabilities must be 1. The probabilities are 3c, 3c and 6c, so:
[tex]3c + 3c + 6c = 1[/tex]
[tex]12c = 1[/tex]
[tex]c = \frac{1}{12}[/tex]
So the probability distribution is:
[tex]P(X = -1) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 0) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]
[tex]P(X = 1) = 6c = 6\frac{1}{12} = \frac{1}{2} = 0.5[/tex]
Mean:
Sum of each outcome multiplied by its probability. So
[tex]E(X) = -1(0.25) + 0(0.25) + 1(0.5) = -0.25 + 0.5 = 0.25[/tex]
The mean of the distribution is 0.25.
Variance:
Sum of the difference squared between each value and the mean, multiplied by its probability. So
[tex]V^2(X) = 0.25(-1-0.25)^2 + 0.25(0 - 0.25)^2 + 0.5(1 - 0.25)^2 = 0.6875[/tex]
The variance of the distribution is of 0.6875.
Identify an equation in point-slope from for the line perpendicular to y=-4x-1 that passes through (-2, 4)
Answer:
y - 4 = ¼(x + 2)
Step-by-step explanation:
Point-slope form equation is given as y - b = m(x - a). Where,
(a, b) = a point on the line = (-2, 4)
m = slope = ¼ (sleep of the line perpendicular to y = -4x - 1 is the negative reciprocal of its slope value, -4 which is ¼)
✔️To write the equation, substitute (a, b) = (-2, 4), and m = ¼ into the point-slope equation, y - b = m(x - a).
y - 4 = ¼(x - (-2))
y - 4 = ¼(x + 2)
None of the options are correct
You are dealt one card from a 52-card deck.
a) Find the odds in favor of getting a red king.
b) Find the odds against getting a red king.
Answer:
(a)So, there are 2 kings in red- one of hearts and the other of diamonds. Therefore, the probability of selecting a red king from a deck of cards= 2/52 or 1/26.
(b) There are 6 red face cards in a 52-card deck (so 46 other cards). PROBABILITIES compare the number of favorable outcomes to the total number of possible outcomes: The PROBABILITY of getting a red face card is 6/52 = 3/26.
The odds in favor of getting a red king will be 1/26. And the odds against getting a red king will be 25/26.
What is probability?Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.
You are dealt one card from a 52-card deck.
Total events = 52
The odds in favor of getting a red king will be
Favorable events = 2
Then the probability will be
P = 2/52
P = 1/26
The odds against getting a red king will be
q = 1 – P
q = 1 – 1/26
q = 25/26
More about the probability link is given below.
https://brainly.com/question/795909
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sets A and B have 3 and 6 elements respectively. what can be the minimum number of elements in AUB
Answer:
6
Step-by-step explanation:
n(AUB) = n(A) + n(B) - n(AnB)
n(AUB) can have the minimum number of elements if n(AnB) has the maximum number of elements.
n(AnB) maximum = 3
so n(AUB) = 3+6-3 = 6
If y- 1 equals 10 then y
Answer:
11
Step-by-step explanation:
y-1=10
Any figure that crosses equal sign, the operational sign changes.
y=10+1
y= 11
I need help with this.
Answer:
A and b Are in quadrant 2. F and D are in quadrant 1. F is in quadrant 3 and C is in quadrant 4
Step-by-step explanation:
each quadrant is in the boxes and the question is asking what is each coordinate is in what quadrant
Which of the following numbers is rational? Assume that the decimal patterns continue.
Answer:
[tex]\sqrt{49}[/tex]
Step-by-step explanation:
Define a rational number by a number able to expressed a fraction where the denominator is not 0 or 1.
Non-terminating (never-ending) decimals cannot be expressed as a fraction and therefore are irrational. However, recall that [tex]\sqrt{49}=7[/tex], which can be expressed as a fraction (e.g. [tex]\frac{14}{2}[/tex], etc). Thus, the answer is [tex]\boxed{\sqrt{49}}[/tex].
HELP ASAP! I don’t know how to solve this problem nor where to start. Can someone please help me out here?
===============================================
Explanation:
It might help to draw out the picture as shown below. The pool itself (just the water only) is the inner rectangle. The outer rectangle is the pool plus the border of those 1 by 1 tiles.
The pool is a rectangle 90 feet by 80 feet. If we add on the tiles, then we get a larger rectangle that is 90+2 = 92 feet by 80+2 = 82 feet.
We add on 2 since we're adding two copies of "1" on either side of each dimension.
The larger rectangle's area is 92*82 = 7544 square feet
The smaller rectangle's area is 90*80 = 7200 square feet
The difference in areas is 7544-7200 = 344 square feet.
Each 1 by 1 tile is of area 1*1 = 1 sq foot, meaning that 344 tiles will get us the 344 square foot border around the pool.
How would I draw the reflection over the line y=2x+5?
Answer:
Step-by-step explanation:
In an examination every student took history or geography or both of 500 candidates 60% took history whiles 72% took geography. How many students took both subjects
Answer:
80 students
Step-by-step explanation:
Answer:
80
Step-by-step explanation:
60% of 500 = 300
72% of 500 = 360
40% of 500 = 200
28% of 500 = 140
300+360 = 660
660 - 2x = 500
660 - 500 = 2x
160 = 2x
2x = 160
x = 80
