Answer:
3 does not represent x okconsider the word meeting. how many unique subsets of 5 letters (of the 7) exist? how many different strings could be made from 5 of those 7 letters?
There are 1260 different strings that can be made from 5 of the 7 letters in the word "meeting."
To determine the number of unique subsets of 5 letters from the word "meeting," we can use the combination formula:
\(n_Cr = n! / r!(n-r)!\)
Where n is the total number of items (in this case, the number of letters in the word "meeting") and r is the number of items being selected (in this case, 5 letters).
So, for "meeting," n = 7 and r = 5.
Plugging these values into the formula gives:
\(7C5 = 7! / 5!(7-5)! = 21\)
Therefore, there are 21 unique subsets of 5 letters that can be formed from the letters in the word "meeting."
To determine the number of different strings that can be made from 5 of those 7 letters, we can use the permutation formula:
\(n_Pr = n! / (n-r)!\)
Where n is the total number of items (in this case, the number of letters in the word "meeting") and r is the number of items being selected (in this case, 5 letters).
So, for "meeting," n = 7 and r = 5.
Plugging these values into the formula gives:
7P5 = 7! / (7-5)!
= 7! / 2!
= 2520 / 2
= 1260
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Question Shown On Photo
Answer: b
Step-by-step explanation:
Using Green's Theorem, calculate the area of the indicated region. The area bounded above by y=7 and below by y=7/25x^2
The area of the indicated region bounded by y=7 and y=7/25x^2 is XXX square units.
To calculate the area using Green's Theorem, we need to express the region in terms of a curve. Green's states that closed the line Theorem line integral integral of over a a vector field around a closed curve is equal to the double integral of the curl of the vector field over the region bounded by the curve.
In this case, we can rewrite the given equations in terms of x and y to define the boundary of the region. The upper boundary is y=7, and the lower boundary is y=7/25x^2. To find the points of intersection between these two curves, we can equate them:
7 = 7/25x^2
Solving this equation, we find x = ±5. Now we have the boundaries of the region in terms of x values.
To express the region in terms of a line integral, we need to define a vector field F = (M, N). In this case, we can take M = 0 and N = x. Now we can apply Green's Theorem:
Area = ∬ D dA = ∮ C N dx = ∮ C x dx
To calculate the line integral, we need to parameterize the curve C that encloses the region. Since the region is bounded by two curves, we need to split the curve into two parts. Let's consider the upper curve C1: y = 7.
Parameterizing C1, we have:
x = t
y = 7, for t ∈ [5, -5]
Now we can calculate the line integral over C1:
∮ C1 x dx = ∫[5,-5] t dt = [t^2/2] evaluated from -5 to 5 = 25/2 - 25/2 = 0
Next, let's consider the lower curve C2: y = 7/25x^2.
Parameterizing C2, we have:
x = t
y = 7/25t^2, for t ∈ [-5, 5]
Now we can calculate the line integral over C2:
∮ C2 x dx = ∫[-5,5] t dt = [t^2/2] evaluated from -5 to 5 = 25/2 - 25/2 = 0
Since both line integrals are zero, the area of the region bounded by y=7 and y=7/25x^2 is 0 square units.
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What is the approximate probability of exactly two people in a group of seven having a birthday on April 15? (A) 1.2 x 10^-18 (B) 2.4 x 10^-17 (C) 7.4 x 10^-6 (D) 1.6 x 10^-4
The approximate probability of exactly two people in a group of seven having a birthday on April 15 is (C) \(7.4 x 10^-^6\)
How we get the approximate probability?To calculate the probability of exactly two people in a group of seven having a birthday on April 15, we can use the binomial distribution formula:
\(P(X = k) = C(n, k) * p^k * (1 - p)^(^n^-^k^)\)
Where:
P(X = k) is the probability of exactly k successes (in this case, k = 2)n is the number of trials (in this case, n = 7)p is the probability of success in a single trial (in this case, p = 1/365, assuming that all days of the year are equally likely for a birthday)C(n, k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items (in this case, C(7, 2) = 21)So, plugging in the values, we get:
\(P(X = 2) = C(7, 2) * (1/365)^2 * (1 - 1/365)^(7 - 2)\)
\(= 21 * (1/365)^2 * (364/365)^5\)
\(= 2.38 x 10^-5\)
The probability of exactly two people in a group of seven having a birthday on April 15 can be calculated using the binomial distribution formula.
The formula takes into account the number of trials, the probability of success in a single trial, and the number of successes desired.
In this case, we want to find the probability that exactly two people in a group of seven have a birthday on April 15, assuming that all days of the year are equally likely for a birthday.
Plugging in the values into the formula gives us an approximate probability of \(7.4 x 10^-^6\), which is the answer (C).
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the area under the normal curve between and a number that is less than is approximately equal to one-fourth of the total area under the entire curve. what is the value of ?
The value of is 1.645. This is derived from the area under the normal curve between 0 and 1.645 being equal to 0.25, which is one-fourth of the total area under the entire curve.
To calculate this, we must first understand the concept of the Standard Normal Distribution. The Standard Normal Distribution is a normal distribution with a mean of 0 and a standard deviation of 1. This is the basis of the calculation.
Next, we need to understand the concept of the cumulative probability density function. This is a function that gives the probability that a variable will take a value that is less than or equal to a given value.
For our calculation, we will use the cumulative probability density function for the Standard Normal Distribution.
Now, to calculate the value of , we can use the cumulative probability density function. We will set the cumulative probability density function equal to 0.25.
This is the probability that a variable will take a value that is less than or equal to . Solving for, we get 1.645. This is the value of.
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Franks buys a riding lawn more with a credit card for 2,000$. The card has an annual interest rate of 20%. Suppose Frank pays $200 a month for his credit card bill. How many months will it take Frank to pay off the credit card balance?
someone help me please
Answer:
1) angle 1 is 55 degrees
2) angle 2 is 55 degrees
3) angle 3 is 70 degrees
4) angles 1 and 2 are vertical
Step-by-step explanation:
1) angle 1 = 180 - (85 + 40)
2) angle 2 has the same measure of angle 1
3) angle 3 is 180 - (55 + 55)
4) angles 1 and 2 are vertical and congruent
2x+3y=3,2y+3z=4,2x+2z=8
Answer:
x=6/5
y=1/5
z=14/5
i think i not 100% sure
You are given that xo = O is a regular singular point of the DE xy" - y + 5y = 0. Find roots r2 r₁, of the indicial equation. If y, is the corresponding series solution to r₁, find the coefficients in this series (an explicit formula for an, in terms of n should be obtained). Only write the general form y2 that can be obtained by this method (DO NOT evaluate series coefficients for y₂). ([2] bonus) Find the radius of convergence of the series solution y₁ only by using the DE.
The series solution be,
⇒ y₁(x) = \(x^{(r_1)}\) Σ(n=0 to ∞) \(c_1_n\) \(x^n\)
Radius of convergence = 2.1
The given differential equation is,
xy" - y + 5y = 0.
The indicial equation for the given differential equation is given by,
⇒ r(r-1) + 5 = 0
Solving for r using the quadratic formula, we obtain,
⇒ r₁ = 1/2 + √(21)/2 ≈ 2.7913
⇒ r₂ = 1/2 - √(21)/2 ≈ -1.7913
Since x₀ = 0 is a regular singular point,
we can assume that the series solution for y takes the form,
⇒ y(x) = Σ(n=0 to ∞) \(c_n x^n\)
Setting r = r₁, we have,
⇒ y₁(x) = \(x^{(r_1)}\)Σ(n=0 to ∞) \(c_1_n x^n\)
Differentiating y1(x) with respect to x, we get,
⇒ y'₁(x) = \(x^{(r_1-1)}\)Σ(n=0 to ∞) \(c_1_{(n+1)} x^n\)
And differentiating again, we get,
⇒ y''₁(x) = \(x^{(r_1-2)}\) Σ(n=0 to ∞) \(c_1_{(n+2)(n+1)} x^n\)
Substituting these expressions into the differential equation, we obtain,
⇒ \(x^{(r_1)[r_1(r_1-1)}\)Σ(n=0 to ∞) \(c_nx^n\) + 5Σ(n=0 to ∞) \(c_nx^n\)] - \(x^{(r_1)}\))Σ(n=0 to ∞) \(c_nx^{(n+2)}\) = 0
Multiplying out and collecting terms with the same powers of x, we get,
⇒ \(x^{(r_1)}\)[\(r_1(r_{(1-1)})\)c₁₀ + 5c₁₀] + \(x^{(r_1+1)}\)[r1(r1-1)c₁₁ + 5c₁₁ - c₁₀] +\(x^{(r_1+2)}\)[r1(r1-1)c₁₂ + 5c₁₂ - c₁₁] + ...
Since the coefficient of \(x^{(r_1)}\) is nonzero, we can divide the entire equation by \(x^{(r_1)}\) to obtain,
⇒ r1(r1-1)c₁₀ + 5c₁₀ + c₁₁x + (r1(r1-1)c₁₁ + 5c₁₁ - c₁₀)x²+ ...
Comparing coefficients of like powers of x, we obtain a recurrence relation for the coefficients,
c₁₁ = -5c₁₀/r1
c₁₂ = [c₁₁(5-r1) - r1(r1-1)c₁₀]/2x2
c₁₃ = [c₁₂(6-r1) - c₁₁(5-r1)*c₁₀]/3x2 ...
Using this recurrence relation and the initial condition y(xo) = 0, we can solve for the coefficients c₁₀, c₁₁, c₁₂, ... and obtain the series solution y1(x) for r1.
Hence the solution series be,
⇒ y₁(x) = \(x^{(r_1)}\) Σ(n=0 to ∞) \(c_1_n\) \(x^n\)
To find the radius of convergence of the series solution y₁, we can use the ratio test.
According to the ratio test, if the limit of\(|c_{n+1}x^{n+1}/c_nx^n|\) as n approaches infinity exists and is less than 1, then the series converges absolutely for all values of x such that |x| < R, where R is the radius of convergence.
Therefore, after applying the ratio test to the series solution y₁(x), we get,
Radius of convergence = (√(21) + 6)/5
= 2.1
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1. the expected value of a random variable can be thought of as a long run average.'
Yes it is correct that the expected value of a random variable can be interpreted as a long-run average.
The expected value of a random variable is a concept used in probability theory and statistics. It is a way to summarize the average behavior or central tendency of the random variable.
To understand why the expected value represents the average value that the random variable would take in the long run, consider a simple example. Let's say we have a fair six-sided die, and we want to find the expected value of the outcomes when rolling the die.
The possible outcomes when rolling the die are numbers from 1 to 6, each with a probability of 1/6. The expected value is calculated by multiplying each outcome by its corresponding probability and summing them up.
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help me please it’s almost due at 10 am
Answer:
a no. is the answer
Step-by-step explanation:
b=a+13
or, 14 = 1+13
or, 14= 14 {True}
Answer:
b=a+13
b=1+13
b=14
again,
b=a+13
b=6+13
b=19
so the relationship between a & b is b=a+13
Find f(2) if f(x)=(x+1)^2
a.6
b.9
c.5
Answer:
b. 9
Step-by-step explanation:
f(2) if f(x)=(x+1)^2
= (2 + 1)^2 = (3)^2 = 9
i hope its help
A plane flies 452 miles north and then 767 miles west. What is the magnitude and direction of the plane's resultant vector?
Answer:
The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north.
Step-by-step explanation:
• To find the magnitude of the resultant vector, we have to use Pythagoras's theorem:
\(\boxed{a^2 = b^2 + c^2}\)
where:
a ⇒ hypotenuse (= resultant vector = ? mi)
b, c ⇒ the two other sides of the right-angled triangle (= 452 mil North, 767 mi West).
Using the formula:
resultant² = \(452^2 + 767^2\)
⇒ resultant = \(\sqrt{452^2 + 767^2}\)
⇒ resultant = 890.3 mi
• To find the direction, we can find the angle (labeled x in diagram) that the resultant makes with the north direction:
\(tan (x) =\frac{767}{452}\)
⇒ \(x = tan^{-1} (\frac{767}{452} )\)
⇒ \(x = \bf{59.5 \textdegree}\)
∴ The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north .
Answer:
\(\displaystyle Approximately\:59°\:at\:a\:magnitude\:of\:approximately\:890\:miles\)
Step-by-step explanation:
\(\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:\theta \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:\theta \\ \frac{OPPOCITE}{ADJACENT} = tan\:\theta \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:\theta \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:\theta \\ \frac{ADJACENT}{OPPOCITE} = cot\:\theta\)
We must use trigonometry to help us find the direction of the aeroplane's resultant vector. Do as I do:
\(\displaystyle \frac{452}{767} = cot\:x \hookrightarrow cot^{-1}\:\frac{452}{767} = x; 59,488772482...° = x \\ \\ \boxed{59° \approx x}\)
Now, we will use the Pythagorean Theorem to find the magnitude of the aeroplane's resultant vector. Do as I do:
\(\displaystyle a^2 + b^2 = c^2 \\ \\ 767^2 + 452^2 = c^2 \\ \sqrt{792593} = \sqrt{c^2}; 890,27692321... = c \\ \\ \boxed{890 \approx c}\)
Therefore, the direction and magnitude of the aeroplane's resultant vector are approximately eight hundred ninety miles at an angle of elevation of fifty-nine degrees.
I am joyous to assist you at any time.
What are the next 3 numbers in the sequence? 2, 4, 9, 18, 23, 46, 51
Answer:
102, 107, 214Step-by-step explanation:
2
4 = 2×2
9 = 4 + 5
18 = 9×2
23 = 18 + 5
46 = 23×2
51 = 46 + 5
51×2 = 102
102 + 5 = 107
107×2 = 214
Find all 3 solutions: 3 − 42 − 4 + 5 = 0
Answer:
Step-by-step explanation:
If you mean 3x^3 - 42x^2 - 4x + 5 = 0 you can graph it manually or with technology
The roots are 14.09, 0.30 and -0.39 to nearest hundredth.
Examine the following diagram: 2 lines intersect to form 4 angles. From the top, clockwise, the angles are 1, 4, 2, 3. Which statement is not true of the given diagram? m∠2 + m∠3 = 180° m∠2 + m∠4 = 180° ∠3 and ∠4 are vertical angles ∠2 ≅ ∠4
Answer:
The answer is D on edg 2020
Step-by-step explanation:
brainliest plz
Answer:
Its D
Step-by-step explanation:
∠2 ≅ ∠4
The curved parts of the figure are arcs centered at points A and C. What is the approximate length of boundary ABCD
Using the formula to calculate the length of arcs, the approximate length of boundary ABCD is 23.1
The arc length is defined as the interspace between the two points along a section of a curve.
The formula for calculating arc length is :\(2\pi r*\frac{theta}{360}\)
DC = 5
AB = 5
AD = \(2*\frac{22}{7} *5*\frac{30}{360} = 2.619\)
BC = \(2*\frac{22}{7} *5*\frac{120}{360} = 10.4762\)
Length of ABCD = AB + BC +CD + AD = 23.1
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what is the volume of the circular cone below?
Answer:
200.96
Step-by-step explanation:
Volume of cone=(1/3)*pi*r^2*h
Volume=(1/3)*pi*16*12=64*3.14=200.96
p = 6, q = 7 and r = 4 Work out a2 pr
Answer:
a times 48
Step-by-step explanation:
a times 2 times p(6) times r(4)
2 times 6 is 12
multiply 12 by 4 to get 48
that is how you get a times 48
Investors buy a studio apartment for $180,000 . Of this amount, they have a down payment of $36,000. Their down payment is what percent of the purchase price? What percent of the purchase price would a $9,000 down payment be?
Answer:
Step-by-step explanation:
From the question, we are informed that investors buy a studio apartment for $180,000 and that they have a down payment of $36,000. The percentage of the down payment on the purchase price will be:
= 36000/180000 × 100
= 1/5 × 100
= 20%
What percent of the purchase price would a $9,000 down payment be?
This will be:
= (9000 / 180000) × 100
= 0.05 × 100
= 5%
Answer:
20%
5%
Step-by-step explanation:
Price of a studio apartment = $180,000
Down payment = $36,000
Their down payment is what percent of the purchase price?
= Down payment / Price of a studio apartment × 100
= $36,000 / $180,000 × 100
= 0.2 × 100
= 20%
What percent of the purchase price would a $9,000 down payment be?
= Down payment / Price of a studio apartment × 100
= $9,000 / $180,000 × 100
= 0.05 × 100
= 5%
Which expression is equivalent to n+n+n?
A. 3^n
B. 3n
C. n^3
D. n+3
Answer:
B. 3n
Step-by-step explanation:
n + n + n = 3n
------------------------------------------
3n = n + n + n
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The veterinarian orders 15 mg of Vitamin K. The vial is labeled 10mg/mL how many mL is needed?
please explain how to do it
Each ml of the vial contains 10 mg of Vitamin K. So to obtain 15 mg of Vitamin K, we needs a volume 1.5 ml of the solution.
We can calculate the required amount in two ways. We can use either proportions, or we can use the unit value determination.
By using proportions.In 1 ml we have 10mg , to get 15 mg we can use x ml
\(\frac{1}{10} = \frac{x}{15}\)
\(x = \frac{15* 1}{10}\)
x = 1.5
So, to get 15 mg of Vitamin K, we need 1.5 ml of solution.
By finding the unit valueVolume required to get 10 mg of vitamin K = 1 ml
Volume required to get 1 mg of vitamin K = \(\frac{1}{10}\) ml = 0.1 ml
Volume required to get 15 mg of Vitamin K = 15 × 0.1 = 1.5 ml
So volume required to get 15mg = 1.5 ml
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When it is born a kitten weighs 110g when it is two months old it weighs 550g calculate the percentage increase in its mass
Given:
Initial weight of kitten = 110g
Present weight of kitten = 550g
To find:
The percentage increase in its mass.
Solution:
To get the percentage increase in its mass, we need to find the percentage increase in its weight.
\(\%Increase=\dfrac{\text{Present value - Initial value}}{\text{Initial value}}\times 100\)
\(\%Increase=\dfrac{550-110}{110}\times 100\)
\(\%Increase=\dfrac{440}{110}\times 100\)
\(\%Increase=4\times 100\)
\(\%Increase=400\)
Therefore, the percentage increase in kitten's mass is 400%.
the measure of the total audience size for a given platform is determined by which metric?
Audience reach is a metric that is used to measure of the total audience size for a specific provide platform.
Audience reach answers the question of how many people have had the opportunity to consume (i.e. read, watch, and/or hear) news coverage of whatever you're watching. This metric is based on known circulation, viewership, audience size and followers of media outlets or social media users who publish the content in question. For the audience size of the publication/social media user providing the content is identified and then this number is added to the audience size of all other outlets publishing the content to give the total audience reach.
The first relates to viewership data for traditional online news content. Some in the measurement industry use the value of unique website visitors per month for audience reach calculations, while others use daily website traffic data. The second thing to keep in mind is that some PR or media measurement firms may use multipliers when calculating audience reach to account for dozens of people read that one copy.Hence, required answer is audiance reach.
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Solve the given differential equation. y′=(cos2x)(cos26y)
The given differential equation is y' = (cos(2x))(cos(26y)). (1/26) ln|sec(26y) + tan(26y)| = (1/2) sin(2x) + C. This is the general solution to the given differential equation
To solve the differential equation y' = (cos(2x))(cos(26y)), we begin by applying separation of variables. We can rewrite the equation as:
dy / dx = (cos(2x))(cos(26y))
Now, we separate the variables by multiplying both sides by dx:
1 / cos(26y) dy = cos(2x) dx
Next, we integrate both sides with respect to their respective variables. On the left side, we integrate with respect to y, and on the right side, we integrate with respect to x:
∫(1 / cos(26y)) dy = ∫cos(2x) dx
The integral on the left side can be evaluated using the substitution u = 26y:
(1/26) ∫(1 / cos(u)) du = ∫cos(2x) dx
Simplifying further:
(1/26) ln|sec(u) + tan(u)| = (1/2) sin(2x) + C
where C is the constant of integration. To obtain the final solution, we substitute u back in terms of y:
(1/26) ln|sec(26y) + tan(26y)| = (1/2) sin(2x) + C
This is the general solution to the given differential equation.
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Please help please please I’ll give brainly
omar mows lawns for $9.25 an hour. he spends $7.50 on gas for the mower. if he earned 149.75, how many hours, h, did he work?
Answer:
Step-by-step explanation: So amount Earned per hour is 9.25
h = time
and 7.5=amount he spent / money made=9.25h-7.5 !
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1. In circle P, what is the measure of AB?
128°
P
B
AC is a diameter and ZAPB is a right angle.
60 ft
60 ft
30t)
60 ft
60ft
30 ft.
Answer:
7290ft^2
Step-by-step explanation:
60*30=1800
then multiply that by 4 because of the 4 rectangle
1800*4=7200
multiply 30*30 to get 90 then add that on
7290
find the number of $4$-digit numbers where the second digit is even, and the fourth digit is at least twice the second digit. (note that digits are read from the left, so the first digit is the leftmost digit, and so on.)
There will be a total of 1620 four digit numbers having an even second digit and a fourth digit that is atleast twice of the second digit.
Calculation:Possible second digits allowed = 0,2,4
digits 6 and 8 are also even but cant be included as their twice yeild double digits.
For each of the allowed digits, the possible fourth digit ranges from 0-9(if second digit is zero), 4-9(if second digit is considered as 2) and 8-9(if second digit is 4). Hence the total number of fourth digits allowed = 10+6+2=18.
The first digit can be any non zero number whereas the third digit can be from 0-9.
Hence the total number of four digits allowed: 9×10×18 = 1620.
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