An equation that has fractions with xs in the numerator, denominator, or both is referred to as rational. A rational equation looks like this: (4 / (x + 1)) - (3 / (x - 1)) = -2 / (x^2 - 1).
Consider the last time you used a fraction to solve an equation. 1/3 x = 8. The 3 in the denominator is a prisoner in our eyes, and we wish to free it. We multiply both sides of the equation by 3 to release the 3. Consider it as 3 notifying both parties of his departure. 3 (1/3 x) = 8 (3). (3).This procedure eliminated the fraction x = 24 and released our denominator. We add one more step to it when we need to solve rational equations. Sometimes, even though our answer to a rational equation appears to be sound, it actually contains a virus that prevents it from working. We refer to these as superfluous solutions. To answer a rational equation, follow these steps:
1. Determine the common denominator.
2. Divide all sums by the lowest common denominator.
3. Simplify.
4. Verify the solution(s) to make sure there aren't any unnecessary ones.
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Rate=10ft/sec Time=6 seconds
I don't know so like ya I don't know
How many ways can you arrange 5 numbers?.
In 120 ways 5 numbers can be arranged through permutations.
Define permutation.A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation." The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Given,
In following ways 5 numbers can be arranged through permutations,
5!
5 × 4 × 3 × 2×1
120
In 120 ways 5 numbers can be arranged through permutations.
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pls help with this question
Answer:
Step-by-step explanation:
54=t
Laurie goes for a run every morning. She leaves her house at 6:15 a.m. She returns from her run at 6:55 a.m.
How much time does Laurie spend running every day?
Answer:
40min per day
Step-by-step explanation:
Answer: 40 minutes
Step-by-step explanation: All you have to do is subtract 55 and 15, which equals 40 minutes.
hope this helps!
please give brainliest!
mike can wash a car in 3 hours. sabrina can wash the same car in 2 hours. to the nearest minute, how long would it take them to wash the car together?
Number of hours taken by Mike and Sabrina to wash a car when they work together is equal to (6/ 5) hours .
As given in the question,
Number of hours taken by Mike to wash a car = 3 hours
Work done by Mike in 1 hour = 1/3
Number of hours taken by Sabrina to wash a car = 2 hours
Work done by Sabrina in 1 hour = 1/2
Amount of work done by Mike and Sabrina together in 1 hour
= (1/3) + (1/2)
= ( 2 + 3 ) / 6
= 5/6
Now,
1 work done by Mike and Sabrina together = 6/5 hours
Therefore, number of hours taken them together to wash a car is
(6/5) hours.
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Verify that the given point is on the curve and find the lines that are (a) tangent and (b) normal to the curve at the given point. x^2 + y^2 = 25, (4, 3) The point is on the curve because when is substituted for x and is substituted for y, the resulting statement is = 25, which is a statement. (Simplify your answers.)
The equation of the tangent would be y = -4x/3 - 25/3 and the equation of the normal would be y = 3x/4.
What is a parabola?
A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.
The given equation is x² + y² = 25 ; (4, 3)
Now when we put x = 4 and y = 3
then LHS = RHS.
Now find the slope:
2x + yy' = 0
⇒ y' = -x/y
Now at (4, 3) slope would be y' = -4/3.
The equation of the tangent would be
y - y1 = m(x - x1)
y - 3 = (-4/3)(x-4)
3y - 9 = -4x + 16
4x + 3y = 25
y = -4x/3 - 25/3
Now equation of the normal is:
y - y1 = (-1/m)(x - x1)
y - 3 = 3/4(x - 4)
y = 3x/4
Hence, the equation of the tangent would be y = -4x/3 - 25/3 and the equation of the normal would be y = 3x/4.
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(2a²b⁵/18a⁴b)¹/² simplify
The result for simplifying;
[tex] {( \frac{2a²b×b⁴}{2a²b×9 {a}^{2} } )}^{ \frac{1}{2} } [/tex]
is;
[tex] \frac{ {b}^{2} }{3b} [/tex]
Simplifying Algebraic expressionSimplification of an algebraic expressions is the process of writing an expression in the most efficient and compact way, that is in their simplest form, without changing the value of the original expression.
The greatest common factor the numerator and denominator is 2a²b and so we divide through with it to give;
[tex] {( \frac{b⁴}{9 {a}^{2} } )}^{ \frac{1}{2} } [/tex]
evaluate the square root, we have;
[tex] {( \frac{2a²b⁵}{18 {a}^{4}b } )}^{ \frac{1}{2} } = {( \frac{b²}{3a})} [/tex]
Therefore,
[tex] {( \frac{b²}{3a})} [/tex]
is the result after simplifying the algebraic expression
[tex] {( \frac{2a²b⁵}{18 {a}^{4}b } )}^{ \frac{1}{2} } [/tex]
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A ubmarine travel 7. 1 km due Eat from it bae and then turn and travel due North for 6. 8 km. How far away i the ubmarine from it bae?
Give your anwer rounded to 1 DP
The Submarine is 7.74 Km away from its base .
In the question ,
it is given that ,
the distance travelled by Submarine from base in East direction = 4.2 Km let the distance from base to east direction be denoted by AB ,that means AB = 4.2 Km
the distance travelled by Submarine from East to North direction = 6.5 Km let the distance from east to north direction be denoted by BC . that means BC = 6.5 Km
the given situation form a right triangle ,
So , the distance from submarine to its base is the hypotenuse of the right triangle , that is AC .
So By Pythagoras Theorem ,
AC² = AB² + BC²
Substituting the values , we get
AC² = 4.2² + 6.5²
AC² = 17.64 + 42.25
AC² = 59.89
AC = √59.89
AC = 7.7388
AC = 7.74
Therefore , The Submarine is 7.74 Km away from its base .
The given question is incomplete , the complete question is
A Submarine travel 4. 2 km due Eat from it base and then turn and travel due North for 6. 5 km. How far away is the submarine from it base ?
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explain how you would graph the line containing a slope of -1/5 that goes throught the point (1,-4)
The line containing the slope -1/5 and coordinates (1,-4) can be graphed by moving one unit negative of y and running 5 towards of x axis
Slope is defined as the rate of change of y to rate of change of x
How to graph the slope of a line?
To graph an equation in point slope form,
The first step is to extract the known point and slope from the equation.
The equation of the line is given by: y−yₐ=m(x−xₐ)
From the parameter; M=[tex]\frac{Y-Y_{1} }{X-X_{1} }[/tex]
The given parameters are
[tex]-\frac{1}{5} =\frac{y+4}{x-1}[/tex]
Solving the equation,
x+1=-y+20
x+y=20-1
x+y=19
The slope -1/5 is used to find which way the line extends.
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What is the base of an triangle that has an area of 24 square units and a height of 12 units
Answer:
The base equals 4 units².
Step-by-step explanation:
Formula:
A = hbB/2
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 13 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
base = 4 units
Step-by-step explanation:
[tex]A=bh/2\\bh=2A[/tex]
[tex]b=2A/h[/tex]
Replace values:
[tex]b=2(24)/12=48/12[/tex]
[tex]b=4[/tex]
Hope this helps
The average annual salary in pennsylvania was $25,000 in 1992. assume that salaries were normally distributed for a certain group of wage earners, and the standard deviation of this group was $3,000. find the probability that for a randomly selected sample of 10 individuals, the mean salary was less than $24,000.
Answer:
0.6293
Step-by-step explanation:
The [tex]z[/tex] score for $24000 is [tex]\frac{24000-25000}{3000} \approx 0.333[/tex].
[tex]P(z<0.333)=0.6293[/tex]
Elliot loves carrot chips and buys one ounce bags to pack with her lunch. According to the label, there are an average of 25 chips per ounce. Elliot suspects that the true average is higher and decides to investigate. She selects 12 bags of chips (which she is willing to consider a random sample) and finds the sample average number of chips per bag is 26.6 with a sample standard deviation of s = 4.6. What is the associated standard score for this hypothesis test? z-2.05 2-4.17 2-26.6 - 1.20 MacBook Air 000 000 F4 F5 F6 F7 F8 F9 a
Using the test statistic z, the value of z is 1.20.
In the given question,
Given:
Sample Size(n) = 12
Population Mean([tex]\mu[/tex]) = 25
Standard Deviation(S) = 4.6
Statistic of intereset(x) = 26.6
The test statistic z is
[tex]z=\frac{x-\mu}{\frac{s}{\sqrt{{n}}}}[/tex]
Putting the value
[tex]z=\frac{26.2-25}{4.6/\sqrt{12}}[/tex]
z = 1.6/(4.6/3.46)
z = 1.6/1.329
z = 1.20
Hence, the value of z is 1.20.
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(20 pts) Basic Probability (a) (4 pts) Which of the following expressions is guaranteed to be 1, given two random variables X and Y, and no independence or conditional independence assumptions between them are given? For each expression, show why and why not it is guaranteed to be 1 . -y∑ P(X=x∣Y=y)-x∑ P(X=x∣Y=y)x∑y∑ P(X=x∣Y=y)-x∑P(X=x)+ y∑P(Y=y)(b) (4 pts) Given two Boolean random variables A and B , where P(A)= 21 ,P(B)= 4 1, andP(A∣¬B)= 31, apply Bayes's rule and calculate the value ofP(A∣B)
After applying Baye's Rule , the value of P(A/B) is 1 , the correct option is (d) .
In the question ,
it is given that ,
probability of A is P(A) = 1/2 ,
P(B) is = 1/3 , and
P(A/~B) = 1/4
we know that Baye's Rule for any two events A and B is ,
P(A/B) = (P(B/A) × P(A))/ P(B)
Substituting the values of P(A) and P(B) from above in the Baye's Rule ,
we get ,
P(A/B) = 3/2 × P(B/A)
given that P(A/~B) = 1/4 ,
and we know that , P(B/A) = 1 – P(~B/A) ....equation(1)
by Baye's rule ,
P(~B/A) = (P(A/~B) × P(~B)) / (P(A))
= (1/4 * 2/3 )/(1/2)
= 1/3
Substituting it in equation(1) , we get
P(B/A) = 1 - 1/3
= 2/3
Substituting the value of P(B/A) in P(A/B) = 3/2 × P(B/A) ,
we get ,
P(A/B) = 3/2 × 2/3
P(A/B) = 1
Therefore , the value of P(A/B) is 1 .
The given question is incomplete , the complete question is
Given two Boolean random variables, A and B, where P(A) = 1/2 , P(B) = 1/3, and P(A/~B) = 1/4 , Apply Baye's Rule and calculate the value of P(A/B) ?
A. 1/6
B. 1/4
C. 3/4
D. 1
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a fire department in a small town keeps track of the number of fires it has to fight each day for a year and records the 365 values central limit theorem
By using the concept of bell shaped curve of normal distribution, it can be concluded that
The histogram would not look like a bell shaped curve because occurance of fire may not be constant in all the case.
What is normal distribution?
Normal distribution is a continuous type probability distribution whose probability density function is given by
f(x) = [tex]\frac{1}{\sigma \sqrt{2\pi}}e^-{\frac{z^2}{2}[/tex]
Where z = [tex]\frac{x - \mu}{\sigma}}[/tex] where [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation
A fire department in a small town keeps track of the number of fires it has to fight each day for a year and records the 365 values central limit theorem.
Here, in this case it is not confident that the histogram would not look like a bell shaped curve because occurance of fire may not be constant in all the case.
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suppose we flip a fair coin five times and each time it lands heads up. the probability of landing heads up on the next flip is . a. 1 b. .5 c. .75 d. 0
Probability is simply how likely something is to happen, so the probability of landing heads up on the next flip is 1/2.
How is probability determined?The probability is obtained by dividing the total number of outcomes by the entire number of potential ways an event may occur. Odds are a separate concept from probability. The probability of an event happening is divided by the probability that it won't, and the result is the odds.
What is probability?Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A value among 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
P(H)= Probability of getting head while flipping a coin is 1/2
and,
P(T)= Probability of getting tail while flipping a coin is 1/2
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What are some real life examples of parallel lines and transversals?.
Some of the real life examples of parallel lines cut by transversal are: chessboard, graph paper,railway tracks,net on the tennis court etc.
When two lines don't intersect, they are said to be parallel. Parallel lines are two lines that run parallel to each other and meet at infinity.
A transversal is formed when a line intersects two lines at distinct points.
Real life examples of parallel lines cut by transversal line are:
Tiles on the floorGrills on windows and in doorwaysThe checkered pattern on bedsheets, dining tablecloths, shirtsChessboardGraph paperBookshelvesMain roads and internal roadsRailway tracks- the rails and sleepers across themA musical keyboard standNet on the tennis court The railings and posts on staircasesFencesThus, in real life situations parallel lines cut by transversal can be observed very frequently.
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a skier skis ccw along a circular ski trail that has a radius of 1.9 km. she starts at the northern most point of the trail and travels at a constant speed, sweeping out 3.1 radians per hour. let t represent the number of hours since she started skiing. write an expression in terms of t to represent the number of radians that would need to be swept out from the east side of the ski trail to reach the skier's current position. write an expression in terms of t to represent the skier's distance to the east of the ski trail (in km). write an expression in terms of t to represent the skier's distance to the north of the ski trail (in km).
The expressions are written as
(a) The expression from east side of ski trail to reach skier's current position is θ = π/2 + 3.1 × t
(b) The expression for skier's distance to east of ski trail is 1.9 × cos(π/2 + 3.1 × t) km .
(c) The expression for skier's distance to north of ski trail is 1.9 × sin(π/2 + 3.1 × t) km .
In the question ,
it is given that ,
the radius of the circular ski trail is = 1.9 km
The Skier starts from the Northern most point
the radians that is sweeped in per hour is = 3.1 radians per hour
that means the angular speed is = 3.1 radians per hour ,
Part(a)
From the above data the expression in terms for t that represents number of radians swept out from each side of ski trail to reach skier's current position is written as ,
θ = π/2 + 3.1 × t
Part(b)
From the above data , expression in terms of t to represent skier's distance to the east of ski trail is written as ,
we know that , x = rcosθ
Substituting the value of θ from part(a) ,
we get ,
= 1.9 × cos(π/2 + 3.1 × t) km
Part(c)
From the above data , expression in terms of t to represent skier's distance to the north of ski trail is written as ,
we know that , y = rsinθ
Substituting the value of θ from part(a) ,
= 1.9 × sin(π/2 + 3.1 × t) km
Therefore , The expressions are (a) for radians is θ = π/2 + 3.1 × t
(b) the distance to the east is 1.9 × cos(π/2 + 3.1 × t) km ,
(c) the distance to the north is 1.9 × sin(π/2 + 3.1 × t) km .
The given question is incomplete , the complete question is
A skier skis ccw along a circular ski trail that has a radius of 1.9 km. she starts at the northern most point of the trail and travels at a constant speed, sweeping out 3.1 radians per hour. let t represent the number of hours since she started skiing.
(a) write an expression in terms of t to represent the number of radians that would need to be swept out from the east side of the ski trail to reach the skier's current position.
(b) write an expression in terms of t to represent the skier's distance to the east of the ski trail (in km).
(c) write an expression in terms of t to represent the skier's distance to the north of the ski trail (in km).
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assume that a bond sells at $92.10 and its modified duration is 4.03. compute dollar duration. answer with two decimal digits accuracy and the correct sign. example:-800.00
The dollar duration of the given bond is $3.71
Dollar duration:
Dollar duration means a linear approximation of how a bond's value will change in response to changes in interest rates.
Given,
Here we have to assume that a bond sells at $92.10 and its modified duration is 4.03.
And we need to compute dollar duration. answer with two decimal digits accuracy and the correct sign.
As per the formula of dollar duration, the values of
bond price = $92.10
duration = 4.03
interest rate = 0.01
So, the dollar duration is calculated as follows,
=> dollar duration = 0.01 x 92.10 x 4.03
=> dollar duration = 3.71
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in 2020, 63% of high school graduates were enrolled in colleges or universities. if five high school graduates are randomly selected, what is the probability that no more than three are enrolled in college or university?
The probability that no more than three are enrolled in college or university is P(x≤3)=(C⁵ₓ(0.63)ˣ(0.37)⁵⁻ˣ
What is meant by probability?Probability is the branch of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.
When we are confused about the outcome of an event, we might discuss the probabilities of certain outcomes—how likely they are. Statistics is the study of events that are guided by probability.
Probability (P) = 0.63
n= 5
By using binomial distribution,
We know that,
P(x=x)= Cⁿₓ(p)ˣ(1-p)ⁿ⁻ˣ
P(x≤3)=(C⁵ₓ(0.63)ˣ(0.37)⁵⁻ˣ
The probability that no more than three are enrolled in college or university is P(x≤3)=(C⁵ₓ(0.63)ˣ(0.37)⁵⁻ˣ
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Do you agree with all equilateral triangles are similar to isosceles triangles why justify with an example?.
Yes, I agree with all equilateral triangles are similar to isosceles triangles because Since equilateral triangles have three equal sides and isosceles only have two, all equilateral triangles are in fact isosceles.
Define triangle.When three straight lines come together, a triangle is created. Every triangle has three corners and three sides (angles). The vertex of a triangle is the intersection of two sides. Each polygon has a unique name depending on how many sides it has. For instance, the polygon with three sides is known as a triangle since the word "tri" denotes the number three. Additionally, the name of the polygon suggests that it contains three angles. "Poly" is a prefix that means many.
Given,
All equilateral triangles are similar to isosceles triangles,
Since equilateral triangles have three equal sides and isosceles only have two, all equilateral triangles are in fact isosceles.
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calculate two iterations of newton's method to approximate a zero of the function using the given initial guess. (round your answers to four decimal places.) f(x)
The answer of two iterations of newton's method to approximate a zero of the function using the given initial guess is 1.5262!
Iterative formula, what is it?Iteration refers to doing a procedure repeatedly. Starting with an initial value, enter it into the iteration formula to get a new value. Next, use the new value for the next substitution, and so on, to solve an equation using iteration.
By Newton's Method, we have new guess of a zero of a function that are f(x), xn+1,
and by using the previous guess, xn, like so-
xn+1 = xn - f(xn)/f'(xn)
and herethe case is f(x) = cos(x), and so f'(x) = -sin(x).
Also, furthermore, cos(x)/(-sin(x)) = -cot(x).
here, we have to simplify the formula to get a better guess for a zero to:
xn+1 = xn + cot(xn)
x1 = 0.6, so x2 = 0.6 + cot(0.6) = 2.06170...
And x3 = 2.06170... + cot(2.06170...) = 1.52615...
Ans = 1.5262!
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if a person is making the median salary for a construction worker, they are making more than what percentage of teachers?
The person is making money more than the half of the population of the teachers.
Given, a person is making the median salary for a construction worker.
we have to find that more than how many teachers the person is making money
as, we know that the median is more than the half of the population.
So, the person is making money more than the half of the population of the teachers.
Hence, the person is making money more than the half of the population of the teachers.
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Warp-O Corporation common stock has a market price of
$45
per share. Warp-O has a beta of 1.4. The rate of return on Treasury bonds is currently
6%
and the retum on the S\&.P 500 is
13%
. What is the required rate of return on Warp-O common stock? a)10.2%
d)24.2%
b)13.0%
e)35.1%
c)15.8%
Option c 15.8% is the required rate of return for Warp-O common stock.
Given,
The market price of share = $45
Beta = 1.4
The rate of return on Treasury bonds = 6%
Market rate of return = 13%
We have to find the required rate of return on Warp-O common stock;
Here,
Rate of return = The rate of return on Treasury bonds + beta × (market rate of return -The rate of return on Treasury bonds )
= 6% + 1.4 × (13% - 6%)
= 6% + 1.4 ×7%
= 6% + 9.8%
= 15.8%
That is,
The required rate of return on Warp-O common stock is option c 15.8%
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Chuck will go shopping for probability books for K hours. Here, K is a random variable and is equally likely to be 1, 2, 3, or 4. The number of books N that he buys is random and depends on how long he shops. We are told that
pN|K(n | k) = 1/k1k for n = 1,... ,k.
The probability that Chuck will shop for k hours be,
C(n , k).p^k.q^(n - k)
Given, Chuck will go shopping for probability books for K hours.
K is a random variable and is equally likely to be 1, 2, 3, or 4.
The number of books N that he buys is random and depends on how long he shops.
The probability that chuck will shop for k hours be,
P(X = k) = C(n , k).p^k.q^(n - k)
So, we can find the probability that chuck will shop for k hours by,
C(n , k).p^k.q^(n - k)
Hence, the probability that Chuck will shop for k hours be,
C(n , k).p^k.q^(n - k)
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riteria used to allocate fixed costs to a department include: relative benefits question 6 options: relative benefits ability to bear equity all of the above
Option (d) is correct. Criteria for assigning fixed costs to sectors include relative utility, sustainability, and fairness.
Fixed cost and allocation:
Fixed costs are costs that are essentially constant and do not change with fluctuations in the output of the relevant sector. Fixed costs are borne by the company and exist independently of business activities. Rent, insurance, and depreciation are examples of fixed costs. Cost attributes help identify, total, and assign costs to cost objects.
Fixed cost allocation involves identifying the beneficiaries of outputs and allocating costs to beneficiaries in proportion to the benefits received. Fixed costs can also be allocated in relation to the payer's ability to bear the allocated costs. Fairness is a criterion met where cost allocation is the basis for determining a satisfactory price (such as government contracts).
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The population of the state of Calisota is 48.2 million in 2013 , and 49.9 million in 2017. If this growth rate holds , what will the population be in 2024 , to the nearest tenth of a million ?
The population be in 2024 , to the nearest tenth of a million is 397.5
What will the population be in 2024?We find the difference (subtract) between the original population and the population at Time 1, divide by the initial population, then multiply by 100 to obtain the Population Growth (PG).Population after n years equals P x (1+R/100)n if growth is constant at R% per year. 3. If the population is declining at a constant rate of R% annually, the population after n years will be equal to P x (1-R/100)n.
Population after n years equals
P x (1+R/100)n
48.2 * (1 - 49.9)7
397.5
The population be in 2024 , to the nearest tenth of a million is 397.5
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FILL IN THE BLANK. 1. the steps of the analytical problem-solving model include: identifying the problem,___, selecting alternatives, implementing a solution, and evaluating the situation.
The steps of the analytical problem-solving model include: identifying the problem, exploring alternatives, building an implementation plan, implementing a solution, and evaluating the situation.
What is analytical problem solving ?Analytical problem solving, as we've defined it above, refers to the approaches and methods you use rather than the particular issue you're trying to resolve.
Analytical issue solving is a crucial prerequisite for problem resolution; the problem itself does not determine whether you need it.
Analytical problem solving involves recognising a problem, investigating it, and then creating ideas (such as causes and solutions) around it.
Solving analytical problems calls for inquiry, examination, and analysis that encourages additional study of the subject (including causality, symptoms, and solution).
According to the steps involved in analytical problem solving model:
The ability to examine a situation, The ability to research and focus on key aspects,The ability to analyze the facts and data around the situationThe ability to prioritize and identify critical aspectsThe ability to build an argument to define a problem The ability to investigate and propose root cause(s), while also highlighting the strengths and weaknesses of this argument.To learn more about analytical model, visit:
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A sinusoidal function of the form y = a sin(x - c) + d is
changed by increasing d by 2. The new graph will have
moved:
A sinusoidal function of the form y = a sin(x - c) + d is changed by increasing d by 2. The new graph will have moved right.
Define sine function.The sine function in trigonometry is the ratio of the hypotenuse's length to the opposite side's length in a right-angled triangle. To determine a right triangle's unknown angle or sides, utilize the sine function. The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: sin = Perpendicular / Hypotenuse.
Given,
A sinusoidal function of the form y = a sin(x - c) + d is changed by increasing d by 2.
The new graph will have moved right.
For periodic functions, phase shift refers to a horizontal shift to the left or the right. The sine wave is moved to the left if c = 2. if, the sine wave is then three degrees to the right. Despite going in the opposite way from what you may anticipate, this follows the general transformational principles for all functions.
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What are the perimeter and the area of a rectangle that is 3/4 yd long and a 1/3 yard wide
Answer:
Step-by-step explanation:
1/4 if you multiplying
1 1 /12 if you adding
Answer:
perimeter: [tex]2\frac{1}{6}[/tex] yards
Area: [tex]\frac{1}{4}[/tex] [tex]yards^{2}[/tex]
Step-by-step explanation:
perimeter is 2(l)+2(w)
And area is (l)(w)
So to find perimeter we fill in the formula
2(3/4)+2(1/3)
6/4+2/3
Find common denominator
6*3/4*3+2*4/3*4
18/12+8/12
26/12
2 2/12
2 1/6 is the perimeter
Now for the area we multiply width by length
3/4x1/3
3/12
1/4 is the area
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Americans average 6.9 hours of sleep on weeknights, according to a report released in 2011 by the National Sleep Foundation. A student in a statistics class at Los Medanos College wondered if the average amount of sleep on weeknights is different for LMC students. She collected data from a survey of 43 randomly selected students at LMC. Respondents averaged 7.12 hours of sleep a night with a standard deviation of 1.45 hours.
The null and alternative hypothesis test using μ as mean hours of sleep for LMC students is [tex]H_0[/tex] : μ = 6.9 and ([tex]H_a[/tex] : μ ≠ 6.9).
Given:
Americans average 6.9 hours of sleep on weeknights, according to a report released in 2011 by the National Sleep Foundation. A student in a statistics class at Los Medanos College wondered if the average amount of sleep on weeknights is different for LMC students. She collected data from a survey of 43 randomly selected students at LMC. Respondents averaged 7.12 hours of sleep a night with a standard deviation of 1.45 hours.
here
μ = 6.9
σ = 1.45
Null hypothesis:
[tex]H_0[/tex] : μ = 6.9
Alternative hypothesis:
([tex]H_a[/tex] : μ ≠ 6.9)
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Full question:
Americans average 6.9 hours of sleep on weeknights, according to a report released in 2011 by the National Sleep Foundation. A student in a statistics class at Los Medanos College wondered if the average amount of sleep on weeknights is different for LMC students. She collected data from a survey of 43 randomly selected students at LMC. Respondents averaged 7.12 hours of sleep a night with a standard deviation of 1.45 hours.
what are the null and alternative hypothesis?(use μ = mean hours of sleep for LMC students).