Thus, the computer was initially worth $3340 as the PC will be worth $835 after six years.
what is unitary method ?In mathematics, the unitary approach entails determining the value of a single unit in a certain circumstance and using that value to resolve other issues that are connected to it. It is a quick and efficient method for handling issues involving direct proportion, indirect proportion, and other circumstances of a same nature. In disciplines including mathematics, science, business, and engineering, the unitary technique is widely employed.
given
Let V be the computer's starting value.
The computer's value drops to V/2 after four years.
The computer's value is decreased to V/2 1/2 = V/4 after six years.
We are informed that the PC will be worth $835 after six years. When we set this equal to V/4, we obtain:
V/4 = 835
Adding 4 to both sides results in:
V = 4 × 835 = $3340
Thus, the computer was initially worth $3340 as the PC will be worth $835 after six years.
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The number of cases of a disease
increases by the same factor each year, as
shown in the table below.
Write an expression for the number of
cases of the disease after n years.
Start
End of year 1
End of year 2
End of year 3
Number of cases
1400
2100
3150
4725
Answer:
N*r^n
Step-by-step explanation:
Let the initial number of cases at the start of year 1 be represented by N.
From the given information, we know that the number of cases increases by the same factor each year. Let this factor be represented by r.
Then, at the end of year 1, the number of cases would be N*r, since it has increased by a factor of r.
Similarly, at the end of year 2, the number of cases would be Nrr, or N*r^2.
At the end of year 3, the number of cases would be Nrrr, or Nr^3.
We can use this pattern to write a general expression for the number of cases after n years:
N * r^n
where N is the initial number of cases, r is the common factor by which the number of cases increases each year, and n is the number of years elapsed.
g the probability that a patient recovers from a stomach disease is 0.8 exactly 14 recover? at least 10 recover?
A patient's probability of recovering is 0.8, so the likelihood that they won't is 0.2.
The probability that a patient will recover from a stomach disease is 0.8. Assume that 20 persons have reportedly got this illness.
Let X = # of recoveries out of 20 patients who caught the condition while PMF for X and resolve issues. Imagine that a 20-person sample was chosen at random.
Here, Bernoulli trials are applicable.
Recall that the chance of k successes in n trials using the Bernoulli approach is given by:
P(k)=( n/k )p (power k) * (q power n−k)
where q=1-p is the probability that an attempt would fail
where q=1-p is the probability that an attempt would fail
Here, let's make recovery a success. Hence, p = 0.8, q = 0.2, and n = 20
The probability that at least 10 recoveries will occur is
P(X10) = P(10) + P(11) + P(12) +... + P (20)
The complete question will be:
The probability that a patient recovers from a stomach disease is 0.8. Suppose twenty people are known to have contracted this disease. What is the probability that at least ten recover?
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In terms of the water lily population change, the value 3.915 represents: the value 1.106 represents:
The value 1.106 represents the slope of the regression line or the rate of change of y with respect to x.
In the given regression equation y = 3.915(1.106)x:
The value 3.915 represents the y-intercept or the predicted value of y when x=0. In the context of the water lily population change, this value could represent the initial population of water lilies or the minimum population that can sustain in the given environment.The value 1.106 represents the slope of the regression line or the rate of change of y with respect to x. In the context of the water lily population change, this value could represent the rate at which the water lily population increases or decreases with respect to some independent variable x, such as time or environmental factors.Learn more about slope here https://brainly.com/question/19131126
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ASAP
Ω = {whole numbers from 2 to 9} A = {even numbers} B = {prime numbers} List the elements in:
a. A’
b. A∩B
c. A∪B
Answer:
a. A' = {3, 5, 7, 9} (complement of A)
b. A∩B = {2} (intersection of A and B, which contains only the even prime number 2)
c. A∪B = {2, 4, 6, 8, 3, 5, 7} (union of A and B, which contains all even numbers and all prime numbers between 2 and 9)
which property is shown 16x5x2=2x5x16
Answer:
Commutative property
The Commutative property is most simply shown with: a x b = b x a. In multiplication, the values can shift or "commute" in any order
it is estimated that 45% of the senior class will go to prom this year. if you randomly choose 10 seniors and ask them if they are going to prom, would you use the normal approximation to predict these results?
Yes, we would use the normal approximation to predict these results.
When it comes to hypothesis testing and confidence intervals, the normal distribution plays a crucial role.
When sample sizes are large enough, the normal distribution can be used as a reasonable approximation for the binomial distribution.
This is because the binomial distribution approaches the normal distribution as sample size increases.
To calculate the normal approximation, you will need to determine the mean and standard deviation of the binomial distribution.
The mean is np and the standard deviation is the square root of np(1-p),
where n is the sample size and p is the probability of success.
The probability of success in this case is 45%, or 0.45.
Therefore, the mean is 10 * 0.45 = 4.5 and the standard deviation is the square root of 10 * 0.45 * (1 - 0.45) = 1.37.
Now that you have the mean and standard deviation, you can use the normal distribution to make predictions about the sample.
If you want to find the probability that exactly 5 students will go to prom, for example, you would use the formula for the normal distribution with a mean of 4.5 and a standard deviation of 1.37.
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Triangle A: All sides have length 12 cm.
Triangle B: Two sides have length 10 cm, and the included angle measures 60°.
Triangle C: Base has length 15 cm, and base angles measure 40°.
Triangle D: All angles measure 60°.
Which triangle is not a unique triangle? (5 points)
a
Triangle A
b
Triangle B
c
Triangle C
d
Triangle D
triangle C
Step-by-step explanation:
If you draw it out, it looks unique
A figure displays two complementary nonadjacent angles. If one angle measure is 79", what is the other angle measure?
(1 point)
O 21"
O 121°
O 101'
O 11"
ANSWER-
Let the nonadhacent anglesof complementary angle be x and y where, x=79 and y =?
WE KNOW,
x+y=90
or,79+y=90
or, y=90-79
:. y=11,,
Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form. ( − 3 , − 4 ) and ( − 5 , − 6 ) (−3,−4) and (−5,−6)
The length of the hypotenuse is 2 times the square root of 5. The Pythagorean theorem can be used to determine the length of the hypotenuse.
How to find distance between two points ?To graph the right triangle with the given points as the hypotenuse, we first plot the points on a coordinate plane . The two points form the endpoints of the hypotenuse, which is the line segment connecting them. We can find the length of this line segment using the distance formula:
distance = [[tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2]}[/tex]
In this case, we have:
distance = [[tex]\sqrt{(-5 - (-3))^2 + (-6 - (-4))^2}[/tex]]
distance = [tex]\sqrt{(-5 - (-3))^2 + (-6 - (-4))^2}[/tex]]
distance = [[tex]\sqrt{4 + 4}[/tex]]
distance = [[tex]\sqrt{8}[/tex]]
We can simplify [tex]\sqrt{8}[/tex] by factoring out the perfect square factor of 4:
distance = [[tex]\sqrt{4 * 2}[/tex]]
distance = [tex]\sqrt{4} *\sqrt{2}[/tex]
distance = 2 * [tex]\sqrt{2}[/tex]
Thus, the distance between the two points is 2 * [tex]\sqrt{2}[/tex] ] units.
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X^4-3x^2+9x name the polynomial
Answer:
biquadratic polynomial
Step-by-step explanation:
it has degree 4
if the number of samples were doubled, what would be the new confidence interval (keeping the same confidence level?)
If the number of samples is doubled, the new confidence interval would be 9.61, 10.39 or narrower (smaller) while keeping the same confidence level.
. When calculating the confidence interval, the standard error is used, along with the sample mean and the critical value from the distribution. If we have a larger sample size, we can be more confident in our estimate of the population parameter because the sample mean will more closely resemble the population mean. As a result, the confidence interval can be narrower, indicating a higher degree of precision. For Example:Suppose a sample of 50 was taken, and the mean weight of an object was 10 grams with a standard deviation of 2 grams.
At a 95 percent confidence level, the confidence interval for the mean weight would be 10 ± (1.96)(2/√50) = (9.15, 10.85)Now suppose that the sample size is doubled to 100. The standard error will be cut in half, i.e., 2/√100 = 0.2. As a result, the new confidence interval would be 10 ± (1.96)(0.2) = (9.61, 10.39). Notice that the new confidence interval is narrower, indicating a higher degree of precision while keeping the same confidence level.
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GIVING BRAINLIEST FOR RIGHT ANSWER
Answer:
4
Step-by-step explanation:
Answer:
[tex]x\leq 6[/tex]
Step-by-step explanation:
Simplify each epression and state the domain restrictions for each expression. You
MUST show your work (either typing or attaching a file) for full credit.
1.
2.
9x+3
12x+4
2x²+10x
x²+10x+25
The answer and workout is provided in the attachment.
You want to cover a circular window with tinted paper. The window has a radius of 6 inches. How many square inches of tinted paper will you need to use to cover the window
Answer:113.04 in squared
Step-by-step explanation: a=3.14Rsquared
A=3.14 x 6squared 6 x 6=36
A=3.14 x 36
3.14 x 36 = 113.04 inches squared or 113 inches squared
To cover the circular window, you will require a piece of tinted paper measuring approximately 113 in²
The area of the circular window can be found using the formula for the area of a circle:
A = πr²
where A is the area of the circle, π is the mathematical constant pi (approximately 3.14), and r is the radius of the circle.
In this case, the radius is given as 6 inches, so we can substitute that value into the formula:
A = π (6 inches)²
A = π (36 square inches)
A ≈ 113.04 square inches
Rounding to the nearest tenth gives:
A ≈ 113 square inches
Therefore, you will need approximately 113 square inches of tinted paper to cover the circular window.
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isaac is designing a circular table top that he plans to paint white. the table top has a circumference of 18.84 feet. using 3.14 for , what is the area of the table top rounded to the nearest hundredth?the area of the table top is
The area of the table top is approximately 28.27 square feet. To find the area of a circular table top with a given circumference, we can use the formula A = πr², where r is the radius.
To find the area of the table top, we need to use the formula for the area of a circle, which is:
A = πr²
We are given the circumference of the table top, which is:
C = 2πr
We can solve for r by dividing both sides by 2π:
r = C / (2π) = 18.84 / (2 * 3.14) = 3
Now we can substitute this value for r into the formula for the area of a circle:
A = π(3)² = 9π
Using 3.14 for π, we get:
A ≈ 28.26
Rounding to the nearest hundredth, the area of the table top is approximately 28.27 square feet.
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PLEASE HELP!!
Solve and explain
Answer:Tham I can’t even se the letters you should have posted each question one by one
Step-by-step explanation:
good luck
A triangle with side lengths 7, 6, 4 is
Acute
Right
Obtuse
Right
so 7 is the hypotenuse because it is the biggest. so you have to use 6 and 4 in the formula to see if they equal 7.
(a)²+(b)²=c²
(6)²+(4)²=c²
36+16=c²
(square root) 52=c²
the square root of 52 is 7
so therefore it is a right triangle.
Arrange jn order smallest to largest. 11%, 0. 2, 13%, 3/20, 1/8
Arranged from smallest to largest, the given values are 0.2, 3/20, 1/8, 11%, and 13%.
To compare these values, we need to convert the percentages to decimals. We can do this by dividing them by 100. So, 11% becomes 0.11 and 13% becomes 0.13.
Next, we can convert 3/20 and 1/8 to decimals by dividing them using a calculator. We get:
3/20 = 0.15
1/8 = 0.125
Now, we can arrange these values in ascending order:
0.2 < 0.125 < 0.15 < 0.11 < 0.13
Therefore, the values arranged in order from smallest to largest are 0.2, 3/20, 1/8, 11%, and 13%.
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9 km
7 km
3 km
3 km
3 km
2 km
8 km
9 km
3 km
7 km
Answer: what do you mean? I need more info-
Step-by-step explanation:
I can answer it with more info :)
Let alpha = phi/2008 . Find the smallest positive integer n such that 2 [cos(alpha) sin(alpha) + cos (4 alpha) sin (2 alpha) + cos (9 alpha) sin (3 alpha) +.....+ cos (n^2 alpha) sin(n alpha)] is an integer
n = ceil(sqrt((2008/4phi)[90 - arccos(k(2 cos(phi/2008)))]))
How to find integer?Simplifying equation:2 [cos(alpha) sin(alpha) + cos(4 alpha) sin(2 alpha) + cos(9 alpha) sin(3 alpha) + ... + cos(n^2 alpha) sin(n alpha)]
= [sin(2 alpha) + sin(8 alpha) + sin(18 alpha) + ... + sin(n^2 alpha)].
Using the formula for the sum of a geometric series:sin(2 alpha) + sin(8 alpha) + sin(18 alpha) + ... + sin(n^2 alpha)
= (sin(2 alpha) - sin(2n^2 alpha))/(1 - sin(2 alpha))
= (2 sin(n^2 alpha) cos(n^2 alpha))/(2 cos(alpha) - 1)
= [sin(2n^2 phi/2008)]/(2 cos(alpha) - 1)
To find an integer value:[sin(2n^2 phi/2008)]/(2 cos(alpha) - 1)
sin(2n^2 phi/2008) = k(2 cos(alpha) - 1)
cos(90 - 2n^2 phi/2008) = k(2 cos(alpha) - 1)
Now, we need to find the smallest positive integer n90 - 2n^2 phi/2008 = ±arccos(k(2 cos(alpha) - 1))
Solving for n, we get:n^2 = (2008/4phi)[90 ± arccos(k(2 cos(alpha) - 1))]
n = ceil(sqrt((2008/4phi)[90 - arccos(k(2 cos(phi/2008)))]))
We can find the smallest positive integer n by incrementing the value of k starting from 1 until ceil(k^2*alpha) is greater than or equal to n.
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HELP ME PLEASE ILL GIVE YOU STARS
Answer:
multiply BD and AC and you got it
Step-by-step explanation:
if yuo put ABD triangle over CEB you got a sqare, if you do it again you got a aqare 20x10
the nonparametric tests discussed in your book (wilcoxon rank sum test, sign test, wilcoxon signed rank sum test, kruskal-wallis test, and friedman test) all require that the probability distributions be:
Nonparametric tests can be useful in situations where the data may not follow a specific distribution or where the assumptions of a parametric test are not met.
The nonparametric tests mentioned in your question do not assume any specific probability distribution for the data. Hence, they are called nonparametric tests. These tests are used when the assumptions required for parametric tests (e.g., normality) are not met, or when the data is measured on ordinal or nominal scales rather than continuous ones.
The Wilcoxon rank-sum test, sign test, and Wilcoxon signed-rank test are used to compare two independent or dependent samples. The Kruskal-Wallis test and Friedman test are used to compare three or more independent or dependent samples.
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6y^2+11y-7
Solve this pls show work
Step-by-step explanation:
hope this will help u
A set of blocks contains blocks of heights 1, 2, and 4 centimeters. Imagine constructing towers by piling blocks of different heights directly on top of one another. (A tower of height 6 cm could be obtained using six 1 cm blocks, three 2 cm blocks, one 2 cm block with one 4 cm block on top, one 4 cm block with one 2 cm block on top, and so forth.) Lett, be the number of ways to construct a tower of height n cm using blocks from the set. (Assume an unlimited supply of blocks of each size.) Use recursive thinking to obtain a recurrence relation for ty, ty, tzo Imagine a tower of height k cm. Either the bottom block has height 1 cm or it has height 2 cm or it has height cm. If the bottom block has height 1 cm, then the remaining blocks make up a tower of height x cm. By definition of t, there are tk-1 such towers. If the bottom block has height 2 cm, then the remaining blocks make up a tower of height x cm. By definition of there are x cm, then the remaining blocks make tx-2 such towers. If the bottom block has height such towers up a tower of height x cm. By definition of there are 1 Select X Therefore, for each integer, n 25,
Answer: Based on the problem statement, we can define a recurrence relation as follows:
t(n) = t(n-1) + t(n-2) + t(n-4)
This means that the number of ways to construct a tower of height n cm can be obtained by considering the possible heights of the bottom block in the tower. If the bottom block has height 1 cm, then the remaining blocks make up a tower of height (n-1) cm, for which there are t(n-1) ways to construct it. If the bottom block has height 2 cm, then the remaining blocks make up a tower of height (n-2) cm, for which there are t(n-2) ways to construct it. If the bottom block has height 4 cm, then the remaining blocks make up a tower of height (n-4) cm, for which there are t(n-4) ways to construct it.
Since we are assuming an unlimited supply of blocks of each size, we can use these blocks repeatedly to construct towers of different heights. Also, we can use dynamic programming to compute the values of t(n) for each integer n from 1 to 25, by using the recurrence relation above and the base cases:
t(0) = 1 (there is only one way to construct a tower of height 0 cm, which is to not use any blocks)
t(n) = 0 for n < 0 (there is no way to construct a tower of negative height)
Using these, we can compute the values of t(n) for n = 1, 2, ..., 25, as follows:
t(0) = 1
t(1) = t(0) = 1
t(2) = t(1) + t(0) = 2
t(3) = t(2) + t(1) = 3
t(4) = t(3) + t(2) + t(0) = 6
t(5) = t(4) + t(3) + t(1) = 10
t(6) = t(5) + t(4) + t(2) = 19
t(7) = t(6) + t(5) + t(3) = 32
t(8) = t(7) + t(6) + t(4) = 61
t(9) = t(8) + t(7) + t(5) = 104
t(10) = t(9) + t(8) + t(6) = 195
t(11) = t(10) + t(9) + t(7) = 332
t(12) = t(11) + t(10) + t(8) = 626
t(13) = t(12) + t(11) + t(9) = 1065
t(14) = t(13) + t(12) + t(10) = 2002
t(15) = t(14) + t(13) + t(11) = 3405
t(16) = t(15) + t(14) + t(12) = 6403
t(17) = t(16) + t(15) + t(13) = 10946
t(18) = t(17) + t(16) + t(14) = 20618
t(19) = t(18) + t(17) + t(15) = 350
Step-by-step explanation:
calculate the width of an 80% ci for the mean of a normal distribution with unknown variance, sample mean 9, sample variance 6 and sample size 15. use two decimal places.
With the given parameters, the width of the 80% CI for the normal distribution's mean is roughly 1.5.
The following formula can be used to determine the width of an 80% confidence interval (CI) for the mean of a normal distribution with unknown variance, the sample mean 9, sample variance 6, and sample size 15:
width = t * (s / √(n))
where s is the sample standard deviation (the square root of the sample variance), n is the sample size, and t is the value from the t-distribution with n-1 degrees of freedom for an 80% CI (from a t-table or calculator).
We must first determine the sample standard deviation:
s = √(6) ≈ 2.45
Then, we can find the worth of t from a t-table or mini-computer for a 80% CI with 14 levels of opportunity (15-1):
t = 1.339Lastly, these numbers can be used to calculate the 80% CI width:
width = 1.339 * (2.45 / √(15)) = 1.5With the given parameters, the width of the 80% CI for the normal distribution's mean is roughly 1.5.
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
40 min 25 min
Answer:
Part A is 8/13 of the whole
Part B is 5/13 of the whole
Step-by-step explanation:
Assuming there are no other parts,
the Whole = A + B is the denominator:
Whole = 40 + 25 = 65
Part A = 40 and Part B = 25 are numerators for each fraction.
The fractions are then:
40/65 and 25/65
Meaning:
Part A is 40/65 of the whole
Part B is 25/65 of the whole
Reducing the fractions, it is also true that:
Part A = 8/13 of the whole
Part B = 5/13 of the whole
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
Answer:
(a) No, because for each input there is not exactly one output.
Step-by-step explanation:
You want to know if the relation shown in the graph is a function.
FunctionA relation is a function if its graph passes the vertical line test. That is, a vertical line cannot intercept the graph of the relation at more than one point.
The points (-1, -2) and (-1, 3) will both be intercepted by the vertical line x = -1. This tells us the relation is not a function, because it has two outputs for that input.
<95141404393>
Solve for y
y-5.4=4.86
Answer: y - 10.26
Step-by-step explanation: Add 5.4 on both sides and that leaves you with y
begging for help lol pleaseee
Step-by-step explanation:
Find the area of the yellow circle using pie times radius squared. Then find the area of the entire circle using the same formula then take the answer for the area of the entire circle - area of the yellow circle
Water tank A has 220 gallons of water and is being drained at a constant rate of 5 gallons per minute.
• Water tank B has 180 gallons of water and is being drained at a constant rate of 3 gallons per minute.
Part A
How much time, in minutes, do water tank A and water tank B have to be drained in order for them to have the same amount of water?
PART B
Which water tank, A or B, will be completely drained first?
How much less time, in minutes, will it take this water tank to completely drain than the other water tank?
By answering the presented question, we may conclude that
a) both tanks will have the same amount of water after 20 minutes.
b) difference in time required to thoroughly drain them is: 60 - 44 = 16 minutes.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
Part A:
Let's assume that after t minutes, the amount of water remaining in tank A is x gallons, and the amount of water remaining in tank B is also x gallons. We can write equations based on the given information:
Tank A: x = 220 - 5t
Tank B: x = 180 - 3t
To find the time when both tanks have the same amount of water, we can set these two equations equal to each other and solve for t:
220 - 5t = 180 - 3t
40 = 2t
t = 20
Therefore, both tanks will have the same amount of water after 20 minutes.
Part B:
To determine which tank will be completely drained first, we need to find the time it takes for each tank to be completely drained. For tank A, we can set x = 0 in the equation we found in part A:
0 = 220 - 5t
t = 44
So it will take 44 minutes for tank A to be completely drained.
For tank B, we can set x = 0 in the equation given in the problem:
0 = 180 - 3t
t = 60
So it will take 60 minutes for tank B to be completely drained.
Therefore, tank A will be completely drained first. The amount of time it takes for tank A to be completely drained is 44 minutes, and the amount of time it takes for tank B to be completely drained is 60 minutes. The difference in time is:
60 - 44 = 16 minutes.
The difference in time required to thoroughly drain them is: 60 - 44 = 16 minutes.
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