The probability that z is between 1.57 and 1.87 is approximately 0.0275. This would also give us a result of approximately 0.0275.
Assuming you are referring to the standard normal distribution, we can use a standard normal table or a calculator to find the probability that z is between 1.57 and 1.87.
Using a standard normal table, we can find the area under the curve between z = 1.57 and z = 1.87 by subtracting the area to the left of z = 1.57 from the area to the left of z = 1.87. From the table, we can find that the area to the left of z = 1.57 is 0.9418, and the area to the left of z = 1.87 is 0.9693. Therefore, the area between z = 1.57 and z = 1.87 is:
0.9693 - 0.9418 = 0.0275
So the probability that z is between 1.57 and 1.87 is approximately 0.0275.
Alternatively, we could use a calculator to find the probability directly using the standard normal cumulative distribution function (CDF). Using a calculator, we would input:
P(1.57 ≤ z ≤ 1.87) = normalcdf(1.57, 1.87, 0, 1)
where 0 is the mean and 1 is the standard deviation of the standard normal distribution. This would also give us a result of approximately 0.0275.
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A segment that connects two points on a circle is called a
A. circumference
B. chord
C. radius
D. diameter
A segment that connects two points on a circle is called a chord, which makes the option B correct.
What is a chord in circlesIn the context of circles, a chord refers to a line segment that connects two points on the circumference of the circle. It can also be defined as the longest possible segment that can be drawn between two points on a circle. Every chord in a circle creates two arcs, one on each side of the chord.
Note that diameter is a special type of chord that passes through the center of the circle. It is the longest possible chord in a circle, and it divides the circle into two congruent semicircles.
Therefore, a segment that connects two points on a circle is called a chord.
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How many more bushels did mr myers pick of golden delicious apples than of red delicious apples
The amount of golden delicious apples than red delicious apples that Mr. Myers picked would be 14 1/8.
How many more apples did Mr. Myers pick?The extra amount of golden delicious apples that Mr. Myers picked in comparison to the red delicious apples that Mr. Myers picked would be gotten by subtracting the amount of golden delicious apples from red delicious apples as follows:
27 2/8 - 13 1/8
= 14 1/8
So, the amount with which the number of golden delicious apples that Mr. Myers got was greater than the red delicious apples is 14 1/8
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Complete Question:
Mr.Myers picked 13 1/8 bushels of red delicious apples and 27 2/8 bushels of golden delicious apples. How many bushels of golden delicious apples than of red delicious apples did he pick?
A town has a population of 15,000 and it grows at 3% each year. To the nearest year, how long will it be until the population reaches 24,600?
To the nearest year, it will take 10 years for the population to reach 24,600.
Now, For this problem, we can use the formula for exponential growth:
P(t) = P₀ (1 + r)ⁿ
Where:
P(t) is the population after t years
P₀ is the initial population
r is the annual growth rate (as a decimal)
n is the number of years
Plugging in the values given:
P₀ = 15,000
r = 0.03
P(t) = 24,600
We can solve for n by dividing both sides by P0 and then taking the logarithm of both sides:
(1 + r)ⁿ = P(t) / P₀ t log(1 + r)
= log(P(t) / P0)
t = log(P(t) / P₀) / log(1 + r)
Plugging in the values given:
t = log(24,600 / 15,000) / log(1 + 0.03) t
t ≈ 10 years
Therefore, to the nearest year, it will take 10 years for the population to reach 24,600.
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find the taylor polynomial 2() for the function ()=63 at =0.
The second-degree Taylor polynomial for the function ()=63 at =0 is simply 63.
To find the Taylor polynomial 2() for the function ()=63 at =0, we need to use the formula for the nth-degree Taylor polynomial:
2() = f(0) + f'(0)() + (1/2!)f''(0)()^2 + (1/3!)f'''(0)()^3 + ... + (1/n!)f^(n)(0)()^n
Since we are only interested in the second-degree Taylor polynomial, we need to calculate f(0), f'(0), and f''(0):
f(0) = 63
f'(x) = 0 (the derivative of a constant function is always 0)
f''(x) = 0 (the second derivative of a constant function is always 0)
Substituting these values into the formula, we get:
2() = 63 + 0() + (1/2!)0()^2
2() = 63
Therefore, the second-degree Taylor polynomial for the function ()=63 at =0 is simply 63.
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Use an ordinary truth table to answer the following problems. Construct the truth table as per the instructions in the textbook. Given the argument: K ⊃ Q / Q ⊃ ∼ K // K ≡ Q This argument is:
The given argument "K ⊃ Q / Q ⊃ ∼ K // K ≡ Q" is valid.
Is the argument "K ⊃ Q / Q ⊃ ∼ K // K ≡ Q" valid?To determine the validity of the argument "K ⊃ Q / Q ⊃ ∼ K // K ≡ Q," we construct an ordinary truth table. The argument consists of two premises and a conclusion. The symbol "⊃" represents the conditional implication, "∼" represents negation, and "≡" represents equivalence.
We assign truth values (T or F) to the atomic propositions K and Q and evaluate the truth values of the premises and the conclusion based on the given argument. By systematically filling out the truth table, we can examine all possible combinations of truth values for K and Q.
After constructing the truth table, we observe that in every row where the premises K ⊃ Q and Q ⊃ ∼ K are true, the conclusion K ≡ Q is also true. Therefore, the argument is valid.
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Let f and g be functions such that, f(0)=2, g(0)=3, f'(0)=-10, g'(0)=-3. Find h'(0) for the function h(x)=g(x)f(x). h'(0)=??
If f and g be functions such that, f(0)=2, g(0)=3, f'(0)=-10, g'(0)=-3, then :
h'(0) = -36.
To find h'(0), we can use the product rule for derivatives. The product rule states that if h(x) = f(x)g(x), then h'(x) = f'(x)g(x) + f(x)g'(x).
Applying this to our function h(x) = g(x)f(x), we get:
h'(x) = g'(x)f(x) + g(x)f'(x)
Now we can evaluate this expression at x = 0, since we are looking for h'(0). Plugging in the given values, we get:
h'(0) = g'(0)f(0) + g(0)f'(0)
= (-3)(2) + (3)(-10)
= -6 - 30
= -36
Therefore, we can state that the value of h'(0) = -36.
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8. Max is remodeling his house and is trying to come up with dimensions for his
bedroom. The length of the room will be 5 feet longer than his bed, and the
width of his room will be 7 feet longer than his bed. The area of his bed and the
room together is given by the function:
A(x) = (x + 5) (x + 7)
Part A: Find the standard form of the function A(x) and the y-intercept. Interpret
the y-intercept in the context.
Standard Form: A(x)
y- intercept:
Interpret the y-intercept:
=
The y-intercept represents the area of the bed and room together when the length and width of the bed are both zero and the function is given by the relation A(x) = x² + 12x + 35
Given data ,
To find the standard form of the function A(x), we first expand the expression:
A(x) = (x + 5) (x + 7)
A(x) = x² + 7x + 5x + 35
A(x) = x² + 12x + 35
So the standard form of the function A(x) is:
A(x) = x² + 12x + 35
To find the y-intercept, we set x = 0 in the function:
A(0) = 0² + 12(0) + 35
A(0) = 35
So the y-intercept is 35. In the context of the problem, the y-intercept represents the area of the bed and room together when the length and width of the bed are both zero.
Hence , the function is solved
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Students at Euler Middle School are talking about ways to raise money for a school party. One student suggests a game called Heads or Tails. In this game, a player pays 50 cents and chooses heads or tails. The player then tosses a fair coin. If the coin matches the player's call, the player wins a prize. A. Suppose 100 players play the game. How many of these players would you
expect to win?
b. Suppose the prizes awarded to winners of Heads or Tails cost 40 cents
each. Based on your answer to part (a), how much money would you expect the students to raise if 100 players play the game? Explain. I need the answer to question b only.
In the Heads or Tails game, the player pays 50 cents and chooses either heads or tails. After that, the player tosses a fair coin. If the coin matches the player's call, then the player wins a prize. if 100 players play the game, then we can expect that the students will raise $20.00 as the cost of prizes to be given to the winners.
Answer to part (a):
Probability of winning the game = 1/2
Probability of losing the game = 1/2
Expected number of players who would win = Number of players × Probability of winning
= 100 × 1/2= 50
Expected number of players who would lose = Number of players × Probability of losing
= 100 × 1/2= 50
Therefore, we can expect 50 players to win the game.
Answer to part (b):
The cost of each prize is 40 cents. The expected number of players who would win the game is 50.
Therefore, the total cost of prizes would be:
The total cost of prizes = Cost of each prize × Expected number of players who would win
= 40 × 50
= 2000 cents or $20.00
Therefore, if 100 players play the game, then we can expect that the students will raise $20.00 as the cost of prizes to be given to the winners.
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calculate the fundamental vector product: r(u,v)=2ucos(v)i 2usin(v)j 2k
Step-by-step explanation:
the answer is 2k(2ucos)2usin(vi)
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The both angles are 75 degrees.
How to find angles in parallel lines?When parallel lines are cut by a transversal line angles relationships are formed such as corresponding angles, alternate exterior angles, alternate interior angles, same side interior angles, vertically opposite angles etc.
Therefore, let's use the angle relationships to find the angles in the parallel lines as follows:
Hence,
15x = 12x + 15(alternate interior angles)
15x - 12x = 15
3x = 15
divide both sides by 3
x = 15 / 3
x = 5
Therefore,
15(5) = 75 degrees
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18. Ten apples, four of which are rotten, are in a refrigerator. Three apples are randomly selected without replacement. Let the random variable x represent the number chosen that are rotten. Construct a table describing the probability distribution, then find the mean and standard deviation for the random variable x. (Hint: you can use Table A-1 to find the probabilities)
The standard deviation of x can be 0.725.
The table describing the probability distribution of x is as follows
x P(X=x)
0 10/120
1 48/120
2 42/120
3 20/120
To find the probabilities, we can use the hypergeometric distribution formula:
P(X=x) = (C(4,x) * C(6,3-x)) / C(10,3)
where C(n,r) represents the number of combinations of n things taken r at a time.
The mean of x can be found using the formula:
E(X) = Σ(x * P(X=x))
= 0*(10/120) + 1*(48/120) + 2*(42/120) + 3*(20/120)
= 1.4
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Which numbers round to 4.9 when rounded to the nearest tenth? Mark all that apply.
A 4.95
B 4.87
C 4.93
D 5.04
E 4.97
Answer:
B, C
Step-by-step explanation:
A would round up to 5
B would round up to 4.9
C would round down to 4.9
D would round down to 5
E would round up to 5
Out of all these only B and C round to 4.9
Answer:
B and C
Step-by-step explanation:
A 4.95 --- this would round to 5.00.
B 4.87 - - - this would round to 4.9
C 4.93 - - - this would round to 4.9
D 5.04 - - - - this would round to 5.0
E 4.97 - - - this would round to 5.0
Becoming a fine artist can happen overnight.
True
False
Answer:
Step-by-step explanation:
True. But there is a very high chance of not happening
Consider a city X where the probability that it will rain on any given day is 1%. You have a weather prediction algorithm that predicts the weather at the start of each day and obeys two rules: a. Before a rainy day, it'll predict rain with probability 90% b. Before a dry (no rain) day, it'll predict rain with probability 1%. Find the probability that 1. The probability that it won't rain given that your algorithm predicted a rainy day. 0.01 X 0.01 2. The probability that it will rain given that your algorithm predicted a dry day. 0.1 X 0.1
The probability that it won't rain given that your algorithm predicted a rainy day is approximately 9.1%. The probability that it will rain given that your algorithm predicted a dry day is approximately 0.01%.
What are the probabilities of no rain after a rainy prediction and rain after a dry prediction?When the algorithm predicts rain, it has a 90% accuracy rate, meaning that it correctly predicts rain 90% of the time. However, since the overall probability of rain in city X is only 1%, most of the algorithm's rainy predictions will be false positives. Using conditional probability, we can calculate the probability of no rain given a rainy prediction as follows: (0.01 * 0.1) / (0.01 * 0.1 + 0.99 * 0.9) ≈ 0.0091 or 9.1%.
Conversely, when the algorithm predicts a dry day, it has a 99% accuracy rate, meaning that it correctly predicts no rain 99% of the time. Since the overall probability of rain is 1%, the algorithm's dry predictions will mostly be true negatives. Using conditional probability again, we can calculate the probability of rain given a dry prediction as follows: (0.99 * 0.01) / (0.99 * 0.01 + 0.01 * 0.9) ≈ 0.0001 or 0.01%.
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Calculate the area of the following parallelogram: parallelogram with a 4 inch side, a 10 inch side, and 3 inches tall 26 in2 30 in2 40 in2 28 in2
The area of the parallelogram is 21 in².
What is area?Area is the region bounded by a plan shape.
To calculate the area of the parallelogram, we use the formula below
Formula:
A = h(a+b)/2...................... Equation 1Where:
A = Area of the parallelogramh = Height of the parallelograma, b = The two parallel sides of the parallelogramFrom the question,
Given:
h = 3 incha = 4 inchb = 10 inchSubstitute these values into equation 1
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what is the upper sum for f(x)=17−x2 on [3,4] using four subintervals?
the upper sum for f(x) = 17 - [tex]x^{2}[/tex] on the interval [3, 4] using four subintervals is approximately 6.46875.
To calculate the upper sum, we divide the interval [3, 4] into four subintervals of equal width. The width of each subinterval is (4 - 3) / 4 = 1/4.
Next, we evaluate the function at the right endpoint of each subinterval and multiply it by the width of the subinterval. For this function, we need to find the maximum value within each subinterval. Since the function f(x) = 17 - [tex]x^{2}[/tex] is a downward-opening parabola, the maximum value within each subinterval occurs at the left endpoint.
Using four subintervals, the right endpoints are: 3 + (1/4), 3 + (2/4), 3 + (3/4), and 3 + (4/4), which are 3.25, 3.5, 3.75, and 4 respectively.
Evaluating the function at these right endpoints, we get: f(3.25) = 8.5625, f(3.5) = 10.75, f(3.75) = 13.5625, and f(4) = 13.
Finally, we calculate the upper sum by summing the products of each function value and the subinterval width: (1/4) × (8.5625 + 10.75 + 13.5625 + 13) = 6.46875.
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A, b & c form a triangle where
∠
bac = 90°.
ab = 4.4 mm and ca = 4.7 mm.
find the length of bc, giving your answer rounded to 1 dp.
In a right triangle where angle BAC is 90°, and given the lengths AB = 4.4 mm and CA = 4.7 mm, the length of BC, is approximately 6.3 mm which is found using the Pythagorean theorem.
In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides (AB and CA).
Using the given values, AB = 4.4 mm and CA = 4.7 mm, we can apply the Pythagorean theorem to find BC. The equation is:
[tex]BC^{2}[/tex]= [tex]AB^{2}[/tex] + [tex]CA^{2}[/tex]
Substituting the values, we have:
[tex]BC^{2}[/tex]= [tex]4.4 mm^{2}[/tex] +[tex]4.7 mm^{2}[/tex]
[tex]BC^{2}[/tex] = 19.36 [tex]mm^{2}[/tex] + 21.81 [tex]mm^{2}[/tex]
[tex]BC^{2}[/tex] = 41.17 [tex]mm^{2}[/tex]
Taking the square root of both sides to solve for BC, we get:
BC ≈ √41.17 mm
BC ≈ 6.411 mm (rounded to three decimal places)
Rounding to one decimal place, the length of BC is approximately 6.3 mm.
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5.2 in
7 in
9 in
4.7 in
A) A researcher believes that a particular study exhibits large sampling error. What does the researcher mean by sampling error? B) How can sampling error be diminished? C) Discuss why one of the following methods of sample selection might yield sampling error: convenience, snowball, or judgmental.
Sampling error refers to the discrepancy between sample characteristics and population characteristics. It can be diminished by increasing the sample size, using random sampling techniques, and improving response rates.
A) Sampling error refers to the difference between the characteristics of a sample and the characteristics of the population from which it was drawn.
In other words, sampling error refers to the degree to which the sample statistics deviate from the population parameters.
B) Sampling error can be diminished by increasing the sample size, using random sampling techniques to ensure that the sample is representative of the population, and minimizing sources of bias in the sampling process.
C) Convenience sampling, snowball sampling, and judgmental sampling are all methods of non-probability sampling, which means that they do not involve random selection of participants.
As a result, these methods are more likely to yield sampling error than probability sampling methods.
Convenience sampling involves selecting participants who are readily available, which may not be representative of the population of interest.
Snowball sampling involves using referrals from existing participants, which may create biases in the sample.
Judgmental sampling involves selecting participants based on the researcher's judgment of who is most relevant to the study, which may not be representative of the population of interest.
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In a recent election Corrine Brown received 13,696 more votes than Bill Randall. If the total numb
Corrine Brown received
votes.
The number of votes for each candidate would be:
Corrine Brown = 66,617
Bill Randall = 52,920
How to determine the number of votesTo determine the number of votes for each candidate, we will make some equations with the values given.
Equation 1 = CB + BR = 119,537
(BR + 13,696) + BR = 119,537
2BR + 13,696 = 119,537
Collect like terms
2BR = 119,537 - 13,696
2BR = 105841
Divide both sides by 2
BR = 52,920
This means that Corrine Brown received 52,920 + 13,696 = 66,617
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Complete Question:
In a recent election corrine brown received 13,696 more votes than bill Randall. If the total number of votes was 119,537, find the number of votes for each candidate
The length of life, in hours, of a drill bit in a mechanical operation has a Weibull distribution with a = 2 and B = 50. Find the probability that the bit will fail before 10 hours of usage. The probability is approximately: O 1 O 0 O 0.5 O 0.8
The probability that the bit will fail before 10 hours of usage is:
P(X < 10) = F(10) = 1 - e^(-(10/50)^2) ≈ 0.3935
The Weibull distribution is given by the probability density function:
f(x) = (a/B) * (x/B)^(a-1) * e^(-(x/B)^a)
where a and B are the shape and scale parameters, respectively.
In this case, a = 2 and B = 50. We want to find the probability that the bit will fail before 10 hours of usage, i.e., P(X < 10), where X is the random variable representing the length of life of the drill bit.
Using the cumulative distribution function (CDF) of the Weibull distribution, we have:
F(x) = 1 - e^(-(x/B)^a)
Substituting the values of a and B, we get:
F(x) = 1 - e^(-(x/50)^2)
So the answer is approximately 0.4.
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determine and from the given parameters of the population and sample size. u=83. =14, n=49
The population mean, denoted by u, is 83, and the standard deviation of the population, denoted by sigma, is 14. The sample size, denoted by n, is 49.
Hi! I'd be happy to help you with your question. Based on the given parameters of the population and sample size, we need to determine µ (mean) and σ (standard deviation).
From the information provided, we have the following parameters:
1. Population mean (µ) = 83
2. Population standard deviation (σ) = 14
3. Sample size (n) = 49
Using these parameters, we can determine the mean and standard deviation for the sample. Since the population mean is given, the sample mean will also be 83.
To find the standard error (SE), which is the standard deviation for the sample, use the formula:
SE = σ / √n
Plugging in the values, we get:
SE = 14 / √49
SE = 14 / 7
SE = 2
So, the sample mean (µ) is 83, and the sample standard deviation (SE) is 2.
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P is a function that gives the cost, in dollars, of mailing a letter from the United States to Mexico in 2018 based on the weight of the letter in ounces,w
Given that P is a function that gives the cost, in dollars, of mailing a letter from the United States to Mexico in 2018 based on the weight of the letter in ounces, w.In order to write a function, we must find the rate at which the cost changes with respect to the weight of the letter in ounces.
Let C be the cost of mailing a letter from the United States to Mexico in 2018 based on the weight of the letter in ounces, w.Let's assume that the cost C is directly proportional to the weight of the letter in ounces, w.Let k be the constant of proportionality, then we have C = kwwhere k is a constant of proportionality.Now, if the cost of mailing a letter with weight 2 ounces is $1.50, we can find k as follows:1.50 = k(2)⇒ k = 1.5/2= 0.75 Hence, the cost C of mailing a letter from the United States to Mexico in 2018 based on the weight of the letter in ounces, w is given by:C = 0.75w dollars. Answer: C = 0.75w
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List three different ways to write 511 as the product of two powers. Explain why all three of your expressions are equal to 511.
Three different ways to write [tex]5^{11}[/tex] as the product of two powers are:
[tex]5^{1} * 5^{10} \\\\5^{5} * 5^{6} \\\\5^{3} * 5^{8}[/tex]
How to write the powers in different waysTo write the powers in different ways that all translate to 5 raised to the power of 11, we need to first recall that the product of the same bases is gotten by summing up the bases.
In this case, 1 times 10 is 1 plus 10 which is 11. The same applies for 5 and 6 and 3 and 8. So, the above are three ways to rewrite the expression.
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use direct integration to determine the mass moment of inertia of the homogeneous solid of revolution of mass m about the x- and y-axes. ans: ixx = (2/7)mr 2 , iyy = (1/7)mr 2 (2/3)mh2
the mass moment of inertia about the x-axis is ixx = (2/7)[tex]mr^{2}[/tex] and about the y-axis is iyy = (1/7)[tex]mr^{2}[/tex] + (2/3)[tex]mh^{2}[/tex]
To find the mass moment of inertia, we consider the solid of revolution as a collection of infinitesimally thin disks or cylinders stacked together along the axis of revolution. Each disk or cylinder has a mass element dm.
For the mass moment of inertia about the x-axis (ixx), we integrate the contribution of each mass element along the axis of revolution:
ixx = ∫ [tex]r^{2}[/tex] dm
Since the solid is homogeneous, dm = ρ dV, where ρ is the density and dV is the volume element. For a solid of revolution, dV = πr^2 dh, where h is the height of the solid.
Substituting the expressions and performing the integration, we get:
ixx = ∫ [tex]r^{2}[/tex] ρπr^2 dh
= ρπ ∫ [tex]r^{4}[/tex] dh
= [tex](1/5)\beta \pi r^{4}[/tex] h
Since the solid is homogeneous, the mass m = [tex]\beta \pi r^{2}[/tex] h. Substituting this in the equation above, we get:
ixx = (1/5)m [tex]r^{2}[/tex]
Similarly, for the mass moment of inertia about the y-axis (iyy), we integrate along the radius r:
iyy = ∫[tex]r^{2}[/tex] dm
= ∫ [tex]r^{2}[/tex] [tex]\beta \pi r^{2}[/tex] dh
= ρπ ∫ [tex]r^{4}[/tex] dh
= (1/5)[tex]\beta \pi r^{4}[/tex] h
Since the height of the solid is h, substituting [tex]\beta \pi r^{2}[/tex] h = m, we get:
iyy = (1/5)m [tex]r^{2}[/tex] + [tex](2/3)mh^{2}[/tex]
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HELP, I HAVE BEEN SCREAMING AT MY PC IN MY HEAD IM GOING CRAZY
Answer:
Step-by-step explanation:
The answer is choice B.
No matter what the equation for each angle,
they still add to 180°. All interior angles of a triangle
add to 180°.
3. What percentage of the shirt cost is the discount?
shirt cost
discount
write dissociation reactions for the following ionic compounds (example: bai2(s) ba2 (aq) 2 i−(aq) ): a) kcl(s) b) cabr2(s) c) fe2(so4)3(s)
Potassium chloride (KCl) is a binary ionic compound consisting of potassium cations (K+) and chloride anions (Cl-). a) KCl(s) → K+(aq) + Cl-(aq). b) CaBr2(s) → Ca2+(aq) + 2Br-(aq). c) Fe2(SO4)3(s) → 2Fe3+(aq) + 3SO42-(aq).
a) KCl(s) → K+(aq) + Cl-(aq)
Potassium chloride (KCl) is a binary ionic compound consisting of potassium cations (K+) and chloride anions (Cl-). When KCl is dissolved in water, it dissociates into its constituent ions, i.e., K+ and Cl-. This process is represented by the above chemical equation.
b) CaBr2(s) → Ca2+(aq) + 2Br-(aq)
Calcium bromide (CaBr2) is also a binary ionic compound consisting of calcium cations (Ca2+) and bromide anions (Br-). When CaBr2 is dissolved in water, it dissociates into its constituent ions, i.e., Ca2+ and 2Br-. This process is represented by the above chemical equation.
c) Fe2(SO4)3(s) → 2Fe3+(aq) + 3SO42-(aq)
Iron(III) sulfate (Fe2(SO4)3) is a complex ionic compound consisting of two iron cations (Fe3+) and three sulfate anions (SO42-). When Fe2(SO4)3 is dissolved in water, it dissociates into its constituent ions, i.e., 2Fe3+ and 3SO42-. This process is represented by the above chemical equation.
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The singular points of the differential equation xy''+y'+y(x+2)/(x-4)=0 are Select the correct answer. 0 none 0, -2 0, -2, 4 0, 4
The singular point(s) of the differential equation are x = 4.
To find the singular points of the differential equation xy'' + y' + y(x + 2)/(x - 4) = 0, we need to find the values of x at which the coefficient of y'' or y' becomes infinite or undefined, since these are the points where the equation may behave differently.
The coefficient of y'' is x, which is never zero or undefined, so there are no singular points due to this term.
The coefficient of y' is 1, which is also never zero or undefined, so there are no singular points due to this term.
The coefficient of y is (x + 2)/(x - 4), which becomes infinite or undefined when x = 4, so 4 is a singular point of the differential equation.
Therefore, the singular point(s) of the differential equation are x = 4.
Note that this analysis does not consider any initial or boundary conditions, which may affect the behavior of the solution near the singular point(s).
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find the first three nonzero terms in the taylor polynomial approximation to the de y″ 9y 9y3=6cos(4t) , y(0)=0,y′(0)=1.
The first three nonzero terms in the Taylor polynomial approximation to $y(t)$ are $t + \frac{1}{3}t^2 + O(t^3)$.
Using these initial conditions, we can write the first few terms of the Taylor polynomial approximation as:
\begin{align*}
y(t) &\approx y(0) + y'(0)t + \frac{y''(0)}{2!}t^2 \
&= t + \frac{1}{2}y''(0)t^2 \
&= t + \frac{1}{2}\left(\frac{6\cos(0)}{9\cdot 0 + 9}\right)t^2 \
&= t + \frac{1}{3}t^2
\end{align*}
Therefore, the first three nonzero terms in the Taylor polynomial approximation to $y(t)$ are $t + \frac{1}{3}t^2 + O(t^3)$.
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