The inverse of matrix A is:
A^-1 = |-3 -2|
|-2 -1|
Using Adjoint of a Matrix A=2 -1 0
0 1 2
1 1 0
The first step is to find the determinant of the matrix A:
|A| = 2(10 - 21) - (-1)(10 - 12) + 0(11 - 10)
= 4 + 2 + 0
= 6
Next, we need to find the adjoint of matrix A, which is the transpose of its cofactor matrix. The cofactor matrix is obtained by taking the determinant of the submatrix obtained by removing each element of the original matrix in turn and multiplying it by (-1)^(i+j), where i and j are the row and column indices of the removed element, respectively.
Cofactor matrix of A is
| 1 2 -1|
|-2 0 2|
|-1 2 1|
Taking the transpose of the cofactor matrix, we get the adjoint matrix of A as follows:
A^T = | 1 -2 -1 |
| 2 0 2 |
|-1 2 1 |
To find the inverse of A, we use the formula:
A^-1 = (1/|A|) A^T
Substituting the values, we get:
A^-1 = (1/6) | 1 -2 -1 |
| 2 0 2 |
|-1 2 1 |
Using Gauss Jordan A= |1 3|
|2 5|
We can find the inverse of a matrix using Gauss-Jordan elimination method as follows:
|1 3|1 0| |1 3|0 1|
|2 5|0 1|-> |0 1|-2/3 -1/3|
Therefore, the inverse of matrix A is:
A^-1 = |-2/3 -1/3|
| 1/3 1/3|
Using Equations and Identity Matrix A= |1 -2|
|2 -3|
We can find the inverse of a matrix A using the equations AX=I, where I is the identity matrix and X is the matrix that represents the inverse of A. The solution is given by:
|1 -2| |x11 x12| |1 0|
|2 -3| |x21 x22| = |0 1|
Multiplying the matrices, we get:
x11 = -3
x12 = -2
x21 = -2
x22 = -1
Therefore, the inverse of matrix A is:
A^-1 = |-3 -2|
|-2 -1|
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Suppose your parents have 2 options to purchase a plot of land on which they plan to build a barn.
Option 1: They can purchase the land for $30,000 cash.
Option 2: They can purchase the land with $7,500 down, and then pay $2,500 semi-annually for the next 10 years,
at an interest rate of 5%.
Calculate the present value for both options, and tell which will save them the most money.
Option 1 will save your parents the most money.
Option 2 will save your parents the most money.
It is not possible to determine which option will save the most money because the question does not state how large the
barn will be.
The options both cost the same, so neither one will save them money.
Answer:
PV = $30,000; this saves the mostPV = $46,473 — the higher-cost optionStep-by-step explanation:
You want the present value and the lower-cost choice for two payment plans:
$30,000 cash$7500 down and $2500 semi-annually for 10 years at 5%Present valueThe present value of 20 semiannual payments of $2500 discounted at the rate of 5% can be found by a financial calculator to be $38,973. Together with the $7500 down payment, the present value of Option 2 is ...
Option 2 = $7500 +38,973 = $46,473
The present value of $30,000 cash is $30,000.
ComparisonOption 1 has a present value of $30,000.
Option 2 has a present value of $46,473.
Option 1 will save your parents the most money.
__
Additional comment
The total cash outlay for option 2 is $7500 + 20×2500 = $57,500. For this option to be the same cost as option 1, the account would need to earn interest at the rate of 18.4%.
There are various ways to estimate the interest earned. One of them is to compute half the value of simple interest on the interval. That is, the interest could be estimated as (1/2)(5%/yr)(10 yr) = 25%. This suggests the PV would be about 1/1.25 times the sum of payments, or 40000. That's close enough to the actual value of 39000 to tell you that Option 1 is the better choice.
help asap please
A dog is tied to a wooden stake in a backyard. His leash is 3 meters long and he runs around in circles pulling the leash as far as it can go. How much area does the dog have to run around in? Use 3.14 for pi.
The area the dog have to run around in is 28.26 square meters
How much area does the dog have to run around in?From the question, we have the following parameters that can be used in our computation:
His leash is 3 meters long and he runs around in circles
This means that
Radius, r = 3 meters
The area is calculated as
Area = 3.14r^2
So, we have
Area = 3.14 * 3^2
Evaluate
Area = 28.26
Hence, the area is 28.26 square meters
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An elementary teacher wants to know if the school has a higher proportion of left-handed students than the usual proportion of 0.10. The teacher surveys a random sample of 50 students, and finds that 7 are left-handed. 1) What is the sample proportion ? O 0.14 O 0.10 07 2) What is the hypothesized proportion po? O 0.14 O 0.5 O 0.10 3) What is the sample size n? O 50 O 7 4) What is the test statistic z? O 0.943 0 -0.815
1) The sample proportion is 0.14 (7 left-handed students out of 50 total students surveyed).
2) The hypothesized proportion po is 0.10 (the usual proportion of left-handed students).
3) The sample size n is 50 (the number of students surveyed).
4) The test statistic z is 1.32.
1) The sample proportion is calculated by dividing the number of left-handed students by the total number of students surveyed. In this case, 7 left-handed students out of 50 gives a sample proportion of 7/50 = 0.14.
2) The hypothesized proportion (p₀) is the usual proportion of left-handed students, which is given as 0.10.
3) The sample size (n) is the total number of students surveyed, which is 50.
4) The test statistic (z) can be calculated using the formula: z = (sample proportion - hypothesized proportion) / sqrt((hypothesized proportion * (1 - hypothesized proportion)) / sample size). In this case, z = (0.14 - 0.10) / sqrt((0.10 * (1 - 0.10)) / 50) = 0.04 / sqrt(0.09 / 50) ≈ 0.943.
To calculate the test statistic z, we use the formula:
z = (sample proportion - hypothesized proportion) / standard error
The standard error is calculated as:
standard error = sqrt((po * (1-po)) / n)
Plugging in the values, we get:
standard error = sqrt((0.10 * (1-0.10)) / 50) = 0.0499
Then,
z = (0.14 - 0.10) / 0.0499 = 1.32
Since the calculated z-value of 1.32 is greater than the critical value of 1.645 (using a significance level of 0.05 for a two-tailed test), we can conclude that there is not enough evidence to reject the null hypothesis that the proportion of left-handed students at the school is the same as the usual proportion of 0.10.
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Question # 7
Multiple Choice
10 students were randomly sampled and asked their shoe size. Which line plot displays the data for this sample?
9, 7, 8, 10, 9, 10, 11, 8, 8, 9
Answer:
The answer to your problem is, B.
Step-by-step explanation:
The sizes what are given.
There are:
3 - 9's
3 - 8's
1 - 7
2 -10's
1-11
Which concludes to the second graph has the right amount of x's for the given shoe sizes.
Thus the answer to you problem is, B
Find the radius of convergence, r, of the series. [infinity] n!xn 6 · 13 · 20 · ⋯ · (7n − 1) n = 1 r = find the interval, i, of convergence of the series. (enter your answer using interval notation. )
The radius of convergence doesn't exists, r, of the series n! x n: 6 × 13 × 20 × ⋯ × (7n − 1) as interval of convergence is (-1/7, 1/7).
To find the radius of convergence of the series, we can use the ratio test:
lim |a_{n+1}/a_n| = lim |(7(n+1)-1)/n+1| = 7
Since the limit exists and is finite, the series converges for |x| < 1/7. Therefore, the radius of convergence is r = 1/7.
To find the interval of convergence, we need to check the endpoints x = -1/7 and x = 1/7. When x = -1/7, the series becomes:
[tex](-1)^n[/tex] 6 × 13 × 20 × ⋯ × (7n − 1) n = 1
which does not converge since the terms do not approach zero. When x = 1/7, the series becomes:
6/7 × 13/7 × 20/7 × ⋯
which also does not converge since the terms do not approach zero. Therefore, the interval of convergence is (-1/7, 1/7).
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The question is -
Find the radius of convergence if exists, r, of the infinity series. n! x n: 6 × 13 × 20 × ⋯ × (7n − 1) n = 1 r = ? find the interval, i, of convergence of the series if exists and if it does mention the reason. (enter your answer using interval notation.)
How many terms are in the simplest form of the product?
(x + y)(a + b)
A.2
B.3
C.4
D.5
Answer:
There are two terms in the simplest form of the product (x + y)(a + b):
The first term is the product of x and a, which is xa.
The second term is the product of y and b, which is yb.
So, the simplified product is xa + yb. Therefore, the answer is A. 2.
Assume that it is possible for two people to be the same height. Consider the following argument: Bob is the tallest person. --(P) No one is taller than Bob and no one different from Bob is the same height as Bob. --(C) (a) Using the following predicate symbols and constant: B: Bob T(a,b): a is taller than b. H(a,b): a is the same height as b. a = b: a is the same person as b Translate (P) and (C) into predicate logic formulas: (b) Although the informal argument seems to be valid, actually it is invalid. Prove that the argument is invalid by constructing a model in which the predicate formula for (P) is true and the predicate formula for (C) is false.
We have a counterexample that shows the argument is invalid.
(a) Predicate Logic Formulas:
(P) B is the tallest person: ∀x [(x ≠ B) → T(B, x)]
(C) No one is taller than Bob and no one different from Bob is the same height as Bob: ∀x [(x ≠ B) → T(B, x)] ∧ ∀y [(y ≠ B ∧ ¬(y = B ∧ H(B, y))) → T(y, B)]
In (P), we have used the universal quantifier ∀ to express that the statement applies to all people x. The symbol ≠ denotes "not equal to", and the predicate T(a, b) represents "a is taller than b". So, the formula states that for all x, if x is not Bob, then Bob is taller than x.
In (C), we have combined two quantified statements using the conjunction operator ∧. The first statement ∀x [(x ≠ B) → T(B, x)] is the same as in (P), and it means that no one is taller than Bob. The second statement ∀y [(y ≠ B ∧ ¬(y = B ∧ H(B, y))) → T(y, B)] uses a new predicate symbol H(a,b) to represent "a is the same height as b". The formula says that for all y, if y is not Bob and y is not the same height as Bob, then y is shorter than Bob.
(b) The argument is invalid. To show this, we need to construct a model in which (P) is true and (C) is false. Let's consider a universe of discourse with three people: Alice, Bob, and Charlie. We can assign the following heights to them:
Alice is shorter than Bob
Bob is the same height as Charlie
So, we have H(A, B), ¬H(A, C), and H(B, C). Note that we have not specified the relative heights of Bob and Charlie, so they could be the same or Bob could be taller.
Now, let's interpret the predicate T(a, b) as "a is at least as tall as b", so T(B, A) and T(C, B). The formula for (P) is true in this model, since there is no person taller than Bob.
However, the formula for (C) is false, because Charlie is not shorter than Bob. In fact, they are the same height according to our assignment. So, we have a counterexample that shows the argument is invalid.
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Rewrite the equation below so that it does not have fractions or decimals.
5/6x+2= 3/8
The equation without decimal and fraction is 20x = -39.
Given is an equation 5x/6 +2 = 3/8
So, [tex]\frac{5x}{6} +2 = \frac{3}{8} \\\\[/tex]
Multiply the equation by 48,
[tex]\frac{5x}{6} +2 = \frac{3}{8} \\\\40x + 96 = 18\\\\40x = -78\\\\\\20x = -39[/tex]
Hence the equation without decimal and fraction is 20x = -39.
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For a list size of 1000, on average, the sequential search makes about ____________________ key comparisons.500100250400
For a list size of 1000, the sequential search would make about 500 key.
The sequential search algorithm searches a list item by item until the desired item is found or the end of the list is reached. On average, for a list size of 1000, the sequential search would make about 500 key comparisons. Therefore, the correct answer is 500.
Here's a concise description of the sequential search algorithm:
1.Start at the beginning of the list.
2.Compare the target value with the current element.
3.If they match, return the current position.
4.If they don't match, move to the next element.
5.Repeat steps 2-4 until the target is found or the end of the list is reached.
If the target is not found, return a designated value (e.g., -1) to indicate its absence.
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a consignment of 12 electronic components contains 1 component that is faulty. two components are chosen randomly from this consignment for testing. a. how many different combinations of 2 components could be chosen? b. what is the probability that the faulty component will be chosen for testing?
Answer:
a. The number of different combinations of 2 components that can be chosen from a group of 12 is given by the formula:
nC2 = (n!)/(2!(n-2)!), where n is the total number of components
Substituting n = 12, we get:
nC2 = (12!)/(2!(12-2)!) = (12 x 11)/2 = 66
Therefore, there are 66 different combinations of 2 components that can be chosen from the group of 12.
b. The probability that the faulty component will be chosen for testing depends on the number of ways in which the faulty component can be chosen, and the total number of ways in which any 2 components can be chosen.
The probability of choosing the faulty component on the first pick is 1/12, as there is one faulty component out of a total of 12 components.
After the first component has been picked, there will be 11 components left, including one faulty component. Therefore, the probability of picking the faulty component on the second pick, given that the first pick did not pick the faulty component, is 1/11.
Therefore, the probability of picking the faulty component on either the first or second pick is:
P(faulty component) = P(faulty on first pick) + P(faulty on second pick, given not picked on first pick)
P(faulty component) = (1/12) + ((11/12) x (1/11))
P(faulty component) = 1/12 + 1/12
P(faulty component) = 1/6
Therefore, the probability of choosing the faulty component for testing is 1/6 or approximately 0.1667.
find the value of x goes with the figure how do I do this?
The calculated value of the variable x in the figure is 6 degrees
Finding the value of x in the figureFrom the question, we have the following parameters that can be used in our computation:
The figure
By the given congruent angles, we have the following equation
9x - 14 = 6x + 4
Collect the like terms in the equation
so, we have the following representation
9x - 6x = 14 + 4
Evaluate the like terms
So, the equation becomes
3x = 18
Divide both sides of the equation by 3
x = 6
Hence, the value of the variable x in the figure is 6
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Help me and thank you.
The volume of the given cube is determined as (q cm)³.
What is the volume of the cube?The volume of a cube is calculated from the cube its edge length.
Mathematically, the formula for the volume of a cube is calculated by applying the following formula.
V = L x L x L = L³
where;
L is the edge length of the cubeThe volume of the given cube is calculated as follows;
V = q cm x q cm x q cm
V = (q cm)³
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PLS HELP HELP
Simplify
sqrt y^6 where y≥0
The simplified expression for this problem is given as follows:
[tex]\sqrt{y^6} = y^3[/tex]
How to simplify the expression?The expression for this problem is defined as follows:
[tex]\sqrt{y^6}[/tex]
The power of a power rule is used when a single base is elevated to multiple exponents, and the simplified expression is obtained keeping the bases and multiplying the exponents.
The square root is equivalent to an exponent of 1/2, while the exponent of y is of 6, hence the exponent f the simplified expression is given as follows
1/2 x 6 = 3.
Hence the simplified expression for this problem is given as follows:
[tex]\sqrt{y^6} = y^3[/tex]
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A country can use all its resources to produce Product A and Product B. If you know the opportunity cost of
producing Product A in terms of Product B, how can you quickly determine the cost of Product B in terms of
product A? Explain in one to two sentences, using an example.
You can take the reciprocal of the opportunity cost of producing Product A in terms of Product B to determine the cost of producing Product B in terms of Product A,
To determine the cost of producing Product B in terms of Product A, you can take the reciprocal of the opportunity cost of producing Product A in terms of Product B.
If the opportunity cost of producing 1 unit of Product A is 2 units of Product B, then the cost of producing 1 unit of Product B would be 1/2 unit of Product A.
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"A system can be defined as any set of independent parts
performin a specific function or set of functions.
True
False
Variation in a system can be maxiized by standardizing
operations.
True
False"
Question consists of two statements and you want to know if they are true or false.
1. "A system can be defined as any set of independent parts performing a specific function or set of functions."
Answer: True. A system can indeed be defined as a set of independent parts that work together to perform a specific function or set of functions.
2. "Variation in a system can be maximized by standardizing operations."
Answer: False. Variation in a system is actually minimized by standardizing operations. Standardizing operations helps to reduce variability and increase consistency in a system's performance.
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Question 7 (Drag&Drop 2pts): A system of equations is given. Identify the steps in the correct
order to explain how to eliminate the x in the system of equations.
STEPS
Step 1: 5x + 4y = -14
3x + 6y = 6
Step 2: -15x12y = -42
Step 3: 15x + 30y = 30
Step 4: -15x - 12y = -42
15x + 30y = 30
Equation 1: 5x + 4y = -14
Equation 2: 3x + 6y =6
EXPLANATION
The steps in order to solve the equation 5x + 4y = -14 and 3x + 6y =6 are step 1, 2, 3, and 4 respectively.
The equations 5x + 4y = -14 and 3x + 6y = 6, we have to use the steps 1, 2, 3 and 4 in the same order as stated in the question.
First, multiply Equation 1 by -3 and Equation 2 by 5, respectively, to obtain -15x - 12y = -42 and 15x + 30y = 30.
Step 2: Combine Equations 1 and 2 to take the x-variable out, resulting in 15y=-12.
Step 3: Calculate y by multiplying both sides by 15, which results in y=-4/5.
Step 4: To solve for x, enter y=-4/5 into Equation 1 or Equation 2, which will result in x = 2.
So, the correct order of the steps to eliminate x from the given equations is 1, 2, 3 and 4 respectively.
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the length of time needed to complete a certain test is normally distributed with mean 77 minutes and standard deviation 11 minutes. find the probability that it will take less than 63 minutes to complete the test. a) 0.8984 b) 0.9492 c) 0.1016 d) 0.5000 e) 0.0508 f) none of the above
The probability that it will take less than 63 minutes to complete the test is 0.1016, which corresponds to option c) in your list.
To solve this problem, we first need to standardize the value of 63 minutes using the formula:
z = (x - μ) / σ
where:
x = 63 (the given value)
μ = 77 (the mean)
σ = 11 (the standard deviation)
Plugging in these values, we get:
z = (63 - 77) / 11
z = -1.27
Next, we use a standard normal distribution table (or a calculator) to find the probability that a standard normal variable is less than -1.27. The table gives us a probability of approximately 0.1016.
However, we are not dealing with a standard normal distribution, but rather a normal distribution with a specific mean and standard deviation. To account for this, we need to use the following formula:
P(X < 63) = P(Z < -1.27) = Φ(-1.27)
where Φ is the standard normal cumulative distribution function. Using a standard normal distribution table (or a calculator), we find that Φ(-1.27) is approximately 0.1016.
Therefore, the answer is (c) 0.1016.
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A soccer coach wants to choose one starter and one reserve player for a certain position. If the candidate players are 8 players, in how many ways can they be chosen and ordered?
There are 56 ways to choose and order one starter and one reserve player from a group of 8 players.
The number of ways to choose and order one starter and one reserve player from a group of 8 players can be calculated using the multiplication principle of counting.
First, we can choose one player to be the starter in 8 ways. Then, we can choose one player from the remaining 7 players to be the reserve in 7 ways.
Using the multiplication principle, we multiply the number of ways to choose the starter by the number of ways to choose the reserve to get the total number of ways to choose and order one starter and one reserve player from 8 players:
8 × 7 = 56
Therefore, there are 56 ways to choose and order one starter and one reserve player from a group of 8 players.
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A 35-year-old person who wants to retire at age 65 starts a yearly retirement contribution in the amount of $5,000. The retirement account is forecasted to average a 6.5% annual rate of return, yielding a total balance of $431,874.32 at retirement age.
If this person had started with the same yearly contribution at age 40, what would be the difference in the account balances?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
$378,325.90
$359,978.25
$173,435.93
$137,435.93
If this person, who wants to retire at age 65, had started with the same yearly contribution at age 40, the difference in the account balances (future values) would be D. $137,435.93.
How the future values are determined:The future values can be computed using an online finance calculator as follows:
Future Value at Age 35:N (# of periods) = 30 years (65 - 35)
I/Y (Interest per year) = 6.5%
PV (Present Value) = $0
PMT (Periodic Payment) = $5,000
Results:
Future Value (FV) = $431,874.32
Sum of all periodic payments = $150,000.00
Total Interest = $281,874.32
Future Value at Age 40:N (# of periods) = 25 years (65 - 40)
I/Y (Interest per year) = 6.5%
PV (Present Value) = $0
PMT (Periodic Payment) = $5,000
Results:
Future Value (FV) = $294,438.39
Sum of all periodic payments = $125,000.00
Total Interest = $169,438.39
Difference in future values = $137,435.93 ($431,874.32 - $294,438.39)
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a coin is flipped 25 times, and we would like to know the probability that 15 or more of those flips are heads side up. is it geometric distribution a coin is flipped 25 times, and we would like to know the probability that 15 or more of those flips are heads side up. is it geometric distribution
The probability for each k value is from 15 to 25 and sum them up to get the final probability.
The situation you described is not a geometric distribution. Instead, it follows a binomial distribution. A binomial distribution is appropriate here because we have a fixed number of trials (25 coin flips), each trial has two outcomes (heads or tails), and the probability of success (getting heads) remains constant throughout the trials.
To calculate the probability of getting 15 or more heads in 25 coin flips, you can use the binomial formula:
[tex]P(X = k) = C(n, k) * p^k * (1-p)^{(n-k)}[/tex]
where n is the number of trials (25), k is the number of successful outcomes (15 or more), p is the probability of success (0.5 for a fair coin), and C(n, k) represents the number of combinations of n items taken k at a time.
You'll need to calculate the probability for each k value from 15 to 25 and sum them up to get the final probability.
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A math textbook has a length of 22 cm, a width of 27 cm, and a height of 3.5
cm. A science textbook has a length of 21 cm, a width of 27 cm, and a height
of 4 cm.
Which textbook has a greater volume?
OA. The science textbook, with a volume of 2376 cm³
OB. The math textbook, with a volume of 2464 cm³
OC. The math textbook, with a volume of 2079 cm³
OD. The science textbook, with a volume of 2268 cm³
The science textbook has a greater volume than the math textbook, so option D is correct, the science textbook, with a volume of 2268 cm³.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.
Using this formula, we can calculate the volumes of the math and science textbooks:
Math textbook:
V = 22 cm × 27 cm × 3.5 cm
= 2079 cm³
Science textbook:
V = 21 cm × 27 cm × 4 cm
= 2268 cm³
Therefore, the science textbook has a greater volume than the math textbook, so option D is correct, the science textbook, with a volume of 2268 cm³.
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Convert 0.0045 to a percent.
Select one:
0.045%
0.45%
4.5%
45%
Answer: 0.045%
Step-by-step explanation:
how much time do americans spend eating or drinking? suppose for a random sample of 1001 americans, the mean time eating or drinking per day is 1.22 hours with a sample standard deviation of 0.65 hours. (a) construct and interpret a 99% confidence interval for the mean amount of time americans spend eating or drinking per day. (b) suppose you want to conduct your own survey. using the sample standard deviation above, how large of a sample is required to estimate the mean time americans spend eating or drinking per day within 15 minutes of the true mean and with 95% confidence?
a. we are 99% confident that the true population mean time Americans spend eating or drinking per day falls between 1.166 and 1.274 hours.
b. There will be 70 sample is required to estimate the mean time Americans spend eating or drinking per day within 15 minutes of the true mean and with 95% confidence
(a) To construct a 99% confidence interval for the mean time Americans spend eating or drinking per day, we can use the formula:
CI = x ± z*(σ/√n)
where x is the sample mean, σ is the population standard deviation (which is unknown, so we use the sample standard deviation), n is the sample size, and z* is the critical value for a 99% confidence interval (which we can find using a table or calculator).
Plugging in the values given, we get:
CI = 1.22 ± 2.58*(0.65/√1001) ≈ 1.22 ± 0.054
So the 99% confidence interval for the mean time Americans spend eating or drinking per day is (1.166, 1.274) hours.
We can interpret this interval as saying that we are 99% confident that the true population mean time Americans spend eating or drinking per day falls between 1.166 and 1.274 hours.
(b) To find the sample size required to estimate the mean time Americans spend eating or drinking per day within 15 minutes of the true mean with 95% confidence, we can use the formula:
n = (z*σ/E)^2
where E is the margin of error (which is 15 minutes = 0.25 hours), z* is the critical value for a 95% confidence interval (which is 1.96), and σ is the sample standard deviation (which is 0.65).
Plugging in the values given, we get:
n = (1.96*0.65/0.25)^2 ≈ 69.88
So we need a sample size of at least 70 to estimate the mean time Americans spend eating or drinking per day within 15 minutes of the true mean with 95% confidence.
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Mrs. Powell is making a piñata like the one shown below for her son's
birthday party. She wants to fill it with candy. What is the volume of the
piñata? Use the solve a simpler problem strategy.
The volume of the piñata is
1152 cubic in
How to solve for the volume of the piñataThe volume is solved by breaking the composite shape into two prisms
square prism and triangular prismThe volume is solved individually and then added together
Volume of square prism
= area x thickness
= 12 x 12 x 6
= 864 square in
Volume of triangular prism
= area x thickness
= 1/2 x 8 x 12 x 6
= 288 square in
The volume of the piñata
= 864 square in + 288 square in
= 1152 cubic in
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Show that the function f(x)= 1 3x3−2x2 7x has no relative extreme points. Relative extreme points exist when____f'(x)=0 or f''(x)=0___. In this case, because _f'(x) or f''(x)____=_____. ____has no x-int, has no y-int, has multiple x-int, has multiple y-int____ the function f(x)=2/3x^3-4x^2+10x has no relative extreme points
The f'(x) has two x-intercepts, but f''(x) is always positive, indicating that f(x) has no relative extrema. This means that the function is either always increasing or always decreasing, and there are no maximum or minimum points.
The function f(x) =
[tex](1/3)x^3 - (2/7)x^2 - 1x[/tex]
has no relative extreme points. To find the relative extreme points of a function, we need to find the critical points where either the derivative f'(x) is equal to zero or the second derivative f''(x) is equal to zero.
Taking the derivative of f(x), we get f'(x) = x^2 - (4/7)x - 1. Setting f'(x) equal to zero and solving for x, we get x =
[tex](2 ± \sqrt{} (30))/7[/tex]
Upon further analysis of the second derivative f''(x) = 2x - (4/7), we see that it is always positive for all values of x.
There are no relative extreme points as the function f(x) does not have any points where the slope is zero and the curvature changes from positive to negative or vice versa.
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Elizabeth and Nicholas want to buy a new home in Sunset Park. They
need to borrow $270,000. Their bank offers an opportunity for the couple
to buy down the quoted interest rate of 4.8% by 0.125% per point
purchased. Each point will cost 1% of the amount borrowed. What will be
the cost to purchase 1 points?
Based on the above, the cost to purchase 1 point is $2,700.
What is the cost about?In order to know the expense of acquiring 1 point, it is imperative to ascertain the extent by which the interest rate would decrease through the purchase of 1 point.
The purchasing of each point results in a 0.125% reduction of the interest rate, so rate of interest shall be:
4.8% - 0.125%
= 4.675%
So, the cost of 1 point is 1% of the amount borrowed, that is $270,000. hence, the cost of 1 point is:
1% x $270,000
= $2,700
Therefore, the cost to purchase 1 point is $2,700.
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how many flip-flops are needed to design a counter to count in the following sequence:12, 20, 1, 0, and then repeat?
We need four D flip-flops to design a counter to count in the sequence 12, 20, 1, 0, and then repeat.
To count in the sequence 12, 20, 1, 0 and then repeat, we need a counter that has at least four states: 12, 20, 1, and 0. Each state corresponds to a unique output value, and the counter changes state after each clock pulse.
To implement the counter, we can use four D flip-flops, one for each state. The flip-flops will store the current state of the counter and change state on the rising edge of the clock signal. The outputs of the flip-flops will be combined to produce the counter's output.
Therefore, we need four D flip-flops to design a counter to count in the sequence 12, 20, 1, 0, and then repeat.
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For number 1-3, identify wether or not the relation shown is a function?
1. Yes
2. No
3. Yes
Step-by-step explanation:A function is a relationship with unique x-values.
Defining a Function
For a relationship to be a function, the x-values cannot repeat. This means that inputs, aka x-values, can only have one possible output value, also called y-values. For example, if inputting x = 5 resulted in both y = 3 and y = 7, then the relationship would not be a function.
However, y-values do not have to be unique. Functions can repeat y-values and still be functions.
Answers
Now, let's apply this definition to the problems above.
1. The first question gives us a table of x and y-values. From the x-values in the left column, we can see that x-values do not repeat. This means the relationship is a function.
2. The second question gives the inputs and outputs of a function. From looking at the outputs for 0, we can tell that x = 0 produces multiple outputs. This means that not all x-values are unique. Thus, the relationship is not a function.
3. The third image is a graph. At no point on the graph do x-values repeat. Each x-value has one y-value. So, the relationship is a function. Specifically, this graph represents a quadratic function.
A student needs to decorate a box as part of a project for her history class. A model of the box is shown.
A rectangular prism with dimensions of 24 inches by 15 inches by 3 inches.
What is the surface area of the box?
234 in2
477 in2
720 in2
954 in2
The surface area of the box is 954 in².
Option D is the correct answer.
We have,
The surface area of a rectangular prism is the sum of the areas of all its faces.
The box has six faces, and each face is a rectangle.
The top and bottom faces have dimensions of 24 inches by 15 inches,
So each has an area of:
24 in × 15 in
= 360 in²
There are two of these faces, so their combined area is:
2 × 360 in²
= 720 in²
The front and back faces have dimensions of 24 inches by 3 inches,
So each has an area of:
24 in × 3 in
= 72 in²
There are two of these faces, so their combined area is:
2 × 72 in²
= 144 in²
The left and right faces have dimensions of 15 inches by 3 inches, so each has an area of:
15 in × 3 in
= 45 in²
There are two of these faces, so their combined area is:
2 × 45 in² = 90 in²
Adding up all the face areas gives:
720 + 144 + 90
= 954 in²
Therefore,
The surface area of the box is 954 in².
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PLEASE ANSWER!!!! QUICK!!!1
A pair of standard dice are rolled. Find the probability of rolling a sum of 3 these dice
P(D1 + D2 = 3) --
Be sure to reduce
Answer:
The sum of two dice can range from 2 to 12. To get a sum of 3, the only possible combinations are (1,2) and (2,1), since there is only one way to get each of those sums.
There are a total of 6 x 6 = 36 possible outcomes when two dice are rolled, since each die has 6 possible outcomes.
Therefore, the probability of rolling a sum of 3 is:
P(D1 + D2 = 3) = number of ways to get a sum of 3 / total number of possible outcomes
P(D1 + D2 = 3) = 2 / 36
Simplifying by dividing both the numerator and denominator by 2, we get:
P(D1 + D2 = 3) = 1 / 18
Therefore, the probability of rolling a sum of 3 with two standard dice is 1/18.
Step-by-step explanation:
in answer :)
Answer:
1/18
Step-by-step explanation:
got it right