Sure, I'd be happy to help you with that. Based on the information provided, we know that HA Leonardo received three books for his birthday and two of them cost a total of 760. To find out the cost of the third book, we need to subtract the cost of the two books from the total amount paid, which is 1125.
To do this, we can use a simple equation:
Total cost of three books - Total cost of two books = Cost of third book
So, we can plug in the values we know:
1125 - 760 = Cost of third book
Solving for the cost of the third book:
365 = Cost of third book
Therefore, the third book cost 365.
In summary, HA Leonardo received three books for his birthday and two of them cost 760. The total amount paid was 1125, so the cost of the third book was 365.
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find the surface area of the above solid a.81cm b.78cm c.84m d.72cm
In Exercises 7-9, solve the formula for the indica
7. Force: f = ma; Solve for m.
Answer:
F= ma is the formula of Newton’s Second Law of Motion.
Newton’s Second Law of Motion is defined as Force is equal to the rate of change of momentum. For a constant mass, force equals mass times acceleration.
a 1\$ lottery ticket has the following prizes: 10\$ cash for 3 people; 50\$ cash for 2 people ; 100\$ cash for 1 person. winners are chosen randomly. if 300 people bought this lottery, what is the expected profit of a random person?
If winners are chosen randomly from the 300 people who bought this lottery, the expected profit of a random person is $0.766..
Expected value or profit :The expected profit under a probability demand distribution is calculated by multiplying the profit amount by the probability of achieving that profit.
It is denoted as E(X) . We have given that,
A $1 lottery ticket has a number of prizes.
Probability of winning first prize , $10 = p₁ = 3/300 = 1/100
probability of winning a 2nd prize, $50
= p₂= 2/300= 1/150
probability of winning a 3rd prize, $100
= p₃ = 1/300 = 1/300
E = expectation value = ∑ Vᵢpᵢ where Vᵢ = value of prize, pᵢ = probability of winning prize,
E = $10 ×1/100 + $50×1/150 + $100×1/300
=> E = $10/100 + $50/150 + $100/300
Taking LCM as 300 on right hand side,
=> E =( $30+ $100+$100)/300
=> E = $(230/300) = $0.766
So, expected winnings for a person buying one ticket is $0.766..
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a basketball player hits three-point shots 41% of the time. if she takes 4 shots during a game, what is the probability that she hits all 4 shots?
The probability that the basketball player hits all 4 shots is approximately 0.0416 or 4.16%.
To determine the probability that a basketball player hits all 4 shots during a game, when the player hits three-point shots 41% of the time, we have to apply binomial probability distribution.
Let X be the number of successful shots when taking 4 shots, the probability of success in each trial, p = 0.41 and the number of trials, n = 4.
Therefore, we can use the binomial probability distribution as given below: `P(X = k) = (n choose k) × p^k × q^(n-k)
`Where q = 1 - p = 1 - 0.41 = 0.59 is the probability of failure.In this case, k = 4, and we can calculate P(X = 4) as follows:`P(X = 4) = (4 choose 4) × 0.41^4 × 0.59^(4-4)`= (1) × (0.41)^4 × (0.59)^0= 0.0416
Therefore, the probability that the basketball player hits all 4 shots is approximately 0.0416 or 4.16%.
Note: A probability is a number between 0 and 1, and it can be represented as a fraction, decimal or percentage. In this case, we have represented the answer in percentage format.
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Ut = 4uxx, 0 < x < 2,t > 0 u(0,t) = 1, u(2,t) = 2, u(x,0) = sin(17x) — 4 sin(Tt x/2) u = =
The solution of the given equation is\(u(x,t) = ∑(-1)n+1 4/(nπ) sin(nπ/4) sin(nπx / 2) exp(-n^2 π^2 t / 4)\)
The given equation is Ut = 4uxx, 0 < x < 2,t > 0u(0,t) = 1, u(2,t) = 2, u(x,0) = sin(17x) — 4 sin(Tt x/2)
The general form of the solution is given as:
\(u(x,t) = B0 + B1 x + ∑[Bn cos(nπx / L) + Cn sin(nπx / L)] exp(-n^2 π^2 t / L^2)\)
Where,\(Bn = (2/L) ∫f(x) cos(nπx / L) dx; from x = 0 to L . . . . . (1)\)
\(Cn = (2/L) ∫f(x) sin(nπx / L) dx; from x = 0 to L . . . . . (2)\)
\(L = 2Bn\)
First we need to find the values of B0 and B1.
Given initial conditions are\(u(x,0) = sin(17x) — 4 sin(Tt x/2)\)
We can write \(u(x,0) = B0 + B1 x + ∑[Bn cos(nπx / L) + Cn sin(nπx / L)]\)
From the given function, comparing the coefficients of the Fourier series, we have
\(B0 = 0, B1 = 0, Bn = (2/L) ∫f(x) cos(nπx / L) dx; from x = 0 to L = 0; for n = 1, 2, 3, .......\)
\(Cn = (2/L) ∫f(x) sin(nπx / L) dx; from x = 0 to L = (-1)n+1 4/(nπ)sin(nπ/4); for n = 1, 2, 3, .......L = 2.\)
Using the values of Bn and Cn, we can write the solution as \(u(x,t) = ∑(-1)n+1 4/(nπ) sin(nπ/4) sin(nπx / 2) exp(-n^2 π^2 t / 4)\)
Therefore, the solution of the given equation is\(u(x,t) = ∑(-1)n+1 4/(nπ) sin(nπ/4) sin(nπx / 2) exp(-n^2 π^2 t / 4)\)
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A) Addition
B) Subtraction
C) Multiplication
D) Exponent
3+16 divided by 4
4 x 7 - 2 x 6 divided by 3
5 (power of 2) - 4 x (2 power of 3) -3)
(-3 (power of 4) divided 9 x (4-5 (power of 3) + 8
Answer:
3+16 divided by 4 is 4.75
4×7-2×6..... is5.33
168
Rewrite the equation below so that it does not have fractions
2/3x-5=3/4
Answer:
Step-by-step explanation:
The best way to do this problem is to find the lowest common denominator.
2/3 : 3*2/(3*3)
3/4 : 3*3 / 3*4
Notice what you have done. You have multiplied both denominators by something that gets rid of the denominators, or will when you multiply by 4 * 3 = 12
So multiply the equation by 12
(2/3 x- 5 = 3/4 ) 12
8x - 60 = 9 Add 60 to both sides
8x - 60 = 9 Combine
8x = 69 Divide by 8
x = 69/8
x = 8 5/8
The polygons below are similar, find the value of x.
Answer:
x = 7
Step-by-step explanation:
Since, both the polygons are similar, therefore their corresponding sides would be in proportion.
\( \therefore \: \frac{30}{4 + 3x} = \frac{36}{30} \\ \\ \therefore \: \frac{30}{4 + 3x} = \frac{6}{5} \\ \\ 6(4 + 3x) = 30 \times 5 \\ \\ 24 + 18x = 150 \\ \\ 18x = 150 - 24 \\ \\ 18x = 126 \\ \\ x = \frac{126}{18} \\ \\ x = 7\)
Last week, Latoya drove 259 miles. This week, she drove k miles. Using k, write an expression for the total number of miles she drove in the two weeks.
Answer:
259+k=x
Step-by-step explanation:
x= total number of miles
The graph shows a proportional relationship between the number crates and the number of apples per crate.
What is the constant of proportionality in terms of the number of apples to the number of crates?
A. 30
B. 35
C. 40
D. 50
Answer:
its 40
Step-by-step explanation:
Answer:
b40
Step-by-step explanation:
it is 40 because on the graph it shows that you don't start at the first crate but the 2nd you do and you have to figure out if the crate was one how many apples would their be
please choose me as Brainliest
HURRY I NEED HELP
!!!
A line passes through (-1,7) and (2, 10). What is the equation of the line?
3x - y = -16
x - y = -8
x - y = -12
Зх — у = -4
Answer:
It is x - y = -8
Answer: the man who answered first is right its -x+y=8
Step-by-step explanation:
i took de test
Brainliest to right answer
Answer:
(-8) is the missing value here, so
the coordinates will be (-8,8)
Answer:
-8
Step-by-step explanation:
→ Substitute y = 8 into -4x - y = 24
-4x - 8 = 24
→ Add 8 to both sides to isolate -4x
-4x = 32
→ Divide both sides by -4 to isolate x
x = -8
For a standard normal distribution, a negative value of z indicates _____.
For a standard normal distribution, a negative value of z indicates that the observed value is below the mean of the distribution.
In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, a negative value of z indicates that the observed value is located below the mean. The z-score represents the number of standard deviations a data point is away from the mean.
A negative z-score means that the observed value is lower than the mean, indicating that it falls to the left of the center of the distribution. This means that the data point is relatively lower compared to the average and can provide information about its position within the distribution and its deviation from the mean.
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Feri invests some money.
The rate of interest for the first year is 2.5%.
At the end of the second year the overall percentage increase of Feri's investment is 6.6%.
Find the rate of interest for the second year.
The rate of interest for 2nd year is 4.1%
How to find the interest rate for the second yearFrom the given parameters;
Rate of interest for 1st year = 2.5
As we know the formula for Simple interest is given by
=> I = (PTR)/100
We will use this formula in the following problem
Let 100 be Feri's investment
At the Rate of interest of 2.5
Interest on 100 = [(100(1)(2.5)]/100 = 2.5
Total amount at end of 1st year = 100 + 2.5 = 102.5
Let x be the rate of interest for 2nd year
At the rate of interest of x
interest on 100 = [(100(1)(x)]/100 = x
Total amount at end of 2st year = 102.5 + x
Given that, at end of the 2 years, the rate of interest becomes 6.6%
Interest on 100 at the rate of 6.6%
=> [(100(1)(6.6)]/100 = 6.6
=> total amount = 100 + 6.6 = 106.6
As we know in both cases, the amount must be equal
=> 102.5 + x = 106.6
=> x = 4.1
Therefore, The rate of interest for 2nd year = 4.1
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we find t=2.73 with 5 degrees of freedom. what is the appropriate p-value.
The appropriate p-value for a t-value of 2.73 with 5 degrees of freedom is approximately 0.05. This indicates that there is a 5% chance of observing a t-value as extreme as 2.73 or more extreme, assuming the null hypothesis is true.
In statistics, the p-value measures the strength of evidence against the null hypothesis. The null hypothesis states that there is no significant difference or effect in the population being studied. The p-value is calculated by determining the probability of obtaining a test statistic (in this case, the t-value) as extreme as or more extreme than the observed value, assuming the null hypothesis is true.
To determine the appropriate p-value for a t-value, we typically consult a t-distribution table or use statistical software. In this case, with 5 degrees of freedom and a t-value of 2.73, we look up the critical value or use software to find the corresponding p-value. The p-value associated with a t-value of 2.73 and 5 degrees of freedom is approximately 0.05.
The p-value of 0.05 indicates that there is a 5% chance of obtaining a t-value as extreme as 2.73 or more extreme, assuming the null hypothesis is true. Generally, a p-value of 0.05 or lower is considered statistically significant, implying that the observed result is unlikely to have occurred by chance alone. If the p-value is below a predetermined significance level (often denoted as α, commonly set at 0.05), we reject the null hypothesis in favor of an alternative hypothesis. If the p-value is above the significance level, we fail to reject the null hypothesis.
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X+4=10
Solve this question???
Answer:
x+4=10
10-4=6
x=6
Step-by-step explanation:
subtract 4 from both sides
Answer:
x = 6
Step-by-step explanation:
Inverse operations
10 - 4 = x
10 - 4 = 6
x = 6
what's y and x pls I need answer
Answer:
1) x = 21deg, y = 146deg
2) x = 52deg, y = 128deg
3) x = 20deg, y=80deg (assuming we're computing angles of the kite, not of the triangles).
4). a = 116deg, c = 64deg
Step-by-step explanation:
Problem 1:
The kite is symmetrical, so y = 146deg.
we can compute x as 360deg - 146deg - 146deg - 47deg; because the sum of angles is 360deg in a quadrangle.
360deg - 146deg - 146deg - 47deg = 21deg
Problem 2:
y = 128deg; as it's symmetrical
x = 180deg - y = 52deg
Problem 3:
The smallest triangle has angles y/2, 50deg and 90deg, so
y/2 = 180deg - 90deg - 50deg = 40deg
y = 80deg (this assumes y is the angle of the kite, not half).
Similarily,
x/2 = 180deg - 80deg - 90deg = 10deg
x = 20deg (again, assuming x is the angle of the kite, not half).
Problem 4:
a = 116deg
c = 180deg - 116deg = 64deg (see problem 2).
PLS HELP ME FAST I NEED THE ANSWER IN THE NEXT FIVE MINUTES
Answer: The answer to that would be -17/6.
Step-by-step explanation: I literately just did this problem I think. I also have a fractions calculator.
Anyway I hope this helps!!!!!!!!!!
Answer:
- 17/6
Step-by-step explanation:
1/2 + 2/3b when b=-5
The first thing you need to do is replace the variable b with -5:
\(\frac{1}{2} +\frac{2}{3} (-5)\)
Now solve:
\(\frac{1}{2} +\frac{2}{3} (-5)= -\frac{17}{6}\)
a sample is obtained from a population by grouping people according to age and then randomly selecting 5 people from each group. what type of sampling technique is this?
The type of sampling technique described is stratified random sampling.
In stratified random sampling, the population is first divided into homogeneous subgroups or strata based on some criteria, such as age, gender, income, or education level. In this case, the population was grouped according to age. Then, a random sample is selected from each stratum.
By doing so, the sample represents the entire population better than simple random sampling, as each subgroup is represented proportionally to its size in the population. This technique ensures that there is less variation within each subgroup, which can result in more precise estimates of the population parameters.
In summary, stratified random sampling is a type of probability sampling technique where the population is divided into subgroups, and a random sample is selected from each subgroup.
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What is the slope the line that passes through the points:
(-6, 14), (2, -18)
O-
4
О O
1
4
4.
-4
(-6, 14) and (2, -18)
To Find:The slope of the line that passes through the point.
Slope Formula:y2 - y1 / x2 - x1
Solution:-18 - 14 / 2 + 6
= -32 / 8
= -4
Answer:Option D. -4
A tank contains 50 liters of oil at time t = 4 hours. Oil is being pumped into the tank at a rate R(t) where R(t) is measured in liters per hour, and t is measured in hours. Selected values of R(t) are given in the table above. Using a right Riemann sum with three subintervals and data from the table, what is the approximation of the number of liters of oil that are in the tank at time t = 15 hours?
The volume of oil inside the tank at \(t = 15\,h\) is approximately 66.556 liters.
How to estimate volume capacity by Riemann sumIn this question we must estimate the volume by Riemann sum, which consist in sum of all areas of the trapezoids of equal width in the volume rate versus time graph. The right Riemann sum with three intervals for this case is described below:
\(Q = \Sigma \limits_{i=0}^{2} \left\{R_{i}+\frac{1}{2}\cdot [R_{i+1}-R_{i}] \right\}\cdot \Delta t\)
\(Q = \left[6.5+\frac{1}{2}\cdot (6.2-6.5) \right]\cdot (3.667)+\left[6.2+\frac{1}{2}\cdot (5.9-6.2)\right]\cdot (3.667) +\left[5.9+\frac{1}{2}\cdot (5.6-5.9) \right]\cdot (3.667)\)
\(Q \approx 66.556\,L\)
The volume of oil inside the tank at \(t = 15\,h\) is approximately 66.556 liters. \(\blacksquare\)
Remark
The table of the volume rate versus time is missing, all missing values of the table are included below:
\(R(4) = 6.5\,\frac{L}{h}\), \(R(7.667) = 6.2\,\frac{L}{h}\), \(R(11.333) = 5.9\,\frac{L}{h}\), \(R(15) = 5.6\,\frac{L}{h}\)
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Read the case study on page 326~327 of your textbook. Using the information and data provided in the text answer the following questions:
1. What changes or patterns do you see in the data? What remedies might be suggested for any problems?
2. Has the CEO carried out his or her responsibility for educating the board? Why or why not?
3. Depending on the answer to question 2, what strategies would you recommend at this point?
4. What quality data should be reported and utilized by this board of directors?
5. Given this administration’s style and leadership approach, do you think the minutes of the board meeting reflect actual board meeting discussions?
6. Is the board actually using the information provided to make decisions that affect quality and performance improvement?
1. If any problems are identified, suggest potential remedies such as process improvements, employee training, quality control measures, or changes in strategy.
2. Consider whether the CEO has effectively communicated the company's goals, performance metrics, challenges, and strategies to the board.
3. If the CEO has fulfilled their responsibility, focus on refining the communication process and ensuring that the board receives timely and relevant information.
4. Emphasize the importance of accurate, timely, and actionable data that enables the board to make informed decisions.
5. Consider whether the minutes provide a clear and objective summary of the discussions and whether they align with the organization's leadership style and approach.
6. Evaluate whether the board's decisions and initiatives align with the organization's goals and objectives for quality and performance improvement.
To identify changes or patterns in the data, carefully analyze the provided data in the case study. Look for trends, variations, or any significant shifts in the data over time. Consider factors such as growth rates, financial performance, customer satisfaction ratings, employee turnover, or any other relevant metrics. If any problems are identified, suggest potential remedies such as process improvements, employee training, quality control measures, or changes in strategy.
Assess whether the CEO has fulfilled their responsibility for educating the board by evaluating the level of knowledge and understanding demonstrated by the board members. Determine if the board members have been provided with sufficient information and resources to make informed decisions. Consider whether the CEO has effectively communicated the company's goals, performance metrics, challenges, and strategies to the board.
Based on the assessment in question 2, recommend appropriate strategies. If the CEO has not adequately educated the board, suggest initiatives such as regular training sessions, workshops, or providing comprehensive reports to enhance their understanding of the business. If the CEO has fulfilled their responsibility, focus on refining the communication process and ensuring that the board receives timely and relevant information.
Determine the key quality-related data that should be reported and utilized by the board of directors. This may include data on customer satisfaction, product quality metrics, employee engagement and satisfaction, financial performance indicators, market share, or any other relevant measures that align with the organization's goals and objectives. Emphasize the importance of accurate, timely, and actionable data that enables the board to make informed decisions.
Evaluate the minutes of the board meetings to assess if they accurately reflect the discussions held during the meetings. Look for comprehensive records of agenda items, decisions made, action items assigned, and any important points or concerns raised by board members. Consider whether the minutes provide a clear and objective summary of the discussions and whether they align with the organization's leadership style and approach.
Assess whether the board is utilizing the information provided to make decisions that impact quality and performance improvement. Look for evidence of the board actively discussing and considering the quality-related data, asking relevant questions, and taking actions based on the information. Evaluate whether the board's decisions and initiatives align with the organization's goals and objectives for quality and performance improvement.
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Problem Description: An example of arithmetic progression would be a series of integers (which we will call terms) like: 3, 7, 11, 15, 19, 23, 27, 31, ... Note that 3 is the first term, 7 is the second term, 11 is the 3rd term, etc. 4 is the common difference between any two consecutive terms. Now, if we know that the progression has 100 terms, we would be interested in calculating the 100th term as well as the sum and the float average of all 100 terms. The following formulas can be used to calculate these items: LastTerm = FirstTerm + (NumberOfTerms - 1) x CommonDifference Sum of all terms = NumberOfTerms x (FirstTerm + LastTerm) / 2 Average of all terms = (Sum of all terms) / NumberOf Terms The program should adhere to the following pseudocode: 1. Prompt for and read the first term 2. 3. Prompt for and read the common difference Prompt for and read the number of terms Calculate the last term (see formula above) 4. 5. Calculate the sum of all the terms (see formula above) Calculate the average of all the terms (see formula above) 7. Display the results 6. Your program must match the following sample run (between the lines of dashes). Note that the 3, 3, and 100 on the first three lines were entered by the user. You should also check results for other set of inputs as well. Enter first term: 3 Enter common difference: 3 Enter number of terms: 100 The last term is 300 The sum of all the terms is 15150 The average of all the terms is 151.5
The last term is 300
The sum of all the terms is 15150.0
The average of all the terms is 151.5
Here is an example solution in Python that follows the given pseudocode:
# Prompt for and read the first term
first_term = int(input("Enter first term: "))
# Prompt for and read the common difference
common_difference = int(input("Enter common difference: "))
# Prompt for and read the number of terms
number_of_terms = int(input("Enter number of terms: "))
# Calculate the last term
last_term = first_term + (number_of_terms - 1) * common_difference
# Calculate the sum of all the terms
sum_of_terms = number_of_terms * (first_term + last_term) / 2
# Calculate the average of all the terms
average_of_terms = sum_of_terms / number_of_terms
# Display the results
print("The last term is", last_term)
print("The sum of all the terms is", sum_of_terms)
print("The average of all the terms is", average_of_terms)
If you run this code and enter the values from the sample run (first term: 3, common difference: 3, number of terms: 100), it will produce the following output:
The last term is 300
The sum of all the terms is 15150.0
The average of all the terms is 151.5
The program prompts the user for the first term, common difference, and number of terms. Then it calculates the last term using the given formula. Next, it calculates the sum of all the terms and the average of all the terms using the provided formulas. Finally, it displays the calculated results.
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Can you guys help me with this I have to turn it in a few
Answer:
x=126
Step-by-step explanation:
HELPPP SOLVE THIS PLEASE ALL OF IT
Answer:
f = 3
g = -1
h = 6
r = 18
Step-by-step explanation:
Box 1
f(x) = \(2x^{4}\)-\(12x^{3}\)+\(16x^{2}\)+4x+15 with x = 3
f(3) = \(2(3^{4)}\) - \(12(3^{3} )\) + \(16(3^{2})\)+ 4(3) + 15
Reorder
Evaluate
Multiply
3f = 2 x 81 - 12 + 27 +16 x 9 + 12 +15
3f = 162 - 324 + 144 + 12 + 15
3f = 9
3 ÷ 3
f = 3
Box 1
g(x) = \(3x^{3}\) - \(16x^{2}\) - 7x - 36 with x = 6
g(6) = \(3(6^{3} )\) - \(16(6^{2})\) - 7(6) - 36
g6 = 3 x 216 - 576 - 42 - 36
g6 = -6
6 ÷ 6
g = -1
Box 2
h(x) = \(5x^{3}\) - \(2x^{2}\) - 3 with x = -1
h(-1) = \(5(-1^{3} )\) - \(2(-1^{2})\) -3
h-1 = -5 + 2 -3
h-1 = -6
-1 ÷ - 1
h = -6
Box 2
r(x) = \(4x^{4}\) - \(9x^{2}\) + 5x - 2 with x = 2
r(2) = \(4(2^{4} )\) - \(9(2^{2} )\) + 5(2) - 2
r2 = 64 - 36 + 10 - 2
r2 = 36
2 ÷ 2
r = 18
The graph represents the purchasing power of your
income if the inflation rate is eight percent.
What is your current monthly income, if your
purchasing power is $2,300?
Your current monthly income, before the effect of inflation, is approximately $2,129.63.
To determine your current monthly income, we need to account for the effect of inflation on the purchasing power of your income. Given that the inflation rate is eight percent, we can calculate the original income before the inflation adjustment.
Let's denote your current monthly income as "X."
The purchasing power after accounting for eight percent inflation is $2,300. This means that your original income, before the inflation adjustment, would have had a higher value. We need to find this original income.
Inflation reduces the purchasing power of your income, so we need to increase the current purchasing power by the inflation rate to find the original income. In this case, we'll increase $2,300 by eight percent:
Original Income = $2,300 / (1 + 0.08)
Original Income = $2,300 / 1.08
Original Income ≈ $2,129.63
Therefore, your current monthly income, before the effect of inflation, is approximately $2,129.63.
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Which statements are true regarding the transformation? Select three options. The rule for the transformation is (x, y) → (–x, –y). The coordinates of L' are (–2,–2). The coordinates of M' are (–4,4). The coordinates of N' are (6,–1). The coordinates of N' are (–1,–6).
Answer: A, B, and E
Step-by-step explanation:
On edgenuity
Answer:
A B and E is correct on edge 2021
Step-by-step explanation:
trust me i got it correct on edge
the number of points held by a sample of the nhl's highest scorers for both the eastern conference and the western conference is shown below. at , can it be concluded that there is a difference in means based on these data? assume the variables are normally distributed and the variances are unequal.
If the null hypothesis is rejected, then you can conclude that there is a difference in means based on the provided data. If not, then there isn't enough evidence to support a difference in means.
if there is a difference in means between the number of points held by a sample of NHL's highest scorers in the Eastern and Western conferences. To answer this, you'll need to follow these steps:
1. Identify the data: You need to have the points data for the NHL's highest scorers from both the Eastern and Western conferences.
2. Calculate the means: Calculate the average number of points for both conferences' samples.
3. Determine the variables: Since you've mentioned that the variables are normally distributed and have unequal variances, we can use the independent two-sample t-test with unequal variances (Welch's t-test) to determine if there is a significant difference in means.
4. Perform Welch's t-test: Using the means, variances, and sample sizes of both groups, calculate the t-value and degrees of freedom.
5. Compare the t-value to the critical t-value: Determine the critical t-value at a specified significance level (commonly α = 0.05) using the degrees of freedom. If the calculated t-value is greater than the critical t-value, you can reject the null hypothesis and conclude that there is a significant difference in means.
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Write the function g(x) as a transformation of the parent function
f(3) = |sc|, where the graph has been vertically compressed by a factor of
ş, shifted right 2 units, and shifted up 10 units.
A g(x) = 12 +2] +10
B g(x) = {\2 + 101 – 2
C g(x) = - +2] + 10
D g(x) = 42-2/+10
The only information you have about a certain function f[x] is:
-1 ≤ f[x] ≤ 1
for all the x's between -[infinity] and [infinity].
Is it possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity]?
Why?
Yes, it is possible for a plot of a partial expansion of f[x] to share ink with the plot of f[x] all the way from -[infinity] to + [infinity].
Explanation:
We can approximate f(x) as a Fourier series, as follows:
\($$f(x) = \sum_{n=0}^{\infty}a_n\cos\left(\frac{n\pi x}{L}\right)+\sum_{n=1}^{\infty}b_n\sin\left(\frac{n\pi x}{L}\right)$$\)
If f(x) is an odd function, the cosine terms are gone, and if f(x) is an even function, the sine terms are gone.
We can create an approximation for f(x) using only the first n terms of the Fourier series, as follows:
\($$f_n(x) = a_0 + \sum_{n=1}^{n}\left[a_n\cos\left(\frac{n\pi x}{L}\right)+b_n\sin\left(\frac{n\pi x}{L}\right)\right]$$\)
For any continuous function f(x), the Fourier series converges uniformly to f(x) on any finite interval, as given by the Weierstrass approximation theorem.
However, if f(x) is discontinuous, the Fourier series approximation does not converge uniformly.
Instead, it converges in the mean sense or the L2 sense. The L2 norm is defined as follows:
\($$\|f\|^2 = \int_{-L}^{L} |f(x)|^2 dx$$\)
Hence, it is possible for a plot of a partial expansion of f(x) to share ink with the plot of f(x) all the way from -[infinity] to + [infinity].
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