The approximation of the integral ∫cos(x³ - 5) dx using composite Simpson's rule with n = 3 is approximately 1.01259.
The integral ∫cos(x³ - 5) dx using composite Simpson's rule with n = 3, we need to divide the integration interval into smaller subintervals and apply Simpson's rule to each subinterval.
The formula for composite Simpson's rule is
I ≈ (h/3) × [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + ... + 2f([tex]x_{n-2}[/tex]) + 4f([tex]x_{n-1}[/tex]) + f([tex]x_{n}[/tex])]
where h is the step size, n is the number of subintervals, and f([tex]x_{i}[/tex]) represents the function value at each subinterval.
In this case, n = 3, so we will have 4 equally-sized subintervals.
Let's assume the lower limit of integration is a and the upper limit is b. We can calculate the step size h as (b - a)/n.
Since the limits of integration are not provided, let's assume a = 0 and b = 1 for simplicity.
Using the formula for composite Simpson's rule, the approximation becomes:
I ≈ (h/3) [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + f(x₄)]
For n = 3, we have four equally spaced subintervals:
x₀ = 0, x₁ = h, x₂ = 2h, x₃ = 3h, x₄ = 4h
Using these values, the approximation becomes:
I ≈ (h/3) × [f(0) + 4f(h) + 2f(2h) + 4f(3h) + f(4h)]
Substituting the function f(x) = cos(x³ - 5):
I ≈ (h/3) [cos((0)³ - 5) + 4cos((h)³ - 5) + 2cos((2h)³ - 5) + 4cos((3h)³ - 5) + cos((4h)³ - 5)]
Now, we need to calculate the step size h and substitute it into the above expression to find the approximation. Since we assumed a = 0 and b = 1, the interval width is 1.
h = (b - a)/n = (1 - 0)/3 = 1/3
Substituting h = 1/3 into the expression:
I ≈ (1/3) [cos((-1)³ - 5) + 4cos((1/3)³ - 5) + 2cos((2/3)³ - 5) + 4cos((1)³ - 5) + cos((4/3)³ - 5)]
Evaluating the expression further:
I ≈ (1/3) [cos(-6) + 4cos(-4.96296) + 2cos(-4.11111) + 4cos(-4) + cos(-3.7037)]
Approximating the values using a calculator, we get:
I ≈ 1.01259
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The Σx = 68, y = 79, xy = 1200 x² = 600 and N = 12 determine the equation of the least square line. Leave answer in 2 decimal places.
To determine the equation of the least squares line, we need to find the slope (m) and the y-intercept (b) using the given data. The formula for the least squares line is:
y = mx + b
where:
m is the slope of the line
b is the y-intercept of the line
We can use the following formulas to calculate the slope and y-intercept:
m = (NΣxy - ΣxΣy) / (NΣx² - (Σx)²)
b = (Σy - mΣx) / N
Given the values:
Σx = 68
Σy = 79
Σxy = 1200
Σx² = 600
N = 12
Let's substitute these values into the formulas:
m = (12 * 1200 - 68 * 79) / (12 * 600 - (68)²)
b = (79 - m * 68) / 12
Calculating the values:
m = (14400 - 5372) / (7200 - 4624)
m = 9028 / 2576
m ≈ 3.5039
b = (79 - 3.5039 * 68) / 12
b = (79 - 238.2752) / 12
b ≈ -13.2738
Therefore, the equation of the least squares line is:
y ≈ 3.5039x - 13.2738
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The equation of the least squares line is y = 1.25x + 10.75
To determine the equation of the least squares line, we need to find the slope (b) and y-intercept (a) using the following formulas:
b = (NΣxy - ΣxΣy) / (NΣx² - (Σx)²)
a = (Σy - bΣx) / N
Given the following values:
Σx = 68
Σy = 79
Σxy = 1200
Σx² = 600
N = 12
Let's calculate the slope (b) first:
b = (12 × 1200 - 68×79) / (12×600 - 68²)
b ≈ 1.25
Now we can calculate the y-intercept (a):
a = (79 - 1.25×68) / 12
a = 10.75
Therefore, the equation of the least squares line is: y = 1.25x + 10.75.
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Saul's Corner Market sells large candy bars for $2 each. A bag of pretzels is $3. On Tuesday, the store sold twice
as many candy bars as Monday but the same number of pretzels. On Wednesday, the store sold the same
number of candy bars as Monday but only half the amount of pretzels. On Thursday, the store sold three times
as much as they sold on Tuesday. On Friday, the store sold 12 fewer candy bars and 5 more bags of pretzels
compared to Wednesday.
Let c represent the number of candy bars sold and p represent the number of pretzels sold on Monday. Write
an expression for each day to show the amount of money that the store brought in from candy bars and
pretzels.
1. Monday
2. Tuesday
3. Wednesday
4. Thursday
5. Friday
6. Monday through Friday
Answer:
Step-by-step explanation:
Monday: c and p
Tuesday: 2c+p
Wednesday: 2c+p/2
Thursday: 6c+3p/2
Friday: (2c-12)+(p/2+5)
Adding them all up, you get, for Monday-Friday: (13c-12)+(9p/2+5)
I'm not sure how to explain this to you though, you just follow the directions they gave, to multiply and subtract.
Hope this is helpful!
Please help me it’s due today
Need help solving this problem.
Answer:
The measure of angle CDE is 37 degrees
Step-by-step explanation:
The following data are cost (in cents) per ounce for nine different brands of sliced Swiss cheese (www .consumerreports.org):
29 62 37 41 70 82 47 52 49
a. Compute the variance and standard deviation for this data set. s2 = 279.111; s = 16.707
b. If a very expensive cheese with a cost per slice of 150 cents was added to the data set, how would the values of the mean and standard deviation change?
a. The variance of the data set is 279.111 and the standard deviation is 16.707.
b. Adding an expensive cheese increases the mean to 55.9 and the standard deviation to 48.53.
a. To compute the variance and standard deviation for the given data set, we can use the following formulas:
Variance (s²) = [(Σx²) - (Σx)² / n] - 1
Standard Deviation (s) = √(Variance)
Using the given data set: 29, 62, 37, 41, 70, 82, 47, 52, 49
Step 1: Calculate the mean (x) of the data set.
Mean (x) = (Σx) / n
Σx = 29 + 62 + 37 + 41 + 70 + 82 + 47 + 52 + 49 = 409
n = 9 (number of data points)
Mean (x) = 409 / 9 = 45.44 (rounded to two decimal places)
Step 2: Calculate the sum of squares (Σx²) for the data set.
Σx² = 29² + 62² + 37² + 41² + 70² + 82² + 47² + 52² + 49² = 151509
Step 3: Substitute the values into the variance formula and calculate the variance.
Variance (s²) = [(Σx²) - (Σx)² / n] - 1
Variance (s²) = (151509 - (409)² / 9) / (9 - 1) = 279.111 (rounded to three decimal places)
Step 4: Calculate the standard deviation by taking the square root of the variance.
Standard Deviation (s) = √(Variance)
Standard Deviation (s) = √279.111 = 16.707 (rounded to three decimal places)
b. If a very expensive cheese with a cost per slice of 150 cents was added to the data set, the values of the mean and standard deviation would change. To find the new mean and standard deviation, we need to incorporate the additional data point and recalculate.
New Σx = Σx + 150 = 409 + 150 = 559 (updated sum of the data points)
New n = n + 1 = 9 + 1 = 10 (updated number of data points)
New Mean (x) = New Σx / New n = 559 / 10 = 55.9 (rounded to one decimal place)
The addition of the expensive cheese increased the mean.
To calculate the new variance and standard deviation, we follow the same steps as in part a using the updated Σx and n values:
New Σx² = Σx² + (150)² = 151509 + 22500 = 174009
New Variance (s²) = [(New Σx²) - (New Σx)² / New n] - 1 = (174009 - (559)² / 10) / (10 - 1) = 2355 (rounded to three decimal places)
New Standard Deviation (s) = √New Variance = √2355 = 48.53 (rounded to two decimal places)
Therefore, the addition of the expensive cheese increased both the mean and the standard deviation of the data set.
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PLZZZZZ HELP ASAP!
Jake has $5,625 in his savings account. Each month he makes a car payment from his savings account without making additional deposits.
Which table shows the amount of money in Jake's savings account after each month if it is a linear relationship?
Help is much needed. You will get lots of point too!
AH PLEASE SOMEONE HELP
Answer:
Variant b
Step-by-step explanation:
If you multiply it should be a+b but if you divided
A+b-c
Find the values of the sine, cosine, and tangent for angle a
[tex]sina=\frac{2\sqrt{13} }{13} \\cosa=\frac{3\sqrt{13} }{13}\\tana=\frac{2}{3}[/tex]
Answer:
A.
Step-by-step explanation:
correct on edge2021
Question is in picture
Answer:
27.5ft
Step-by-step explanation:
a² + b² = c²
Plug in what you have:
a² + 12² = 30²
Get a by itself:
a² = 30² - 12²
Simplify:
a² = 900 - 144
Simplify:
a² = 756
Simplify:
√a = √756
Then you get 27.49 and when you round you get 27.5
A soccer ball has an interior
diameter of 22cm. How
many cubic centimeters of air
does a soccer ball contain,
rounded to the nearest
hundredth?
Answer:
5575 cm³
Step-by-step explanation:
The volume of a sphere is V = (4/3)πr³. If we substitute r = (d/2 where r is the radius and d the diameter), this formula becomes:
πd³
V = (4/3)π·d³/8, or V = -------------
6
and so, if d = 22 cm, the volume is:
π(22 cm)³
V = ------------------- = 5575 cm³
6
A school janitor has mopped 1/3 of a classroom in 5 minutes. At what rate is he mopping?
simplify your answer and write it as a proper fraction, mixed number, or whole numer.
___ classrooms per minute
Given,A school janitor has mopped 1/3 of a classroom in 5 minutes.We have to find the rate at which he is mopping.Using the concept of unitary method,Rate of mopping 1 classroom in 5 × 3 = 15 minutes= 1/15 of a classroom in 1 minute.Rate of mopping 1/3 classroom in 5 minutes = (1/3) ÷ 5= 1/15 classroom per minuteHence, the required rate at which he is mopping is 1/15 classroom per minute.
Answer: 1/15.
To determine the rate at which the janitor is mopping, we can calculate the fraction of the classroom mopped per minute.
Given that the janitor mopped 1/3 of the classroom in 5 minutes, we can express this as:
(1/3) classroom / 5 minutes
To simplify this fraction, we divide the numerator and denominator by the greatest common divisor, which is 1:
(1/3) classroom / (5/1) minutes = (1/3) classroom × (1/5) minutes
Multiplying the numerators and the denominators gives us:
1 classroom × 1 minute / 3 × 5
Simplifying further:
1 classroom × 1 minute / 15
Therefore, the rate at which the janitor is mopping is 1/15 classrooms per minute.
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The given information is that the janitor mopped 1/3 of a classroom in 5 minutes. We have to find out at what rate is he mopping.
The rate of mopping is 1/15 classrooms per minute.
Let's try to solve the problem below. The given fraction is 1/3 of a classroom that was mopped in 5 minutes. We need to find the rate of mopping which can be calculated by dividing the fraction of the classroom mopped by the time it took to mop it. The rate of mopping can be found by performing the following calculation:
Rate of mopping = Fraction of the classroom mopped/Time taken to mop
= 1/3/5
= 1/15
So the rate of mopping is 1/15 classrooms per minute. This is the simplified answer.
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If you roll a six sided die, what is the probability that you do not roll a one or two?
Answer:
66.6%
Step-by-step explanation:
You have a 1/6 chance to roll any number. That is a 16.6% chance per number.
So, that means you have a 4/6 (2/3 simplified) probability of not rolling a one or two. That is a 66.6% chance.
[NOTE: The '6' at the end of '16.6%' and '66.6%' is a repeating decimal]
Given some scores on an entrance exam, which are roughly normally distributed, we are told they have a mean of 82 and a standard deviation (std dev) of 5. If some student received a 90 on the exam, what would there z-score be calculated as?
The z-score for a student who received a score of 90 on the entrance exam is 1.6.
What is the formula for calculating the area of a triangle?The z-score for a student who received a score of 90 on the entrance exam, with a mean of 82 and a standard deviation of 5, can be calculated as follows:
z = (x - μ) / σx is the student's score (90 in this case)μ is the mean (82)σ is the standard deviation (5)Plugging in the values:
z = (90 - 82) / 5Simplifying:
z = 8 / 5Calculating:
z = 1.6Therefore, the z-score for the student who received a score of 90 on the exam is 1.6.
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Write 9020000 in standard form?
Answer:
9.02 x 10^6
Step-by-step explanation:
hope this helps!
Ared candle is 8 inches tall and burns at a rate of inch per hour. 1 A blue candle is 6 inches tall and burns at a rate of inch per hour. 5 After how many hours will both candles be the same height? Enter your answer in the box.
Answer:
After 8 hrs both candles would've burned out completely, so they'll, more or less, be at the same height.
A survey of 150 college students was done to find out what elective course they were taking Lot A the set of those taking ort, B the set of those taking basketweaving, and C - the set of those taking canoeing. The study revealed the following information A-45 IAN B = 12 181 55 ANC-15 C-40 BC-2 Anno 2 How many students were not taking any of these electives?
A survey of 150 college students was done to find out what elective course they were taking Lot A the set of those taking ort, B the set of those taking basketweaving, and C - the set of those taking canoeing. The study revealed the following information A-45 IAN B = 12 181 55 ANC-15 C-40 BC-2 Anno 2
Based on the given information, we can calculate the number of students who were not taking any of the elective courses.
Let's break down the information provided:
A: The set of students taking Art elective = 45
B: The set of students taking Basket weaving elective = 12
C: The set of students taking Canoeing elective = 40
A ∩ B: The set of students taking both Art and Basket weaving electives = 2
A ∩ C: The set of students taking both Art and Canoeing electives = 15
B ∩ C: The set of students taking both Basket weaving and Canoeing electives = 0 (not specified)
A ∩ B ∩ C: The set of students taking all three electives = 2
To find the number of students who were not taking any of these electives, we need to subtract the total number of students taking at least one elective from the total number of students surveyed.
Total students surveyed = 150
Students taking at least one elective = A ∪ B ∪ C
Students taking at least one elective = A + B + C - (A ∩ B) - (A ∩ C) - (B ∩ C) + (A ∩ B ∩ C)
Students taking at least one elective = 45 + 12 + 40 - 2 - 15 - 0 + 2
Students taking at least one elective = 82
Students not taking any of these electives = Total students surveyed - Students taking at least one elective
Students not taking any of these electives = 150 - 82
Students not taking any of these electives = 68
Therefore, there were 68 students who were not taking any of the elective courses using set theory.
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Help please
Mark True or False in the table on your answer document to indicate whether
each comparison is true
Answer:
1. false
2. false
3. true
Step-by-step explanation:
If p is prime, then there exists a field of order p². O True False
The statement "If p is prime, then there exists a field of order p²" is true. For any prime number p, there exists a finite field of order p².
Is it true that if p is prime, there exists a field of order p²?Yes, it is true that if p is a prime number, then there exists a field of order p². In mathematics, a field is a specific type of algebraic structure with two operations, addition and multiplication, that satisfy certain properties. The order of a field refers to the number of elements in the field. For any prime number p, there exists a unique finite field of order p², often denoted as GF(p²) or Fp². This field consists of p² elements and is crucial in various areas of mathematics, such as number theory, cryptography, and coding theory.
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Find the value of each trigonometric ratio. Express your answer as a fraction in lowest terms .
Answer:
The answers are in the attachment above
good day mate
Angle ∠B is a right-angle then the measure of angle ∠A is 43.6 degrees and the measure of angle ∠C is 46.4 degrees.
What is a right-angle triangle?It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function. The Pythagoras is the sum of the square of two sides is equal to the square of the longest side.
The triangle ΔABC is given.
The angle ∠B is a 90°.
Then the value of the angle ∠C will be
[tex]\rm C = \sin ^{-1} \dfrac{21}{29}\\\\C = 46.40^o[/tex]
Then the value of the angle ∠A will be
∠A + ∠C = 90°
∠A + 46.40° = 90°
∠A = 43.6°
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PLSSS HELP IMMEDIATELY!!!! i’ll give brainiest, if u don’t provide just a link! answer choices: (4,6) , (0,1) , (0,0) , (5,4)
Answer:
try (4,5)
Step-by-step explanation:
that is where the points meet I think it is that I am not sure sorry if it is wrong
Shania is making lasagna. The recipe she uses calls for 2 1/3 cups of spaghetti sauce. If she doubles the recipe, how much spaghetti sauce will she need?
Answer:
4 2/3 cups
Step-by-step explanation:
f(x) = 2x+10. If f(x)= -2, find x.
Answer:
x=-5
Step-by-step explanation:
Graph each set of numbers on the number line and order the numbers from greatest to least 0.5, -1, -1/4, 0
Answer:
0.5, 0, -1/4, -1
3.1. Two friends. Ben and Mike, take part in a 15km fun
run. Ben took 1 h 23 min 12 sec and Mike took 1 h 39
min 4 sec. How long did Ben wait at the finish line for
Mike?
Answer: 15.867 min
Step-by-step explanation:
Given
Ben took [tex]1\ h\ \text{and}\ 23\ min\ 12\ s[/tex] to complete 15 km
While Mike take [tex]1\ hr\ 39\ min\ 4\ s[/tex] to complete the same
converting time into miniutes
Ben time
[tex]\Rightarrow 60+23+\frac{12}{60}=83.2\ min[/tex]
Mike time
[tex]\Rightarrow 60+39+\frac{4}{60}=99.0667\ min[/tex]
So, mike waited for
[tex]\Rightarrow 99.067-83.2=15.867\ min[/tex]
The following contingency table gives the results of a sample survey of South African male and female respondents with regard to their preferred fastfood outlet: PREFERRED FAST FOOD OUTLET Burger King McDonalds TOTAL 50 No. of Males No. of Females 20 130 100 120 TOTAL 270 150 110 140 400 0.1.1.1 What is the probablyf randomly selecting a respondent who is male and prefer Burger 01.12 What is the probably selecting a female respondent, even that the preferred fastfood out? 0.1.1.3 What is the probability of selecting a respondent who is female or who prefers McDonalds? 12) (2) Events X and Yare such that PC) = 0.20 and PCXUY) = 0.55. Given that Xand Yare independent and non-mutually taclusive, determine P(Y). Give your final answer as a percentage to two decimal places (5) 13 (2) 2.1.3.1 Helen is the manager of a Finance Department. She has fifteen (15) members of stuff working for her. She has to choose five (5) members of her staff for a research team. How many different teams can she select from the fifteen members of staff 2.1.22 There are twelve (12) teams in a basketball league. What is the probability of correctly predicting the top three teams at the end of the 3) season in the correct order?
Q1.1.1 The probability of randomly selecting a male respondent from the sample is 0.4. Q.1.1.2 The probability of randomly selecting a respondent who is female and prefers HP is 0.275. Q.1.1.3 The probability of selecting a male respondent, given that the preferred brand is Lenovo is 0.4545. Q.1.1.4 The probability of selecting a respondent who is male or who prefers HP is 0.575. Q.1.1.5 The probability of selecting a respondent who does not prefer Lenovo is 0.725.
Q.1.1.1 What is the probability of randomly selecting a male respondent from the sample?
The probability of randomly selecting a male respondent is given by the number of male respondents divided by the total number of respondents:
Probability = No. of Males / Total = 160 / 400 = 0.4
Q.1.1.2 What is the probability of randomly selecting a respondent who is female and prefers HP?
The probability of randomly selecting a respondent who is female and prefers HP is given by the number of females who prefer HP divided by the total number of respondents:
Probability = No. of Females who prefer HP / Total = 110 / 400 = 0.275
Q.1.1.3 What is the probability of selecting a male respondent, given that the preferred brand is Lenovo?
The probability of selecting a male respondent, given that the preferred brand is Lenovo, is given by the number of males who prefer Lenovo divided by the total number of respondents who prefer Lenovo:
Probability = No. of Males who prefer Lenovo / Total No. of respondents who prefer Lenovo = 50 / 110 = 0.4545
Q.1.1.4 What is the probability of selecting a respondent who is male or who prefers HP?
The probability of selecting a respondent who is male or who prefers HP is given by the sum of the probabilities of selecting a male respondent and selecting a respondent who prefers HP, minus the probability of selecting both (to avoid double counting):
Probability = (No. of Males / Total) + (No. of Females who prefer HP / Total) - (No. of Males who prefer HP / Total)
Probability = (160 / 400) + (110 / 400) - (40 / 400) = 0.4 + 0.275 - 0.1 = 0.575
Q.1.1.5 What is the probability of selecting a respondent who does not prefer Lenovo?
The probability of selecting a respondent who does not prefer Lenovo is given by the number of respondents who do not prefer Lenovo divided by the total number of respondents:
Probability = (Total - No. of respondents who prefer Lenovo) / Total
Probability = (400 - 110) / 400 = 290 / 400 = 0.725
The complete question is:
The following contingency table gives the results of a sample survey of South African male and female respondents with regard to their preferred brand of notebook:
HP Lenovo Dell Total
No. of Females 110 60 70 240
No. of Males 40 50 70 160
Total 150 110 140 400
Q.1.1.1 What is the probability of randomly selecting a male respondent from the sample?
Q.1.1.2 What is the probability of randomly selecting a respondent who is female and prefers HP?
Q.1.1.3 What is the probability of selecting a male respondent, given that the preferred brand is Lenovo?
Q.1.1.4 What is the probability of selecting a respondent who is male or who prefers HP?
Q.1.1.5 What is the probability of selecting a respondent who does not prefer Lenovo?
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AC and BD are diameters of the given circle. OC is 6 centimeters and ABO = CBO. what is AO. A 3/ B 4/ C 5/ D 6
Answer:
A
Step-by-step explanation:
Use pie= 22/7 to approximate the circumference of a circle whose diameter is 28 inches.
Answer:
88 inches
Step-by-step explanation:
formula for circumference: 2pir or pi*diameter
22/7*28=88
88 inches
Find the product
(10^2)^3
Answer:
Well first you must do what's in the parenthesis.
10^2 = 100
100^3 = 1000000
When describing the results of an observational study, the mathematical relationship between the relative risk (RR) and the odds ratio (OR) is referred to as: a. The rare disease assumption b. The built-in bias c. The relative odds approach d. Effect modification e. All of the above
Previous question
The mathematical relationship between the relative risk (RR) and the odds ratio (OR) is (c) The relative odds approach.
How to find the mathematical relationship between the relative risk (RR) and the odds ratio (OR)?The mathematical relationship between the relative risk (RR) and the odds ratio (OR) is often described as the relative odds approach.
This approach quantifies the relationship between RR and OR and provides insights into the association between exposure and outcome in observational studies.
The rare disease assumption (a) refers to the assumption made in case-control studies that the odds ratio approximates the relative risk when the outcome is rare.
It is not specifically related to the mathematical relationship between RR and OR.
The built-in bias (b) does not directly relate to the mathematical relationship between RR and OR.
It refers to biases inherent in the study design or data collection process.
Effect modification (d) refers to a situation where the association between an exposure and outcome differs depending on the levels of another variable.
While effect modification can influence the relationship between RR and OR, it is not the specific term used to describe their mathematical relationship.
In summary, the mathematical relationship between RR and OR is best described as the relative odds approach (c), while the other options (a, b, d) are not directly related to this specific relationship.
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