Katie outscored approximately 1.39% of the students in her section.
How to calculate percentage of the students in her section did katie outscore?If Katie received a z-score of 2.2, this means that her score was 2.2 standard deviations above the mean of the exam scores for her section.
We can use a standard normal distribution table or calculator to find the percentage of scores that fall above a z-score of 2.2.
Using a standard normal distribution table, we can find the proportion of scores that fall below a z-score of 2.2, and then subtract this from 1 to find the proportion of scores that fall above a z-score of 2.2.
The table value for a z-score of 2.2 is approximately 0.9861, which means that approximately 98.61% of the scores fall below a z-score of 2.2. Therefore, approximately:
1 - 0.9861 = 0.0139, or 1.39%
of the scores fall above a z-score of 2.2.
This means that Katie outscored approximately 1.39% of the students in her section.
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ILLUSTRATIVE MATHEMATICS
Class B would be the one where pupils spend the least amount of time on their homework.
Class A has the least amount of variation in homework time.
The proportion of all students that prefer to use a metal pen would be 40 %.
The bookstore should not believe that the results represent the preferences accurately as the different is significant.
How to find the less variable class?The least amount of time was spent on homework by students in Class B, as seen by the fact that some of them only put in 10, 15, and 20 minutes, as opposed to 35 minutes for students in Class A.
Due to their smaller range, Class A also had less variability in the amount of time spent on homework:
Class A range :
= 100 - 35
= 65 minutes
Class B range :
= 80 - 10
= 70 minutes
How to find the proportion ?Proportion of students who prefer metal pens = (Number of students who prefer metal pens) / (Total number of students in the sample) = 4/10 = 0.40
= 40 %
Proportion of students who prefer metal pens on day 2 = 8/10 = 0.8
= 80%
The preferences of the student population are significantly different, according to these results.
The bookstore needs to collect more information in order to have a better knowledge of the preferences of the student population given the stark disparity in the results from the two days.
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En una progresión geométrica, sabemos que el primer término es
6 y el cuarto 48. Calcular el término general
The general term of the geometric progression is given by an = 6 × [tex]2^{n-1}[/tex]
In a geometric progression, each term is obtained by multiplying the previous term by a fixed ratio. Let us call this ratio "r".
So, if the first term is 6, the second term will be 6r, the third term will be 6r², and the fourth term will be 6r³.
We are given that the fourth term is 48, so we can write
6r³ = 48
Dividing both sides by 6, we get
r³ = 8
Taking the cube root of both sides, we get
r = 2
Now that we know the value of "r", we can use the formula for the nth term of a geometric progression to find the general term
an = a₁ × [tex]r^{n-1}[/tex]
Substituting the given values, we get:
an = 6 × [tex]2^{n-1}[/tex]
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hi pls help state testing is coming up !!
Equation 2(m + 3) + m - 2 matches with the expression 3m + 4
How to Match EquationsFirst, we can simplify the equations:
2(m + 3) + m - 2 = 3m + 45(m + 1) - 1 = 5m + 4m + m + m + 1 + 3 = 3m + 4Now we can match each equation with the corresponding expression:
3m + 4 matches with 2(m + 3) + m - 2
5m + 4 matches with 5(m + 1) - 1
3m + 4 matches with m + m + m + 1 + 4
Therefore, the equations match with the expressions as follows:
Equation 1: 2(m + 3) + m - 2 matches with 3m + 4
Equation 2: 5(m + 1) - 1 matches with 5m + 4
Equation 3: m + m + m + 1 + 3 matches with 3m + 4
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4x + 12 less than or equal to -8
Answer: 1:4 x - 12 = 8. 4x−12=8. Add 12 to both sides. Add 12 to both sides.
2: 4x=8+12. 4x=8+12. Add 8 and 12 to get 20. Add 8 and 12 to get 20.
3: 4x=20. 4x=20. Divide both sides by 4. Divide both sides by 4.
4: x=\frac{20}{4} x=420 Divide 20 by 4 to get 5. Divide 20 by 4 to get 5.
the experimental probability.
The table shows the outcomes of rolling two
number cubes at the same time and finding the
product of the two numbers.co
7. What is the theoretical probability, expressed as
a fraction, of rolling a product greater than 12?
1
1
2 2
3
3
4
5
6
Florida's B.E.S.T. Assessment Practice Workbook 2 of 2
لیا
4
5
6
2
2
4
6
800
10
12
3
3
6
9
12
15
12
16
20
24
15
20 25
30
18 24 30 36
4
4
8
80 2
5
5
10
8. If Alan rolls two number cubes 300 times, about how many times would he expect a
product greater than 10? Round to the nearest whole number.
6
6
12
18
Answer:
7. To find the theoretical probability of rolling a product greater than 12, we need to count the number of outcomes where the product is greater than 12 and divide by the total number of possible outcomes.
From the table, we can see that the outcomes with a product greater than 12 are: (2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), and (6, 6). This gives us a total of 15 outcomes with a product greater than 12.
The total number of possible outcomes is 6 x 6 = 36, since there are 6 possible outcomes for each of the two number cubes.
Therefore, the theoretical probability of rolling a product greater than 12 is 15/36, which simplifies to 5/12.
8. To find the approximate number of times Alan would expect to roll a product greater than 10 in 300 rolls, we can multiply the total number of rolls by the probability of rolling a product greater than 10.
From the table, we can see that the outcomes with a product greater than 10 are: (2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6), (3, 4), (4, 3), (5, 2), (6, 2), (4, 2), (5, 2), and (6, 2). This gives us a total of 21 outcomes with a product greater than 10.
The probability of rolling a product greater than 10 is 21/36, which simplifies to 7/12.
Multiplying the total number of rolls (300) by the probability (7/12), we get:
300 x 7/12 = 175
So Alan would expect to roll a product greater than 10 about 175 times in 300 rolls.
The graph shows two accounts with the same principle and annual interest rate, use the graph to estimate the answer to the question.
About how much more compound interest than simple interest is earned after 45 years?
The amount of compound interest that was earned more than simple interest after 45 years is about 485 dollars
Simple interest and Compound interestFrom the question, we are to determine how much more compound interest than simple interest is earned after 45 years
In order determine how much more compound interest is earned than simple interest after 45 years, we will determine the simple interest earned in any year after the 45th year. We will also determine the corresponding compound interest for the particular year.
Finally, we will determine the difference of the interests.
From the graph,
The interests around the 46th year are:
Compound interest = 1200 dollars
Simple interest = 715 dollars
Thus,
Difference = 1200 dollars - 715 dollars
Difference = 485 dollars
Hence,
The amount of compound interest that was earned more than simple interest is about 485 dollars
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refer to exercise 9.10. having looked at the collected sample, we consider an alternative supplier. a sample of 150 items produced by the new supplier contains 13 defective items. is there significant evidence that the quality of items produced by the new supplier is higher than the quality of items in exercise 9.10? what is the p-value?
what is the formula for the edge length of the simple cubic unit cell based on the radius, r, of the atom?
The formula for the edge length, a, of the simple cubic unit cell is given by a = 2r. This means that the edge length is twice the radius of the atom.
The simple cubic unit cell is the most basic type of crystal structure, and consists of atoms arranged in a cube shape with one atom at each corner.
The edge length of the cube is equal to the distance between adjacent atoms, which in this case is 2r (since the radius of each atom extends to the center of the adjacent atoms). Therefore, the formula for the edge length is a = 2r.
Hence, the edge length of the simple cubic unit cell can be calculated using the formula a = 2r, where r is the radius of the atom.
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The two-way frequency table contains data about students' preferred exercise.
Enjoys swimming Enjoys cycling Row totals
Likes running 28 62 90
Does not like running 46 64 110
Column totals 74 126 200
What is the joint relative frequency of students who do not like to run but enjoy cycling?
64%
55%
32%
23%
Answer:
14%
Step-by-step explanation:
like running and summing=28
28/200=14
:in percent form it is 14%
I need help mad fast
The probability of the events
1. The point is on QR = 44.44%
2. The point is on PQ = 22.22%
3. The point is on RS = 33.33%
4. The point is not on RS = 66.67%
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur.
Probability is expressed can be as ;
Probability = sample space / Total out come.
In percentage , the total probability is 100% it is equivalent to 1 in fraction.
The total length PS is calculated as ;
8+4+6 = 12 + 6
= 18
The probability of event (PQ) in percentage = 8/18 × 100
= 44.44%
The probability of event ( QR) = 4/18 × 100
= 22.22%
The probability of event ( RS) = 6/18 × 100
= 600/18 = 33.33%
The probability of the point not on RS = 100-33.33
= 66.67%
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In order to estimate the effect on wage of years of schooling, researcher B analysed the dataset that researcher A collected in Question 3. Researcher B considers the following regression equation log(income)= β0+ β1educi + ... +ui; where educ1 is years of schooling for individual i and includes additional terms associated with other characteristics in the dataset. When research B was carefully examining omitted factors in the error term Uj, she realised that unobserved factors such as motivation, and work_ethici would determine the income level and be correlated with the variable of interest, educi. If researcher B's conjecture regarding the unobserved factors is correct, then:a. The OLS estimator β1 would not be computed. b. The OLS estimator β1 would be biased. c.The OLS estimator β1 would suffer imperfect multicollinearity. d. The OLS estimator β1 would have a large standard error.
If researcher B's conjecture regarding the unobserved factors is correct, then b. The OLS estimator β1 would be biased.
When there are omitted variables that are correlated with the variable of interest (in this case, years of schooling), the OLS estimator becomes biased. This means that the estimate of the effect of years of schooling on income is no longer accurate or unbiased. Therefore, researcher B's regression results may not provide a true estimate of the effect of education on wages due to the potential bias caused by the omitted variables.
Your answer: If researcher B's conjecture regarding the unobserved factors is correct, then b. The OLS estimator β1 would be biased. This is because the unobserved factors like motivation and work_ethic would be correlated with the variable of interest, educi, which can lead to biased estimates in the regression analysis.
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If a is a non-zero, real number and a(x − 3)² − b = c,
• Prove that x = 3 ± √b+c/a Show your work.
If a = 2 and b = 5, determine what condition(s) on c will restrict the
solutions for x to real numbers.
Explain your reasoning.
Enter your proof, your answer, and your explanation in the space provided.
If a is a non-zero, real number and equation a(x − 3)² − b = c then x = 3 ± √b+c/a and the condition on c that restricts the solutions for x to real numbers is c ≥ -5.
To prove that x = 3 ± √(b+c)/a, let's start with the given equation: a(x - 3)² - b = c.
Add b to both sides of the equation to isolate the quadratic term:
a(x - 3)² = c + b.
Divide both sides by 'a' to obtain the quadratic term by itself:
(x - 3)² = (c + b)/a.
Take the square root of both sides to solve for x:
x - 3 = ±√(c + b)/a.
Add 3 to both sides to isolate x:
x = 3 ± √(c + b)/a.
Therefore, we have proven that x = 3 ± √(b+c)/a.
Now, let's consider the case where a = 2 and b = 5.
Substituting these values into the equation x = 3 ± √(b+c)/a, we have:
x = 3 ± √(5 + c)/2.
For the solutions to be real numbers, the expression under the square root (√(5 + c)) must not be negative. In other words, (5 + c) ≥ 0.
Therefore, the condition on c that restricts the solutions for x to real numbers is c ≥ -5.
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An office manager paid $675.95 to build a web site. The office manager bought a software package for $68.50 and paid an employee $127.95 for each hour she worked on the website. What is x, the number of hours the employee worked on the website
An office manager paid $675.95 for computer equipment. The office manager bought one monitor for $127.95 and hard drives for $68.50 each. What is x, the number of hard drives the office manager bought?
A sales manager paid $675.95 for advertising. The sales manager paid $127.95 per hour for consulting and received a $68.50 discount. What is x, the number of hours the manager paid for consulting?
A business owner paid a total of $675.95 for two employees to work the same number of days. The business owner paid one employee $68.50. The business paid a second employee $127.95 per day. What is x, the number of days the employees worked?
Answer:
The situation best represented by the given information is option B: An office manager paid $675.95 for computer equipment. The office manager bought one monitor for $127.95 and hard drives for $68.50 each. What is x, the number of hard drives the office manager bought?
To represent this situation as an equation, let x be the number of hard drives. The total cost of the computer equipment is the cost of the monitor plus the cost of the hard drives:
675.95 = 127.95 + 68.50x
Now, we can solve for x to find the number of hard drives the office manager bought.
HELP PLEASE ASAP 20 points
Answer:
55 degrees
Step-by-step explanation:
To solve this problem, all you have to do is 60 + 65 and subtract it from 180. We can do this because those 3 angles create a linear pair.
Answer: 55
Step-by-step explanation:
The 3 angles form a line, <4 60 and 65. since it is a line the 3 angles add up to 180
<4 +60 + 65 =180 solve for <4 by subtracting 60 and 65 from both sides
<4 = 55
Give the OTHER guy brainliest please. I liked his answer.
Due now!!!!!!!!!!!!!!
Tanya has captured many purple-footed bog frogs. She weighs each one and then counts the number of yellow spots on its back. This trend line is a A. strong fit for these data.
When is a trend line a strong fit ?A trend line's ability to accurately predict one variable based on the values of another is directly correlated with how closely it follows the overall pattern of the data points. Essentially, a well-fitted trend line indicates a high degree of correlation between the variables being analyzed.
Looking at the trend line for Tanya's data, we can see that the trend line is a strong fit because the points around it are very close to it which means it can predict values better.
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the expression to the left of the equals sign is not a valid target for an assignment. matlab
Answer:
The comparison operator is == if( image(j,k,m) == i)
you welcome
Step-by-step explanation:
help me 7th grade math
a. 5/36
count how many sets add up to 6 and then put that number over the total number of sets
So there are 5 sets that add to 6 and 36 total sets so the answer is 5/36
Hope this helps!
When the algorithm converges. what are the distance vectors from router 'X' to all routers? Write your answer aS U.VWXy What are the initial distance vectors for router 'W"?
The routing algorithm would then iteratively update these distances based on new information from the network until convergence is reached.
I am an AI language model and I need more information about the context and specific details regarding the algorithm and network topology in order to provide an accurate answer.
When an algorithm converges, it means that it has reached a stable state and no more changes are expected. In this context, it usually refers to a routing algorithm that has calculated the shortest paths between routers. The distance vectors from router 'X' to all routers would be the final set of shortest distances to each of the other routers in the network. These can be represented as UVWXy, where U, V, W, and y are the distances from router 'X' to routers U, V, W, and y, respectively.
For the initial distance vectors for router 'W', we would consider the direct connections between router 'W' and its neighboring routers at the beginning of the algorithm. The initial distance vectors would be the distances from router 'W' to its neighbors before any routing updates occur. The routing algorithm would then iteratively update these distances based on new information from the network until convergence is reached.
Please provide more details about the network, and I can give you a more specific answer.
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To determine the distance vectors from router 'X' to all routers when the algorithm converges, I would need more information about the specific routing algorithm being used.
Different routing algorithms, such as Distance Vector or Link State, have different convergence behaviors and update mechanisms. If you can provide the details of the routing algorithm, I can help you determine the distance vectors.
Regarding the initial distance vectors for router 'W', again, it depends on the specific network configuration and the routing algorithm being used. In most routing algorithms, the initial distance vectors are typically set to some predefined values. It could be a cost of infinity for unreachable destinations or a cost based on the direct links to neighboring routers. Without more information about the network topology and routing algorithm, I cannot provide the specific initial distance vectors for router 'W'.
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suppose another dog weighs 25.7 pounds and consumes 70 ounces of food per week. what is the residual associate to this individual using the least squares estimate? provide your answer accurate to 1 digit past the decimal point.
The residual concerning this individual using the least squares estimate is 13.025 ounces under the given condition that another dog weighs 25.7 pounds and consumes 70 ounces of food per week.
Let's us consider x = weight of a dog in pounds
y = amount of food consumed by a dog in ounces per week.
Then the least squares estimate of y given x is
y = 2.75x - 17.5
Utilizing this equation, we can say that a dog weighing 25.7 pounds will consume
y = 2.75(25.7) - 17.5
= 56.975
To evaluate the residual concerning thr individual using the least squares estimate,
Residual = Observed value - Predicted value
= 70 - 56.975
= 13.025 ounces
The residual concerning this individual using the least squares estimate is 13.025 ounces under the given condition that another dog weighs 25.7 pounds and consumes 70 ounces of food per week.
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Clarence's office recycled a total of 27 kilograms of paper over 3 weeks. How many weeks will it take Clarence's office to recycle a total of 36 kilograms of paper? Solve using unit rates.
Answer: number of recycled paper in 1 week: 27/3= 9 kilograms
Clarence's office will recycle a total of 36 kilograms of paper in : 36/9= 4 weeks
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
12 weeks is your answer
5,500 dollars is placed in a savings account with an annual interest rate of 2.8%. If no money is added or removed from the account, which equation represents how much will be in the account after 7 years?
Answer:
$6,578
Step-by-step explanation:
((5500 * 0.028) * 7) + 5500, where parentheses is the interest rate
(5500 * 0.028) * 7
154 * 7
1078
1078 + 5500
6578
Brainliest? ;)
It helps me a lot!
6010
Mary and Chance walk in the same direction along a straight path. For 0 ≤t≤ 20, Mary's velocity at time t is
given by M(t) = 72-30+50.5 and Chance's velocity at time t is given by C(t) = 8.5t³e-0.45t. Both M (t) and
C(t) are positive for 0 < t < 20 and are measured in meters per minute, and t is measured in minutes. Mary is
12 meters ahead of Chance at time t = 0, and Mary remains ahead of Chance for 0 < t ≤ 20.
6010 (2-36-30.5) (24-3)
-6010
(2643)
(a) Find the value of to M(t)dt. Using correct units, interpret the meaning of to
The average distance Mary travel
context of the problem.
Lt ²-3€+50:51
15
-15
M(t)dt in the
(b) At time t= 10, is Mary speeding up or slowing down? Give a reason for your answer. Mary is slowms.
49.17
M-7.03
m (16) = 6010 / 120.5
?
down because relowty is
Positin gaz allelere
(c) Is the distance between Mary and Chance at time t = 18 increasing or decreasing? Give a reason for your
answer.
MC18) - (C₁Y) = -1.021 It is decreams becaun Chance's unloch,
Mary's
(d) What is the maximum distance between Mary and Chance over the time interval 0 < t < 20 ? Justify your
answer.
a. The value of to M(t)dt based on the information is 544.09m/s.
b) Mary speed is increasing
c) The distance is increasing
d) The max Distance between Mary and Chance over the time interval is -443.553.
How to explain the informationWe need to find the maxima or minima, (-ve value of D(t) means Chance is ahead of Mary).
Solve for t OR (You can also plot d and get the max value of D).'
Either way at (t = 9.273) we get a minima of, -443.553 , which is the max distance difference between them.
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a conclusion that a linear model between the variable and age is appropriate is supported by which plot or plots? responses the plot for variable a only the plot for variable a only the plot for variable b only the plot for variable b only the plot for variable c only the plot for variable c only the plots for variables a and c the plots for variables a and c the plots for variables b and c
The correct option is 1, A conclusion that a linear model between the variable and age is appropriate is supported by the plot A only.
A mathematical representation of a linear connection between a dependent variable and one or more independent variables is called a linear model. It is presumptive that the variables have a linear connection, which means that when the independent variable varies, the dependent variable changes at a fixed pace.
Y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept, is the most basic form of a linear model. The y-intercept of the line reflects the value of the dependent variable when the independent variable is equal to zero, while the slope of the line shows the rate of change of the dependent variable with respect to the independent variable.
Linear models are widely used in many fields, including statistics, economics, engineering, and physics, to analyze and predict the behavior of systems that exhibit a linear relationship between variables. They can be used for simple predictions or as a building block for more complex models.
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Complete Question:-
A researcher studying koi fish collected data on three variables, A, B, and C. The following residual plots show the residual for a model for predicting each variable from the age of the fish.
A conclusion that a linear model between the variable and age is appropriate is supported by which plot or plots?
1.)A Only
2.)B Only
3.)C Only
4.)A and C only
5.)B and C only
How many solutions are possible?
y = 5x + 8
y = 3x + 4
two
No
infinite
one
since there are only two variables, there are only two solutions
A new credit card holder must decide between two credit cards. The first card offers a current APR of 13.99%. The second card has a current daily periodic interest rate of 0.035%. Which card would be the better choice?
The second card is the better choice because the daily periodic interest on the first card is 0.038%, compared to 0.035% on the second card.
The second card is the better choice because the daily periodic interest on the first card is 0.035%, compared to 0.038% on the second card.
The first card is the better choice because the daily periodic interest on the first card is 0.035%, compared to 0.038% on the second card.
The first card is the better choice because the daily periodic interest on the first card is 0.038%, compared to 0.035% on the second card.
Based on the comparison of daily periodic interest rates, the second card with a 0.035% daily periodic interest rate is a better choice for a new credit card holder than the first card with a 0.03832% daily periodic interest rate.
You decide which credit card is a better choice by comparing their interest rates.
To make a fair comparison, let's first convert the Annual Percentage Rate (APR) of the first card into a daily periodic interest rate. The APR of the first card is 13.99%. To find the daily periodic interest rate, we divide the APR by 365 (the number of days in a year):
13.99% / 365 = 0.03832%
Now we can compare the daily periodic interest rates of both cards. The first card has a daily periodic interest rate of 0.03832%, and the second card has a daily periodic interest rate of 0.035%.
Since the daily periodic interest rate of the second card (0.035%) is lower than the first card (0.03832%), the second card would be the better choice for a new credit card holder. A lower daily periodic interest rate means that the cardholder will be charged less interest on their outstanding balance, which can save them money over time. Hence, The correct option is The second card is the better choice because the daily periodic interest on the first card is 0.035%, compared to 0.038% on the second card.
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Find the first four terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1
an = n
The first four terms of the sequence are 1, 2, 3, and 4.
What is sequence and series?An ordered list of numbers or objects that adhere to a particular pattern or rule is referred to as a sequence in mathematics. Every number in the sequence is referred to as a term, and its location in the sequence is referred to as its index or subscript. The total of the terms in a sequence, on the other hand, makes up a series. In other words, a series is created by adding up each phrase in a sequence. In other terms, a series is a single number that represents the total of a sequence of numbers, whereas a sequence is a list of numbers.
The given sequence is represented by the pattern:
an = n
Substituting values of n starting from 1 we have:
a1 = 1
a2 = 2
a3 = 3
a4 = 4
Hence, the first four terms of the sequence are 1, 2, 3, and 4.
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0.7006652 / ____________ = 0.1234 Which of the following goes in the blank to make the second equation true?
Answer: 0.08646208568
Step-by-step explanation:
Division and Multipulication are the invesre of eachother . So when we do the inverse of division, we will get an equation of 0.7006652 ×0.1234.
Find the length of a side of a square if its area is: 4/25 cm^2
Answer:
Side = 2/5 cm
Step-by-step explanation:
Area of square = side²
(4/25) cm² = side²
√((4/25)cm²) = √(side²)
√(4cm²) / √(25cm²) = side
(2 / 5) cm = side
side = 2/5 cm
find the fourth roots of cos200+isin200
The fourth roots of cos20+sin20 are 0.9421925652434.(cos5 + isin5).
What is De Moivre's Theorem?This theorem states that if z is a complex number and n is any positive integer, then zⁿ = (rⁿ)(cosnθ + isinnθ), where r is the modulus of z and θ is the argument of z.
The fourth roots of cos20+sin20 can be found using De Moivre's Theorem.
In this case, z = cos20+sin20 and n = 4.
First, we need to determine the modulus of z. This can be found using the Pythagorean Theorem, which states that r² = (cos20)² + (sin20)². Plugging in the values we get:
r² = (cos20)² + (sin20)²
= (0.93969262)²+ (0.34202014)²
= 0.88772683.
Taking the square root of both sides gives us
r = √0.88772683
= 0.9421925652434.
Now that we have the modulus, we can use De Moivre's Theorem to find the fourth roots of z.
We have z⁴ = (r⁴)(cos4θ + isin4θ).
Plugging in the values we get:
(0.9421925652434)⁴ = (r⁴)(cos4(20) + isin4(20)).
Taking the fourth root of both sides gives us r = 9421925652434.
Finally, we can solve for the fourth roots of z.
We have [tex]z^{^(1/4)}[/tex] = (0.9421925652434)(cos(20/4) + isin(20/4)).
Plugging in the values we get: [tex]z^{^(1/4)}[/tex] == (0.94409403)(cos5 + isin5). Therefore, the fourth roots of cos20+sin20 are 0.9421925652434.(cos5 + isin5).
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Jessica pours herself a cup of boiling water, at 100°C, to make tea. After 312minutes, the temperature of her tea has decreased to 58°C. What was the average change in temperature each minute?
The required average change in temperature each minute is a decrease of 0.13°C.
What is average?The average of the values is the ratio of the total sum of values to the number of values.
We can use the formula:
average change = (final temperature - initial temperature) / time
Here, the initial temperature is 100°C, the final temperature is 58°C, and the time is 312 minutes.
So,
average change = (58 - 100) / 312
average change = -0.1346...
Rounding to two decimal places, we get:
average change = -0.13°C per minute.
So, the average change in temperature each minute is a decrease of 0.13°C.
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