Find the complex Fourier series of the periodic function: -1 0 < x < 2 f(x) = 2 2 < x < 4 f(x + 4) = f(x)
Answers
Therefore, the complex Fourier series is:
\(f(x) &= a_0 + \sum_{n=1}^{\infty} \left[ (a_n \cdot \cos(n\omega x)) + (b_n \cdot \sin(n\omega x)) \right] \\&= \begin{cases}-1 & \text{for } 0 < x < 2 \\2 & \text{for } 2 < x < 4 \\\end{cases}\end{align*}\)
Given:
\(\[f(x) = \begin{cases} -1, & 0 < x < 2 \\2, & 2 < x < 4 \\f(x+4) = f(x) & \text{for all } x\end{cases}\]\)
Complex Fourier series coefficients:
The complex Fourier series coefficients are given by:
\(\[c_k = \frac{1}{T} \int_{0}^{T} f(x) \cdot e^{-j\frac{2\pi kx}{T}} dx\]\)
where T is the period of the function.
For the interval [0,2]
Since \($f(x) = -1$ for $ 0 < x < 2$\)
The function can be expressed as a constant value within this interval. Therefore, we can write:
\(\[f(x) = -1, \quad 0 < x < 2\]\)
For the interval [2, 4]
Since \($f(x) = 2 $ for $ 2 < x < 4$\)
the function can be expressed as another constant value within this interval. Therefore, we can write:
\(\[f(x) = 2, \quad 2 < x < 4\]\)
Complex Fourier series:
Substituting the values of f(x) into the complex Fourier series formula, we have:
\(\[f(x) = \sum_{k=-\infty}^{\infty} c_k e^{j\frac{2\pi kx}{T}}\]\)
Calculating the coefficients:
For the interval [0, 2]:
Since f(x) = -1, we can calculate the coefficient \($c_k$\) as follows:
\(\[c_k = \frac{1}{2} \int_{0}^{2} (-1) \cdot e^{-j\frac{2\pi kx}{2}} dx\]\)
Simplifying the integral, we get:
\(\[c_k = \frac{1}{2} \left[ -\frac{j}{\pi k} e^{-j\pi kx} \right]_{0}^{2}\]\)
Evaluating the expression at x = 2 and subtracting the evaluation at x = 0, we have:
\(\[c_k = \frac{1}{2} \left( -\frac{j}{\pi k} e^{-j2\pi k} + \frac{j}{\pi k} \right)\]\)
For the interval [2, 4]:
Since f(x) = 2, we can calculate the coefficient \($c_k$\) as follows:
\(\[c_k = \frac{1}{2} \int_{2}^{4} 2 \cdot e^{-j\frac{2\pi kx}{2}} dx\]\)
Simplifying the integral, we get:
\(\[c_k = \left[ -\frac{j}{\pi k} e^{-j\pi kx} \right]_{2}^{4}\]\)
Therefore, the complex Fourier series is:
\(f(x) &= a_0 + \sum_{n=1}^{\infty} \left[ (a_n \cdot \cos(n\omega x)) + (b_n \cdot \sin(n\omega x)) \right] \\&= \begin{cases}-1 & \text{for } 0 < x < 2 \\2 & \text{for } 2 < x < 4 \\\end{cases}\end{align*}\)
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Related Questions
The final model from the Example is shown.
Draw a line around the part of the model that
represents 1 square yard.
Please help thank you
Answers
Answer:
Can anyone check out my page and answer my question??
Step-by-step explanation:
.
The area of the given model is 4/6 square yards.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
From the given figure, length of a rectangle is 4/3 yards and the width is 1/2 yards.
Here, area of a model is 4/3 × 1/2
= 4/6 square yards
Therefore, the area of the given model is 4/6 square yards.
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4. Tyquan had his car towed by Lakeview's Towing Service. It cost him $3.00 per mile to have it towed
plus a flat fee of $70.00. The function for his cost is represented by the function C(m) = 3m + 70. What
does C(22) represent in this situation?
a. Tyquan had hisbear towed for 136 mile and it cost $22.00
b. Tyquan had his car towed for 22 miles and it cost him $136.00
c. Tyquan had his car towed for 3 miles at $70.00
d. Tyquan had his car towed 22 miles for $70.00
Answers
The answer is b. because the other ones don't charge money according to the number of miles.
Answer:
The structure that you used in your research paper can also be used for your presentation. For example, just like how your
Step-by-step explanation:
What is the forecast for May using a five-month moving average?(Round answer to the nearest whole number.) Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47
A. 43 B. 47 C. 52 D. 38 E. 39
Answers
The forecast for May using a five-month moving average is 39 (Option E).
Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.
According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47
We have to add the sales of these five months, which gives:
27 + 40 + 42 + 41 + 47 = 197
To find the moving average for May, we divide this sum by 5:
197 / 5 = 39.4
Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.
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The midpoint of AB is M (-5,0). If the coordinates of A are (-8,5), what are the coordinates of B?
Answers
The coordinates of the endpoint B is (-2,-5).
What are the coordinates of endpoint B?The midpoint formula is expressed as;
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
Given the data in the question;
Midpoint M( -5,0 )
x = -5y = 0Endpoint A ( -8,5 )
x₁ = -8y₁ = 5Endpoint B
x₂ = ?y₂ = ?Plug the given values into the above formula and solve for x₂ and y₂.
M = ( (x₁+x₂)/2, (y₁+y₂)/2 )
(x,y) = ( (x₁+x₂)/2, (y₁+y₂)/2 )
x = (x₁+x₂)/2
2x = x₁ + x₂
2( -5 ) = -8 + x₂
-10 = -8 + x₂
-10 + 8 = x₂
-2 = x₂
x₂ = -2.
y = (y₁+y₂)/2
2y = (y₁+y₂)
2y = y₁ + y₂
2( 0 ) = 5 + y₂
0 = 5 + y₂
-5 = y₂
y₂ = -5
Therefore, the endpoint B is (-2,-5).
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I GOT THIS WRONG!! So what is the answer??
BOTS=BAN/REPORT
TROLL=BAN/REPORT
Answers
Use one of the sets and divide them to find the proportional relationship.
3 / 43.5 = 0.06896
Now since it's not in the answer choices, you round it.
0.06896 rounded to the nearest tenths is 0.7
Find the power set for the following sets (Write 3 examples of each)
a) Two sets A & B both having any 2 elements
b) Two sets A & B both having any 3 elements
c) Two sets A & B both having any 4 elements
Answers
Given statement solution is :- a) Power set for two sets A and B with any 2 elements:
Set A: {1, 2}, Set B: {3, 4}
Power set of A: {{}, {1}, {2}, {1, 2}}
Power set of B: {{}, {3}, {4}, {3, 4}}
b) Power set for two sets A and B with any 3 elements:
Set A: {1, 2, 3}, Set B: {4, 5, 6}
Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}
c) Power set for two sets A and B with any 4 elements:
Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}
Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},
a) Power set for two sets A and B with any 2 elements:
Set A: {1, 2}, Set B: {3, 4}
Power set of A: {{}, {1}, {2}, {1, 2}}
Power set of B: {{}, {3}, {4}, {3, 4}}
Set A: {apple, banana}, Set B: {cat, dog}
Power set of A: {{}, {apple}, {banana}, {apple, banana}}
Power set of B: {{}, {cat}, {dog}, {cat, dog}}
Set A: {red, blue}, Set B: {circle, square}
Power set of A: {{}, {red}, {blue}, {red, blue}}
Power set of B: {{}, {circle}, {square}, {circle, square}}
b) Power set for two sets A and B with any 3 elements:
Set A: {1, 2, 3}, Set B: {4, 5, 6}
Power set of A: {{}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Power set of B: {{}, {4}, {5}, {6}, {4, 5}, {4, 6}, {5, 6}, {4, 5, 6}}
Set A: {apple, banana, orange}, Set B: {cat, dog, elephant}
Power set of A: {{}, {apple}, {banana}, {orange}, {apple, banana}, {apple, orange}, {banana, orange}, {apple, banana, orange}}
Power set of B: {{}, {cat}, {dog}, {elephant}, {cat, dog}, {cat, elephant}, {dog, elephant}, {cat, dog, elephant}}
Set A: {red, blue, green}, Set B: {circle, square, triangle}
Power set of A: {{}, {red}, {blue}, {green}, {red, blue}, {red, green}, {blue, green}, {red, blue, green}}
Power set of B: {{}, {circle}, {square}, {triangle}, {circle, square}, {circle, triangle}, {square, triangle}, {circle, square, triangle}}
c) Power set for two sets A and B with any 4 elements:
Set A: {1, 2, 3, 4}, Set B: {5, 6, 7, 8}
Power set of A: {{}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}}
Power set of B: {{}, {5}, {6}, {7}, {8}, {5, 6}, {5, 7}, {5, 8}, {6, 7}, {6, 8}, {7, 8}, {5, 6, 7}, {5, 6, 8}, {5, 7, 8}, {6, 7, 8},
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helpp!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
b
Step-by-step explanation:
first, multiply the diameter by 3.14 to get the circumference.
After going through all the numbers I found that b had the closet answer
c = d(3.14)
c = 19(3.14)
c = 59.66
I really need help..im confused
Answers
The coefficient of determination, also known as R-squared, represents the proportion of the dependent variable's variance that can be explained by the independent variable(s) in a regression model. A higher R-squared indicates a better fit of the model to the data and suggests that a greater proportion of the variation in the dependent variable (lobster length in this case) can be attributed to the independent variable (age).
In this scenario, the linear model has a coefficient of determination of 0.8724503, indicating that approximately 87% of the variation in lobster length can be explained by age. This suggests a strong relationship between age and length in a linear fashion.
Conversely, the exponential model has a lower coefficient of determination of 0.6730372, indicating that only about 67% of the variation in lobster length is associated with age. While this is still a moderate level of association, the linear model provides a better fit to the data and explains a higher proportion of the variation in length.
Therefore, based on the coefficient of determination, the linear model would be the better choice for projecting the length of a lobster.
HURRY PLEASE!!!
In circle Y, what is the measure of arc TU?
59°
67°
71°
118°
Answers
Answer:
71°
Step-by-step explanation:
m∠1 = (SR + TU)/2
m∠1 = 63°
SR = 55°
substitute into the equation
63° =(55° - TU) / 2
TU = (63° * 2) - 55°
TU = 71°
4. How many ways are there to select a first-prize winner, a second-prize winner, and a third-prize winner from 100 different people who have entered a contest
Answers
There are 970,200 ways to select a first-prize winner, a second-prize winner, and a third-prize winner from 100 different people in the contest.
To determine the number of ways to select a first-prize winner, a second-prize winner, and a third-prize winner from 100 different people who have entered a contest, you can use the concept of permutations. In this case, you are choosing 3 winners from 100 people, and the order of selection matters.
The formula for permutations is P(n, r) = n! / (n-r)!, where n is the total number of elements, r is the number of elements to be chosen, and ! denotes the factorial.
Using this formula, you have:
P(100, 3) = 100! / (100-3)!
= 100! / 97!
= (100 × 99 × 98 × 97!)/(97!)
The 97! terms cancel out, leaving:
= 100 × 99 × 98
= 970,200
So, there are 970,200 ways to select a first-prize winner, a second-prize winner, and a third-prize winner from 100 different people who have entered a contest.
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54Find the exact value of x.
Answers
5/x = x/ 9
Cross-multiply
x² =45
Take the square root of both-side
x = 3√5 or 6.7082039325
Zahara asked the students in her class their gymnastic scores and recorded the scores in the table shown below:
Gymnastic Scores
Score Number of Students
0 1
1 1
2 2
3 6
4 4
5 3
6 2
Based on the table, what is the mean gymnastic score?
Answers
Answer:
It would be 3.5
Step-by-step explanation:
1+1+2+6+4+3+2
so the mean is 3.5
Suppose we have to allocate 4 tasks \( (1,2,3 \), and 4 ) between four people. The costs are set out in the following table: Mohamed to tasks? a. 4 b. 2 C. 1 d. 3
in the table below. Find the least s
Answers
Answer:
Step-by-step explanation:
To find the least cost allocation of tasks between four people, we need to determine the assignment that results in the minimum total cost. From the given information, we can allocate tasks by assigning a number to each person for each task.
Let's denote the people as A, B, C, and D, and the tasks as 1, 2, 3, and 4. The costs for each assignment are given in the table below:
Task 1 Task 2 Task 3 Task 4
Person A 4 3 5 2
Person B 2 4 3 1
Person C 3 1 2 5
Person D 1 2 4 3
To find the least cost allocation, we need to select one task for each person such that the sum of the costs is minimized.
Based on the table, the least cost allocation would be as follows:
Person A - Task 2 (cost: 3)
Person B - Task 4 (cost: 1)
Person C - Task 3 (cost: 2)
Person D - Task 1 (cost: 1)
The total cost for this allocation is 3 + 1 + 2 + 1 = 7.
Therefore, the least cost allocation of tasks between the four people would be:
a. Person A - Task 2
b. Person B - Task 4
c. Person C - Task 3
d. Person D - Task 1
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In a ________ method, relationships between variables are studied by making observations or measures of the variables of interest.
Answers
In a nonexperimental method, relationships between variables are studied by making observations or measures of the variables of interest.
What is nonexperimental research?Research without either the manipulation of an independent variable, the random assignment of individuals to conditions or orders of conditions, or both, is referred to as non-experimental research.
The non-experimental study is entirely dependent on variables that the researcher has no control over. By whatever means, they cannot manipulate, control, or change the subjects. Thus, all they can do is continue their research while monitoring and interpreting their subjects.
It is safe to assume that a non-experimental research design is used when there is no specific cause-effect study problem and the researcher simply wants to grasp a topic in depth without constraining it with variables. They examine the natural phenomena as they take place.
Therefore, in a nonexperimental method, relationships between variables are studied by observing or measuring the variables of interest.
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30 points :)
The cost of a cheese pizza is $9.99 plus $0.35 for each additional topping, t.
Write an inequality that can be used to represent the cost of a pizza that is at most $12.
What is the most number of toppings that a pizza can have and still be at most $12?
Please show your work
Answers
9.99 + 0.35t ≤ 12
12 - 9.99 = 0.35t (at its most)
2.01 = 0.35t
Rounded down, 2.01 / 0.35 = 5
5 toppings
It is impossible to get 10 kings when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is
Answers
On solving the provided question, we can say that it has 0% prοbability, making the answer zerο (0).
What is probability?Probability theοry, a subfield of mathematics, gauges the likelihοod of an occurrence or a claim being true. An event's prοbability is a number between 0 and 1, where apprοximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A prοbability is a numerical representation of the likelihood or likelihoοd that a particular event will occur.
In a deck of cards we have 4 kings. οne in each suit.
Tοtal number of cards in a pack 52.
There is οnly 4 king in a deck of cards, 10 kings are nοt possible.
This is impοssible event. Hence it has a probability zero(0).
The prοbability is 0.
Cοnsequently, it has 0% prοbability, making the answer zero (0).
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Complete question:
Emily liked to shoot baskets. She took 50 shots a day and kept track of how many she made for 10 days. Here are the number of shots she made: 22, 25, 27, 37, 32,
19, 25, 45, 32, 33
Answers
Answer:
if I have to calculate the average then it's a
add all of them and divide by 10
answer is 29.7
find the standard matrix for the linear transformation t. t(x, y, z) = (2x − 8z, 8y − z)
Answers
The standard matrix for t is [ 2 0 -8 ] [ 0 8 -1 ]. To find the standard matrix for the linear transformation t, we need to find the images of the standard basis vectors of R^3 under t.
The standard basis vectors of R^3 are e1 = (1, 0, 0), e2 = (0, 1, 0), and e3 = (0, 0, 1).
t(e1) = (2(1) - 8(0), 8(0) - 0) = (2, 0)
t(e2) = (2(0) - 8(0), 8(1) - 0) = (0, 8)
t(e3) = (2(0) - 8(1), 8(0) - 1) = (-8, -1)
The standard matrix for t is the matrix whose columns are the images of the standard basis vectors of R^3 under t.
Therefore, the standard matrix for t is
[ 2 0 -8 ]
[ 0 8 -1 ]
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what is this
please help
Answers
Answer:
The answers are the 2nd box, 4th box, and 5th box.
When finding the margin of error for the mean of a normally distributed population from a sample, what is alpha, assuming a confidence level of 74%?
Answers
The value of α = 0.26 finding by using normal distribution.
What is a normal distribution?A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
Given that,
confidence level = 74%
alpha = ?
The significance level α is the probability of making the wrong decision when the null hypothesis is true. Alpha levels which is also called as significance levels are used in hypothesis tests.
Mathematically, the value of α is determined by subtracting the level of confidence from 1, and then writing the result as a decimal.
As the confidence level is given as 74%, so the significance level would be,
α = 1 - confidence level
= 1 - 0.74
α = 0.26
Hence, The value of α = 0.26.
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8) Anthony wants to earn at least $41,000 this year. So far, he has earned $34,000. How much
more does Anthony need to earn to meet his goal?
Inequality:
Solution:
Answers
Ansswer:
7,000
Step-by-step explanation:
41,000 - 34,000 = 7,000
The circumference of a circle is 3π in.
What is the area of the circle
Answers
Answer: 7.07in²
Step-by-step explanation:
To find radius,
2πr = 3π
r = \(\frac{3\pi}{2\pi}\)
r = 1.5
To find area,
A = πr²
= π × 1.5²
= (2.25π)in²
= 7.07in² (3sf)
3. Jill sold a third of her comic books and then bought 24 more.
She now has 30. With how many did she begin?
Help me out
Answers
Answer:
18
Step-by-step explanation:
30-24= 6
so when she sold them she had 6 left over
it says she sold one third so we need to find out that 6 is a third of what
to find that out now we multiply 6x3=18
jill had 18 books to start out with
7 minus 5 times a number x is greater than 19.
Answers
Answer:
7 - 5x > 19
Step-by-step explanation:
Answer:
7-5x>19
or
7-5*10>19
Step-by-step explanation:
Consider a continuous-time Markov chain with three states 1, 2, 3, 4, 5 and transition rates q12=1, q13 = 2, q21 = 0, q23 = 3, q31 = 0, q32 = 0. (1) Write the system of ODEs for the corresponding transition probabilities Pᵢⱼ (t) . (2) Suppose that the initial state is 1. What is the probability that after the first transition, the process X(t) enters state 2?
Answers
the probability of transitioning from state 1 to state 2 after the first transition is:
P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3
To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.
Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.
The ODEs for the transition probabilities can be written as follows:
dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)
dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)
dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)
dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)
dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)
dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)
where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.
Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.
To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.
The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:
total_rate = q₁₂ + q₁₃
Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:
P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate
In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.
Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:
P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3
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Solve for a.
"15-a=11"
A.26
B.11/15
C.-4
D.4
Answers
Answer:
D. a=4Step-by-step explanation:
To solve for a, you isolate it on one side of the equation.
First thing you do is subtract by 15 from both sides.
\(\rightarrow \sf{15-a-15=11-15}\)
Solve.
Add or subtract the numbers from left to right.
11-15=-4
-a=-4
Then, divide by -1 from both sides.
\(\sf{\dfrac{-a}{-1}=\dfrac{-4}{-1}}}\)
Solve.
Divide the numbers from left to right.
-4/-1=4
\(\rightarrow \boxed{\sf{a=4}}\)
Therefore, the answer is d. 4.
I hope this helps, let me know if you have any questions.
an experienced plumber can do the finishing plumbing work on a house in 8 hours. an inexperienced plumber will take 12 hours to do the same job. if two experienced men and three inexperienced men work on an emergency finishing project, how many hours will they take to do the job? 4.8 hours 3 hours 2 hours
Answers
Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
The number of hours will they take to do the job is 2. Below is the solution:
2(1/8) + 3(1/12) = 1/x
1/4 + 1/4 = 1/x
1/2 = 1/x
x = 2
The Cougars basketball team played 10 games this season and lost them all. The number
of points the team scored in each game, arranged from least to greatest, are shown
below:
78, 79, 79, 80, 83, 83, 85, 86, 87, 90
The team fired the coach and brought in a new coach who promised the team’s mean
score for the entire season (including the 10 games he didn’t coach) would increase to 90
points per game by the time he finished coaching his 10th game.
What will the mean score need to be in the 10 games the new coach leads the team in
order for his promise to be realized?
Answers
the mean score in the 10 games the new coach leads the team must be 96.
What is mean?
In mathematics and statistics, the mean (also called the average) of a set of numbers is the sum of those numbers divided by the total number of numbers.
The sum of the scores in the 10 games played so far is:
78 + 79 + 79 + 80 + 83 + 83 + 85 + 86 + 87 + 90 = 840
To achieve a mean score of 90 for the entire season, the total score for all 20 games (10 played so far and 10 to be played under the new coach) must be:
20 x 90 = 1800
Since the team lost all 10 games played so far, the total score for the 10 games under the new coach must be:
1800 - 840 = 960
Therefore, the mean score in the 10 games the new coach leads the team must be:
960 / 10 = 96
So the team must average a score of 96 points per game in the 10 games played under the new coach in order to achieve a mean score of 90 for the entire season.
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What is the value of the expression 5y2 + 10y-2when y=4
Answers
Answer:
118
Step-by-step explanation:
5y² + 10y - 2 y = 4
5(4)² + 10(4) - 2
= 5(16) + 40 - 2
= 80 + 40 - 2
= 120 - 2
= 118
To find the value of the expression 5y^2 + 10y - 2 when y = 4, we can substitute y = 4 in the expression and simplify as follows:
5y^2 + 10y - 2, when y = 4
= 5(4)^2 + 10(4) - 2 [Substituting y = 4]
= 5(16) + 40 - 2
= 80 + 38
= 118
Therefore, the value of the expression 5y^2 + 10y - 2 when y = 4 is 118.
A consumer charges a $2,530.16 purchase on a credit card. The card has a daily interest rate of 0.042%. If the balance is paid off at the end of 30 days, how much interest will the consumer pay?
Answers
The amount of interest that the customer will pay is given as follows:
$31.88.
How to obtain the simple interest?The balance of an account after t periods is given as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.Hence the interest accrued is given as follows:
I(t) = Prt.
The parameters for this problem are given as follows:
P = 2530.16, r = 0.00042, t = 30.
Hence the interest is given as follows:
I(30) = 2530.16 x 0.00042 x 30
I(30) = $31.88.
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