Answer: y is all real numbers
Step-by-step explanation:
Using Laplace Transforms, find the solution of the initial value problem: d²y +9y =9. sin(t). U(t - 3), = y(0) = y'(0) = 0 dx²
The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.
To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:
Take the Laplace transform of the given differential equation.
Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:
s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))
Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:
s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))
Solve for Y(s).
Combining like terms, we have:
Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))
Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:
Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)
Simplifying further, we have:
Y(s) * (s⁴ + 10s² + 9) = 9s² + 9
Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):
Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)
Partial fraction decomposition.
To proceed, we need to decompose the right side of the equation using partial fraction decomposition:
Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)
Multiplying through by (s⁴ + 10s² + 9), we have:
9s² + 9 = A(s² + 9) + B(s² + 1)
Equating the coefficients of like powers of s, we get:
9 = 9A + B
0 = A + B
Solving these equations, we find:
A = 0
B = 0
Therefore, the decomposition becomes:
Y(s) = 0/(s² + 1) + 0/(s² + 9)
Inverse Laplace transform.
Taking the inverse Laplace transform of the decomposed terms, we find:
L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}
The inverse Laplace transform of 0/(s² + 1) is 0.
The inverse Laplace transform of 0/(s² + 9) is 0.
Combining these terms, we have:
Y(x) = 0 + 0
Therefore, the solution to the initial value problem is:
y(x) = 0
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At the school carnival, the soccer team sold hamburgers and hot dogs. a person buying one hamburger and one hot dog will spend $17.65. the soccer team sold 22 hamburgers and 39 hot dogs and made $511.55. how much does each item cost?
The cost of one hamburger and one hot dog = $10.4 and $7.25.
What is a linear equation?a connection between two or more factors that results in a linear model when displayed on a graph. The variable will have a degree of one.
Y = mx + c is the linear equation.
where the line's y-intercept is represented by c and its m-slope by a slope.
x + y = 17.65 ...(1)
22x + 39y = 511.55 ...(2)
22(17.65 - y) + 39y = 511.55
388.3 - 22y + 39y = 511.55
17y = 123.25
y = $7.25
x + 7.25 = 17.65
x = 17.65 - 7.25
x = $10.40
The cost of the hamburger and hot dog will be $10.4 and $7.25
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What is the net pay for 40 hours worked at $8.95 an hour with deductions for Federal tax of $35.24, Social Security of $24.82, and other deductions of $21.33?
$276.61
$326.25
$358.00
$368.91
After deducting the amounts for Federal tax, Social Security, and other deductions, the net pay for working 40 hours at an hourly wage of $8.95 is $276.61. Option A.
To calculate the net pay, we need to subtract the deductions from the gross pay.
Given:
Hours worked = 40
Hourly wage = $8.95
Federal tax deduction = $35.24
Social Security deduction = $24.82
Other deductions = $21.33
First, let's calculate the gross pay:
Gross pay = Hours worked * Hourly wage
Gross pay = 40 * $8.95
Gross pay = $358
Next, let's calculate the total deductions:
Total deductions = Federal tax + Social Security + Other deductions
Total deductions = $35.24 + $24.82 + $21.33
Total deductions = $81.39
Finally, let's calculate the net pay:
Net pay = Gross pay - Total deductions
Net pay = $358 - $81.39
Net pay = $276.61
Therefore, the net pay for 40 hours worked at $8.95 an hour with deductions for Federal tax of $35.24, Social Security of $24.82, and other deductions of $21.33 is $276.61. SO Option A is correct.
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Note the correct and the complete question is
What is the net pay for 40 hours worked at $8.95 an hour with deductions for Federal tax of $35.24, Social Security of $24.82, and other deductions of $21.33?
A.) $276.61
B.) $326.25
C.) $358.00
D.) $368.91
The value of a company's equipment is $35,000
and decreases at a rate of 6% per year. Write a
function to model this situation, then find the value
of the company's equipment after 3 years.
Answer:
35000(.94)ˣ
29070.44
Step-by-step explanation:
Function:
35000(.94)ˣ (where x= years)
35000(.94)³=29070.44
I will give 15 points
Answer:
llllllllllsgduehidhejeiwhu
Ned thinks that the customer is rude to him because he had to seat her in an area of the bar where it is crowded and loud. Ned takes a ________ view of the customer.
Ned thinks that customer is rude to him because he seat her in area of bar where it's crowded and loud, then Ned takes a Situationist view of the customer, Option (d) is correct.
Ned takes a situationist view of the customer, as he believes that her rudeness is a result of the specific situation in which he had to seat her in a crowded and loud area of the bar.
The situationist perspective emphasizes that behavior is influenced by external-factors rather than personal disposition. According to this viewpoint, Ned attributes the customer's behavior to the uncomfortable environment rather than assuming that she is inherently rude.
By considering the situational factors, Ned demonstrates an understanding that people's behavior can be shaped by their immediate surroundings, suggesting that he does not judge the customer based solely on her personal characteristics.
Therefore, the correct option is (d).
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The given question is incomplete, the complete question is
Ned thinks that the customer is rude to him because he had to seat her in an area of the bar where it is crowded and loud. Ned takes a ________ view of the customer.
(a) Conditionist
(b) Dispositionist
(c) Sexist
(d) Situationist
The chart below represents data collected from 10 eighth grade boys
showing their height in inches and their weight in pounds.
Height
(inches)
60 63 65 61 70 55 58 61 64 57
Weight
(pounds) 125 139 155 136 170 108 116 139 129 121
Which statement best describes the association between height and
weight of the ten boys?
A. The data shows a negative, linear association.
B. The data shows a positive, linear association.
C. The data shows a non-linear association.
D. The data shows no association.
B. The data shows a positive, linear association.
To determine the association between height and weight of the ten boys, we will first observe the data points provided. We can compare the increase or decrease in height with the corresponding increase or decrease in weight to identify a pattern.
Here's a list of height and weight pairs:
(60, 125), (63, 139), (65, 155), (61, 136), (70, 170), (55, 108), (58, 116), (61, 139), (64, 129), (57, 121)
Upon observing these pairs, we can see that as height increases, weight generally increases as well. For example, when height increases from 55 inches to 70 inches, weight increases from 108 pounds to 170 pounds. This pattern can also be seen in other data pairs.
This means that there is a direct relationship between the height and weight of the boys, where taller boys tend to weigh more, and shorter boys tend to weigh less.
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if we want to provide a 99onfidence interval for the mean of a population, what will the confidence coefficient be?
If we want to provide a 99% confidence interval for the mean of a population, the confidence coefficient will be 0.99. This means that there is a 99% probability that the true population mean falls within the calculated interval.
The confidence coefficient for a confidence interval represents the level of confidence we have in our estimate.
In the case of a 99% confidence interval, the confidence coefficient is 0.99. This means that we are 99% confident that the true population mean falls within the calculated interval. The confidence coefficient is derived from the desired level of confidence, which is typically expressed as a percentage.
A higher confidence level corresponds to a larger confidence coefficient. In practical terms, a 99% confidence interval indicates that if we were to repeat the sampling process multiple times and construct 99% confidence intervals, approximately 99% of those intervals would contain the true population mean.
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What is the equation of the following line written in general form? (The y-intercept is -1.)
Answer:
2x-y-1=0
Step-by-step explanation:
.
It is estimated that a driver takes, on average, 1.2 seconds from seeing on obstacle to react by applying the brakes to stop or swerving. How far will a car, moving at 34 miles per hour in a residential neighborhood, travel (in feet) before a driver reacts to an obtacle
To find out how far a car will travel (in feet) before a driver reacts to an obstacle, given that the car is moving at 34 miles per hour in a residential neighborhood, we need to convert the speed of the car from miles per hour to feet per second. This can be done using the conversion factor that 1 mile per hour is equal to 1.46667 feet per second. Therefore, 34 miles per hour is equal to 34 x 1.46667 = 49.86678 feet per second.
We know that the average reaction time of the driver is 1.2 seconds, and we can use the following formula to calculate the distance traveled by the car before the driver reacts to the obstacle:
d = v x t
where d is the distance, v is the velocity, and t is the time taken. Using the formula above, we can calculate the distance traveled by the car before the driver reacts to the obstacle as:
d = 49.86678 x 1.2 = 59.84014 feet
Therefore, the car will travel 59.84014 feet before a driver reacts to an obstacle.
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There were 800 residents in a small town in California. Of the 800 residents, 200 visited a local pharmacy store. Mr. Phillip wants to know the customer satisfaction of the residents who visited the store. He was able to obtain information from all 200 residents. Is this an example of a population or a sample
In this scenario, the information obtained from all 200 residents who visited the store represents a subset of the total population. Therefore, it is an example of a sample.
In statistics, a population refers to the entire group of individuals or objects that we want to study and make inferences about. In this scenario, the population would consist of all the residents of the small town in California, which includes the 800 residents.
However, Mr. Phillip was only able to obtain information from a subset of the population, specifically the 200 residents who visited the store. This subset, known as the sample, is a smaller representative group selected from the population to gather information and make inferences about the larger population.
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Can somebody help me, please?
I just need help with #12
the first attachment is supposed to help and the second attachment has the question I need to be answered. Please show your work
Answer: x = 9.6
=========================================================
Explanation:
We have two smaller right triangles that are glued together so to speak.
The base of the smaller triangle on the left is 5 while the height is h.
Let's use the tangent rule to find the value of h
tan(angle) = opposite/adjacent
tan(55) = h/5
5*tan(55) = h
h = 5*tan(55)
h = 7.14074003371058
Make sure your calculator is in degree mode. That value of h above is approximate.
--------------------------
Now focus on the smaller triangle on the right
It has the same height value h. This side is the adjacent side while x is the hypotenuse.
We'll use the cosine ratio
cos(angle) = adjacent/hypotenuse
cos(42) = h/x
cos(42) = 7.14074003371058/x
x*cos(42) = 7.14074003371058
x = 7.14074003371058/cos(42)
x = 9.6088135029715
x = 9.6
What is 8z+x−5−9z+2
written in simplest form?
Answer:
Simplifying the expression 8z+x−5−9z+2:
8z - 9z + x - 5 + 2
= -z + x - 3
Therefore, 8z+x−5−9z+2 simplified to -z + x - 3.
Write a numerical or variable expression for the quantity: the number of days in w weeks.
w ÷ 7
w + 7
7w
7 – w
Answer:
7w is the answer
7 ×number of weeks
Four hundred draws will be made at random with replacement from the box |[1][3][5][7]| (a) Estimate the chance that the sum of the draws will be more than1,500. (b) Estimate the chance that there will be fewer than 90 [3] 's.
(a) The chance that the sum of the draws will be more than 1,500
(b) The chance that there will be fewer than 90 occurrences of the number 3.
(a) To estimate the chance that the sum of the draws will be more than 1,500, we need to consider the possible combinations and their probabilities. Since there are four numbers in the box, each with an equal chance of being drawn, we can calculate the mean and standard deviation of the draws. With this information, we can use statistical methods such as the normal distribution to estimate the probability of the sum exceeding 1,500.
(b) To estimate the chance that there will be fewer than 90 occurrences of the number 3, we need to calculate the probability of drawing a 3 in each individual draw and then consider the distribution of the number of 3's over the 400 draws. Using statistical techniques such as the binomial distribution, we can estimate the probability of having fewer than 90 occurrences of 3 in the 400 draws.
Both estimations involve applying statistical methods to analyze the probabilities of specific events occurring in the random drawing process. The precise calculations and estimations would require detailed information about the probabilities of drawing each number and the distribution of these numbers in the box.
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The temperature dropped 4°F one hour later. What is the current
temperature if the temperature was 8°F one hour ago?
Answer: 4°F
Step-by-step explanation:
8-4=4
What is the complete factorization of the polynomial below?
O A. (x+2)(x+)(**)
OB. (x-2)(x+)(x-)
C. (x-2)(x+)(x+1)
OD. (x+2)(x+1)(x-1)
The complete factorization of the polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)
What is an equation?
An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.
A polynomial is an expression consisting of coefficients and variables forming an equation.
Given the polynomial:
x³ + 2x² -x - 2
Factorizing:
= (x + 2)(x² - 1)
= (x + 2)(x + 1)(x - 1)
The polynomial x³ + 2x² -x - 2 is equal to (x + 2)(x + 1)(x - 1)
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Brainliest!!!
If you select a card at random from a standard deck of 52 cards, what is the probability of selecting a red card, a black queen, and a 4 or a face card?
so the probability will be: p(red)=2652=0.5 or 50% as we could guess immediatelly.
In a Healthy Jogging event, a few hundred participants were expected to jog 7 800 000 metres altogether. They had jogged 25 000 metres in the first few minutes. How many thousands must be added to 25 000 to make 7 800 000?
we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.
Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.
Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.
We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-
7800000-25000= 7775000m
hence, to make 7800000 from 25000 we have to add 7775000.
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What is the equation of the line that is parallel to y=1/3x+4 and passes through (-3, 1);
A y=-3x – 8
B y= 3x + 10
C y=-1/3x
D y= 1/3x+2
Answer:
Step-by-step explanation:
\(y = \frac{1}{3} x +4\) , \(slope, m_1 = \frac{1}{3}\)
Let the slope of the new line be \(m_2\)
Since the lines are parallel , \(m_1 = m_2\)
\(m_2 = \frac{1}{3}\)
\((x_1, y_1) = (-3, 1) \ , \ m_2 = \frac{1}{3}\\\\Equation \ of \ the \ new \ line : (y - y_1) = m(x - x_1)\)
\(y - 1 = \frac{1}{3}(x -(-3)) \\\\y - 1 = \frac{1}{3}(x +3)\\\\y - 1 =\frac{1} {3}x + 1 \\\\y = \frac{1}{3}x + 2\)
If the circumference of a right cylinder is tripled, the volume will increase by a factor of _____.
Answer:the answer is 9
Step-by-step explanation:
if the highest number in a range is 40 and lowest is 22, an estimate of the standard deviation is 3.
By using standard deviation, it can be concluded that
The given estimate of standard deviation = 3 is not true
What is Standard Deviation?
At first, it is important to know about variance.
Variance is the sum of the square of deviation from mean divided by the total number of observations. Standard Deviation is the square root of variance.
Highest number = 40 and lowest number = 22
Range = 40 - 22 =18
Standard deviation = \(18 \div 4\)
Standard deviation = 4.5
So the above statement is false
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What should I complete the answer with equal to, greater than, or less than?
To complete the blank, the answer will be represented as: 9 × \(1 \frac{4}{5} \) is greater than \(1 \frac{4}{5} \).
We need to convert the number on Left Hand Side and Right Hand Side from mixed fraction to fraction.
LHS = 9 × ((5×1)+4)/5
Solving the brackets
LHS = 9 × (9/5)
Multiply the numbers
LHS = 81/5
Converting the numbers on RHS
RHS = ((5×1)+4)/5
RHS = 9/5
We see that number of LHS is greater than RHS, hence, greater than will be the correct option.
Alternatively, we do not to solve the numbers. As both LHS and RHS contain same mixed fraction, with extra presence of 9 on LHS with multiplication sign. It simply increases the value of LHS number and hence it will be greater.
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Find the domain, range, y intercept(s), intervals where the graph is positive, interval(s) where the graph is decreasing, and interval(s) where the graph is increasing
Step-by-step explanation:
It is worked out step by step.
It has been reported that 80% of federal government employees use e-mail. If a sample of 215 federal government employees is selected, find the mean, variance, and standard deviation of the number who use e-mail.
The mean, variance, and standard deviation of the number of federal government employees who use e-mail are 172, 34.4, and 5.87, respectively.
Given that 80% of federal government employees use e-mail, the probability of an individual employee using e-mail is:
p = 0.80.
If a sample of 215 federal government employees is selected, the number of employees who use e-mail, X, follows a binomial distribution with parameters n = 215 and p = 0.80.
The mean of the number of employees who use e-mail is:
μ = np
= (215)(0.80)
= 172
The variance of the number of employees who use e-mail is:
\(\sigma ^2 = np(1-p) = (215)(0.80)(0.20) = 34.4\)
The standard deviation of the number of employees who use e-mail is:
\(\sigma = \sqrt{(\sigma ^2) } = \sqrt{(34.4) } = 5.87\) (rounded to two decimal places).
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Can someone please help me with this? Thank you!! <3
Answer:
The third prime factor is 5.
Step-by-step explanation:
What you have so far is 18
You need to multiply 18 by something to get 90
The easiest way about finding out what the fact is is to set up this equation
18*x = 90 Divide by 18
x = 90/18
x = 5 5 is a prime factor, you don't need to break it down.
8) When two numbers are multiplied together, the product is the same regardless
of the order of the multiplicands. For example a xb = bxa
A. Associative Property
B. Distributive Property
C. Conmutative Property
Answer:
C. Conmutative Property
If 560 mg is 80% of a dose of medicine, how much is a full dose?
Answer:
PLEASE GIVE BRAINLIEST AND THANKS
700mg
Step-by-step explanation:
560 divided by 80= 7
7 x 100=700mg
What is the solution for x in the equation? 10x-4.5+3x=12x-1.1
Answer:
\( putting \: the \: like \: terms \: together\\ 10x + 3x - 12x = 4.5 - 1.1 \\ x \: = 3.4\)
What is the y-intercept of the function f(x)=4 – 5x?
A:-5
B:-4
C:4
D:-5
Answer:
C. 4
Step-by-step explanation:
Rewrite the equation in terms of y = mx + b
f(x) = -5x + 4