Answer:
0.0274
Step-by-step explanation:
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What is the solution to the equation? 3|x| − 1 = 8
x = 3 or 9
x = −9 or 9
x = −3 or 3
x = −3 or −9
please help
Answer:
x = 3
Step-by-step explanation:
3|x|- 1= 8
=3x = 8 + 1
=3x = 9
=3x/3 = 9/3
x = 3.
Answer:
The equation is 3|x| - 1 = 8. To solve this equation, we first need to consider the absolute value of x.
The absolute value of x is defined as |x| = x for x ≥ 0, and |x| = -x for x < 0.
We have 3|x| - 1 = 8, so we have to consider two cases:
x ≥ 0: in this case, |x| = x and we have 3x - 1 = 8, which gives x = 3 or x = 9.
x < 0: in this case, |x| = -x and we have 3(-x) - 1 = 8, which gives -3x - 1 = 8, and then x = -3 or x = -9.
So the solution to the equation is x = 3 or 9 or x = -3 or -9.
Step-by-step explanation:
The expression (8)(2)(−1.5) represents the change in the scuba diver’s elevation after 8 minutes.
Find the change in elevation.
The change in elevation of the scuba diver after 8 minutes is -24.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers. Unknown variables, numbers, and arithmetic operators make up an algebraic expression. It contains no equality or inequality symbols.
The expression (8)(2)(-1.5) represents the change in the scuba diver's elevation after 8 minutes.
To determine the change in elevation, we need to evaluate the expression.
(8)(2)(-1.5) = (16)(-1.5) = -24
Thus, the change in elevation is -24.
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which of the following refers to a statement that says that a change in one variable tends to follow or be associated with a change in another variable?
Correlation: A correlation is a statement that suggests there is a relationship between two variables, where a change in one variable tends to follow or be associated with a change in another variable.
A correlation is a statement that suggests there is a relationship between two variables. It does not necessarily mean that a change in one variable will cause a change in the other variable, but that a change in one tends to follow or be associated with a change in the other. For example, a correlation could be made between the amount of rainfall a region receives and the number of plants that are able to grow there. If the rainfall increases, then the number of plants that can grow in the region is likely to increase as well. A correlation can be either positive or negative, with a positive correlation meaning that an increase in one variable will likely result in an increase in the other, and a negative correlation meaning that an increase in one variable will likely result in a decrease in the other. Correlation can be used to make predictions, but should not be confused with causation, as correlation does not necessarily imply causation.
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The complete question: which of the following refers to a statement that there is a relationship between two variables that can change in one variable tends to follow or be associated with a change in another variable?
72 is 120% of what number?
Answer:60 percent
Step-by-step explanation:
Step 1) 72 = 120% × Y
Step 2) 72 = 120/100× Y
Multiplying both sides by 100 and dividing both sides of the equation by 120 we will arrive at:
Step 3) Y = 72 × 100/120
Step 4) Y = 72 × 100 ÷ 120
Step 5) Y = 60
a student sets up the following equation to convert a measurement. (the stands for a number the student is going to calculate.) fill in the missing part of this equation. note: your answer should be in the form of one or more fractions multiplied together
The missing part of the equation should be like 1000 g / 1 kg × 100 cm / 1 m
Given,
The set of units used in the final response is different. In particular, kilogram (kg) and meters (m) are converted to gramm(g) and centimeter (cm), respectively (cm). You must multiply the initial value by proportions to achieve this adjustment.
It is crucial to organize these proportions in a way that permits unit cancellation when writing them down. As an illustration, since kg and m are both in the numerator, they must be in the denominators of the conversions.
Proportions:
1 kg = 1,000 g
1 m = 100 cm
Here,
The complete equation is like;
-4.3 × 10⁴ (kg × m / s) × (1000 g / 1 kg) × (100 cm / 1 m) = ? (g × cm / s)
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Complete question is attached
A line that has a slope or 1/5 and passes through (-10,4)
The Equation of the line which has a slope of 1/5 and passes through (-10,4) will be [tex]y = \frac{1}{5} x + 6[/tex] .
Given, We have the slope of the line = 1/5 and a point (-10,4) though which the line passes. We know that the form of a linear line is y=mx + c (slope intercept form) where m is the gradient/slope of the line and c is the point where it intercepts the y axis on the graph. We can directly put the value slope in the place of m.
To find C , we can put the coordinates of the given point in the equation to solve for C. Therefore :
⇒ y = mx + c
⇒y = 1/5 x + c
⇒4 = 1/5 x (-10) + c
⇒4 = -2 + c
⇒ 4 +2 = c
⇒c = 6
Putting all the values in equation gives us the linear equation of the line : [tex]y = \frac{1}{5} x + 6[/tex]
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The complete question is :
What is the locus/ linear equation/ equation of the line that has a slope of 1/5 and passes through coordinates (-10,4)?
Anna bought a bike horn. She paid $11.59 and received $9.67 in change. How much did the bike horn cost?
Answer:
$1.92
Step-by-step explanation:
$11.59 - $9.67 = $1.92
Which numbers lie between -2 and -3 on the number line? Select all that apply.
Answer:
-2.5, -2.02, -11/4
Step-by-step explanation:
Any number beginning with -2 will be the answer. -11/4 is -2.75 when converted to a decimal!
Find the volume of a square based pyramid with a base length of 9 and a height of 11
Answer: It is 36cm the height of it and the length W times L
Step-by-step explanation:
a customer service representative must sped different amounts of time with each customer to resolve various concerns the amount of time spent with each customer can be modeled by the following distribution find the percentile
The value of [tex]P$$(2 < x < 10)$[/tex] is 0.5350
What is meant by percentile?A score at or below which a given percentage falls is known as the k-th percentile in statistics, as is a score below which a given percentage k of scores in the frequency distribution falls. A percentile is the difference between a given score and the scores of the other members of a group. The proportion of other scores that a given score outperformed is displayed. In the 85th percentile, for instance, signifies that your test result of 75 is higher than the scores of 85% of other students.The exponential distribution is the probability distribution of the interval between events in a Poisson point process, that is, an event-producing process where events happen continuously and independently at a fixed average rate. It is an example of the gamma distribution.As per the Function, [tex]$P(x < x)=1-e^{-m x}$[/tex]
Where [tex]$x \sim E x p(0.2)$[/tex]
Therefore, [tex]$m=0.2$[/tex]
[tex]$$P(2 < x < 10)=P(x < 10)-P(x < 2)$$[/tex]
Applying all data
[tex]& \mathrm{P}\left(2 < \mathrm{x} < 10=\left(1-e^{0.2 \times 10}\right)-\left(1-e^{0.2 \times 2}\right)\right. \\[/tex]
=0.6703-0.1353=0.5350
The complete question is,
A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be
modelled by the following distribution: X-Exp(0.2)
Find [tex]$P(2 < x < 10)$[/tex].
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inquiry HOW can you use a bar diagram to show a percent of change?
A bar diagram can be used to show a percent of change by the method of comparing two bars.
What is a bar diagram?
Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.
A bar diagram can be used to show a percent of change by comparing the size of two or more bars. The bars can represent the original value and the final value, and the difference in size between the two bars will indicate the percent of change.
For example, if the original value is represented by a bar that is 10 units tall and the final value is represented by a bar that is 12 units tall, the percent of change would be 20% (the difference in height between the two bars divided by the original value).
The percent of change can also be labeled or annotated on the graph.
Therefore, bar graph is helpful in denoting the percent of change.
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solve:
g(16)=-1/2x+5
pls show work
The function g(16) = -1/2 x + 5 is solved by substitution to get -3
What is substitution as used in math?The process of changing an algebraic letter to it's value corresponds to the procedure known as substitution.
In the problem, the equation g(16) = -1/2 x + 5,
Considering the equation, the value of x is 16. The letter x will be replaced by 16 in the equation
g(16) = - 1/2 x + 5
g(16) = - 1/2 * 16 + 5
g(16) = - 8 + 5
g(16) = -3
Substituting x = 16 in the equation g(16) = -1/2 x + 5 results to a solution of -3
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if a student scored 84, 72, and 83 on the quizzes, exams, and final respectively, calculate the student's final grade. express your answer to three significant figures.
The student's final grade is 78.9.
The final grade of the student is determined using the weight average. A weighted average refers to a type of mean that gives differing importance to the values in a dataset. It is used when the relative significance of values in a dataset are to be considered. The formula for finding the weighted average is the sum of all the variables multiplied by their weight, then divided by the sum of the weights.
Based on the provided information, as student score 84 on quizzes with weighted 30%, 72 on exams with weighted 40%, and 83 on final exam with weighted 30%, hence
Final grade = (84*0.3 + 72*0.4 + 83* 0.3)/(0.3 + 0.4 + 0.3) = (25.2 + 28.8 + 24.9)/1 = 78.9
Note: The question is incomplete. The complete question probably is: For a chemistry class, a student's grades are weighted as follows: quizzes are 30%, exams are 40%, and the final exam is 30%. If a student scored 84, 72, and 83 on the quizzes, exams, and final respectively, calculate the student's final grade. express your answer to three significant figures.
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Answer:
79.6
Step-by-step explanation:
(86x.3)+(73x.4)+(82x.3)
A formula for calculating the magnitude of an earthquake is M=23log(EE0)
that uses the common (base 10) logarithm. This is called the Moment Magnitude Scale (MMS), an alternative to the more well known Richter Scale. One earthquake has magnitude 3.9
on the MMS. If a second earthquake has 700
times as much energy as the first, find the magnitude of the second quake.
Round to the nearest hundredth.
The magnitude of the second earthquake was
The magnitude of the second earthquake is given as follows:
5.80.
How to obtain the magnitude of the second earthquake?The magnitude of an earthquake is given by the equation presented as follows:
[tex]M = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]
The first earthquake has a magnitude of 3.9, hence it's energy is obtained as follows:
[tex]3.9 = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]
[tex]\log{\left(\frac{E}{E_0}\right)} = \frac{3.9 \times 3}{2}[/tex]
[tex]\log{\left(\frac{E}{E_0}\right)} = 5.85[/tex]
As the power of 10 is the inverse function of the logarithm, we have that:
[tex]\frac{E}{E_0} = 10^5.85[/tex]
[tex]\frac{E}{E_0} = 707946[/tex]
[tex]E = 707946E_0[/tex]
The second earthquake has 700 times as much energy as the first, hence the energy is of:
[tex]E = 700 \times 707946E_0[/tex]
[tex]E = 495562049E_0[/tex]
Then the magnitude of the second earthquake is given as follows:
[tex]M = \frac{2}{3}\log{\left(\frac{495562049E_0}{E_0}\right)}[/tex]
[tex]M = \frac{2}{3}\log{(495562049)}[/tex]
M = 5.80.
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There are integers b, c for which both roots of the polynomial x^2-x-1 are also roots of the polynomial x^5-bx-c. Determine the product bc.
It is discovered that the phrase under the division symbol is 3x2 - (b - 2)x - c, meaning that b = 5 and c = 3.
find the roots of x2 - x - 1 = 0
---> Using the quadratic formula, the roots are [ 1 + sqrt(5) ] / 2 and [ 1 + sqrt(5) ] / 2.
Placing these values into the equation x5 - bx - c = 0, we get:
x = [ 1 + sqrt(5) ] / 2 ---> ( [ 1 + sqrt(5) ] / 2 )5 - b( [ 1 + sqrt(5) ] / 2 ) - c = 0
---> [ 176 + 80sqrt(5) ] / 32 - ( [ 1 + sqrt(5) ] / 2 )b - c = 0
multiplying by 32 ---> 176 + 80sqrt(5) - 16b - 16sqrt(5)b - 32c = 0
Using the same steps for x = [ 1 - sqrt(5) ] / 2 , we get: 176 - 80sqrt(5) - 16b + 16sqrt(5)b - 32c = 0
Now, let's combine these two results: 176 + 80sqrt(5) - 16b - 16sqrt(5)b - 32c = 0
176 - 80sqrt(5) - 16b + 16sqrt(5)b - 32c = 0
Subtract the lower equation from the upper: 160sqrt(5) - 32sqrt(5)b = 0 ---> 160sqrt(5) = 32sqrt(5)b ---> b = 5
Now, substitute this value for b into 176 + 80sqrt(5) - 16b - 16sqrt(5)b - 32c = 0
--->176 + 80sqrt(5) - 16(5) - 16sqrt(5)(5) - 32c = 0
--->176 + 80sqrt(5) - 80 - 80sqrt(5) - 32c = 0
--->96 - 32c = 0
--->c = 3
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Complete the missing values in the solution to the equation.
The missing value in the solution to the equation is 4. The value of x is 4 and y is -6 which is (4, -6).
What is solution to a equation?A solution to an equation is a value or values that make the equation true. For example, if the equation is x + 3 = 7, then the solution to the equation would be x = 4.
To solve an equation, you must use a combination of addition, subtraction, multiplication, division, and algebraic manipulations to isolate the unknown variable. For instance, to solve the equation x + 3 = 7, you would subtract 3 from both sides of the equation to find x = 4.
It is important to note that an equation may have more than one solution. For example, the equation x2 + 4 = 0 has two solutions, x = 2 and x = -2.
In some cases, equations may not have a solution. This happens when the equation is not true for any value of the unknown variable. For example, the equation 0 = 1 is not true for any value of x, so it does not have a solution.
In summary, a solution to an equation is a value or values that make the equation true. To solve an equation, you must use a combination of addition, subtraction, multiplication, division, and algebraic manipulations to isolate the unknown variable. An equation may have multiple solutions or no solution at all.
The given equation is 4x + y = 10.
We have the value of y is -6,
To find the value of x, using the equation 4x + y = 10
4x - 6 = 10
4x = 10 +6
4x = 16
x = 4
The missing value in solution is 4.
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Every week, Enrique walks one mile each day for 4 days of the week. He can usually walk 1 mile in about 14 to 16 minutes.
Estimate the number of minutes Enrique will spend walking over an 8 week period. Explain how you determined your estimate.
Write an equation that represents the number of miles, m, Enrique walks in w weeks.
An equation that represents the number of miles, m, Enrique walks in w weeks will be N = 32T.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that every week, Enrique walks one mile each day for 4 days a week. He can usually walk 1 mile in about 14 to 16 minutes. Estimate the number of minutes Enrique will spend walking over an 8-week period.
The expression for the total time will be calculated as:-
N = 32 x T
Here, T is the time in minutes for running per mile.
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16 years ago, Thomas invested $3,000 into a bank account with a 5% return compounded annually. Which of the following equations indicates the total amount of money Thomas has after t years of his original investment? A=3,000(.5)^tA=3,000(1.05)^t A = 3,000(.5)^(1/16)A = 3,000(1.05)^(1/16)
Thomas invested $3,000 into a bank account with a 5% interest return compounded annually. then the following equations indicates the total amount of money 3000(1.05)^1/16
Thomas invested $3,000 into a bank account with a 5% return compounded annually.
A: represents the current balance or compound amount in the account.
P: represents the principal (the original amount deposited).
R: annual interest rate (in decimal form).N: the number of times per year that interest is compounded .T: time in years the money has been invested.
The formula of interest is A=P (1+r)ⁿ
A=Final amount
P= Principal ( deposit invested)
r= interest rate
n= time
So, in this case
P=$3,000
r= 5% or 0.05
n=1/ 16
Replacing
A=3000(1+0.05)^1/16
A=3000( 1.05)^1/16
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Question:
(a) Find the equation for the family of linear functions with slope 2 and sketch several members of the family.
(b) Find an equation for the family of linear functions such that f(2)=1 and sketch several members of the family.
(c) Which functions belong to both families?
Slope-intercept form
Equation of slope-intercept form is given as y=mx+b where m is the slope of the line and c is the y-intercept. m is used to measure the steepness of the graph. This form is simply the method of writing the equation of a line so that the slope and y-intercept are rapidly apparent.
For a family of linear functions with slope 2, the equation is y = 2x + b, where b is the y-intercept. For a family of linear functions such that f(2) = 1, the equation is y = x + b, where b is the y-intercept. Both families of linear functions have the same equation, y = x + b, and all functions belonging to both families have a slope of 1 and a y-intercept of b.
(a) The equation for the family of linear functions with slope 2 is y = 2x + b, where b is the y-intercept. To sketch several members of the family, plot several points (x, y) with the equation, then connect the points to form a line.
(b) The equation for the family of linear functions such that f(2) = 1 is y = x + b, where b is the y-intercept. To sketch several members of the family, plot several points (x, y) with the equation, then connect the points to form a line.
(c) The equation for both families of linear functions is y = x + b, where b is the y-intercept. All functions belonging to both families have a slope of 1 and a y-intercept of b.
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A 300g ball collides with a wall. The figure(Figure 1)shows the ball's velocity and the force exerted on the ball by the wall. What is vfx, the ball's rebound velocity?
The rebound velocity of the ball, vfx, is 10.0 m/s, calculated using the equation vfx = 2vix - viy, where vix is the initial velocity along the x-axis (4.0 m/s) and viy is the initial velocity along the y-axis (-2.0 m/s).
Using the equation vfx = 2vix - viy, the rebound velocity of the ball is calculated as follows:
vfx = 2(4.0 m/s) - (-2.0 m/s) = 10.0 m/s
1. Identify the initial velocity, vix, of the ball along the x-axis, which is 4.0 m/s.
2. Identify the initial velocity, viy, of the ball along the y-axis, which is -2.0 m/s.
3. Use the equation vfx = 2vix - viy to calculate the rebound velocity of the ball, vfx.
4. Calculate vfx = 2(4.0 m/s) - (-2.0 m/s) = 10.0 m/s.
The rebound velocity of the ball is 10.0 m/s.
The rebound velocity of the ball, vfx, is 10.0 m/s, calculated using the equation vfx = 2vix - viy, where vix is the initial velocity along the x-axis (4.0 m/s) and viy is the initial velocity along the y-axis (-2.0 m/s).
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You invest $1,200 that is compounded continuously at 9% for 10 years. What is the equation you use?
Answer:
FV = $1,200 * e^(0.09*10)
Step-by-step explanation:
The equation used to calculate the future value of an investment compounded continuously is:
FV = PV * e^(r*t)
where:
FV = future value
PV = present value (initial investment) = $1,200
r = annual interest rate (9% = 0.09)
t = number of years (10 years)
So, the future value of the investment would be:
FV = $1,200 * e^(0.09*10)
P( – 3, – 5) after a reflection over the y-axis.
Answer: 3,-5
Step-by-step explanation:
Answer: (3, -5)
......................................
Before women were allowed to vote, both men and women organized, protested, and marched. Finally, in 1920, the 19th Amendment to the Constitution gave women the right to vote.
How does this example support the author's main purpose in the book?
It shows how citizens' actions affect today's issues.
It analyzes how citizenship was different in the past.
It explains what an amendment to the Constitution is.
It shows that citizens' actions can change society.
Answer:
it analyses how citizenship was different in the past
Which word is used incorrectly?
The mailperson's job is to put the envelope's in every mailbox on the block.
OÀ
A
O
O
B
C
D
every
mailperson's
block
envelope's
The word used incorrectly in the sentence is "envelopes".
The word used incorrectly in the sentence is "envelopes". The comment should be "envelopes" instead. This is because "envelopes" is a plural noun, referring to more than one envelope. The apostrophe in "envelopes" implies possession, indicating that the envelopes belong to someone or something, but it is not necessary for this context.
Hence, the correct sentence should be "The mailperson's job is to put the envelopes in every mailbox on the block."
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What is the formula for computing the present value of F in a financial transaction involving compound interest?
Answer: A
Step-by-step explanation:
Present value of F (P) = Compound amount (F) (1+periodic rate)
a model of a car is 4 inches long. if the actual car is 10 feet long, find the scale of the model. a. 4 in
Scale of the model is found to be 1 : 30 using the ratio method.
A model of a car is 4 inches long.
The actual car is 10 feet long.
4 in. = 10 ft. ( since given )
Divide both sides by 4, we get
∴ 1 in. = 2.5 ft.
We use the ratio here to compare the lengths of the actual car and its model.
A ratio scale is a quantitative measurement scale that is used to compare numbers.
The model is 4 inches long while the actual car is 10 feet long.
One foot is equal to 12 inches. Therefore the car in terms of inches is:
10 feet × 12 inches = 120 inches
The ratio scale is the length of the model of the car : length of the actual car
= 4 : 120
= 1 : 30
Therefore the scale of the model is 1: 30.
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use the following dataset to answer the question 11 to 14
History class final test scores
79, 82, 85, 91, 97, 73, 88, 87, 85, 92, 90, 85, 86, 91, 94, 85, 92
what is the average class score? Round your answer to the nearest whole number.
Answer:
82
Step-by-step explanation:
average class score=total number of test scores/number of test scores
sum up the scores 79+82+85+91+97+73+88+87+85+92+90+85+86+91+94+85+92
=1482÷18=82.33333
=82
Mary pays income tax according to the graduated schedule shown below.
A 3-column table with 6 rows. Column 1 is labeled If taxable income is over with entries 0 dollars, 7,825 dollars, 31,850 dollars, 77,100 dollars, 160,850 dollars, 349,700 dollars. Column 2 is labeled but not over with entries 7,825 dollars, 31,850 dollars, 77,100 dollars, 160,850 dollars, 349,700 dollars, no limit. Column 3 is labeled the tax is with entries 10 percent of the amount of 0 dollars, 782 dollars and 50 cents plus 15 percent of the amount of 7,825 dollars, 4,386 dollars and 25 cents plus 25 percent of the amount of 31,850 dollars, 15,698 dollars and 75 cents plus 28 percent of the amount over 77,100 dollars, 39,148 dollars and 75 cents plus 33 percent of the amount of 160,850 dollars, 101,469 dollars and 25 cents plus 35 percent of the amount over 349,700 dollars.
If Mary’s taxable income is $68,562, how much income tax does she owe, rounded to the nearest dollar?
a.
$13,564
b.
$17,140
c.
$21,527
d.
$12,349
Mary owes $13564 income tax.
What is income tax?Governments apply income taxes as a sort of tax on the income produced by people and businesses under their control. Government duties, public services, and citizen goods are all paid for through income tax revenue.
Given that the taxable income is $68,562.
Income tax is the tax charged on an individual's or entity's income
Using the table as a guide, $68,562 falls within the income range $31,850 - $77,100
So, the tax is $4386 added to 25% of the excess over $31850
This is calculated as:
tax = $4386 + 25%(income - 31,850)
In our case,
income = $68562
Substitute $68,562 for income
Tax = $4386 + 25%(68,562 - 31,850)
Solve the expression in the bracket
tax = 4386 + 9178
Add the terms of the expression
tax = 13,564
therefore, Mary owes $13564 in income tax.
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Let f be the function given by f(t) =3/1+t^2 a. Find the first four nonzero terms and the general term for the power series expansion of f(t) about t=0. b. Given g(x)=ſ8(t)dt , find the first four nonzero terms and the general term for the power series expansion of g(x) about x=0. c. Find the interval of convergence of the power series for g(x).
a) The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6
b) The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7.
c) The interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).
What is a function?
A function is a mathematical relationship between two variables, often denoted as "f(x)" or "y = f(x)". A function assigns a unique output to each input within its domain. In other words, for every value of x, there is a corresponding value of y, and each value of x can only correspond to one value of y.
a. To find the first four nonzero terms and the general term for the power series expansion of f(t) about t=0, we need to find the Taylor series of f(t) centered at 0. The general term of a Taylor series is given by:
f(t)^(n) / n! * (t-0)^n
The Taylor series of f(t) = 3/(1+t^2) centered at 0 is:
f(t) = 3 - 3t^2 + 3/3t^4 - 3/5t^6 + ...
The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6
b. To find the first four nonzero terms and the general term for the power series expansion of g(x) = ∫f(t)dt about x=0, we need to integrate the Taylor series of f(t) term by term.
g(x) = ∫f(t)dt = (3t - 3/3t^3 + 3/5t^5 - ...) from 0 to x
g(x) = 3x - 3/3x^3 + 3/5x^5 - ...
The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7
c. The interval of convergence of a power series is the set of values of x for which the series converges. To find the interval of convergence for g(x), we can use the ratio test.
The ratio test states that if the limit of |a(n+1)x^(n+1)|/|a(n)x^n| as n approaches infinity is less than 1, the series converges for all x.
|3/7x^7|/(|3/5x^5|) = |x^2|/(|3/5|) < 1 when |x| < sqrt(5/3)
So, the interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).
Hence,
a) The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6
b) The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7.
c) The interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).
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2. question 2 fill in the blanks to make the print prime factors function print all the prime factors of a number. a prime factor is a number that is prime and divides another without a remainder.
A Prime factor is a natural number that has only two factors namely 1 and the number itself. One is not a prime number. Prime factors are odd in nature except for 2 because 2 is the only even prime factor. Example of prime factors are 2,3,5,7,11 etc
def print_prime_factors(number):
factor = 2
while factor <= number:
# Check if factor is a divisor of number
if number % factor == 0:
# If it is, print it and divide the original number
print(factor)
number = number / factor
else:
# If it's not, increment the factor by one
factor+=1
return "Done"
print_prime_factors(100)
Complete question- Above mentioned is the correct code with all blanks filled.
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