Answer: To find the domain of a function, you need to identify all the possible input values (x) for which the function produces a valid output (y). In other words, you need to find the set of all values of x for which the function is defined and produces real outputs.
Step-by-step explanation: Here are the general steps to find the domain of a function:
Look for any values of x that could lead to undefined results. For example, if the function involves a square root, the value inside the square root cannot be negative, so you need to ensure that the expression inside the square root is non-negative.
Look for any values of x that could lead to division by zero. For example, if the function involves a fraction, the denominator cannot be zero, so you need to ensure that the denominator is not equal to zero.
Look for any other restrictions on the input values based on the definition of the function. For example, some functions may require that x be a certain type of number, such as an integer or a positive real number.
Write the domain of the function as a set of possible input values. For example, you might write the domain as an interval of real numbers or a set of discrete values.
It is important to note that some functions may have restricted domains due to the nature of the function, while other functions may have unrestricted domains that encompass all real numbers.
Question 2 of 5
What is this expression in simplified form?
[tex]\sqrt[3]32[/tex]
There are 7 apple pies.
All of the pies are the same size.
3 people will share the pies equally.
How much pie will each person get?
A.
3
7
of a whole pie
B.
3
4
of a whole pie
C.
4
3
of a whole pie
D.
7
3
of a whole pie
The fraction for the given situation is 7/3. Therefore, option D is the correct answer.
Given that, there are 7 apple pies.
3 people will share the pies equally.
Equal share of pie = Number of apple pies/Number of people
Equal share of pie = 7/3
So, the fraction is 7/3 of a whole
Therefore, option D is the correct answer.
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If z is a standard normal variable, find the probability.
The probability that z lies between 0 and 3.01
Group of answer choices
0.9987
0.1217
0.5013
0.4987
The probability that z lies between 0 and 3.01 is: 0.9987 - 0.5 = 0.4987 So, the answer is 0.4987. To find the probability that z lies between 0 and 3.01 for a standard normal variable, you need to look up the values in a standard normal (z-score) table or use a calculator with the normal distribution function.
For z = 0, the probability is 0.5 (due to symmetry of the standard normal distribution). For z = 3.01, the probability is approximately 0.9987. To find the probability between 0 and 3.01, subtract the probability of z = 0 from the probability of z = 3.01.
0.9987 - 0.5 = 0.4987
So, the probability that z lies between 0 and 3.01 is approximately 0.4987. Your answer is 0.4987.
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Help me find what X is
Answer:
x = 68°
Step-by-step explanation:
There is Two Option:
Option One: Looking at the side length we can determine that the triangle is an isosceles triangle. Which mean two angle/side are the same.
Use the Degree Angle to solve for x.
56 + 56 + x = 180
x + 112 = 180
x = 68°
Option Two: Using Law of Sine
[tex]\frac{A}{sin(A)}=\frac{B}{sin(B)} =\frac{C}{sin(C)}[/tex]
[tex]\frac{4.5}{sin(x)} =\frac{4}{sin(56)}[/tex]
[tex]sin(x)=\frac{sin(56)}{4} *4.5[/tex]
[tex]x=sin^{-1}(\frac{4.5*sin(56)}{4})[/tex]
x = 68°
You will construct the circumcenter. You will need to construct the perpendicular bisectors of AB, BC, and/or AC. Then find the intersection of the perpendicular bisectors to find the point that is equidistant to A, B, and C.
To construct the circumcenter of triangle ABC, we need to find the point that is equidistant to its three vertices A, B, and C. We can do this by constructing the perpendicular bisectors of the sides AB, BC, and AC, and finding their intersection point.
Here are the steps to construct the circumcenter:
Draw triangle ABC.
Construct the perpendicular bisectors of sides AB and BC. To do this, find the midpoint of each side (label them M and N, respectively), and draw a perpendicular line to each side that passes through its midpoint. Label the points where the perpendicular bisectors intersect AB and BC as P and Q, respectively.
Construct the perpendicular bisector of side AC using the same method. Label the point where this bisector intersects AC as R.
Draw lines connecting each vertex of the triangle to the intersection point of the perpendicular bisectors. These lines are the radii of the circumcircle.
The intersection point of the perpendicular bisectors is the circumcenter of triangle ABC. Label this point as O.
Now, we have constructed the circumcenter O of triangle ABC, which is the point that is equidistant to its three vertices A, B, and C.
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Suppose you borrow $197,500 on a 30 year adjustable rate mortgage loan. The fixed period is five years and the initial interest rate is 4.25%.
Question 2
Assume that you make all payments exactly as scheduled. How much will you owe at the end of the five year fixed period?
Answer:
Assuming that the loan has monthly payments, the total number of payments in the 30-year loan would be 30 x 12 = 360.
To calculate how much is owed at the end of the five-year fixed period, we need to first determine how much of the principal (the borrowed amount) will be paid off during that time.
Using an amortization calculator, we can determine that with a 4.25% interest rate and monthly payments of $972.38, the principal paid off after five years will be approximately $25,732.37.
At the end of the five-year fixed period, the remaining principal balance will be $197,500 - $25,732.37 = $171,767.63. This will be the amount owed at the end of the fixed period.
Step-by-step explanation:
Help me please I’m stuck
Answer:
Step-by-step explanation:
5 +2/10
since 5 is on outside you can just add them
Let A and B be two events. Suppose that P (A)=0.45 and P(B)=0.16.
(a) Find ,P(A or B) given that and are independent.
(b) Find ,P(A or B) given that and are mutually exclusive.
Answer: The answer is 0.16. i hope I helped you god bless you.
Step-by-step explanation:
The Federal Pell Grant Program gives grants to low-income undergraduate students. According to the National Postsecondary Student Aid Study conducted by the U.S. Department of Education in 2008, the average Pell grant award for 2007-2008 was $2,600. We wonder if the mean amount is different this year for Pell grant recipients at San Jose State University. Suppose that we randomly select 50 Pell grant recipients from San Jose State University. For these 50 students, the mean Pell grant award is $2,450 with a standard deviation of $600. Let μ = the mean amount of Pell grant awards received by San Jose State University Pell grant recipients this year. We test the following hypotheses. The sample size is greater than 30, so a t-model is a good fit for the sampling distribution. Use this information to answer the next two questions.
a. What is the t-test statistic? If necessary, round to two decimal places.
b. What is the P-value?
a. To find the t-test statistic, we first need to calculate the standard error of the mean using the formula: standard deviation / square root of sample size. In this case, the standard error of the mean is 600 / square root of 50, which is approximately 84.85.
Then, we can calculate the t-test statistic using the formula: (sample mean - hypothesized population mean) / standard error of the mean. In this case, the t-test statistic is (2450 - 2600) / 84.85, which is approximately -1.77.
b. To find the P-value, we need to consult a t-distribution table or use statistical software. Using a two-tailed t-test with 49 degrees of freedom (50-1), we find that the P-value associated with a t-test statistic of -1.77 is approximately 0.084. Therefore, there is a 8.4% chance of obtaining a sample mean of $2,450 or less if the true mean amount of Pell grant awards received by San Jose State University Pell grant recipients this year is actually $2,600.
Note: A common threshold for statistical significance is a P-value of less than 0.05. Since the P-value in this case is greater than 0.05, we cannot reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean amount of Pell grant awards received by San Jose State University Pell grant recipients this year is different from $2,600.
a. To find the t-test statistic, we will use the following formula:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
Here, sample mean = $2,450, population mean = $2,600, sample standard deviation = $600, and sample size = 50.
t = ($2,450 - $2,600) / ($600 / sqrt(50))
t = (-$150) / ($600 / 7.071)
t = (-$150) / $84.85
t ≈ -1.77
The t-test statistic is approximately -1.77.
b. To find the P-value, we need to use a t-distribution table or software to determine the probability of obtaining a t-test statistic as extreme or more extreme than our calculated value. We are doing a two-tailed test, so we need to find the area in both tails.
Looking up the t-test statistic -1.77 in a t-distribution table with 49 degrees of freedom (sample size - 1), we find the P-value is between 0.05 and 0.10. For a more accurate P-value, use software or an online calculator.
So, the P-value is between 0.05 and 0.10.
Find the area of the figure below
The area of the shape is 89m²
What is area of shape?The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.
The original shape is a rectangle and a triangle cut out from it.
The area of the shape = area of rectangle - area of triangle
area of rectangle = 13× 8
= 104m²
Area of the triangle = 1/2bh
= 1/2 × 5 × 6
= 5×,3
= 15m²
therefore area of the shape = 104-15 = 89m²
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Look at how we construct a confidence interval for a population proportion. One sigma/(sqrt(n)) thing to notice is the effect of sample size on standard error which will effect
the length of the confidence interval. Larger sample sizes will lead to smaller standard errors.
hat p plus/minus z * sigma/(sqrt(n))
Is the following: True or False?
All other things being equal in constructing a confidence interval for a population proportion, the confidence interval constructed using a sample size of n = 500a compared to n = 200 will be a better estimate for the population proportion. That is, the confidence interval will have a shorter length.
True
False
The following statement is true. All other things being equal in constructing a confidence interval for a population proportion, the confidence interval constructed using a sample size of n = 500a compared to n = 200 will be a better estimate for the population proportion.
That is, the confidence interval will have a shorter length. A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain level of confidence, based on a sample of data. It is commonly used in inferential statistics to estimate the range of values for a population parameter, such as a mean or proportion, based on sample data.
A confidence interval is typically represented by two values, an upper limit and a lower limit, and a confidence level, expressed as a percentage. The confidence level indicates the probability that the true population parameter falls within the interval. For example, a 95% confidence interval indicates that there is a 95% probability that the true population parameter falls within the interval.
The width of the confidence interval depends on the sample size, the variability of the data, and the chosen level of confidence. As the sample size increases, the width of the interval decreases, while increasing the level of confidence increases the width of the interval.
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an online clothing company sells custom sweatshirts. The company charges $4.99 for shipping plus 6 dollars for each sweatshirt. Write a linear function rule that models cost y in dollars for any number of sweatshirts X
Please hurry I’m giving a lot of points
Answer:
6.50x+3.99
Step-by-step explanation:
every order of sweat shirts is charged 3.99
each individual sweatshirt costs 6.50 therefore x being the number purchased times 6.50 is the cost of the sweatshirts that plus the 3.99 is your total cost
Answer: y = $6x + $4.99
Step-by-step explanation:
$4.99 is only used once since you're shipping one load. There are x sweatshirts at the price of $6 each. Y is the total cost when you plug in an amount of sweatshirts for x.
hope this helps!
brainliest+100 points
read instructions
Answer:
16 i think
Step-by-step explanation:
Answer:
We know that
Area of rectangle: Length" Breadth
For Question
Area of respective Rectangle are:
A : 13*(x+12) ft²
B : 10*8=80ft²
C : (x+10)*7 ft²
D : (x+10)*(10-7)=(x+10)*3 ft2
E : 6*6 =36 ft²
F : 7*6= 42 ft²
G : (x+8)*(x+7) ft²
H : (3x+23)*(2x+17) ft²
I. : (2x+16)*(x+8) ft²
what would the new ordered pair of M' be after reflecting the shape over the x-axis
Answer: The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. What is this?
Step-by-step explanation: I would hope this helps! a picture would better help me understand your question!!
3
Victoria bought an area rug for her living room. The rug is a rectangle with
a width of 32 feet and a length of 60 feet. How much money will he spend
if carpet costs $5.35 per square foot?
Answer:
$10272
Step-by-step explanation:
You want the cost of a rug 32 ft by 60 ft at the rate of $5.35 per square foot.
AreaThe area of the rug is ...
32 ft × 60 ft = 1920 ft²
CostAt $5.35 per square foot, the cost is ...
(1920 ft²)($5.35/ft²) = $10,272
The cost of the area rug will be about $10,272.
A square pyramid is sliced in such a way that the plane passes through all five faces of the pyramid, what is the resulting cross section?
When a square pyramid is sliced in such a way that the plane passes through all five faces of the pyramid, the resulting cross-section is a pentagon.
The square pyramid has a square base and four triangular faces, so when a plane passes through all five faces, it intersects each of the four triangular faces to form a trapezoid. These four trapezoids combine to form a pentagon.
The resulting cross-section can vary depending on the angle at which the plane intersects the pyramid. If the plane intersects the pyramid at a right angle to the base, the resulting pentagon will be a regular pentagon. If the plane intersects the pyramid at an angle, the resulting pentagon will be irregular.
In summary, when a square pyramid is sliced in such a way that the plane passes through all five faces of the pyramid, the resulting cross-section is a pentagon, which can be regular or irregular depending on the angle of intersection.
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HELPPPPP
Sparrowtown Street and Seaside Avenue intersect. If the diagonal distance across the
intersection is 8 meters and Sparrowtown Street is 5 meters wide, how wide is Seaside
Avenue? If necessary, round to the nearest tenth.
Submit
meters
The wideness of Seaside Avenue is 6.2 meters wide.
How to find the wideness of the Seaside AvenueThe wideness is calculated using Pythagorean theorem
Let's call the width of Seaside Avenue "x".
The description matched a right triangle where the diagonal distance is the hypotenuse and the two legs are 5 and x. The using Pythagoras theorem we have that
5² + x² = 8²
Simplifying and solving for x
x² = 8² - 5²
x² = 39
x ≈ 6.2
Therefore, Seaside Avenue is approximately 6.2 meters wide.
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What is the surface area of the cylinder with height 8 km and radius 7 km? Round your answer to the nearest thousandth.
Answer:
301.593
Step-by-step explanation:
surface area = circumference x height + 2 x circle area
= 4 x 2 x π x 8 + 2 x π x 4^2
= 25.1327412287 x 8 + 6.28318530718 x 16
= 201.06192983 + 100.530964915
= 301.592894745 ≈ 301.593
A nature trail is 7/10 of a mile long’ lola has walked 1/5 of a mile so far, how many miles does she have left?
Step-by-step explanation:
Im a fifth grader so I gave it my best shot and there might be more steps to it but I'm pretty sure its 2/10
Which formula can be used to find the volume, V , of the opposite solid figure represented below
Answer:
Step-by-step explanation:
b
4. Ms. Horvath brought 7 cows averaging 1,250 pounds, 15 steers av- eraging 595 pounds, and 12 heifers averaging 545 pounds to your livestock market. The cows sold for $61.50 per 100 pounds (cwt), the steers for $106 per cwt, and the heifers for $97.75 per cwt. The selling expenses are shown in picture
What did the livestock market pay Ms. Horvath for the cattle?
The amount that the livestock market pay Ms. Horvath for the cattle is $5161.44.
How to calculate the amountThe overall total of selling expenses incurred for cows totaled to $76.06 -- comprised of commission, head charge, beef promotion, and insurance costs, along with vet-testing. In order to calculate the expenditure for steers, we multiplied 0.03 with 630.17, 3 with 15, 1 with 15, and 0.00065 with 630.17; resulting in the final amount of $79.32.
For heifers, similar procedures resulted in a total cost of 64.32, attained by multiplying 0.03 with 532.44, 3 with 12, 1 with 12, and 0.00065 with 532.44.
The gross sum paid to Ms. Horvath amounted to $5,161.44 after subtracting from her cumulative sale price - 7 times 768.75, 15 times 630.17, and 12 times 532.44 - the aggregated total of the running expenditures: $219.70 (or $76.06 + $79.32 + $64.32).
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28. How do cyclic redundancy checks work?
Cyclic redundancy checks work by using a generator polynomial to calculate a unique value (CRC) based on the original data. This value is then appended to the data and verified by the receiver to ensure data integrity.
Cyclic Redundancy Checks (CRC) work as an error-detecting method used to ensure data integrity during transmission or storage. The process involves the following steps:
1. A predetermined polynomial (called the generator polynomial) is chosen for the CRC algorithm.
2. Before transmitting data, the sender divides the original data by the generator polynomial, using binary division.
3. The remainder obtained from the division is treated as the CRC value.
4. The sender appends the CRC value to the end of the original data, forming the transmitted message.
5. The receiver, upon receiving the message, performs the same binary division using the same generator polynomial.
6. If the remainder from the receiver's division matches the CRC value sent by the sender, it is assumed that the data is error-free.
7. If the remainder does not match, the receiver knows that an error occurred during transmission and can request the sender to retransmit the data.
In summary, cyclic redundancy checks work by using a generator polynomial to calculate a unique value (CRC) based on the original data. This value is then appended to the data and verified by the receiver to ensure data integrity.
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Using the UIP equation, assume that the expected future rate (after one year) for euros (in terms of dollars) equals $1.20, while the current spot rate is 1.15. The current interest rate on euro deposits is 2%, and the interest rate on dollar deposits is 3%. Should you invest in:
a)the US
b) or in Europe?
c)It is indifferent
d)Neither one In Europe In the US
The current interest rate on euro deposits is 2%, and the interest rate on dollar deposits is 3% .You should invent in d)Neither one In Europe In the US.
Using the UIP (Uncovered Interest Parity) equation, we can determine whether it is better to invest in Europe or the US. The expected future exchange rate is $1.20/€, while the current spot rate is $1.15/€. The interest rate on euro deposits is 2%, and the interest rate on dollar deposits is 3%.
The UIP equation is given by:
(Expected future exchange rate - Current spot rate) / Current spot rate = (Interest rate in domestic currency - Interest rate in foreign currency)
In this case, the domestic currency is USD and the foreign currency is EUR. Plugging in the values, we get:
($1.20 - $1.15) / $1.15 = (0.03 - 0.02)
Solving for the equation:
0.0435 ≈ 0.01
The difference in interest rates (1%) is approximately equal to the expected appreciation of the euro against the dollar (4.35%). Therefore, according to the UIP equation, there should be no significant difference between investing in Europe or the US, as the potential returns are nearly equal when considering currency movements and interest rates.
In conclusion, based on the UIP equation, you can choose to invest in either Europe or the US, as the expected returns are similar. However, it is important to consider additional factors, such as risk tolerance and investment objectives, before making a final decision. The correct answer is d.
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Find the maturity value of a $15,000 investment with a interest rate of 6%, compounded quarterly for 5 years.
a. $21,435.67
b. $22,127.56
c. $20,202.83
d. $23,896.21
The amount in the account after 5 years is $20202.83. Option C is correct.
Solving compound interest problemsGiven the following parameters
Principal = $15,000
Rate r = 6% = 0.06
Time n = 5 years
The formula for finding compound interest is expressed as:
A = P(1 + r/n)^nt
A = 15,000(1 + 0.06/4)^4(5)
A = 15,000(1 + 0.015)^20
A = 15,000(1.015)^20
A = 15,000(1.3469)
A = $20202.83
Hence the amount in the account after 5 years is $20202.83
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is the following capacity problem feasible? week 1 2 3 4 5 ri 75 100 200 100 250 ci 100 200 300 50 50
Based on the given information, the capacity problem seems to be infeasible or unrealistic. This is because the resource demands (ci) for week 3, 4, and 5 are significantly higher than the available resources (ri) for those weeks. This implies that there is a problem with capacity constraints and the organization may not be able to meet the demand for those weeks.
Hi there! Based on the given data for capacity (ci) and requirements (ri) over weeks 1 to 5, the capacity problem appears feasible. Here's the comparison for each week:
Week 1: ri = 75, ci = 100 (Capacity is sufficient)
Week 2: ri = 100, ci = 200 (Capacity is sufficient)
Week 3: ri = 200, ci = 300 (Capacity is sufficient)
Week 4: ri = 100, ci = 50 (Capacity is insufficient)
Week 5: ri = 250, ci = 50 (Capacity is insufficient)
The capacity problem is feasible for weeks 1 to 3, but not for weeks 4 and 5, as the capacity is insufficient to meet the requirements in those weeks.
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Function [tex]y = f(x)[/tex] is continuous on [tex]R[/tex].
The function satisfy [tex]f(x)+x=\int\limits^2_0 {[f(x)-x]} \, dx[/tex]
∀[tex]x[/tex]∈[tex]R[/tex].
Find the value of m so that [tex]\int\limits^2_0 {[mx+f(x)]} \, dx=0[/tex].
A. m = -2
B. m = 0
C. m = -3
D. m = -1
The value of m so that the condition satisfies is -2, the correct option is A.
We are given that;
y=f(x) is continuous
Now,
To find the numbers c that satisfy the conclusion of the Mean Value Theorem, we need to solve the equation:
f’© = [f(2) - f(0)] / (2 - 0)
f’(x) = 8x - 2
f(2) = 4(2)^2 - 2(2) + 3 = 23
f(0) = 4(0)^2 - 2(0) + 3 = 3
f’© = (23 - 3) / (2 - 0)
f’© = 10
8m - 2 = 10
8m = 12
m = 12/8
m = -2
Therefore, by the given function the answer will be -2.
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Serena is measuring the length of beetles for a science project .One beetle measures 4/5 cm and another measure 7/10 cm. What is the difference in the beatles length
The difference in the Beatles length is 1 / 10 centimetres.
How to find the difference in the beetles length?Serena is measuring the length of beetles for a science project .One beetle measures 4/5 cm and another measure 7/10 cm.
Therefore, the difference in the beetles length can be calculated as follows:
Hence,
difference between the beetles length = 4 / 5 - 7 / 10
difference between the beetles length = 8 - 7 / 10
difference between the beetles length = 1 / 10 centimetres
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the value of [tex]\sqrt{x}[/tex] 97 is between what two numbers
The calculated value of the expression √97 is between 8 and 10
Evaluating the value of the expression in numbersFrom the question, we have the following parameters that can be used in our computation:
√97
The above expression is a radical expression, and at the same time it is an irrational number
This is because
Radicals are represented by square rootsSquare roots that are not perfect squares are irrational numbersWhen evaluated, we have
√97 = 9.848.....
This number is between 8 and 10
Hence, the value of the expression is between 8 and 10
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Please help I need to show my work
from the picture above, we can see that the focus point of the parabola is at (2 , -4) and its vertex at (2 , -5), so the "p" distance from each other is just 1 unit, since the vertical parabola is opening upwards, that means "p" is positive or just p=1.
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\cap}\qquad \stackrel{p~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=2\\ k=-5\\ p=1 \end{cases}\implies 4(1)(~~y-(-5)~~) = (~~x-2~~)^2 \\\\\\ 4(y+5)=x^2+4x+4\implies 4y+20=x^2+4x+4 \\\\\\ 4y=x^2+4x-16\implies {\Large \begin{array}{llll} y=\cfrac{1}{4}x^2+x-4 \end{array}}[/tex]
Consider the three-place Boolean function f defined by the following rule:
For each triple
(x1, x2, x3)
of 0's and 1's,
f(x1, x2, x3) = (7x1 + 2x2 + 4x3) mod 2.
(a)
Find
fâ(1, 1, 1) and fâ(0, 0, 1).
fâ(1, 1, 1)
=
fâ(0, 0, 1)
=
(b)
Describe f using an input/output table.
Input Output
x1 x2 x3 f
1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0
Considering the three-place Boolean function f defined
(a) f(1, 1, 1) = (7(1) + 2(1) + 4(1)) and f(0, 0, 1) = (7(0) + 2(0) + 4(1))
(b) Using an input/output table f is an odd parity function.
A Boolean function is a mathematical function that takes input values and returns a binary output value. In the given problem, the three-place Boolean function f is defined by the rule (7x1 + 2x2 + 4x3) mod 2, where x1, x2, and x3 are binary inputs.
To find f(1, 1, 1), we substitute x1=1, x2=1, and x3=1 in the given function. Therefore, f(1, 1, 1) = (7(1) + 2(1) + 4(1)) mod 2 = 1.
Similarly, to find f(0, 0, 1), we substitute x1=0, x2=0, and x3=1 in the given function. Therefore, f(0, 0, 1) = (7(0) + 2(0) + 4(1)) mod 2 = 0.
To describe f using an input/output table, we consider all possible input combinations of x1, x2, and x3 and evaluate the function for each combination. The resulting input/output table is as follows:
Input Output
x1 x2 x3 f
0 0 0 0
0 0 1 0
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 0
From the input/output table, we can see that the function f returns 1 when the sum of 7x1, 2x2, and 4x3 is odd and returns 0 when it is even. Thus, we can conclude that f is an odd parity function.
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