1) The standard labor hours allowed to ship 120,000 items is 2,400.
2) The standard variable overhead cost allowed to ship 120,000 items is $7,800.
3) The variable overhead spending variance is -$440.
4) The variable overhead efficiency variance is -$325.
What is the Cost?Cost can refer to a variety of measures used to quantify the expense or effort required to solve a problem or perform a task.
According to the given information1) The standard labor hours allowed (SH) to ship 120,000 items can be calculated as follows:
Standard labor hours allowed = Number of items × Direct labor hours per item
Standard labor-hours allowed = 120,000 × 0.02
Standard labor-hours allowed = 2,400
Therefore, the standard labor hours allowed to ship 120,000 items is 2,400.
2) The standard variable overhead cost allowed (SH × SR) to ship 120,000 items can be calculated as follows:
Standard variable overhead cost allowed = Standard labor-hours allowed × Variable overhead rate per labor-hour
Standard variable overhead cost allowed = 2,400 × $3.25
Standard variable overhead cost allowed = $7,800
Therefore, the standard variable overhead cost allowed to ship 120,000 items is $7,800.
3) The variable overhead spending variance can be calculated as follows:
Variable overhead spending variance = Actual variable overhead cost incurred − Standard variable overhead cost allowed
Variable overhead spending variance = $7,360 − $7,800
Variable overhead spending variance = -$440
Therefore, the variable overhead spending variance is -$440, indicating that the actual variable overhead cost incurred was lower than the standard variable overhead cost allowed.
4) The variable overhead rate variance and the variable overhead efficiency variance can be calculated using the following formulas:
Variable overhead rate variance = (Actual variable overhead rate − Standard variable overhead rate) × Actual labor hours incurred
Variable overhead efficiency variance = (Actual labor-hours incurred − Standard labor-hours allowed) × Standard variable overhead rate
First, we need to calculate the actual variable overhead rate:
Actual variable overhead rate = Actual variable overhead cost incurred ÷ Actual labor hours incurred
Actual variable overhead rate = $7,360 ÷ 2,300
Actual variable overhead rate = $3.21 per labor-hour
Using this information, we can calculate the variable overhead rate variance:
Variable overhead rate variance = ($3.21 − $3.25) × 2,300
Variable overhead rate variance = -$92
Therefore, the variable overhead rate variance is -$92, indicating that the actual variable overhead rate was lower than the standard variable overhead rate.
Next, we can calculate the variable overhead efficiency variance:
Variable overhead efficiency variance = (2,300 − 2,400) × $3.25
Variable overhead efficiency variance = -$325
Therefore, the variable overhead efficiency variance is -$325, indicating that the actual labor hours incurred were more than the standard labor hours allowed.
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The ratio of union members to nonunion members working for a company is 4 to 5. If there are 140 nonunion members working for the company,
what is the total number of employees?
The total number of employees is 112.
Explain numbers
Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.
According to the given information
Let's use x to represent the total number of employees.
According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.
So, we can set up the following proportion:
4/9 = x/(x - 140)
To solve for x, we can cross-multiply and simplify:
4(x - 140) = 9x
4x - 560 = 9x
560 = 5x
x = 112
Therefore, the total number of employees is 112.
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2.Each curve is a transformation of the graph of the parent function y = √x.
Write an equation for each curve.
A.
B.
C.
D.
Since each curve is a transformation of the graph of the parent function y = √x, an equation for each curve are as follows;
A. y = √(-x + 2)
B. y = -√(x - 1) + 3
C. y = √(x - 3)
D. y = √x - 2
E. y = -√(x + 2)
What is a translation?In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent the parent functions.In order to write an equation that models curve A, we would have to apply a reflection and horizontal translation to y = √x by 2 units left.
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A principal of $1500 is invested at 8.5% interest, compounded annually. How much will the investment be worth after 14 years?
Use the calculator provided and round your answer to the nearest dollar.
You have a jar of marbles, each marble is numbered 1-35. 10 Marbles are Blue, 12 Marbles are Green, and 13 Marbles are Red. You draw a random marble.What is the probability that you pull out a marble that is Green or an even number.
The probability of drawing a marble that is green or even-numbered is 28/35
Calculating the probabilityThe total number of marbles in the jar is 35, of which 10 are blue, 12 are green, and 13 are red.
We need to find the probability of drawing a marble that is green or an even number.
First, let's find the number of even-numbered marbles.
Out of 35 marbles, 17 of them are even-numbered (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34).
There are 12 green marbles, and 17 even-numbered marbles,
Therefore, there are 12 + 17 - 1 = 28 marbles that are either green or even-numbered.
The probability of drawing a marble that is green or even-numbered is
28/35
So the probability of drawing a marble that is green or even-numbered is 28/35
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25. Find m/T. 0 (9x-17) T (4x + 28) S R
Answer:
The given expression is:
m/T = 0(9x-17) / (T(4x + 28)S R)
Since the numerator is multiplied by 0, the entire expression becomes 0, regardless of the value of the denominator. Division by 0 is undefined in mathematics, as it is not a valid operation. Therefore, the result of m/T in this case is undefined.
You can double check urself ;D
Workout 461÷4 give your answer as a whole number and a reminder
Step-by-step explanation:
the answer is 115 remainder 1
Find the inradius of triangle ABC.
Find the circumradius of triangle ABC.
The sides of the triangle are 5, 29, and 42.
Identify the correct equation of the graph.
-10
O f(b) = (6+4)² +8
O f(b) = (b+8)² +4
Of(b)=(6-8)²-4
O
-5
10
5
-5
-10
V
5
O f(b) = (b-8)² +4
Of(b) = (6-4)²-8
Of(b) (6-4)² +8
10
Check
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
Explain about the quadratic function in vertex form:A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.
The vertex of the parabola is located at this lowest or highest point.
Vertex form of a quadratic function:
f(x) = a(x – h)² + k, where a, h, and k are constants.
The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).
(h,k) are the vertex of parabola.
From the given graph:
f(b) is the given function:
Vertex (h,k) = (8, 4)
Thus, h= 8 and k = a = 1, x = b.
Put the values in quadratic function:
f(b) = 1(b – 8)² + 4
f(b) = (b – 8)² + 4
Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.
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Problem Walk-Through
Stocks A and B have the following probability distributions of expected future returns:
Probability
0.1
0.2
0.5
0.1
0.1
A
(7%)
6
14
23
31
B
(39%)
0
23
25
45
a. Calculate the expected rate of return, FB, for Stock B (A = 12.90%.) Do not round Intermediate calculations. Round your answer to two decimal places.
%
b. Calculate the standard deviation of expected returns, GA, for Stock A (08= 21.64 %.) Do not round intermediate calculations. Round your answer to two decimal places.
%
Now calculate the coefficient of variation for Stock B. Do not round intermediate calculations. Round your answer to two decimal places.
Is it possible that most investors might regard Stock B as being less risky than Stock A?
I. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
II. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
III. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
IV. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
V. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
-Select-
c. Assume the risk-free rate is 1.5%. What are the Sharpe ratios for Stocks A and B? Do riot round intermediate calculations. Round your answers to four decimal places.
Stock A:
Stock B:
Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b?
I. In a stand-alone risk sense A is less risky than B. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and
hence be more risky in a portfolio sense.
II. In a stand-alone risk sense A is more risky than B. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and
hence be less risky in a portfolio sense.
A is riskier than B in terms of pure risk. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio if it has a lower correlation to the market than Stock A.
What is Expeced return?The profit or loss an investor can anticipate realising from an investment is known as the expected return. Calculating an expected return involves multiplying possible outcomes by their likelihood before adding the results. The expected return is computed by summing the results of multiplying all possible outcomes by the likelihood that each one will occur (as illustrated below).
Expeced return=Sum(probability*return)
Standard Deviation=[tex]\sqrt{sum(probability*(return-expected\ return)^2}[/tex]
Coefficient of Variation=Standard Deviation/Expected Return
1. Expected Returns:
Stock B=0.1*(-38%)+0.2*0%+0.5*21%+0.1*26%+0.1*36%=12.900%
2. Standard Deviation:
Stock A=[tex]\sqrt{(0.1*(-11\%-11.3\%)^2+0.2*(5\%-11.3\% +0.5*(13\%-11.3\%)^2+)^2 0.1*(18\%-11.3\%)^2} \\+0.1*(31\%-11.3\%)^2)[/tex]
= 10.120%
3. Coefficient of Variation:
Stock B=19.892%/12.9%=1.5420
4. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio if it has a lower correlation to the market
than Stock A.
5. Sharpe Ratio:
Stock A=(11.3%-3.5%)/10.120%=0.7708
Stock B=(12.9%-3.5%)/19.892%=0.4726
6. A is riskier than B in terms of pure risk. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio
if it has a lower correlation to the market than Stock A.
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What is the value of k?
help pleaseeeee
The value of k in the given diagram is 10.
What is a linear pair?A linear pair refers to two adjacent angles that are created when two lines intersect. The defining characteristic of a linear pair is that the sum of their measures is always equal to 180 degrees, which makes them supplementary angles. Essentially, a linear pair is a type of angle pair where the two angles are not only adjacent to each other, but they also add up to a straight angle. Linear pairs are frequently found in various geometric shapes, including triangles, quadrilaterals, and polygons. They also have real-world applications in areas such as architecture and engineering.
We know that sum of angles of a triangle is 180.
So in tringle XYZ,
Angle ZXY + Angle XYZ + Angle YZX = 180
Given angle values ZXY = 6k+10, YZX = 4K+5 and ZYM = 115
We see that Angle XYZ + Angle ZYM = 180, since they are a linear pair.
This means Angle XYZ = 180 - Angle ZYM = 180 - 115 = 65
Hence, Angle ZXY + Angle XYZ + Angle YZX = 180
6k+10 + 65 + 4K+5 = 180
10k + 80 = 180
10k = 180 - 80 = 100
k = 100/10 = 10
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what is the value of y
Answer:
y = 163 since vertical angles are congruent.
pls help :)
Angie is really fit and wants to test her endurance by competing in a swimming competition over four days. On the first day, she covers 25 per cent of the distance. On the second day, she covers one third of the remaining distance, on the third day, 25 per cent of the remaining distance and, on the final day, she swims half of the remaining distance. She still has 15km to swim to complete the competition. Form a linear equation and find the total distance of the swimming competition. (Use x as the total distance of the swimming competition).
Answer: Total distance of the swimming competition is 55.56 km.
Step-by-step explanation:
Let x be the total distance of the swimming competition.
On the first day, Angie covered 25% of the total distance, which means she swam 0.25x km.
On the second day, she covered one-third of the remaining distance, which is (1 - 0.25)x = 0.75x km.
So, she swam (1/3) * 0.75x = 0.25x km on the second day.
On the third day, she covered 25% of the remaining distance, which is (1 - 0.25 - 1/3)x = 0.42x km.
So, she swam 0.25 * 0.42x = 0.105x km on the third day.
On the final day, she swam half of the remaining distance,
which is (1 - 0.25 - 1/3 - 0.5)x = 0.125x km.
The total distance she swam is the sum of the distances swum on each day:
0.25x + 0.25x + 0.105x + 0.125x = 0.73x
We know that the total distance of the competition is x - 15 km (since she still has 15 km left to swim).
So we can set up the equation:
0.73x = x - 15
Solving for x, we get:
x-0.73x = 15
0.27x = 15
x = 55.56
Therefore, the total distance of the swimming competition is 55.56 km.
The value of a certain collectible card in dollars from January 2020 to May 2021 can be modeled by the function V(m)=250m² -3,500m + 18,000, where mis
the approximate number of months since the start of 2020.
Over what period was the value of the card declining?
To respond to the question, we must identify the m-values for which V(m) equation decreases. The value of the card decreased during the course of the time from January 2020 to July 2020 (about 7 months),
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
We must identify the values of m for which the function V(m) is dropping in order to estimate the time span during which the value of the card was declining.
The function V(m)'s derivative is provided by:
V'(m) = 500m - 3,500
By setting V'(m) = 0 and solving for m, we may determine the crucial point(s):
500m - 3,500 = 0
m = 7
V''(m) = 500
To respond to the question, we must identify the m-values for which V(m) decreases. The value of the card decreased during the course of the time from January 2020 to July 2020 (about 7 months), as we know that V(m) is falling for m 7.
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On January 1, Year 2, Kincaid Company's Accounts Receivable and the Allowance for Doubtful Accounts carried balances of $74,600 and $3,700, respectively. During Year 2, Kincaid reported $208,000 of credit sales, wrote off $2,000 of receivables as uncollectible, and collected cash from receivables amounting to $258,900. Kincaid estimates that it will be unable to collect one percent (1%) of credit sales.
What effect will recognizing the uncollectible accounts expense for Year 2 have on the elements of the financial statements?
Multiple Choice
Decrease total assets and net income
Decrease total assets and increase retained earnings
Increase total assets and decrease net income
Increase total assets and retained earnings
The correct answer is: Decrease total assets and net income.
What is statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.
The recognition of uncollectible accounts expense for Year 2 will decrease total assets and net income.
When uncollectible accounts expense is recognized, it is recorded as a debit to the allowance for doubtful accounts and a credit to the uncollectible accounts expense account. This reduces the balance of accounts receivable, which is a current asset, and thus decreases total assets. Additionally, recognizing this expense reduces net income by the same amount.
Therefore, the correct answer is: Decrease total assets and net income.
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if the pink lines are parallel, solve for n
The option that is true about the equations for these two lines iis that they represent the same lines.
How to explain the informationThe trick to questions like this is to get both equations into the slope-intercept form. That is done for our first equation (y = 3x + 5). However, for the second, some rearranging must be done:
5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5
Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.
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Two lines are described by the equations:
y = 3x + 5 and 5y – 25 = 15x
Which of the following is true about the equations for these two lines?They represent perpendicular lines.
None of the other answers
They represent non-perpendicular, intersecting lines.
They represent the same lines.
They represent parallel lines.
Is the graph increasing, decreasing, or constant?
-8 -6 4
A. Decreasing
B. Increasing
C. Constant
-2
4-
2
-2
AY
2
4
6
8
SUBMIT
Is the graph increasing, decreasing, or constant: C. Constant.
What is a graph?In Mathematics and Geometry, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.
By critically observing the graph shown above, we can reasonably infer and logically deduce that the graph is constant because it assumes only one y-value, which is represented by this equation y = 3.
In conclusion, the above is constant, rather than increasing or decreasing.
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Work out sheet below please
Using division we know that per pound the loose sweets have a better value which is £0.0089 per pound.
What is division?The division is one of the four basic arithmetic operations or the process by which two numbers are added together to produce a new number.
Multiplication, addition, and subtraction make up the remaining operations.
We may examine the quotient and the division's remainder using the division formula Dividend = (Divisor Quotient) + Remainder.
We can multiply our quotient by the divisor to check its accuracy if the remainder is 0.
If the product and dividend are equal, the quotient is correct.
So, the price per gram when pre-packed:
1.49/120 = £0.012
Now, the price per gram when the product is loose:
0.89/100 = £0.0089
Now, we know that per pound the loose sweets are better.
Therefore, using division we know that per pound the loose sweets have a better value which is £0.0089 per pound.
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x=10 3x+5y=20 in the system of equations, what is the value of x
Estimate the difference. Round each number to the nearest whole number, then subtract.
10
19
19
4
19
-
2
The difference is approximately
Answer:
To estimate the difference, we need to round each number to the nearest whole number and then subtract the rounded numbers.
Rounding each number to the nearest whole number, we get:
10 rounded to the nearest whole number is 10
19 rounded to the nearest whole number is 19
19 rounded to the nearest whole number is 19
4 rounded to the nearest whole number is 4
19 rounded to the nearest whole number is 19
-2 rounded to the nearest whole number is -2
Subtracting the rounded numbers, we get:
10 - 19 - 19 - 4 - 19 - (-2) = 10 - 19 - 19 - 4 - 19 + 2 = -49
Therefore, the estimated difference is -49.
ZA =
Round your answer to the nearest hundredth.
Angle A equals 41.81°
c:
please answer in detail
Answer:
y = 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x + 3 ← is in slope- intercept form
with slope m = 2
• Parallel lines have equal slopes , then
slope of line AB is m = 2
line AB crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 2x + 4 ← equation of line AB
Home values in a town have declined 26% per year for each of the past
four years. What was the total percentage decrease in home values
during the four-year period?
Answer: 104%
Step-by-step explanation: 26% times 4 years
Which is the largest of the followin fractions? 7/12, 2/3,5/6,3/4, 5/8, (a) 2/3 (b) 3/4 (c) 5/ 5
Answer:
Step-by-step explanation:it is 5/5 because it is a whole number and all the others aren’t
The density function of a distribution is f(x)=1/2σ*e^(−|x|/σ),where σ is the parameter.
1(5). Find the moment estimate of σ.
2(5). Find the mle of σ.
The log-likelihood function is l(σ) = -n*log(2σ) - sum(|[tex]x_i[/tex]|)/σ.
the moment estimate of σ is σ = 0.
What is moment?A moment is a quantitative measure of the shape of a probability distribution. Specifically, it is a mathematical calculation that involves taking the product of the distribution's values and certain pre-determined values (such as powers of the variable). Moments are often used to estimate certain parameters of a distribution, such as its mean, variance, or skewness.
Moment estimate of σ:
The kth moment about the origin is defined as E[[tex]X^k[/tex]] = integral from -inf to inf of [tex]x^k[/tex] * f(x) dx.
The first moment about the origin is E[X] = integral from -inf to inf of x * f(x) dx.
E[X] = integral from -inf to inf of x * (1/2σ*[tex]e^{(-|x|/\sigma))[/tex] dx
Let's split the integral into two parts: from -inf to 0 and from 0 to inf.
integral from -inf to 0 of x * (1/2σ[tex]e^{(-|x|/\sigma))[/tex]dx = integral from -inf to 0 of -x * (1/2σ[tex]e^{(-|x|/\sigma))[/tex] dx = 1/2σ * integral from 0 to inf of x * [tex]e^{(-x/\sigma)[/tex] dx
integral from 0 to inf of x * e^(-x/σ) dx is the definition of the gamma function with shape parameter 2 and scale parameter σ, which is Γ(2, σ) = 1 * σ² = σ².
Therefore, E[X] = 1/2σ * σ² = σ/2.
The second moment about the origin is E[X²] = integral from -inf to inf of x² * (1/2σ*[tex]e^{(-|x|/\sigma))[/tex] dx.
E[X²] = 1/2σ * integral from -inf to inf of x² * [tex]e^{(-|x|/\sigma))[/tex] dx
Let's split the integral into two parts: from -inf to 0 and from 0 to inf.
integral from -inf to 0 of x² * (1/2σ [tex]e^{(-|x|/\sigma))[/tex] dx = integral from -inf to 0 of x² * (1/2σ[tex]e^{(x/\sigma)[/tex]) dx = 1/2σ * integral from 0 to inf of x² * [tex]e^{(-x/\sigma)[/tex] dx
integral from 0 to inf of x² * [tex]e^{(x/\sigma)[/tex]) dx is the definition of the gamma function with shape parameter 3 and scale parameter σ, which is Γ(3, σ) = 2 * σ³.
Therefore, E[X²] = 1/2σ * 2σ³ = σ².
The moment estimate of σ is obtained by solving the equation E[X²] = σ² for σ:
σ² = E[X²] = integral from -inf to inf of x² * (1/2σ*[tex]e^{(-|x|/\sigma)[/tex]) dx
= 1/2σ * integral from -inf to inf of x² * [tex]e^{(-|x|/\sigma)[/tex] dx
= 1/2σ * 2σ³
= σ²
Simplifying the equation, we get:
σ² = σ²/2
Multiplying both sides by 2, we get:
2σ² = σ²
Therefore, the moment estimate of σ is σ = 0.
MLE of σ:
The likelihood function is given by L(σ) = (1/2σ)ⁿ *[tex]e^{(-sum(|x_i|)/\sigma)[/tex], where n is the sample size and [tex]x_i[/tex]are the observed values.
The log-likelihood function is l(σ) = -n*log(2σ) - sum(|[tex]x_i[/tex]|)/σ.
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4.4.3 Quiz: Stretching and Compressing Functions
f(x) = x². What is g(x)?
10
g(x)
Y
5- f(x)
O B. g(x) =
(2,2)
Click here for long description
2
O A. g(x) = (x)²
O c. g(x) =
OD. g(x) = 2x²
2
5
x²
x²
X
The equation of the function g(x) is g(x) = 1/2x²
Calculating the function g(x)If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.
Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).
To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):
[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]
So, we have
a = 1/2
Recall that
g(x) = f(ax)
So, we have
g(x) = f(1/2x)
This means that
g(x) = 1/2x²
Hence. the function is g(x) = 1/2x²
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The angle measures for 2 supplementary angles are 3x and 2x +40.
What is the value of x?
Answer:
28°
Step-by-step explanation:
If the angles are supplementary, they add up to 180°.
(3x) + (2x + 40) = 180
5x + 40 = 180
- 40 - 40
5x = 140
x = 28°
Al has a goal to read 2,000 pages over
summer break. He has read 1,248 pages.
How many more pages does Al need to
read to reach his goal?
Al needs to read 752 more pages to reach his goal of 2,000 pages.
What is subtraction?The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign.
To find out how many more pages Al needs to read to reach his goal of 2,000 pages, we can subtract the number of pages he has already read from his goal:
Number of pages Al needs to read = Goal - Pages already read
Number of pages Al needs to read = 2,000 - 1,248
Number of pages Al needs to read = 752
Therefore, Al needs to read 752 more pages to reach his goal of 2,000 pages.
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Approximately of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
The fraction of Earth that is not made up of ocean = 1/4.
Explain about the fraction:The numbers we are familiar with are whole numbers, such as 1, 2, and so on.
Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.
In essence, a fraction explains how a portion of a group interacts with the entire group.
Given that-
fraction of Earth made up of water = 3/4The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water
The fraction of Earth that is not made up of ocean = 1 - 3/4
The fraction of Earth that is not made up of ocean = (4 - 3)/4
The fraction of Earth that is not made up of ocean = 1/4
Thus, the fraction of Earth that is not made up of ocean = 1/4.
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Complete question:
Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?
Solve by using matrices.
2x -y + 3z = 180
-4x + 2y + 3z = 225
3x - 4y = 270
X
= -66, y = [?], z =
Enter
Solving the system of equations using matrices is : = -66, y = 163, and z = 11.
Solving the system of equations using matrices ?To solve this system of equations using matrices, we can write it in the form AX = B, where:
A = coefficient matrix
X = variable matrix (containing x, y, and z)
B = constant matrix (containing the constants on the right-hand side of each equation)
So, we have:
| 2 -1 3 | | x | | 180 |
| -4 2 3 | x | y | = | 225 |
| 3 -4 0 | | z | | 270 |
We can solve for X by multiplying both sides of the equation by the inverse of A:
X = A^-1 * B
First, we need to find the inverse of A. We can do this by using the formula:
A^-1 = (1 / det(A)) * adj(A)
where det(A) is the determinant of A and adj(A) is the adjugate (transpose of the cofactor matrix) of A.
| 2 -1 3 |
| -4 2 3 |
| 3 -4 0 |
det(A) = 2(20 - 3(-4)) - (-1)(-40 - 33) + 3(-4*(-1) - 2*3) = 16
| 2 -1 3 |
| -4 2 3 |
| 3 -4 0 |
The cofactor matrix is:
| 2 9 6 |
| 12 0 -2 |
| 13 -9 8 |
Taking the transpose of the cofactor matrix gives us the adjugate of A:
| 2 12 13 |
| 9 0 -9 |
| 6 -2 8 |
So, we have:
A^-1 = (1 / det(A)) * adj(A) = (1 / 16) *
| 2 12 13 |
| 9 0 -9 |
| 6 -2 8 |
Multiplying A^-1 by B gives us:
| x | | -66 |
| y | = | 163 |
| z | | 11 |
Therefore, x = -66, y = 163, and z = 11.
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!!PLEASE HELP WILL GIVE BRAINLIST!!
Determine whether the numbers can represent the side lengths of a triangle. If they can, classify the triangle as right, acute, or obtuse.
The side lengths will all make up a triangle, each can be classified as:
6. Isosceles triangle 7. Obtuse triangle 8. Scalene triangle
How to Classify a Triangle?To determine whether the given numbers can represent the side lengths of a triangle or not, we need to check if the sum of the two smaller sides is greater than the largest side.
If this condition is satisfied for all three pairs of sides, then the numbers can represent the side lengths of a triangle.
6. The numbers 4, 5, and 5 can represent the side lengths of a triangle because 4 + 5 > 5, 5 + 4 > 5, and 5 + 4 > 5. This triangle is isosceles because two sides have the same length.
7. The numbers 10, 17, and 26 can represent the side lengths of a triangle because 10 + 17 > 26, 17 + 26 > 10, and 26 + 10 > 17. This triangle is obtuse because the square of the longest side (26^2 = 676) is greater than the sum of the squares of the other two sides (10^2 + 17^2 = 369).
8. The numbers 2, 10, and 12 can represent the side lengths of a triangle because 2 + 10 > 12, 10 + 12 > 2, and 12 + 2 > 10. This triangle is scalene because all three sides have different lengths.
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