We conclude that there is a significant difference between the standard deviations of the base and modified product's length.
To test if there is a difference between the standard deviations of the two populations, we can use the F-test.
a) The critical values for the F-distribution with 11 and 11 degrees of freedom at α = 0.01 are 0.250 and 4.025 (found using a statistical table or calculator).
b) The test statistic for the F-test is calculated as:
[tex]F = s1^2 / s2^2[/tex]
where s1 and s2 are the sample standard deviations of the base product and the modified product, respectively.
s1 = 7 cm (given in the problem)
s2 = 3 cm (calculated from the sample data)
Thus, the test statistic is:
F = ([tex]7^2[/tex]) / ([tex]3^2[/tex]) = 16.33
c) To determine if there is a difference between the standard deviations, we compare the test statistic to the critical values. Since our test statistic (16.33) is greater than the critical value of 4.025, we reject the null hypothesis that the standard deviations are equal. Therefore, we conclude that there is a significant difference between the standard deviations of the base and modified product's length.
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A water tanks holds 204 gallons but id leaking at a rate of 3 gallons per week. A second water tank holds 306 gallons but id leaking at a rate of 5 gallons per week. After how many weeks will the amount of water in the two tanks be the same?
Answer:
51 weeks
Step-by-step explanation:
Let y represent the total amount of water and w represent the number of weeks. We have the equation for each tank below
First tank: y = 204 - 3w
Second tank: y = 306 - 5w
After how many weeks will the amount of water in the two tanks be the same?
204 - 3w = 306 - 5w
204 + 2w = 306
2w = 102
w = 51 weeks
So, after 51 weeks, the amount of water in the two tanks will be the same.
Use the method of Cholesky factorization to solve the system of equations: - X1 – 2x2 + 2x3 = 4 -2x1 +522 - 3x3 = -7 2.01 - 3x2 + 6x3 = 10
The solution to the system of equations is :
x1 = 3, x2 = -1, and x3 = 2.
To use the method of Cholesky factorization to solve this system of equations, we need to first write the system in matrix form as AX = B, where:
A = 1 -2 2
-2 5 -3
2 -3 6
X = x1
x2
x3
B = 4
-7
10
Next, we need to perform Cholesky factorization on matrix A. This involves finding a lower triangular matrix L such that A = LL^T, where L^T is the transpose of L. To do this, we use the following algorithm:
1. Set L11 = sqrt(A11).
2. For i = 2 to n, do the following:
a. Set Lii = sqrt(Aii - sum(Lik^2, k=1 to i-1)).
b. For j = i+1 to n, set Lij = (Aij - sum(Lik*Ljk, k=1 to i-1)) / Lii.
Applying this algorithm to matrix A, we get:
L = 1 0 0
-2 1 0
2 -1 1
Now we can solve for X by first solving L*Y = B for Y using forward substitution, and then solving L^T*X = Y for X using backward substitution. The solutions for Y and X are:
Y = 4
1
3
X = 3
-1
2
Therefore, the solution to the system of equations is x1 = 3, x2 = -1, and x3 = 2.
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Drop shipping involves: transferring orders to another company having an integrated e-procurement and e-commerce platform local warehousing good relationships with transportation companies
The retailer only purchases the product when a customer places an order, which reduces the financial risks associated with holding inventory.
Drop shipping is a supply chain management method in which a retailer does not keep goods in stock but instead transfers orders and shipment details to a manufacturer, wholesaler, or another retailer, who then ships the goods directly to the customer.
In drop shipping, the retailer acts as an intermediary between the customer and the supplier, without actually holding any inventory. The retailer displays the products on their online store, and when an order is placed, the retailer forwards the order details and shipment information to the supplier. The supplier then ships the product directly to the customer.
To effectively implement drop shipping, the retailer needs to have a good relationship with the supplier who is responsible for shipping the product. The supplier must have an integrated e-procurement and e-commerce platform to receive orders and track inventory. The supplier must also have local warehousing or distribution centers close to the customer's location to ensure quick delivery and minimize shipping costs.
Having good relationships with transportation companies is also critical for the success of drop shipping. Retailers must have reliable shipping partners that can handle the transportation of goods from the supplier to the customer.
Overall, drop shipping allows retailers to offer a wider range of products to customers without the need for inventory management or warehousing. The retailer only purchases the product when a customer places an order, which reduces the financial risks associated with holding inventory.
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the national center for health statistics (nchs) report published in 2005 entitled health, united states indicated that in 2002 americans paid an average of $3,302 per year on health care and prescription drugs. researchers hypothesized that in 2005 average expenditures decreased primarily due to the availability of generic drugs. 100 americans were sampled and their expenditures on health care and prescription drugs in 2005 recorded. the sample data are: n
The analysis of the sample data (n=100) would help understand the impact of generic drugs on healthcare and prescription drug costs in the United States.
To understand how the availability of generic drugs may have affected the average expenditures on healthcare and prescription drugs in 2005, according to the National Center for Health Statistics (NCHS) report.
In 2002, Americans paid an average of $3,302 per year on healthcare and prescription drugs, as stated in the NCHS report titled "Health, United States." Researchers hypothesized that by 2005, the average expenditures would decrease primarily due to the increased availability of generic drugs. To test this hypothesis, a sample of 100 Americans was taken, and their expenditures on healthcare and prescription drugs in 2005 were recorded.
The sample data (n=100) would then be analyzed to determine if there was a significant decrease in average expenditures compared to the 2002 average of $3,302. This analysis would help understand the impact of generic drugs on healthcare and prescription drug costs in the United States.
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Find the area of polygon A
A: 4
B: 160
C: 80
D: 20
When a $10 check written on the First National Bank is deposited in an account at the Second National Bank, then A) the liabilities of the First National Bank decrease by $10. B) the reserves of the First National Bank increase by $10. C) the liabilities of the Second National Bank decrease by $10. D) the assets of Second National Bank decrease by $10.
When a $10 check written on the First National Bank is deposited in an account at the Second National Bank, the correct option is C) the liabilities of the Second National Bank decrease by $10. This is because the Second National Bank's liability to the account holder increases by $10, while its liability to the First National Bank decreases by $10. However, none of the other options are correct.
Option A) is incorrect because the liabilities of the First National Bank do not decrease as a result of the check being deposited in the Second National Bank. The liability of the First National Bank to the account holder is transferred to the Second National Bank.
Option B) is incorrect because the reserves of the First National Bank do not increase by $10 when the check is deposited in the Second National Bank. Reserves refer to the amount of money that banks hold in order to meet their depositors' demands for cash withdrawals. When the check is deposited in the Second National Bank, the reserves of the First National Bank remain the same.
Option D) is incorrect because the assets of the Second National Bank do not decrease by $10 when the check is deposited. The asset of the Second National Bank increases by $10 due to the deposit of the check.
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HELPPP MEEEEEE FAST PLEASE!
The area of the composite figure is
120 square ftHow to find the area of the composite figureThe area is calculated by dividing the figure into simpler shapes.
The simple shapes used here include
rectangle andtriangleArea of rectangle = length x width
= 12 x 7
= 84 square ft
Area of triangle = 1/2 base x height
= 1/2 x 12 x 6
= 36 square ft
Total area
= 84 square ft + 36 square ft
= 120 square ft
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A cube of side 5 is built with black and white cubes of side 1, so that the cubes next to each other have different colors and the corner cubes are black, as shown in the figure. How many white cubes were used?
Answer: 62
Step-by-step explanation:
top row has 12
the next row has 1 more =13
and it alternates
12+13+12+13+12=62
Assume that based on the data collected, you conduct a test of hypothesis to see if the true mean is below the desired specification and obtain a p-value of 0.095 (please note that this value might not match the answer you selected in the previous question). Complete the conclusion of this test by selecting the correct choice to fill in the blanks in the statement below: There is __________ evidence supporting the claim that __________ is __________ 57 Pa.
There is weak evidence supporting the claim that the true mean is below the desired specification of 57 Pa.
Based on the given information, the p-value obtained from the hypothesis test is 0.095. The p-value represents the probability of observing a test statistic as extreme or more extreme than the one obtained, assuming the null hypothesis (i.e., the true mean is not below 57 Pa) is true. Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. This means that we do not have enough evidence to claim that the true mean is significantly below 57 Pa.
Therefore, the conclusion is that there is weak evidence supporting the claim that the true mean is below the desired specification of 57 Pa.
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Assignment Booklet 5 2 thematics 30-2 2. Solve each equation and identify the non-permissible values. Record the answers as exact values (no decimals!) harks) 2. a. 1 + X 4 х 1 b. 3n-1 3n +6 + 2 n
The non-permissible values are any values of n that would make the original equation undefined. In this case, there are no such non-permissible values.
a.
The given equation is:
[tex]1 + x^4 = x[/tex]
Rearranging terms, we get:
[tex]x^4 - x + 1 = 0[/tex]
To solve this equation, we can use the quartic formula:
x = [ -b ± sqrt( b^2 - 4ac ) ] / 2a
Here, a = 1, b = -1, and c = 1, so we have:
x = [ -(-1) ± sqrt( (-1)^2 - 4(1)(1) ) ] / 2(1)
x = [ 1 ± sqrt( -3 ) ] / 2
Since the discriminant is negative, the solutions are complex:
x = [ 1 ± i*sqrt(3) ] / 2
Therefore, the non-permissible values are any values of x that would make the original equation undefined. In this case, there are no such non-permissible values.
b.
The given equation is:
3^(n-1) / (3^n + 6) + 2^n = 0
To solve for n, we can start by simplifying the first term:
3^(n-1) / (3^n + 6) = 3^(-1) / (1 + 2*3^(-n))
Substituting this into the original equation, we get:
3^(-1) / (1 + 2*3^(-n)) + 2^n = 0
Multiplying both sides by (1 + 23^(-n)), we get:
3^(-1) + 2^n(1 + 2*3^(-n)) = 0
Simplifying, we get:
2^n + 2*3^(n-1) = 0
Dividing both sides by 23^(n-1), we get:
(1/2)(1/3)^n + 1 = 0
Multiplying both sides by -2 and taking the logarithm of both sides, we get:
n = log(2/3) / log(3) - log(2)
Therefore, the solution is:
n = log(2/3) / log(3) - log(2)
The non-permissible values are any values of n that would make the original equation undefined. In this case, there are no such non-permissible values.
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An architect makes a blueprint for a custom-built house, the customer requests that the room under the roof is constructed at maximum volume. What dimensions for this room should the architect put on his blueprint if the length of the house is 100 feet, the width is 40 feet and the height of the space under the roof is 16 feet?
The length and width of the room should be 50 feet, and the height should be 16 feet, in order to maximize the volume.
We have,
Volume = Length x Width x Height
Since we want to maximize the volume, we need to make the length, width, and height of the room as equal as possible.
So,
Length = Width
Now we can substitute the given values into the formula and solve for the dimensions of the room:
Volume = Length x Width x Height
Volume = (Length)² x Height
Volume = (Length)² x 16 (since the height of the room is 16 feet)
Volume = 16 (Length)²
The length of the house is 100 feet, and we have set the length and width of the room to be equal, so:
Length + Width = 100
Length + Length = 100
2 Length = 100
Length = 50
Therefore,
The length and width of the room should be 50 feet, and the height should be 16 feet, in order to maximize the volume.
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An experiment consists of spinning the spinner shown. All outcomes are equally likely. Find P(>5). Express your answer as a fraction in simplest form.
The probability of getting a number greater than 5 is 1/4, expressed as a fraction in simplest form.
The spinner shown has 8 equal sectors, numbered 1 through 8. Since all outcomes are equally likely, the probability of obtaining any particular outcome is 1/8.
To find the probability of getting a number greater than 5, we need to count the number of favorable outcomes and divide by the total number of possible outcomes.
There are two favorable outcomes are 6 and 8. Therefore, the probability of getting a number greater than 5 is
P(>5) = favorable outcomes / total outcomes
= 2/8
= 1/4
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-- The given question is incomplete, the complete question is given below
"An experiment consists of spinning the spinner shown. All outcomes are equally likely. Find P(>5). Express your answer as a fraction in simplest form."
2.
P
R
S
T
Vertical Angles
Q
The vertical angles in the diagram are;
a. <RUP and <SUQ
b. <SUP and <RUQ
What are vertical angles?Two angles are said to be vertical angles if they are opposite to each other and are formed by two lines intersecting at a point. One common property of vertical angles is that they have equal measures.
The intersection of the two lines produce a series of angles which have some similar or common properties.
Now considering the attachment in the question, it can be deduced that;
a. <RUP is vertical to <SUQ; as such they have equal measure.
b. <SUP is vertical to <RUQ; so they have equal measure.
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A chain saw requires 5 hours of assembly and a wood chipper 2 hours. A maximum of 20 hours of assembly time is
available. The profit is $190 on a chain saw and $210 on a chipper. How many of each should be assembled for
maximum profit?
An assembly time, chain saw requires 5 hours of assembly and a wood chipper 2 hours. From linear programming for maximum profit, number of chain saw assembled are 0 and number of wood chipper are 10.
This problem is related to the topic of linear programming. We use a graphical method to solve the equation. To determine the maximum profit we write the equation of profit. Let we consider x chain saw and y wood chipper. We have a chain saw requires 5 hours of assembly. But wood chipper require 2 hours of assembly. Maximum hours of assembly time available = 20 hours
So, 5x + 2y ≤ 20 --(1) and x ≥ 0, y≥ 0
Profit of chain saw = $190
Profit on wood chipper = $210
Maximize profit, Max Z = 190x + 210y
Now, using graphical method, draw a graph is present in above figure. To determine the profit at point A and B
At point A( 0, 10)
Z = 190 ×(0)+ 210× (10) = 2100 --(1)
At point B(5,0)
Z = 190×(5)+230×(0) = 950 --(2)
Clearly from equation (1), maximum profit is at point A, number of chain saw assembled are 0 and number of wood chipper arre 10.
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Is there a rigid transformation that would map ΔABC to ΔDEC?
Answer:
Step-by-step explanation:
Yes, there is a rigid transformation that can map triangle ΔABC to triangle ΔDEC.
A rigid transformation is a transformation that preserves the size, shape, and orientation of a figure. It includes translations, rotations, and reflections. In order for triangle ΔABC to be mapped to triangle ΔDEC, the two triangles must have the same size, shape, and orientation. This can be achieved through a combination of translation, rotation, and/or reflection. For example, if triangle ΔABC is translated by a certain vector and then rotated or reflected, it can be mapped onto triangle ΔDEC.
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The study of the new CPMP Mathematics methodology described in Exercise 7 also tested staudent's abilities to solve word problems. This table shows how the CPMP and traditional groups performed. What can you conclude?
Math program n Mean Standard deviation
CPMP 320 57. 4 32. 1
Traditional 273 53. 9 28. 5
The CPMP mathematics methodology seems to be more effective on average at helping students solve word problems compared to the traditional method.
There is a greater variation in performance among students in the CPMP group. We can compare the CPMP and traditional math program groups' performance on solving word problems by looking at the mean and standard deviation.
1) Observe the mean scores:
- CPMP: 57.4
- Traditional: 53.9
The CPMP group has a higher mean score than the traditional group, indicating that students in the CPMP group performed better on average.
2) Observe the standard deviations:
- CPMP: 32.1
- Traditional: 28.5
The CPMP group has a higher standard deviation than the traditional group, meaning that the scores in the CPMP group are more spread out. This suggests there's a greater range of performance levels among students in the CPMP group.
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In circle F with m ∠ � � � = 2 3 ∘ m∠EHG=23 ∘ , find the angle measure of minor arc � � ⌢. EG
If a circle has a radius of 2 meters and a central angle EOG that measures 125° then length of the intercepted arc EG is 4.4 m
The circumference of the circle is calculated through the equation,
C = 2πr
Substituting the known values,
C = 2π(2 m) = 4π m
The measure of the arc is the circumference times the ratio of the given central angle to the total revolution,
A = (4π m)(125°/360°)
The measure of the arc is 4.36 m or 4.4 m.
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A circle has a radius of 2 meters and a central angle EOG that measures 125°. What is the length of the intercepted arc EG? Use 3.14 for pi and round your answer to the nearest tenth.
A.0.7 m
B.1.4 m
C.2.2 m
D.4.4 m
A ceramic tile has a star-shaped
pattern composed of four quarter-
circles inside a square with side
lengths of 3 inches. What is the area
of the star? Use 3.14 for pi and round
your answer to the nearest tenth.
The value of area of the star is, A = 1.9 inches
We have to given that;
A ceramic tile has a star-shaped pattern composed of four quarter- circles inside a square with side lengths of 3 inches.
Hence, We get;
Radius of circular cone = 3/2 = 1.5 inches
Now, The value of area of the star is,
A = area of square - area of 4 quarter circle
A = 3 x 3 - 4 (1/4 x 3.14 x 1.5 x 1/5)
A = 9 - 7.065
A = 1.935 inches
A = 1.9 inches
Thus, The value of area of the star is, A = 1.9 inches
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Addisonisasalesperson.Shesoldacoatfor$75andearned10%commission.HowmuchcommissiondidAddisonearn?
You have a combination lock that has the numbers 1-40 on the dial. You
forgot the combination, but you remember that the combination is three
numbers, the last digit of all three numbers is 6, and none of the numbers
are between 1 and 10. You make a random guess with what you know.
What is the probability that you will get the combination?
Answer:
1/870 ≈ 0.0011494 or about 0.115% (rounded to 6 decimal places)
Step-by-step explanation:
The first digit can be any of the numbers between 10 and 40, except for those that end in 6 (since the last digit of all three numbers is 6). This leaves us with 30 numbers to choose from for the first digit. Similarly, the second digit can be any of the numbers between 10 and 40, except for those that end in 6 and the one chosen for the first digit. This leaves us with 29 numbers to choose from for the second digit.
For the third digit, we have only one option since we know it ends in 6.
So the total number of possible combinations is:
30 * 29 * 1 = 870
Out of these, only one combination is the correct one. Therefore, the probability of guessing the combination correctly on the first try is:
1/870 ≈ 0.0011494 or about 0.115% (rounded to 6 decimal places)
What is the average rate of change for this quadratic function for the interval
from x=-4 to x = -2?
A. 6
B. -12
C. -6
OD. 12
The average rate of change of the given function graph between the two given values is: 6
How to find the average rate of change of a function?The Average Rate of Change of a function is one that is defined as the average rate at which one quantity is changing with respect to another thing changing. Thus, an average rate of change function is basically a process that helps to calculate the amount of change in one item divided by the corresponding amount of change in another.
It is given by the formula:
f'(x) = [f(b) - f(a)]/(b - a)
From the graph attached, we have that:
f(-4) = -6
f(-2) = 6
Thus:
f'(x) = (6 - (-6))/(-2 - (-4))
f'(x) = (6 + 6)/(-2 + 4)
f'(x) = 6
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complete the division equation. How many times does jack need to fill the glass?
Answer:
Alot
Step-by-step explanation:
Think abt it
The library scene, which Hankla built the dinosaur skeletons for, is pictured below. If the Coahuilaceratops skull in the center of the image is 6.2 feet wide at its widest point, what’s the scale of the image?
The scale of the image , at its widest point, can be found to be 1 cm : 1. 77 feet .
How to find the scale ?When measured with a ruler, the widest point on the Coahuilaceratops skull in the center of the image would be 3. 5 cm .
Yet, the widest point of the Coahuilaceratops skull is measured to be 6. 2 feet.
The scale is thefore :
3. 5 cm : 6. 2 feet
Simplified, we have :
3. 5 cm / 3. 5 : 6. 2 feet / 3. 5
1 cm : 1. 77 ft
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Which of these is a correct expansion of (3x – 2)(2x2 + 5)?
A. 3x • 2x2 + 3x • 5 + (–2) • 2x2 + (–2) • 5
B. 3x • 2x2 + 3x • 5 + 2 • 2x2 + 2 • 5
C. 3x • 2x2 + (–2) • 2x2 + 2x2 • 5 + (–2) • 5
The correct expansion of (3x – 2)(2[tex]x^2[/tex] + 5) is 3x * 2[tex]x^2[/tex] + 3x * 5 + (–2) * 2[tex]x^2[/tex] + (–2) * 5. Thus option A is the most appropriate option as the answer the above question
The expansion of the given algebraic expression follows the distributive rule of multiplication that is (a + b)(c + d) = ac + ad + bc + bd.
Thus the first term of the first expression which is 3x is multiplied by the the second expression and we get 3x • 2[tex]x^2[/tex] + 3x • 5 + (–2)
Then the second term that is -2 is multiplied by the second expression and we get 5 + (–2) • 2[tex]x^2[/tex] + (–2) • 5
Then we add both expressions and get the answer 3x * 2[tex]x^2[/tex] + 3x * 5 –2 * 2[tex]x^2[/tex] –2 * 5.
After further simplification of the above expression we get, 6[tex]x^3[/tex] + 15x - [tex]4x^2[/tex] - 10.
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Factor to find the TWO equivalent expressions of 36a−16
To factor 36a - 16, we can begin by finding the GCF to get 4(9a - 4). Another equivalent expression is 2(18a - 8) using different factorizations of 4 and 8. So, the correct answer is A) and C).
To factor 36a - 16, we can begin by finding the greatest common factor (GCF) of the two terms, which is 4
36a - 16 = 4(9a - 4)
Next, we can expand the parentheses in the expression 4(9a - 4) to get:
36a - 16 = 4(9a - 4) = 36a - 16
So, the factored form of 36a - 16 is
36a - 16 = 4(9a - 4)
To find another equivalent expression, we can use a different factorization of 4, such as 2 x 2. Then
36a - 16 = 2 x 2 x 9a - 2 x 2 x 4
= 2(2 x 9a - 2 x 4)
= 2(18a - 8)
So, the correct option is A) and C).
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roland received a score of 70 on a test for which the mean score was 65.5. Roland has learned that Z-score for his test 0.6. What is the standard deviation for this set of test scores?
If Roland has Z-score for his test 0.6, the standard deviation for this set of test scores is 7.5
To find the standard deviation for this set of test scores, we can use the z-score formula:
Z-score = (X - μ) / σ
Where:
- Z-score is 0.6 (given)
- X is Roland's score of 70
- μ is the mean score of 65.5
- σ is the standard deviation we need to find
Now we can plug in the values and solve for σ:
0.6 = (70 - 65.5) / σ
Next, we can rearrange the equation to solve for σ:
σ = (70 - 65.5) / 0.6
Finally, calculate the standard deviation:
σ = 4.5 / 0.6
σ ≈ 7.5
The standard deviation for this set of test scores is approximately 7.5.
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Clark finds that in an average month, he spends $35 on things he really doesn't need and can't afford. About how much does he spend on these items in a year?
Clark would spend about $420 on these items in a year.
Given that Clark finds that in an average month, he spends $35 on things he really doesn't need and can't afford.
If Clark spends $35 on things he doesn't need or can't afford in an average month, then he would spend:
$35/month x 12 months/year = $420/year
Therefore, Clark would spend about $420 on these items in a year.
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Consider a sample of 53 football games, where 27 of them were won by the home team. Use a. 05 significance level to test the claim that the probability that the home team wins is greater than one-half
The calculated test statistic is 0.571. P 0.5, the null hypothesis.
A one-tailed z-test can be used to verify the assertion that there is a higher than 50% chance of the home side winning.
p > 0.5, where p is the percentage of football games won by the home team in the population.
The test statistic is calculated as:
(p - p) / (p(1-p) / n) = z
If n = 53 is the sample size, p = 0.5 is the hypothesized population proportion, and p is the sample fraction of football games won by the home team.
The percentage of the sample is p = 27/53 = 0.5094.
The calculated test statistic is:
z = (0.5094 - 0.5) / √(0.5(1-0.5) / 53) = 0.571
We determine the p-value for this test to be 0.2826 using a calculator or a table of the normal distribution as a reference.
We are unable to reject the null hypothesis since the p-value is higher than the significance level of 0.05. Therefore, at the 5% level of significance, we lack sufficient data to draw the conclusion that there is a better than 50% chance of the home team winning.
The calculated test statistic is:
z = (0.5094 - 0.5) / √(0.5(1-0.5) / 53)
= 0.571
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Use the table to find the value of the expression.
(f(g(4)) =
X
1
2
3
4
f(x)
0
1
-1
2
D
g(x)
3
4
3
2
The value of the expression (f(g(4)) is 1.
To find the value of f(g(4)), we need to first find g(4), which is 2 (since g(4) = 2). Then, we need to find f(2), which is also 1 (since f(2) = 1). Therefore, f(g(4)) = 1.
Here's a step-by-step process for finding this:
Find g(4), Look for the row where x = 4 in the table for g(x). This is the fourth row, and the value in the g(x) column for this row is 2. So g(4) = 2.
Find f(g(4)), Now that we know g(4) = 2, we can look for the row where x = 2 in the table for f(x). This is the second row, and the value in the f(x) column for this row is 1. So f(2) = 1.
Write the final answer, Since f(g(4)) = f(2) = 1, we can say that the value of the expression is 1.
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Juan tiene 21 años menos que Andrés y sabemos que la suma de sus edades es 47. ¿Qué edad tiene cada uno de ellos?
Juan is 13 years old.
Andrés is 34 years old.
We have,
Let's assume that Juan's age is x.
Then, we know that Andrés' age is x + 21.
We also know that the sum of their ages is 47:
x + (x + 21) = 47
Simplifying the equation:
2x + 21 = 47
Subtracting 21 from both sides:
2x = 26
Dividing by 2:
x = 13
So Juan is 13 years old.
To find Andrés' age, we can substitute Juan's age into the equation we used earlier:
x + 21 = 13 + 21 = 34
Thus,
Juan is 13 years old.
Andrés is 34 years old.
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The complete question.
Juan is 21 years younger than Andrés and we know that the sum of their ages is 47. How old is each of them?
