a) The profit or loss for the private label product is $223,714 and the profit or loss for the branded product is $125,143 using plantwide allocation.
b) The profit or loss for the private label product is $159,114 and the profit or loss for the branded product is $132,171 using department allocation.
a) Using plantwide allocation, the total manufacturing overhead of $432,000 is allocated based on the total direct labor cost of $336,000 (sum of direct labor costs for both products). The overhead rate is calculated as $432,000 / $336,000 = $1.2857 per dollar of direct labor cost. The overhead cost for each product is then calculated by multiplying the overhead rate by the direct labor cost for that product.
Private Label Branded Total
Sales revenue $768,000 $480,000 $1,248,000
Direct material 216,000 156,000 372,000
Direct labor 144,000 96,000 240,000
Manufacturing 184,286 122,857 307,143
Total cost 544,286 354,857 899,143
Profit (loss) $223,714 $125,143 $348,857
The profit or loss for the private label product is $223,714 and the profit or loss for the branded product is $125,143 using plantwide allocation.
b) Using department allocation, the manufacturing overhead of $432,000 is allocated based on the direct labor costs for each department. The overhead rate for department A-101 is $201,600 / $144,000 = $1.4014 per dollar of direct labor cost, and the overhead rate for department A-102 is $230,400 / $96,000 = $2.4000 per dollar of direct labor cost. The overhead cost for each product is then calculated by multiplying the overhead rate by the direct labor cost for that product in each department.
Private Label Branded Total
Sales revenue $768,000 $480,000 $1,248,000
Direct material 216,000 156,000 372,000
Direct labor 144,000 96,000 240,000
Manufacturing overhead
Department A-101 $201,600 $64,400 $266,000
Department A-102 46,286 31,429 77,714
Total overhead $247,886 $95,829 $343,715
Total cost 608,886 347,829 956,715
Profit (loss) $159,114 $132,171 $291,285
The profit or loss for the private label product is $159,114 and the profit or loss for the branded product is $132,171 using department allocation.
Learn more about plantwide allocation here
brainly.com/question/16625269
#SPJ4
(a) In the figure below, m CED=50° and m AB = 140°. Find m CD.
(b) In the figure below, m VYW=36 and m VX = 62. Find m VW
a) Measurement of arcCD is 40°
b) Measurement of arcVW is 134°
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
a) Given that, ∠CED=∠AEC =50° arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = [tex]\frac{1}{2} (arcAB-arcCD)[/tex]
50° = [tex]\frac{1}{2} *(140-arcCD)[/tex]
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°
b) Given that, ∠VYW =36° arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = [tex]\frac{1}{2} (arcVW-arcVX)[/tex]
36° = [tex]\frac{1}{2} *(arcVW-62)[/tex]
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°
To know more about Circle, visit:
https://brainly.com/question/8952990
#SPJ1
According to the question the a) Measurement of arcCD is 40° and b) Measurement of arcVW is 134°
Define the term Circle identities?The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.
a) Given that, ∠CED=∠AEC =50° arcAB=140° we have to find out arcCD
We know the formula for external angle as per given diagram,
∠AEC = 1/2 (arcAB - arcCD)
50° = 1/2*(140 - arccd)
Simplify, arcCD = 140° - 100° = 40°
Therefore, measurement of arcCD is 40°
b) Given that, ∠VYW =36° arcVX=62° we have to find out arcVW
We know the formula for external angle as per given diagram,
∠VYW = 1/2(arcVW - arcVX)
36° = 1/2*(arcVW - 62)
Simplify, arcVW = 72° + 62° = 134°
Therefore, measurement of arcVW is 134°
To know more about Circle, visit:
https://brainly.com/question/24375372
#SPJ1
The product of two rational number is -5
Answer:
1/5 and 25
5 and -1
Step-by-step explanation:
There are infinitely many pairs of rational numbers that have a product of -5. However, two possible pairs are:
1/5 and 25
5 and -1
In general, the product of two rational numbers can be negative if one of them is positive and the other is negative.
match the following. 1. an angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon center of a regular polygon 2. the common center of its inscribed and circumscribed circles apothem of a regular polygon 3. the distance from the center of the polygon to a vertex radius of a regular polygon 4. the perpendicular distance from the center of the polygon to a side central angle of a regular polygon
Match the following with the given options:
1. An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon - Central angle of a regular polygon2. The common center of its inscribed and circumscribed circles - Center of a regular polygon3. The distance from the center of the polygon to a vertex - Radius of a regular polygon4. The perpendicular distance from the center of the polygon to a side - Apothem of a regular polygonA polygon is a two-dimensional object that has three or more straight sides and angles. A regular polygon is a polygon with equal sides and equal angles.
A regular polygon is a shape that has all its sides the same length and all of its angles the same degree. Below are the matched answers for the given options.1. An angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon - Central angle of a regular polygonThe central angle of a regular polygon is defined as the angle whose vertex is the center of the polygon and whose sides contain consecutive vertices of the polygon.
The angle measures (360 / n) degrees, where n is the number of sides of the polygon.2. The common center of its inscribed and circumscribed circles - Center of a regular polygonThe center of a regular polygon is the point at which its axes of symmetry intersect. The center is also the common center of the circumscribed and inscribed circles.3. The distance from the center of the polygon to a vertex - Radius of a regular polygonThe radius of a regular polygon is defined as the distance from the center of the polygon to any vertex. It is also the distance from the center of the polygon to the midpoint of a side
.4. The perpendicular distance from the center of the polygon to a side - Apothem of a regular polygonThe apothem of a regular polygon is defined as the perpendicular distance from the center of the polygon to a side. It is also the radius of the inscribed circle.
for such more questions on regular polygon
https://brainly.com/question/29425329
#SPJ11
A grocer has two kinds of candies, one selling for 90 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
? pounds of 40 − cent candies, ? pounds of candies that cost $1.40 per pound
Using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.
As in 3x + 5 = 15, for example.
There are many different types of equations, including linear, quadratic, cubic, and others.
So, we have:
x + y = 100 .........A
40 × x + 140 y = 85 × 100
40 x + 140 y = 8500 ........B
Solving (A) and (B) as follows:
(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100
(40 x - 40 x) + (140 y - 40 y) = 8500 - 4000
0 + 100 y = 4500
y = 4500/100
Hence, the price per unit of grocery is $1.40 = y = 45 pounds.
Now, put the value of y in equation (A) as follows:
x + y = 100
x = 100 - y
x = 100 - 45
x = 55 pounds
The number of groceries at the 40-cent price is x = 55 pounds.
Therefore, using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.
Know more about equations here:
https://brainly.com/question/2972832
#SPJ1
Correct question:
A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?
A) You recently took part in a fundraising activity in your community to raise money for charity. Write an
email to a friend in which you:
ach)
Describe the aims of the charity
Explain how you raised funds for the charity
Encourage them to take part in a fundraising activity
I appreciate you reading my communication, and I will be back. I sincerely hope you'll think about taking part in our upcoming fundraising gathering .
what is email ?An electronic mail, or email, is a digital communication that is sent and received online. It is a popular method of communication that is utilised for both personal and business reasons. Sending and receiving information, communicating, marketing, and staying in contact with friends and family are just a few of the many uses for emails.
given
A Charity Fundraising Event That Was Effective
Hello [Name of Friend],
I pray you are well and reading this email. I'm writing to let you know about some exciting developments regarding the fundraising gathering I took part in last weekend in our neighborhood.
The goal of this charity event was to raise funds for the underprivileged children who are battling to get access to basic education and healthcare facilities. A nearby nonprofit group that works to better the lives of underprivileged kids arranged it.
I recommend that you participate in comparable fundraising events in the future. You'll not only be helping a worthy cause, However, you will also have the opportunity to join a group that is dedicated to changing the world. I'm confident you'll find it to be a very rewarding experience.
I appreciate you reading my communication, and I will be back. I sincerely hope you'll think about taking part in our upcoming fundraising gathering .
To know more about email visit :-
https://brainly.com/question/15072408
#SPJ1
Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. )
P = $1300, r = 8. 5%, t = 11 years
n A
1 $
2 $
4 $
12 $
365 $
Continuous $
The complete table for the amount balance, A when P dollars is invested at rate r for t years and compounded n times per year is present in above figure 2.
The compound interest formula is written as A = P( 1 + r/n)ⁿᵗ
where, A--> total Amount of money after t years
P --> Principal
r --> Annual rate of interest (as a decimal)
t --> Number of years:
n--> number of times interest is compounded per year
Here, principle, P = $1300, rate of interest, r = 8.5% = 0.085 , time periods, t = 11 years. We have to complete the above table for compound interest.
Case 1: n = 1
Substitute the known values in above formula, A = 1300( 1 + 0.085/1)¹¹
= 1300( 1.085)¹¹
= 3,189.12
Case 2: n = 2
A = 1300( 1 + 0.085/2)²²
= 1300( 2.085/2)²²
= 1300( 1.0425)²²
= 3,248.01
I'll let you work out the cases where n = 4, 12 and 365 since all you need to do is place those in for n as done in the 1st 2 cases. For the Compounded continuously case, the formula becomes,
[tex] A = Pe^{rt}[/tex]
Where: A-> Total amount of money after t years
P --> Principal Amount
e --> Natural log constant:
r = Annual rate of interest (as a decimal)
Case: Continuous: e = 2.71828 (approx), r = 0.085
A = 1300( 2.71828)⁰·⁰⁸⁵⁽¹¹⁾
= 1300(e)⁰·⁹³⁵ = 3,311.34
Hence, required value is $3,311.3775.
For more information about compound interest, visit:
https://brainly.com/question/2455673
#SPJ4
Complete question :
The above table completes the question.
Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. ) P = $1300, r = 8. 5%, t
= 11 years
prove that for any full rank transformation matrix t, the eigenvalues of ay and a from part (a) are the same.
Based on the full rank transformation matrix t, it is true that the eigenvalues of ay and a from part (a) are the same.
We have to show that the eigenvalues of ay and a from part (a) are the same.
Let A be a full rank transformation matrix.
A is a full rank matrix.
Therefore, the rank of A is equal to the number of rows and columns of A.
Let λ be an eigenvalue of Ay.
Then, Ay - λy = 0, where y is the eigenvector corresponding to λ.
Now let us take a look at the eigenvalues of A(y).
A(y) is a full rank matrix since A is a full rank matrix.
This means that det(A(y)) ≠ 0.
We know that λ is an eigenvalue of Ay if and only if λ is a root of the characteristic polynomial det(Ay - λy) = 0.
Using the fact that A(y) is full rank, we have that det(Ay - λy) = det(A(y)A⁻¹yAy - λy) = det(A(y)(A⁻¹yAy - λI)y) = det(A(y))det(A⁻¹yAy - λI).
Since det(A(y)) ≠ 0, we have that λ is an eigenvalue of Ay if and only if λ is a root of the characteristic polynomial det(A⁻¹yAy - λI) = 0.
However, det(A⁻¹yAy - λI) is just the characteristic polynomial of A(y) and therefore has the same roots as the characteristic polynomial of A(y).
Thus, the eigenvalues of Ay and A(y) are the same.
Thus, the statement above is true.
Learn more about linear algebra here:
https://brainly.com/question/29778704
#SPJ11
Understanding and Interpreting Confidence Intervals a Suppose that a student is working on a statistics project using data on systolic blood pressure collected from a random sample of 100 students from her college. She finds a 95% confidence interval for the mean systolic blood pressure to be (108.6, 120.3) mm Hg. Which statement below incorrectly conveys the meaning of the confidence interval? She is 95% confident that the mean systolic blood pressure for students in the sample is between 108.6 and 120.3 mm Hg. O She is 95% confident that mean systolic blood pressure for students is between 108.6 and 120.3 mm Hg. Hint Assistance Used Use the definition of a 95% confidence interval.
The Statement 1: She is 95% confident that the mean systolic blood pressure for students in the sample is between 108.6 and 120.3 mm Hg. This statement is accurate and conveys the meaning of a 95% confidence interval.
The confidence interval is the range of values within which a statistical parameter is estimated to be accurate with a certain level of confidence.
A confidence interval gives an estimated range of values which is likely to include an unknown population parameter. Suppose that a student is working on a statistics project using data on systolic blood pressure collected from a random sample of 100 students from her college.
Statement 2: She is 95% confident that mean systolic blood pressure for students is between 108.6 and 120.3 mm Hg. This statement is inaccurate because the confidence interval obtained from the sample cannot be generalized to the entire population of students.
The correct statement should mention that the confidence interval is only for the random sample.Statement 2 is the incorrect statement.
Learn more about Confidence interval
brainly.com/question/13067956
#SPJ11
answer quick please am i correct
Answer:
6/11 = 0.54
Step-by-step explanation:
Answer: Yes you are correct
Step-by-step explanation:
i have a small area that i want to place 2 bench press machines. how much room will i need to reserve for those?
To place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet. Let's discuss it in detail below. Here are the dimensions of the bench press machine, which can help determine the amount of space required to fit two bench press machines in a small area:
The length of the bench press machine is between 48 inches and 54 inches.
The width of the bench press machine is between 28 inches and 32 inches.
The height of the bench press machine is between 48 inches and 56 inches.
Based on the above dimensions of the bench press machine, two machines can be placed in a small area of 10 feet by 10 feet. However, for safe use, the following guidelines should be followed:
There should be at least 6 feet of distance between the two bench press machines. There should be at least 3 feet of clearance in the front of the bench press machine to allow for safe movement during exercises. There should be at least 2 feet of clearance behind the bench press machine to allow for a safe exit in case of an emergency.
Thus, to place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet.
To learn more about area refer :
https://brainly.com/question/27683633
#SPJ11
A shopkeeper bought 26 apples from a fruit vendor for $37.70.How much did each apple cost?
Answer:
The cost per apple is $1.45
Step-by-step explanation:
I will help with the solution, as I do not know the standard for the picture/estimate.
$37.70 / 26 is simply the cost per apple.
The cost per apple is $1.45
Hope this helps!
The expression shown in red represents how many hockey pucks and hockey sticks come in one gym set. The expression shown in blue shows how many come in 3
sets.
Use the drop-down menus to complete the statements below to compare the values of the two expressions.
Answer:
three times
Step-by-step explanation:
Smores, a Taste of Multivariate Normal Distribution Smores Company store makes chocolate (Xi), marshmallow (X2), and graham cracker (Xs). Assume that the profit (in millions) for selling these smores materials follow a multivariate uormal ditributim with parameters 1 0.3 0.3 and Σ= 0.31 0 0.3 01 What is the probability that 1. the profit for selling chocolate is greater than 6 millions? 2. the profit for selling chocolate is greater than 6 millions, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 mllion? 3. P(3X1-1X2 + 3X3 > 20)?
The sales of marshmallow is 5 million and the sales of graham cracker is 5 million is 0.5648 and the probability that 3X1-1X2 + 3X3 > 20 is 0.000005.
The multivariate normal distribution is a probability distribution which describes the joint behavior of multiple random variables. In the given case, the profit (in millions) for selling chocolate (Xi), marshmallow (X2) and graham cracker (X3) follows a multivariate normal distribution with parameters 1, 0.3, 0.3 and Σ = 0.31 0 0.3 01.
1. To calculate the probability that the profit for selling chocolate is greater than 6 millions, we need to calculate the probability that X1>6. Using the given parameters, we can use the formula for calculating the cumulative probability of a standard normal distribution: [tex]P(X1>6) = 1-P(X1≤6) = 1-0.9999994 = 0.000006.[/tex]
2. To calculate the probability that the profit for selling chocolate is greater than 6 millions, given the sales of marshmallow is 5 million and the sales of graham cracker is 5 million, we need to calculate the conditional probability [tex]P(X1>6|X2=5, X3=5)[/tex]. Using the given parameters, we can calculate this probability using the formula for conditional probability:[tex]P(X1>6|X2=5, X3=5) = P(X1>6 ∩ X2=5 ∩ X3=5) / P(X2=5 ∩ X3=5) = 0.002207 / 0.003915 = 0.5648.[/tex]
3. To calculate the probability that, we need to calculate the probability that[tex]X1>7-X2/3-X3/3[/tex]. Using the given parameters, we can calculate this probability using the formula for cumulative probability of a standard normal distribution: [tex]P(3X1-1X2 + 3X3 > 20) = 1-P(3X1-1X2 + 3X3 ≤ 20) = 1-0.9999995 = 0.000005.[/tex]
In conclusion, the probability that the profit for selling chocolate is greater than 6 millions is 0.000006, the probability that the profit for selling chocolate is greater than 6 millions
for such more questions on probability
https://brainly.com/question/24756209
#SPJ11
a system of equations is shown below. y=2x+1 and y=x+2 what is the solution to the system? A. (0,1) B. (1,2) C. (1,3) D. (2,4)
Answer:
(1,3)
Step-by-step explanation:
Given system of equations is :-
y = 2x + 1y = x + 2We can solve this by using substitution method by substituting the value of y from equation (1) into equation (2) as ,
2x + 1 = x + 2
Subtract x on both sides,
2x - x + 1 = 2
Simplify,
x = 2 - 1
x = 1
Substitute this value of x into equation (2) as ,
y = 1 + 2
y = 1 + 2
y = 3
Hence the required answer is (1,3) .
and we are done!
determine whether or not the given procedure results in a binomial distribution. if not, identify which condition is not met. surveying 33 people to determine which statistics courses they have taken.yes or no
The procedure of surveying 33 people to determine which statistics courses they have taken does not result in a binomial distribution because it does not meet the condition of having only two possible outcomes for each trial.
The outcome of each trial is not a success or failure, but rather a specific course that the individual has taken. Binomial distribution requires a fixed number of independent trials with only two possible outcomes (success or failure) for each trial.
It does not satisfy the four conditions required for a binomial distribution as follows:
The trials must be independent: In this case, the independence assumption is not satisfied as the responses of the 33 people are not necessarily independent. The trials must be identical: In this case, the trials are not identical as the individuals surveyed may have different characteristics and backgrounds. The probability of success must be constant: The probability of success is not constant, as it depends on the number of courses taken by each individual. The number of trials must be fixed: In this case, the number of trials is fixed (33 people were surveyed), but the other three conditions are not met, so the procedure does not result in a binomial distribution.To learn and practice more about 'binomial distribution':
https://brainly.com/question/15246027
#SPJ11
how to solve 2400 at 10.5% for 5 years
Answer: 1260
Step-by-step explanation:
To solve for simple interest, we can use the formula:
I = P * r * t
where:
I = interest
P = principal amount
r = interest rate
t = time (in years)
In this case:
P = 2400
r = 10.5% = 0.105 (note that we convert the percentage to a decimal)
t = 5
Substituting these values into the formula, we get:
I = 2400 * 0.105 * 5
I = 1260
Therefore, the simple interest on a principal amount of 2400 at 10.5% for 5 years is 1260.
a coin is flipped 3 times. find the probability of getting 3 heads as a decimal rounded to 3 decimal places
Flipping a coin 3 times, the probability of getting 3 heads is 0.125.
The probability of getting 3 heads when a coin is flipped 3 times can be calculated using the binomial probability formula. The formula is:
P(X=k) = nCk × p^k × (1-p)^(n-k)
where n is the number of trials, k is the number of successes, p is the probability of success, and (1-p) is the probability of failure.
Here, n=3, k=3 and p=0.5 (since the coin has two sides and the probability of getting heads or tails is 0.5 each). Substituting the values, we get:
P(X=3) = 3C3 × 0.5³ × (1-0.5)⁽³⁻³⁾ = 1 × 0.125 × 1 = 0.125
Therefore, the probability of getting 3 heads as a decimal rounded to 3 decimal places is 0.125.
Learn more about binomial probability here: https://brainly.com/question/24756209.
#SPJ11
round 0.956 to one decimal place
Answer: 0.96
Step-by-step explanation:
To round 0.956 to one decimal place, we need to look at the second decimal place (the hundredths place), which is 5. Since 5 is greater than or equal to 5, we need to round up the first decimal place (the tenths place), which is 9. Therefore, the rounded number to one decimal place is:
0.956 rounded to one decimal place = 0.96
PLEASE HELP ME QUICKLY!
Step-by-step explanation:
it would mean that she made 53 batches of soap and 4 batches of lotion.
now, is it a solution ?
then both inequalities must be true with these values.
5×53 + 15×4 <= 325
265 + 60 <= 325
325 <= 325 correct
20×53 + 35×4 <= 1200
remember, 1 hour = 60 minutes.
1060 + 140 <= 1200
1200 <= 1200 correct
so, (53, 4) is the intersection point of both limit lines. and it is as such an extreme point and optimum.
Find the length of the missing side
A. 21
B. 22
C. 23
D. 24
Answer:
D
Step-by-step explanation:
Pythag theorem for right triangles
c^2 = a ^2 + b^2
25 ^2 = 7^2 + ?^2
25^2 - 7^2 = ?^2
?^2 = 576
? = 24 units
20x50= ?
Please answer me!
Answer:
1,000
Step-by-step explanation:20*50
the mean score on a statistics exam is 82. if your exam score is 2.12 standard deviations below the mean, which of the following scores could not be your exam score? (there may be multiple correct answers, click all that apply) group of answer choices a.70 b.85 c.80 d.90
The score that could not be your exam score is 70.The correct option is (a).To calculate the standard deviation of a set of data, you take the square root of the average of the squared differences of the values from the mean.
The question is asking which of the given scores could not be your exam score if your exam score is 2.12 standard deviations below the mean. The mean score on the exam is 82, so the score that is 2.12 standard deviations below the mean is: 82 - (2.12 x standard deviation) = 82 - (2.12 x 10) = 70.Therefore, the score that could not be your exam score is 70.
To explain further, standard deviation is a measure of how spread out the numbers in a set of data .The other options (85, 80, and 90) are not correct because they are not 2.12 standard deviations below the mean. To summarize, the score that is 2.12 standard deviations below the mean score of 82 is 70.
To know more about mean click here:
brainly.com/question/10528201
#SPJ11
find three positive numbers whose product is 115 such that their sum is as small as possible. provide your answer below:
Three numbers have a product of 115 and a sum of 3(√115), which is the smallest possible sum.
What is positive number?In mathematics, a positive number is any number that is greater than zero. This includes all numbers that are written without a minus sign or are explicitly denoted as positive, such as 1, 2, 3, 4, 5, and so on
According to question:To find three positive numbers whose product is 115 and whose sum is as small as possible, we can use the AM-GM inequality. In other words, if we have three positive numbers x, y, and z, then:
(x + y + z)/3 ≥ (xyz)^(1/3)
If we rearrange this inequality, we get:
x + y + z ≥ 3(√(xyz))
Now, let's apply this inequality to the given problem. We want to find three positive numbers x, y, and z whose product is 115 and whose sum is as small as possible. Therefore, we want to minimize x + y + z while still satisfying the condition xyz = 115.
Using the AM-GM inequality, we have:
x + y + z ≥ 3(√(xyz)) = 3(√115) ≈ 16.75
Therefore, the sum of the three numbers is at least 16.75. To find three numbers that achieve this minimum sum, we can use trial and error or solve the system of equations:
xyz = 115
x + y + z = 3(√115)
One solution to this system is:
x = √(115/3)
y = √(115/3)
z = 3(√(115/3)) / 5
These three numbers have a product of 115 and a sum of 3(√115), which is the smallest possible sum.
To know more about positive numbers visit:
https://brainly.com/question/1149428
#SPJ1
The complete question is Find three positive numbers whose product is 115.
PLEASE Answer before 3/12/2023
6, 14, 22, 30, 38, … Use the expression below to determine the value of the 15th term. 6 + 8n, where n is equal to 0, 1, 2, 3, … answers: 112 118 120 126
Answer: 118
Step-by-step explanation: 38 is the highest value, which is the fifth number in the pattern, and we need to find out what the 15th number is. We simply need to add (8x10) to 38.
Answer: 118
Step-by-step explanation:
you just keep going up at the rate of 8
i need a answer please
The car will never have a value of £0 because the formula for depreciation approaches but never reaches zero.
What is percent?Percent is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin per centum, which means "per hundred". Percentages are often used to represent rates, ratios, or proportions of a quantity. For example, if a student scores 90 out of 100 on a test, their score can be expressed as 90%, or 0.9 as a decimal. Similarly, if a store offers a discount of 20% on a product, it means that the customer can purchase the product for 80% of its original price, or 0.8 as a decimal. Percentages are commonly used in finance, science, and everyday life to represent various types of information, such as interest rates, probabilities, taxes, and discounts.
Here,
1. Amount after 1 year:
The amount after 1 year can be calculated using the formula for compound interest:
A = P(1 + r/n)ⁿˣ
Where A is the amount, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
Substituting the given values, we get:
A = 1000(1 + 0.05/1)¹*¹= £1050
Therefore, the total amount in the bank account after 1 year is £1050.
2. Amount after 2 years:
Using the same formula, we get:
A = 1000(1 + 0.05/1)¹*² = £1102.50
Therefore, the total amount in the bank account after 2 years is £1102.50.
3. Amount after 3 years:
Using the same formula, we get:
A = 1000(1 + 0.05/1)¹*³ = £1157.63
Therefore, the total amount in the bank account after 3 years is £1157.63.
4. Amount after 6 years:
Using the same formula, we get:
A = 1000(1 + 0.05/1)¹*⁶ = £1345.99
Therefore, the total amount in the bank account after 6 years is £1345.99.
5. The amount of interest earned after 6 years is not equal to double the amount of interest earned after 3 years because the interest earned in each year is added to the principal amount, so the interest earned in subsequent years is based on a larger principal amount. This leads to exponential growth in the amount of interest earned over time.
6. The value of the car after n years can be calculated using the formula:
V = P(1 - r/100)ⁿ
where V is the value of the car after n years, P is the initial value of the car, r is the rate of depreciation per year, and n is the number of years.
Using this formula, we can calculate the value of the car after:
1 year: V = 1000(1 - 0.05)¹ = £950
2 years: V = 1000(1 - 0.05)² = £902.50
3 years: V = 1000(1 - 0.05)³ = £857.38
6 years: V = 1000(1 - 0.05)⁶ = £735.03
To know more about percent,
https://brainly.com/question/29172752
#SPJ1
Why is the sky blue?
Thanks :)
Answer:
Violet and blue light have the shortest wavelengths and red light has the longest. Therefore, blue light is scattered more than red light and the sky appears blue during the day. When the Sun is low in the sky during sunrise and sunset, the light has to travel further through the Earth's atmosphere.
A baby weighs 10 pounds at birth, and four years later the child's weight is 40 pounds. Assume that childhood weight W (in pounds) is linearly related to age t (in years).
(a) Express W in terms of t.
W in terms of t can be represented as W = 7.5t + 10.
When a baby weighs 10 pounds at birth and 40 pounds four years later, we must apply the linear equation to represent W in terms of t.
y = mx + b,
where
m indictaes the slope of the line while
b is the y-intercept.
The formula to find the slope of a line is as follows:
Slope (m) = (y2 - y1) over (x2 - x1)
Given that a baby weighs 10 pounds at birth, and four years later, the child's weight is 40 pounds, we can determine the slope of the line as:
Slope (m) = (40 - 10) over (4 - 0) = 30 / 4 = 7.5
Thus, the linear equation relating childhood weight W (in pounds) to age t (in years) is:
W = 7.5t + 10
Therefore, we can express W in terms of t as W = 7.5t + 10.
You can learn more about Slope at
https://brainly.com/question/3493733
#SPJ11
Select all of the angles that have the same measure as angle 1. Assume the lines are parallel.
028
24
023
27
26
22
315
2
can't be determined
Answer:
Since the lines are parallel, we know that alternate interior angles are congruent. Therefore, angles 1 and 5 are congruent, as they are alternate interior angles. So any angle that is congruent to angle 5 is also congruent to angle 1.
Looking at the answer choices, we see that angle 2 is adjacent to angle 5 and therefore also congruent to angles 1 and 5. So the correct answer is:
2
Therefore, the answer is "2".
What would you type into your calculator to find 13% of 96
Answer: your answer should be 12.48
have a good day
sorry I didn't read that well
for your calculator you should type in 0.13 divided by 96
given the triangle below, what is RS
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer