Ethan and Calvin meet daily in the elevator. One morning they found that if they multiply their current ages, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Ethan and Calvin.
Answers
The sum of Ethan and Calvin's current ages is approximately 45.65.
Let's assume Ethan's current age is represented by 'E', and Calvin's current age is represented by 'C'.
From the given information, we can establish the following equations:
The product of their current ages is 238:
E × C = 238
The product of their ages after four years is 378:
(E + 4) × (C + 4) = 378
We can solve this system of equations to determine the values of E and C, and then calculate their sum.
From equation 1, we can express E in terms of C:
E = 238 / C
Substituting this value of E into equation 2:
(238 / C + 4) × (C + 4) = 378
Expanding and simplifying the equation:
(238 + 4C) × (C + 4) = 378
\(238C + 952 + 4C^2 + 16C - 378 = 0\\4C^2 + 254C + 574 = 0\)
Now, we can solve this quadratic equation for C using the quadratic formula:
C = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values:
a = 4, b = 254, c = 574
C = (-254 ± √(\(254^2\)- 4 × 4 × 574)) / (2× 4)
After solving, we find two possible values for C: C ≈ -73.85 and C ≈ -39.65
Since age cannot be negative, we discard the negative value. Thus, C ≈ 39.65.
Plugging this value of C back into equation 1:
E × 39.65 = 238
E ≈ 238 / 39.65
E ≈ 6
Therefore, Ethan's current age (E) is approximately 6 and Calvin's current age (C) is approximately 39.65.
The sum of their current ages is:
6 + 39.65 ≈ 45.65
Hence, the sum of Ethan and Calvin's current ages is approximately 45.65.
for such more question on current ages
https://brainly.com/question/25922783
#SPJ8
Related Questions
A 95% confidence interval for mean waiting time at an emergency room ( ER) of 128 minutes, 147 minutes
Answers
The friend's claim is not supported by the confidence interval, as the lower bound of the interval is above 120 minutes.
What is the interpretation of a x% confidence interval?The bounds of the confidence interval are given by the estimate of the parameter plus/minus the margin of error.
The meaning of the interval is that it is x% likely that the population parameter(mean/proportion/standard deviation) is between the bounds a and b of the confidence interval.
Hence the interpretation of this interval is:
We are 95% sure that the true mean waiting time at an emergency room is between 128 minutes and 147 minutes.
Two hours are equivalent to 120 minutes, hence the friend's claim is not supported by the interval, as both bounds of the interval are above 120.
Missing InformationThe problem is given by the image shown at the end of the answer.
More can be learned about confidence intervals at https://brainly.com/question/17073112
#SPJ1
What is B^2+8b+7??
Can someone explain it step by step please?
Answers
Step-by-step explanation:
B^2+8b+7 is a quadratic expression. It can be factored as (b+7)(b+1).
To factor a quadratic expression, you can use the following steps:
1. Find two numbers that add up to the coefficient of the middle term (8) and multiply to the constant term (7).
2. Write the quadratic expression as a product of two binomials, with the two numbers you found in step 1 as the coefficients of the terms in each binomial.
In this case, the two numbers that add up to 8 and multiply to 7 are 7 and 1. So, we can factor B^2+8b+7 as follows:
(b+7)(b+1)
This means that B^2+8b+7 is equal to the product of (b+7) and (b+1).
Here is a step-by-step explanation of how to factor B^2+8b+7:
1. The coefficient of the middle term is 8.
2. The constant term is 7.
3. The two numbers that add up to 8 and multiply to 7 are 7 and 1.
4. Therefore, B^2+8b+7 can be factored as (b+7)(b+1).
To solve it, you can use the quadratic formula, which is:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 8, and c = 7.
So, substituting the values, we get:
x = (-8 ± √(8^2 - 4(1)(7))) / 2(1)
x = (-8 ± √(64 - 28)) / 2
x = (-8 ± √36) / 2
x = (-8 ± 6) / 2
x = -1 or -7
Therefore, B^2+8b+7 is equal to -1 or -7.
Put the following equation of a line into slope-intercept form, simplifying all fractions. 3y-9x=-6
Answers
Answer: y=3x-2
Step-by-step explanation:
3y-9x=-6
First you will need to add 9x to the other side so your equation will look like 3y=9x-6. Then you need to divide all the numbers by 3. So 3y divided by 3 and 9 divided by 3 and -6 divided by 3. Your final answer should be y=3x-2.
Answer:
This equation in slope intercept form would be y = 3x - 2
Step-by-step explanation:
The following is how to solve this equation:
3y - 9x = -6
+9x +9x
----------------------
3y = 9x - 6
divide each of the numbers by 3
So the answer is y = 3x - 2
martian addition Table
Answers
Answer:
martial addition
Step-by-step explanation:
qqqqghhfgjfcg
1 2 3 4 5 6 7 8 9 10
this is a type of martion addition
Phoebe rounded a number to the nearest tenth and got 6.5. When she rounded it to the nearest whole number, she got 7. Which number could be the number she rounded?
Answers
Answer:
6.7
please give brainliest
Given: Quadrilateral DEFG is inscribed in circle P.
Prove: m∠D+m∠F=180∘
Answers
The sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.
To prove that m∠D + m∠F = 180∘, we can use the property of angles inscribed in a circle.
In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Therefore, if we can show that arc DE + arc FG = 360∘, we can conclude that m∠D + m∠F = 180∘.
Let's start the proof:
1. Quadrilateral DEFG is inscribed in circle P. This means that all the vertices of the quadrilateral lie on the circumference of the circle.
2. Let's consider arc DE and arc FG. These arcs are intercepted by angles ∠D and ∠F, respectively.
3. By the property of angles inscribed in a circle, we know that the measure of an inscribed angle is equal to half the measure of its intercepted arc.
4. Therefore, m∠D = 1/2(arc DE) and m∠F = 1/2(arc FG).
5. We want to prove that m∠D + m∠F = 180∘. This is equivalent to showing that 1/2(arc DE) + 1/2(arc FG) = 180∘.
6. Combining the fractions, we have 1/2(arc DE + arc FG) = 180∘.
7. Now, we need to show that arc DE + arc FG = 360∘.
8. Since quadrilateral DEFG is inscribed in circle P, the sum of the measures of all the arcs intercepted by the sides of the quadrilateral is equal to 360∘.
9. This means that arc DE + arc EF + arc FG + arc GD = 360∘.
10. However, we can observe that arc EF and arc GD are opposite sides of the same chord, so they have equal measures. Therefore, arc EF = arc GD.
11. Substituting arc GD with arc EF in the equation from step 9, we have arc DE + arc EF + arc FG + arc EF = 360∘.
12. Simplifying the equation, we get 2(arc DE + arc EF + arc FG) = 360∘.
13. Dividing both sides by 2, we have arc DE + arc EF + arc FG = 180∘.
14. Comparing this result with step 7, we can conclude that arc DE + arc FG = 180∘.
15. Finally, going back to our initial goal, we can now substitute arc DE + arc FG with 180∘ in the equation from step 6: 1/2(180∘) = 180∘.
16. Simplifying, we have 90∘ = 180∘, which is a true statement.
17. Therefore, we have proven that m∠D + m∠F = 180∘.
Thus, we have successfully proved that the sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.
For more questions on quadrilateral .
https://brainly.com/question/23935806
#SPJ8
On a survey, 8 students reported how many minutes it takes them to travel to school. Here are their responses.9, 11, 3, 14, 14, 7, 14, 6Find the mean travel time for these students.If necessary, round your answer to the nearest tenth.
Answers
SOLUTION
The arithemetic mean of a set of data is the sum of the datas divided by the number of data given.
Hence
\(\begin{gathered} \text{Mean}=\frac{sum\text{ of the data}}{n} \\ \text{where n= number of student=8} \end{gathered}\)Given the set of data below
\(9,\: 11,\: 3,\: 14,\: 14,\: 7,\: 14,\: 6\)The sum of the data is
\(9+11+3+14+14+7+14+6=78\)Hence
\(\text{Mean}=\frac{78}{8}=9.75\)The mean travel time for these students is 9.8 minutes to the nearest tenth.
Find the slope of the treadmill.
Answers
A small publishing company is planning to publish a new book. The production cost will include one-time fixed cost such as editing and variable costs (such as printing) There are two production method it could use. With one method, the one time fixed cost will total $57,641, and a variable cost will be $10 per book. With the other method, the one time fixed cost will total $16,682 and a variable cost will be $19.25 per book. For how many books produces will the costs from the two methods be the same?
Answers
Answer:
4,428 books
Step-by-step explanation:
make the equation 57,641+10x=16,682+19.25x
(you’re using that equation because the numbers have to be equal at the end. also “x” is the variable) after that subtract 16,682 from both sides that should give you (40,959+10x= 19.25x) after that subtract 10x from both sides, that should give you (40,959 = 9.25x) Lastly divide both sides by 9.25 and you should get x=4,428.
The sum of a number qnd seven is ten. What is the number?
Answers
Answer:
3
Step-by-step explanation:
Let's write the statement as an equation and solve for that number.
x+7=10
x=3
Step-by-step explanation:
\(\bold{x + 7 = 10}\)
\( \longmapsto \: x = 10 - 7\)
\( \longmapsto \: 10 - 7 = 3\)
\(\bold{x = 3}\)\(\bold{Hope}\)\(\bold{It}\) \(\bold{Helps!}\)
\(\bold{Study}\)\(\bold{Well}\)~
Robert earns $300 every week. What equation shows the relationship between salary per week (s), number of weeks worked (w), and total income (t).
w = 300 − 30
s − h = t
w − h − t = s
t = 300w
h = 300w
Answers
A line passes through the points (-5,-11)and (3,-11) write the equation of the line using point slope form then converted to slope intercept form
Answers
The Slope Intercept Form is y = -11
What is Slope?
The slope or gradient of a line in mathematics is a quantity that specifies both the direction and the steepness of the line. The letter m is frequently used to represent slope; there is no obvious answer to why the letter m is chosen for slope.
Solution:
Given:
(x1 , y1) = (-5, -11) and
(x2, y2) = (3, -11)
Slope = y2 -y1 / x2 - x1 = -11+11 / 3+5
Slope = 0
Point Slope Form:
y - y1 = m (x - x1)
y + 11 = 0
Slope Inetrcept Form:
y = mx + b
y = 0 - 11
y = -11
To learn more about Slope frrom the given link
https://brainly.com/question/25722412
#SPJ1
Jason tried to find an expression equivalent to the rational expression −4x4+12x3−7x+22x2+1 by using polynomial long division. His work is shown below.Jason concluded that −2x2+7x+−14x+22x2+1 was equivalent to the rational expression. Jason's conclusion is incorrect.
Which statement BEST explains where Jason made an error?
Answers
She made a mistake in multiplying 2x²+1 by -2x². which is the correct answer would be an option (B).
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The rational expression is given in the question as:
\(\dfrac{\left(-4x^4+12x^3-7x+2\right)}{2x^2+1}\)
Divide the leading term of the dividend by the leading term of the divisor:
\(=-2x^2+6x+\dfrac{2x^2-13x+2}{2x^2+1}\)
Write down the calculated result in the upper part of the table.
Multiply it by the divisor
\(=-2x^2+6x+1+\dfrac{-13x+1}{2x^2+1}\)
\(\mathrm{Long\:division}\:\dfrac{\left(-4x^4+12x^3-7x+2\right)}{2x^2+1}:\quad -2x^2+6x+1+\dfrac{-13x+1}{2x^2+1}\)
Thus, Jason made a mistake in multiplying 2x²+1 by -2x².
Hence, the correct answer would be option (B).
Learn more about the algebraic expression here :
brainly.com/question/21751419
#SPJ1
What is the formula forfinding the area of a circle using its radius or diameter.
Answers
Answer:
The formula for finding the area of a circle using its radius is:
The formula for finding the area of a circle using its radius is:A = πr²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.
The formula for finding the area of a circle using its radius is:A = πr²where A is the area of the circle and r is its radius.The formula for finding the area of a circle using its diameter is:A = (π/4)d²where A is the area of the circle and d is its diameter.Note that π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter and is approximately equal to 3.14
Step-by-step explanation:
Hope it Helps
The formula for finding the area of a circle using its radius is π * r².
The formula for finding the area of a circle using its diameter is (π/4) * d².
The formula for finding the area of a circle using its radius is:
A = π * r²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
r represents the radius of the circle.
If you have the diameter of the circle instead of the radius, you can use the following formula:
A = (π/4) * d²
where:
A represents the area of the circle,
π (pi) is a mathematical constant approximately equal to 3.14159, and
d is the diameter of the circle.
For more information on the Area of Circle, click:
https://brainly.com/question/14068861
Over the last three evenings, Yolanda received a total of 105 phone calls at the call center. The first evening, she received 9 more calls than the second evening. The third evening, she received 4 times as many calls as the second evening. How many phone calls did she receive each evening?
Answers
Answer:
Day 1: 25, Day 2: 16, Day 3: 64
Step-by-step explanation:
First you need to form an equation using unknowns, below i have used x to represent the number of calls
Day 1: x+9
Day 2: x
Day 3: 4x
105-9 (as day 1 is x+9) = 96
4 + 1 + 1 = 6 (6x)
96/6 = 16
x = 16, so Day 2 = 16
16 + 9 = 25
16 x 4 = 64
To check, 16 + 25 + 64 = 105
Hope this helps :D
Which of these events is not mutually exclusive?
A) the chance that you will get a heads or tails when you flip a coin once.
B) the chance that you will only study for the test alone or with a friend.
C) the chance that you will meet your friends for pizza or at a chinese restaurant for dinner today at 6.
D) the chance that you will answer the ringing phone or take a walk.
Answers
The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.
Mutually exclusive events are events that cannot occur at the same time, or that do not have any overlap. In the case of flipping a coin, the possibility of getting a head and the possibility of getting tails are independent of each other, and both can occur simultaneously. Therefore, the chance that you will get heads or tails when you flip a coin once is not mutually exclusive.
On the other hand, the other events listed (B, C, and D) are mutually exclusive. The chance that you will only study for the test alone or with a friend cannot occur simultaneously, as you can either study alone or with a friend, but not both. Similarly, the chance that you will meet your friends for pizza or at a Chinese restaurant for dinner today at 6 cannot occur at the same time, as you can either go to the pizza place or the Chinese restaurant, but not both. And the chance that you will answer the ringing phone or take a walk cannot occur simultaneously, as you can either answer the phone or take a walk, but not both.
To learn more about the mutually exclusive, visit:
brainly.com/question/28565577
#SPJ4
The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.
this question is related to probability.
mutually exclusive
Mutually exclusive events are those events that do not occur at the same time.
For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results. Such events are also called disjoint events since they do not happen simultaneously.
probability
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Learn more about probability here :-
https://brainly.com/question/30034780
#SPJ4
The following selected information was extracted from the records of B Solomon.
1. B Solomon, the owner of Solomon Traders, bought a new Machine for R250 000 on 1 July 2013.
2. On 1 October 2014, he purchased a second Machine for R350 000 cash.
3. On 30 June 2015, the Machine bought during 2013 was sold for R120 000 cash.
4. It is the business’ policy to depreciate Machines at 20% per annum on cost.
REQUIRED:
Prepare the following ledger accounts reflecting all applicable entries, in the books of Solomon Traders, properly balanced/closed off, for the years ended 31 March 2016:
1.1. Accumulated depreciation.
1.2. A Machines realisation.
NB: Show all calculations as marks will be awarded for calculations.
Answers
1.1. Accumulated depreciation:
The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.
1.2. Machine realization:
The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.
1.1. Accumulated Depreciation:
To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.
Machine bought on 1 July 2013:
Cost: R250,000
Depreciation rate: 20% per annum on cost
Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000
Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000
Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000
Accumulated depreciation for the machine bought on 1 July 2013:
As of 31 March 2014: R50,000
As of 31 March 2015: R100,000
As of 31 March 2016: R150,000
1.2. Machine Realisation:
To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.
Machine's original cost: R250,000
Accumulated depreciation as of 30 June 2015: R100,000
Net book value as of 30 June 2015:
R250,000 - R100,000 = R150,000.
On 30 June 2015, the machine was sold for R120,000.
Realisation amount: R120,000
To record the sale:
Debit Cash: R120,000
Debit Accumulated Depreciation: R100,000
Credit Machine: R250,000
Credit Machine Realisation: R120,000
Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).
These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.
For similar question on depreciation.
https://brainly.com/question/15998639
#SPJ8
the least common multiple of the two numbers is 40 the ratio of the greater number is the to the lessor number is 5, 4
Answers
if 40 is the least frequent multiple of two whole numbers. The higher number to lesser number ratio is 4:5. The two digits after that are 8 and 10.
What is Least Common Multiple (LCM)?Least Common Multiple is the meaning of the abbreviation LCM.
The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.
It can also be computed using two or more numbers.
Finding the LCM of a given collection of numbers can be done in a variety of ways.
Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple.
The smallest number among all numbers is called the least common multiple of two or more numbers.
According to our question-
The number LCM is equal to 40.
4 × 5 × x = 40
20 × x = 40
20x=40
x=2
The larger number is equal to 4 x=4(2)=8.
The smaller value is =5x=5(2)=10.
learn more about lcm click here:
https://brainly.com/question/233244
#SPJ4
Complete question-
The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 4:5. What are the two numbers?
A puzzle has 1080 pieces. How many pieces are 80% of the puzzle?
Answers
Answer:
864
Step-by-step explanation:
80/100 simplified is 4/5
so you do 4/5 of 1080
which is 1080 divided by 5 that is 216
and then 216 x 4 which is 864
Got this question for homework. I don't know how to solve it, got a few more like this so I would like to see how to do it more than the actual answer.
Answers
Part 1
Subtracting 5 from both sides yields
\(x=f(x)-5\)
Part 2
When the output, f(x) is 2, we can substitute that in to obtain
\(x=2-5=-3\)
What is the equation of the line that passes through the point (-6, -2) and has a
slope of -1/6?
Answers
Answer:
y=-1/6x-3
Step-by-step explanation:
y-y1=m(x-x1)
y-(-2)=-1/6(x-(-6))
y+2=-1/6(x+6)
y=-1/6x-6/6-2
y=-1/6x-1-2
y=-1/6x-3
Hey Whoever help me i will mark brainliest King or queen
Answers
Answer: 0.40 of a cup
Step-by-step explanation: i think im right
Please gimme the variables to define the sytem and 2 system of equations
Answers
Answer:
\(8.5x+4y=99.5,\ x+y=17\)
Step-by-step explanation:
\(\mathrm{System\ of\ equations:}\\8.5x+4y=99.5\\x+y=17\\\mathrm{where,}\ x\ \mathrm{is\ the\ number\ of\ popcorns\ and\ }y\mathrm{\is\ the\ number\ of\ candies}\)
Hello :-) just need help on solving this one
1/3(k-9)=1/3k+1/3
Answers
Answer:
There are no solutions to that.
C.
Find an equation equivalent to r = 1 + 2 sine in rectangular coordinates.
a. V2 + y2 x
= x² + y2 + 2y
x2 + y2 = 1Vx2 + y2 + 2y
b. x2 + y2 = 1x+y + 2x
d. Vo? + y2 = x2 + y2 + 2x
Answers
Click on the correct answer.
One morning it rains 1/2 inch. That afternoon it rains another 1/3 of an inch.
What is the total amount of rainfall?
1/6 of an inch
2/6 of an inch
2/5 of an inch
5.6 of an inch
Answers
write an equation in point-slope form for the line through the given point with the given slope
(10,-9)m is -2
Answers
Answer:
Step-by-step explanation:
Point: 10,-9
k=-2
y=-2x+b
So: 9, -7
8,-5
7,-3
6,-1
5,1
4,3
3,5
2,7
1,9
0,11
y=-2x+11
Answer:
y + 9 = - 2(x - 10)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - 2 and (a, b ) = (10, - 9 ) , then
y - (- 9) = - 2(x - 10) , that is
y + 9 = - 2(x - 10)
Raven and Tyler are selling their cups of hot chocolate for $2.25. They sold 11 cups. They are also selling candy canes on the side for $0.75. They spent $7.50 on supplies that they will have to pay back to the bank.
What did they earn before deducing the money needed for supplies?
Answers
The amount they earn from the sale of candy canes and cups of hot chocolate before deducting the money needed for supplies is; $31.50.
How much did they earn from candy canes?It follows from the task content that the amount earned by Raven and Tyler as in the task content is to be determined.
Since they sell their cups of hot chocolate for $2.25 in which case they sold 11 cups.
However, the question requires that the amount which they earn from the sale of candy canes is to be determined.
On this note, since each candy cane is sold for $0.75, it follows that the amount earned on 9 candy cones is;
= 9 × $0.75
= $6.75
Therefore, the amount earned from the candy canes is; $6.75.
Also, the amount earned on the 11 cups of chocolate sold is; 11 × $2.25 = $24.75.
Ultimately, the total amount they earn before deducting the money needed for supplies is; $6.75 + $24.75 = $31.50.
Read more on amount earned;
https://brainly.com/question/14220233
#SPJ1
Given that f(x) = 2x - 5, find the value of x that makes f(x) = 15.
а
5
b
10
20
Od
25
Answers
if you plug in 10 for x it will make you multiply 2 time 10 which gives you 20 then subtract 5 which gives you 15
Answer:
When x=10 f(x) is equal to 15
Step-by-step explanation:
Just substitute the two equations, 15=2x-5 -> 20=2x -> x=10.
Select the correct answer.
From the following balances for Alpha Inc., calculate the working capital of the company.
Amount ($)
50,000
80,000
10,000
80,000
2,000
Items
Accounts payable
Inventory
Tax payable
Cash at bank
Prepaid rent
OA. $62,000
OB. $102,000
OC. $60,000
O D. $222,000
Answers
Explaining: color chicken is the pa