John is twice as old as his son. In 42 years, the ratio of their ages will be 4:3. What is the son's current age?
Answers
Answer: Jhon is 42 years old, and his son is 21 years old.
Step-by-step explanation:
Let's define:
J = John's age
S = Age of the son.
We know that:
"John is twice as old as his son"
J = 2*S
"In 42 years, the ratio of their ages will be 4:3. What is the son's current age?"
In 42, their ages will be:
J + 42 and S + 42.
And the ratio 4:3 means that:
(J + 42) = (4/3)*(S + 42)
Then we have the system of equations:
J = 2*S
(J + 42) = (4/3)*(S + 42)
To solve it we can first replace the first equation into the second one, to get:
(2*S + 42) = (4/3)*(S + 42)
2*S - (4/3)*S = (4/3)*42 - 42
S*(6/3 - 4/3) = (1/3)*42
S*(2/3) = (1/3)*42
S = (3/2)*(1/3)*42 = 21.
And we can find Jonh's age if we use the first equation:
J = 2*S = 2*21 = 42
Jhon is 42 years old, and his son is 21 years old.
Related Questions
A tank contains 50 kg of salt and 1000 L of water. A solution of a concentration 0.025 kg of salt per liter enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the same rate.
Answers
(a) The initial concentration of the solution in the tank is 0.05 kg/L. (b) After 2.5 hours, the amount of salt in the tank remains unchanged at 50 kg. (c) As time approaches infinity, the concentration of salt in the solution remains constant at 0.05 kg/L.
(a) The initial concentration of the solution in the tank can be calculated by dividing the total amount of salt initially present by the total volume of the solution initially.
Total amount of salt initially = 50 kg
Total volume of the solution initially = 1000 L
Concentration of the solution initially = (Total amount of salt initially) / (Total volume of the solution initially)
Concentration of the solution initially = 50 kg / 1000 L = 0.05 kg/L
Therefore, the concentration of the solution in the tank initially is 0.05 kg/L.
(b) Find the amount of salt in the tank after 2.5 hours.
In this case, we need to consider the amount of salt entering and leaving the tank over time.
Amount of salt entering the tank per minute = concentration of the incoming solution × rate of incoming solution
Amount of salt entering the tank per minute = 0.025 kg/L × 10 L/min = 0.25 kg/min
Amount of salt leaving the tank per minute = concentration of the solution in the tank × rate of outgoing solution
Amount of salt leaving the tank per minute = (amount of salt in the tank) / (total volume of the solution in the tank) × 10 L/min
Since the incoming and outgoing rates are equal (10 L/min), the amount of salt in the tank after a certain time remains constant. Let's calculate the amount of salt in the tank after 2.5 hours (150 minutes).
Amount of salt entering the tank in 150 minutes = 0.25 kg/min × 150 min = 37.5 kg
The amount of salt in the tank after 2.5 hours remains the same as the initial amount, as there is no net change in the salt content.
Therefore, the amount of salt in the tank after 2.5 hours is 50 kg.
(c) Find the concentration of salt in the solution in the tank as time approaches infinity.
As time approaches infinity, the concentration of salt in the solution in the tank will be determined by the ratio of the total amount of salt in the tank to the total volume of the solution in the tank.
Total amount of salt in the tank = 50 kg
Total volume of the solution in the tank = 1000 L
Concentration of salt in the solution as time approaches infinity = (Total amount of salt in the tank) / (Total volume of the solution in the tank)
Concentration of salt in the solution as time approaches infinity = 50 kg / 1000 L = 0.05 kg/L
Therefore, as time approaches infinity, the concentration of salt in the solution in the tank will be 0.05 kg/L, the same as the initial concentration.
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Complete question:
A tank contains 50 kg of salt and 1000 L of water. A solution of a concentration 0.025 kg of salt per liter enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the same rate. (a) What is the concentration of our solution in the tank initially? (b) Find the amount of salt in the tank after 2.5 hours. (c) Find the concentration of salt in the solution in the tank as time approaches infinity.
does this function equal 4 on the interval [4, 5]?
\( \frac{10 \cos(xπ) }{x-2} \)
Answers
=- No way
Step-by-step explanation:
The width of a rectangle measures (3s+t) centimeters, and its length measures (3s-9t) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
-16+12s
6s-8
12s+1-18t
12s-16t
Answers
Answer:
Step-by-step explanation:
Hello!
2(3s+7) + 2(3s-9t)
= 6s +14 + 6s -18t
= 12s -18t +14
Find the measures of 21 and 2
Answers
Measure 2 would be 121 degrees (vertical angle theorem)
Pls help
Thank you ❤️
Answers
Answer:
the difference is 78
the avg drop is 3 degrees per kilometer
Step-by-step explanation:
Hope this helps
the difference of eleven and four times five
Answers
Answer:11-4x5 = 11-20 = -9 or you could treat the "difference" as always positive, the absolute value of -9, or 9
Step-by-step explanation: sorry i don’t know
Answer:
9?
Step-by-step explanation:
Megan has a piece of fabric which is a right triangular shape. The length of leg 1 is 4 m. The length of the other leg is twice the length of leg 1. What would be the length of the third side of the fabric?
8.94 m
7.21 m
6.93 m
4.47 m
Answers
Answer:
8.94 m
Step-by-step explanation:
Use the Pythagorean Theorum - \(a^2 + b^2 = c^2\). Use leg 1 as a, leg 2 as b, and the third side as c.
We know leg 1 is 4, and that leg 2 is twice as long as leg 1...
\((4)^2 + (4*2)^2 = c^2\)
Now, we use the Order of Operations to find \(c^2\)...
\(4^2+8^2=c^2\\16+64=c^2\\80=c^2\)
Now, we find the square root of \(c^2\) to find c...
\(\sqrt{80} =8.94\)
So, the length of the third side is 8.94 m.
samples of size 10 are selected from a manufacturing process. the mean of the sample ranges is 0.8. what is the estimate of the standard deviation of the population? (round your answer to 3 decimal places.)
Answers
The estimated standard deviation of the population is approximately 0.133 (rounded to 3 decimal places).
To estimate the standard deviation of the population, we will use the formula of the standard deviation using the sample means, also known as the standard error. The formula gives the standard error (SE):
SE = (s / √n)
Where:
s is the standard deviation of the sample means
n is the sample size
In this case, we know, the mean of the sample ranges is 0.8, but we don't have the exact sample data. As a result, we are unable to calculate the standard deviation (s).
However, we can an assumption that the sample ranges are normally distributed, which gives us the idea to use the relationship between the range and the standard deviation. For normally distributed data, the range is approximately equal to 6 times the standard deviation. Mathematically, we can express this as:
Range ≈ 6s
Given that the mean of the sample ranges is 0.8, we have the following:
0.8 ≈ 6s
Now, let's solve for s:
s ≈ 0.8 / 6 ≈ 0.133
So, the estimate of the population's standard deviation is approximately 0.133 (rounded to 3 decimal places).
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A randomized controlled trial in which each subject is assigned to a combination of at least two independent variables is an example of a/an:
Answers
A randomized controlled trial in which each subject is assigned to a combination of at least two independent variables is an example of a Factorial Design.
In statistics, a full factorial experiment is one in which all potential combinations of the levels across all of the factors are taken into account by the experimental units. A full factorial experiment has two or more factors with discrete possible values or "levels" in its design. A fully crossed design is another name for a full factorial design. Using such an experiment, the researcher can examine how each element affects the response variable as well as how different factors interact with one another.
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The standard deviation is _____ when the data are all concentrated close to the mean, exhibiting little variation or spread.
Answers
The standard deviation is relatively small when the data are all concentrated close to the mean, exhibiting little variation or spread.
The standard deviation could be a degree of the changeability or spread of a set of information. It is calculated by finding the square root of the normal of the squared contrasts between each information point and the cruel(mean).
In other words, it tells us how much the information values are scattered around the mean.
When the information is all concentrated near the cruel(mean), it implies that the contrasts between each information point and the cruel are moderately little.
This comes about in a little while of squared contrasts, which in turn leads to a little standard deviation. On the other hand, when the information is more spread out, it implies that the contrasts between each information point and the cruel are bigger.
This comes about in a bigger entirety of squared contrasts, which in turn leads to a bigger standard deviation.
For case, let's consider two sets of information:
Set A and Set B.
Set A:
2, 3, 4, 5, 6
Set B:
1, 3, 5, 7, 9
Both sets have the same cruel(mean) (4.0), but Set A encompasses a littler standard deviation (1.4) than Set B (2.8).
This is because the information values in Set A are all moderately near to the cruel(mean), while the information values in Set B are more spread out.
Subsequently, we will say that the standard deviation is generally small when the information is all concentrated near the mean, showing a small variety or spread.
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TRUE or FALSE?
Both horror and comedy can use dramatic irony because both horror and comedy
use what the audience knows to create either suspense or humor.
True
Or
False
Answers
Answer:
True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
can you please solve this question 5x-4=31
Answers
Step-by-step explanation:x=7
5x-4=31
5x=31+4
5x=35
x=35/5
x=7
Answer:
x = 7
Step-by-step explanation:
Given
5x - 4 = 31 ( add 4 to both sides )
5x = 35 ( divide both sides by 5 )
x = 7
How do I find the surface area of a cylinder?
Answers
Answer:
SA = 2πr² + 2πrh
Step-by-step explanation:
2πr² will provide the surface area of the top and bottom of the cylinder
2πrh will provide the surface area of the cylinder portion that connects the top and bottom
E1.8 (lo 2), ap evilene company makes industrial-grade brooms. it incurs the following costs.
1. salaries for broom inspectors.
2. copy machine maintenance at corporate headquarters.
3. hourly wages for assembly workers.
4. research and development for new broom types.
5. salary for factory manager.
6. depreciation on broom-assembly equipment.
7. salary for the ceo administrative assistant.
8. wood for handles.
9. factory cleaning supplies.
10. lubricants for broom-assembly factory equipment.
11. salaries for customer service representatives.
12. salaries for factory maintenance crew.
13. sales team golf outings with customers.
14. salaries for the raw materials receiving department employees. 1
5. advertising expenses. 1
6. depreciation on the cfo company car.
17. straw for brooms. 1
8. salaries for sales personnel.
19. shipping costs to customers.
instructions a. indicate whether each cost is direct materials, direct labor, manufacturing overhead, or nonmanufacturing.
indicate whether each cost is a product cost or a period cost.
Answers
Based on the costs to AP Evilene Company which makes industrial-grade brooms, the classifications of the costs are:
Product and ManufacturingPeriod and nonmanufacturing Product and Direct labor Period and nonmanufacturing Product and ManufacturingProduct and ManufacturingPeriod and nonmanufacturing Product and Direct materialsProduct and ManufacturingProduct and ManufacturingPeriod and nonmanufacturingProduct and ManufacturingPeriod and nonmanufacturing Period and nonmanufacturing Period and nonmanufacturing Period and nonmanufacturing Product and Direct materialsPeriod and nonmanufacturing Period and nonmanufacturing What are the types of costs?There are period costs which are those which are only incurred in a period of production and are not related to production of goods and services but instead to the selling of them.
Product costs are incurred when the business produces a good or service. They can be direct labor or materials, or a manufacturing overhead that is indirectly related to production.
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Solve for x.. 5x+18=45
Answers
Answer: x=5.4
Step-by-step explanation:
5x+18=45
-18 on both sides
45-18=27
5x=27
divide 5 on both sides
x=5.4
Answer: x=5.4
Step-by-step explanation:
5x=27
x=5.4
a chart that compares three set of values in a three-dimensional chart is _____.
Answers
A chart that compares three sets of values in a three-dimension chart is called surface.
A two-dimensional collection of points (flat surface), a three-dimensional collection of points with a curved cross section (curved surface), or the perimeter of any three-dimensional solid are all examples of surfaces in geometry.
A surface is typically a continuous boundary that separates two areas of a three-dimensional space. For instance, a sphere's surface divides its interior from its exterior, and a horizontal plane divides the half-planes above and below it. Despite the fact that regions they contain are three-dimensional and have a volume, surfaces are basically two-dimensional and have an area. Despite this, surfaces are frequently referred to by the names of the regions they surround. Differential geometry studies the characteristics of surfaces, particularly the concept of curvature.
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A number to the 8th power divided by the same number to the 5th power equals 512. What is the number?
The number is
Answers
Answer:
8
Step-by-step explanation:
Let the long-run profit function for a representative firm is given by π i
=p 2
−2p−399, where p is the price of computer. The inverse market demand for computer is given by p=39−0.009q, where q is unit of computers. Suppose technology for producing computers is identical for all firms and all firms face identical input prices. (a) Find the firm's output supply function. (b) Find the market-equilibrium price and the equilibrium number of firms. (c) Find the number of computers sold by each firm in the long run.
Answers
(a) The firm's output supply function is given by q = (p + 199) / 2.
(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.
(c) Each firm sells 70 computers in the long run.
To find the firm's output supply function, we need to maximize the firm's profit function, which is given by π = p^2 - 2p - 399. In the long run, firms will produce where marginal cost equals marginal revenue. Marginal revenue can be obtained by differentiating the inverse market demand function with respect to q, and marginal cost is equal to the derivative of the profit function with respect to q. Equating the two, we get:(39 - 0.009q) = (2q - 2) / q
Simplifying the equation, we find:
q = (p + 199) / 2
This represents the firm's output supply function.
To find the market-equilibrium price and the equilibrium number of firms, we need to find the intersection point of the market demand and supply. Substituting the output supply function into the inverse market demand function, we have:p = 39 - 0.009((p + 199) / 2)
Simplifying and solving for p, we get:
p ≈ $32.56
Substituting this price back into the output supply function, we find:
q = (32.56 + 199) / 2 ≈ 115.78
Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:
Number of firms = q / 70 ≈ 10
Since each firm sells 70 computers in the long run, and there are 10 firms, the total number of computers sold by each firm is:70 * 10 = 700
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Please help this is a geometry problem
Answers
Answer:
36√3
Step-by-step explanation:
Given a=36 and ∠α=30°,
b = √c^2 - a^2
= √72^2 - 36^2
= √3888
= 62.35383 = 36√3
Thanks.
Smith City received 2. 45 inche of rain on Monday and 1. 72 inche of rain on Tueday. Write an equation howing a way to etimate to the nearet inch the total rainfall for the two day
Answers
an equation showing a way to estimate to the neasrt inch the total rainfall for the two day 2.45 + 1.72 ≈ 4.2 inches
1. Add the two amounts of rainfall together: 2.45 + 1.72
2. Round the answer to the nearest inch: 4.2 inches
3. The equation to estimate the total rainfall for the two days is 2.45 + 1.72 ≈ 4.2 inches.
This equation provides a simple way to estimate the total rainfall for two days. By adding the two amounts of rainfall, we can then round the answer to the nearest inch to obtain the estimated total rainfall. This equation can be used to quickly and accurately estimate rainfall totals for any two-day period.
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On a piece of paper, graph f(x) = (3x if x< 3) (f(x) = 2x if x > 3) Then determine which answer
choice matches the graph you drew.
Answers
\(if\ \alpha < 3\)
\(f(\alpha )=3\alpha\)
\(if\ x\ \geqslant 3\)
\(f(x)=2x\)
\(Sin\ you\ get\ the\)
\(yoiclure\ on\ the\)
\(right.\)
I hope this helps you
:)
The choice that matches the graph of the function as is defined to us is: Graph A.
What is a function?A function in math is a rule or expression that defines a relationship between one variable (the input or independent variable) and another variable (the output or dependent variable).
We are given a function f(x) as:
f(x)= 2x if x < 3 and 4 if x ≥ 3
This means that in the region (-∞,3) the graph of a function is a straight line that passes through the origin and has a open circle at x=3. and in the region [3,∞) the graph is a straight horizontal line i.e. y=4.
Hence, the graph of this function is: Graph A.
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write the general form of the equation of a line that is parallel to the given line and passes through the given point.
y= -1/3x+2 (-4,0)
Answers
Answer:
y = -1/3x - 4/3
Step-by-step explanation:
y = -1/3x + b
0 = -1/3(-4) + b
0 = 4/3 + b
-4/3 = b
What are the conditions for one-sample t-procedures?.
Answers
The conditions for conducting one-sample t-procedures are as follows:
1. Random Sample: The data should be obtained from a random sample or a randomized experiment to ensure that it is representative of the population of interest. This condition helps to minimize bias and ensure the validity of statistical inference.
2. Independence: The observations within the sample should be independent of each other. In other words, the values should not be influenced by each other and should be selected or measured independently. Violation of independence can lead to inaccurate results.
3. Normality or Large Sample Size (Central Limit Theorem): The population from which the sample is drawn should follow a normal distribution, or the sample size should be sufficiently large. If the population is known to be normally distributed, there are no specific requirements on the sample size. However, if the population distribution is unknown, the sample size should generally be at least 30 to apply the Central Limit Theorem, which states that the sample mean tends to follow a normal distribution, regardless of the population distribution shape.
4. Outliers: The presence of outliers can have a significant impact on the results of t-procedures. It is important to check for and address any outliers in the data. Outliers can distort the distribution and violate the assumptions of the t-test.
5. Equal Variances (for two-sample t-test): In the case of a two-sample t-test, if comparing two groups, the variances of the two populations should be equal. This assumption is necessary for calculating the correct degrees of freedom and obtaining accurate results. If the variances are not equal, a modified version of the t-test, called the Welch's t-test, can be used instead.
It is important to carefully assess these conditions before conducting one-sample t-procedures to ensure that the results are valid and reliable. Violations of these conditions may require alternative statistical tests or adjustments to the analysis.
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Suppose pricing playstations is a repeated game in which walmart and target will be selling the game system in competition over a long period of time. in this case, what is the most likely outcome?
Answers
While an equilibrium outcome around a competitive price level is a likely expectation in a repeated pricing game, the specifics of the outcome would depend on the specific circumstances, strategies, and changes in the market over time.
In a repeated game of pricing competition between Walmart and Target over a long period of time, the most likely outcome would depend on several factors, including the strategies employed by both players and the dynamics of the market.
However, in a competitive market, it is often expected that price competition will lead to a near-equilibrium outcome over time. The outcome is likely to stabilize around a price level where both companies achieve a balance between maximizing their profits and remaining competitive.
This equilibrium price level could be influenced by factors such as the companies' cost structures, market demand, brand loyalty, and market share. The outcome could also be influenced by strategic considerations, such as collusion, price matching policies, or other competitive strategies that the companies may adopt.
It's important to note that predicting the precise outcome of a repeated game in a real-world market is challenging due to various factors and uncertainties involved. Market conditions, consumer preferences, and the strategies employed by both companies can change over time, leading to shifts in the competitive dynamics and outcomes.
Therefore, while an equilibrium outcome around a competitive price level is a likely expectation in a repeated pricing game, the specifics of the outcome would depend on the specific circumstances, strategies, and changes in the market over time.
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Per has 32 cans of lead paint. If he drinks 16 , adn buys 2 times as many as he had, how many cans of paint would per have?
Answers
Answer:
the answer is 32
Step-by-step explanation:
A $ 280 suit is marked down by 30%. find sale price
Answers
Answer:
196
Step-by-step explanation:
If the suit is marked down by 30% that means you must pay
100-30 or 70%
280 * 70%
280 *.7
196
1) Which is the best estimate for the amount of grass in the lawn
A.125ft
B.125sq ft
C.1,250ft
D.1,250sq ft
2) Which is the best estimate for the total length of the bricks?
A.125ft
B.125sq ft
C.1,250ft
D. 1,250sq ft
Answers
Answer:
for number one the answer is D). 1,250 sq ft. for number 2 it is A.) 125 ft
Thats all you really need to answer, it doesnt ask for you to explain it or anything.
The typical value of homes in Sparta is $139,594. If a home appreciates at 2.1% each year, what will the value be 7 years from now?
Answers
Answer:
161453.307585
Step-by-step explanation:
139,594(1 + 0.021)^7
139,594(1.021)^7
139,594 x 1.1565920282
161453.307585
Please help ASAP geometry
Answers
The rounded area of the figure is approximately 86.9 square units.
To find the area of the figure, we need to calculate the sum of the area of the rectangle and the area of the semicircle.
Rectangle Area:
The length of the rectangle is 14 units and the width is 8 units. The area of a rectangle is calculated by multiplying its length and width. Therefore, the area of the rectangle is 14 × 8 = 112 square units.
Semicircle Area:
The semicircle is removed from one of the short sides of the rectangle. The radius of the semicircle is half the width of the rectangle, which is 8/2 = 4 units.
The area of a semicircle is given by (π × r^2) / 2, where r is the radius. Therefore, the area of the semicircle is (π × 4^2) / 2 = 8π square units.
Total Area:
Now we can calculate the total area by subtracting the area of the semicircle from the area of the rectangle:
Total Area = Rectangle Area - Semicircle Area
= 112 - 8π
To round to the nearest tenth, we need to evaluate the numerical value of π. Using an approximation of π as 3.14, we can calculate the total area:
Total Area ≈ 112 - 8 × 3.14
≈ 112 - 25.12
≈ 86.88
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How long do drivers generally need to wait at a red light in Washington DC what data would you collect
Answers
In Washington DC, drivers generally need to wait between 30 to 120 seconds at a red light.
To collect data on this, you would need to measure the duration of time that drivers wait at multiple red lights throughout the city and calculate the average wait time. Other data that could be collected include the time of day and location of the intersection, as well as any traffic patterns or incidents that could impact wait times.
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