Type I error is considered more serious because it can lead to false conclusions and wrong decisions. On the other hand, a Type II error is less serious because it is relatively easy to correct. It is better to avoid Type I errors because they can have serious consequences.
When it is difficult to perform sampling and there is high population variance, the type II error is more likely to be made.Type II error: It is failing to reject a false null hypothesis, is more likely to be made when it is difficult to perform sampling and there is high population variance. It is also known as a false negative. It denotes that the null hypothesis that is rejected is true and occurs when there is insufficient evidence to reject the null hypothesis.
When the significance level, alpha, is too high or the sample size is too small, the chances of committing a Type II error increase. In statistics, there are two different types of errors, Type I and Type II. In hypothesis testing, we make an assumption and then compare it to the available data. We reject the null hypothesis if the data contradicts it, or we accept it if the data is consistent with it.
A Type I error occurs when we reject the null hypothesis even though it is true. In other words, we conclude that there is a significant difference between the population means when there isn't one. A Type II error occurs when we accept the null hypothesis even though it is false. In other words, we conclude that there isn't a significant difference between the population means when there is one.Both types of errors have their own consequences, but they are not equally severe.
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In a certain shipment, the weights of twelve books average 2. 75 pounds. If one of books is removed, the weights of the remaining books average 2. 70 pounds. What was the weight, in pounds, of the book that was removed?
Answer:
Let's call the weight of the book that was removed "x".
The total weight of the twelve books can be represented as 12 times the average weight of 2.75 pounds:
12(2.75) = 33
After the book is removed, there are only 11 books left, and their total weight can be represented as 11 times the new average weight of 2.70 pounds:
11(2.70) = 29.7
We can set up an equation using these two expressions and the weight of the book that was removed:
33 - x = 29.7
Solving for x, we get:
x = 33 - 29.7
x = 3.3
Therefore, the weight of the book that was removed was 3.3 pounds.
Social scientists gather data from samples instead of populations because
a. samples are much larger and more complete.
b. samples are more trustworthy.
c. populations are often too large to test.
d. samples are more meaningful and interesting
Social scientists gather data from samples instead of populations because c. populations are often too large to test.
Social scientists often cannot test an entire population due to its size, so they gather data from a smaller group or sample that is representative of the larger population. This allows them to make inferences about the larger population based on the data collected from the sample. The sample size must be large enough to accurately represent the population, but it is not necessarily larger or more complete than the population itself. Trustworthiness, meaning, and interest are subjective and do not necessarily determine why social scientists choose to gather data from samples.
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Match each equation with its solution set. 2(4 - 4x) = 4- 8x 8(x+4) = 8x + 32 2(4 -4x) = 8x + 4 8(x + 4) = 8x + 4 A. all real numbers B. No solution C. 1/4 D. 4
1. Given the equation:
\(2\left(4-4x\right)=4-8x\)to solve for x:
\(\begin{gathered} 8-8x=4-8x \\ 8=4 \end{gathered}\)b. no solution
2. Given the equation:
\(8\left(x+4\right)=8x+32\)to solve for x:
\(\begin{gathered} 8x+32=8x+32 \\ 8x-8x=32-32 \\ 0=0 \end{gathered}\)a. all real numbers
3. Given the equation:
\(2\left(4-4x\right)=8x+4\)to solve for x:
\(\begin{gathered} 8-8x=8x+4 \\ 8-4=8x+8x \\ 4=16x \\ x=\frac{1}{4} \end{gathered}\)c. 1/4
4. Given the equation:
\(8\left(x+4\right)=8x+4\)to solve for x:
\(\begin{gathered} 8x+32=8x+4 \\ 32=4 \end{gathered}\)b. no solution
what are all the commom factors of 15, 45, & 90? :l
Answer: the answer is 15
Good luck, hope i helped
Answer:
1, 3, 5
Step-by-step explanation:
1 is a common factor because all numbers are divisible by 1
3 is a common factor because all the numbers are divisible by 3 (or in other words multiples of 3)
5 is a common factor of all those numbers because the last digit place in 15, 45 and 90 end in 5 and/or 0
If you're looking at 90 individually, then the common factors are 1, 2, 3, 5, 6, 9, 10, 15, 30, 45, 90
If you're looking at 45 individually, then the common factors are 1, 3, 5, 9, 15, 45
If you're looking at 15 individually, then the common factors are 1, 3, 5, 15
Help meeeeeeeeee! Please
Answer:
40 is
Rational numberIntegerWhole numberNatural numberBut it is not an
Irrational numberIn a binomial situation, n=18 and π=0.60. Determine the standard
deviation*
Answer:
Use colon method
Step-by-step explanation:
So it is more easy
let f(x,y,z)=x^3y^4 z^4 and x=s^3t^2, y=st, and z=st. calculate the primary derivatives
Therefore, the primary derivatives are: df/dx = 3x^2 * y^4 * z^4, df/dy = 4x^3 * y^3 * z^4, df/dz = 4x^3 * y^4 * z^3.
To calculate the primary derivatives of f(x, y, z) = x^3 * y^4 * z^4, where x = s^3 * t^2, y = st, and z = st, we need to differentiate f with respect to each variable x, y, and z.
The partial derivative with respect to x (df/dx) is obtained by treating y and z as constants and differentiating x^3 with respect to x:
df/dx = 3x^2 * y^4 * z^4
The partial derivative with respect to y (df/dy) is obtained by treating x and z as constants and differentiating y^4 with respect to y:
df/dy = 4x^3 * y^3 * z^4
The partial derivative with respect to z (df/dz) is obtained by treating x and y as constants and differentiating z^4 with respect to z:
df/dz = 4x^3 * y^4 * z^3
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a pilot and two passengers landed on a 2,100 foot east-west gravel strip with an elevation of 1,800 feet. the temperature is warmer than expected and after computing the density altitude it is determined the takeoff distance over a 50 foot obstacle is 1,980 feet. the airplane is 75 pounds under gross weight. what would be the best choice?
Based on the given information, the best choice would be to reduce the aircraft weight by at least 100 pounds. This would allow the aircraft to take off within the available runway distance of 2,100 feet
Based on the given information, the pilot and the two passengers landed on a 2,100 foot east-west gravel strip with an elevation of 1,800 feet. After computing the density altitude, it is determined that the takeoff distance over a 50 foot obstacle is 1,980 feet. The airplane is 75 pounds under gross weight. In this case, the best choice would be to reduce the aircraft weight by at least 100 pounds.
Here's why:
Since the takeoff distance over a 50-foot obstacle is 1,980 feet, this distance is greater than the available runway of 2,100 feet. This means that the aircraft will not be able to take off from the runway. Therefore, the pilot needs to take necessary steps to ensure that the aircraft can take off safely.
One option is to reduce the aircraft's weight, which would decrease the required takeoff distance. Since the aircraft is only 75 pounds under gross weight, the pilot would need to reduce the weight by at least 100 pounds to ensure a safe takeoff. This would allow the aircraft to take off within the available runway distance of 2,100 feet.
Therefore, reducing the weight by 100 pounds would be the best choice.
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You are a district sales manager at the sales target for your team135,000 per month ?
You are a district sales manager at the sales target for your team 135,000 per month. Your team's annual sales target is $1,620,000.
To calculate the annual sales target for your team, you need to multiply the monthly target by 12 (the number of months in a year):
Annual sales target = Monthly sales target x 12
Given that the monthly sales target for your team is $135,000, the annual sales target would be:
Annual sales target = $135,000 x 12
= $1,620,000
A Sales Manager is a professional responsible for managing a team of sales representatives within a specific geographic area or district. The role typically involves setting and achieving sales targets, developing and implementing sales strategies, and managing relationships with key customers.
Sales Managers are responsible for recruiting, training, and supervising sales staff, as well as monitoring their performance and providing coaching and guidance as needed. They also work closely with other departments within the organization, such as marketing and finance, to ensure that sales goals are aligned with overall business objectives. They must possess strong leadership and communication skills, as well as a deep understanding of their company's products or services and the competitive landscape in which they operate.
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Complete Question:-
You are a district sales manager at the sales target for your team 135,000 per month ? What is your annual sales?
If you are not a goofy ah please answer this
Answer:
72
Explanation:
First, we can find the top and bottom smaller squares of the rectangular prism. Since we are working with a variety of rectangles, we only need to use the equation L×W.
To start with, let's multiply 2×3, which gives us 6, the surface area of both the bottom and top rectangles, so now we need to multiply it by 2 to account for both of them. 6×2=12
Now, we'll find the surface area of the bigger rectangles in the middle, which are 6 by 3, so again we will need to multiply length times width, then by 2 to count both rectangles. 6×3=18×2=36
Finally, we can find the surface area of the smaller rectangles in the middle, which are 6 by 2. 6×2=12, then multiply by 2 since there are 2 of those rectangles, 12×2=24
Now to find the total surface area, we need to add the gathered surface area from each shape, 12+36+24=72
2. Let A and B be invertible 5 x 5 matrices with det. A = 3 and det B = 8. Calculate: (a) det(A? B-) (b) det (24).
(a) The determinant of A inverse multiplied by B inverse is 3/8. (b) The determinant of 24 is 24 to the power of 5.
(a) We know that det(A) × det(A inverse) = 1, and similarly for B. So, det(A inverse) = 1/3 and det(B inverse) = 1/8.
Using the fact that the determinant of a product is the product of the determinants, we have det(A inverse × B inverse) = det(A inverse) × det(B inverse) = 1/3 × 1/8 = 1/24.
Therefore, det(A × B inverse) = 1/det(A inverse × B inverse) = 24/1 = 24.
(b) The determinant of a scalar multiple of a matrix is the scalar raised to the power of the dimension of the matrix.
Since 24 is a scalar and we are dealing with a 5 x 5 matrix, the determinant of 24 is 24 to the power of 5, or 24⁵.
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20 cupcakes and 90% should be outer cupcakes
so percent of cupcakes should be out of cupcakes that will leave 70 I guess to be regular and 20 / 90% is 2 2 2 2 2 2 2 2 2 2 2
PLEASE HELP IM STUCK PLEASE HELP
Answer:
y = 3x + 5
Step-by-step explanation:
x = number of years
• bush grows 3cm per year
• the initial height is 5cm
3cm per year times x number of years: y = 3x
Add the initial height of 5cm: y = 3x + 5
find the least common denominator of the rational expressions?
The least common denominator (LCD) of the rational expressions is (x+1)(x-1).
When adding or subtracting rational expressions, we need to find a common denominator. The least common denominator (LCD) is the smallest multiple of the denominators of the rational expressions.
To find the LCD, we follow these steps:
Factor the denominators of the rational expressions.Identify the common factors.Take the product of the highest powers of each common factor.If there are any unique factors, include them as well.Simplify the resulting expression to obtain the LCD.Let's consider an example to illustrate this process:
Example:
Find the LCD of the rational expressions:
x/(x+1) and 1/(x-1)
Step 1: Factor the denominators:
x+1 and x-1
Step 2: Identify the common factors:
There are no common factors in this case.
Step 3: Take the product of the highest powers of each common factor:
Since there are no common factors, we skip this step.
Step 4: Include any unique factors:
The unique factors are x+1 and x-1.
Step 5: Simplify the resulting expression:
The LCD is (x+1)(x-1).
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The least common denominator of the rational expressions in this problem is given as follows:
4x(x + 5).
How to obtain the least common denominator?The rational expressions for this problem are defined as follows:
9/(4x + 20), 10/(x² + 5x).
The denominators are given as follows:
4x + 20.x² + 5x.The denominators can be simplified as follows:
4x + 20 = 4(x + 5).x² + 5x = x(x + 5).The least common denominator is the multiplication of the unique factors, hence it is given as follows:
4x(x + 5).
Missing InformationThe expression that completes this problem is given as follows:
9/(4x + 20), 10/(x² + 5x).
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what is 20% by 37 decreased
Answer:
37 decreased by 20% is 29.6.
Step-by-step explanation:
To do this, what we do is simply take 20% of 37 and subtract it from 37.
20% of 37. A trick to easily figure this out is multipling 37 by 20 and dividing by 100.
37*20 = 740
740 / 100 = 7.40
37 - 7.40 = 29.6
37 decreased by 20% is 29.6.
The table shows the length and width of proportional rectangles.
Length (in inches) 8 12 24 32
Width (in inches) 10 15 30 40
Using the table, find the width of a rectangle that has a length of 72.
80
90
100
105
The width of the rectangle from the length is 90 inches
How to find the width of a rectangle from the lengthFrom the question, we have the following parameters that can be used in our computation:
Length (in inches) 8 12 24 32
Width (in inches) 10 15 30 40
Also, we have
Width = 72
Since the table is a proportional table, we have the following ratio
Ratio = Length : Width
This gives
Length : Width = 8 : 10
So, we have
72 : Width = 8 : 10
Multiply by 9
72 : Width = 72 : 90
By comparison, we have
Width = 90
Hence, the width is 90
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Does the point ( 4 , 47) lie on the line y = 10 x – 3 ?
Show your working .
Answer
Step-by-step explanation:
To find out if a point (x, y) is on the graph of a line, we plug in the values and see if we get a true statement, such as 10 = 10. If we get something different, like 6 = 4, we know that the point is not on the line because it does not satisfy the equation. In the given choices, when we plug in (1, 10) we get 10 = 7 + 2, which is false, making this is the desired answer.
(4, 47) gives 47 = 10(4) - 3 = 37
47=37 is a false statement
Rebecca ran 12 1/4 miles in 2 1/2 hour. What was her average speed in miles per hour?
a. 4.9 mph
c. 30.625 mph
b. 4.8 mph
d. 5.5 mph
Answer: A
Step-by-step explanation: Divide your miles by hour hours:
12.25/2.5 = 4.9
Her average speed was 4.9 miles per hour
WILL MARK BRAINLIEST!
Simplify 3 - (2x² + 3) + (x² - 2x + 3)
Answer:
-x^2-2x+3
Step-by-step explanation:
3 - (2x² + 3) + (x² - 2x + 3)
Distribute the minus sign
3 - 2x² - 3 + x² - 2x + 3
Combine like terms
- 2x² + x² - 2x + 3-3+3
-x^2-2x+3
Assume three cards are drawn from a standard 52-card deck without replacement. Answer each of the following questions. a) What is the probability that the third card will be the two of clubs? b) Are your odds better for choosing the two of clubs on your first, second, or third draw? c) How can you use this example to illustrate the difference between independent and dependent events? d) How do the marginal, joint, and conditional probabilities change if we instead drew the cards with replacement?
a) The probability that the third card will be the two of clubs is 1/50 since there are 50 cards left in the deck after the first two cards have been drawn, and only one of them is the two of clubs.
b) Your odds are the same for choosing the two of clubs on each draw since the probability of drawing the two of clubs does not change with each draw.
c) This example illustrates the difference between independent and dependent events. In the case of drawing cards without replacement, the events are dependent since the outcome of one draw affects the probability of the next draw.
d) If we drew the cards with replacement, the marginal probabilities would not change since the probability of drawing any particular card is always 1/52. However, the joint probabilities would change since each draw is now independent.
a) To find the probability that the third card will be the two of clubs, we need to calculate the joint probability of not drawing the two of clubs in the first two draws and drawing it in the third. The probability of not drawing the two of clubs in the first draw is 51/52, and in the second draw, it is 50/51. The probability of drawing the two of clubs in the third draw is 1/50. So, the joint probability is (51/52) * (50/51) * (1/50) = 1/52.
b) The odds of choosing the two of clubs are the same for each draw: 1/52 for the first, second, or third draw. This is because the probability is based on the number of favorable outcomes (one card) over the total possible outcomes (52 cards) in a standard deck.
c) This example illustrates the difference between independent and dependent events. In this scenario, the events are dependent because each card drawn affects the remaining cards in the deck. If the events were independent, the probability of drawing the two of clubs would not change after drawing the first or second card.
d) If we draw cards with replacement, the marginal, joint, and conditional probabilities change because the events become independent. With replacement, the probability of drawing the two of clubs remains constant at 1/52 for each draw. The joint probability of not drawing the two of clubs in the first two draws and drawing it in the third becomes (51/52) * (51/52) * (1/52), and conditional probabilities will not be affected by the previous draws.
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Complete the long division problem on your own sheet of paper. Then, fill in the digits. 8) 4 1 6
For given division,
416 is dividend
8 is divisor
0 is remainder and
52 is quotient
Long division:
long division is a standard division algorithm suitable for dividing multi-digit numbers that is simple enough to perform by hand.
In the case of long division of numbers, the remainder is always smaller than the divisor. We can verify the quotient and the remainder of the division using the division formula,
Dividend = (Divisor × Quotient) + Remainder.
The above formula is also known as division algorithm.
Example:
a ÷ b
a is called dividend and b is called divisor
For given question,
416 ÷ 8
that is,
8 ) 416 ( 52
40
16
16
0
416 is dividend
8 is divisor
0 is remainder
and 52 is quotient
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Write each of the following mathematical expressions in a python expression (DO NOT INCLUDES WHITE SPACES IN YOUR ANSWER). Assume x,y and z are float variables. (1+x)(1+y)(1+z)= x+y2+z4= xyz(1+x)3=
Write the Python expressions for the following mathematical expressions: (1 + x) * (1 + y) * (1 + z), x + y² + z⁴ , and xyz * (1 + x)³ .
(1 + x) * (1 + y) * (1 + z), x + y**2 + z**4, xyz * (1 + x)**3.The given mathematical expressions can be written as Python expressions as follows:
(1 + x) * (1 + y) * (1 + z) can be written as `(1 + x) * (1 + y) * (1 + z)`x + y ² + z⁴ can be written as `x + y**2 + z**4`xyz * (1 + x)**3 can be written as `xyz * (1 + x)**3`In Python, the `**` operator represents exponentiation, so `y**2` denotes y squared and `z**4` denotes z to the power of 4.
The multiplication operator `*` is used for multiplication, and the addition operator `+` is used for addition.
Parentheses `()` are used to group operations and ensure the correct order of evaluation.
These Python expressions can be used to calculate the respective mathematical expressions for given values of x, y, and z.
The expressions follow the mathematical operations and precedence rules, allowing for accurate computation in Python.
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for each diagram, determine whether angles 1 & 2 are adjacent angles, heeeelp please :(
Answer:
Diagram 5: Not adjacent angles
Diagram 6: Not adjacent angles
Diagram 7: Are adjacent angles
Diagram 8: Are adjacent angles
Step-by-step explanation:
In order for angles to be adjacent, they need to have all of three things:
1. Have a common vertex
2. Have a common side
3. Must not overlap
Diagram 5 does not have a common side between angles 1 and 2, so it is not adjacent.
Diagram 6 does not even have angles 1 and 2 connected in any way so it is not adjacent.
Diagrams 7 and 8 have all three conditions, so those diagrams are adjacent.
The world's largest sunflower was about 300 inches tall. julie says her sunflower will be that tall after 3 months. is julie's answer reasonable? explain why or why not.
Julie's claim that her sunflower will be 300 inches tall after just 3 months is not reasonable.
Sunflowers typically have a growth cycle that spans several months, and their growth rate varies depending on various factors such as sunlight, soil quality, water availability, and genetics. While sunflowers can grow quite tall, reaching heights of 10-15 feet or more, it usually takes them a significant amount of time to achieve such heights.
It is highly unlikely for a sunflower to grow to a height of 300 inches (25 feet) in just 3 months. Such rapid growth would be extraordinarily uncommon and would require exceptional conditions, which are typically not achievable in a regular home garden or natural environment.
Furthermore, the average growth rate of a sunflower is around 2-3 inches per week under optimal conditions. Considering this rate, even with ideal circumstances, it would take approximately 3 to 4 months for a sunflower to grow to a height of 300 inches.
In conclusion, Julie's claim is not reasonable as it goes against the typical growth pattern and rate of sunflowers. The claim of achieving a height of 300 inches in just 3 months is highly improbable and would require extraordinary circumstances.
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whats five and twenty-three thousandths wirten as a decimal giving brainest
Answer:
5.023 I believe
Step-by-step explanation:
Factor 12+54. Write your answer in the form a(b+c) where a is the GCF of 12 and 54
For the answer of factors of expression (12 + 54), in the form of a(b + c), where a is the GCF of 12 and 54 is equals to 6( 2 + 9).
In math, to factor a number means to express it as a product of (other) whole numbers, called its factors. For example, if 7x5 = 35, 7 and 5 are both factors. The divisors that give the remainder to be 0 are the factors of the number. We have an expression of numbers, 12 + 54. We have to write this expression in form of a( b + c), where a is GCF of 12 and 54. Now, we can write the factors of 12 and 54 are 12 = 2×2×3
54 = 2×3 ×3×3
The greatest common factor, GCF of 12 and 54 is 2×3 = 6. So, 12 + 54 = 6× 2 + 6×9
Taking out the common factor 6 from above expression, 6( 2 + 9) which is required form a( b + c). Hence, required expression is 6( 2 + 9).
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A Small Publishing Company is planning to publish a new look. The Production Costs will include one-time fixed cost (such as edition) andVariable Casts (such as Printing). The One-time fixed Costs will total $10,300. The Vouciable Casts will be $12 per book. The Publisher Will Sell the finished froduct to bookstores at a price of $118.25 per bookHow Many books must the Publisher Produce and sell So that the producation Costs will equal the money from Sales?
Using the provided values and making an equivalent equation and equating the equation to solve for the number of books required to break even, The answer is 97 books should be produced and sold.
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.
What are the methods to solve system of equations?There are three ways to solve systems of linear equations :
GraphingSubstitution methodElimination methodrequired equation,
10300 + 12x = 118.25x
solving for x , we get,
106.25x = 10300
x=10300/106.25
=97
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What is the common difference between successive terms in the sequence? 0.36, 0.26, 0.16, 0.06, -0.04, -0.14, ... a) -0.1 b) -0.1, 0.1 c) -0.1, 0.2 d) 0.1
The common difference between successive terms in this sequence is -0.1.
The common difference between successive terms in a sequence is the constant value that is added or subtracted to each term to obtain the next term in the sequence. To find the common difference in the given sequence, we need to subtract each term from the term that follows it.
Subtract the first term (0.36) from the second term (0.26): 0.26 - 0.36 = -0.1
Subtract the second term (0.26) from the third term (0.16): 0.16 - 0.26 = -0.1
Subtract the third term (0.16) from the fourth term (0.06): 0.06 - 0.16 = -0.1
Based on the calculations, the common difference between successive terms in this sequence is -0.1. Therefore, the correct answer is a) -0.1.
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a bank's loan officer rates applicants for credit. the ratings are normally distributed with a mean of 210.0 and a standard deviation of 50.0. if an applicant is randomly selected, find the probability of a rating that is between 176.0 and 214.0.
The probability of a rating that is between 176 and 214 is,
\(P(176\leq x\leq 214)=0.21994\)
Since the credit ratings are normally distributed.
Now, apply the formula for normal distribution. Which is shown below,
\(z=\frac{x-u}{sd}\)
x=credit ratings for applicants.
u=mean.
sd standard deviation.
From the given information, µ = 210 and σ = 50
For x = 176,
\(z=\frac{176-210}{50} =-0.68\)
In the normal distribution table, the probability corresponding to the -0.68 z-score is 0.25175
For x =214,
\(z=\frac{214-210}{50} =0.08\)
In a normal distribution table, the probability corresponding to the z score of 0.08 is 0.03788
Thus,
\(P(176\leq x\leq 214)=0.25175-0.03181=0.21994\)
Hence, The probability of a rating that is between 176 and 214 is,
\(P(176\leq x\leq 214)=0.21994\)
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Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. the first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.
1. Write an equation for each tank representing the total amount of water in gallons in the tank, y, in terms of the number of hours, x, that the tank drains
2. what is the solution to this system of equations.
3. suppose Aiko starts draining the tanks at the same time. When will both tanks have the same amount of water? How much water is in each tank at that time
The answers to each part is mentioned above.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.
( 1 ) -Equation for tank {1} -
y = 175 - 25x
Equation for tank {2} -
y = 200 - 30x
( 2 ) -For the solution we can write -
175 - 25x = 200 - 30x
- 25x + 30x = 200 - 175
5x = 25
x = 5
and
y = 200 - 150
y = 50
( 3 ) -For the same amount of water we can write -
175 - 25x = 200 - 30x
- 25x + 30x = 200 - 175
5x = 25
x = 5 hours
In tank (1), there is : 175 - 25 x 5 = 50 gallons
In tank (2), there is : 200 - 30 x 5 = 50 gallons
Therefore, the answers to each part is mentioned above.
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