1)
In this question, we have been given Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.
1 minute = 9 liters
⇒ 60 seconds = 9 liters
⇒ 20 seconds = 3 liters
We need to find the amount of water in the tank A
a) when 4 minutes
Given that, 1 minute = 9 liters
Let y1 liters of water in the tank A after 4 minutes
So, we get an equation,
y1 = 9 × 4
y1 = 36 liters
36 + 124 (initial water level) = 160 liters
Hence, 160 liters of water in the tank A after 4 minutes been passed.
b) when 80 seconds
From given information, 20 seconds = 3 liters
Let y2 liters of water in the tank A after 80 seconds
So, we get an equation,
20 (y2) = 3 × 80
y2 = 12 liters
12 + 124 (initial water level) = 136 liters
Hence, 136 liters of water in the tank A after 80 seconds been passed.
Now we need to find the amount of time passed when Tank A contains the following amounts of water.
i) 151 liters
151 - 124 = 27 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t1 be the required time.
so, we get an equation,
9 × t1 = 1 × 27
t1 = 27 / 9
t1 = 3 minutes
This means, 3 minutes have passed when Tank A contains 151 liters of water.
ii) 191.5 liters
191.5 - 124 = 67.5 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t2 be the required time.
so, we get an equation,
9 × t2 = 1 × 67.5
t2 = 67.5 / 9
t2 = 7.5 minutes
t2 = 7 minutes 30 seconds
This means, 7 minutes 30 seconds have passed when Tank A contains 191.5 liters of water.
iii) 270.25 liters
270.25 - 124 = 146.25 liters of more water filled.
As we know, 1 minute = 9 liters ..............................(Given)
Let t1 be the required time.
so, we get an equation,
9 × t1 = 1 × 146.25
t3 = 146.25 / 9
t3 = 16.25 minutes
t3 = 16 minutes 15 seconds
This means, 16 minutes 15 seconds have passed when Tank A contains 270.25 liters of water.
----------------------------------------------------------------------------------------------------
2)
In this question, Tank B, which initially contained 80 liters of water, is being drained at a rate of 2.5 liters per minute.
⇒ 1 minute = 2.5 liters of water drained
⇒ 60 seconds = 2.5 liters
⇒ 10 seconds = 0.42 liters
We need to find the amount of water drained from tank B
a) after 30 seconds
Let x1 be the amount of water drained after 30 seconds
Given that, 1 minute = 2.5 liters
So, we get an equation.
10 (x1) = 30 × 0.42
x1 = 3 × 0.42
x1 = 1.26 liters
b) after 7 minutes
Let x2 be the amount of water drained after 30 seconds
Given that, 1 minute = 2.5 liters
So, we get an equation.
x2 = 7 × 2.5
x2 = 17.5 liters
Now, we need to find the time in which the water is draining when Tank B contains
i) 75 liters
80 - 75 = 5 liters of more water drained.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t1 be the required time.
so, we get an equation,
2.5 × t2 = 5
t1 = 5 / 2.5
t1 = 2 minutes
This means, after 2 minutes Tank B contains 5 liters of water.
ii) 32.5 liters
80 - 32.5 = 47.5 liters of more water drained.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t2 be the required time.
so, we get an equation,
2.5 × t2 = 47.5
t2 = 47.5 / 2.5
t2 = 19 minutes
This means, after 19 minutes Tank B contains 32.5 liters of water.
iii) 18 liters
80 - 18 = 62 liters of more water filled.
As we know, 1 minute = 2.5 liters water drained ............(Given)
Let t3 be the required time.
so, we get an equation,
2.5 × t3 = 62
t3 = 5 / 2.5
t3 = 24.8 minutes
t3 = 24 minutes 48 seconds
This means, after 24 minutes 48 seconds Tank B contains 18 liters of water.
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hi please help me ii need this one right now
Answer:the graph is not linear
Step-by-step explanation:
How+long+will+it+take+for+$2900+to+grow+to+$25,600+at+an+interest+rate+of+10.4%+if+the+interest+is+compounded+quarterly?+round+the+number+of+years+to+the+nearest+hundredth.+group+of+answer+choices
The number of years to the nearest hundredth is t = 21 years and 3 months.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
It is given that:
A = $25,600
P = $29,00
r = 10.4 = 0.104
n = 4
[tex]\rm 25600 = 2900(1+\dfrac{0.104}{4})^{4t}[/tex]
After solving:
t = 21.212 years
Or
t = 21 years and 3 months
Thus, the number of years to the nearest hundredth is t = 21 years and 3 months.
The complete question is:
How long will it take for $2900 to grow to $25,600 at an interest rate of 10.4% if the interest is compounded quarterly round the number of years to the nearest hundredth?
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How many units from zero is 0 on the number line? What is the opposite of 0?
Answer:
The absolute value of a number is the distance between the number and zero on a number line. Every number and it opposite are the same distance from zero on the number line.
what is 11 9/8 as a mixed number in the simplest form
Answer:
97/8
Step-by-step explanation:
first we multiply 11 x 8 to get 88
then we add the numerator (number on top,9) so we add 88+9 to get 97
now we can write our answer
97/8
it cannot be simplified any more than this.
i hope this helped and if you have any questions just ask!
Can someone please solve it ?
Answer:
A. because all of the numerators are larger than the denominators, there will be a product left over.
Step-by-step explanation:
2.2 question 7) Which lines are perpendicular? The_____ lines are perpendicular (blue and green) How do you know? The product of their slopes is....
The following addition problem is not correct if the numbers are interpreted as base 10. In what number base is the problem correct? 66 87 85 48
The base is 24.
Let the base be b. we know that b>8
If we added everything, it would look something like this:
66 + 87 + 85 + 48
=132
Adding up the one's digit gives us 26, so we have 26 mod b=2
The only options for b are b = 12 or 24.
If b = 12, the sum of the one's digit would be [tex]22_{12}[/tex] so we could carry the 2 to the tens column. Adding everything up would give us [tex]24_{12}[/tex] the answer is [tex]242_{12}[/tex]
That means the base is 24.
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HELP ME QUICK PLEASE!!
Manny took home a couple of his friends after soccer practice. He originally had 4 gallons of gas in his car. He used 1.05 gallons of gas to take one friend home and three tenths gallon to take the other friend home. How much gas did he have left in his car after taking both friends home?
A: 1.04 gallons
B: 2.95 gallons
C: 3.70 gallons
D: 2.65 gallons
D) 2.65 gallons of gas left in his car after taking both friends home when 1.05 gallons of gas is used to take one friend home and three tenths gallon to take the other friend home.
Manny used 1.05 + 0.3 = 1.35 gallons of gas to take his friends home.
Since he originally had 4 gallons of gas, he had 4 - 1.35 = 2.65 gallons of gas left in his car after taking both friends home.
So the answer is D.
Here is the solution in more detail:
Manny started with 4 gallons of gas.
He used 1.05 gallons of gas to take one friend home.
He used 0.3 gallons of gas to take the other friend home.
The total amount of gas he used was 1.05 + 0.3 = 1.35 gallons.
Therefore, he had 4 - 1.35 = 2.65 gallons of gas left in his car.
I hope this helps! Let me know if you have any other questions.
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Open the cpt manual to the page that contains code 40490. what section of the cpt coding manual is this code listed in?
The section of the CPT coding manual is the code 40490 is listed in is "digestive system."
What is CPT codes?CPT is the language used by providers and payers when billing medical procedures and services for reimbursement.
Some key features regarding the CPT codes are-
CPT or Current Procedural Terminology, is a set of medical codes used to describe the procedures and services performed by physicians, allied health care professionals, provided by trained practitioners, healthcare facilities, outpatient facilities, and laboratories.CPT codes, in particular, are used to notify services and procedures to both federal and private payers for repayment of rendered healthcare services.CPT codes were developed by the American Medical Association (AMA) in 1966 to standardize reporting of medical, surgery, and diagnosis and treatment procedures and services performed in both inpatient and outpatient settings. Each CPT system defines a written description of a process or service, removing the need for the patient's subjective interpretation of what was provided.To know more about the CPT codes, here
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Unit 2 Logic and Proof Homework 1 Inductive reasoning
Answer:
The answers for this question is given below in the explanation section, kindly refer.
Step-by-step explanation:
Find the next 5 terms:
1) 28 < 33, 38, 43, 48, 53 => In every next term 5 is added.
2) 64 < 32, 16, 8, 4, 2 => In every next step the term is divided by 2.
3) 64 < 125, 216, 343, 512, 729 => In every next step it is a cube of next number.
4) 13 < 17, 19, 23, 29, 31 => In every next term it is the next prime number.
5) V < VI, VII, VIII, IX, X => In every next term it is the next roman numeral.
6) 8 < 13, 21, 34, 56, 90 => In every next term it is the sum of previous two terms.
7) => In every next term the arrows rotate clockwise in direction.
T/F:
8) False => 17+19 = 36, which is not a prime number.
9) True
10) True
11) True
12) True
13) True
14) False => ostrich, penguin, etc.
15) True
16) False => (a + b)² = a² + b² + 2ab
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Consider this set of numbers: 1, 1, 2, 2, 3, 3, 4, 7, 7, 7, 8, 9. the _____ of the set is 7.
Answer:
mode
Step-by-step explanation:
The mode of the set is 7, as 7 is the number that occurs the most frequently.
________ is a statistical measure of how much scores in a sample vary around the mean. multiple choice normal distribution standard deviation frequency accuracy
Standard deviation is a statistical measure of how much scores in a sample vary around the mean. The correct option is B.
What is the standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Therefore, the standard deviation is a statistical measure of how much scores in a sample vary around the mean. The correct option is B.
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candice is a building manager for the crowley enterprise office building
one of her responsibilities is cleaning the office building's 200-gallon
aquarium. for cleaning, she must remove the fish from the aquarium
and drain the water. the water drains at a constant rate of 10 gallons
per minute.
The independent variable is the cause. Its value is independent of other variables in your study. The dependent variable is the effect. Its value depends on changes in the independent variable.
The independent variable, as indicated in the name is not influenced by other variables but can predetermine its own self.
So, the independent variable is the water in the 200 gallon aquarium
Now, the dependent variable is the tested variable and is depends on the independent variable, which is the time it takes to drain the 200 gallon aquarium.
Hence, independent variable is volume of water in the aquarium and dependent variable is time it will take to drain the aquarium.
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Find the equation of the given table in slope intercept form. The answer must be in y=mx+b format! Please show work asap!!
Answer: y = 6.75x + 6
Step-by-step explanation:
Answer:
y=6.75x+6
Step-by-step explanation:
y=mx+b
we can find it by doing [tex]\frac{y^{2}-y^{1} }{x^{2} -x^{1} }[/tex]
I'm going to choose 2,19.5 and 5,39.75
[tex]\frac{39.75-19.5}{5-2}[/tex] we get [tex]\frac{20.25}{3}[/tex] simplified to 6.75
now we know that the slope is 6.75 we can find the y-intercept by plugging in one pair, I'm going to put the 2,19.5 in
19.5=(6.75)2+b then multiply 6.75 by 2
19.5=13.5+b then subtract 13.5 from both sides to remove the 13.5 on B to separate it
6=b so the y-intercept is 6
Write the rational number 36/5 as a decimal
Answer:
36/5 as a decimal is 7.2
Step-by-step explanation:
In the fraction 36/5, 36 is the numerator and 5 is the denominator, the fraction bar means "divided by". Therefore, the fraction 36/5 is same as "36 divided by 5" or "36 ÷ 5".
When we calculated 36 divided by 5, we found that 36/5 in decimal form is:
36 ÷ 5 = 7.2
Therefore, the decimal form of 36/5 is 7.2
each problem, create a table
Write an equation, in slope-intercept form, to model each situation.
1. You rent a bicycle for $20 plus $2 per hour.
Y=2x120
Answer:
You have a fixed cost ($20) and a variable cost ($2*number of hours you rent the bike)
Cost = Variable Cost + Fixed Cost
Let y = your Cost and x = the number of hours you rent the bike. The fixed cost is $20.
y = ($2 per hour)*(x hours) + $20
y = 2x + 20
Find each product.
29. (r-1)(7r+2)
31. x²(3x-2)(5x+1)
37. (m-n+k)(m+2n-3k)
43. (2m+3)(2m-3)
45. (4x²-5y)(4x²+5y)
Answer:
29. 7r^2-5r-2
31. 15x^4-7x^3-2x^2
37. -3k^2-2km+5kn+m^2+mn-2n^2
43. 4m^2-9
5. 16x^4 - 25y^2
Step-by-step explanation:
To solve these you expand the polynomial and use the FOIL method.
Use the graph to determine
A) The function’s domain
B) The function’s range
C) The X-intercepts
D) Y-intercepts
E) The missing function values indicated by question marks below
Answer:its C
Step-by-step explanation:
they x will intercept when you do it right
Name the angle in as many different ways as possible.
Answer:
WXZ, ZXW, 1
Step-by-step explanation:
Simplify $(-3x^2 y)(5x^4 y^3).$
Answer: [tex]-15x^6y^4[/tex]
Step-by-step explanation:
(-3x^2 y)(5x^4 y^3)=
-3x^2 *5x^4 *y*y^3=
-3*5*x^2 *x^4 *y^4=
-15*x^(2+4) *y^4=[tex]-15x^6y^4[/tex]
There are two squares with the same side lengths scaled copies of one another explain your reasoning
A square is a rectangle with equal lengths on each side. The two squares with the same length side will be lengths scaled copies of one another.
A rectangle whose all sides are equal is called a square.
A square is always a rectangle, parallelogram, and a quadrilateral but its reverse statement may or may not be true.(ie it is not always necessary that a rectangle is a square or a parallelogram is a square).
As it is known that two squares are always similar to each other which is because all the angles of a square are always 90°. Therefore, any two squares are always similar to each other.
Now, as it is given that the two square have the same length sides. Therefore, the two squares with the same length side will be lengths scaled copies of one another. This is because all the sides are equal and all the angles are equal.
Hence, the two squares with the same length side will be lengths scaled copies of one another.
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can someone solve this please, thank you
Answer:
110
Step-by-step explanation:
13x - 20 + 7x = 180
20x -20 = 180
20x = 200
x = 10
13(10) - 20
=110
Which statement correctly explains how Mari could find the solution to the following system of linear equations using elimination?
Multiply the first equation by 7 and the second equation by 2, and then add.
Multiply the first equation by 3 and the second equation by 5, and then subtract.
Multiply the first equation by –7 and the second equation by 2, and then add.
Multiply the first equation by –3 and the second equation by -5, and then subtract.
Multiply the first equation by 7 and the second equation by 2, and then add.
2f - 5g=-9
-7f + 3g=4
To eliminate any variable , we need to make the coefficients same with different sign and add it
the coefficient of 'f' in first equation is 2
the coefficient of 'f' in second equation is -7
We already have different sign so we make the coefficients same
To make the coefficient same , we multiply the first equation by 7 and second equation by 2
So equation becomes
14f - 35g = -63
-14f + 6g = 8
Now when we add both equations, 'f' gets cancelled
-29g = -55
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Answer:
A
Step-by-step explanation:
Edge2022
Which expression is equivalent to (2^-1)^3
The solution is [tex]\frac{1}{8}[/tex] .
To understand this problem we need to know the concept of surds and indices, powers and exponents.
If we write [tex]x^{2}[/tex] it means that x must be multiplied by itself two times.
But if we write [tex]x^{-2}[/tex] it means [tex]\frac{1}{x^{2} }[/tex].
Which means if an number has negative power then it must be written in the inverse format to make it positive.
Given here is [tex](2^{-1})^{3}[/tex]
⇒[tex](\frac{1}{2}) ^{3}[/tex]
⇒[tex]\frac{1}{8}[/tex] is the required solution of the problem.
This can also be solved in other ways by multiplying the powers and then inverting the fraction to make it positive.
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Kehlani invests money in an account paying simple interest. No money is added or removed from the investment. To find the balance after a year, she multiplies her current balance by 1.072. What percent simple interest does the account earn per year?
The percent of simple interest that the account has will be 7.2%.
How to calculate the rate?From the information, Kehlani invests money in an account paying simple interest. No money is added or removed from the investment. To find the balance after a year, she multiplies her current balance by 1.072.
The percent of simple interest that the account has will be:
= 1.072 - 1
= 0.072
= 7.2%
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the number of triangles is 1/3 the number of sides
Answer:
y=(1/3) or y=1/3x
Step-by-step explanation:
Without the parenthesis, your equation can be interpreted as Y = one over 3x
The equation which represents the number of triangles is 1/3 the number of sides is t = (1/3) × s.
Let's denote the number of sides of a polygon as "s" and the number of triangles that can be formed within the polygon as "t."
The equation for the number of triangles being 1/3 the number of sides is:
t = (1/3) × s
This equation states that the number of triangles (t) is equal to one-third of the number of sides (s) in a given polygon.
Hence, the equation which represents the number of triangles is 1/3 the number of sides is t = (1/3) × s.
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Complete question:
Write an equation for the number of triangles is 1/3 the number of sides.
Identify a counterexample for the following statement:
"If a number is a perfect square, then it can't end with a 1."
Answer:
81
Step-by-step explanation:
81 is a perfect square, and also ends with 1.
Ronald wants to rent a car to take a trip and has a budget of $60. there is a fixed rental fee of $25 and a daily fee of $5. write an inequality that would be used to solve for the maximum number of days for which ronald can rent the car on his budget. 25 5x ≤ 60 25 5x ≥ 60 25x 5 ≤ 60 25x 5 ≥ 60
Answer:
60>x>25
Step-by-step explanation:
Write two expressions that represent the volume of the cube, one with exponents and one without.
What is the value of the "?" in the figure below
Answer:
I think it is none of the choices.
Step-by-step explanation:
