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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Keenan got 13 /25 for his Mathematics Test write this as a decimal fraction
Answer: Answer is 0.52
Step-by-step explanation:
So we have the fraction 13 Out of 25.
step 1: here we divide numerator(which is 13) by denominator(which is 25).
step 2: first we make denominator 100 by multiplying by 25 with 4 and also 13 with 4.
ie. [tex]\frac{13 * 4}{25 * 4}[/tex]
step 3: we get [tex]\frac{52}{100}[/tex]
step 4: now we can easily write the decimal fraction. ie. 0.52
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Solve the simultaneous equations
y=2-5x
y = x² – 2x – 8
Answer:
Step-by-step explanation:
sub equation 1 into 2
2-5x=x²-2x-8
0=x²-2x+5x-8-2
0=x²+3x-10
0=(x-2)(x+5)
x=2 or x=-5
sub x into equation 1
y=2-5(2) or y=2-5(-5)
y=-8 y=27
Caleb earns points on his credit card that he can use towards future purchases. He earns four points per dollar spent on flights, two points per dollar spent at hotels, and one point per dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned 14,660 points. The amount of money spent on flights was $140 more than twice the amount of money spent on hotels. Write the system representing this situation. *Use "f" for flights *Use "h" for hotels *Use "t" other *do NOT use commas
Answer:
Caleb earns points on his credit card that he can use towards future purchases. He earns four points per dollar spent on flights, two points per dollar spent on hotels, and one point per dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned 14,660 points. The amount of money spent on flights was $140 money than twice the amount of money spent on hotels. Find the amount of money spent on each type of purchase.
PLEASE SOLVE THIS FOR MEEEE<333
Jackson and Flora both have bank accounts, and they use credit cards.
Use the number line to determine if they can pay off the credit card bill.
A. Jackson has $20 in his account. He uses a credit card to spend $30 on a
coat and $10 on a movie. Jackson then deposits $50 into his account.
How much will Jackson have left after he pays the credit card bill?
What is the answer for this question
The values for the net change and average change is given as-
7. Net change = 2 , Average change = 2/3.
8. Net change = -2, Average change = -1/2.
9. Net change = -4, Average change = 4/5.
10. Net change = 4, Average change = 2/3.
What is defined as the net change and the average change?Given two points on the graph of f(x), (a,f(a)) and (b,f(b)), the net change would be the contrast between the different f(x) values.
So, net change is estimated by f(b)−f(a).The ratio of the net change to a change between the 2 input values is equal to the average net change and average rate of change. Taking the same two points, the following formula can be used to calculate the average rate of change: [f(b)−f(a)]/(b - a)In other words, the average rate of change is the slope of the line connecting any two points.Part 7:
The points on x axis are;
a = 1 and b = 4
f(b) = f(4) = 5
f(a) = f(1) = 3
Thus, net change is; f(b)−f(a)
= f(4) - f(1)
= 5 - 3
net change = 2
The average change;
= [f(b)−f(a)]/(b - a)
= [f(4) - f(1)]/(4 - 1)
net change = 2/3.
Part 8:
The points on x axis are;
a = 1 and b = 5
f(b) = f(5) = 2
f(a) = f(1) = 4
Thus, net change is; f(b)−f(a)
= f(5) - f(1)
= 2 - 4
net change = -2
The average change;
= [f(b)−f(a)]/(b - a)
= [f(5) - f(1)]/(5 - 1)
net change = -2/4 = -1/2
Part 9:
The points on x axis are;
a = 0 and b = 5
f(b) = f(5) = 2
f(a) = f(0) = 6
Thus, net change is; f(b)−f(a)
= f(5) - f(0)
= 2 - 6
net change = -4
The average change;
= [f(b)−f(a)]/(b - a)
= [f(5) - f(0)]/(0 - 5)
net change = -4/-5 = 4/5
Part 10:
The points on x axis are;
a = -1 and b = 5
f(b) = f(5) = 4
f(a) = f(-1) = 0
Thus, net change is; f(b)−f(a)
= f(5) - f(-1)
= 4 - 0
net change = 4
The average change;
= [f(b)−f(a)]/(b - a)
= [f(5) - f(-1)]/(5 + 1)
net change = 4/6 = 2/3
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I need help on the problem i'm stuck
The number of hours Becky took to finish typing the essay is 3 hours.
What is division?A division is a process of splitting a specific amount into equal parts.
We have,
Number of words in the essay = 4,100
Becky can type 20 words per minute.
Becky has already typed 500 words.
So the remaining words are:
= 4,100 - 500
= 3,600
Now,
The number of hours to complete 3,600 words:
= 3,600 minutes / 20
= 180 minutes
We know that,
1 hour = 60 minutes
3 hours = 180 minutes
= 3 hours
Thus the number of hours Becky took to finish typing the essay is 3 hours.
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In consecutive odd integers, three times the largest integer is fifteen less than two-thirds the smallest integer. find both integers. someone help please
Value of both the integers as three times the largest consecutive integer is 15 less than 2/3 the smallest one is -7, -9.
As given,
Let x, x +2 be two consecutive odd integers
Three times largest integer=3( x+2)
15 less than 2/3 smallest integer=(2/3)x -15
Equation :
3(x+2)=(2/ 3)x -15
⇒ 3x +6=(2x -45)/3
⇒ 9x-2x= -18 -45
⇒ 7x=-63
⇒ x =-9
and x+2 =-7
Therefore, value of both the integers as three times the largest consecutive integer is 15 less than the 2/3 the smallest one is -7, -9.
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(3x^3)^3 is equivalent to
Answer: (3x^3)^3 = 3^3 (x^3)^3 = 27 (x^3)^3 = 27^3x3 = 27^9
27^9
Answer:
27x^9
Step-by-step explanation:
Distribute.
3^3 (x^3)^3
27 (x^3)^3
Power of a power.
27x^3 times 3
Multiply.
27x^9
Use the roster method to write the given set the set of integers x that satisfy 2x-1= -13
The only set of elements that satisfied the equation 2x-1= -13 is {-6}.
What is a set?A set is a combination of specific quantities in which the meaning of each variable must be the same.
For example {1,2,3,4,5,6...} is a set of natural numbers in which each variable is representing a natural number so the overall meaning is the same among all.
Another example could be a set of whole numbers like that.
Given the equation,
2x-1= -13
By taking -1 right-hand side
2x = -13 + 1 = -12
By dividing 2
x = -6
Hence "The only set of elements that satisfied the equation 2x-1= -13 is {-6}".
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Please help
This graph shows a portion of an odd function. Use the graph to complete the table of values.
From the odd function, the table is completed as follows:
x = -2, f(x) = -2.x = -3, f(x) = -1.x = -4, f(x) = -2.x = -6, f(x) = -3.What are even and odd functions?In even functions, we have that f(x) = f(-x) for all values of x.In odd functions, we have that f(x) = -f(x) for all values of x.If none of the above statements are true, the function is neither.For this problem, we have that it is an odd function, then:
Since f(2) = 2, f(-2) = -f(2) = -2.Since f(3) = 1, f(-3) = -f(3) = -1.Since f(4) = 2, f(-4) = -f(4) = -2.Since f(6) = 3, f(-6) = -f(6) = -3.More can be learned about odd functions at https://brainly.com/question/2284364
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How do I know what the answer is
The Arithmetic sequences are-
-5, 5, -5, 5, - 5, 5.... Not Arithmetic sequences96, 48, 24, 12, 6... Not Arithmetic sequences18, 5.5, -7, -19.5, -32... Arithmetic sequences-1, -3, -9, -27, -81.... Not Arithmetic sequences16, 32, 48, 64..... Arithmetic sequencesWhat is defined as the arithmetic series?Arithmetic sequences are those in which the difference d among successive terms remains constant. An arithmetic sequence's general term can be written as: an = a₁ + (n)d in terms of first term a₁, common difference d, and index n.The common difference must be same for the sequence to be arithmetic;
d₁ = a₂- a₁
d₂ = a₃ - a₂
Thus, d₁ = d₂
Check the common differences for given sequences are-
A. -5, 5, -5, 5, - 5, 5....
d₁ = 5 - (-5) = 10
d₂ = -5 - 5 = -10
d₁ ≠ d₂, not a Arithmetic sequences
B. 96, 48, 24, 12, 6...
d₁ = 48 - 96 = -48
d₂ = 24 - 48 = -24
d₁ ≠ d₂, not a Arithmetic sequences
C. 18, 5.5, -7, -19.5, -32...
d₁ = 5.5 - 18 = -12.5
d₂ = -7 - 5.5 = - 12.5
d₁ = d₂, Arithmetic sequences
D. -1, -3, -9, -27, -81....
d₁ = -3 -(-1) = -2
d₂ = -9 - (-3) = -6
d₁ ≠ d₂, not a Arithmetic sequences
E. 16, 32, 48, 64.....
d₁ = 32 - 16 = 16
d₂ = 48 - 32 = 16
d₁ = d₂, Arithmetic sequences
Thus, the common difference must be equal for Arithmetic sequences.
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Find the remainder for this calculation.
161 4
40 Remainder 1
hope this helps :)
Write an explicit formula for this geometric sequence: 1, 5, 25, 125, 625
Answer:
[tex]a_{n}[/tex] = 1 [tex](5)^{n-1}[/tex]
Step-by-step explanation:
the explicit formula for a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{5}{1}[/tex] = 5 , then
[tex]a_{n}[/tex] = 1 [tex](5)^{n-1}[/tex]
If the odds against debroah's winning first prize are 3 to 5, what is the probability that she will win 1st prize?
Answer:
See below
Step-by-step explanation:
Odds AGAINST are 3 to5 then odds FOR are 2 to 5
2/5 = .4 = 40% chance of winning
Mary plans to invest 2,500 for 10 years she invest in a savings account that pays 4.5 % simple intrest she made no additional deposit or withdrawals how much money will she have at the end of 10 years in the account
1125 money will she have at the end of 10 years in the account after Simple Interest.
What is a basic example and interest?
Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.Mary plans to invest = 2500
t = 10 yr
r = 4.5 %
simple intrest = prt/100
= 2500 * 10 * 4.5 /100
= 1125
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You are dealt one card from a standard 52-card deck. find the probability of being dealt in a queen? quiizlet
The probability of being dealt in a queen is 1/13.
What is probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.To find the probability:
Total number of cards = 52Number of cards om 52 deck of cards = 4So, P = favourable events / total number of eventsThen, P = 4/52Probability = 1/13Therefore, the probability of being dealt in a queen is 1/13.
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$500 is earning 8% simple unrest rate. What is the interest owed
The interest owed is $40
How to calculate the interest ?Interest is the amount of money paid when a loan is collected
The amount is $500
The interest rate is 8%
Therefore the interest owed can be calculated as follows
= 8/100 × 500
= 0.08 × 500
= 40
Hence the interest owed is $40
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9(y^2+x)=18 in standard form
Answer:
9y^2 + 9x - 18 or 9(y^2 + x - 2)
Step-by-step explanation:
9(y^2+x)=18
9y^2 + 9x=18
9y^2 + 9x - 18 = 0
9(y^2 + x - 2) = 0
What is the solution set of this compound inequality? 1 ≤ |x + 3| ≤ 4
The solution is:
[tex]-7\leq x\leq -4[/tex] or [tex]-2\leq x\leq 1[/tex]
20 girls and 32 boys volunteer to plants trees at a school. The principal divides the girls and boys into
identical groups that have girls and boys in each group. What is the greatest number of groups the
principal can make?
The greatest number of groups the principal can make is
The principle can makes 4 groups with 7 girls and 8 boys.
What is HCF?The biggest number that divides each of the two or more numbers is known as the HCF, or highest common factor. The Greatest Common Measure (GCM) and Greatest Common Divisor are further names for HCF (GCD). The least common multiple, or LCM, is used to determine the smallest common multiple of any two or more numbers. LCM and HCM are two separate approaches.
According to the given statement ;
We are given that 28 girls and 32 boys volunteer to plant at a school.
The principle divided the girls and boys into identical groups that have girls and boys in each group.
We have to find that how much the principle can make greatest number of groups.
We will find HCF of 28 and 32
28= 2X2X7
32= 2X2X2X2X2
Highest common factor of 28 and 32 =2X2=4
Therefore, the principle can makes 4 groups with 7 girls and 8 boys.
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Describe the transformation from the parent function to the graph f(x) = 3|x+1|−6
the 3 will make the parent function (vertical or horizontal) (shift or stretch or compass or reflect) (up or down or left or right or by a factor) (3 or -3 or 1 or -1 or 6 or -6)
the x+1 will make the parent function (vertical or horizontal) (shift or stretch or compass or reflect) (up or down or left or right or by a factor) (3 or -3 or 1 or -1 or 6 or -6)
the -6 will make the parent function (vertical or horizontal) (shift or stretch or compass or reflect) (up or down or left or right or by a factor) (3 or -3 or 1 or -1 or 6 or -6)
Using translation concepts, we have that:
The 3 will make the parent function vertically stretch by a factor of 3.The x + 1 will make the parent function shift horizontally left 1 unit.The -6 will make the parent function shift vertically down 1 unit.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is:
g(x) = |x|.
The translated function is:
f(x) = 3|x + 1| - 6.
The multiplication by 3 means that the function was stretched vertically by a factor of 3, hence:
The 3 will make the parent function vertically stretch by a factor of 3.
At x -> x + 1, we have that the function was shifted one unit left, hence:
The x + 1 will make the parent function shift horizontally left 1 unit.
For the subtraction by 6, the function was shifted down 6 units, hence:
The -6 will make the parent function shift vertically down 1 unit.
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someone please help me
Answer:
45
Step-by-step explanation:
180 - 45 - 90 = 45
What is the domain and range of this picture?
Find the value of |-4 + 3| · 8.
-8
56
8
-56
?
The value of expression |-4 + 3| · 8 is 8.
What is Modulus function?
A modulus function is a function which gives the absolute value of numbers or variable.
The expression is given as;
| -4 + 3 | * 8
Now, Solve the expression as;
⇒ | -4 + 3 | * 8
⇒ | - 1 | * 8
⇒ 1 * 8
⇒ 8
Since, Modulus of a negative number gives the positive of that number.
Hence, The value of expression |-4 + 3| · 8 is 8.
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The volume of a cylinder closed at one end is 1056cm^2 with height 21cm, find the total surface area
Answer: ≈578 cm²
Step-by-step explanation:
[tex]V_{cyl}=1056\ cm^3\ \ \ \ H=21\ cm\\V_{cyl}=\pi R^2H\\1056=\pi *R^2*21\\1056=21\pi *R^2\\[/tex]
Divide both parts of the equation by 21π:
16=R²
4²=R²
4=R
[tex]S{tot\ sur}=\pi R^2+2\pi RH\\S{tot\ sur}=\pi R*(R+2H)\\S{tot\ sur}=\pi *4*(4+2*21)\\S{tot\ sur}=4\pi *(4+42)\\S{tot\ sur}=4\pi *46\\S{tot\ sur}=184\pi \\S{tot\ sur}\approx578\ cm^2[/tex]
Two players are playing chess and usually player a wins 65 percent of games. they will play 3 games and the winner is:_________
In each game, the probability that player A wins the game is 13/20 and player B wins the game is 7/20.
What is probability?Probability is a branch of mathematics with numerical characterizations of how likely an event is really to occur or how probable a proposition is to be true. The probability of an event is a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.To find the probability:
To find the probability that player a wins the game and by what probability player b wins the game.So, 65/100 = 13/20.So, the probability of player b will be 7/20.Therefore, in each game, the probability that player A wins the game is 13/20 and player B wins the game is 7/20.
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What is the solution (x,y) to the system of equations above?
Answer:
B
Step-by-step explanation:
Solve for x in the diagram below.
X =
хо
100°
3x°
Answer:
20
Step-by-step explanation:
the line equals 180 degrees total.
so subtract the angle we already know from the total...
180- 100=80
then, make an equation with the last two variables since we know both of them added together should equal 80
80=x +3x
Combine like terms
80=4x
Divide by 4
20=x
Translate algebraic words to symbols. Triple the product of ab
Answer:
3ab
Step-by-step explanation:
Triple means multiply by 3.
The product of ab is simply ab.
Answer: 3ab