The probabilities from the venn diagram are:
Let A be the event that the Mechanic is AC repairman and T be the event that he does tune ups.
[tex]P(A\cap T)=\frac{2}{13}[/tex]The probability that he does tune ups is:
[tex]P(T)=\frac{3}{13}[/tex]Hence the required probability is given by:
[tex]P(A|T)=\frac{P(A\cap T)}{P(T)}=\frac{\frac{2}{13}}{\frac{3}{13}}=\frac{2}{3}[/tex]Hence the probability is 2/3.
Find the coordinates of the point P along the directed line segment AB so that AP to PB is the given ratio. A(-2, -4), B(6, 1); 3 to 2
In order for the ratio of AP to PB to be 3/2, the coordinates of point P along the directed line segment AB are (14/5, -1).
What exactly is a section formula?The section formula returns the coordinates of a point that divides the line connecting two points in a ratio, either internally or externally.
Section formula is given as follows:
[tex](\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})[/tex]
In math, how do you find coordinates?Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to find the y-coordinate.It is given that the coordinates of the points A and B are A(-2, -4), B(6, 1) and AP/PB = 3/2
Let the coordinates of the point P be (a, b).
By using section formula,
(a, b) = [tex](\frac{mx_{2 }+nx_{1} }{m+n} , \frac{my_{2} +ny_{1} }{m+n})[/tex]
(a, b) = [tex](\frac{3(6)+2(-2)}{3+2} , \frac{3(1) +2(-4)}{3+2} )[/tex]
(a, b) = [tex](\frac{18 - 4}{5} , \frac{3-8}{5})[/tex]
(a, b) = [tex](14/5, -5/5)[/tex]
(a, b) = [tex](14/5, -1)[/tex]
Therefore, the coordinates of the point P along the directed line segment AB so that the ratio of AP to PB is 3/2 are (14/5, -1).
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In the Honor Society at Carter Middle School, 54% of the members are girls. There are 108 girls in the Honor Society. How many members are there in total?
Answer:
46x2=92 108+92= 200 total members
Step-by-step explanation:
108/2=54% so 46%x2members = 92 members.
What is 5xy-x squared t + 2xy + 3x squared t
The expression 5xy - x²t + 2xy + 3x²t has a value of 7xy + 2x²t
How to evaluate the expression?From the question, the expression is given as
5xy - x squared t + 2xy + 3x squared t
Rewrite the above expression properly
This is represented as
5xy - x²t + 2xy + 3x²t
Next, we collect the like terms in the above expression
So, we have the following equation
5xy - x²t + 2xy + 3x²t = 5xy + 2xy - x²t + 3x²t
Evaluate the like terms in the above expression
So, we have the following equation
5xy - x²t + 2xy + 3x²t = 7xy + 2x²t
The equation cannot be further simplified
Hence, the value of 5xy - x²t + 2xy + 3x²t is 7xy + 2x²t
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let P = (x,y) and Q = (1, 5). suing formula that you know for slope write an eqation in these terms of coordinates that says that the slope of line PQ is 3. show how this slope equation can be rewritten in the form y - 5 =3 (x -1).this linear eqation is said to be in point-slopr form. explain the terminology find coordinates for three diffrent points p that fit this equation
The equation of a line in point-slope form is y - 5 = 3( x - 1).
What is the equation of a line in slope intercept form?Equation of a line in slope intercept form is y = mx + b, where slope = m and y-intercept = b.The slope of a line is defined as the rate of change of the y-axis with respect to the x-axis.
We know the equation of a line in point-slope form is y - y₁ = m(x - x₁).
Given P = (x,y) and Q = (1,5) or (x₁, y₁).
∴ Equation of a line in point-slope form given (x₁,y₁) = (1,5) and slope(m) = 3 is y - 5 = 3( x - 1).
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example: suppose that the probability that an item produced by a certain machine will be defective with probability 0.1. find the probability that a sample of 10 items will contain at most 1 defective item.
The probability that a sample of 10 items will contain at most 1 defective item is 0.7361
Consider X to denote the number of defective items which follows binomial distribution with sample size, n equals to 10.
The probability p of an item produced by a certain machine will be defective is 0.1.
Therefore, the probability q of an item produced by a certain machine will not be defective is:
(1−0.1)
=0.9
The probability of at most one defective item can be calculated as follows:
[tex]P(X\leq 1)=P(X=0)+P(X=1)\\[/tex]
[tex]=^{10} C_{0} p^{0} (1-p)^{10} +^{10} C_{1} p^{1}(1-p)^{9}[/tex]
[tex]=(0.9)^{10} +10(0.1)(0.9)^{9}[/tex]
[tex]=0.7361[/tex]
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Amber wants to put carpet on the floor of her bedroom. The floor is a square with an area of 7.29 square feet.
How long should the piece of carpet be on each side?
Answer:
2.7 feet
Step-by-step explanation:
S = a²
S = 7.29
a = sqrt(7.29) = 2.7
Answer:
2.7
Step-by-step explanation:
Area is [tex]side^{2}[/tex]
a= [tex]s^{2}[/tex]
[tex]\sqrt{7.29}[/tex] = 2.7
2.7 x 2.7 = 7.29
You and your friends plan to attend the county fair this weekend. The admission to the fair is $5 and the cost per ride is 50 cents. If your parents gave you $20, write and solve a linear equation to find how many rides you can go on.
The linear equation to find how many rides you can go on is 5 + 0.5x = 20 and there'll be 30 rides.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
The linear equation will be:
Let the number of rides be x.
This will be:
5 + (0.5 × x) = 20
5 + 0.5x = 20
Collect like terms
0.5x = 20 - 5
0.5x = 15
Divide
x = 15 / 0.5
x = 30
The number of rides is 30
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There will be 30 rides, and the linear equation to determine the total number of rides is 5 + 0.5n = 20.
What are the equations?Mathematical statements which have at least two terms with equal quantities or variables are called equations.
Let n be the total number of rides.
The fair's entrance fee is $5, and each ride costs 50 cents, and parents gave $20 which is given in the question.
According to the given situation, the required equation as
⇒ 5 + 0.5 × n = 20
⇒ 5 + 0.5n = 20
⇒ 0.5n = 20 - 5
⇒ 0.5x = 15
Divide by 0.5 into both sides of the equation,
⇒ n = 15 / 0.5
⇒ n = 30
Therefore, the total number of rides will be 30.
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50 POINTSS
Write a matrix representing the system of equations
x+2y+z=5
2x-y+2z=15
3x+y-z=8
Solve the system by transforming your matrix into a reduced row echelon form. State the solution as an ordered triple.
The solved matrix system is (x y z) =(4,-1, 3)
The problem we are dealing with is related to gauss -Jordan elimination is a calculation that can be utilized to illuminate systems of linear conditions and to discover the inverse of any invertible matrix. It depends upon three elementary row operations one can utilize on a matrix: Swap the positions of two of the rows and Multiply one of the rows by a nonzero scalar. Add or subtract the scalar numerous of one row to another row.
For the given equations
x+2y+z=5
2x-y+2z=15
3x+y-z=8
In the matrix form
1 2 1 | 5
2 -1 2 | 15
3 1 -1 | 8
R2 -> R2-2R1
1 2 1 | 5
0 -5 0 | 5
3 1 -1 | 8
R3->R3-3R1
1 2 1 | 5
0 -5 0 | 5
0 -5 -4 | -7
R2->R2/(-5)
1 2 1 | 5
0 1 0 | -1
0 -5 -4 | -7
R3->R3-(-5).R2
1 2 1 | 5
0 1 0 | -1
0 0 -4 | -12
R3= R3/(-4)
1 2 1 | 5
0 1 0 | -1
0 0 1 | 3
R1= R1-1R3
1 2 0 | 2
0 1 0 | -1
0 0 1 | 3
R1= R1-2R2
1 0 0 | 4
0 1 0 | -1
0 0 1 | 3
x | 4
y | -1
z | 3
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A cup of popcorn at the movie theater sells for $0.25 per cubic inch. A medium sized popcorn is served in a cylindrical cup that is 6 inches in height and 4 inches in diameter. How much would it cost to the nearest cent?
PLEASE HELP :(!
Surface area - The cost of medium popcorn will be $473.25.
What is surface area?
The surface area of a three-dimensional object is the space taken up by its outer surface.
For instance,
The surface area of a cube is what we need to calculate the amount of paint needed to paint it. It is consistently expressed in square units.
The surface area of the cylinder with the top open = πr(r + 2h)
we are given that,
r = 2in
h = 6in
taking π as 3.14, and substituting these vales in the above equation,
surface area = π x 2 (2 x 2 x 6)
= 3.14 x 2 (2 x 2 x 6)
= 1893in²
cost = 1893 x 0.25
= $473.25
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Not sure how to find the area of this shape. Please help asap
Answer:
6.75m^2
Step-by-step explanation:
The shape is made up of a trapezoid on top and a rectangle on the bottom.
The rectangle's area is easier, so first:
Area_rectangle
= length × width
= 2.5 × .5
= 1.25 m^2
For area of a trapezoid, you need three measures: both bases and the height.
One base is 3m. The other base is the top side of the rectangle, so it is 2.5m.
The height is
2.5 - .5
because the height of the trapezoid is not including the rectangle, so take away .5
Trapezoid's height is 2.5 - .5 is 2.
Area_trapezoid
= 1/2 (base+base)height
= 1/2 (3+2.5)2
=5.5
Area_total
= Trapezoid+rectangle
= 5.5 + 1.25
=6.75m^2
The total area is 6.75square meters.
Answer:
Area = 6.75 meter square.
Step-by-step explanation:
Describe the relationship between the 5's in the number 655,572:
The five in the 55 place is 5 times greater than the 5 in
the thousands places.
Answer:
im jus trying to get points lol
Step-by-step explanation:
How much do you owe at the end of four weeks
Given:
If you borrow $100, you will have an interest of $10.
Asked: How much do you owe at the end of four weeks?
Solution:
To solve this problem, we need to find the rate, r.
According to the given, we can get the rate by:
$100 x rate = $10
rate = $10/$100
rate = 0.10
Now, if you borrow $1100, you will pay at the end of four weeks the amount of:
$1100 x 0.10 = $110
Total amount = $1100 + $110 = $1210
ANSWER: You will owe $1210 at the end of four weeks.
Answer:
You will owe $1210 at the end of four weeks.
Complete the point-slope equation of the line through (-9,6)(−9,6)left parenthesis, minus, 9, comma, 6, right parenthesis and (-7,-8)(−7,−8)left parenthesis, minus, 7, comma, minus, 8, right parenthesis.
The point slope equation of the line that passes through the points (-9,6) and (-7,-8) is 7x + y = -57 .
The point slope equation of the line passing through the points (x₁,y₁) having slope as m is given by the formula .
y-y₁ = m(x-x₁)
In the question ,
it is given that
the required line passes through the points (-9,6) and (-7,-8) ,
So , the slope(m) is = (-8-6)/(-7 -(-9))
= -14/(-7+9)
= -14/2
= -7
the equation of the line passing through (-7,-8) and slope as 7 in the point slope form is
(y -(-8)) = -7(x -(-7))
y + 8 = -7x -49
7x + y = -8-49
7x + y = -57
Therefore , The point slope equation of the line that passes through the points (-9,6) and (-7,-8) is 7x + y = -57 .
The given question is incomplete , the complete question is
Write the point slope equation of the line that passes through the points (-9,6) and (-7,-8) .
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The number of maps remaining at an information booth can be modeled by the function f(x)=274-32r where x is the number of hours that have
elapsed since the booth opened. Which statement is true?
O Every hour 274 maps are given away
O Every hour, 242 maps are given away
O There were 32 maps at the booth before it opened
O There were 274 maps at the booth before it opened
Find the value of x.
Answer:
x=110
Step-by-step explanation:
You can set the equation up like this:
100=x-10
Make x by itself
x=110
You are creating identical candy bags using 36 chocolate bars and 81 caramel bars. what is the greatest number of bags you can fill using all the candy?
The greatest number of bags that can be filled using all the candy is 9.
The greatest number of bags that can be filled using all the candy can be determined by calculating the greatest common factor (GCF).
The greatest common factor of two or more numbers is a term used in mathematics that can be described as the greatest number among all the common factors of these numbers. If x and y are two numbers, GCF is the largest number that divides both x and y without leaving any remainder.
As there are 36 chocolate bars and 81 caramel bars, therefore we determine the GCF of 36 and 81;
The common factors of 36 and 81 are found to be: 1, 3 and 9
Hence the greatest common factor (GCF) out of these is 9.
Therefore the greatest number of bags that can be filled using all the candy is calculated to be 9
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question 2 (10 points)
Answer:
The answer is 476, so the third option is correct.
Step-by-step explanation:
Step 1: Recall the Order Of Operations
The order of operations tells us in which order we have to solve expressions, if there are different operations.
The order is (from first solved to lastly solved) Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
Step 2: Calculate the expression
As we can see, there are parentheses present, so we will solve the expression in them first:
[tex](6+4)\\=(10)[/tex]
The expression becomes:
[tex]10\cdot 49 -7\cdot 2[/tex]
Multiplication should occur first before the subtraction, so let's multiply the numbers:
[tex]10\cdot49-7\cdot2\\\\\text{Multiply the first expression:}\\=490-7\cdot 2\\\\\text{Multiply the second expression:}\\=490-14[/tex]
Now, you can subtract the numbers:
[tex]490-14\\=476[/tex]
9. For f(x) = -x + 8, which statement is true? A f(x + k) = f(x) + k B f(x- k) = f(x) - k Cf(x + k) = f(x) + f(k) D f(x - k) = f(x) + k
Answer:
D. f(x - k) = f(x) + k
Step-by-step explanation:
You want to know the effect on f(x) = -x +8 when x is replaced by x±k.
Function evaluationA function is evaluated by replacing the independent variable in its definition by the function argument.
f(x) = -x +8
f(x +k) = -(x +k) +8 = (-x +8) -k = f(x) -k
When the sign of k changes, we have ...
f(x -k) = f(x) +k
The correct statement for the function is: f(x -k) = f(x) +k. And option(D) is write answer.
How to perform function evaluation?
In mathematics, function expression is mainly consist of dependent variable and the independent variable. And the function is evaluated by replacing the independent variable in its definition by the function argument.
According to the question, the given function expression is: f(x) = -x +8
Now, to know the effect on f(x) = -x +8 when x is replaced by x ± k. This transformation is known as scaling translation.
Therefore, the function expression can be written as:
f(x) = -x +8
⇒ f(x +k) = -(x +k) +8 = (-x +8) -k = f(x) -k
When the sign of k changes, we get: f(x -k) = f(x) +k
Hence, the correct statement for the function is: f(x -k) = f(x) +k
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7.
Ms. Maglione wants to join a gym. The gym wants to charge Ms. Maglione a one
time membership fee for this year of $125 that will cover maintenance and
upkeep of the gym. The cost per month to be a member will be $15. Which
equation best models this situation?
The linear equation that best models the situation is: y = 15x + 125.
How to Write a Linear Equation that Models a Situation?To write a linear equation, you need to determine the value of the unit rate or slope (m), and the value of the y-intercept or starting value (b). The linear equation in slope-intercept form that models the relationship between two variables x and y is expressed as, y = mx + b.
From the information given, we have:
The one-time membership fee is the starting value or y-intercept (b) = $125The cost per month to be a member is the unit rate or slope (m) = $15Let y represent total cost
let x represents number of months.
To write the linear equation that models this situation, substitute m = 15 and b = 125 into y = mx + b:
y = 15x + 125.
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Write the phrase "six more than nine times n is twenty" as an equation:
The phrase "six more than nine times n is twenty" as an equation will be; (6+9)n=20
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The phrase "six more than nine times n is twenty" as an equation will be;
Since we are multiplying n by the addition of 6 and 9, we put 6 and 9 in parenthesis with the n on the outside which is equal to 20.
Then 6 + 9 goes inside the parenthesis.
Therefore, it will be;
(6+9)n=20
Hence, The phrase "six more than nine times n is twenty" as an equation will be; (6+9)n=20
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Graph the linear equation 65 points
You can see the three points where the result is equal to an integer in the photo below. Good luck!
can yall help me with
Answer:
B
Step-by-step explanation:
x(2y - 3) ← multiply each term in the parenthesis by x
= 2xy - 3x
If two out of every fifteen trick or treaters that came to your house last halloween were dressed as spider-man, what proportion of trick or treaters were not dressed as spider-man?
Given:
The fraction of treaters dressed up us halloween, x=2/15.
Let the total trickers be taken as 1.
Now, the proportion of treakers that were not dressed up as spiderman is,
[tex]\begin{gathered} y=1-x \\ =1-\frac{2}{15} \\ =\frac{15-2}{15} \\ =\frac{13}{15} \end{gathered}[/tex]Which is the better buy? 2-cup carton of milk for $0.56 2-quart carton of milk for $3.76
Given:
2-cup carton of milk = $0.56
2-quart carton of milk for $3.76
To find which of them is a better buy, let's calculate the price of each cup for both.
i) 2-cup carton of milk = $0.56
1 cup =
[tex]\frac{0.56}{2}\text{ = }0.28[/tex]Here, 1 cup carton of milk is $0.28
ii) 2-quart carton of milk = $3.76
Given that 1 quart = 4 cups
2 quart = 4 * 2 = 8 cups
Thus
1 cup =
[tex]\frac{3.76}{8}\text{ = }0.47[/tex]Here, a cup carton of milk is $0.47
$0.28 is less than $0.47, therefore the better buy would be 2-cup carton of milk for $0.56.
Therefore, the best buy would be 2-cup carton of milk for $0.56, because it is cheaper.
ANSWER:
2-cup carton of milk for $0.56
Please help with grade 8th made assignment:((
Converting each of the question mentioned decimal into fractions in their simplest form, we get,
(i) 0.6 with 6 recurring = (2/3)
(ii) 3.405 with (405) recurring = (378/37)
(iii) 0.75 with (75) recurring = (25/33)
(iv) 0.3 with 3 recurring = (1/3)
As per the question statement and the attached reference along with the question, we are provided with four recurring decimal values.
We are required to convert each of the decimal values into fractions in their simplest form.
Starting with (i), 0.6 with 6 recurring = 0.66666...
Now, let [x = 0.6666...]
Or, [10x = 6.6666...]
Or, [(10x - x) = (6.6666...) - (0.6666...)]
Or, (9x = 6)
Or, [x = (6/9)]
Or, [x = (2/3)]
Or, [0.6666... = (2/3)]
Similarly for (ii), 3.405 with (405) recurring = 3.405405405405...
Now, let [x = 3.405405405...]
Or, [1000x = 3405.405405405...]
Or, [(1000x - x) = (3405.405405405...) - (3.405405405...)]
Or, (999x = 3402)
Or, [x = (3402/999)]
Or, [x = (378/37)]
Or, [3.40540405... = (378/37)]
Coming to (iii), 0.75 with (75) recurring = 0.757575...
Now, let [x = 0.757575...]
Or, [100x = 75.757575...]
Or, [(100x - x) = (75.757575...) - (0.757575...)]
Or, (99x = 75)
Or, [x = (75/99)]
Or, [x = (25/33)]
Or, [0.757575... = (25/33)]
Finally coming to (iv), 0.3 with (3) recurring = 0.333...
Now, let [x = 0.333...]
Or, [10x = 3.333...]
Or, [(10x - x) = (3.333...) - (0.333...)]
Or, (9x = 3)
Or, [x = (3/9)]
Or, [x = (1/3)]
Or, [0.333... = (1/3)]
Recurring Decimal: A recurring decimal is a decimal in which, a particular digit or sequence of digits repeat(s) itself indefinitely after a certain point.Fractions: Any mathematical quantity which is not a whole number, and is expressed as a quotient of two numbers, one at the numerator (top) and the other at the denominator (bottom), separate by a (/) in between, is known as a fraction.To learn more about Recurring Decimals & Fractions, click on the link below.
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what does the sales discount 2/10, n/30 mean? multiple choice question. for every day the bill is overdue past 10 days, you will be charged 2% interest. you can take a 10% discount if you pay within 2 days, or a 30% discount if you pay today. you can take a 10% discount if you pay within 2 days, or the full amount is due within 30 days. you can take a 2% discount if you pay within 10 days, or the full amount is due within 30 days.
The correct answer is The complete price (minus returns) is due within 30 days, or a 2 percent discount for payments made within 10 days.
2. Net Sales are Going Up.
Explanation:
1. The breakdown of a company's sales discounts with terms 2/10, n/30 is as follows:
The % discount is represented by 2,
You must pay the business within 10 days to be eligible for the discount.
If you were unable to pay the corporation within the first 10 days, you would have had n/30 days to do so. You are not eligible for the discount if you pay during this time frame after the first 10 days.
Consequently, the parameters of the sales discount mentioned above are a 2 percent discount for payment within 10 days, or the full amount (less returns) due within 30 days.
2. As goods are returned and risk must be managed, sales returns and sales allowances have the impact of lowering the net sales total. Therefore, if they decrease, net sales increase.
A decrease in the credit card company's discount also causes a rise in sales because it increases the amount made per sale or transaction and decreases the amount the company must provide in discounts.
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At the mall you purchase 3 hot dogs and 1 soda. The cost of the soda is $2.25. Your total cost is $15.75. Write and solve an equation to find the cost of 1 hot dog.
Answer:
Bodzmkoutdoii6iriutdiudiwtyaoroyrisr
The graph of the quadratic function y=x^2-2x+3 is shown below
The graph of the quadratic function y = x² - 2x + 3 is shown in attached figure.
What is Quadratic equation?
An equation is called a quadratic equation if the highest power of variable of the equation is 2.
Given that;
The quadratic equation is,
y = x² - 2x + 3
Now,
The graph of the quadratic function y = x² - 2x + 3 has vertex (1, 2).
Thus,
The graph of the quadratic function y = x² - 2x + 3 is shown in attached figure with vertex (1, 2).
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8(q-2) = 44+5(2q-12)
The value of q in the given equation is 0.
This is a problem from an algebraic equation, we can solve this problem by following a few steps.
The given equation is,
8(q-2) = 44+5(2q-12)
Let's simplify the equation.
8(q-2) = 44+5(2q-12)
Or, 8q- 16= 44+ 10q- 60
Now, we have to organize the equation.
8q- 10q= 44- 60+ 16
Or, -2q = 0
Or, q = 0/2 ( dividing both side by 2 )
Or, q = 0
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The complete question is:
Find the value in the given equation,
8(q-2) = 44+5(2q-12)
A pet store clerk suggested 5 small fish for a 6-gallon fish tank. What size tank would be suggested to hold 40 small fish?
33-gallon tank
48-gallon tank
160-gallon tank
200-gallon tank
The size of the tank would be suggested to hold 40 small fish is 48 gallons. (Solved using ratios)
What is a ratio?
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains seven apples and six lemons, the apple-to-lemon ratio is seven to six. Similarly, the proportion of lemons to oranges is 6:7, while the proportion of oranges to overall fruit is 8:14. (or 4:7). A ratio can be defined by providing both constituent integers, which are written as "a to b" or "a:b," or by providing only the value of their quotient a/b. Equal quotients result in equal ratios. A and B are frequently referred to as ratio words, with A being the antecedent and B being the consequent.
This can be solved using ratios
size of tank = 40x6/5 = 48 gallon
The size of the tank would be suggested to hold 40 small fish is 48 gallons.
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