You are making identical bagel platters using
40 plain bagels, 30 raisin bagels, and 24 blueberry
bagels. What is the greatest number of platters
that you can make if there are no leftover bagels?
Answers
94 bagels in total so 100 would be plenty
Related Questions
Station 5
The ratio of the number of dollars Jada has to the number of dollars Kelly has is 4:7. Kelly
gives Jada $6.00. The ratio of the number of dollars Jada has to the number of dollars Kelly
has changes to 6:5. How many dollars do Jada and Kelly each have now?
Answers
The number of dollars Jada and Kelly each have now is $18 and $15.
What are ratios?Mathematicians refer to a comparison of two or more integers as a "ratio."It acts as a measuring tool to demonstrate how large or small one amount is in contrast to another. In a ratio, two quantities are compared by utilizing division. The "antecedent" in this instance is the dividend, while the "consequent" is the divisor.Given:
Ratio of the number of dollars Jada has to the number of dollars Kelly has = 4:7
Changed ratio after Kelly gives Jada $6.00 = 6:5
Let the number of dollars Jada and Kelly have be 4x and 7x.
Kelly gives Jada $6.00,
So,
Number of dollars Jada has now is $(4x + 6).
Number of dollars Kelly has now is $(7x - 6).
The ratio of the number of dollars is changed to 6:5.
⇒ \(\frac{4x + 6}{7x -6} = \frac{6}{5}\)
⇒ 5(4x + 6) = 6(7x - 6)
⇒ 20x + 30 = 42x - 36
⇒ 42x - 20x = 30 + 36
⇒ 22x = 66
⇒ x = 3
Number of dollars Jada has now = (4x + 6) = $18
Number of dollars Kelly has now = (7x - 6) = $15
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Suppose Y(t) = 25e^3t + 12 represents the number of bacteria present at time t minutes. At what time will the population reach 100 bacteria? ( Note: Answers are expressed in terms of natural logarithm
Answers
Given:
The given function is:
\(Y(t)=25e^{3t}+12\)
Where Y represents the number of bacteria present at time t minutes.
To find:
The time taken by bacteria population to reach 100 bacteria.
Solution:
We have,
\(Y(t)=25e^{3t}+12\)
Putting \(Y(t)=100\), we get
\(100=25e^{3t}+12\)
\(100-12=25e^{3t}\)
\(88=25e^{3t}\)
Divide both sides by 25.
\(\dfrac{88}{25}=e^{3t}\)
Taking ln on both sides, we get
\(\ln (\dfrac{88}{25})=\ln e^{3t}\)
\(\ln(\dfrac{88}{25})=3t\) \([\because \ln e^x=x]\)
Divide both sides by 3.
\(\dfrac{1}{3}\ln(\dfrac{88}{25})=t\)
Therefore, the required time is \(\dfrac{1}{3}\ln(\dfrac{88}{25})\) minutes.
which statements are true select all that apply. Extra points!!!
Answers
2 is true
3. is false
4. is true
1 & 3 are false
2 & 4 are true
Please help me out‼️‼️‼️‼️〽️
Answers
We can see that the dot plot is seen below.
What is a dot plot?We can see here that An example of a graphical representation of data is a dot plot. It is a number line with dots above each value to indicate the frequency or count of that value.
Depending on the type of data being shown, the dots are often arranged either horizontally or vertically.
Dot plots are known to be useful for showing the distribution of data, particularly for small data sets.
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Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
4. Find the average value of the given function on the given interval. Then find all points c whose existence is guaranteed by the Mean Value Theorem for Integrals. (a) f(x) = x2 – 8x + 10 on (2, 5] (b) f(x) = Vx on [1, 16]
Answers
The average value of the given function on the given interval is = 7/2 and 6.25 respectively
What is Average?
The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
(a) f(x) = x2 – 8x + 10
f = 1/b-a \(\int\limits^b_a {f(n)} \, dx\)
f = 1/5-2 \(\int\limits^5_2 {x^{2} -8x+10} \, dx\)
Here, a=2
b=5
f(x) =x2 – 8x + 10
f = 1/3 (x³/3 - 8x²/2+10x)5/2
f = -25/9 -20/9
f = -45/9
= -5
Mean Value Theorem
If f(x) = continous on (a, b)
If f(x) = differentiable on (a, b)
Then f(c) = f(b) -f(a)/b-a
were c∈ (a,b)
Here, f(c) = f(-5)-f(2)/5-2
f(c) = -5+2/3
f(c) = -1 ......................(1)
Here, f(x) = x²-8x+10
f(c) = c²-8c+10
f(x) = 2c-8...................(2)
equating 1&2
2c -8 = -1
2c = -1 +8
c = 7/2
c∈ (2,5)
(b) f(x) = Vx on [1, 16]
f = \(\sqrt{x}\) on (1 ,16)
f= 1/b-a \(\int\limits^b_a {f(n)} \, dx\)
f = 1/16-1 \(\int\limits^6_1 {\sqrt{x} } \, dx\)
f = ( 2x (3/2)/45)₁¹⁶
f = 128/45-2/45
f = 126/45
= 14/5
Mean Value Theorem
f(x) = \(\sqrt{x}\)
f(c) =\(\sqrt{c}\)
f(c) = 1/2\(\sqrt{c}\)....................(1)
we know that
f(c) = f(b)-f(a)/b-a
f(c) = f(16)-f(1)/16-1
f(c) = \(\sqrt{16}\) -\(\sqrt{1}\)/15
f(c) = 4-1/15
= 3/15.....................(2)
Equating (1) and (2)
1/2\(\sqrt{c}\) = 3/15
2\(\sqrt{c}\) = 15/3
2\(\sqrt{c}\) = 5
\(\sqrt{c}\) = 5/2
c = (5/2)²
=25/4
c≅ 6.25
6.25 = (1 ,16)
The average value of the given function on the given interval is = 7/2 and 6.25 respectively
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The sum of twice a number, m, and 7 is equal to 15 less than the number,
m. What is the value of m?
Answers
Answer:
2m+7 = m-15
2m-m+7 = -15
1m = -15-7
1m = -22
m = -22
Expand and simplify (2x - 1)(x + 3)(x - 5)
Answers
Answer:
2x^3-5x^2-28x+15 -------------------------expanded
2x^3-5x^2-28x+15--------------------simplified
Step-by-step explanation:
\left(2x-1\right)\left(x+3\right)\left(x-5\right)
=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)
simplyfied
\left(2x^2+5x-3\right)\left(x-5\right)
=2x^2x+2x^2\left(-5\right)+5xx+5x\left(-5\right)-3x-3\left(-5\right)
=2x^3-5x^2-28x+15
plzz help its timed ill give brainliest
Answers
What is 3/8 x 3/8 x 3/8 written as a power
Answers
Answer:
3/8^3
Step-by-step explanation:
its like 1/2 x 1/2 x1/2 its 1/2^3
or 7x7x7x7x7=7^5 its the same concept....
it's for todayyyyyyyyyyyyyyyy
Answers
hi
a) m = 2
b) m = 4
c) n = 5
d) n= 3
e) m = 6
f) n = 4
Evalute 3n² - 8n - 9, given n(n - 3) = 10.
Answers
Answer:
19 or 26
Step-by-step explanation:
You want the value of 3n² -8n -9, given that n(n -3) = 10.
Values of nWe recognize that 10 = 5·2 and that these factors differ by 3. This means n(n -3) = 10 is equivalent to saying n ∈ {-2, 5}.
Expression in nThe value of 3n² -8n -9 will be one of ...
(3n -8)n -9 = (3(-2) -8)(-2) -9 = (-14)(-2) -9 = 19 . . . . for n = -2
or
(3(5) -8)(5) -9 = (7)(5) -9 = 26 . . . . . . . for n = 5
The expression 3n² -8n -9 will be either 19 or 26.
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Jordan’s family exchanged 250 dollars for 5000 pesos. Jordan bought a sweater for 550 pesos. How many dollars did the sweater cost? If Jordan’s family exchanges 200 dollars at the same rate, how many pesos will they have?
Answers
If Jordan’s family exchanges 200 dollars at the same rate, they will have 4000 pesos
If Jordan’s family exchanged 250 dollars for 5000 pesos, then;
250 dollars = 5000 pesos
In order to determine the cost of sweater bought at 550 pesos, we can write:
x = 550 pesos
Divide both expressions
250/x = 5000/550
5000x = 137,500
x = 137,500/5000
x = 27.5
Hence the sweater cost $27.5
If Jordan’s family exchanges 200 dollars at the same rate, then;
$200 = y
250 dollars = 5000 pesos
Dividing both expressions
200/250 = y/5000
250y = 1000000
y = 1,000,000/250
y = 4000pesos
Hence if Jordan’s family exchanges 200 dollars at the same rate, they will have 4000 pesos
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Answer:
200=4000
Step-by-step explanation:
I got it right on my test
A multiplication table. In the row labeled 3, the numbers 9, 12, 15, 18, and 21 are highlighted. In the row labeled 6, the numbers 18, 24, 30, 36, and 42 are highlighted. Look at the highlighted portions in the rows for 3 and 6. What do the two sets of numbers have in common? They both show products of multiplying by
Answers
The common number in both sets will be 18. And the row labeled 6 is the multiplication of the row labeled 3 with 2.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
A multiplication table.
In the row labeled 3, the numbers 9, 12, 15, 18, and 21 are highlighted.
In the row labeled 6, the numbers 18, 24, 30, 36, and 42 are highlighted.
Look at the highlighted portions in rows 3 and 6.
The common number in both sets will be 18.
The row labeled 6 is the multiplication of the row labeled 3 with 2.
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Answer: the person above is wrong
its 3, 4, 5, 6, and 7
Help me pleaseeeeee!
Answers
Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn
In algebra, what is a rectangle?A rectangle is a type οf quadrilateral that has its parallel sides equal tο each οther and all the fοur vertices are equal tο 90 degrees. Hence, it is alsο called an equiangular quadrilateral. Since, the οppοsite sides are equal and parallel, in rectangle, therefοre, it can alsο be termed as a parallelοgram.
Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn
check the attachment given belοw tο understand.
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You have $1,300 in savings for retirement. If your investments earn 12% annually, how much will you have in your retirement account in 11 years?
Answers
1300x.12=156
156x11+1300=3016
Please mark brainliest
Step-by-step explanation:
Answer :- Amount (after 11 years) = $4522.11
i really need help, can someone please help me with this math question
Answers
The functions for this problem are defined as follows:
(t + s)(x) = x³ + 5x².(ts)(x) = \(5x^5\)(t - s)(-2) = -28.How to obtain the functions?The functions for this problem are given as follows:
s(x) = 5x².t(x) = x³.The addition and subtraction functions for this problem are given as follows:
(t + s)(x) = x³ + 5x².(t - s)(x) = x³ - 5x².At x = -2, the numeric value of the subtraction function is given as follows:
(t - s)(-2) = -2³ - 5(-2)²
(t - s)(-2) = -28.
The product function for this problem is given as follows:
(ts)(x) = \(5x^5\)
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Answer the question below using the following amortization table.
What is the regular monthly payment?
O $352.15
O $703.01
O $1758.17
O $1055.16
Answers
Answer: $1,758.17
Adding the principal paid and interest paid will result in $1,758.17 for every month/column.
For example,
Month 21 - $688.68 + $1,069.49 = $1,758.17
Month 22 - $692.73 + $1, 065.44 = $1,758.17
And so on..
As $1,758.17 is the constant total when you add principal paid and interest paid in every month, that is your answer.
The chocolate candy below is being wrapped in a cardboard box. How many square centimeters area needed for the box?
Answers
The total area of cardboard needed is equal to 121.34 square centimeters.
How many square centimeters area needed for the box?This is equal to the surface of the given chocolate.
First, we will have two sides that are rectangles measuring 16cm by 2.6cm, so the area is:
\(A = 16cm*2.6cm = 41.6cm^2\)
Then we have another rectangular side which is the bottom one, that is a rectangle of 2.2cm by 16cm, so the are is:
\(A' = 2.2cm*16cm = 35.2cm^2\)
Finally, we have the areas of the two triangular faces, the areas of these are:
\(A'' = 2.2cm*3cm/2 = 1.47cm^2\)
Then the total area of cardboard needed is:
\(area = 2*A + A' + 2*A'' = 2*41.6cm^2 + 35.2cm^2 + 2* 1.47cm^2 = 121.34 cm^2\)
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I need help with this question
Answers
The value of h is 0.895, the arc cosine of h is 0.462 and it terminates in the correct quadrant
Lastly, the measure of angle θ is 1.46 π
Calculating the value of hGiven that
Terminal point = (-1.79, -0.89)
This means that
(x, y) = (-1.79, -0.89)
Also, we have
Radius, r = 2 units
So, the value of h is
h = |x|/r
This gives
h = |-1.79|/2
Evaluate
h = 0.895
Calculating the arc cosine of hIn part (a) of this solution, we have
h = 0.895
Take the arc cos of both sides
So, we have
cos⁻¹(h) = cos⁻¹(0.895)
Evaluate the arc cos using a calculator
So, we have the following representation
h = 0.462 rad
This angle is in the first quadrant
It means that the angle terminates in the correct quadrant
For the value of θ, we have the following
This is calculated as
θ = π + tan⁻¹(-0.89/-1.79)
Evaluate
θ = π + 0.46 π
Evaluate
θ = 1.46 π
Hence, the measure of angle θ is 1.46 π
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P=x-2 ÷ x+1 for what value of x is P undefined
Answers
Answer:
x = - 1
Step-by-step explanation:
P = \(\frac{x-2}{x+1}\)
the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.
x + 1 = 0 ( subtract 1 from both sides )
x = - 1
P is undefined when x = - 1
A soda factory makes 9 flavours of soda. Each case of soda has 7 cans of each flavour. How many cans of soda does the factory put in 7 cases?
Answers
The factory will put 441 cans of soda in 7 cases.
If each case of soda contains 7 cans of each flavor, and the factory is putting 7 cases, we can calculate the total number of cans by multiplying the number of flavors, cans per flavor, and cases.
Given:
Number of flavors = 9
Cans per flavor = 7
Number of cases = 7
To calculate the total number of cans, we can multiply these values:
Total cans = Number of flavors × Cans per flavor × Number of cases
Total cans = 9 × 7 × 7
Total cans = 441
To arrive at this answer, we multiplied the number of flavors (9) by the number of cans per flavor (7) to get the number of cans per case (63). Then, we multiplied the cans per case (63) by the number of cases (7) to obtain the total number of cans (441).
Hence, the factory will put 441 cans of soda in 7 cases.
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At a university, Todd deposits $100 into his cafeteria account. He spends $5 on dinner every day. Seth deposits $140 into his account. He spends $5 on lunch and $5 on dinner every day. After how many days will Todd and Seth have the same amount of money in their accounts? 16 8 4 2
Answers
Answer:
The answer is 8 days.
Step-by-step explanation:
By applying the correct equations to Todd and Seth's balances for each day we end up with Todd and Seth having an equal balance in their accounts by day 8, alternatively, we can show that Todd and Seth have the same amount of money in their accounts by day 8 with this table
Day - Todd - Seth
1 - 95 - 130
2 - 90 - 120
3 - 85 - 110
4 - 80 - 100
5 - 75 - 90
6 - 70 - 80
7 - 65 - 70
8 - 60 - 60
The figure below shows a rectangular prism and a cube: How many such cubes are required to completely pack the prism without any gap or overlap? the length is 5in. width is 4/5and the height is 1 3/5the cube side is 1/5
Answers
Answer:
Explanation:
The dimensions of the rectangular prism are:
• Length = 5in.
,• Width = 4/5 in.
,• Height =1 3/5 in.
The cube has a side length of 1/5 inches.
The number of cubes to pack the prism is determined using the formula below:
\(\begin{gathered} \text{Number of Cubes=}\frac{\text{Volume of }Rec\tan gular\text{ Prism}}{\text{Volume of one cube}} \\ =\frac{\text{lwh}}{s^3} \\ =\frac{5\times\frac{4}{5}\times1\frac{3}{5}}{(\frac{1}{5})^3} \\ =(5\times\frac{4}{5}\times1\frac{3}{5})\div(\frac{1}{5})^3 \end{gathered}\)The operation is simplified below:
\(\begin{gathered} =\mleft(5\times\frac{4}{5}\times\frac{8}{5}\mright)\div\frac{1}{5^3} \\ =\frac{32}{5}\times5^3 \\ =32\times25 \\ =800\text{ cubes} \end{gathered}\)800 cubes are required to completely pack the prism without any gap or overlap.
5. Charlie deposits $1000 into his investment account. The account grows at a rate
of 8% per year. How much money total is in the account on the first day on
the 11th year.
Answers
Answer:
1100
Step-by-step explanation:
First, we start off by finding 10% which is $100. We divide that by 10 to get $10 which is 10%. Now we need to multiply 10% (which is $10) by 10 which is $100. That gives you this answer
The total amount in the account on the first day of the 11th year is if Charlie deposits $1000 into his investment account. The account grows at a rate of 8% per year is $1880.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given data:
Charlie deposits, P = $1000 into his investment account.
The account grows at a rate, r = 8% per year.
The time, t = 11 year
Calculate the simple interest as shown below,
\(SI = (P\times r\times t) / 100\)
SI = (1000 × 8 × 11) / 100
SI = $880
Calculate the total amount by the formula given below,
Amount = A
\(A = P + SI\)
A = 1000 + 880
A = $1880
Therefore, the total amount in the account on the first day of the 11th year is if Charlie deposits $1000 into his investment account. The account grows at a rate of 8% per year is $1880.
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Which of the lines below has a negative slope? A B C D A. Line A O B. Line B G Line C D. Line D
Answers
Answer:
A. Line A
Step-by-step explanation:
Line A is decreasing so it has a negative slope.
Help please i need this asap!! I'll give 100 points
Answers
The range is expressed in interval notation as (-1, ∞)
How to find the function (f+g)(x)?To find the linear function f(x), let us use the table given.
A linear function with the following equation that passes through the points (a, g(a)) and (b, g(b)):
\(g(x) - g(a) = \frac{g(b)-g(a)}{b-a} (x-a)\)
Because the g(x) line crosses through points (-6, 14) and (-3, 8), we have:
a = -6, g(a) = 16, b = -3 and, g(b) = 10
Therefore g(x)
\(g(x) - (16) = \frac{10-16}{-3-(-6)} (x--(6))\\g(x) - 16 = \frac{10-16}{-3+6} (x+6)\\g(x) - 16 = \frac{-6}{3} (x+6)\\g(x) - 16 = -2(x +6)\\g(x) = -2x -12+16\\g(x) = -2x+4\)
now find the (f+g)(x).
\((f+g)(x) = f(x) + g(x) = x^{2} + 2x -5 -2x + 4\\(f+g)(x) = f(x) + g(x) = x^{2} - 1\\\)
(f+g)(x) = (x-1)(x+1), therefore we get the values x = 1 and x = -1
The parabola's vertice has x-coordinate 0 (the midway between the roots). At x = 0, we get:
\((f +g)(x) = 0^{2} - 1 = -1\)
Furthermore, because the coefficient of \(x^{2}\) is 1, which is positive, this function indicates a parabola that has been opened upwards.
As a result, the function's minimal value is y = -1. As a result, the function's range includes all real numbers equal to or greater than -1.
The range is expressed in interval notation as (-1, ∞)
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Consider a linear regression situation with a quantitative response variable Y, a quantitative explanatory variable X, and one categorical explanatory variable with 3 levels. Three indicator variables A1, A2 and A3 are defined, with Ak = 1 if the individual is from level k, and O otherwise (for k=1,2,3). To allow different slopes (for the relationship between X and Y) for each level of the categorical variable, which of the following terms need to be included in the model in addition to Bo + B1X + 8? O A1, A2, and A3. O Aj and A2, but not A3. O A X, A2X, and A3X. O AjX and A2 X, but not A3X.
Answers
Include all three indicator variables (A1, A2, and A3) in the model
To allow different slopes in the relationship between X and Y for each level of the categorical variable, the model should include terms A1X and A2X in A1 and A2 respectively. For example, the model can be expressed as:
Bo + B1X + B2A1X + B3A2X + B4A3
where B2 and B3 represent the slope of the relationship between X and Y for people at levels 1 and 2 of the categorical variable, respectively. represent. The value of X remains constant.
Include all three indicator variables (A1, A2, and A3) in the model. This allows to compare the effect of a given level of a categorical variable on the response variable while keeping the value of X constant. For example, if you include only A1 and A2 in your model, you cannot compare the effects of level 3 of the categorical variables on the response.
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Answers
- This year at least one of their clients will have a starting salary of at least $40,000.
There is not enough information to determine whether this statement is true or false. The mean starting salary from last year does not provide information on this year's salaries.
- Last year some of their clients had a starting salary of exactly $40,000.
This statement is true. Since the mean includes all starting salaries, it is possible for some clients to have had a starting salary of exactly $40,000.
- Last year fewer than half of their clients had a starting salary of $40,000 or less.
This statement is false. Since the mean starting salary is $40,000, it is impossible for fewer than half of the clients to have had a starting salary of $40,000 or less.
- Last year some of their clients had a starting salary of more than $36,000.
This statement is true. Since the mean starting salary is $40,000, it is possible for some clients to have had a starting salary of more than $36,000.
- Last year at least one of their clients had a starting salary of at least $40,000.
This statement is true. Since the mean starting salary is $40,000, it is possible for at least one client to have had a starting salary of at least $40,000.
Therefore, the statements that must be true based on the given information are:
- Last year some of their clients had a starting salary of exactly $40,000.
- Last year some of their clients had a starting salary of more than $36,000.
- Last year at least one of their clients had a starting salary of at least $40,000.
• I am a fraction less than 1.
My denominator is a multiple of 5.
My denominator is less than 20.
• My numerator is a multiple of 4.
My numerator is 3 less than my
denominator.
Answers
Answer:
12/15
Step-by-step explanation:
3x5=15
4x3=12
15-12=3
Therefore the answer is 12 over 15