Answer:
The total number of burgers sold is: 50
Problem Statement
The question tells us a restaurant sold 35 burgers with cheese and also that the ratio of burgers sold with cheese compared to burgers sold without cheese is 7:3.
We are asked to find the total amount of burgers sold; with and without the cheese.
SOLUTION
The question already told us that the ratio of burgers sold with cheese to those without cheese is 7:3. This means that for every 7 burgers with cheese sold, the restaurant also sold 3 burgers without any cheese.
This further implies that out of 10 burgers sold at a time, the restaurant must have sold 7 cheeseburgers and 3 burgers without cheese.
This means that we can say:
[tex]35\text{ burgers represent }\frac{7}{10}\text{ of burgers sold by the restaurant}[/tex]If this is the case, then we can also say that:
[tex]\frac{3}{10}\text{ of the total burgers sold is without cheese}[/tex]Thus, we can write an equation stating that "35 burgers plus 3/10 of the total burgers (B) must be equal to the total number of burgers (B)"
This is done below:
[tex]\begin{gathered} 35+\frac{3}{10}\times B=B \\ 35+\frac{3B}{10}=B \\ \text{Multiply both sides by 10} \\ 350+3B=10B \\ \text{Subctract 3B from both sides} \\ 350+3B-3B=10B-3B \\ 350=7B \\ \text{Divide both sides by 7} \\ \frac{350}{7}=\frac{7B}{7} \\ 50=B \\ \\ \therefore B=50 \end{gathered}[/tex]Final Answer
Thus, the total number of burgers sold is: 50
A QUESTION ON A PROFICIENCY TEST IS MULTIPLE CHOICE WITH 4 POSSIBLE ANSWERS, 1 OF WHICH IS CORRECT. ASSUMING THAT ALL RESPONSES ARE RANDOM GUESSES FIND THE PROBABILITY THAT AMOUNG 12 TEST SUBJECTS, EXACTLY 5 ANSWERS ARE CORRECT
In this scenario, there are only 2 possible outcomes. It is either the answer is correct or wrong.Since the outcomes are independent, it means that it is binomial probability. We would apply the binomial distribution formula which is expressed as
P(x) = nCx * p^x * q^(n - x)
where
n is the sample size
x is the number of successes
p is the probability of success
q = 1 - p = probability of failure
From the information given,
p = 1/4 = 0.25
q = 1 - 1/4 = 3/4 = 0.75
n = 12
x = 5
We want to find P(x = 5)
P(x = 5) = 12C5 * 0.25^5 * 0.75^(12 - 5)
P(x = 5) = 0.103
The probability that among 12 test subjects, exactly 5 answers are correct is 0.103
l
The population of people in a town increases by 100 each year. Which equation represents the situation? Let p represent the amount the population has increased and t represent the number of years.t = 100 + pp = 100 + tt = 100pp = 100t
From the problem, the population increases by 100 each year.
a constant increase of 100 means that the slope of a line is 100.
Slope is the same as constant increase or rate of increase.
The equation of the line with a slope is :
[tex]y=mx+b[/tex]where m is the slope and b is the initital population.
Since we dont have an initital population, b = 0.
The equation will be :
[tex]y=100x[/tex]It is stated also that P represents the population that has increased. So y will be p.
and t represent the number of years. So x will be t.
That will be :
[tex]p=100t[/tex]ANSWER :
The equation is p = 100t
Please helpWrite 78 percent as fraction In simplest form
Step 1:
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Step 2:
[tex]\begin{gathered} 78\text{ percent = }\frac{78}{100} \\ To\text{ write to the simplest fraction} \\ \text{Divide both the numerator and the denominator by 2} \\ \frac{78}{100}\text{ = }\frac{39}{50} \end{gathered}[/tex]Final answer
[tex]\frac{39}{50}[/tex]A skateboarding ramp is 11in. high and rises at an angle if 23⁰. How long is the base of the ramp? Round to the nearest inch *round to the nearest integer as needed*
Translate the following into an inequality:What number divided by five is more than 6?k ≥ 6 ÷ 5k ÷ 5 ≥ 6k ÷ 5 > 65 ÷ k > 6
We need to translate into an inequality the following problem:
What number divided by five is more than 6?
Let's call k the number we are looking for. Then, that "number divided by five" can be translated as:
[tex]k\div5[/tex]Now, "more than" is represented using the symbol ">" (with the opened end turned to the greater amount.
Thus, since the above expression "is more than 6", this can be translated as:
Answer
[tex]k\div5>6[/tex]Find the area of the triangle with base 15 cm and height 18 cm.
From the problem, we have a triangle with base of 15 cm and a height of 18 cm.
The area of the triangle is :
[tex]A=\frac{bh}{2}[/tex]where b = base and h = height.
Using the formula above, the area will be :
[tex]A=\frac{15(18)}{2}=135[/tex]The answer is 135 cm^2
Which expression is equivalent to one sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x?
negative one eighteenth times x minus three
negative one eighteenth times x plus 3
one eighteenth times x minus 3
one and seven eighteenths times x plus three
PLS HURRY 30PTS
The equivalent expression will be;
⇒ ''negative one eighteenth times x plus 3''
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The algebraic expression is,
''Sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x''
Now,
Since, The algebraic expression is,
''One sixth times the quantity 4 times x plus 18 end quantity minus 13 over 18 times x''
Hence, The mathematical expression is,
⇒ 1/6 (4x + 18) - 13/18x
⇒ 4/6x + 3 - 13/18x
⇒ 12/18x - 13/18x + 3
⇒ - 1/18x + 3
Thus, The equivalent expression is,
''negative one eighteenth times x plus 3''
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5Graph the solution to – 2 < 2d – 2 < 6 -
Answer:
Explanation:
Here, we want to solve and graph the compound inequaqlity
We start by solving the sides, one at a time
[tex]\begin{gathered} -2\text{ < 2d-2} \\ -2+2\text{ < 2d} \\ 0\text{ < 2d} \\ 0\text{ < d} \end{gathered}[/tex]For the second part, we have:
[tex]\begin{gathered} 2d-2\text{ }\leq\text{ 6} \\ 2d\leq\text{ 6 + 2} \\ 2d\leq\text{ 8} \\ d\text{ }\leq\frac{8}{2} \\ d\leq\text{ 4} \end{gathered}[/tex]Now, let us write the solution in compound from:
[tex]0\text{ < d }\leq\text{ 4}[/tex]Finally, we proceed to plot the graph as follows:
a single pump is filling a storage container with water at a rate of 60 gallons per minute. after 30 minutes, an additional pump turns on and the container begins to fill at a total rate of 130 gallons per minute for an additional 30 mins. the container already had 1500 gallons of water when it began to be filled a) create a graph showing the amount of water the tank contains for the first 60 minutes b) write a piecewise defined functions for the volume, V, as a function of time, t, measured in minutes
Now we graph the piecewise defined function:
Gonna owns 5/6 of section of land. she plants peanuts on 2/3 of her land what fraction of the entire section is planted with gonnas peanuts Please put your answer in simplest form
We know that
• Gonna owns 5/6 of the section of land.
,• She plants peanuts on 2/3 of her land.
We have to find 2/3 of 5/6, let's multiply these fractions.
[tex]\frac{2}{3}\cdot\frac{5}{6}=\frac{2\cdot5}{3\cdot6}=\frac{10}{18}=\frac{5}{9}[/tex]Therefore, Gonna plants peanuts on 5/9 of her land.Round 32020.20 to the nearest tenth
We have to round 32020.20 to the nearest tenth.
In this case, the number is expressed with decimals up to the hundred (2 decimals).
As the decimals in the hundreds is 0, we don't even need to round it, as we can ignore this and write the number as:
[tex]32020.2[/tex]In this case, the decimal is in the tenths without the need of rounding.
Answer: 32020.2
Solve (x - 5)2 = 3.O A. x = -51 1/3O B. x = 3 15O C. x = 5+:13O D. x = 8 and x = -2
In order to solve the given expression follow these steps:
1. Take the square roots on both sides in order to get rid of the power on the left side:
√(x-5)² = ±√3
x - 5 = ±√3
2. add 5 on both sides:
x-5 + 5 = 5 ±√3
x = 5 ±√3
Then, the solution is x = 5 ±√3
please help me with this problem i mostly need the answers because i don’t have a calculator with me
The compound interest model is given by the following expression:
[tex]y=a(1+\frac{r}{n})^{nx}[/tex]Where a is the principal (initial amount), r is the interest rate in decimal form, n is the number of times compounded in a year and x is the number of years.
a) In this case, $4 are invested at 1% interest rate, then a = 4, r = 0.01 (1%) and n = 4 (compounded quarterly) and the above equation can be rewritten to get a model that led us to calculate the value of your shares over the time like this:
[tex]y=4(1+\frac{0.01}{4})^{4x}[/tex]b) By replacing 0 for x, we can determine the y-intercept of the model, like this:
[tex]y=4(1+\frac{0.01}{4})^{4(0)}=4(1+\frac{0.01}{4})^0[/tex]The result of raising any number to 0 is 1, then we get:
[tex]y=4(1+\frac{0.01}{4})^0=4(1)=4[/tex]Then, the y-intercept if this model is 4 and it represents the initial amount invested ($4)
c) By replacing 10 for x, we get:
[tex]y=4(1+\frac{0.01}{4})^{4(10)}=4(1+\frac{0.01}{4})^{40}=4.42[/tex]Then, after 10 years the estimated value of the shares will be $4.42
d) for a $4 stock with 2% interest compounded semiannually the model changes, we can write it like this:
[tex]y=4(1+\frac{0.02}{2})^{2x}[/tex]By replacing 10 for x, we get:
[tex]y=4(1+\frac{0.02}{2})^{2(10)}=4.88[/tex]As you can see, after 10 years the estimated value of the shares will be $4.88, which is greater than the previous penny stock investment, you would have shared better.
Of all the people going, 5/8 are children and 3/8 are adults. How much moreis 5/8 than 3/8?Explain your answer using equations, diagrams, and words.
Given, the fraction of children, C=5/8.
The fraction of adults, A=3/8.
Therefore 5/8 is more than 3/8 is given by,
[tex]\begin{gathered} \text{Percent}=\frac{C-A}{A}\times100 \\ =\frac{\frac{5}{8}-\frac{3}{8}}{\frac{3}{8}}\times100 \\ =\frac{\frac{5-3}{8}}{\frac{3}{8}}\times100 \\ =\frac{2}{3}\times100 \\ =66.67 \end{gathered}[/tex]Therefore, 5/8 is more than 3/8 by 66.67%.
In each of the figures, there are 8 boxes. In the first figure showing the fraction of children, two boxes are shaded more than the figure for adults. In the second figure for the fraction of adults, only 3 boxed are shaded.
So, the % by which 5/8 is more than 3/8 can be found as
[tex]\begin{gathered} \text{percentage}=\frac{Number\text{ of extra shaded boxes in first figure}}{\text{Number of shaded boxes in second figure}}\times100 \\ =\frac{2}{3}\times100=66.67 \end{gathered}[/tex]5/8 is 5 parts of 8. 3/8 is 3 parts of 8. So, if the total number of people is 8, five people are children and three people are adults.
So, number of children is 2 more than the number of adults, whose number is 3.
Therefore, the fraction for number of children more than the adults with respect to the number of adults is 2/3. In percentage,
[tex]\text{percentage}=\frac{2}{3}\times100=66.67[/tex]So, 5/8 is more than 3/8 by 66.67%.
9) Write the slope-intercept form of an equation for
the line of fit. Use points (15, 40) and (41, 61).
The linear equation that passes through (15, 40) and (41, 61) is:
y = (21/26)*x + 725/26
How to get the linear equation?A general line is written as:
y = m*x + c
Where m is the slope and c is the intercept of the y-axis.
If the linear equation passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
slope = (y₂ - y₁)/(x₂ - x₁)
In this case the line passes through (15, 40) and (41, 61), then the slope is:
m = (61 - 40)/(41 - 15) = 21/26
Then the line is:
y = (21/26)*x + c
To find the value of c we can replace the values of one of the poitns, if we use the first one we will get:
40 = (21/26)*15 + c
40 = 315/26 + c
40 - 315/26
725/26 = c
The linear equation is.
y = (21/26)*x + 725/26
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A large amount of peanuts was divided equally into 6 small bags. The total number of peanuts, p, was 342. Whichstatements can be used to write an expression and then find the number of peanuts that ended up in each bag?Check all that apply.The operation is division.The operation is multiplication.The variable is the number of bags.342 divided by 6 equals 57.Write the division expression as a fraction,To evaluate, substitute 342 for the variable.Each bag will have 57 peanuts.The constant is 342.
342 peanuts were divided equally into 6 small bags. "p" represents the total number of peanuts
To determine how many peanuts go in each bag, you have to divide the total amount of peanuts by the number of bags:
[tex]\frac{p}{nº\text{bags}}=\frac{342}{6}=57[/tex]The variable of this example is the number of peanuts, and the constant is the number of bags.
So, the statements that apply are:
- The operation is a division
- 342 divided by 6 equals 57
-Each bag will have 57 peanuts.
-To evaluate, substitute 342 for the variable.
-Write the division expression as a fraction,
1/4 -86.205/4.121121112....123253^2/5 [tex] \sqrt{ \frac{4}{9} } [/tex][tex] \sqrt{20} [/tex]-1/2[tex]\pi[/tex].1223334444....16666....[tex] ^{3} \sqrt{27} [/tex][tex] - \sqrt{25} [/tex][tex]3\pi[/tex][tex] \binom{12}{4} [/tex][tex] \sqrt{17} [/tex]Okay finally tell me which numbers go in :Natural NumbersWhole Numbers Integers Rational Numbers Irrational Numbers
Natural numbers are the non-negative integers
So we will put inside its circle all the positive integers and zero
Let us find them using the 1st picture
there are 0 and square root 36 because its value is 6
Whole numbers are positive numbers only
So we can put 0 in a natural circle and 6 in the whole part and 12/4 because it equals 3
Integers are positive and negative whole numbers
We have -8 and - square root 25 because it equals -5
So put -8 and - square root 25 in the integer circle
Rational numbers are all numbers can but in the form of the fraction
So we will choose the number with decimal or fraction
6.2, -1/2, 2.21 on the rational part
The rest of the numbers are irrational numbers
Put them in the part of irrational numbers
expression and assume that X, y, and z denote any positive real numbers
a) given equation is,
[tex]\begin{gathered} \sqrt[8]{x^8y^4z^{4\:}} \\ =\sqrt[8]{x^8}\sqrt[8]{y^4z^4} \\ =x\sqrt[8]{y^4z^4} \end{gathered}[/tex]b) the given equation is
[tex]\begin{gathered} \sqrt[3]{\sqrt{64x^6}} \\ =\sqrt[3]{8x^3} \\ =2\sqrt[3]{x^3} \\ =2x \end{gathered}[/tex]Which choice is equivalent to the quotient shown here when x > 0?A.2xB.2x2C.D.
Given
[tex]\sqrt{22x^6}\div \sqrt{11x^4}[/tex]Solution
[tex]\begin{gathered} \frac{\sqrt{22x^6}}{\sqrt{11x^4}}=\sqrt{\frac{22x^6}{11x^4}} \\ \\ =\sqrt{\frac{22x^6}{11x^4}} \\ \\ =\sqrt{2x^2} \\ \\ =x\sqrt{2} \end{gathered}[/tex]The final answerOption C[tex]x\sqrt{2}[/tex]
Multiply and simplify. 3/9 x 5/9
Answer:
5/27
Step-by-step explanation:
3/9 x 5/9
= ( 3 x 5 )/( 9 x 9 )
9 can be splitted as 3 x 3
= ( 3 x 5 )/( 3 x 3 x 9 )
= 5/( 3 x 9 )
= 5/27
Answer:
[tex]\frac{5x}{27}[/tex]
Step-by-step explanation:
Cancel the number 3/9 = 1/3
= 1/3 x 5/9
Apply the function rule
1 · x · 5
3 · 9
Multiply the numbers 1 · 5 = 5
[tex]\frac{5x}{3 }[/tex]· [tex]9[/tex]
Now just Multiply the numbers: 3 · 9 = 27
= [tex]\frac{5x}{27}[/tex]
Micaela and Danielle each improved their yards by planting daylilies and shrubs. They bought their supplies from the same store. Micaela spent $74 on 12 daylilies and 10 shrubs. Danielle spent $39 on 7 daylilies and 5 shrubs. Find the cost of one daylily and the cost of one shrub.
Solution:
Given:
Let the cost of each daylily be d
Let the cost of each shrub be s
Generating the system of equations;
[tex]\begin{gathered} 12d+10s=74.................(1) \\ 7d+5s=39.....................(2) \end{gathered}[/tex]Equation (2) multiplied by 2;
[tex]\begin{gathered} 12d+10s=74..............(1) \\ 14d+10s=78...............(2) \\ \\ Subtracting\text{ equation \lparen1\rparen from equation \lparen2\rparen; equation \lparen2\rparen- equation \lparen1\rparen} \\ 14d-12d=78-74 \\ 2d=4 \\ Dividing\text{ both sides by 2;} \\ d=\frac{4}{2} \\ d=2 \end{gathered}[/tex]Substituting the value of d into equation (2);
[tex]\begin{gathered} 7d+5s=39 \\ 7(2)+5s=39 \\ 14+5s=39 \\ 5s=39-14 \\ 5s=25 \\ Dividing\text{ both sides by 5;} \\ s=\frac{25}{5} \\ s=5 \end{gathered}[/tex]Therefore, the cost of one daylily is $2 and the cost of one shrub is $5.
7. Which simplified expression represents the expression below? * 102" (102c)-2 31-5 10^-1x^2 1/4 0 x2 o none of these
You have the following expression:
10x⁴(10x)⁻²
in order to simplify the previous expression proceed as follow:
10x⁴(10x)⁻² = 10x⁴/(10x)² = 10x⁴/10²x²
by simplifying the previous fraction, you obtain:
10x⁴/10²x² = 10⁻¹x²
where you have taken into account that the quotient between factors with different exponents, is equal to the same factor powered to the difference of the exponents:
Hence, the answer is:
10⁻¹x²
A water footprint is a measure of the appropriation of fresh water.The per capita water footprint (in mega gallons) in a certain countryfor a recent year can be approximated by a normal distribution, asshown in the figure.(a) What water footprint represents the 86th percentile?(b) What water footprint represents the 28th percentile?(c) What water footprint represents the third quartile?
To answer this question, we can use the standard normal distribution to find the asked percentiles. We will need the z-scores to find the values for them.
The z-scores are given by the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Where
• x is the raw value (the one we need to find here)
,• μ is the population's mean. In this case, μ = 1.75 Mgal.
,• σ is the population's standard deviation. In this case, σ = 2.82 Mgal.
Finding the 86th percentile
The 86th percentile represents the value for which 86% of the cases are less than this value, and, therefore, 14% are above this value.
Then we can find it, if we know the value for which, z, in the standard normal table, represents the cumulative probability (0.86) for the distribution. If we consult the table, we have:
[tex]P(z<1.08)=0.8599\approx0.86[/tex]Therefore, the value for z is, approximately, z = 1.08, and we can use this value to find the value for x (the 86th percentile, in this case):
[tex]\begin{gathered} 1.08=\frac{x-1.75}{2.82} \\ (1.08)(2.82)=x-1.75 \\ (1.08)(2.82)+1.75=x \\ x=4.7956 \end{gathered}[/tex]Therefore, the 86th percentile, if we round the value to two decimal places, is, approximately, x = 4.80.
Finding the 28th percentile
We can apply the same procedure as before. Then we have:
[tex]P(z<-0.58)=0.2809_{}[/tex]Then we have:
[tex]\begin{gathered} -0.58=\frac{x-1.75}{2.82} \\ (-0.58)(2.82)=x-1.75 \\ (-0.58)(2.82)+1.75=x \\ x=0.1144 \end{gathered}[/tex]If we round the result to two decimal places, we have that the 28th percentile is x = 0.11 (approximately).
Finding the footprint for the third quartile
The third quartile is equivalent to the 75% percentile. Then we can use the same process as before to find the value of z that represents it as follows:
[tex]P(z<0.675)=0.7502_{}[/tex]And we can apply the same formula as before:
[tex]\begin{gathered} 0.675=\frac{x-1.75}{2.82} \\ (0.675)(2.82)=x-1.75 \\ (0.675)(2.82)+1.75=x \\ x=3.6535 \end{gathered}[/tex]If we round this value to two decimal places, we have x = 3.65 (approximately).
A store pays $62 for leaf blower. The store marks up the price by 40%. what is the new pricem
A store pays $62 and they mark up the price by 0.4 of the price:
[tex]\begin{gathered} \text{New price= 62+(62}\cdot0.4) \\ \text{New price=86.8 usd} \end{gathered}[/tex]It’s polynomial operations I need the answer and all the work written out.
Answer:
[tex]x^2+14x^3y^2-6x[/tex]Explanation:
Given the below polynomials expression;
[tex](4x^2+7x^3y^2)-(-6x^2-7x^3y^2-4x)-(10x+9x^2)[/tex]The 1st step to solving the above is to clear the brackets while minding the signs as shown below;
[tex]4x^2+7x^3y^2+6x^2+7x^3y^2+4x-10x-9x^2[/tex]The 2nd step is to group like terms;
[tex]4x^2+6x^2-9x^2+7x^3y^2+7x^3y^2+4x-10x[/tex]Let's go ahead and evaluate;
[tex]x^2+14x^3y^2-6x[/tex]You have a choice between 2 jobs, one pays $8.25/hr but requires you to spend $20 to get a uniform. The other pays $7.50/hr. At how many hours will the job be equal?
Step-by-step explanation + Answer:
x = 1st job
y = 2nd job
x + y = 22......x = 22 - y
7x + 8.25y = 171.50
7(22 - y ) + 8.25y = 171.50
154 - 7y + 8.25y = 171.50
-7y + 8.25y = 171.50 - 154
1.25y = 17.50
y = 17.50 / 1.25
y = 14 <== 14 hrs at the 8.25 per hr job
x + y = 22
x + 14 = 22
x = 22 - 14
x = 8 <=== 8 hrs at the 7 per hr job
Use graphs to find the set.(−2,4) ∪ [−1,6]Im not for sure on how to solve the set?
Answer:
A. The set is {-1, 0, 1, 2, 3, 4, 5, 6}
Explanation:
Note the following;
*When we use parentheses or open brackets, ( ), in an interval notation, it signifies that those points are excluded in the set.
*When we use closed or square brackets, [ ], in an interval notation, it signifies that those points are inclusive in the set.
*The union symbol (U) is used to join two intervals together.
Given the interval notation, (−2,4) ∪ [−1,6], since there -2 and 4 are in parentheses, it means that they are not included in the set while -1 and 6 are included in the set since they are in square brackets. So the members of the set can be represented in a graph as;
A cylinder has a height of 44.5 inches and a radius of 22.8 inches. Which of the following measurements is closest to the lateral surface area of the cylinder in square inches? F 6,374.9 in.2 G 145,274.5 in.? H 3,185.8 in. ? J 2,029.2 in.2 2.
We have the following:
The formula for the lateral surface area of a cylinder is as follows
[tex]LSA=2\cdot\pi\cdot r\cdot h[/tex]replacing:
[tex]\begin{gathered} LSA=2\cdot3.14\cdot22.8\cdot44.5 \\ LSA=6371.7 \end{gathered}[/tex]Therefore the answer is F 6374.9 in ^ 2
When planning a cruise, you have a choice of 2 destinations: Cozumel (C) or Jamaica (J); a choice of 3 types of rooms: balcony (B), inside view (I), or ocean view (O); and a choice of 2 types of excursions: water sports (W) or horseback riding (H). If you are choosing only one of each, list the sample space in regard to the vacations (combinations of destinations, rooms, and excursions) you could pick from.
Given:
When planning a cruise:
you have a choice of 2 destinations: Cozumel (C) or Jamaica (J)
and a choice of 3 types of rooms: balcony (B), inside view (I), or ocean view (O)
and a choice of 2 types of excursions: water sports (W) or horseback riding (H)
We will list the sample space in regard to the vacations
First, we will draw the tree diagram
The tree diagram will be as shown in the following figure:
So, there are 12 outcomes you could pick from.
The sample space will be as follows:
CBW, CBH, CIW, CIH, COW, COH
JBW, JBH, JIW, JIH, JOW, JOH
write a ratio that is equivalent to the ratio: 9/12
the given ratio is
9/12
divide numerator and denominator by 3
[tex]\frac{\frac{9}{3}}{\frac{12}{3}}=\frac{3}{4}[/tex]so the equivalent ratio is 3/4