Adam bought 26.14 ounces of orange juice.
To solve the problem, we need to determine how many ounces of orange juice Adam bought with $3.42, given that the cost per ounce is $0.12. We can set up a simple proportion to find the answer.
First, we convert the cost of orange juice per ounce from a fraction to a decimal. The cost is $0.12 per ounce, which can also be written as [tex]$\frac{12}{100}$[/tex] dollars per ounce. Simplifying this fraction gives us [tex]$\frac{3}{25}$[/tex] dollars per ounce.
Next, we convert the total amount spent by Adam, $3.42, into a fraction. This is equivalent to [tex]$\frac{342}{100}$[/tex] dollars.
Now, we set up the equation to find the number of ounces (let's call it [tex]$x$[/tex]) that Adam bought:
[tex]\[ \frac{3}{25} \times x = \frac{342}{100} \][/tex]
To solve for [tex]$x$[/tex], we multiply both sides of the equation by the reciprocal of [tex]$\frac{3}{25}$[/tex], which is [tex]$\frac{25}{3}$[/tex]:
[tex]\[ x = \frac{342}{100} \times \frac{25}{3} \][/tex]
Multiplying the numerators and denominators separately, we get:
[tex]\[ x = \frac{342 \times 25}{100 \times 3} \][/tex]
Simplifying the right side of the equation by canceling out common factors (25 cancels with 100 to become 4, and 3 cancels with 342 to become 114), we have:
[tex]\[ x = \frac{114 \times 4}{4} \][/tex]
This simplifies to:
[tex]\[ x = 114 \][/tex]
However, we must remember that the original amount spent was $3.42, not $342. Therefore, we must divide our result by 100 to account for the cent conversion:
[tex]\[ x = \frac{114}{100} \][/tex]
[tex]\[ x = 1.14 \][/tex]
This result represents the number of ounces Adam bought in addition to the whole number of ounces he could buy with whole dollars. Since $3.00 would buy [tex]$\frac{3}{0.12}$[/tex] ounces, we need to add this to our 1.14 ounces to get the total:
[tex]\[ x_{total} = 1.14 + \frac{3}{\frac{12}{100}} \][/tex]
[tex]\[ x_{total} = 1.14 + \frac{3 \times 100}{12} \][/tex]
[tex]\[ x_{total} = 1.14 + \frac{300}{12} \][/tex]
[tex]\[ x_{total} = 1.14 + 25 \][/tex]
[tex]\[ x_{total} = 26.14 \][/tex]
Centennial park is evaluating the capacity of the park and have determined that 15 people can comfortably stand in a section that is 5ft by 8ft , the park has dimensions that are 400yds by 200 yds estimate the number of people who can fit in the park
We have been given that 15 people can comfortably stand in a section that is 5ft by 8ft .
Hence, the area of this section is given by
[tex]A=5\times 8\\ A=40 ft^2[/tex]
Hence, we can say that 15 people can comfortably stand in an area 40 square feet.
Now, we know that 1 yard is equal to 3 feet.
Hence, the area of the section 400yds by 200 yds is equal to
[tex]400\times 3 \times 200 \times 3\\ =720000 ft^2[/tex]
Now, in 40ft^2, 15 people can stand comfortably.
Hence, in 720000 ft^2, number of people can stand comfortably is
[tex]\frac{15}{40} \times 720000\\ \\ =270000[/tex]
Therefore, 270000 people can stand in the park of dimension 400 yds by 200 yds
Hey can you please help me posted picture of question
hey can you please help me posted picture of question
There are 50 total patrons. 16 like lattes, 12 like espressos, and 8 like both drinks.
Add the two totals for patrons that like either lattes or espressos:
[tex] 16 + 12 = 28 [/tex]
8 patrons like both drinks, so subtract this from the amount of patrons that like either drink:
[tex] 28 - 8 = 20 [/tex]
20 patrons like at least one drink.
Subtract the amount of patrons that like a drink from the total amount of patrons:
[tex] 50 - 20 = \boxed{30} [/tex]
30 patrons like neither drink.
Solve 5x 2 - 7x + 2 = 0 by completing the square. What is the constant added on to form the perfect square trinomial?
Answer: 49/100 is correct
( that other answer was bothering me )
In a class, 12 out of 25 students are female. what percent of students are female?
Simplify (3x+8)(x+1) using a table, the Distributive Property, and the FOIL
method. Which method is most efficient? Explain.
Final answer:
To simplify (3x+8)(x+1), we can use the FOIL method, the Distributive Property, or a multiplication table, all leading to the same simplified expression: 3x² + 11x + 8. The FOIL method is typically the most efficient for binomials.
Explanation:
The question asks to simplify the expression (3x+8)(x+1) using a table, the Distributive Property, and the FOIL method and to determine which method is most efficient.
Using the FOIL Method
FOIL stands for First, Outer, Inner, Last and represents a quick way to multiply two binomials:
First: Multiply the first terms in each binomial (3x×x = 3x²).
Outer: Multiply the outer terms (3x×1 = 3x).
Inner: Multiply the inner terms (8×x = 8x).
Last: Multiply the last terms in each binomial (8×1 = 8).
Adding these products together, we get 3x² + 3x + 8x + 8, which simplifies to 3x² + 11x + 8.
Using the Distributive Property
This involves expanding the expression by multiplying each term in the first polynomial by each term in the second: (3x+8)(x) + (3x+8)(1), which also simplifies to 3x² + 11x + 8.
Using a Table
Create a table where you list each term of the first polynomial in the first row and the terms of the second polynomial in the first column, and then fill in the table with the products of the intersecting terms. The sum of these products will also yield 3x² + 11x + 8.
While all three methods will give the correct answer, the FOIL method is generally seen as the most efficient for this particular problem, as it provides a straightforward, step-by-step process that is easy to follow and remember for multiplying two binomials.
A car tire has a radius of 15 inches. Suppose the car is traveling at 60 miles per hour (1 mile = 5,280 feet). What is the approximate rate of spin, in revolutions per minute, of the tire? Round the answer to the nearest whole number.
A cat and a dog have a race. The cat’s strides are 30% shorter than the dog’s but it makes 30% more strides than the dog. Which of them will win the race?
the answer would be 90% because when you multiply 30% x 30% =90% its the same as 3 x 3 = 9
What is the gcf of 108 and 132
Answer:
12
Explanation:
The greatest common factor (GCF) is the largest factor two numbers share within their respective factor trees. In order to find the GCF, list factors of each number and then select the biggest one they have in common.
Factors of 108 are:
1, 108; 2, 54; 4, 27; 6, 18; 9, 12
Factors of 132 are:
1, 132; 2, 66; 3, 44; 4, 33; 6, 22; 11, 12
As can be observed, the largest number they have in common is 12. Therefore the GCF of 108 and 132 is 12.
Daisies cost $0.99 each and tulips cost $1.15 each. Maria bought a boquet of daisies and tulips. It contained 12 flowers and cost $12.52. Find the number of daisies and the number tulips in the bouquet
Maria bought 8 daisies and 4 tulips in the bouquet.
Explanation:Let's assume that Maria bought x daisies and y tulips. Since the total number of flowers in the bouquet is 12, we can write the equation: x + y = 12.
Also, the total cost of the bouquet is $12.52. Using the cost per flower, we can write another equation: 0.99x + 1.15y = 12.52.
Now we have a system of equations that we can solve. Multiplying the first equation by 0.99, we get 0.99x + 0.99y = 11.88. Subtracting this equation from the second equation eliminates the x term, giving us 0.16y = 0.64. Dividing both sides by 0.16, we find that y = 4.
Substituting this value back into the first equation, we can solve for x: x + 4 = 12, x = 8.
Therefore, Maria bought 8 daisies and 4 tulips in the bouquet.
a golf course charges $10 to golf or $150 for a summer pass. Write an inequality to represent the number of times you would need to golf in order for the summer pass to be a better deal
Answer:I
Step-by-step explanation:
Alexander is riding his bicycle to school. After one mile he is a third of the way there. How much more does he have to ride
Which pair of expressions is equivalent?
-5n+22>=-73
[tex] - 5n + 22 \geqslant - 73 = [/tex]
Solve the given differential equation. y' = 5x^2 − 1/ 5 + 4y
A jar contains two red marbles, three green marbles, ten white marbles and no other marbles. two marbles are randomly drawn from the jar without replacement. what is the probability that these two marbles drawn will both be red? express your answer as a common fraction.
the denominator HAS to be 15C2
but what's the numerator?
A suit regularly costs $389.90., Bob buys it on sale for $ 265.00 . How much does he save?
Josh is hiking Glacier National Park. He has now hiked a total of 1 7 km 17 km17, space, k, m and is 2 km 2 km2, space, k, m short of being 1 2 2 1 start fraction, 1, divided by, 2, end fraction of the way done with his hike. Write an equation to determine the total length in kilometers ( h ) (h)left parenthesis, h, right parenthesis of Josh's hike.
17 + 2 = 19 km is 1/2 of the total length, that is,
19 = (1/2)h
(1/2)h = 19 multiply both sides by 2
h = 2*19
h = 38 km
The total length in kilometers is 38 km.
Tree a lived for 6 decades and 5 years. Tree b lived for 58 years. Which tree lived longer
Final answer:
Tree A, which lived for 65 years (6 decades and 5 years), lived longer than Tree B, which lived for 58 years.
Explanation:
To answer which tree lived longer, we can calculate the age of both trees. Tree A lived for 6 decades and 5 years. Since one decade is equal to 10 years, 6 decades would be 6 x 10 years, which is 60 years. Adding the additional 5 years, Tree A lived for a total of 60 + 5 = 65 years.
Tree B lived for 58 years. Comparing both ages, Tree A lived for 65 years while Tree B lived for 58 years. Therefore, Tree A lived longer than Tree B.
What is the midpoint between the points (1, 3) and (5, 7)?
A. (4, 4)
B. (7, 9)
C. (3, 5)
D. (2, 2)
describe a situation where it is easier to use decimals than fractions and explain why
When you must multiply non whole numbers, decimals are easier to manipulate in the sense that setting up a multiplication problem with decimals rather than fractions is much simpler and easier to calculate.
The rate of the number of bags mishandled by the airlines fell to 4.77 bags per 1000 passengers in 2011. At this rate,
estimate how many bags would be mishandled for 1650 passengers.
Now evaluate f(x) = 2x4 - 4x3-11x2+3x-6 for x=-2 f (-2) =
The answer to the given solution is 8.
Given that,
The equation is [tex]f(x) = 2x^4 - 4x^3-11x^2+3x-6[/tex].The x = -2.Based on the above information, the calculation is as follows:
[tex]f(x) = 2x^4 - 4x^3-11x^2+3x-6\\\\= 2(-2)^4 - 4(-2)^3-11(-2)^2+3(-2)-6\\\\= 2\times 16 - 4\times -8 - 11\times 4+ 3 \times -2 - 6\\\\[/tex]
= 32 + 32 - 44 - 6 - 6
= 8
Therefore we can conclude that the answer is 8
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What is the GCF
135, 189 , 297
5,895÷36
show all your work
hey can you please help me posted picture of question
Which type of triangle is formed by joining the vertices A(-3, 6), B(2, 1), and C(9, 5)?
plz help me
it sounds confusing
Please please help!!
Use multiplying by 1 to find an expression equivalent to 3/14 with a denominator of 14 y.