The Royal Fruit Company produces two types of fruit drinks. The first type is 80% pure fruit juice, and the second type is 100% pure fruit juice. The company is attempting to produce a fruit drink that contains 95% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 220 pints of a mixture that is 95% pure fruit juice?
Answer:
55 from un-pure and 165 from pure
Step-by-step explanation:
to get 220 pints with 95% purity you need a mixture of 209 parts to 11 parts (220 *0.95 and 220 * 0.05)
we call the un-pure mixture a and the pure mixture b
all un-pure parts come from a and b in the following ratios
11 = 0.2a + 0b (each pint of mixture a adds 0.2 pints of unpure stuff and each pint of b adds no unpure stuff)
which we can then solve as:
a = 55
all pure parts come from a and b in the following rations
209 = 0.8a + 1b (each pint of mixture a adds 0.8 pints of pure stuff and each pint of b adds a full pint of the pure stuff)
now we can replace a with 55 (from above)
209 = 44 + b, and solve to
b = 165
now to double check
55 * (0.8x + 0.2y) + 165x would give you
44x + 11y + 165x, which is
11x + 209y and if you then check the ratio
209 / (209+11) = 0.95 again
There will be 55 pints and of un-pure and 165 pints of pure fruit drinks.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
To get 220 pints with 95% purity you need a mixture of 209 parts to 11 parts (220 *0.95 and 220 * 0.05)
We call the un-pure mixture a and the pure mixture b
All un-pure parts come from a and b in the following ratios
11 = 0.2a + 0b (each pint of mixture a adds 0.2 pints of unpure stuff and each pint of b adds no unpure stuff)
which we can then solve as:
a = 55
All pure parts come from a and b in the following rations.
209 = 0.8a + 1b (each pint of mixture a adds 0.8 pints of pure stuff and each pint of b adds a full pint of the pure stuff)
Now we can replace a with 55 (from above)
209 = 44 + b, and solve to
b = 165
Now to double check
55 x (0.8x + 0.2y) + 165x would give you
44x + 11y + 165x, which is
11x + 209y and if you then check the ratio
209 / (209+11) = 0.95
Therefore, there will be 55 pints of unpure and 165 pints of pure fruit drinks.
To know more about an expression follow
https://brainly.com/question/14022405
#SPJ2
please help asap for brainlist
Answer:
3rd one i think so or it will be last question
which grade question is this
The sum of two numbers is 80
their difference is 38.
The product of these 2 numbers is __?
i need help with this!!
Answer:
Answer: x <-4Step-by-step explanation:
you need to do it step by step and use something that will help
8x-4<-36
8x<-36+4
8x<-32
Answer: x<-4
Brennan studied the relationship shown in the table.
x 3 4 5 6 7
y 36 48 60 72 ?
Which expression describes a method Brennan could use to determine the y-value when x equals 7?
Answer:
y = 12x
Step-by-step explanation:
Note the relationship
x = 3 : y = 36 , that is 36 = 12 × 3
x = 4 : y = 48, that is 48 = 12 × 4
x = 5 : y = 60 , that is 60 = 12 × 5
x = 6 : y = 72 , that is 72 = 12 × 6
The value of y is obtained by multiplying corresponding x value by 12
Then
x = 7 → y = 12 × 7 = 84
in general for any x
y = 12x
The ratio of green balloons to blue balloons is 6 to 9 if there are 1620 blue balloons how many green balloons are there
3 pairs of $23.67 gloves. what is the unit price?
Answer:
7.89 dollars
Step-by-step explanation:
The unit price would be the price of one pair of gloves.
So divide the total cost by the number of pairs bought.
23.67/3= 7.89
56 x 4 + 5 - 53=x
(x) x 23 + 500
Step-by-step explanation:
56× 4=224
224+5= 229
229-53=176
176×23=4048
4048+500=4548
The answer is = 4548
A cash card has a starting value of $25. If the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month.
The relationship between the number of months after the first year and the amount remaining on the card is .
The independent variable is the _____________?
The dependent variable is the ______________?
Answer:
The relationship between the number of months after the first year and the amount on the remaining card is linear and inverse ( Which meant that ,when the number of months after the first year increases , the amount on the remaining car decreases , in a linear way ) .The Independent variable is the numbers of months after the first year .The Dependent variable is the amount on the remaining card , Bcoz this amount depends on the time it has passed since the first year , ( which is our independent variable!).If we call "Y" our dependent variables and "X" our Independent variable , This relationship can be written as Y= 25 - 2.5x.If no months had passed since the first year, then x= 0 and the amount in the card equals $25 , While if one month has passed since the first year x= 1 and y= 22.5 ( The amount in the card in this case is $22.5 .Step-by-step explanation:
Hope this helps you !!out of 300 students at rsm summer camp 180 are boys what fraction of all students are boys
Answer:
3/5
Step-by-step explanation:
so first of all...
out of
300
students,
180
are boys.
180/300
which, simply by 60
3/5
so.. 3/5 of the people at rsm (whatever that is) summer camp are boys! Explanation isn't good, but you didn't really ask for it so i think you're ok... I guess. Now i just need an answer to my problem...
In rsm summer camp, fraction of boys is 3/5.
What is a fraction?A fraction is a numeral that represents a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Total number of students at rsm summer camp = 300.
Total number of boys at rsm summer camp = 180.
To find the fraction of boys to all students.
Fraction of boys = number of boys / total number of students
= 180 / 300
= 18 / 30
= 3 / 5
The required fraction of boys is 3/5.
To know more about Fraction on:
https://brainly.com/question/10708469
#SPJ2
what is 1/2 (6x+10) - 25
Answer:
3x - 20
Step-by-step explanation
simplify 1/2
STEP 3
Pulling out like terms
3.1 Pull out like factors :
6x + 10 = 2 • (3x + 5)
Equation at the end of step
3 (3x + 5) - 25
Final result : 3x - 20
In a two digit number, the sum of the digit is 14. Twice the tens digit exceeds the units digit by one. Find the numbers?
Answer:
59
Step-by-step explanation:
x= tens place of number
y= ones place of number
set up equations:
"sum of the digit is 14"
sum is the result of addition
x+y=14
"Twice the tens digit exceeds the units digit by one"
2x is bigger than y by 1
if 2x is bigger, then add 1 to the opposite side to balance the equation:
2x=y+1
with 2 equations you can solve for 2 variables:
2x=y+1
2x-1=y
substitute into x+y=14
x+(2x-1)=14
3x-1=14
3x=15
x=5
------
subtitute to find y
x+y=14
5+y=14
y=9
number is 59
If there are 30 boys and 12 girls in a room, fill out all of the possible ratios of boys to girls that could be made
Answer:
30:12
Step-by-step explanation:
On a map, two cities are 5 3/4 inches apart. the scale of the map is 1/2 inch equals 3 miles. what is the actual distance between the towns?
Answer:
18
Step-by-step explanation:
5.5 x 3=16.5
Add 1.5 and you get 18
Suppose $22,825 is deposited into a savings account with a simple interest rate of 4.03%. Find the account balance after 5 years and 3 months.
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Based on the information that's given, the account balance after the years given will be $27654.20.
The formula for simple interest is calculated as:
= PRT / 100
where,
Principal = $22825
Rate = 4.03%
Time = 5 years, 3 months = 5.25 years
Therefore, the simple interest will be:
= ($22825 × 4.03 × 5.25) / 100
= $4829.20
Therefore, the amount will be:
= $22825 + $4829.20
= $27654.20
Learn more about simple interest on:
https://brainly.com/question/25747402
Answer:
The amount will be $27654.20
Step-by-step explanation:
what is the total number of edges on a rectangular prism
Answer:
12 edges
Step-by-step explanation:
A rectangular prism has 6 faces, 8 vertices (or corners) and 12 edges.
Answer:
12
Step-by-step explanation:
Can someone please give me the (Answers) to this? ... please ...
Answer:
For A1-4 I am pretty sure the answers are: Question 1.) 3/1 (or 3) Question 2.) -6/6 (also can be written as -1) Question 3.) 9/5 and Question 4.) -4/3
Step-by-step explanation:
For Question 1 you just rise 3 and run 1 which gets you 3/1
For Question 2, to get from coordinate 2 to 8 you add 6, and to get from coordinate -10 to -16 you subtract 6. This leaves you with -6/6 (or -1)
For Question 3, the slope is written within the equation (y=9/5x-5) the 9/5 is the slope.
For Question 4, you take 4x+3y=6 and turn it into y=mx+b form, to do so you subtract 4x on both sides leaving you with 3y=-4x+6. Then you divide 3 on both sides, y=-4x/3 + 6/3. Then the result would be y=-4/3x+2 which means that the slope is -4/3.
I am not sure if these are all correct, but i hope it helps! :)
Layla has 5.49 pounds of wood she divides it into 7
so basically 5.49÷7
Answer:
0.7842857142857143
Step-by-step explanation: i would right an explanation but i cant put it all so you will just have to trust me
3. Solve by graphing. Round each answer to the nearest tenth.
x^2 - 7x = 11
Answer:
-1.3, 8.3
Step-by-step explanation:
Based on the graph below, the solutions are -1.3 and 8.3.
the equation above models h, the height of a firework shell in feet, t seconds after launch. what is the height in feet, of the firework shell 2 seconds after launch?
The circle passes through the point (-1.5, 2.5). What is its radius?
Choose 1 answer
2.5
V1.5
1.5
/2.5
what is the x coordinate to the solution for the following system of equations
x = 2y
4x - 3y = 15
Answer:
x=6
Step-by-step explanation:
x=2y
4x-3y=15
4(2y)-3y=15
8y-3y=15
5y=15
y=3
x=2y
x=2(3)
x=6
HELP PLEASE!!!
What is the ratio of 1713.57^2/4113.87^3.
Answer:
4.21747×10^-5
Step-by-step explanation:
Your calculator can do the division for you. The ratio is about 4.21747×10^-5.
__
This is approximately 10/237109.
) It took 2 pumps 6 hours to pump the water out of a pond. How long would it take if 3 pumps
were used?
Answer:
it would take 2 hours with 3 pumps
Step-by-step explanation:
hope this helps! :D
Jerry took a test that had 45 questions on it. He got 36 correct. Enter the
percentage of questions Jerry got correct.
Answer:
80% is what he got on the test
Solve for the value of A
SOMEONE PLEASE HELP ME ILL GIVE YOY BRAINLIST AND POINTS
(6a - 8) + 50 = 90
6a - 8 + 50 = 90
6a + 42 = 90
6a = 90 - 42
6a = 48
a = 48/6
•°• a = 8
2. Approximate e?. Round your answer to the nearest tenth
Answer:
1096.6
Step-by-step explanation:
The answer would be 1096.63316, but since you are rounding to the nearest tenth, then your answer would be 1096.6.
Answer:
1096.6.
Step-by-step explanation:
e = about 2.7
2.7^7is about 1046
7/13 as a decimal rounded to the nearest hundredth
Answer:
0.54
Step-by-step explanation:
Answer:
0.54
Step-by-step explanation:
calculator. easy.
What is the area of the square?
32 square units
64 square units
24 square units
16 square units
Answer:
64 square units
Step-by-step explanation:
All you have to do is multiply 8 by 8 to get 64.
WILL GIVE BRAINLIEST!! ILL GIVE LINK IF YOU NEED IT
Answer: As x increases, the slope of the graph increases.