To create 9 gallons of a 30% alcohol solution, mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution by setting up and solving a system of equations based on volumes and concentrations.
Explanation:To find out how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of a 30% alcohol solution, we can set up a system of equations based on the volumes and concentrations of the solutions. Let's let x represent the volume of the 20% solution and y represent the volume of the 50% solution.
Since the total volume of the mixture should be 9 gallons, we have our first equation:
x + y = 9Next, we consider the concentration of alcohol in the final mixture. The amount of pure alcohol from the 20% solution is 0.20x gallons, and from the 50% solution, it is 0.50y gallons. The final mixture has a concentration of 30%, so the total amount of alcohol in the 9 gallons mixture is 0.30 * 9 gallons. This gives us our second equation:
0.20x + 0.50y = 0.30 * 9Now we have a system of two equations with two variables that can be solved using methods such as substitution or elimination. After solving, we find that x = 6 gallons and y = 3 gallons. Therefore, to obtain 9 gallons of a 30% alcohol solution, you'd need to mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution.
x−18 , if x<18. Please help asap!
If x < 18 then you can subtract both sides by 18 and you would get x - 18 < 18 - 18 = 0
So that would be x - 18 < 0.
Hope this helps.
Which polynomial represents the difference below?
The difference between given two polynomials is [tex](- x^{2} + 12x + 3)[/tex].
What is a polynomial?"A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables."
Given two polynomials are [tex](5x^{2} + 9x + 3)[/tex] and [tex](6x^{2} - 3x)[/tex].
Therefore, the difference between these two polynomials
[tex]= (5x^{2} + 9x + 3) - (6x^{2} - 3x)\\= (5x^{2} - 6x^{2}) + (9x + 3x) + 3\\= - x^{2} + 12x + 3[/tex]
Learn more about polynomial here:
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27 33 34 35 37 39 40 41 54 84,75,90,87,99,91,85,88,76,92,94 median: first quartile: third quartile: interquartile range:
Final answer:
For the given data, the median is 85, the first quartile is 37, the third quartile is 90.5, the interquartile range (IQR) is 53.5, and the range is 72.
Explanation:
The median in a dataset is the middle value when the values are arranged in numerical order. For the given data 27, 33, 34, 35, 37, 39, 40, 41, 54, 75, 84, 75, 90, 87, 99, 91, 85, 88, 76, 92, 94, after arranging them in ascending order, the median (Q2) is the value positioned at the center of the dataset. Since there are 21 values, the median is the 11th value, which is 85. The first quartile (Q1) is the median of the first half (lower half) of the dataset, which is the value in the 5.5th position, so we average the 5th and 6th values to get 37. Similarly, the third quartile (Q3) is the median of the second half (upper half) of the dataset, which would be the average of the 16th and 17th values, yielding 90.5. The interquartile range (IQR) is the difference between the third quartile and the first quartile, so IQR = Q3 - Q1 = 90.5 - 37 = 53.5. The range of the dataset is the difference between the maximum and minimum value which is 99 - 27 = 72.
What percent of 7 is 2?
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Round off 1563385 to the nearest million?
To round 1,563,385 to the nearest million, we look at the hundred-thousands digit (5), and since it's 5 or greater, we round up to 2,000,000.
To round off 1,563,385 to the nearest million, look at the hundred-thousands digit, which is 5 in this case.
If it is 5 or greater, we round up; if it is less than 5, we round down.
Since our hundred-thousands digit is 5, we round up, so 1,563,385 rounded to the nearest million is 2,000,000.
340 students went to the first dance but only 306 went to the second. What is the percent decrease in the attendance from the first to the second dance
37% of a certain country's voters think that it is too easy to vote in their country. you randomly select 12 likely voters. find the probability that the number of likely voters who think that it is too easy to vote is (a) exactly three, (b) at least four, (c) less than eight.
The probability that the number of likely voters who think that it is too easy to vote is:
a) exactly three = 0.17422
(b) at least 4 = 0.70533
(c) less than eight = 0.96406
How to use binomial probability theorem?
The general formula for binomial probability theorem is:
P(X = x) = ⁿCₓ * pˣ * (1 - p)⁽ⁿ ⁻ ˣ⁾
Where:
n = 12
p = 0.37
(a) exactly three,
P(x = 3) = ¹²C₃ * 0.37³ * 0.93⁹
= 0.17422
(b) at least 4,
P(4 ≤ x ≤ 12) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + P(11) + P(12)
= 0.70533
(c) less than eight.
P(x < 8) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7)
= 0.96406
how many problems must be answered correctly on a math test with 60 problems to get a score of 85%
Which values are outliers?
5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9
Select Outlier or Not Outlier for each data point.
Data Outlier Not Outlier
0.8
1.1
10.2
10.9
The outliers are 0.8, 1.1, 10.2, and 10.9. The rest are not outliers.
A value is typically considered an outlier if it is less than Q1 - 1.5 [tex]\times[/tex] IQR or greater than Q3 + 1.5 [tex]\times[/tex] IQR.
First, we need to arrange the data in ascending order:
0.8, 1.1, 4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4, 10.2, 10.9
Next, we find the first quartile (Q1), which is the median of the first half of the data:
(4.9 + 5.2) / 2 = 5.05
We find the third quartile (Q3), which is the median of the second half of the data:
(6.1 + 7.4) / 2 = 6.75
Now, we calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 6.75 - 5.05 = 1.7
The lower bound for outliers is:
Q1 - 1.5 [tex]\times[/tex] IQR = 5.05 - 1.5 [tex]\times[/tex] 1.7 = 5.05 - 2.55 = 2.5
The upper bound for outliers is:
Q3 + 1.5 [tex]\times[/tex] IQR = 6.75 + 1.5 [tex]\times[/tex] 1.7 = 6.75 + 2.55 = 9.3
Now we can determine which values are outliers:
0.8 is less than the lower bound (2.5), so it is an outlier.
1.1 is less than the lower bound (2.5), so it is an outlier.
10.2 is greater than the upper bound (9.3), so it is an outlier.
10.9 is greater than the upper bound (9.3), so it is an outlier.
The remaining values (4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4) are not outliers as they fall within the range of Q1 - 1.5 [tex]\times[/tex] IQR and Q3 + 1.5 [tex]\times[/tex] IQR.
Patrick's favorite shade of purple paint is made with 4 ounces of blue paint for every 3ounces of red paint.
Which of the following paint mixtures will create the same shade of purple?
Choose 2 answer
Blue : 4x2=8
Red : 3x2=6
Blue :4x5=20
Red:3x5=15
The following mixtures will create Patrick's favorite shade of purple:
:8ounces of blue paint mixed with 6ounces of red paint
:20 ounces of blue paint mixed with 15 ounces of red paint
Answer:
actually its b and d
Step-by-step explanation:
according to khan academy
by what power of 10 should you multiply the divisor to make it a whole number?
0.82÷6.232
Value of m varies directly as value of n and n=5 when m=12. What is n when m=18?
1. A line passes through the ordered pairs (7,2) and (5,4). What is the slope? please show work
2. A sphere has a diameter od 20 cm. What would be the volume of sphere?
Anna plans a business model to compete with two video stores, where she hopes to draw in customers from one store but not lose money on the deal. Movie Mania charges a subscription fee of $30 and an additional $5 per movie, x. Movie Time charges a subscription fee of $25 and an additional $6 per movie, x. Based on this information, which system of inequalities could be used to determine how many movies need to be rented for a customer on Anna’s plan, y, to pay her more than they would at Movie Time, but less than they would at Movie Mania?
Answer:D. y<5x+30/x
y>6x+25/x
Step-by-step explanation:
got right on edmentum
if a circle has a radius of 13 and a sector defined by a 7.4 degree arc, what is the area, in cm2, of the sector? round your answer to the nearest tenth.
What is the correct inverse function for f(x) = e2x ?
the snowfall in year 1 was 2.03 meters .the snowfall in year 2 was 1.6 meters .how many total meters of snow fell in years 1 and 2
Name the pattern block used to cover 1 third of the hexagon
Please help me with coordinates. IT'S DO IN 3 HOURS
Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. what is the probability that in a randomly selected hour the number of watches produced is greater than 500
Answer: 0.5
Step-by-step explanation:
Given : The number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100.
i.e. [tex]\mu = 500\text{ and } \sigma= 100[/tex]
Let x be the number of watches produced every hour.
Then, the probability that in a randomly selected hour the number of watches produced is greater than 500 will be :
[tex]P(x>500)=1-P(x\leq500)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{500-500}{100})\\\\=1-P(z\leq0)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.5\ \ [\text{ By z-table}]\\\\=1-0.5=0.5[/tex]
Hence, the probability that in a randomly selected hour the number of watches produced is greater than 500 =0.5.
A piece of cardboard has two circles punched out of it. What is the approximate area of the remaining cardboard? Use 3.14 for pie and round to the nearest whole number.
227 cm2
246 cm2
258 cm2
276 cm2
simplify the expression (-5)2. -10 10 -25 25
Factor completely.
3x squared + 2xy - y squared
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What are the values of the variable in 37=30-x^2
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Mr Walton ordered 12 pizzas,for the art class celebration one fourth of the pizza had only mushrooms. how many of the pizza has only mushrooms
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Can someone help me with this problem? please explain.