Students should add 8.6 fluid ounces of 12% ethylene glycol.
Using the relation between concentration and volume of solution to find the required amount of 12% ethylene glycol to be used. Let the required amount of 12% ethylene glycol be x fluid ounces. Forming the relation as follows -
C₁ × V₁ + C₂ × V₂ = C₃ × V₃
C₁ and V₁ represents 2% ethylene glycol, C₂ and V₂ represents 12% ethylene glycol and C₃ and V₃ represents 5% ethylene glycol solution. As V₂ is x, so, V₃ will be (20 + x).
Keep the values in formula to find the value of x
2%×20 + 12%×x = 5%×(20 + x)
Solving the equation for the value of x
2/100×20 + 12/100×x = 5/100×20 + 5/100×x
0.4 + 0.12x = 1 + 0.05x
Rearrange the equation -
0.12x - 0.05x = 1 - 0.4
Performing subtraction on both sides -
0.07x = 0.6
Shifting 0.07 to Right Hand Side and performing division
x = 0.6 ÷ 0.07
x = 8.6 fluid ounces
Hence, 8.6 fluid ounces of the 12% ethylene glycol should be added.
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A group of friends wants to go to the amusement park. They have no more than $325
to spend on parking and admission. Parking is $13, and tickets cost $39 per person,
including tax. Write and solve an inequality which can be used to determine p, the
number of people who can go to the amusement park.
Find the area of parallelogram ABCD with vertices A (-2, 6) , B(4, 6) , C(5, -4) , and D(-1, -4) . The area of parallelogram ABCD is square units.
Using the distance between two points to find the side lengths, the area of the parallelogram is of 60.3 square units.
What is the area of a parallelogram?The area of a parallelogram of dimensions l and w is given by the multiplication of these dimensions, that is:
A = lw.
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence, for this problem, the side lengths are:
AB: [tex]\sqrt{(4+2)^2+(6-6)^2} = 6[/tex]BC: [tex]\sqrt{(5-4)^2+(-4-6)^2} = 10.05[/tex]CD: [tex]\sqrt{(-1-5)^2+(-4+4)^2} = 6[/tex]DA: [tex]\sqrt{(-2+1)^2+(6+4)^2} = 10.05[/tex]Hence:
l = 6, w = 10.05, and:
A = 6 x 10.05 = 60.3.
The area of the parallelogram is of 60.3 square units.
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help please with this math question
Answer:
-47^6
Step-by-step explanation:
Answer:
Step-by-step explanation:
4x-6x²-2
Step one use PEMDAS
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
as a guidance
Everything in the parenthesis is simplified, and there isn't any exponent so we onto step 3 which is multiply.
There is a negative infant of the parenthesis -(2x²+8-3x)
that negative sign actually is a -1
therefore multiply -1 to each number inside the parenthesis
Product: -2x²-8+3x
Last step combine like terms
-4x²-2x²=-6x²
x+3x= 4x (remember there is an invisible 1 infront of that x variable)
6-8=-2
Find the volume of a cube that has a total surface area of 54 square millimeters.
The volume of a cube that has a total surface area of 54 square millimeters is 27 cubic millimeters
How to determine the volume?The surface area is given as
A = 54
This is calculated using
A = 6L^2
So, we have
6L^2 = 54
Divide
L^2 = 9
This gives
L = 3
The volume is
V = L^3
This gives
V = 3^3
Evaluate
V = 27
Hence, the volume of a cube that has a total surface area of 54 square millimeters is 27 cubic millimeters
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A movie theatre sells child tickets for $7.50, adult tickets for $9.75, and student tickets for
$8. The movie theatre sold twice as many child tickets as student tickets. If a total of 191
tickets for the film were sold and the total income was $1593.50, how many of each ticket
were sold?
Find the number of child, adult, and student tickets
Answer:
child: 74 adult: 117 student: 37
Step-by-step explanation:
x=2z
x+y+z=191
7.5x+9.75y+8z=1593.5
The number of tickets sold for child is 86.
The number of tickets sold for adults is 62.
The number of tickets sold for child students is 43.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Total tickets sold = $1593.50 _____(1)
Total number of tickets sold = 191 _____(2)
Let the number of tickets sold for child = P _____(3)
Let the number of tickets sold for adults = Q _______(4)
Let the number of tickets sold for students = R ______(5)
Cost of child ticket = $7.50 ______(6)
Cost of adult tickets = $9.75 ______(7)
Cost of student tickets = $8 _______(8)
We can make equations as:
From (2), (3), (4), and (5)
P + Q + R = 191 ____(9)
From (1), (6), (7), and (8)
7.50P + 9.75Q + 8R = 1593.50 _____(10)
We have,
P = 2R putting in (9) and (10)
2R + Q + R = 191
We get,
3R + Q = 191 _____(11)
15R + 9.75Q + 8R = 1593.50
23R + 9.75Q = 1593.50 _____(12)
From (11).
Q = 191 - 3R putting in (12)
23R + 9.75 (191 - 3R) = 1593.50
23R + 1862.25 - 29.25R = 1593.50
-6.25R = -268.75
R = 43 putting in Q = 191 - 3R
We get,
Q = 191 - 3 x 43 = 191 - 129 = 62
Putting R = 43 in P = 2R
We get,
P = 2x43 = 86
We have,
P = 86, Q = 62 and R = 43
Thus,
The number of tickets sold for child is 86.
The number of tickets sold for adults is 62.
The number of tickets sold for child students is 43.
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The perimeter of Stephanie’s triangle is half the perimeter of Juan’s triangle. Juan’s triangle is shown. Write a numerical expression to describe the perimeter of Stephanie’s triangle
The perimeter of Stephanie’s triangle is half the perimeter of Juan’s triangle.Numerical expression to describe the perimeter of Stephanie’s triangle is S =(1/2) J;
Let as assume that
Stephanie's triangle has a perimeter (S)
And, Juan's triangle has a perimeter (J);
According to question, it implies:
S =(1/2) J;
The whole length of any closed shape's boundary is known as its perimeter. Let's use an illustration to try to comprehend this. You may have a sizable square-shaped farm, for instance. You now decide to fence your farm in order to protect it from stray animals. Finding the entire length of the farm's boundary is as simple as multiplying the length of one side of the farm by 4. There are a lot of situations like this when we can be applying the perimeter-finding notion without even realizing it.
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Patrice is trying a low-calorie diet. She would like to keep her calories consumed between the levels shown in the following compound inequality: 2450 < 2x + 50 and 2x + 50 < 3250. Solve for x in the inequality, and explain what the answer represents.
The solution to the compound inequality is 1200 < x < 1600 and the meaning is she must keep her calories consumed between 1200 and 1600
How to solve for x in the inequality, and explain what the answer represents?The compound inequality is given as
2450 < 2x + 50 and 2x + 50 < 3250
Subtract 50 from both sides of the inequality
So, we have
2400 < 2x and 2x < 3200
Divide through the inequality by 20
So, we have
1200 < x and x < 1600
Combine the inequalities
1200 < x < 1600
Hence, the solution to the compound inequality is 1200 < x < 1600 and the meaning is she must keep her calories consumed between 1200 and 1600
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while standing in front of the school, jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there.
This is an observational study because this is taken as observing all possible ways.
What is observational study?An observational review is utilized to respond to an exploration question dependent simply upon what the scientist notices. There is no impedance or control of the examination subjects, and no control and treatment gatherings. These examinations are much of the time subjective in nature and can be utilized for both exploratory and logical examination purposes. In observational examinations, the analyst isn't permitted to control anything. They just notice and gather patterns inside the set up and hypothesize from those outcomes. Observational examination takes into consideration more precise information assortment, eliminating predispositions and inspecting blunders. Notwithstanding, it tends to be tedious because of extended periods of time of dormancy.
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joyce paid $210 for an item at the store that was 55 percent of the original price. what was the original price?
Answer:
Step-by-step explanation:
Answer : Original price 382
55% of 382 = $210
1: Find m
(25x-5)
12X-
A
(15
Answer:
Step-by-step explanation:
(25x-5) 12X- Ax15
What is the point-slope form of the equation for the line with a slope of 6/19 that passes through the point (−1, 7/5)?
The point-slope form of the equation for the line with a slope of [tex]\frac{6}{19}[/tex] that passes through the point[tex](-1,\frac{7}{5} )[/tex] is [tex]6x-19y=-\frac{163}{5}[/tex]
As per the question statement, we are supposed to find the point-slope form of the equation for the line with a slope of [tex]\frac{6}{19}[/tex] that passes through the point[tex](-1,\frac{7}{5} )[/tex] .
Before solving the question, we need to know about the point - slope form of the line i.e., [tex]y-y_{1} =m(x-x_{1} )[/tex]
where m = slope = [tex]\frac{6}{19}[/tex]
[tex]x_{1} =-1[/tex] and [tex]y_{1} = \frac{7}{5}[/tex]
Now substituting values, we get
[tex]y-\frac{7}{5} =\frac{6}{19} (x-[-1])[/tex]
[tex]y-\frac{7}{5} = \frac{6}{19} (x+1)[/tex]
[tex]19y - \frac{133}{5} = 6x+6[/tex]
Rearranging,
[tex]6x-19y+6+\frac{133}{5} =0[/tex]
[tex]6x-19y+\frac{163}{5} =0[/tex]
[tex]6x-19y=-\frac{163}{5}[/tex]
Hence our required equation is [tex]6x-19y=-\frac{163}{5}[/tex]
Point slope form of equation: The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.To learn more about equations of line, click the link given below:
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66 between numbers 4 and 39 put in four numbers, such that arithmetic sequence would be done. what is the third term of this arithmetic sequence?
The third term of the arithmetic sequence is 18.
How to solve arithmetic sequence?The arithmetic sequence formula can be represented as follows:
nth term = a + (n - 1)d
where
a = first termd = common differencen = number of termsTherefore, 4 numbers are inserted between 4 and 39.
Hence,
a = 4
39 = 4 + 5d
39 - 4 = 5d
35 = 5d
d = 35 / 5
d = 7
Hence, the common difference of the arithmetic sequence is 7.
Therefore, the sequence of the arithmetic sequence is as follows:
4, 11, 18, 25, 32, 39
Therefore, the third term of the arithmetic sequence is 18
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i need help!! ……………….
Answer:
Step-by-step explanation:
The first one its easy
its a data handling question can u guys please help
(i) Maximum students were watching T.V for 4-5 hours.
(ii) 34 students watched T.V for less than 4 hours.
(iii) 14 students spent more than 5 hours watching TV.
Given from the graph we can say that:
The process of acquiring, storing, and displaying data in a way that makes it easy for others to use (read or fetch data), such as in graphs or charts, is known as data handling. Statistics is another name for it. Additionally, it is employed for data comparison and mean, median, and mode extraction.
(i) maximum number of students watching TV =32
Almost 32 students watched TV for 4-5 hours.
(ii) For students watching TV for less than 4 hours = ?
= 4 ₊ 8 ₊ 22
= 34
(iii) students who spent more than 5 hours watching TV = ?
= 8 ₊ 6
= 14
Hence we get the desired answers.
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Mr. Wise is ordering a set of books for his class. Each book costs $6. There is a flat shipping fee of $5. The table below shows the relationship between the total cost, c, and the number of books, b. Fill in the blanks to complete the table. Number of Book, b 2 [a] 6 [b] 10 Total Cost ($), c 17 29 [c] 53 65
Filling the table to show the relationship between the total cost, c, and the number of books ordered is as follows:
Number of Books Total Cost ($)
2 $17 ($6 x 2 + $5)
6 $41 ($6 x 6 + $5)
10 $65 ($6 x 2 + $5)
What is the total cost?The total cost is a function of the number of units and the variable cost per unit plus the fixed costs.
For instance, the total cost of 9 books, in this scenario, is $59 ($6 x 9 + $5).
Data and Calculations:Cost per book = $6
Shipping fee = $5
Number of Books Total Cost ($)
2 $17 ($6 x 2 + $5)
6 $41 ($6 x 6 + $5)
10 $65 ($6 x 2 + $5)
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Sorry if that's hard to see, but I need ur help!
Based on the what we established about the classification of y and using the closure of integers, what does the equation tell you about the type of numbers y must be for the product to be rational? What conclusion can you now make about the result of multiplying a rational and an irrational number
The statements are:
x . y = m/n
substituting the values.
a/b . y = m/n
multiplication property of equality.
b/a . a.b . y = m/n . b/a
simplify.
y = mb/na
The product of a rational number with an irrational number is an irrational number. To see this assume that x is a rational number and y an irrational number. Then let us assume that the product xy is rational, which means that there are integers a,b such that xy=a/b. But then we obtain y=(1/x)(a/b) which is also rational since the set of rational numbers is closed under multiplication. But this is a contradiction since y was assumed to be an irrational number.
Hence we made the required conclusion.
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help!!!!!!!! Solve x/5 -3<5
I need help with introduction to probability lesson. Photo is attached below.
The probability of getting heads is 31/50.
How to calculate the probability?Number of tosses = 50
Number of heads = 31
The probability of getting heads will be:
= Number of heads / Total number of tosses
= 31/50
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xy - 2; use x = 3, and y = 5
Please explain step by step how to solve this type of problem.
Answer: 13
Step-by-step explanation:
x = 3, y = 5
xy - 2=
(3)(5)-2=
15-2=13
Help please!
I also need an explaination on how to do it.
Which expression is equivalent to −4 + 9 − 2x − 9x?
−11x + 5
−11x + 13
−11x − 5
11x + 13
Answer:
−11x + 5Step-by-step explanation:
−4 + 9 − 2x −9x
−4 + 9 + − 2x + −9x
Combine Like Terms:−4 + 9 + −2x +− 9x
( −2x+−9x )+( −4+9 )
−11x + 5
Evaluate expression if r=3, q=1 , and w=-2 .
r + 3q / 4r
Answer:
3+3×1/4×3
3+3/12
3×12+3/12
39/12
does anyone kno the value of x??
Answer:
x=12
Step-by-step explanation:
x÷4=3
x=4x3
x=12
12÷4=3
The principal is measuring the floor of the second-grade classroom.
What is the best estimate for the length of a classroom?
The best measure to do so will be is in feet that is the principal will measure it as 10 feet.
The principal has to measure the floor of the second grade classroom.
The best measure to do so will be is in feet
As centimeters and inches will be too short to measure it and can cause problems while further maintaining the records.
Yards on the other hand is a too big unit of measurement to bthe length of the classroom.
Therefore, the best measure to do so will be is in feet that is the principal will measure it as 10 feet.
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Your question was incomplete. Please refer the content below
The principal is measuring the floor of the second-grade classroom.
What is the best estimate for the length of a classroom?
10 yards
10 centimeters.
10 feet
10 inches
Please help me :3 please explain
Using a proportional relationship, the amounts are given as follows:
Tennis 3, Soccer 7.Tennis 36, Soccer 84.What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
For this problem, we have that:
The input variable is the number of tennis players.The output variable is the number of soccer players.From the first row of the table, the constant is given as follows:
k = 35/15 = 7/3.
Hence the relationship is:
y = 7/3x.
For the second row of the table, we have that x = 3, hence:
y = 7/3 x 3 = 7.
For the third row of the table, we have that y = 84, hence:
84 = 7/3x
x = 84 x 3/7
x = 36.
Then the amounts are given as follows:
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415, 430, 445, 460, ...
Find the 101st term.
Answer:
1915
Step-by-step explanation:
nth term = 15n + 400
term to term = 15
n = position
eg:
n=1
1x15=15 + 400 = 415
n=2
2x15=30 + 400 = 430
n=101
101x15= 1515 + 400 = 1915
Answer:
1915
Step-by-step explanation:
formula for the nth term is
an = d times n + first term - d
an = n*d + a1 - d
find the difference between the numbers
it's 15 which is d
first term is a1 which is 415
a101 = 15 times 101 + (415 minus 15)
a101 = 1515 + 400
a101 = 1915
How do I solve this step by step
The coordinate -1 has a weight of 1, the coordinate 4 has a weight of 2, and the coordinate 9 has a weight of 2. Find the
weighted average.
The weight average of the coordinates is 5
How to determine the weight average?The given parameters are:
Coordinate -1 has a weight of 1Coordinate 4 has a weight of 2Coordinate 9 has a weight of 2The weight average is then calculated as:
Weight average = Sum of (Weight * Coordinate)/Sum of Weights
So, we have:
Weight average = (-1 * 1 + 4 * 2 + 9 * 2)/(1 + 2 + 2)
Evaluate the quotient
Weight average = 5
Hence, the weight average of the coordinates is 5
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how many groups of 1/5 are in 4
Answer:
20
Step-by-step explanation:
To find this, we need to figure out what 1/5 is as a decimal
5/5 = 1, so 5 groups of 1/5 equals 1
Multiply this by 4, 20 groups of 1/5, or 20/5 = 4
Now we confirm this
1/5=0.2
4/0.2=20
So it is true
Hope this helps!^^
simplify (4a-3)(a-9)=4a² -39a+27
Answer:
Step-by-step explanation:
0=0