Use the figures to estimate the area under the curve for the given function using four rectangles.
Answers
To calculate the area for the upper (left) graph, we can use x = 1, 2, 3 and 4 to find the upper limit of each rectangle:
[tex]\begin{gathered} f(1)=\frac{3}{1}+3=6\\ \\ f(2)=\frac{3}{2}+3=4.5\\ \\ f(3)=\frac{3}{3}+3=4\\ \\ f(4)=\frac{3}{4}+3=3.75 \end{gathered}[/tex]Since the x-interval of each rectangle is 1 unit, the area of each rectangle is given by its y-value, so we have:
[tex]\begin{gathered} A=f(1)+f(2)+f(3)+f(4)\\ \\ A=6+4.5+4+3.75=18.25 \end{gathered}[/tex]Now, for the bottom (right) graph, the limits of the rectangles are x = 2, 3, 4 and 5.
So, let's find the value of f(5):
[tex]f(5)=\frac{3}{5}+3=3.6[/tex]So the area is given by:
[tex]\begin{gathered} A=f(2)+f(3)+f(4)+f(5)\\ \\ A=4.5+4+3.75+3.6=15.85 \end{gathered}[/tex]Related Questions
a bottle of juice is 2/3 full the bottle contains 4/5 cup of juice write division problem that represents the capacity of the bottle
Answers
Answer:
x = ( 6 / 5 )y
Step-by-step explanation:
Identify the equaiton.
let x = bottle;
let y = cups;
( 2 / 3 )x = ( 4 / 5 )y;
Multiply both sides by ( 3 / 2 ).
( 3 / 2 )( 2 / 3 )x = ( 3 / 2 )( 4 / 5 )y;
x = ( 12 / 10 )y;
Write the fraction in its simplest form.
x = ( 6 / 5 )y;
It takes 1 + ( 1 / 5 ) of a cup to fill the bottle.
Let p = x^2 + 6.Which equation is equivalent to (22 + 6)^2 – 21 = 4x^2 + 24 in terms of p?Choose 1 answer:А) p^2 + 4p - 21 = 0B) p^2 - 4p - 45 = 0C) p^2 - 4p - 21 = 0D) p^2 + 4p - 45 = 0
Answers
Given:
[tex](22+6)^2-21=4x^2+24[/tex][tex]\text{Let p = x}^2+6[/tex]Let's solve the equation in terms of p:
[tex]undefined[/tex]“ Judy has a bag with 12 DVD’s, 12 marbles, 11 books, and 1 orange. What is the ratio of books to marbles? What is the ratio of DVD’s to the total number of items in the bag? What percentage of the items in the bag are DVD’s? “
Answers
First, let's calculate the total number of items:
[tex]12+12+11+1=36[/tex]The ratio of books to marbles is calculated by dividing the number of books by the number of marbles:
[tex]ratio=\frac{books}{\text{marbles}}=\frac{11}{12}[/tex]The ratio of DVD's to the total number of items is:
[tex]\text{ratio}=\frac{\text{dvds}}{\text{total}}=\frac{12}{36}=\frac{1}{3}[/tex]The percentage of dvd's from the total is:
[tex]\frac{1}{3}=0.3333=33.33\text{\%}[/tex]A Ferris wheel at a carnival has a diameter of 72 feet. Suppose a passenger is traveling at 5 miles per hour. (A useful fact: =1mi5280ft.)
(a) Find the angular speed of the wheel in radians per minute.
(b) Find the number of revolutions the wheel makes per hour. (Assume the wheel does not stop.)
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a) The Ferris wheel has an angular speed is 12.222 radians per minute.
b) The Ferris wheel makes 116.712 revolutions in an hour.
How to understand and analyze the kinematics of a Ferris wheel
Kinematics is a branch of mechanical physics that studies the motion of objects without considering its causes. In other words, kinematics studies displacements, velocities and accelerations in translation, rotation and combined motion. In this case we find a Ferris wheel rotating around its axis at constant rate.
a) Then, the angular speed (ω), in radians per minute, is determined by the following product:
ω = v / R
Where:
v - Linear velocity at the rim of the Ferris wheel, in feet per second.R - Radius of the Ferris wheel, in feet.Please notice that the length of the radius is the half of the length of the diameter.
If we know that v = 5 mi / h and R = 36 feet, then the angular speed of the wheel is:
ω = [(5 mi / h) · (1 h / 60 min) · (5280 ft / 1 mi)] / [(0.5) · (72 ft)]
ω = 12.222 rad / min
The angular speed is 12.222 radians per minute.
b) A revolution is equal to an angular displacement of 2π radians and an hour is equal to 60 minutes. Then, we can derive the number of revolutions in an hour by dimensional analysis:
n = (12.222 rad / min) · (1 rev / 2π rad) · (60 min / h)
n = 116.712 rev / h
There are 116.712 revolutions in an hour.
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Which interval notation represents a function with a domain of all real numbers greater than or equal to 4?A.) -35 D.) y>0 E.) Y<4
Answers
If the domain is all real numbers greater than or equal to 4, the interval will be
[tex]x\ge4[/tex]Find the rate of change of each linear function 1. y = x - 7
Answers
Rate of change = 1
Explanations:The given linear function is:
y = x - 7
The rate of change of the function is gotten by finding the derivative (dy/dx) of the function
dy/dx = 1
The rate of change = 1
Nathalie is finishing a workout on the treadmill. She speeds up before slowing down to a stop. Nathalie draws a graph to represent her workout.
Answers
As the x-axis increases uniformly the y-axis increase and decreases so the horizontal axis must be labeled with time and the vertical axis with speed so option (A) is correct.
What is a graph?A graph is a diametrical representation of any function between the dependent and independent variables.
The graph is easy to understand the behavior of the graph.
The graph of a treadmill workout has been plotted.
We all know that the speed of the treadmill keep fast initially but after some time the speed reduces and it goes to zero lineary.
Therefore,the horizontal axis wich is uniform changes cause to vertical axis with first increase and then decrease shown.
Hence "As the x-axis increases uniformly the y-axis increase and decreases so the horizontal axis must be labeled with time and the vertical axis with speed".
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(a) The perimeter of a rectangular garden is 312 m.If the length of the garden is 89 m, what is its width?Width of the garden: ]וח(b) The area of a rectangular window is 6205 cm?If the width of the window is 73 cm, what is its length?Length of the window: 7 cm
Answers
EXPLANATION
Let's see the facts:
Perimeter = P = 312 m
Length = l = 89m
Width = w = unknown
The perimeter of a rectangle is given by the following relationship:
[tex]P=2(w+l)[/tex]Replacing terms:
[tex]312=2(w+89)_{}[/tex]Applying the distributive property:
[tex]312=2w\text{ + 178}[/tex]Subtracting 178 to both sides:
[tex]312-178=2w[/tex][tex]134=2w[/tex]Dividing 2 to both sides:
[tex]\frac{134}{2}=w[/tex]Simplifying:
[tex]67=w[/tex]Switching sides:
[tex]w=67[/tex]The width of the garden is 67 meters.
Question 1. Write the equation of the line that goes through the points (-2,1) and (4,2).
Answers
Slope-intercept equation:
y=mx+b
Where:
m= slope
b=y- intercept
Point 1 = (x1,y1) = (-2,1)
Point 2 = (x2,y2)= (4,2)
First, find the slope by applying the formula:
[tex]m=\text{ }\frac{y2-y1}{x2-x1}=\frac{2-1}{4-(-2)}=\frac{1}{6}[/tex]Now we have:
y=1/6x+b
Replace x,y by a point ( for example point 1 (-2,1)) and solve for b:
1 = 1/6 (-2) +b
1= -1/3 +b
1+1/3 = b
b= 4/3
Final equation:
y= 1/6x+4/3
Quincy has a jewelry business in which he designs and sells bracelets. His daily profit, Q(x), can be modeled by the function Q(x) = 7.25x − 36.25, where x is the number of bracelets he sells. What is the value of Q(5), and what is its interpretation?
Q(5) = 0; If Quincy sells 0 bracelets, he will earn $5.
Q(5) = 0; If Quincy sells 5 bracelets, he will earn $0.
Q(5) = 5.69; If Quincy sells 5.69 bracelets, he will earn $5.
Q(5) = 5.69; If Quincy sells 5 bracelets, he will earn $5.69.
Answers
The value of Q(5) is zero and represents the zero profit on selling 5 bracelets thus option (B) is correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given,
Daily profit function Q(x) = 7.25x − 36.25 where x is the number of bracelets he sells.
At x = 5 ( selling 5 bracelets)
Q(5) = 7.25(5) - 36.25
Q(5) = 36.25 - 36.25 = 0
It means selling 5 bracelets doesn't give any profit.
Hence "The value of Q(5) is zero and represents the zero profit on selling 5 bracelets".
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Fill in the missing numbers to complete the linear equation that gives the rule for this table.x: 1, 2, 3, 4y: 8, 28, 48, 68Y = ?x + ?
Answers
we have a table that describe the line and we need to finde the slope and the intercept with the y axis, so the slope can be found with this equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So I use the numbers in the table to fill the equation so:
[tex]\begin{gathered} m=\frac{28-8}{2-1} \\ m=\frac{20}{1} \\ m=20 \end{gathered}[/tex]now for the intercept we replace x=0 and use the coordinate (1,8) so:
[tex]20=\frac{y-8}{0-1}[/tex]and we solve for y so:
[tex]\begin{gathered} -20=y-8 \\ -20+8=y \\ -12=y \end{gathered}[/tex]So the equation is:
[tex]y=20x+(-12)[/tex]A car wheel has a radius of 35 cm.(a) What is the circumference of the wheel? Give your answer correct to 2 decimal places.(b) If the wheel rotates 100 000 times, how far does the car travel?
Answers
Explanation
(a) The formula for the circumference of a circle is as follows:
[tex]C=2\pi r[/tex]Where r is the radius of the circle. So, we have:
[tex]X=2\pi r=2\cdot3.1415\ldots\cdot35=219.9114\ldots\approx219.91[/tex]So, the circumference is approximately 219.91 cm.
(b) Assuming the wheel is always in contact and every rotation make sthe exact same length of travel, every rotation will make the car travel approximately 219.91 cm.
If the wheel rotates 100,000 times, the car will travel 100,000 times as many, so it will travel:
[tex]100,000\cdot219.91=21,991,000[/tex]So, the car will travel approximately 21,991,000 cm which is equivalente to 219.91 km.
Answer
(a) the circumference is approximately 219.91 cm
(b) the car will travel approximately 21,991,000 cm or 219,91 km.
we know,
circumference of the wheel= 2 pi r
=2*22/7*35
= 220cm (it covers 220 cm in one rotation)
Now if the wheel rotates 100000 times,
it will travel = 220* 1000000
= 220000000 cm
= 220000000/100m
=2200000m
Parveen wanted to make a temporary shelter for her car, by making a box-like structure with tarpaulin that covers all the four sides and the top of the car (with the front face as a flap which can be rolled up). Assuming that the stitching margins are very small, and therefore negligible, how much tarpaulin would be required to make the shelter of height 2.5 m, with base dimensions 4m×3m ?
Answers
Given:
Length = 4m
Width= 3m
Height = 2.5 m
Therefore, the surface area of rectangle prism is 2lh+2bh+lb
[tex]\begin{gathered} 4\times2.5\times2+3\times2.5\times2+4\times3=10\times2+5\times3+12 \\ =20+15+12 \\ =47 \end{gathered}[/tex]Hence, the required answer is 47m^2.
Let set E be defined as follows:
E = {english, math, french, art}
Which of the following are subsets of set
E
Answers
The subsets of E is all the above .
What are subsets of set ?If every component present in Set A is also present in Set B, then Set A is said to be a subset of Set B. To put it another way, Set B contains Set A. As an illustration, if set A has the elements X, Y, and set B contains the elements X, Y, and Z, then set A is the subset of set B.
If every element in a set A is also an element in a set B, then the set A is a subset of the set B. The set A is therefore contained within the set B. AB is used to represent the subset connection. For instance, if the sets A and B are equal, AB but BB, respectively.
Let the event E = {english, math, french, art}
The subsets of E is all the above .
null set is also subset of E
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set up a trigonometric ratio for angle H and solve for X
Answers
According to the picture, it is necessary to use cosine, which is the ratio between the side that is adjacent to a given angle and the hypotenuse.
In this case, the angle would be H, the adjacent side to it would be x and the hypotenuse 14. It means that cos H is the ratio between x and 14:
[tex]\cos H=\frac{x}{14}[/tex]1. The price for a new iPhone today is $829. In 2010 it was $299 for the new iPhone. What is the percent of change in the price of an iPhone from 2010 to today?
Answers
Given:
a.) The price for a new iPhone today is $829.
b.) In 2010 it was $299 for the new iPhone.
To be able to determine the percent change of price, we will be using the following formula:
[tex]\text{ Percent of Change = }\frac{Price\text{ today - Price in 2010}}{\text{Price in 2010}}\text{ x 100}[/tex]We get,
[tex]\text{ = }\frac{\text{ \$829 - \$299}}{\text{ \$299}}\text{ x 100}[/tex][tex]\text{ = }\frac{\text{ \$530}}{\text{ \$299}}\text{ x 100}[/tex][tex]\text{ = 1.77257525084 x 100 = 1.77 x 100}[/tex][tex]\text{ Percent of Change = 177\% ; an increase}[/tex]Therefore, the percent of change in the price from 2010 and today is an increase of 177%.
Let MF = 3x - 4 and BM = 5x - 5
Answers
Answer:
Explanation:
a)Here, we want to get the value of x
Mathematically, we know that for a triangle with median M, the length of one of the sides is two times the length of the other side of the median
We have this as:
[tex]BM\text{ }=\text{ 2MF}[/tex]Using the side lengths given, we have it that:
[tex]\begin{gathered} 5x-5\text{ = 2(3x-4)} \\ 5x-5\text{ = 6x-8} \\ 6x-5x=8-5 \\ x\text{ = 3} \end{gathered}[/tex]b) We want to find the length of MF. We just have to substitute the value of x in the expression for MP
Mathematically, we have this as:
[tex]MF\text{ = 3(3)-4 = 9-4 = 5}[/tex]c) We want to find the length of BM
[tex]5x-5\text{ = 5(3)-5 = 15-}5\text{ = 10}[/tex]d) Here, we want to find the length of BF
[tex]\begin{gathered} BF\text{ = BM + MF} \\ BF\text{ = 10 + 5 = 15} \end{gathered}[/tex]Good morning, I need help on this questions. Thanks :)
Answers
The observed values are given in the table shown in the question. The line of best fit is given to be:
[tex]y=-1.1x+90.31[/tex]where x is the average monthly temperature and y is the heating cost.
A residual is a difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line). The formula will be:
[tex]Residual=Observed\text{ }y\text{ }value-Predicted\text{ }y\text{ }value[/tex]QUESTION A
The average monthly temperature is 24.9:
[tex]x=24.9[/tex]Observed cost:
[tex]y=51.00[/tex]Predicted cost:
[tex]\begin{gathered} y=-1.1(24.9)+90.31=-27.39+90.31 \\ y=62.92 \end{gathered}[/tex]Residual:
[tex]\begin{gathered} R=51.00-62.92 \\ R=-11.92 \end{gathered}[/tex]QUESTION B
The average monthly temperature is 35.9:
[tex]x=35.9[/tex]Observed cost:
[tex]y=67.00[/tex]Predicted cost:
[tex]\begin{gathered} y=-1.1(35.9)+90.31=-39.49+90.31 \\ y=50.82 \end{gathered}[/tex]Residual:
[tex]\begin{gathered} R=67.00-50.82 \\ R=16.18 \end{gathered}[/tex]Answer: Hl
Step-by-step explanation:
A hummingbird's brain has a weight of approximately 2.94 x 10- ounces. An elephant's brain has a weight ofapproximately 1.76 x 102 ounces.Approximately how many times heavier is the elephant's brain than the hummingbird's brain?A) 60B) 600C) 6,000D) 60,000
Answers
Given the information on the problem,we have to divide the weight of the elephant's brain by the weight of the bird's brain, then, using the rules of exponents, we have the following:
[tex]undefined[/tex]Suppose medical records indicate that the length of newborn babies (in inches) is normally distributed with a mean of 20 and a standard deviation of 2.6. Find the probability that a given infant is longer than 20 inches. [? ]%
Answers
To find the probability we need to use the z score formula, given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where x is the value we like, mu is the median and sigma is the standard deviation.
Then the z score is:
[tex]z=\frac{20-20}{2.6}=0[/tex]Then we have to look for the proability:
[tex]P(z>0)=0.5[/tex]Therefore the probability that a given infant is longer than 20 inches is 0.5 or 50%.
Suppose theta is an angle in the standard position whose terminal side is in quadrant 1 and sin theta = 84/85. find the exact values of the five remaining trigonometric functions of theta
Answers
we know that
The angle theta lies in the I quadrant
[tex]sin\theta=\frac{84}{85}[/tex]step 1
Find out the value of the cosine of angle theta
Remember that
[tex]sin^2\theta+cos^2\theta=1[/tex]substitute given value
[tex]\begin{gathered} (\frac{84}{85})^2+cos^2\theta=1 \\ \\ cos^2\theta=1-\frac{7,056}{7,225} \\ \\ cos^2\theta=\frac{169}{7,225} \\ \\ cos\theta=\frac{13}{85} \end{gathered}[/tex]step 2
Find out the value of the tangent of angle theta
[tex]tan\theta=\frac{sin\theta}{cos\theta}[/tex]substitute given values
[tex]\begin{gathered} tan\theta=\frac{\frac{13}{85}}{\frac{84}{85}}=\frac{13}{84} \\ therefore \\ tan\theta=\frac{13}{84} \end{gathered}[/tex]step 3
Find out the cotangent of angle theta
[tex]cot\theta=\frac{1}{tan\theta}[/tex]therefore
[tex]cot\theta=\frac{84}{13}[/tex]step 4
Find out the value of secant of angle theta
[tex]sec\theta=\frac{1}{cos\theta}[/tex]therefore
[tex]sec\theta=\frac{85}{13}[/tex]step 5
Find out the value of cosecant of angle theta
[tex]csc\theta=\frac{1}{sin\theta}[/tex]therefore
[tex]csc\theta=\frac{85}{84}[/tex]Answer the questions below about the quadratic function.g(x) = 3x² + 12x+8Does the function have a minimum or maximum value?MinimumMaximumWhere does the minimum or maximum value occur?x =0What is the function's minimum or maximum value?
Answers
Plot the function on the graph.
From the graph it can be observed that graph of function opening upwards and it has minimum value at x = -2.
Thus function has minimum value.
The minimum value of the function occurs at x = -2. So mimimum value of function occurs at x = -2.
The value of the function at x = -2 is -4. So function's minimum value is -4.
An airplane takes off from an airport that is 144 ft above sea level. The airplane flies at 30,000 ft. To avoid a storm , the airplane goes up to 35,000 ft. Immediately after passing the storm, the airplane returns to its original altitude. Finally , the airplane lands at an airport that is 1,998 ft above sea level . What integer represents the airplanes changes in altitude to avoid the storm ? Immediately after passing the storm ? the integer □ represents the change in altitude to feet to avoid the storm.the integer □ represents the change in altitude in feet immediately after passing the storm.
Answers
What integer represents the airplanes changes in altitude to avoid the storm ?
changes = 35000 - 30000
= 5000 ft
the integer 5000 represents the change in altitude to feet to avoid the storm.
the integer -5000 represents the change in altitude in feet immediately after passing the storm.
A small college is forming a planning committee from 10 administrators, 16 faculty members, and 9 staff members. In how many ways can a planning committee be formed if there are 3 members from each group?
Answers
The number of ways that the planning committee can be formed if there are 3 members from each group is 6545 ways.
What are combinations?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects. This can be illustrated by ⁿCr
The combination formula is illustrated thus:
ⁿCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time
The number of people will be:
= 10 + 16 + 9
= 35
The number of ways will be:
= ³⁵C₃
= 35! / (35 - 3)! 3!
= 35! / 32! 3!
= 35 × 34 × 33 / 3 × 2
= 6545 ways
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6545 ways can a planning committee be formed if there are 3 members from each group.
What is combination?Combination is a way of selecting items from a collection where the order of selection does not matter.
The formula for combination is ⁿCr = n! / ((n – r)! r!)
Where n is total number of objects and r is number of objects we have to choose.
The committee has 10 administrators, 16 faculty members, and 9 staff members.
The total number of persons
10+16+9
35
Now we need to select 3 persons from 35 persons
n=35 and r=3
³⁵C3 = 35! / ((35 – 3)! 3!)
=35! / ((32)! 3!)
=35×34×33×32! / (32! 3!)
=35×34×33 /6
=6545 ways
Hence in 6545 ways can a planning committee be formed if there are 3 members from each group.
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Determine the prime factorization of 350
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define Prime factorization.
Prime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, 1 and the number itself. Examples of prime numbers are 2,3,5,7...etc.
STEP 2: Find the prime factors of the given number
Prime factorization of any number means to represent that number as a product of prime numbers.
We start by dividing the number by the lowest possible prime numbers.
STEP 3: Express 350 as a product of its prime factors
[tex]\begin{gathered} \text{Prime factors}=2,5,5,7 \\ \text{Product of prime factors=}2\times5\times5\times7 \\ =2\times5^2\times7 \end{gathered}[/tex]Hence, the prime factorization of 350 is given as:
[tex]2\times5^2\times7[/tex]¿Por qué NO puede encontrar el punto medio de una línea?
Answers
Las líneas en un plano cartesiano son infinitas, no tienen un punto de inicio o final, por lo que no es posible determinar un punto medio para ellas.
Simplify.8(10 m)ANSWER CHOICES:80 m18 m810 m80 + m
Answers
To simplify this, we need to apply distributive property.
Given: 8(10 m)
Expand the parenthesis:
[tex]\begin{gathered} 8\text{ }\ast\text{ 10m} \\ =\text{ 80m} \end{gathered}[/tex]ANSWER:
[tex]80m[/tex]Please help this is due tomorrow!!
Answers
The expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The given polynomial expression below is:
⇒ 10x⁵y⁷/5x⁵y · 3x⁴y⁸/3x⁻³y¹⁰
Apply the division operation in the constant terms
⇒ 2x⁵y⁷/x⁵y · x⁴y⁸/x⁻³y¹⁰
Apply the arithmetic operation in the Exponents of the same base variables
⇒ 2y⁶ · x⁷y⁻²
⇒ 2y⁶⁻² · x⁷
⇒ 2y⁴ · x⁷
⇒ 2x⁷· y⁴
Therefore, the expression 2x⁷· y⁴ would be equivalent to the given polynomial expression.
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Determine the probability of the given opposite event.What is the probability of rolling a fair die and not getting an outcome less than 3?
Answers
The Opposite Event rule is the probability that event A happens is equal to one minus the probability that A does not happen.
If P(A) is the probability of A happening, and N(A) is the probability of A don't happen, we can write:
[tex]P(A)=1-N(A)[/tex]Now we can see:
[tex]N(A)=1-P(A)[/tex]This, we if we calculate the probability of getting less than 3, ve can calculate the probability of not getting less than 3.
Then, what are the results that are less than 3? Those are 1 and 2. Thus are the favorable outcomes, and since is a fair dice, there are 6 total possible outcomes.
The probability of A = getting less than 3, is:
[tex]\begin{gathered} P(A)=\frac{2}{6} \\ P(A)=\frac{1}{3} \end{gathered}[/tex]
Now we can calculate the probability of not getting less than 3:
[tex]\begin{gathered} N(A)=1-\frac{1}{3} \\ \end{gathered}[/tex][tex]N(A)=\frac{2}{3}[/tex]
The probability of not getting less than 3 is:
[tex]Probability=\frac{2}{3}\approx0.666[/tex]Or in percentage:
[tex]Probability=66.67\%[/tex]I need help with this questions I don’t. Get it
Answers
You will need 275 ml of the 90% solution
Explanation:Let the amount of the 90% alcohol be x
Amount of the 30% alcohol solution = 385 ml
The amount of the mixture = 385 + x
(30% of 385) + (90% of x) = 55% of (385+x)
[tex]\begin{gathered} (\frac{30}{100}\times385)+(\frac{90}{100}\times x)=\frac{55}{100}\times(385+x) \\ \\ (0.3\times385)+(0.9\times x)=0.55(385+x) \\ \\ 115.5+0.9x=211.75+0.55x \\ \\ 0.9x-0.55x=211.75-115.5 \\ \\ 0.35x=96.25 \\ \\ x=\frac{96.25}{0.35} \\ \\ x=275 \\ \\ \end{gathered}[/tex]You will need 275 ml of the 90% solution