Recall what composition of functions means:
Use one function 's expression as the input of the other function.
so for the case of f(x)=7x=6 and g(x)= 5 (x+6)
we can do the following:
(fog)= f(g(x)) = f (5(x+6)) = 7 (5(x+6)) - 6 = 7 (5x + 30) - 6 = 35 x + 210 - 6 =
35 x + 204.
Now for the second composition:
(gof) = g (f(x))= g (7x-6) = 5 ((7x-6)+6) = 5 ( 7x-6+6) =5 (7x)= 35 x
Therefore these are NOT the same , one gives 35 x + 204, while the other one gives 35 x.
Now for the next question:
If fog (x) = 0 what is the solution for that?
since we found what (fog)(x) is, let's make it equal zero and solve for x:
35 x + 204 = 0
then subtracting 204 from both sides;
35 x = -204
x = -204/35
Now, is (gof)(x) = 0 then we solve for x using the expression we found above:
(gof)(x) = 35 x = 0
that means that x must be zero
x = 0/35 = 0
(fog)(x) is NOT equal to (gof) (x) for the given functions
hi my name is Emma I'm 9 years old and I did not see elementary School can you help me with my math so ya
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Explain how many slices a pizza has
A standard pizza has 8 slices in total.
STEP 2: Interpret the statements
[tex]undefined[/tex]Help me fill out these questions about the graphed rectangle
Step 1
Find the length of IJ
[tex]\begin{gathered} IJ=\sqrt[]{(-3-(-6))^2+(0-(-5))^2} \\ IJ=\sqrt[]{34}=5.830952 \end{gathered}[/tex]Find the length of JK
[tex]\begin{gathered} JK=\sqrt[]{(-6-(-1))^2+(-5-(-8))^2} \\ JK=\sqrt[]{34}=5.830952 \end{gathered}[/tex]Find the length of KL
[tex]\begin{gathered} KL=\sqrt[]{(2-(-1))^2+(-3-(-8))^2} \\ KL=\sqrt[]{34}=5.830952 \end{gathered}[/tex]Find the length of LI
[tex]\begin{gathered} LI=\sqrt[]{(2-(-3))^2+(-3-0)^2} \\ LI=\sqrt[]{34}=5.830952 \end{gathered}[/tex]Therefore all sides are of equal measure.
Step 2
Find the slope of IJ
[tex]\text{Slope}=\frac{5}{3}[/tex]Find the slope of JK
[tex]\text{Slope}=\frac{-3}{5}[/tex]Find the slope of KL
[tex]\text{Slope}=\frac{5}{3}[/tex]Find the slope of LI
[tex]\text{Slope}=-\frac{3}{5}[/tex]For perpendicular lines;
[tex]\begin{gathered} m_2=-\frac{1}{m_1} \\ m_1=\frac{5}{3}_{} \\ -\frac{1}{m_1}=-\frac{1}{\frac{5}{3}}=-1\times\frac{3}{5}=-\frac{3}{5} \end{gathered}[/tex]Adjacent sides of the quadrilateral are perpendicular since all sides are equal.
Adjacent sides include; IJ and Jk, KL, and LI. The slopes of these sides as calculated above show that the lines are perpendicular.
Therefore, the slope of any pair of adjacent sides are negative reciprocals.
That being the case those sides are perpendicular
Therefore as a result of these two things taken together the quadrilateral is a square
Find (x4 - 5x3 + 17x + 3) divided by (x – 3).
First we make x-3=0 and solve for x, that is x=3. Then we write the polynomial with all the monomials (including those that have null coefficient)
[tex]x^4-5x^3+0x^2+17x+3[/tex]and we take over the coefficients, 1, -5, 0, 17, 3. So we start with our method
Now, we take all the new coefficient and low the grade of the polynomial, the new coefficients are 1, -2, -6, -1, 0, so
[tex]1x^3-2x^2-6x-1+\frac{0}{x-3}[/tex]Since the remainder is zero, we can take it off, so x^4-5x^3+17x+3 divided by x-3 is equal to
[tex]x^3-2x^2-6x-1[/tex]write the decimal number that has the specific place value 4 ones, 0 hundredths, 7 tens, 8 hundreds, 0 tenths
8 hundreds means 800.
7 tens means 70.
4 ones means 4
0 hundredths means 0/100=0.01.
0 tenths means 0/10=0.1.
So, the decimal can be written as 874.00.
[tex]874.00[/tex]What is the sum of the terms?X/x^2 +3x^2+2+3/x+1
Solution
We are asked to determine the numerator of the simplified sum.
To get the answer, the solution is shown below:
We have given equation as:
x / (x²+3x + 2) + 3/(x+1) , we need to factor out the denominator of the first term such as x²+3x+2 = (x+2) (x+1)
x / (x+3)(x+1) + 3/(x+1)
Perform combining of terms such as:
x + 3(x+2) x + 3x +6 4X + 6
------------------- = ----------------- = --------------
(x+2) (x+1) (x+2)(x+1) (x+2)(x+1)
Therefore, the numerator simplified sum is "4X + 6".
This graph shows the total number of patients seen by a doctor over the course of a 5-day workweek. What are the domain and range of this relationship? (patients is the labke to the left)
Answer:
0. Domain=(0,5)
,1. Range=(0,60)
Explanation:
From the graph
The point on the graph starts at (0,0) and ends at (5,60).
The domain of the function is the set of all the values of x in the function.
Therefore:
[tex]\text{Domain}=(0,5)[/tex]The range of the function is the set of all the values of y in the function.
Therefore:
[tex]\text{Range}=(0,60)[/tex]4. Tolani has a coin jar containing n nickels and d dimes worth a total of$3.65. The equation 0.05n + 0.1d = 3.65 is one way to represent thissituation. Which equation is equivalent to the equation 0.05n + 0.1d + 3.65?A.5n + d = 365B.0.5n + d = 365C.5n + 10d = 365D.0.05d + 0.1n = 365
Answer:
C. 5n + 10d = 365
Explanation:
Tolani has a coin jar containing n nickels and d dimes worth a total of $3.65.
One way to represent the given problem is:
[tex]0.05n+0.1d=3.65[/tex]The equation above is written in terms of dollars($).
Now:
• 1 dime = 10 cents
,• 1 nickel = 5 cents
,• $3.65 = 3.65 x 100 = 365 cents.
Rewriting the same equation in terms of cents gives:
[tex]5n+10d=365[/tex]An equivalent equation is Option C.
In the trapezoid below, if CD = 15 m, PC = 10 m, and the area of the trapezoid = 185 m 2, find the length of side AB.
ANswer:
Explanation:
The area of a trapezoid is given by
[tex]Area=\frac{a+b}{2}\times h[/tex]where a and b are base lengths and h is the height of the trapezoid.
Now in our case,
[tex]\begin{gathered} a=CD=15 \\ b=AB \\ h=PC=10 \end{gathered}[/tex]and the area is 185 m^2; therefore, our formula gives
[tex]\frac{15+AB}{2}\times10=185[/tex]We just need to solve for AB.
Dividing both sides by 10 gives
[tex]\frac{15+AB}{2}=18.5[/tex]multiplying both sides by 2 gives
[tex]\begin{gathered} 15+AB=18.5\times2 \\ \Rightarrow15+AB=37 \end{gathered}[/tex]subtracting 15 from both sides gives
[tex]\begin{gathered} AB=37-15 \\ \boxed{AB=22.} \end{gathered}[/tex]which is our answer!
Solve this problem using the guess method.
Answer : Force of friction is 2.04N
Given that:
Force = 4N
Mass = 0.200kg
Force of friction ?
[tex]\begin{gathered} F\text{ = ma} \\ \text{Make a the subject of the formula} \\ \frac{f}{m}\text{ = }\frac{ma}{m} \\ a\text{ = }\frac{f}{m} \\ a\text{ = }\frac{4}{0.200} \\ a=20m/s^2 \\ \text{Weight of the block} \\ W\text{ = mg} \\ W\text{ = 0.20 x 9.8 } \\ W\text{ = 1.96N} \\ \text{Force of friction = force applied - weight} \\ \text{Force of friction = }4\text{ - 1.96} \\ \text{Force of friction = 2.04N} \end{gathered}[/tex]Use the given values of the variable to make a vertical table of solutions for the equation.Y=x+5 /2, x=-5,5,7,9
Explanation:
We were given the expression:
[tex]y=\frac{x+5}{2};x=-5,5,7,9[/tex]We will make the vertical table for this equation as shown below:
[tex]\begin{gathered} \begin{equation*} y=\frac{x+5}{2} \end{equation*} \\ \\ when:x=-5 \\ y=\frac{-5+5}{2}=\frac{0}{2}=0 \\ (x,y)=(-5,0) \\ when:x=5 \\ y=\frac{5+5}{2}=\frac{10}{2}=5 \\ (x,y)=(5,5) \\ when:x=7 \\ y=\frac{7+5}{2}=\frac{12}{2}=6 \\ (x,y)=(7,6) \\ when:x=9 \\ y=\frac{9+5}{2}=\frac{14}{2}=7 \\ (x,y)=(9,7) \end{gathered}[/tex]Therefore, we have the vertical table of this equation to be:
How do you keep the answers on your profile for studying????
Given:
Number of sample (n) = 50
mean = 300
standard deviation (s) = 47
confidence level = 95%
The margin of error (MOE) can be calculated using the formula:
[tex]\text{MOE = z }\times\text{ }\frac{s}{\sqrt[]{n}}[/tex]Where z is the z-score at the given confidence level
At 95% confidence level, the z-score is 1.960
The margin of error is thus:
[tex]\begin{gathered} \text{MOE =1.96 }\times\frac{47}{\sqrt[]{50}} \\ =\text{ 13.0277} \end{gathered}[/tex]The formula to calculate the confidence interval is:
[tex]\begin{gathered} CI=\operatorname{mean}\pm z\frac{s}{\sqrt[]{n}}^{} \\ CI\text{ = mean }\pm\text{ margin of error} \end{gathered}[/tex]Where :
[tex]\begin{gathered} \text{lower bound = mean - margin of error} \\ \text{upper bound = mean + margin of error} \end{gathered}[/tex]Substituting:
[tex]\begin{gathered} \text{lower bound = }300\text{ - 13.0277} \\ =\text{ 286.9723} \\ \approx\text{ 287} \\ \text{upper bound = 300 + 13.0277} \\ =\text{ 313.0277} \\ \approx\text{ 313} \end{gathered}[/tex]Hence, if we to randomly sample from this population 100 times. The probability of having a score between 287 and 313 is 0.95
I need help with number 8 use a protractor and a centimeter ruler to measure the Angles and the sides of each triangle. classify each triangle by its angles and sides.
for the triangle number 8:
Use the ruler to measure the side lengths of the triangle
By looking, it will be an equilateral triangle
so, the measure of each angle of the interior angles = 60
Emma drew 5 hearts and 25 circles. What is the ratio of circles to all shapes?
Answer:
[tex]5\colon6[/tex]Explanation:
Here, we want to get the ratio of circles to all shapes
The number of circles is 25
The number of all the shapes is the sum of the number of circles and the hearts
We have this total as 5 + 25 = 30
The ratio is now the division of the number of circles to the total number of shapes
Mathematically, we have this as:
[tex]\frac{25}{30}\text{ = }\frac{5}{6}[/tex]The ratio is 5: 6
Differentiate. I have the answer in blue but I don’t know how to take the derivative of the last two term, so please show work.
1) Let's Differentiate the function below applying the Power Rule.
2) Let's rewrite those radicals as powers firstly
[tex]\begin{gathered} f(x)=9x^3-6\sqrt[]{x}+\frac{3}{x^3}-\frac{5}{\sqrt[4]{x}} \\ f(x)\text{ = }9x^3-6x^{\frac{1}{2}}+3x^{-3\text{ }}-5x^{\frac{-1}{4}} \end{gathered}[/tex]3) Let's apply the Power Rule now, subtracting one unit from the exponent and multiplying the base by the original exponent
[tex]f^{\prime}(x)=27x^2-3x^{-\frac{1}{2\text{ }}}-9x^{-4}+\frac{5}{4}x^{-\frac{5}{4}}[/tex]heyy could you help me with this question I have been stuck for almost an hour
△ABC and △DEF are congruent
AC is congruent to DF because, AC = 9 in, DF = 9 in.
is congruent to EF is corresponding to BC
The triangles are congruent by the SAS Triangle Congruence Theorem onl;y when x = 4
number 8 Investigate the following limits using graph and table use X values: -0.03,-0.02,-0.01,0,0.01,0.02 tell what the limit is if the limit doesn't exist then explain why
Analyze the existence of the following limit:
[tex]\lim _{x\to2}x^2-\frac{2|x-2|}{x-2}[/tex]To better analyze the limit, we'll use some properties to isolate the required part from the others:
[tex]\lim _{x\to2}x^2-\frac{2|x-2|}{x-2}=\lim _{x\to2}x^2-\lim _{x\to2}\frac{2|x-2|}{x-2}[/tex]The first limit is easy to calculate, it's just to replace the value of x. The second limit will be further worked on:
[tex]2^2-2\lim _{x\to2}\frac{|x-2|}{x-2}=4-2\lim _{x\to2}\frac{|x-2|}{x-2}[/tex]Now focus on this part:
[tex]\lim _{x\to2}\frac{|x-2|}{x-2}[/tex]We'll approach the value of x=2 by using the set
X={-0.03, -0.02, -0.01, 0, 0.01, 0.02, 0.03}
Note these values are the infinitesimal approaches to the required value of x=2, thus the values of x to use are x={1.97, 1.98, 1.99, 2, 2.01, 2.02, 2.03}
[tex]\frac{|1.97-2|}{1.97-2}=\frac{|-0.03|}{-0.03}=\frac{0.03}{-0.03}=-1[/tex][tex]\frac{|1.98-2|}{1.98-2}=\frac{|-0.02|}{-0.02}=\frac{0.02}{-0.02}=-1[/tex][tex]\frac{|1.99-2|}{1.99-2}=\frac{|-0.01|}{-0.01}=\frac{0.01}{-0.01}=-1[/tex]The value of x=2 cannot be used because it would produce the division 0/0 and it's undefined.
[tex]\frac{|2.01-2|}{2.01-2}=\frac{|0.01|}{0.01}=\frac{0.01}{0.01}=1[/tex][tex]\frac{|2.02-2|}{2.02-2}=\frac{|0.02|}{0.02}=\frac{0.02}{0.02}=1[/tex][tex]\frac{|2.03-2|}{2.03-2}=\frac{|0.03|}{0.03}=\frac{0.03}{0.03}=1[/tex]We can see this limit results in -1 for the negative values of X and 1 for the positive values of X. Since the limits are not equal, the limit does not exist
You can work a maximum of 55 hours a week. You need to make $350 in order to coveryour expenses. Your window-washing job pays $8.50 an hour and your tutoring job pays $12an hour.
Answer:
x + y <= 55
8.5x + 12y >= 350
Step-by-step explanation:
We use a system of inequalities to solve this question.
I am going to say that:
x is the number of hours working at the window-washing job.
y is the number of hours working at the tutoring job.
You can work a maximum of 55 hours a week.
This means that:
x + y <= 55
You need to make $350 in order to cover your expenses. Your window-washing job pays $8.50 an hour and your tutoring job pays $12 an hour.
This means that:
8.5x + 12y >= 350
The system is given by:
x + y <= 55
8.5x + 12y >= 350
Could use help trying to solve this I keep getting it wrong.
Solution:
The commission rate can be calculated as follows:
[tex]\frac{2500}{50000}=0.05[/tex]this is equivalent :
[tex]0.05\text{ x 100\% = 5\%}[/tex]we can conclude that the correct answer is:
[tex]5\text{ \%}[/tex]Rachel looked at how many people ride the morning ferry. She made a dot plot for the data. :.. 54 55 56 57 58 59 60 61 62 63 Number of people who ride the morning ferry According to Rachel's data, what is the typical number of people who ride the morning ferry? A. 65 people B. 63 people C. 61 people D. 58 people
the typical number of people who ride the morning ferry is the number that repeats the most
in this case, is 61 ( 4 times)
Answer: C. 61
given the value evaluate this functionf(x) = -8x+20; 5-2 [f(-1)]
To calculate: 5 - 2[f(-1)]
We need to calculate first f(-1), so we need to replace x by -1 in the equation of f(x) as:
f(x) = -8x + 20
f(-1) = -8*(-1) + 20
f(-1) = 8 + 20
f(-1) = 28
Now, we can replace f(-1) by 38 and solve as:
5 - 2[f(-1)]
5 - 2*28
5 - 56
- 51
Answer: -51
I need Help and brainly keeps kicking me out of the tutor session
Step 1: Write out the summation of the series given
[tex]\sum ^4_{n\mathop=1}(3n+7)[/tex]Step 2: Expand the summation
[tex]\begin{gathered} \text{when n=1} \\ 3.1+7 \\ =7+3.1 \end{gathered}[/tex][tex]\begin{gathered} \text{when n=2} \\ 7+3.2 \end{gathered}[/tex][tex]\begin{gathered} \text{when n=3} \\ 7+3.3 \end{gathered}[/tex][tex]\begin{gathered} \text{whne n=4} \\ 7+3.4 \end{gathered}[/tex]Hence, the summation of the series is (7+3.1) + (7+3.2) + (7+3.3) + (7+3.4)
A penny dropped from the top of the Empire State building takes 8.82 seconds to reach the street. What is the height of the building?
the time of travel is
t = 8.82 s
the relation between the distance and the time is
given in the question that is
[tex]\sqrt[]{d}=t\times\sqrt[]{4.9}[/tex]put t = 8.82
[tex]\begin{gathered} \sqrt[]{d}=8.82\times\sqrt[]{4.9} \\ \\ \end{gathered}[/tex]square both side,
[tex]d=8.82^2\times4.9[/tex][tex]d=381.18[/tex]so the height is 381.18 m
Us the bar graph to find the experimental probability of rolling a number less than or equal to 4
The total number of times the cube was rolled is given by 13 + 16 + 15 + 17 + 19 + 20 = 100
The probability of rolling each number is given by:
P(1) = 13/100 = 13%
P(2) = 16/100 = 16%
P(3) = 15/100 = 15%
P(4) = 17/100 = 17%
P(5) = 19/100 = 19%
P(6) = 20/100 = 20%
Then the probability of rolling a number less or equal to 4 is given by:
P(<=4) = P(1) + P(2) + P(3) + P(4) = 13% + 16% + 15% + 17% = 61%
Answer:61%
Step-by-step explanation:
Find the x- and y-intercepts of the graph of -2x+5y=16. State each answer as an integer or an improper fraction in simplest form.
The x-intercept is (-8, 0)
The y-intercept is (0, 3 1/5)
Explanation:Given the equation:
-2x + 5y = 16
To find the x-intercept, set y = 0
-2x + 5(0) = 16
-2x = 16
x = -16/2 = -8
The x-intercept is (-8, 0)
To find the y-intercept, set x = 0
-2(0) + 5y = 16
5y = 16
y = 16/5 = 3 1/5
The y-intercept is (0, 3 1/5)
A parachutist's rate during a free fall reaches 90 miles per hour. What is this rate in feet per second? At this rate, how many feet will the parachutist fall during 2seconds of free fall? In your computations, use the fact that I mile is equal to 5280 feet. Do not round your answers.
The rate at which parachutist fall is 90 miles per hour.
Determine the rate of fall in miles per seconds.
[tex]90\text{ mi/hr}\times\frac{1\text{ mi/sec}}{3600\text{ mi/hr}}=\frac{1}{40}\text{ mi/sec}[/tex]Determine the miles fall in 2 seconds.
[tex]\frac{1}{40}\text{ mi/sec}\times2\text{ sec=}\frac{1}{20}\text{ miles}[/tex]Convert 1/20 miles into feet.
[tex]\frac{1}{20}\text{ miles}\times\frac{5280\text{ feet}}{1\text{ mile}}=264\text{ feet}[/tex]So parachutist fall 264 feet during 2 seconds of free fall.
Determine the rate of fall in feet per second.
[tex]\begin{gathered} \text{90 miles/hour}=90\text{ miles/hr}\times\frac{\frac{5280}{3600}\text{ ft/sec}}{1\text{ miles /hr}} \\ =132\text{ ft/sec} \end{gathered}[/tex]Answer:
Rate in feet per second: 132 ft/sec
Distance (in feet) fall in first two seconds: 264 ft
Answer:
Rate in feet per second: 132 ft/sec
Distance (in feet) fall in first two seconds: 264 ft
Step-by-step explanation:
Given that sin A= -4 over 5,and angle A is in quadrant 3, what is the value of cos A?
SOLUTION
From the question we have that
[tex]\begin{gathered} sinA=-\frac{4}{5} \\ in\text{ quadrant 3} \end{gathered}[/tex]We wan to find cos A.
We have
[tex]\begin{gathered} sinA=-\frac{4}{5}=\frac{opp}{hyp} \\ From\text{ Pythagoras } \\ hyp^2=opp^2+adj^2 \\ 5^2=4^2+adj^2 \\ adj^2=25-16 \\ adj^2=9 \\ adj=\sqrt{9} \\ adj=3 \end{gathered}[/tex]And we have
[tex]cosA=\frac{adj}{hyp}=\frac{3}{5}[/tex]Now since cos theta is negative in the 3rd quadrant and angle A is in the third quadrant, then
The answer is
[tex]cosA=-\frac{3}{5}[/tex]Which expression gives the distance between the points(1,-2) and (2, 4)?O A 11 - 23² + (-2-4²O B. (1-2)² + (-2-4²O c. $(1 +23² + (2 - 4²D. (1+2)+(2-4)
As per given by the question,
There are given that two point,
[tex](1,\text{ -2), and (2, 4)}[/tex]Now,
From the given point,
Suppose;
[tex]x_1=1,y_1=-2,x_2=2,y_2=4[/tex]Then,
From the formula of distance between two points,
[tex]d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Then,
Put the value in above formula;
[tex]\begin{gathered} d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2} \\ d=\sqrt[]{(1_{}-2_{})^2+(-2-4)^2} \end{gathered}[/tex]Now,
The above value of d can be written as;
[tex]d=\sqrt[]{(1_{}-2_{})^2+(-2-4)^2}[/tex]Hence, the option first is correct.
What transformations are needed in order to obtain the graph of G(x) from the graph of F(x)? Select all that apply
ANSWER and EXPLANATION
We want to identify the transformations that were made in obtaining:
[tex]g(x)=-|x-4|-2[/tex]from:
[tex]f(x)=|x|[/tex]When a function is transformed by:
[tex]g(x)\to-f(x)[/tex]It implies that there is a reflection across the x-axis.
When a function is transformed by:
[tex]g(x)\to f(x)-k[/tex]It implies that there is a vertical shift downwards by k units.
When a function is transformed by:
[tex]g(x)\to f(x-h)[/tex]it implies that there is a horizontal shift to the right by h units.
Therefore, for the given function, the transformations made are:
* Vertical shift
* Horizontal shift
* Reflection about the x-axis.
Find the sum of the following infinite geometric series.5+2.5+1.25 +0.625+ ...
Answer:
10
Explanation:
The formula for calculating the sum to infinity of a GP is expressed as;
[tex]S_{\infty}=\frac{a}{1-r}[/tex]a is the first term
r is the common ratio
From the given sequence;
First-term a = 5
Common ratio r = 2.5/5 = 1.25/5 = 0.5
Substitute the given values into the formula
[tex]\begin{gathered} S_{\infty\text{ }}=\text{ }\frac{5}{1-0.5} \\ S_{\infty}=\frac{5}{0.5} \\ S_{\infty}=\text{1}0 \end{gathered}[/tex]Hence the sum to infinity of the series is 10
the royal fruit company producers two of fruit drinks. the first type is 55% pure fruit juice and the second type is 80 % pure fruit juice. the company is attempting to produce a fruit that contains 75% pure fruit juice. how many pints of each of the two existing type of drink must be use to make 160 pints of a mixture that is 75% pure fruit water
The royal fruit company producers two of fruit drinks. The first type is 55% pure fruit juice and the second type is 80 % pure fruit juice. The company is attempting to produce a fruit that contains 75% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 160 pints of a mixture that is 75% pure fruit water?
_________________________________________________
A. The first type is 55% pure fruit juice and
B. The second type is 80 % pure fruit juice.
C. The third type is 75 %.
_______________________________
The total pints of C is the result of the mixture of pints of A and B
C= A+B ( i )
The expression that relates the proportion of water and fruit in pints
0.75 C = 0.55 A + 0.8 B (ii)
__________________________________
C= A+B
160 = A+ B
A= 160 -B
Replacing in (ii)
0.75* 160 = 0.55 (160-B) + 0.8 B
120= 88 - 0.55 B + 0.8 B
B (0.8-0.55) = 120 -88
B= 32/ 0.25
B= 128
________________________
A= 160 -B
A= 160 -128
A= 32
Could you confirm for me if you see the updates?
____________________
Verifying
0.75 * 160 = 0.55 A + 0.8 B
120 = 0.55 * 32 + 0.8* 128
120= 17.6 + 102.4
120= 120
_____________________
To produce 160 pints of a mixture that is 75% pure fruit water, we need
32 pints of the first type pint (55% pure fruit juice) and 128 pints of the second type pint (80 % pure fruit juice).
______________
Do you have any questions regarding the solution?
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