Which is closer to the x-axis (1.4 , 2.2) and (4.1 , 2.4) or (3.9) and (8,9) or (1 1/4 , 2) and 1 1/4 , 8)?
Answers
Related Questions
Determine the equation of the line given by the graph.
A) y = 2 3 x − 1
B) y = 3 2 x − 1
C) y = −2 3 x − 1
D) y = −3 2 x − 1
Answers
slope=rise/run=2/3
A) y = (2/3) x − 1
Answer:
A. [tex]y=\frac{2}{3}x-1[/tex]Step-by-step explanation:
The given graph belongs to a linear function, because it's a line.
To find its equation, we first need to find the slope of the line using two points and the formula
[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]
We are gonna use points (0,-1) and (3,1), because the lines crosses through them. Replacing these points in the formula, we have
[tex]m=\frac{1-(-1)}{3 -0 }=\frac{1+1}{3}\\m=\frac{2}{3}[/tex]
Now, we use one points and the point-slope formula
[tex]y -y_{1} =m(x-x_{1} )\\y-(-1)=\frac{2}{3}(x-0)\\ y+1=\frac{2}{3}x\\y=\frac{2}{3}x-1[/tex]
Therefore, the right answer is A.
[tex]y=\frac{2}{3}x-1[/tex]
which of the following describe the given graph of the function over the interval [2,6]
•increasing
•constant
•decreasing
•decreasing to increasing
Answers
Answer:
Increasing
Step-by-step explanation:
We know that, a function can be increasing, decreasing, constant or a mix of these three i.e. a function is:
1. Increasing: if for x < y, f(x) < f(y).
2. Decreasing: If for x < y, f(x) > f(y).
3. Constant: If for any two numbers say x and y, f(x) = f(y).
As we can see from the graph, between [2,6], the value of function at 2 is less than the value of function at 6.
i.e. As 2 < 6, f(2) < f(6).
Which satisfies the definition of an increasing function.
Hence, the graph of the function over [2,6] is increasing.
Help ???!!!! ThankYou !!!
Answers
The first thing Wyatt did was multiply through by 2. The left and right sides were both multiplied by two which makes it 12 on the right and 2x + (6x - 4) on the left. The 1/2 is gone on the left.
It only looks like he used the distributive property because the brackets were removed between recorded steps.
The second thing he did was to collect like terms on the left.
The third thing he did was to add four on both sides of the left and right.
The last thing he did was to divide by 8.
Both A and C are wrong. He did not use the distributive property in any of those steps.
B <<<<< Answer.
A new medical test provides a false positive result for hepatitis 2% of the time that is a perfectly healthy subject being tested for hepatitis will test as being infected 2% of the time. And research, the test is given to 30 healthy (not having hepatitis) subjects. Let X be the number of subjects who test positive for the disease
A. What is the probability that all 30 subjects will appropriately test as not being infected?
B. What are the mean and standard deviation of X?
C. To what extent do you think this is a viable test to use in the field of medicine?
Answers
The probability of success, i.e. the probability that a healthy subject tests positive is given as 2% = 0.02
Part A:
The probability that all 30 subjects will appropriately test as not being infected, that is the probability that none of the healthy subjects will test positive is given by:
[tex]P(X)={ ^nC_xp^x(1-p)^{n-x}} \\ \\ P(0)={ ^{30}C_0(0.02)^0(1-0.02)^{30-0}} \\ \\ =1(1)(0.98)^{30}=0.5455 [/tex]
Part B:
The mean of a binomial distribution is given by
[tex]\mu=np \\ \\ =30(0.02) \\ \\ =0.6[/tex]
The standard deviation is given by:
[tex]\sigma=\sqrt{np(1-p)} \\ \\ =\sqrt{30(0.02)(1-0.02)} \\ \\ =\sqrt{30(0.02)(0.98)}=\sqrt{0.588} \\ \\ =0.7668[/tex]
Part C:
This test will not be a trusted test in the field of medicine as it has a standard deviation higher than the mean. The testing method will not be consistent in determining the infection of hepatitis.
1) Which rate is the lowest price?
$2.50/5lb
$2.40/6lb
$3.00/6lb
$2.40/4lb
2)Select all that apply
Which rates are equivalent to 25 miles per gallon?
150miles/6gallons
50miles/1.5gallons
100miles/3.8gallons
75miles/3gallons
3) which speed is the fastest?
30miles/1hour
90miles/2hours
180miles/3hours
240miles/6hours
Please ASAP thank you:)
Answers
2.4/6 = .40 Lowest price
3.0/6 = .50
2.4/4 = .60
2. 150/6 = 25 Equivalent
50/1.5 = 33.33
100/3.8 = 26.32
75/3 = 25 Equivalent
3. 30/1 = 30
90/2 = 45
180/3 = 60 Fastest
240/6 = 40
Answer:
5 points for this bruuuh
Step-by-step explanation:
Can you use elimination to solve a system of linear equations with three equations
Answers
At a shoe store a sales person earns a weekly salary of $150.a salesperson is also paid $2.00 for each pair of shoes he or she sells during the week what is the algebraic expression
Answers
or 150 + 2.00x but the .00 is not necessary.
x would represent the number of pairs of shoes sold.
Answer:
150 + (2x)
Step-by-step explanation:
At a shoe store a sales person earns a weekly salary = $150.
He or she also paid for the sale of each pair of shoes = $2.00
Let the number of pairs of shoes sold be 'x'
the commission on the shoes sold = 2(x)
So the algebraic expression for her/his weekly pay would be
150 + (2x)
A pair of dice is rolled. find the probabilities of the given events. the sum is 6, given that the sum is less than 8.
Answers
but if the sum is already known to be less than 8 then that means there is only 21 possible rolls, so we would have 5/21 instead of 5/36. 5/21=0.238095(repeating) which to put as a percent is 23.8%
so the probability the sum will be 6 given that the sum is less than 8 is 23.8%
Hope this helps.
Given the condition that the sum of the dice rolled is less than 8, the probability of the dice having a sum of 6 is found by considering all outcomes where the sum is less than 8 and outcomes that result in a sum of 6. The probability turns out to be 20%.
Explanation:This question involves the concept of conditional probability in mathematics. For a pair of six-sided dice, there are 36 equally likely outcomes (Because 6 faces of one die times 6 faces of the other). We are interested in the event of getting a sum of 6, given the sum is less than 8.
We first consider all the outcomes where the sum of two dice is less than 8: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (3,5), (4,1), (4,2), (4,3), (4,4), (5,1), (5,2), (5,3), (6,1), (6,2). There are 25 equally likely outcomes where the sum is less than 8.
Then, consider all the outcomes where the sum of the two dice is equal to 6: (1,5), (2,4), (3,3), (4,2), (5,1). There are 5 equally likely outcomes. So given the condition that the sum is less than 8, the probability of getting a sum of 6 is 5/25 or 20%.
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The length of a rectangle with length 12 yd and width 11 yd is divided by 6.
Answers
I'm assuming that we need to find the area here. The formula to find the area of a rectangle is A = l x w. Using this formula, we can plug in the given values and solve.
WORK:
A = 12/1 x 11/6
A = 132 / 6
A = 22 yards^2
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
amwser is 22
How many differnet points could a parabola intersect a ircle?
Answers
A scatter plot is shown:
A scatter plot is shown. Data points are located at 0 and 0, 1 and 0.25, 2 and 1, 3 and 2, 4 and 3, 5 and 4, 5.5 and 5, 6 and 6, 6.4 and 7, 6.7 and 7.8, 7 and 9.
What type of association does the graph show between x and y?
Linear positive association
Nonlinear positive association
Linear negative association
Nonlinear negative association
Answers
Answer:
The correct option is 2.
Step-by-step explanation:
From the given graph it is noticed that the data points are located at (0,0), (1,0.25), (2,1), (3,2), (4,3), (5,4), (5.5,5), (6,6), (6.4,7), (6.7,7.8) and (7,9).
The rate of change from first two data points is
[tex]m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{0.25-0}{1-0}=0.25[/tex]
The rate of change from next two data points is
[tex]m_2=\frac{2-1}{3-2}=1[/tex]
[tex]m_1\neq m_2[/tex]
The rate of change it not constant, therefore the given data points are non linear.
The value of y increases as the value of x-increases. It means there is a positive relation between x and y.
Therefore the graph represent a Nonlinear positive association between x and y. Option 2 is correct.
Answer:
The correct answer is 2.
3)
Write a function to represent the set of ordered pairs.
{(2, 2), (3, 7), (4, 14), (5, 23)}
A) f(x) = x
B) f(x) = 4x - 6
C) f(x) = x2 - 2
D) f(x) = 2x2 - 6
Answers
Answer:
C
Step-by-step explanation:
f(x) = x2 - 2
Find the measure of an angle between 0 and 360 that is coterminal with 370°
Answers
A 370° angle can be thought of as one 360° and one 10° angle. The 360° would take you one full turn around a circle. The 10° angle would take you 10° into another turn. So simply going 10° would get you to the same place on the circle as going 370°. Make sense?
Final answer:
To find an angle coterminal with 370° that is between 0 and 360 degrees, subtract 360° from 370°, yielding a coterminal angle of 10°.
Explanation:
To find the measure of an angle between 0 and 360 degrees that is coterminal with 370°, we simply subtract 360° from the given angle until the result falls within the desired range. Here is the calculation:
Start with the given angle: 370°.
Subtract 360° from 370° to find the coterminal angle: 370° - 360° = 10°.
The resulting angle of 10° is between 0° and 360° and is therefore the coterminal angle we are seaching for.
What constant term should be used to complete the square? x 2 - 5x + _____ = 7
Answers
25/4 is the anwser. i just took this test
If a storage tank that measures 12 feet by 9 feet by 8 feet is designed to store gas that costs $1.82 per cubic foot, what does it cost to fill the tank to one-half of its capacity?
Answers
We have then:
V = (12) * (9) * (8)
V = 864 feet ^ 3
Then, the cost of filling half the tank is given by:
C = (1/2) * (1.82) * (864)
C = 786.24 $
Answer:
It costs to fill the tank to one-half of its capacity about:
C = 786.24 $
A rectangular piece of sheet metal has a length that is 6 in. less than twice the width. a square piece 3 in. on a side is cut from each corner. the sides are then turned up to form an uncovered box of volume 1536 in. cubed find the length and width of the original piece of metal.
Answers
width=x in
length=2x-6
when 3 inches square is cut from the corner, the new dimensions will be:
width=(x-6) in
length=(2x-6-6)=(2x-12) in
height=3 in
thus the volume will be:
(x-6)(2x-12)3=1536
solving the above we get:
x=-10 or x=22
thus the original:
width=22 in
length=22*2-6=38 in
If the relationship is linear do the variables have a positive or negative association?
a. the variables have a positive association.
b. the variables have a negative association.
c. the relationship is not linear.
Answers
Positive Association Example: (2, 4)
Negative Association Example: (-2, 4)
A linear relationship is a relationship that if graphed, can form a straight line. These relationships can be positive or negative.
Radical Expressions and Data Analysis Unit Portfolio
ALGEBRA 1 B
Directions: Complete each of the tasks outlined below. Task 1
For 7 days keep track of the number of pieces of mail you receive at your home.
a. Put your data into a frequency table having intervals of 0–4, 5–9, 10–14, and 15–19.
b. Use the frequency table to create a histogram of the data.
c. Doyounoticeanypatternsinthehistogram?
Task 2
a. Pick 9 different dog breeds and find their average weights. List each breed and weight. Find the mean, median, and mode of the data. Which measure of central tendency best describes the data? Explain your answer.
b. How much would a 10th dog have to weight for the average weight in part (a) to be 250 pounds? Explain how you determined your answer.
Task 3
Pick a city in Maryland and determine the average high temperatures for each month. Record this in a table.
a. Create a box-and-whisker plot for the data.
b. What is the median temperature?
c. 75%ofthetemperaturesarebelowwhatvalue?Howdoyouknow? d. 75% of the temperatures are above what value? How do you know? e. What conclusions can you draw about the temperature in Maryland?
Answers
a) Data and frequency table are attached in picture #1.
b) The histogram is attached in picture #2
c) As the intervals increase the number of pieces of mail received, the frequency decreases, therefore we can say that are received few pieces of mail are received more often.
TASK 2
a) The list of breeds and weights are reported in picture #3.
In order to find the mean, sum up all the weights and divide by 9:
m = (8 + 10 + 15 + 29 + 32 + 75 + 77 + 80 + 85) / 9 = 45.67 lbs
In order to find the median, you need to select the central value of your distribution: since you have 9 values, the central one will be in the fifth position:
M = 32 lbs
In order to find the mode, you need to select the value which shows more frequently: in this case, every value shows only once, therefore the mode cannot be determined.
The data are best described by the mean because they are almost symmetrically distributed between the least and the biggest values, while the median is more towards the small-weight side of the distribution.
b) In order to have an average of 250 lbs, the tenth dog should weight 2089 lbs.
Indeed, if the average is 250 lbs for 10 dogs, it means that the total sum of their weights is 250 × 10 = 2500 lbs. We know that the sum of the first 9 dogs is 411 lbs, therefore, the tenth dog should weight 2500 - 411 = 2089 lbs.
TASK 3
The city picked is Baltimore, the year 2017.
The table is attached in picture #4.
a) The box-and-whisker plot is attached in picture #5.
b) The median is the central value of the distribution, which is:
42.4, 45.3, 46.8 | 54.7, 57.6, 66.0 | 69.1, 76.5, 80.6 | 85.8, 87.8, 90.0
where we marked with a tally the quartiles.
Since we have 12 values, the median will be the average between the two central values:
M = (66.0 + 69.1) / 2 = 67.1 °F
c) 75% of the temperatures are below 83.2 °F.
Indeed, this value represents the third quartile. The position of the third quartile can be found by the formula:
3/4 · (n + 1) = 3/4 · (12 + 1) = 3/4 · 13 = 9.75
Therefore, since we did not get in integer position, the third quartile will be the average between the numbers in position 9 and 10:
q₀.₇₅ = (80.6 + 85.8) / 2 = 83.2 °F
d) 75% of the temperatures are above 50.8 °F.
Indeed, this value represents the first quartile. Similarly to point c), the position can be found by the formula:
1/4 · (n + 1) = 1/4 · 13 = 3.25
And therefore:
q₀.₂₅ = (46.8 + 54.7) / 2 = 50.8 °F.
e) Baltimore in 2017 had a median high temperature of 67.1 °F.
25% of the year the high temperatures were warmer than 83.2 °F, with no outlier above 90.0 °F which was the hottest temperature.
25% of the high temperatures were colder than 50.8 °F, with no outlier below 42.4 °F, which was the coldest high temperature.
A triangle has an angel of 25 degrees. The other two angles are in a ratio of 15:16. What are the measures of those two angles?
Answers
A) 25 + x + y = 180 which equals
A) x + y = 155
B) 15x = 16y
B) x = 16y / 15
Then substituting this into A)
A) (16y / 15) + y = 155
Multiplying both sides by 15
A) 16y + 15y = 2,325
A) 31y = 2,325
y = 75
Putting this into equation A)
A) 25 + x + y = 180
A) 25 + x + 75 = 180
A) 100 + x = 180
A) x = 80
There’s a positive correlation between the price a passenger pays for a train ticket and the number of stops the train makes during their trip.
Which variable is most likely the lurking variable that explains the correlation?
age of passenger
outside temperature
distance being traveled
expected time of arrival
Answers
Answer:
The variable that is most likely the lurking variable that explains the correlation is:
Distance being traveled.
Step-by-step explanation:
As we know that a lurking variable is a variable that correlates between the dependent and independent variable in a scatter plot or some other statistical model.
Hence, here as the distance traveled increases the number of stops would also increase and more passengers would come and hence the cost of ticket will increase.
Hence, the lurking variable is:
Distance being traveled.
The most likely lurking variable that explains the positive correlation between the price a passenger pays for a train ticket and the number of stops the train makes during their trip is distance being traveled.
Distance being traveled: Longer trips generally cost more, and longer trips are also more likely to include more stops. Therefore, the distance being traveled is a common factor influencing both the price of the ticket and the number of stops, leading to the observed positive correlation.The other variables are less likely to explain the correlation:
Age of passenger: This does not directly affect the number of stops or the ticket price.Outside temperature: This is unrelated to the ticket price and the number of stops a train makes.Expected time of arrival: While it could be related to the overall trip duration, it doesn't directly influence the number of stops or the price independently of the distance being traveled.Hence, the distance being traveled is the lurking variable most likely explaining the correlation between ticket price and the number of stops.
a physics student stands at the top of a hill that has an elevation of 56 meters. He throws a rock and it goes up in the air and then falls back past him and lands on the ground below the path of the rock can be modeled by the equation y=-0.04x^2+1.3x+56 where x is the horizontal distance in meters from the starting point on top of the hill and y is the height in meters of the rock above the ground. How far horizontally from the starting point will the rock land? Round to the nearest hundredth.
Answers
Solution:
The height y of the rock above the ground as a function of the horizontal distance x from the starting point on top of the hill can be modeled by the equation
y = -0.04x^2 + 1.3x + 56
We now set this equation equal to zero because the height of the ground where the rock will land is zero:
0 = -0.04x^2 + 1.3x + 56
Since we have a quadratic equation, we can calculate for the horizontal distance x by using the quadratic formula
x = [-b ± sqrt(b^2 - 4ac)] / 2a
x = {-1.3 ± sqrt[1.3^2 - 4(-0.04)(56)]} / 2(-0.04)
x = (-1.3 ± sqrt(10.65)) / (-0.08)
x = -24.54 meters or 57.04 meters
There are two solutions for x but one is negative, so we choose the positive value.
Ten percent of all dynamite mints candies are orange and 45 percent of all holiday mints candies are orange. two independent random samples, each of size 25, are selected⎯one from dynamite mints candies and the other from holiday mints candies. the total number of orange candies in the two samples is observed. what are the expected total number of orange candies and the standard deviation for the total number of orange candies, respectively, in the two samples?
Answers
1.) To get the total number of orange candies, we must multiply the given percentage to the size of the samples. Then, add the products.
Dynamite mints - 25 x 10% = 2.5
Holiday mints - 25 x 45% = 11.25
Total orange candies - 2.5 + 11.25 = 13.75
2.) To get the standard deviation, we will first find the standard deviation of each sample. Use this formula: standard deviation = √[np(1-p)] The variable n is the size of the sample while the p is the probability or percentage.
Dynamite mints - √[25 x 10% (1 - 10%)] = 1.5
Holiday mints - √[25 x 45% (1 - 45%)] = 2.4874...
After getting the standard deviations, we'll combine then using s^2 (x + y) = s^2(x) + s^2(y)
Standard deviation of orange candies = std of dynamite + std of holiday
Std = √(1.5^2 + 2.4874...^2) = √8.4375... = 2.9046 or 2.905
The mean and standard deviation of the sample of orange sweets can be ibtaide using the binomial approximation relation. Hence, the mean and standard deviation are 13.75 and 2.905
Mean = np
Sample size, n = 25 Proportion, pDynamite mints :
25 x 0.1 = 2.5Holiday mints:
25 x 0.45 = 11.25Total orange candies = (2.5 + 11.25) = 13.75
2.)
Standard deviation, σ = √(npq)
q = 1 - pDynamite mints :
√[25 x 0.1 × (1 - 0.1)] = 1.5
Holiday mints :
√[25 x 0.45 (1 - 0.45)] = 2.4874
Combined standard deviation : s²(x + y) = s²(x) + s²(y)
Std = √(1.5²2 + 2.4874²) = 2.905
Therefore, the mean and sample standard deviation are 13.75 and 2.905 respectively.
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Verify the identity. Help please!!!
Answers
[tex]L.H.S \\ \\ = 1+ sec^{2} *sin^{2}x \\ \\ =1+ \frac{1}{cos^{2}x } sin^{2}x \\ \\ =1+tan^{2}x \\ \\ =sec^{2}x \\ \\ = R.H.S [/tex]
Thus, the Left hand side has been proved equal to Right Hand Side.
What is the factorization of the polynomial below?
–x2 – 15x – 54
A. (x – 9)(x + 6)
B. (x + 9)(x + 6)
C. –1(x + 9)(x + 6)
D. (x + 9)(x – 6)
Answers
Answer:
Option C, -(x + 9)(x + 6) or,
-1(x + 9)(x + 6)
Explanation:
We can begin the factorization process by factoring out the negative -1 from each term in the polynomial. This changes the expression to:
-1(x² + 15x + 54)
This factored-out negative will follow all the way to the answer so any answer not containing a -1 factored out can eliminated. Options A, B, and D do not have this negative. Therefore, they are ruled out. But let's continue to confirm Option C.
With the polynomial within the parentheses in quadratic expression ax² + bx + c form, we start by finding which factor pair for the product and coefficient a and constant c has a sum equating to coefficient b. This may sound complicated but this is not the case in practice.
Coefficient a = 1
Constant c = 54
Coefficient b = 15
The product of a and b = 1(54) = 54
Now, we list factors of 54. I like to list them as factor pairs:
1, 54; 2, 27; 3, 18; 6, 9
Next, find which factor pair has a sum of 15. That would be 6 and 9. We now substitute these values as the coefficients b, separate the terms into pairs as binomials, and factor out their greatest common factors (GCF).
-(x² + 6x + 9x + 54)
-[(x² + 6x) + (9x + 54)]
The GCF between x² and 6x is x. The GCF between 9x and 54 is 9. So:
-[x(x + 6) + 9(x + 6)]
If the binomial within each set of parentheses matches, you have found the factors for your polynomial. They are the polynomial within the binomial within the parentheses and the GCFs that were factored out of each:
-x² - 15x - 54 = -(x² + 15x + 54) = -(x + 9)(x + 6)
Final answer:
The factorization of the polynomials [tex]-x^2 - 15x - 54[/tex] is obtained by finding two numbers that multiply to -54 and add up to -15, which are -9 and -6. The factored form is -1(x + 9)(x + 6).
Explanation:
The factorization of the polynomial [tex]-x^2 - 15x - 54[/tex] can be approached by looking for two numbers that multiply to give the product of the coefficient of x2 (which is -1) and the constant term (which is -54), and at the same time, add up to give the coefficient of x (which is -15). After finding such numbers, we can then express the polynomial in its factored form.
In this case, the numbers that satisfy these conditions are -9 and -6. Multiplying these gives 54 (which is the negative of the constant -54 when considering the leading negative sign of the polynomial), and adding them gives -15.
Therefore, the polynomial can be factored as -1(x + 9)(x + 6), which corresponds to answer option C.
Find the following measure for this figure.
Volume =
275 cubic units
91 2/3 cubic units
36 2/3 cubic units
Answers
Answer:
Step-by-step explanation:
the right answer is B. 91 2/3 Cubic units i got it right on my geometry test :)
Juan visited a candy store and purchased 7 pounds of candy consisting of Atomic Fireballs and Gummi Bears. Atomic Fireballs cost $4.25 per pound and Gummi Bears were on sale for $1.25 per pound. Juan spent a total of $14.75, before taxes. Let x represent the number of pounds of Atomic Fireballs and y represent the number of pounds of Gummi Bears uan purchased. Which of the following graphically represents this situation?
Answers
The Q says for fireballs to be x and gummy bears to be y. So they correspond to their axis. Knowing this you get rid of the last 2 graphs. When you plug in these vertexes into the equations, the only right answer is the graph in picture 2.
Answer:
The 2nd graph correctly represents the situation.
Step-by-step explanation:
Let the number of Atomic Fireballs= x and the number of Gummi bears= y.
Now, Juan purchased total 7 pounds of candies.
So, [tex]x+y=7[/tex]
Also, the cost of Atomic Fireballs and Gummi bears is $4.25 and $1.25 per pound respectively.
Since, Juan spent total $14.75 before taxes.
Then, [tex]4.25x+1.25y=14.75[/tex]
That is, the system of equations is given by,
[tex]x+y=7[/tex]
[tex]4.25x+1.25y=14.75[/tex]
Plotting the equations, we get that,
The 2nd graph shown below correctly represents the situation.
Here is the sample space for three tosses of a coin. {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} calculate te probability that all three coin tosses will give a tails result
Answers
The probability is 0.125
evaluate 3P4, I didn’t understand this question but if you know it would great if you could explain!!!
15,120
36
3,024
504
Answers
Answer:
3,024
Step-by-step explanation:
How much pure acid should be mixed with 6 gallons of a 50% acid solution in order to get a 70% acid solution?
Answers
Final answer:
To obtain a 70% acid solution, mix 4 gallons of pure acid with the existing 6 gallons of 50% acid solution.
Explanation:
To find out how much pure acid should be mixed with 6 gallons of a 50% acid solution to obtain a 70% acid solution, we use the concept of mixtures in percentage problems. Let x be the number of gallons of pure acid to be added.
Firstly, the amount of pure acid in the initial solution is 50% of 6 gallons, which is 3 gallons. When we add x gallons of pure acid, the total volume of the mixture becomes x + 6 gallons, and the total amount of pure acid is x + 3 gallons.
To have a 70% acid solution:
The total amount of pure acid divided by the total volume should equal 70%.
Therefore, the equation is:
(x + 3) / (x + 6) = 0.70
By solving for x:
x + 3 = 0.70(x + 6)
x + 3 = 0.70x + 4.20
x - 0.70x = 4.20 - 3
0.30x = 1.20
x = 1.20 / 0.30
x = 4 gallons
You need to mix 4 gallons of pure acid with the 6 gallons of 50% acid solution to end up with a 70% acid solution.
Look at the question on the first image then answer on the second image
Answers
32^2 +x^2 = 60^2
1024 + x^2 = 3600
x^2 = 3600 - 1024
x^2 = 2576
x = sqrt(2576)
x = 50.75
length = 51 inches