We are asked to determine wheater 6/10 in decimal form is repeating or terminating. To do that we need to divide 6 over 10. To do that, we proceed as follows:
We need to find a number that when multiplied by 10 gives 6. That number is 0.6, because:
[tex]0.6\times10=6[/tex]Therefore 6/10=0.6 Since the numbers after the radix point do not repeat, this is a terminating decimal.
Paolo noticed that Channel 8 devoted 1/6 hour to news story and Channel 12 devoted 1/8 to the same story. Which channel devoted more time? How much more time?
the channel that devoted more time was channel 8, because since 6<8 then it follows thay 1/6>1/8 (the inequiality changes), channel 8 devoted
[tex]\frac{1}{6}-\frac{1}{8}=\frac{8-6}{6(8)}=\frac{2}{48}=\frac{1}{24}\text{more time}[/tex]The same set of data has been fit using two different functions. The following images show the residual plots of each function.
We have the residuals of each function graphed.
They represent the distance, taking into account the sign, of each data point to the line of best fit.
A good fit will have residuals that are close to the x-axis. Also, the distribution for the residuals should not have too much spread, meaning that all the points should have approximately the same residual in ideal conditions.
In this case, we see that Function A has most residuals around the horizontal axis. Except for one of the points, that may be considered an outliert.
In the case of Function B there is a clear pattern (a quadratic relation between x and the residual) that shows that the degree of the best fit function is not the adequate (maybe two degrees lower than what should be).
This results in residuals that have a wide spread depending on the value of x.
Then, we can conclude that Function A has a better fit because the points are clustered around the x-axis.
Answer: Function A has a better fit because the points are clustered around the x-axis [Third option]
Represent each sum as a single rational number. -14+(-8/9) due tomorrow pls answer
the given expression is
-14 + (-8/9)
so,
[tex]\begin{gathered} =-14+\frac{-8}{9} \\ =-14-\frac{8}{9} \end{gathered}[/tex][tex]\begin{gathered} =\frac{-126-8}{9} \\ =-\frac{134}{9} \end{gathered}[/tex][tex]=-\frac{134}{9}=-14\frac{8}{9}[/tex]so the answer is -14 8/9 or -134/9
a sociology Professor assigns letter grades on a test according to the following scheme Scores on the test are normally distributed with the meaning of 67.2 and a standard deviation of 8.5Find the minimum score required for an a grade. Round your answer to the nearest whole number if necessary
In order to have grade A, the score needs to be in the top 9%.
Since the scores are normally distributed, the top 9% scores correspond to 91% of the area under the normal curve. That means we need to find a value of z in the z-table that corresponds to the value 0.91 (that is, 91%).
Looking at the z-table, the value of z for a probability of 0.91 is z = 1.34.
Now, to find the score that this value of z represents, we can use the formula below:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma}\\ \\ 1.34=\frac{x-67.2}{8.5}\\ \\ x-67.2=11.39\\ \\ x=11.39+67.2\\ \\ x=78.59 \end{gathered}[/tex]Rounding to the nearest whole number, the minimum score for grade A is 79.
Help!
find all zeros of p(x). include any multiplicities greater than one.
The most appropriate choice for polynomial will be given by
1) Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]
where [tex]i = \sqrt{-1}[/tex]
2) Zeroes of P(x) = 3, 2i, -2i
3) Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]
4) Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]
What is a polynomial?
An algebraic expression of the form [tex]a_0 + a_1x +a_2x^2 + a_nx^n[/tex] is called a polynomial of degree n.
[tex]1) P(x ) = 3x^3 -10x^2 + 10x -4\\P(2) = 3(2)^3 - 10(2)^2 +10(2) - 4\\[/tex]
[tex]= 24 -40 + 20 -16\\= 0[/tex]
(x - 2) is a factor of P(x)
[tex]P(x) = 3x^2(x - 2) -4x(x - 2) +2(x-2)\\[/tex]
= [tex](x - 2)(3x^2 - 4x + 2)[/tex]
[tex]=(x-2)(x -a)(x - b)[/tex]
where,
[tex]a = \frac{-(-4)+\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\a =\frac{ 4 + \sqrt{-8}}{6}\\a = \frac{4 + 2\sqrt{2} i}{6}\\a = \frac{2(2 + \sqrt{2}i)}{6}\\a = \frac{2 + \sqrt{2}i}{3}[/tex]
[tex]b = \frac{-(-4)-\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\b =\frac{ 4 -\sqrt{-8}}{6}\\b = \frac{4 - 2\sqrt{2} i}{6}\\b = \frac{2(2 - \sqrt{2}i)}{6}\\b = \frac{2 - \sqrt{2}i}{3}[/tex]
Zeroes of P(x) = 2, [tex]\frac{2 + \sqrt{2}i}{3}[/tex], [tex]\frac{2 - \sqrt{2}i}{3}[/tex]
where [tex]i = \sqrt{-1}[/tex]
[tex]2) P(x) = x^3 - 3x^2+4x-12\\P(3) = (3)^3 - 3(3)^2 +4(3) -12\\ P(3) = 0[/tex]
(x - 3) is a factor of P(x)
[tex]x^2(x - 3) + 4(x - 3)\\(x - 3)(x^2 + 4)\\(x - 3)(x -a)(x-b)\\[/tex]
where,
[tex]a = \sqrt{-4}\\a = 2i[/tex]
[tex]b = -\sqrt{-4}\\a = -2i[/tex]
Zeroes of P(x) = 3, 2i, -2i
[tex]3) 2x^3 - 3x^2 +8x-12= 0\\[/tex]
x = 2 satisfies the equation
[tex]2x^2(x -\frac{3}{2}) + 8(x-\frac{3}{2})=0\\(2x^2+8)(x - \frac{3}{2}) = 0\\[/tex]
[tex]2x^2 + 8 = 0[/tex] or [tex]x - \frac{3}{2} = 0[/tex]
[tex]x^2 = -\frac{8}{2}[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x^2 = -4[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x = \sqrt{-4}[/tex] or [tex]x = \frac{3}{2}[/tex]
[tex]x = 2i[/tex] or [tex]x = -2i[/tex] or [tex]x = \frac{3}{2}[/tex]
Roots are 2i, -2i, [tex]\frac{3}{2}[/tex]
4)
[tex]x^4 - 5x^3 +3x^2 +x = 0\\x(x^3 -5x^2 + 3x +1) = 0\\[/tex]
[tex]x = 0[/tex] or [tex]x^3 -5x^2+3x +1 = 0[/tex]
For [tex]x^3 -5x^2+3x +1 = 0[/tex]
x = 1 satisfies the equation
[tex]x^2(x -1) -4x(x-1)-1(x-1) = 0\\(x - 1)(x^2 - 4x -1) = 0\\[/tex]
[tex]x -1 = 0[/tex] or [tex]x^2 - 4x -1 = 0[/tex]
Roots are x = 1 or x = a or x = b
where,
[tex]a = \frac{-(-4) + \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\a = \frac{4+\sqrt{20}}{2}\\a = \frac{4 + 2\sqrt{5}}{2}\\a = \frac{2(2 + \sqrt{5})}{2}\\a = 2 + \sqrt{5}[/tex]
[tex]b = \frac{-(-4) - \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\b = \frac{4-\sqrt{20}}{2}\\b = \frac{4 - 2\sqrt{5}}{2}\\b = \frac{2(2 - \sqrt{5})}{2}\\b = 2 - \sqrt{5}[/tex]
Roots are 0, 1, [tex]2 + \sqrt{5}[/tex], [tex]2 - \sqrt{5}[/tex]
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Rationalize the denominator and simplify the expression below. Show all steps and calculations to earn full credit. You may want to do this work by hand and upload an image of that written work rather than try to type it all out. \frac{8}{1- \sqrt[]{17} }
The Solution:
The given expression is
[tex]\frac{8}{1-\sqrt[]{17}}[/tex]Rationalizing the expression with the conjugate of the denominator, we have
[tex]\frac{8}{1-\sqrt[]{17}}\times\frac{1+\sqrt[]{17}}{1+\sqrt[]{17}}[/tex]This becomes
[tex]\frac{8(1+\sqrt[]{17})}{1^2-\sqrt[]{17^2}}[/tex][tex]\frac{8+8\sqrt[]{17}}{1-17}=\frac{8(1+\sqrt[]{17})}{-16}=-\frac{1+\sqrt[]{17}}{2}[/tex]Thus, the correct answer is
[tex]-\frac{1+\sqrt[]{17}}{2}[/tex]Evaluate 7a - 5b when a = 3 and b = 4 .
Find The distance DB from Cassini yo Tethys when AD is tangent to the circular orbit. Round to the nearest kilometer
we have that
triangle ABD is a right triangle , because AD is a tangent
so
Apply the Pythagorean Theorem
DB^2=AB^2+AD^2
we have
AB is a diameter (two times rhe radius)
AB=2*295,000=590,000 km
AD=203,000 km
substitute
DB^2=590,000^2+203,000^2
DB=623,946 kmyou randomly select one card from a 52 card deck. find the probability of selecting a black three or a red jack
Probability of selecting a black three or a red jack = 1/13
Explanations:There are a total of 52 cards in a deck of cards
Total number of ways of selecting one card from 52 cards = 52C1 = 52 ways
There are two red jacks in a deck of cards
Number of ways of selecting a red jack = 2C1 = 2 ways
There are two blacks 3s in a deck of cards
Number of ways of selecting a black three = 2C1 = 2 ways
[tex]\begin{gathered} \text{Probablity of selecting a black 3 = }\frac{2}{52}=\text{ }\frac{1}{26} \\ \text{Probability of selecting a red jack = }\frac{2}{52}=\frac{1}{26} \end{gathered}[/tex]Probability of selecting a black three or a red jack = (1/26) + (1/26)
Probability of selecting a black three or a red jack = 2/26 = 1/13
I'm having a problem with this logarithmic equation I will include a photo
For the vertical asymptotes, we set the argument of the logarithm to be zero. Therefore,
[tex]\begin{gathered} x-8=0 \\ x-8+8=0+8 \\ x=8 \\ \text{Vertical asymptotes: x = 8} \end{gathered}[/tex]The domain of the function can be found below
[tex]\begin{gathered} x-8>0 \\ solve\text{ the inequality to obtain the domain} \\ x>8 \\ solve\text{ for x to obtain the domain: x>8 or interval form :(8, }\infty\text{)} \end{gathered}[/tex]A population of values has a normal distribution with u = 203.6 and o = 35.5. You intend to draw a randomsample of size n = 16.Find the probability that a single randomly selected value is greater than 231.1.PIX > 231.1) =Find the probability that a sample of size n = 16 is randomly selected with a mean greater than 231.1.P(M > 231.1) =Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or Z-scores rounded to 3 decimal places are accepted.
Part 1:
The probability that a single randomly selected value is greater than 231.1 equals one minus the probability that it is less or equal to 231.1:
P(x > 231.1) = 1 - P(x ≤ 231.1)
Now, to find P(x ≤ 231.1), we can transform x in its correspondent z-score, and then use a z-score table to find the probability:
x ≤ 231.1 => z ≤ (231.1 - 203.6)/35.5, because z = (x - mean)/(standard deviation)
z ≤ 0.775 (rounding to 3 decimal places)
Then we have:
P(x ≤ 231.1) = P( z ≤ 0.775)
Now, using a table, we find:
P( z ≤ 0.775) ≅ 0.7808
Then, we have:
P(x > 231.1) ≅ 1 - 0.7808 = 0.2192
Therefore, the asked probability is approximately 0.2192.
Part 2
For the next part, since we will select a sample out of other samples with size n = 16, we need to use the formula:
z = (x - mean)/(standard deviation/√n)
Now, x represents the mean of the selected sample, which we want to be greater than 231.1. Then, we have:
z = (231.1 - 203.6)/(35.5/√16) = 27.5/(35.5/4) = 3.099
P(x > 231.1) = 1 - P(x ≤ 231.1) = 1 - P(x ≤ 231.1) = 1 - P( z ≤ 3.099) = 1 - 0.9990 = 0.0010
Therefore, the asked probability is approximately 0.0010.
what's the answer for proportions 4/n+2=7/n
Explanation
[tex]\frac{4}{n+2}=\frac{7}{n}[/tex]we need to solve for n
Step 1
cross multiply
[tex]\begin{gathered} \frac{4}{n+2}=\frac{7}{n} \\ 4\cdot n=7(n+2) \\ 4n=7n+14 \\ \end{gathered}[/tex]Step 2
subtract 4n in both sides
[tex]\begin{gathered} 4n=7n+14 \\ 4n-4n=7n+14-4n \\ 0=3n+14 \end{gathered}[/tex]Step 3
subtract 14 in both sides,
[tex]\begin{gathered} 0=3n+14 \\ 0-14=3n+14-14 \\ -14=3n \end{gathered}[/tex]Step 4
Finally, divide both sides by 3
[tex]\begin{gathered} \frac{-14}{3}=\frac{3n}{3} \\ n=-\frac{14}{3} \end{gathered}[/tex]I hope this helps you
How many area codes of the form (XYZ) are possible if the digit 'X' and 'Y' can be any number ( through 9 but they can't repeat and the digit 7 can be any number 1 through 9?
Start to see the possible options
[tex]XYZ=-\cdot-\cdot-_{}[/tex]The first digit will have 10 possible numbers to choose from 0 to 9, however in the second digit since it cannot repeat there will be only 9 possible to choose from. As for ther third number 0 is not an option meaning that there are 9 to choose as well.
[tex]\begin{gathered} XYZ=10\cdot9\cdot9 \\ XYZ=810 \end{gathered}[/tex]Find the volume of a pyramid with a square base, where the side length of the base is19.3 ft and the height of the pyramid is 16.2 ft. Round your answer to the nearesttenth of a cubic foot.
Find the volume of a pyramid with a square base, where the side length of the base is
19.3 ft and the height of the pyramid is 16.2 ft. Round your answer to the nearest
tenth of a cubic foo
Remember that
the volume of the pyramid is equal to
[tex]V=\frac{1}{3}\cdot B\cdot h[/tex]where
B is the area of the base
h is the height
step 1
Find out the area of the base
B=19.3^2
B=372.49 ft2
h=16.2 ft
substitute the given values in the formula
[tex]V=\frac{1}{3}\cdot372.49\cdot16.2[/tex]V=2,011.4 ft3Jacob took a taxi from his house to the airport. The taxi company charged a pick-upfee of $1.30 plus $5 per mile. The total fare was $16.30, not including the tip. Writeand solve an equation which can be used to determine , the number of miles in the
Let the total number of fare be f and total number of miles be m.
Therefore, the total fare f is given by:
[tex]f=1.30+5m[/tex]Substitute f = 16.30 into the equation:
[tex]\begin{gathered} 16.30=1.30+5m \\ 16.30-1.30=5m \\ 15=5m \\ \frac{15}{5}=\frac{5m}{5} \\ 3=m \\ m=3 \end{gathered}[/tex]Therefore, the required number of miles is 3.
what is the domain of this exponential function y=2x-8+2
The given function is
[tex]y=2^{x-8}+2[/tex]The domain is all real numbers, but the range would be all the real numbers greater than 2 because the function approximates to y = 2.
Hence, the answer is the first option.How long does it take Tina to type 864 words, if she took 15 minutes to type out an assignment that comprised 720 words?
Given data:
The given time taken by Tin to type 720 words is t=15 min.
The given expression can be wriiten as,
720 word=15 min
720 words= 15(60 sec)
720 words= 900 sec
1 word = 900/720 sec
=1.25 sec
Multiplying the above equation with 864 on both sides .
864 words= 864(1.25) sec
= 1080 sec
=1080/60 min
= 18 min.
Thus, the time taken bby Tine to type 864 words is 18 min.
Solve the system by graphing:2x – y= -14x - 2y = 6Solution(s):
To find the solution of the system by graphing we need to plot each line in the plane and look for the intersection.
First we need to write both equations in terms of y:
[tex]\begin{gathered} y=2x+1 \\ y=2x-3 \end{gathered}[/tex]now we need to find two points for each of this lines. To do this we give values to the variable x and find y.
For the equation 2x-y=-1, if x=0 then:
[tex]y=1[/tex]so we have the point (0,1).
If x=1, then:
[tex]y=3[/tex]so we have the point (1,3).
Now we plot this points on the plane and join them with a straight line.
Now we look for two points of the second equation.
If x=0, then:
[tex]y=-3[/tex]so we have the point (0,-3)
If x=1, then:
[tex]y=-1[/tex]so we have the point (1,-1).
We plot the points and join them wiith a line, then we have:
once we have both lines in the plane we look for the intersection. In this case we notice that the lines are parallel; this means that they wont intersect.
Therefore the system of equations has no solutions.
Rewrite the expression 3(12 - 10) using the distributive property of multiplication over subtraction.
The resulting expression using the distributive property of multiplication over subtraction is 3(12) - 3(10).
What is distributive property of multiplication?The distributive property of binary operations extends the distributive law, which states that in elementary algebra, equality is always true.
For instance, given the expression;
A(B - C)
We will have to distribute A over B and C to have;
A(B - C) = AB - AC
Applying the rule to the given expression
3 (12 - 10)
3(12) - 3(10)
This shows that the given expression can also be written as 3(12) - 3(10)
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How many soultions?x + 3 = 2x - 18A single solutionInfinite solutionsNo solution
The given equation is expressed as
x + 3 = 2x - 18
Subtracting x from both sides of the equation, it becomes
x - x + 3 = 2x - x - 18
3 = x - 18
Adding 18 to both sides of the equation, it becomes
3 + 18 = x - 18 + 18
21 = x
x = 21
Since there is only one value for x, the correct option is
a. A single solution
Can you help me please and thank you very much
Answer:
∠ FAE = 120°
Step-by-step explanation:
4x and 2x are a linear pair and sum to 180° , that is
4x + 2x = 180
6x = 180 ( divide both sides by 6 )
x = 30
then
∠ FAE = 4x = 4 × 30 = 120°
Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.(3,-5) , (4,5)
We will determine th equation in slope-intercept from of the line as follows:
First, we find the slope:
[tex]m=\frac{5-(-5)}{4-(3)}\Rightarrow m=10[/tex]Then:
[tex]y-5=10(x-4)\Rightarrow y-5=10x-40[/tex][tex]\Rightarrow y=10x-35[/tex]So, the equation of the line in slope-intercept form is:
[tex]y=10x-35[/tex]2. Write a story that can be represented by the equation y = x + 1/4 x.Question 2 On a hot day a football team drank an entire 50-gallon cooler of water and half as much again. How much water did they drink? Create an equation to represent this situation.
y= x+ 1/4 x
Y = dependent variable
x= independent variable
Jenny has a bank account. In the first month, she deposits a certain amount of money (x), and in the month after she deposits 1/4 of that amount.
Find the total amount of money deposited (y).
how do you find a point slope in geometry
see explanation below
Explanation:
To find the point slope form of an equation, we will apply the formula:
[tex]y-y_1=m(x-x_1)[/tex]Given two points, we will be able to find the slope = m
for example: (1, 2), (2, 4)
m = slope = change in y/ change in x
m = (4-2)/(2-1)
m = 2/1
m = 2
Then, we will pick any of the points and insert into the formula for the point slope.
Let's assume we are using point (1, 2) = (x1, y1)
inserting into the formula together with the slope gives:
y - 2 = 2(x - 1)
The above is a point slope for the points given.
The height of a triangle is 4x more than the base, and the area of the triangle is 6 square units. Find the length of the base. Let x =the length of the base.
Write a quadratic equation in factored form. Write entire equation
Answer:
The length of the base is:
3 unitsThe resulting quadratic is
x² - 3= 0Step-by-step explanation:
Base = x
Height = 4x
Area, A = 1/2* base * Height
A = (1/2) * (x) * (4x)
A = 2x² (1)
But, A = 6 (2)
Since (1) = (2);
2x²= 6
x²= 3
Resulting quadratic:
x² - 3= 0
For the difference between 2 squares:
a² - b² = (a-b)(a+b)
Using that identity, we can factorize our quadratic:
(x-3)(x+3) = 0
So, we have 2 roots:
x = 3 and x = -3
Now, noting that length must take a positive value, we go for the first:
x = 3
CONCLUSION:The length of the base is:
3 unitsThe resulting quadratic is
x² - 3= 0Tickets numbered 1 - 10 are drawn at random and placed back in the pile. Find the probability that at least one ticketnumbered with a 6 is drawn if there are 4 drawings that occur. Round your answer to two decimal places.
The probability of a 6 being drawn in one pick is
[tex]\frac{1}{10}[/tex]For 4 drawings, the probability would be
[tex]\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}=\frac{4}{10}=\frac{2}{5}=0.40[/tex]Explain the behavior of f(x)= ln (x-a) when x=a. Give values to x and a such that x-a=0
SOLUTION:
Step 1:
In this question, we are given the following:
Explain the behavior of :
[tex]f(x)\text{ = ln\lparen x-a\rparen}[/tex]when x=a.
Give values to x and a such that:
[tex](x-a)\text{ = 0}[/tex]Step 2:
The graph of the function:
[tex]f(x)\text{ = In \lparen x- a \rparen}[/tex]are as follows:
Explanation:
From the graph, we can see that the function:
[tex]f(x)\text{ = ln\lparen x-a\rparen}[/tex]is a horizontal translation, shift to the right of its parent function,
[tex]f(x)\text{ = In x}[/tex]use the above diagram to answer the following questions.
Remember that the sum of the interior angles is 180. Then, we have the following equation:
[tex]55^{\circ}+65^{\circ}\text{ + }\angle M\text{ = 180}[/tex]This is equivalent to:
[tex]120^{\circ}\text{ + }\angle M=180^{\circ}[/tex]solve for M-angle:
[tex]\text{ }\angle M=180^{\circ}-\text{ 120}^{\circ}=60^{\circ}[/tex]Then, te correct answer is :
[tex]\text{ }\angle M^{}=60^{\circ}[/tex]The padlock for your gym locker uses a 3 number sequence to open the lock. If the numbers go from 1 to 27, how many different sequences are there on the dial without repeating a number?A. 17,550B. 33,696C. 16,848D. 8,775
SOLUTION:
We want to the different sequences possible without repeating a number.
For the first number, there are 27 ways to select it.
Since we aren't allowed to repeat numbers;
There are 26 ways to select the second number.
There are also 25 ways to select the third number.
Therefore, the different sequences possible are;
[tex]No\text{. of ways =}27\times26\times25=17550\text{ ways}[/tex]The functions f(m) = 18 + 0.4m and g(m) = 11.2 + 0.54m give the lengths of two differentsprings in centimeters, as mass is added in grams, m, to each separately.
STEP - BY - STEP EXPLANATION
What to do?
Graph each equation on the same set of axis.
Determine the mass that makes the spring the same length.
Determine the length of that mass.
Write a sentence comparing the two springs.
Given:
f(m) = 18 + 0.4m and g(m) = 11.2 + 0.54m
Step 1
Find the x and y-intercept of both function.
f(m) = 18 + 0.4m
f(0) = 18+0.4(0) = 18
0 = 18 + 0.4m
0.4m = -18
m=-45
The x and y -intercept of the function f(m) are (0, 18) and (-45, 0) respectively.
g(m) = 11.2 + 0.54m
g(0) = 11.2 + 0.54(0)
g(0) = 11.2
0 = 11.2+ 0.54m
0.54m = -11.2
m=20.7
The x and y - intercepts are (0, 11.2) and (20.7, 0).
Step 2
Graph the function.
Below is the graph of the function.
Observe from the graph that that the mass that makes the spring the same length is approximately 48.5 grams.
The length at that point is 37.4 centimeters.
Comparison between the two strings.
The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).
ANSWER
b) 48.6 grams
c) 37.4 centimeters
d) The string with the function f(m) started out longer, but does not stretch as quickly as the other spring with the function g(m).
