A 21-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than six times the length of the first piece. Find the lengths of the pieces
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Given the values of the derivative f′(x) in the table and that f(0)=150, find or estimate f(x) for x=0,2,4,6.
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To find or estimate f(x) for x=0,2,4,6, integrate the given derivative f'(x) with respect to x to find the constant term. Then, add each value of f'(x) in the table to the constant term to obtain the values of f(x) for x=0,2,4,6.
Explanation:To find or estimate f(x) for x=0,2,4,6, we need to use the values of the derivative f'(x) given in the table. Since f'(x) represents the rate of change of f(x) at different values of x, we can use the derivative to find or estimate the values of f(x). Given that f(0) = 150, we can start by finding the constant term of the function using this initial condition.
To find the constant term, we need to integrate the derivative f'(x) with respect to x. This will give us the original function f(x).Integrating f'(x) gives us f(x) = 150 + C, where C is the constant term we need to find.Next, we can use the given values of f'(x) in the table to find or estimate the corresponding values of f(x) for x=0,2,4,6.Let's assume that the third column in the table represents the values of f'(x) at different values of x. We can add each value to the constant term C to obtain the values of f(x) for x=0,2,4,6.Therefore, by integrating f'(x) and adding the constant term, we can find or estimate the values of f(x) for x=0,2,4,6.
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10 x 6 tens-unit form and standard form
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Answer:
Standard form: 600
Unit form: 6 hundreds.
Step-by-step explanation:
We have been given a number [tex]10\times 6[/tex]-tens. We are asked to write our given number in unit form and standard form.
To write our given number in standard form, we will expand our given number as shown below:
6-tens [tex]6\times 10=60[/tex]
[tex]10\times 6[/tex]-tens would be [tex]10\times 60=600[/tex]
Therefore, our given number in standard form would be 600.
We know that unit form is writing a number using place value units.
We can see that our given number has 0 ones, 0 tens and 6 hundreds.
Therefore, our given number in unit form would be 6 hundreds.
We have that the Tens unit form of 10 x 6 and Standard form is mathematically
[tex]6*10^1[/tex]
6tens
From the question we are told that
10 x 6
10 x 6=60
Standard form is a number, between 1 and 10 multiplied by a power of 10
Generally the equation for the Standard form is mathematically given as
x*10^y
Therefore
the Standard form of 10 x 6 is mathematically given as
[tex]6*10^1[/tex]
And
Generally the equation for the Tens unit form of 10 x 6 is mathematically given as
x*tens(10)
Tens-unit form is mathematically given as
6tens
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if a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is represented by 40t-16t^2. what is the maximum height attained by the ball?
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[tex]\bf h(t)=40t-16t^2\implies h(t)=-16t^2+40t+0 \\\\\\ \begin{array}{llll} \qquad \textit{in feet}\\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\textit{initial velocity of the object}\\ \qquad 40\\ h_o=\textit{initial height of the object}\\ \qquad 0\\ h=\textit{height of the object at "t" seconds} \end{cases}[/tex]
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llll} y = &{{ -16}}x^2&{{ +40}}x&{{ +0}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left( \stackrel{\textit{it took this long}}{-\cfrac{40}{2(-16)}}~~,~~\stackrel{\textit{to get this high}}{0-\cfrac{40^2}{4(-16)}} \right)\qquad \stackrel{\textit{maximum height}}{0-\cfrac{40^2}{4(-16)}}[/tex]
The maximum height attained by the ball is 25 feet.
Explanation:The maximum height attained by the ball can be found by determining the vertex of the quadratic equation representing the height of the ball. In the given equation 40t - 16t^2, the coefficient of t^2 is negative, indicating a parabolic shape with a maximum point. The formula for the x-coordinate of the vertex is -b/2a, which in this case is -40/(2*(-16)) = 1.25 seconds. Substituting this value into the equation gives the maximum height: 40(1.25) - 16(1.25^2) = 25 feet.
Find the vertex of the parabola whose equation is y = x2 - 4x + 6.
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Vertex Formula: [tex]x = \frac{-b}{2a}[/tex]
[tex]y = x^2 - 4x + 6 [/tex]
b = (-4)
a = 1
[tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(-4)}{2(1)}[/tex]
[tex]x=\frac{4}{2}[/tex]
[tex]x=2[/tex]
So the vertex x point is at 2 so (x,y) = (2,y)
Now lets find the y by inserting 2 where the x is located in the equation:
[tex]y = x^2 - 4x + 6[/tex]
[tex]y = 2^2 - 4(2) + 6[/tex]
[tex]y = 4 - 8 + 6[/tex]
[tex]y = 2[/tex]
Now that we found the y for the vertex, we have (x,y) = (2,2) and (2,2) is our vertex. We can graph the equation to and see (2,2) is correct.
(3x-3)° [6{x-10)]° what is the value of x
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Divide both sides by 18 °:(x - 1) (x - 10 ° x) = 0
Split into two equations:x - 1 = 0 or x - 10 ° x = 0
Add 1 to both sides:x = 1 or x - 10 ° x = 0
Collect in terms of x:x = 1 or (1 - 10 °) x = 0
Divide both sides by 1 - 10 °:Answer: x = 1 or x = 0
The actual answer to this equation is x=19 not x=1 or n=0
How to find the factor for the expression
4x-6y
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To factor the expression, you must try to find the greatest common factor of 4 and 6 since you x and y have no common factors. The greatest common factor is 2 for 4 and 6, since when you divide out the 2, you are left with 2 and 3 which cannot be factored anymore.
how to round 254 to the nearest hundred
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If the tens place is 5 or above round it to 300, if it is 4 or below round it down to 200.
The tens value is 5 so you would round 254 to 300.
Find the exact circumference of a circle with the given radius. 5 inches C = 2.5 in. 10 in. 25 in.
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Answer: The exact circumference of the circle is [tex]10\pi[\tex] in.
Step-by-step explanation:
Since, the circumference of a circle is,
[tex]C=2\pi r[/tex]
Where, r is the radius of the circle,
Here, r = 5 inches,
Hence, the circumference of the circle is,
[tex]C = 2\pi(5) = 10\pi\text{ in}[/tex]
Thus, The exact circumference of the circle is [tex]10\pi[\tex] in.
Solve the system 2x-2y=10 4x-5y=17
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4x-4y=20,
given:4x-5y=17
y=3
pluck it in
2x-6=10
move the 6 to the right
2x=16
divide
x=8
y=3
Equation 2) 4x - 5y = 17
Multiply ALL of equation 1 by 2.
1) 2(2x - 2y = 10)
Simplify.
1) 4x - 4y = 20
2) 4x - 5y = 17
Subtract equations from one another.
y = 3
Plug in 3 for y in the first equation.
1) 2x - 2y = 10
2x - 2(3) = 10
Simplify.
2x - 6 = 10
Add 6 to both side.s
2x = 16
Divide both sides by 2.
x = 8
------------------------------------
Check your work by plugging in 8 for x, and 3 for y into the original equations.
2x - 2y = 10 & 4x - 5y = 17
1) 2x - 2y = 10
2(8) - 2(3) = 10
Simplify.
16 - 6 = 10
10 = 10
2) 4x - 5y = 17
4(8) - 5(3) = 17
Simplify.
32 - 15 = 17
17 = 17
Therefore, x = 8, y = 3
~Hope I helped!~
The formula s= sa/6 gives the length of the side, s, of a cube with the surface area, sa. How much longer is the side of the cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters ?
Answers
they're on a ratio of 3:2, so if the small is 2, the large one is 3, and if the small one is 120, the large one is 180.
on a 3:2 ratio, 3 is larger than 2 by 1 unit, 1 is 50% of 2, or half, so the longer side is 50% larger.
Answer with explanation:
Side of cube = S
Surface Area of Cube = S.A
Relation between Side of a cube and surface area
[tex]S=\frac{S.A}{6}[/tex]
→If surface area of cube =180 Square meters
Side of cube (S)
[tex]S_{1}=\frac{180}{6}\\\\=30[/tex] meters
→ If surface area of cube =120 Square meters
Side of cube (S)
[tex]S_{2}=\frac{120}{6}\\\\=20[/tex] meters
[tex]S_{1}-S_{2}=30 -20=10\\\\S_{1}=S_{2}+10[/tex]
Side of cubic having surface area 180 square meters is greater by 10 meters, than a cube with the surface area of 120 square meters.
If the circular opening of the pipe has a diameter of 21 inches and the oil was estimated to be flowing at 30 inches/second, how many cubic feet of oil were leaving the pipe each second? Each day?
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First, find the area of the circular opening. A = pi (r^2). Here,
A = pi(10.5 inches)^2.
To obtain the volume of water that flows out of the pipe per second, multiply this area by the 30 inches per second rate.
That comes out to a volume per second of Volume rate = pi*(10.5 inches)^2 * 30 inches per second:
Volume rate = 3.14(110.25 in^2)(30 inches/sec)
= 10390.8 cubic inches per second
Convert this result to cubic feet per second. Recall that 1 cubic foot = (12 inches)^3, or 1728 cubic inches / 1 cubic foot.
Thus, 10390.8 cubic inches per second comes out to
10390.8 cubic inches
---------------------------- = Just over 6 cubic feet per sec.
1728 cu. inches
---------------------
1 cu. ft
How many sec in 1 day? 1 day = 24 hours
1 hour = 60 minutes
60 seconds = 1 minute
Figure out how many seconds there are in 1 day, and then multiply your result by 6 cu. ft. / sec.
To find the flow rate of oil, first calculate the cross-sectional area of the pipe using the formula for the area of a circle, A=πr². Then, multiply the area by the given oil speed to find the volume of oil flowing every second. Multiply this by the number of seconds in a day to find the amount of oil leaving the pipe each day, and remember to convert from cubic inches to cubic feet.
Explanation:The question is asking us to find the volume of oil leaving the pipe per second and per day. To calculate the flow rate of oil, we first find the cross-sectional area of the pipe by using the formula for the area of a circle A=πr², where r is the radius of the pipe (half the diameter). Since the diameter given is 21 inches, the radius is 10.5 inches.
Next, use the given flow rate of 30 inches/second to calculate the volume of oil flowing every second. This is done by multiplying the area by the oil speed V = A * oil speed.
To find the amount of oil leaving the pipe each day, we multiply the volume per second by the number of seconds in a day .
Note: To convert cubic inches to cubic feet (since the question asks for cubic feet), remember there are 1728 cubic inches in 1 cubic foot.
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Find the area of the following circle. Use = 3.14
r = 5 yd.
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Albert thought of a number, added 5, multiplied the result by 2, took away 6 and then divided by 2 to give an answer of 8
Answers
6+5=11
11*2=22
22-6=16
16/2=8
Starting with 8:
8*2 = 16 + 6 = 22/2 = 11- 5 = 6
Now, lets check it and start from the beginning with this new number (6), and follow everything Albert did and we will get 8.
6+5= 11*2= 22-6 = 16/2 = 8
Carlos has 5/8 pound of pumpkin seeds. He puts the seeds evenly into 20 envelopes. How much pumpkin seed is in each envelope?
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20/1 divided by 5/8:
20 x 8 = 160
1 x 5 = 5 = 160/5
Simplify: 32
Hope this helps you!
I hope this helps.Good Luck!
write all names that apply to each number 121/121
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1
one
etc
hope this helps
Min Jee wants to build a small patio using either brick or paver stones. It will be 70 inches long and 49 inches wide. Each brick covers an area of 3 1/2 inches by 7 1/2 inches, and cost $0.59. Each paver covers an areas 8.4 inches by 8.4 inches and costs $1.88. What would be less expensive to use, and by how much?
Answers
1 Paver = 8.4 in by 8.4 in = 70.56 sq. in. and costs $1.88
patio's area 70 * 49 = 3430 sq. in.
number of Bricks to complete the Patio :
3430 / 26.25 = 130.67 round up to 131
total cost of bricks:
131 * $0.59 = $77.29
number of Pavers to complete the Patio:
3430 / 70.56 = 48.6 round up to 49
total cost of pavers:
49 * $1.88 = $92.12
$92.12 - $77.29 = 14.83
the bricks would cost less by $14.83
a 9 pound bag of sugar is being split into containers that hold 2/3 of a pound. how many containers of sugar will the 9 pound bag create?
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well
[tex]\bf 9 \div \frac{2}{3}\implies \cfrac{9}{\frac{2}{3}}\implies \cfrac{\quad \frac{9}{1}\quad }{\frac{2}{3}}\implies \cfrac{9}{1}\cdot \cfrac{3}{2}\implies \cfrac{27}{2} \\\\\\ \textit{2 goes \underline{13 times} into 27, with a \underline{remainder of 1}}\implies 13\frac{1}{2}[/tex]
Answer:
13 1/2
Step-by-step explanation:
If m and n are two positive real numbers whose product is 10, what is the minimum value of m + 2n
Answers
2 + 2(4)
The minimum value of (m + 2n) is 8.95 and this can be determined by using the arithmetic operations.
Given :
If m and n are two positive real numbers whose product is 10.
Given that m and n are two positive real numbers whose product is 10 that is:
mn = 10
[tex]\rm m= \dfrac{10}{n}[/tex] ---- (1)
The minimum value of (m + 2n) can be determined by using the following calculation.
Put the value of m in the given expression.
[tex]\rm = \dfrac{10}{n}+2n[/tex] ---- (2)
Now for minimum value differentiate the above expression with respect to n.
[tex]\rm =-\dfrac{10}{n^2}+2[/tex]
Now equate the above equation to zero.
[tex]\rm \dfrac{10}{n^2}=2[/tex]
[tex]\rm n = \sqrt{5}[/tex]
Now, put the value of n in equation (2).
[tex]\rm Minimum \;Value = \dfrac{10}{\sqrt{5} }+2\sqrt{5}[/tex]
= 8.95
The minimum value of (m + 2n) is 8.95.
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Given that P = (-4, 11) and Q = (-5, 8), find the component form and magnitude of vector QP
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P = (-4,11)
Q = (-5,8)
The x-component of vector QP is
-4 - (-5) = 1
The y-component of vector QP is
11 - 8 = 3
The vector QP is
(1,3) or
[tex]\vec{QP} = \hat{i} + 3\hat{j}[/tex]
The magnitude of the vector is
√(1² + 3²) = √(10)
Answer:
[tex]\vec{QP} = \hat{i}+3\hat{j} \,\, or \,\, (1,3)[/tex]
The magnitude is √(10).
Answer:
<1, 3>, square root of ten
Step-by-step explanation:
Solve for x.y = mx+b
Answers
- _ + _
m m
this is the answer
Solve for x means to isolate x.
y - b = mx
We now divide both sides by m to isolate x.
(y - b)/m = x
How much pure acid should be mixed with 6 gallons of a 20% acid solution in order to get a 90% acid solution?
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now, if we want a 90% solution, and say we add "y" gallons, how much acid is in it? well (90/100) * y, or 0.9y.
now let's add "x" gallons of pure acid, now, pure acid is just pure acid, so is 100% acid, how much acid is there in it? (100/100) * x, or 1x or just x.
we know whatever "x" and "y" amounts are, they -> x + 6 = y
and we also know that x + 1.2 = 0.9y
[tex]\bf \begin{array}{lccclll} &\stackrel{gallons}{acid}&\stackrel{acid~\%}{quantity}&\stackrel{acid~gallons}{quantity}\\ &------&------&------\\ \textit{pure acid}&x&1.00&x\\ \textit{20\% sol'n}&6&0.20&1.2\\ ------&------&------&------\\\ mixture&y&0.90&0.9y \end{array} \\\\\\ \begin{cases} x+6=\boxed{y}\\ x+1.2=0.9y\\ ----------\\ x+1.2=0.9\left( \boxed{x+6} \right) \end{cases} \\\\\\ x+1.2=0.9x+5.4\implies x-0.9x=5.4-1.2\implies 0.1x=4.2 \\\\\\ x=\cfrac{4.2}{0.1}\implies x=\stackrel{gallons}{42}[/tex]
To get a 90% acid solution, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution.
Explanation:To solve this problem, we can use the formula for concentration:
Concentration = (Volume of pure acid) / (Total volume of solution)
Let x represent the volume of pure acid to be added. We know that the total volume of the solution after adding the pure acid is 6 gallons + x gallons. We also know that the concentration of the 20% acid solution is 0.2.
Using the formula, we can set up the equation:
0.9 = x / (6 + x)
Multiplying both sides of the equation by (6 + x), we get:
0.9(6 + x) = x
Simplifying the equation, we have:
5.4 + 0.9x = x
Subtracting 0.9x from both sides of the equation, we get:
5.4 = 0.1x
Dividing both sides of the equation by 0.1, we get:
54 = x
Therefore, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution to get a 90% acid solution.
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What percentage of 3000 is 330
Answers
Answer:
11
Step-by-step explanation:
The perimeter of a square is 26.46 inches. What is the side length of the square?
Answers
Normally it would be:
P=s1+s2+s3+s4
for a square its simply
P=4s
26.46=4S
6.615=S
Each side is 6.615 inches
The side length of a square whose perimeter is 26.46 inches can be calculated by dividing the given perimeter by 4 (the number of sides in a square), resulting in a side length of approximately 6.615 inches.
Explanation:The subject of this question is Mathematics, with the specific topic being measurement and geometry. This question is applicable to Middle School grade levels. The student seeks to determine the side length of a square, knowing the perimeter is 26.46 inches.
To find the side length, we need to recall the formula for the perimeter of a square: P = 4s, where P represents the perimeter and s represents the length of a side. The student's square has a perimeter of 26.46 inches, so the equation would be 26.46 = 4s.
To isolate the value of s, we divide both sides of the equation by 4. This gives us: s = 26.46/4. Upon doing the division, we find that each side of the square is approximately 6.615 inches.
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The gas tank in the car holds 20 gallons of gasoline. You used up 4 gallons and 1 quart on your trip. How much gasoline is left in the tank?
Answers
20-4.25
=15.75
There is 15.75, or 15 3/4, gallons of gasoline left in the tank.
The correct answer is:
Total capacity of tank in quarts:
20 gallons = 20 × 4 = 80 quarts
Gasoline used in quarts:
4 gallons 1 quart = (4 × 4) + 1 = 17 quarts
Gasoline left in the tank in quarts:
80 − 17 = 63 quarts
Gasoline left in the tank in gallons and quarts:
63 quarts = 63 ÷ 4 = 15 remainder 3 = 15 gallons 3 quarts
Describe or show two ways to find the following product: 1/4 x 2/3.
Answers
2/3 = 0.666666667
0.25(0.666666667) = 0.166666667 = [tex] \frac{1}{6} [/tex]
______________________________
[tex] \frac{1}{4} ( \frac{2}{3}) = \frac{2}{12} = \frac{1}{6} = 0.166666667[/tex]
Cody filled a container with 7 3/16 quarts of iced tea. how many 1/4 quart glasses can be served from the container
Answers
[tex]\bf \stackrel{mixed}{7\frac{3}{16}}\implies \cfrac{7\cdot 16+3}{16}\implies \stackrel{improper}{\cfrac{115}{16}} \\\\\\ \textit{how many times does }\frac{1}{4}\textit{ go into }\frac{115}{16}? \\\\\\ \cfrac{\quad \frac{115}{16}\quad }{\frac{1}{4}}\implies \cfrac{115}{16}\cdot \cfrac{4}{1}\implies \cfrac{115}{4}\implies 28\frac{3}{4}[/tex]
Find all points on the circle x 2 + y 2 = 100 where the slope is 3 4
Answers
The points on the circle x² + y² = 100 where the slope of the tangent is ¾ are (6, -8) and (-6, 8). This is found by taking the derivative of the circle equation, setting it equal to the slope, solving for y, substituting this into the original circle equation, and solving for x.
Explanation:The equation of the circle is x² + y² = 100. To find the points on this circle where the slope of the tangent is ¾, we need to find the derivative of this equation. The derivative of y with respect to x is dy/dx = -x/y. Set this equal to ¾ and solve for y, which gives y = -4x/3. Substitute this into the original circle equation to solve for x, which yields x = ± 6. Then substitute these x-values back into the equation y = -4x/3 to get y = ± 8. Therefore, the points on the circle where the slope of the tangent is ¾ are (6, -8) and (-6, 8).
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Final answer:
To find points on the circle x² + y² = 100 where the slope is 3/4, differentiate the circle's equation and set the derivative equal to 3/4. Solve the system of equations involving the circle's equation and the line's equation derived from the slope criteria. This process typically yields two points of intersection due to the geometrical properties of circles and lines.
Explanation:
To find all points on the circle x2 + y2 = 100 where the slope is 3/4, we first acknowledge that the given circle is centered at the origin (0,0) with a radius of 10 units. Since the slope of a tangent to the circle at any point can be found using implicit differentiation, let's differentiate the given equation with respect to x. Doing so, we get 2x + 2yy' = 0 where y' denotes the slope of the tangent to the circle at (x,y). Solving for y', we get y' = -x/y. Setting this equal to the given slope of 3/4, we have -x/y = 3/4.
By cross-multiplying and rearranging, we get 4x + 3y = 0. To find the points of intersection between the line and the circle, we substitute x2 + y2 = 100 into this equation. Solving the system of equations will yield the points on the circle where the slope of the tangent is 3/4.
Note: The exact points of intersection would require solving a resulting quadratic equation, which can give two possible points since a line with a given slope (except vertical) will typically intersect a circle at two points.
spiders can walk on walls write the statement in if then form
Answers
If then because statements are much like they seem.
A customer pays $3.27 for oranges and $4.76 for pears. How many pounds of fruit does the customer buy?
Answers
3.27/1.09=3lbs. of oranges
then take 4.76 and divide that by 1.19 (for the pears)
4.76/1.19=4lbs. of pears
add 4+3 to get how many lbs. in all
4+3=7
A total of 7 pounds of fruit does the customer buy.
Given that, a customer pays $3.27 for oranges and $4.76 for pears.
The cost of 1 pound orages=$1.09 and the cost of 1 pound pears=$1.19
What is a unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, the number of pounds of oranges =3.27/1.09=3 pounds
The number of pounds of pears =4.76/1.19=4 pounds
Total weight=3+4=7 pounds
Therefore, a total of 7 pounds of fruit does the customer buy.
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A lender estimates the closing costs on a home loan of $50,000 as listed below.
Closing Cost
Charge
Loan origination
$200
Title insurance
$530
Attorney’s fees
$600
Appraisal
$265
Inspection
$575
Recording fees
$130
Escrow
$800
If the lender's good faith estimates are accurate, are they a reasonable amount for closing costs? Why or why not?
a.
Yes, because the lender esitmated 3.08% of the home loan in closing costs which falls between 3 - 5%.
b.
Yes, because the lender estimated 4.6% of the home loan in closing costs which does not fall between 3 - 5%.
c.
No, because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3 - 5%.
d.
No, because the lender estimated 17.7% of the home loan in closing costs which does fall between
Answers
Answer:c.
No, because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3 - 5%
Step-by-step explanation:
Summation of the cost of loan =200+530+600+265+575+130+800
=3100
Now percentage of the estimate=
(3100/50000)*100%
=6.2%
C- The lender should not consider them as reasonable amount of closing costs because the lender estimated 6.2% of the home loan in closing costs which does not fall between 3-5%.
The lender cannot be accepting these costs as this will lead to the lender incurring losses over a longer period after doing all the necessary calculations.
The lender has disbursed a home loan of $50000 on which he has estimated certain closing costs and are considered to be true and accurate. The costs are loan origination, title insurance, attorney's fees, appraisal, inspection, recording fees, escrow, etc.The amounts will add up as a summation of all the fees and charges as titles above are mentioned which will end up totaling to $3100[tex]200+530+600+265+575+130+800=3100[/tex]
The calculation of of costs in to the percentage of total home loan is calculated as dividing the cost with total loan amount which will be totaled as 6.2%.[tex]\frac{3100}{50000} *100= 6.2[/tex]
The costing of this home loan is way above the ideal range of 3-5% and is not worth disbursing and may be called back.Hence, the correct option is C that the amounts of $3100 are not a reasonable amount of closing costs because the lender estimated 6.2% of the home loan in closing costs which does not fall between the range of 3-5%.
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