Solved given expression for x using the change of base formula log base b of y equals log y over log b is 4.459
Answer: Option D
Step-by-step explanation:
Given Expression:
[tex]2^{x-1}=11[/tex]
To solve this, first convert the exponential form into log form
If [tex]a^{x}=b[/tex] then [tex]\log _{a}(b)=x[/tex]
So, when comparing the given expression with above, a = 2, x = x – 1 and b = 11 .
[tex]2^{x-1}=11[/tex] become [tex]\log _{2}(11)=x-1[/tex]
Now, apply change of base formula to remove base 3
[tex]\log _{a}(y)=\frac{\log y}{\log a}[/tex]
Hence,
[tex]\log _{2}(11)=\frac{\log 11}{\log 2}[/tex]
Substitute [tex]\log _{2}(11)=x-1[/tex] in above expression, we get
[tex]\frac{\log 11}{\log 2}=x-1[/tex]
[tex]\frac{1.0414}{0.301}=x-1[/tex]
x – 1 = 3.459
x = 3.459 + 1 = 4.459
Final answer:
To solve the equation 2^(x - 1) = 11 for x, one can use the change of base formula by taking the logarithm of both sides, rewriting the equation using logarithm properties, isolating x, and then simply calculating using a calculator, which results in x ≈ 1.289.
Explanation:
To solve 2(x − 1) = 11 for x using the change of base formula, take the logarithm of both sides of the equation and use the formula logb(y) = log(y) / log(b), where y is the number we want to take the logarithm of and b is the base of the logarithm.
Let's start the process:
Apply logarithm to both sides of the equation: log(2(x - 1)) = log(11).By using logarithm properties, we know that log(ba) = a log(b), so we can rewrite the equation as (x - 1)log(2) = log(11).To isolate x, first, divide both sides by log(2), which gives us x - 1 = log(11) / log(2).Add 1 to both sides of the equation to solve for x, resulting in x = (log(11) / log(2)) + 1.Now, calculate the right side of the equation using a calculator:
x = (log(11) / log(2)) + 1 => x ≈ 1.289Hence, the correct answer is B) 1.289.
A box of granola bars has a volume of 210 cubic centimeters. What could be the dimensions of the box?
Answer:
Few of the following CASES can be the solutions:
1. (7 cm , 3 cm, 10 cm) 2.(14 cm , 3 cm, 5 cm)
3.(35 cm , 3 cm, 2 cm) 4.(7 cm , 6 cm, 5 cm)
5.(7 cm , 15 cm, 2 cm)
Step-by-step explanation:
Here, the volume of the box of granola bars = 210 cubic cm.
Let us assume the length of the box = l
The width of the box = w
and The height of the box = h
Also, the box is in shape of a cuboid.
VOLUME OF A CUBOID = Length x Width x Height
⇒l x b x h = 210 .... (1)
Now, we need to find such combinations of (l,b,h) such that their product is 210 cubic centimeters.
There are many number of possible such combinations.
Few of the following CASES can be the solutions:
1. (7 cm , 3 cm, 10 cm)
2.(14 cm , 3 cm, 5 cm)
3.(35 cm , 3 cm, 2 cm)
4.(7 cm , 6 cm, 5 cm)
5.(7 cm , 15 cm, 2 cm)
There can be any other possible such solution as well.
Mai and Tyler work on the equation 2/5b+1=-11 together. Mais soulution is b=-25 and Tyler’s is b=-28. Here is their work. Do you agree with their solutions? Explain or show your reasoning.
Mai’s work : Tyler’s work:
2/5b+1=-11 2/5+1=-11
2/5b=-10. 2b+1=-55
B=-10•5/2. 2b=-56
B=-25. B=-28
PLEASE HELLP ME
Answer:
No I don't agree with their solution; both their answers are wrong.
Correct answer is [tex]b=-30[/tex].
Step-by-step explanation:
Given:
[tex]\frac{2}{5}b+1=-11[/tex]
Now given:
According to Mai [tex]b = -25[/tex] and According to Tyler [tex]b = -28[/tex]
Now we need to find which of them is correct.
So we will solve the given equation we get;
[tex]\frac{2}{5}b+1=-11[/tex]
Subtracting both side by 1 we get;
[tex]\frac{2}{5}b+1-1=-11-1\\\\\frac{2}{5}b =-12[/tex]
Now Multiplying both side [tex]\frac{5}{2}[/tex] we get;
[tex]\frac{2}{5}b\times\frac{5}{2}= -12 \times \frac{5}{2}\\\\b=-6\times 5\\\\b=-30[/tex]
Hence both of them are incorrect, correct answer is [tex]b=-30[/tex].
Both Mai's and Tyler's solutions are incorrect. Mai's solution is incorrect as the correct solution to b is -30, not -25. Tyler's work has several typos that lead to an incorrect solution. To correctly solve the equation, you should subtract 1 from both sides to get 2/5b = -12, then multiply by the reciprocal of 2/5 which gives b = -30.
Explanation:The original equation presented is 2/5b + 1 = -11. Let's verify both Mai's and Tyler's solutions:
Mai's work: In her work, she correctly subtracts 1 from both sides of the equation to isolate the term with b, which gives 2/5b = -12. Multiplying both sides by the reciprocal of 2/5 (which is 5/2) indeed gives b = -30, not b = -25. So, Mai's solution is incorrect.Tyler's work: Tyler's work has significant typos that prevent it from being a correct solution. He reformulated the equation to 2b + 1 = -55 which isn't equivalent to the original equation. So, Tyler's solution is incorrect as well.The correct procedure should be: Subtract 1 from both sides of the equation to get 2/5b = -12. Then multiply both sides by 5/2 to solve for b, which gives a correct solution of b = -30.
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James needs to mix a 20% fungicide solution with a 60% fungicide solution to create 200 milliliters of a 26% solution. How many milliliters of each solution must James use?
170 ml of 20 % fungicide solution is mixed with 30 ml of 60% fungicide solution to create 200 milliliters of a 26% solution
Solution:
The final solution has 200 ml
Let "x" be the ml of 20 % fungicide solution
Then, (200 - x) is the ml of 60% fungicide solution
Then according to question, we can say,
"x" ml of 20 % fungicide solution is mixed with (200 - x) ml of 60% fungicide solution to get 200 ml of 26 % solution
We can frame a equation as:
[tex]x \times 20 \% + (200-x) \times 60 \% = 200 \times 26 \%\\\\\text{Solve the equation for "x" }\\\\x \times \frac{20}{100} + (200-x) \times \frac{60}{100} = 200 \times \frac{26}{100}\\\\\text{Simplify the above expression}\\\\x \times 0.2 + (200-x) \times 0.6 = 26 \times 2\\\\0.2x + 120 - 0.6x = 52\\\\-0.4x = 52 - 120\\\\-0.4x = -68\\\\x = 170[/tex]
Thus 170 ml of 20 % fungicide solution is used
Then , (200 - x) = 200 - 170 = 30 ml of 60% fungicide solution is used
James needs to mix 160 milliliters of the 20% solution with 40 milliliters of the 60% solution, in order to achieve a 26% solution in a total volume of 200 milliliters.
Explanation:To solve the problem, set up two equations based on the total volume and the percentage of the fungicide.
Let x be the volume of the 20% solution, and y be the volume of the 60% solution. Hence, the equation based on volume is x + y = 200 (since the total volume is 200 milliliters).The second equation will be based on the percentage of the fungicide in the solution as follows: 0.20x + 0.60y = 0.26*200 (reflecting the fact that James wants a 26% solution).Solving these two equations simultaneously, we get x = 160 milliliters and y = 40 milliliters.
Therefore, James needs to mix 160 milliliters of 20% fungicide solution and 40 milliliters of 60% fungicide solution to get a 26% solution of 200 milliliters.
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Where is the point of concurrency of the angle bisectors of a triangle?
A.on the triangle
B. outside the triangle
c. inside the triangle
please help me
Answer:
The point of concurrency of the angle bisectors of a triangle is inside the triangle.
Step-by-step explanation:
Considering the triangle ΔABC as shown in attached figure.
As it is clear that
The three angle bisectors of a triangle intersect at one point. Incenter is basically the point of concurrency of the angle bisectors.Each point on the angle bisector is at equal distance from the sides of the angle.As the triangle's incenter is always located inside the triangle, so we can conclude that the point of concurrency of the angle bisectors of a triangle is inside the triangle.
Therefore, the point of concurrency of the angle bisectors of a triangle is inside the triangle
Please check the attached figure below.
Keywords: angle bisectors of a triangle, point of concurrency
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-99 less than a number
Answer:
-99 is less than -98
-99 is less than -97
-99 is less than -96
.
.
.
-99 is less than -1
-99 is less than 0
-99 is less than (any posifive number)
what is the geometric mean of 2 and 135
[tex]\bf \stackrel{\textit{geometric mean of 2 and 135}}{\cfrac{2}{x}=\cfrac{x}{135}\implies 270 = x^2}\implies \sqrt{270}=x[/tex]
Find the sum of the polynomials 3x^5y – 2x^3y^4 - 7xy^5 and -8x^5y+ 2x^3y^4+xy^3
Answer:
the degree of a polynomial is the highest exponent in a term
thus it'd be 7 cuz
2x^3y^4
4 + 3 = 7
Step-by-step explanation:
I think thats write, not completly sure if its wrong lmk
. Which cross section is NOT possible when slicing a square prism with a plane?
A. rectangle
B. triangle
c. hexagon
D. octagon
The answer is D. octagon.
Therefore, the only shapes that can be formed by slicing a square prism with a plane from the given options are a rectangle, a triangle, and an octagon. A hexagon is not possible, making option C the correct answer.
The correct answer is C. A hexagon is not possible when slicing a square prism with a plane.
When slicing a square prism with a plane, the resulting cross section can take on various shapes depending on the angle and position of the cutting plane. Here are the possible cross sections:
- If the plane is parallel to one of the faces of the prism and intersects the prism, the cross section will be a rectangle (Option A).
- If the plane intersects two adjacent edges of the prism, the cross section will be a triangle (Option B).
- If the plane passes through the prism in such a way that it intersects all four edges of one face of the prism, the cross section will be an octagon (Option D), provided that the plane does not intersect the prism at the corners of the square base.
However, a hexagon (Option C) is not a possible cross section when slicing a square prism with a plane. This is because to create a hexagon, the plane would need to intersect three non-adjacent edges of the prism's base, which is geometrically impossible given the right angles of the square base. A hexagon has six sides, and a square prism's base has only four edges, which cannot be divided into three pairs of non-adjacent edges that a plane could intersect to form a hexagon.
A model house is 12 inches wide. If it is built with a scale of 3 in : 20 feet, then how wide is the real house?
Answer:
80 inches wide
Step-by-step explanation:
3 inches = 20 feet. 12/3=4. 4*20=80 inches
Sureepan borrows 40 000 Bhat to buy a new computer. The bank charges 7.5% interest compounded yearly. Sureepan agrees to pay a half of the amount still owing at the end of each year after the interest has been compounded. Determine how much Sureepan would have paid back at the end of 4 years.
Answer:
$42,606.41Explanation:
year 1 (all the values are is $)
Initial debt 40,000Interest of the year (7.5%) 7.5% × 40,000 = 3,000Debt at the end of the year(including the interest) 40,000 + 3,000 = 43,000
Payment at the end of the year(half of the debt) 43,000 / 2 = 21,500
Debt after payment 21,500year 2 (all the values are is $)
Initial debt 21,500Interest of the year (7.5%) 7.5% × 21,500 = 1,612.50Debt at the end of the year(including the interest) 21,500 + 1612.50 = 23,112.50
Payment at the end of the year(half of the debt) 23,112.50 / 2 = 11,556.25
Debt after payment 11,556.25year 3 (all the values are is $)
Initial debt 11,556.25Interest of the year (7.5%) 7.5% × 11,556.25 = 866.72Debt at the end of the year(including the interest) 11,556.25 + 866.72 = 12,422.97
Payment at the end of the year(half of the debt) 12,422.97 / 2 = 6,211.48
Debt after payment 6,211.48year 4 (all the values are is $)
Initial debt 6,211.48Interest of the year (7.5%) 7.5% × 6,211.48 = 465.86Debt at the end of the year(including the interest) 6,211.48 + 465.86 = 6,667.35
Payment at the end of the year(half of the debt) 6,667.35 / 2 = 3,338.67
Amount paid back at the end of 4 years ($) :
21,500 + 11,556.25 + 6,211.48 + 3,338.67 = 42,606.41What is the answer?
Answer:
Step-by-step explanation:
141
Answer:
23
Step-by-step explanation:
3x + 7y = -5
8x + 9y = 6
The question involves solving simultaneous linear equations, a high school level topic in mathematics. Methods like substitution or elimination can be used to find the values of the variables.
The student's question involves solving simultaneous linear equations, which is a topic in mathematics. To solve the given system of equations, one can use methods such as substitution, elimination, or matrix operations like determinants. The elimination method can be particularly efficient. For example, you can multiply the first equation by a number that will allow the x or y terms to cancel out when added or subtracted from the second equation. After simplifying, you're left with one equation in one unknown, which can be easily solved. Then, back-substitute the known value into one of the original equations to solve for the other variable.
Given the equations 3x + 7y = -5 and 8x + 9y = 6, we may choose to multiply the first equation by 3 and the second by 7 (to eliminate the x terms) or to multiply the first equation by 8 and the second by 3 (to eliminate the y terms). Once one variable is eliminated, we solve for the other and use it to find the value of the remaining variable.
how many roots exist for this polynomial function? F(x) = 4x5 – 3x
there is 5 roots hope it helps
Select the correct answer.
Which expression gives the same result as ?
A.
B.
C.
D.
Answer: A. would give the same result as the blank space as generally, when you think the answer is A. you should double check that as teachers know that students will always guess A in a pinch.
Hope this helps! :)Step-by-step explanation:
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?
A.(-2,2)
B.(-1,2)
C.(2,-2)
D.(2,-1)
Answer:
B.(-1,2)
Step-by-step explanation:
In a function, there can not be two different values of y corresponding to the same value of x.
See the graph attached.
Here, the points on the graph are (1,2), (2,-3), (-2,-2) and (-3,1).
If we consider point (-2,2) then there will be two points corresponding to the same x value i.e. (-2,-2) and (-2,2).
Similarly, if we consider the point (2,-2) or (2.-1) then also there becomes more than one values of y for a single value of x i.e. x = 2.
So, if we consider the ordered pair (-1,2) then only the graph still represents a function. (Answer)
Answer:
B.(-1,2)
Step-by-step explanation:
6 x 4237 solve using distributive property
Answer: 25422
Step-by-step explanation:
6(4000+237)
6(4000) + 6(237)
24000 + 1422
24000+1422=25422
Answer:
6·4237 = 25422
Step-by-step explanation:
This is the way multiplication by hand is usually done.
6(4237) = 6(4000 +200 +30 +7) = 6·4000 +6·200 +6·30 +6·7
= 24000 +1200 +180 +42
= 25200 +222 . . . . . add first two terms and last two terms
= 25422
Every item in the Just a Dollar store is priced at $1.00. When Mary Jo opens the store, there is $125.50 in the cash register. When she counts the money in the cash register at the end of the day, the total is $1,085.60. If the sales tax rate is 8.5%, howmany items were sold that day?
Answer:
885
Step-by-step explanation:
Given: Amount available in the cash register= $ 125.50.
Every item is just priced at $1.00
Total amount of money at the end of day= $1085.60
Sales tax rate= 8.5%
First finding total revenue generated at the end of day,
Total revenue at the end of day= [tex]Total\ cash\ at\ the\ end\ of\ day - Cash\ available\ at\ the\ beginning\ of\ day[/tex]
∴ Total revenue at the end of day= [tex]1085.6- 125.5= \$ 960.1[/tex]
Lets assume total number of item sold be "x".
Now, forming an equation to determine the total revenue generated at the end of day.
We know, Total revenue is the number of item sold at $1 and sales tax revenue generated on the number of item sold.
⇒ [tex]\$1 \times x + \frac{8.5}{100} \times x= \$ 960.1[/tex]
⇒[tex]1x+0.085x= 960.1[/tex]
⇒ [tex]1.085x= 960.1[/tex]
dividing both side by 1.085
⇒[tex]x= \frac{960.1}{1.085}[/tex]
∴ x= [tex]884.884[/tex] [tex]\approx 885[/tex]
Hence, total number item sold in the day is 885
I NEED HELP ASAP. PLZ HELP
Answer:
Y=x+1...written on the line between c and b
Step-by-step explanation:
CB is perpendicular to EF.
The slope is 1, the y intercept is 1
Therefore. Y =mx+B is y=1x+1
Everyday Jin reads for 0.75 hours in the mornings and 1.25 hours in the evening. He uses the expression 0.75d + 1.24d to keep track of the number of hours he has read for any number of days, d. If Jim reads for 20 days, how many hours has he read?
Please please please answer. Overdue
Answer:
Step-by-step explanation:
0.75d + 1.25d.......for 20 days
0.75(20) + 1.25(20) = 15 + 25 = 40 hrs <===
The number of hours Jin reads in 20 days is 39.8 hours.
The expression for the given situation is 0.75d + 1.24d.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
In the given expression 0.75d + 1.24d, d is number of days.
Substitute d=20 in 0.75d + 1.24d, we get
0.75(20) + 1.24(20)
= 15+24.8
= 39.8 hours
Hence, the number of hours Jin reads in 20 days is 39.8 hours.
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what is the value of the first 4 in this...4,384,488?
help me plzzzzzzzzz!!!!!!!!!!!!!!!!!!
Answer: ( 12 , 9 )
Step-by-step explanation:
The formula for finding the coordinate of points when a line is externally divided in a given ratio is given by :
x = [tex]\frac{p x_{2}+q x_{1}}{p+q}[/tex]
y = [tex]\frac{p y_{2}+q y_{1}}{p+q}[/tex]
From the question
[tex]x_{1}[/tex] = 2
[tex]x_{2}[/tex] = ?
x = 4
[tex]y_{1}[/tex] = -1
[tex]y_{2}[/tex] = ?
y = 1
p = 1
q = 4
substituting the values into the formula ,we have
x = [tex]\frac{p x_{2}+q x_{1}}{p+q}[/tex]
4 = [tex]\frac{1(x_{2})+4(2) }{1+4}[/tex]
4 = [tex]\frac{x_{2}+8}{5}[/tex]
[tex]x_{2}[/tex] + 8 = 20
[tex]x_{2}[/tex] = 12
Also
y = [tex]\frac{p y_{2}+q y_{1}}{p+q}[/tex]
1 = [tex]\frac{y_{2}+4(-1)}{5}[/tex]
[tex]y_{2}[/tex] - 4 = 5
[tex]y_{2}[/tex] = 9
Therefore , the end of the stencil is located at point ( 12 , 9 )
An auto repair shop charged a customer $280 to repair a car. The bill listed $80 for parts the remainder for labor. If the cost of labor is $50 per hour, how many hours of labor did it take to repair the car?
Given the line below.
Write the equation of the line, in point-slope form. Identify the point (-2, -2) as (x1, y1). Use the box provided to submit all of your calculations and final answer.
Answer:
The equation of the line in point slope form is equal to
[tex]y+2=(x+2)[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(-2,-2) and (2,2)
substitute the values
[tex]m=\frac{2+2}{2+2}=1[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=1\\(x1,y1)=(-2,-2)[/tex]
substitute the values in the formula
[tex]y-(-2)=(1)(x-(-2))[/tex]
[tex]y+2=(x+2)[/tex]
2x-y=-1 in slope intercept form
Answer:
y = 2x + 1Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the equation of a line in a standard form.
Convert to the slope-intercept form:
[tex]2x-y=-1[/tex] add y to both sides
[tex]2x-y+y=-1+y[/tex]
[tex]2x=-1+y[/tex] add 1 to both sides
[tex]2x+1=-1+1+y[/tex]
[tex]2x+1=y\to y=2x+1[/tex]
The slope intercept form of the given equation is y = 2x+1
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
(ii) 3x + 5 = 15
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given that, an equation of a line, 2x-y = -1, we need to convert this into slope intercept form,
The standard form of the equation of a line in slope intercept form, is given by :
y = mx+c
Where, m = slope of the line, c is the y-intercept,
So, the given equation is 2x-y = -1,
Add y both the side,
2x-y+y = -1+y
2x = -1+y
Add 1 in both sides,
2x+1 = y+1-1
y = 2x+1
Hence, the slope intercept form of the given equation is y = 2x+1
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HELP FAST!!! Which angles could form an obtuse triangle? A. 62°, 39°, 79° B. 46°, 92°, 42° C. 40°, 40°, 100° D. 22°, 78°, 80°
Answer:
A. is Obtuse scalene triangle.
Step-by-step explanation:
Hope this help
Answer:
c i think
Step-by-step explanation:
If a population consists of 54,000,000 people and a census is taken, how many people are sampled?
Answer:
A.54,000,000
Step-by-step explanation:
apexs
I am really confused on this. It says find the value of x in each triangle.
Trey is making a small sign in the shape of a triangle for her store. He wants the height of the triangle to be 8 inches. The area of the sign must be less than 20 square inches. (Trey doesn't want to buy more material.) Write an inequality that describes the possible base lengths (in inches) of the triangle. Use b for the base length of the triangular sign.
Answer:
8+b=20
Step-by-step explanation:
3,425,645 rounded to the nearest hundred thousand
Answer:
3,400,000
Step-by-step explanation:
refer to attached for reference
in our case, the digit in the hundred thousands place is the number 4.
How we round this digit depends on the digit directly to the right of it (i.e the ten-thousands place).
If the digit to the right is less than 5, then leave the digit in the hundred thousands place the same and make everything else to the right zeros.
if the digit to the right is 5 or greater, then increase the digit in the hundred thousands place by 1 and then make everything else to the right zeros.
in our case, the digit to the right of the hundred thousands place is the number 2, this is less than 5, so we leave 4 the same and make everything esle to the right zero.
i.e. 3,400,000
3,425,645 rounded to the nearest hundred thousand is 3,400,000. The rounding is based on the digit in the ten thousand's place, which is 4 in this case, so we round down.
Explanation:To round the number 3,425,645 to the nearest hundred thousand, we look at the ten thousand's place which is 2. Since this digit is less than 5, we round down the hundred thousand's place. Therefore, 3,425,645 rounded to the nearest hundred thousand is 3,400,000.
When rounding to the nearest hundred thousand, the digit in the hundred thousand's place becomes the focus. If the digit in the ten thousand's place (to the right of the hundred thousand's place) is 4 or less, the hundred thousand's digit remains the same and all subsequent digits become zero. If the ten thousand's place is 5 or more, the hundred thousand's digit is increased by one, and again, all digits to the right are changed to zero.
In this example, the hundred thousand's digit is 3 and the ten thousand's digit is 4, which tells us to keep the hundred thousand's place as it is and replace the subsequent digits with zeros. This gives us 3,400,000 as the rounded number.
Ashley is taking a road trip from California to Washington. Every 4 hours, she travels between 204 and 272 miles. Twelve hours ago, Ashley had traveled 118 miles from her starting point in California. Which is a reasonable measure of Ashley's distance from her starting point in California now? A. 238 miles B. 596 miles C. 832 miles D. 356 miles
Answer:
Option C. 832 miles
Step-by-step explanation:
Ashley travels between 204 and 272 miles in every 4 hours.
That means she travels between 51 [tex](\frac{204}{4}miles)[/tex] and 68 ([tex]\frac{272}{4}miles)[/tex] per hour.
Therefore, in 12 hours she will travel between 612 (51×12 miles) miles and 816 (68×12 miles).
Since she has already traveled 118 miles before 12 hours then the distance traveled by her till now will be between 730 (612+118 miles) and 934 (816+118 miles).
From the given options, Option C. 832 miles is the reasonable measure of Ashley's distance from the starting point.