SOLUTION
A coin was flipped.
A = probability of it landing on a head
B = probability of it landing on a tail.
We are asked P(A and B), that means probability of landing on a head and on a tail.
A coin can only land on a head or it can land on a tail. It can't land on a head and a tail at the same time.
Therefore the probability of landing on a head and a tail is 0.
Hence, the answer is 0.
Which ordered pair is the y-intercept of y=x² + 6.0 – 4?(1,6)O (60)0 (0, -4)O (6,4)
The equation given is,
[tex]y=x^2+6x-4[/tex]The y-intercept is determined when x coordinate is zero.
Substitute x equals to 0 in the equation,
[tex]y=0^2+6(0)-4[/tex][tex]y=-4[/tex]Thus, the ordered pair of y-intercpet is,
[tex](0,-4)[/tex]The correct option is c.
Beginning with the graph of f(x) = x², what transformations are needed to form g(x) = –(x – 6)² + 3?
A) The graph of g(x) opens upward and is shifted to the right 6 units and up 3 units.
B) The graph of g(x) opens upward and is shifted to the left 6 units and up 3 units.
C) The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
D) The graph of g(x) opens downward and is shifted to the left 6 units and up 3 units.
Answer:
C) The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
Step-by-step explanation:
You want to know what transformations are needed to form g(x) = –(x – 6)² + 3 from f(x) = x².
TransformationsThe function transformations we are typically concerned with are ...
translation horizontally and verticallyscaling horizontally and verticallyreflection across vertical and horizontal linesEach of these has a recognizable influence on the function.
TranslationTranslation by 'h' units to the right and 'k' units up transforms the function to ...
g(x) = f(x -h) +k
ScalingExpanding a graph horizontally by a factor of p and vertically by a factor of q transforms the function to ...
g(x) = q·f(x/p)
ReflectionReflecting a graph horizontally across the y-axis replaces x with -x.
Reflecting a graph vertically across the x-axis replaces f(x) with -f(x).
Given graphComparing g(x) = -(x -6)² +3 to the original f(x) = x², we see that ...
(h, k) = (6, 3)f(x) was replaced by -f(x)This means the graph was shifted right 6 units and up 3 units. The graph was reflected across the x-axis, so the curve opens downward.
Option c, The graph of g(x) opens downward and is shifted to the right 6 and up 3 units. is the correct answer.
What is graph?
In the field of mathematics, a graph is a representation (visual) or diagram that shows the facts or values in an ordered and systematic way.
The relationships between two or more items are frequently represented by the points on a graph.
As given in the question,
[tex]f(x)=x^2[/tex] and [tex]g(x)= -(x-6)^2 + 3[/tex]
Since, [tex]f(x) = x^2[/tex] we are applying the following three rigid transformations on f(x) to obtain g(x):
Reflection around the x-axis in the graph: [tex]f'(x) = -x^2[/tex]Translation in the +x semi-axis in the graph: [tex]f''(x) = -(x-6)^2[/tex]Translation in the +y semi-axis in the graph: [tex]g(x) = -(x-6)^2+3[/tex]Therefore, The graph of g(x) opens downward and is shifted to the right 6 and up 3 units.
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Solve the system. Check the solution.x + y = 8(x=y-3
Answer:
[tex]\begin{gathered} \text{Solution:} \\ (2.5,5.5) \end{gathered}[/tex]Step-by-step explanation:
Given the following system of equations:
[tex]\begin{gathered} x+y=8\text{ (1)} \\ x=y-3\text{ (2)} \end{gathered}[/tex]Since on equation 2, x is already isolated, substitute it into equation 1:
[tex]\begin{gathered} (y-3)+y=8 \\ \end{gathered}[/tex]Solve for y.
[tex]\begin{gathered} 2y=8+3 \\ y=\frac{11}{2}=5.5 \end{gathered}[/tex]Knowing the value of y, plug it into equation (2) and solve for x:
[tex]\begin{gathered} x=y-3 \\ x=5.5-3 \\ x=2.5 \end{gathered}[/tex]Find the equation of the line whose slope is -3 and which passes through the point (5,-2).
Answer:
y = -3x + 13
Step-by-step explanation:
We can use the the point slope form of an equation for this:
y - y1 = m (x - x1)
Replace the y1, x1, and m variables with what we were given:
y - (-2) = -3 (x - 5)
Distribute
y + 2 = -3x + 15
Combine like terms
y = -3x + 13
Find the value of 12.56 is multiplied by 8.8 and result is divided by 1.57.
Given:
12.56 is multiplied by 8.8 and the result is divided by 1.57.
To find the final result:
First, we multiply 12.56 by 8.8.
We get,
[tex]12.56\times8.8=110.528[/tex]Next, the result 110.528 is divided by 1.57.
So, we get
[tex]\frac{110.528}{1.57}=70.4[/tex]Hence, the answer is 70.4.
what is 34.49 divided by 0.2 help!!! due friday
Answer:
17.245
Step-by-step explanation:
34.49 divided by 0.2 is 17.245
7x-3y=11 find ordered pairs
Answer:
[tex](0,-\frac{11}{3} ),(1,-\frac{4}{3} ),(2,1)[/tex]
Step-by-step explanation:
Given Equation:
[tex]7x-3y=11[/tex]Required:
Solve the equation for [tex]y[/tex].Find ordered pairs.Steps:
Subtract 7x from both sides of the equation.
-3y = 11 - 7x
Divide each term in -3y = 11 - 7x by -3 and simplify.
-3y/-3 = 11/-3 + -7x/-3
Simplify the left side.
Cancel the common factor of -3.
-3y/-3 (canceled) = 11/-3 + -7x/-3
Divide y by 1.
y = 11/-3 + -7x/-3
Simplify the right side.
Simplify each term.
Move the negative in front of the fraction.
y = -11/3 + -7x/-3
Dividing two negative values results in a positive value.
y = -11/3 + 7x/3
Choose any value for x that is in the domain to plug in to the equation.
Choose 0 to substitute in for x to find the ordered pair.
Remove parentheses.
y = -11/3 + 7(0)/3
Simplify -11/3 + 7(0)/3.
⇒ Combine the numerators over the common denominator.
y = -11/3 + 7(0) / 3
Simplify the expression.
Multiply 7 by 0.y = -11 + 0/3
Add -11 and 0.y = -11/3
Move the negative in front of the fraction.y = -11/3
Use the x and y values to form the ordered pair.
(0, -11/3)
Choose 1 to substitute in for x to find the ordered pair.
Remove parentheses.
y = -11/3 + 7(1)/3
Simplify -11/3 + 7(1)/3.
Combine the numerators over the common denominator.
y = -11/3 + 7(1)/3
Simplify the expression.
Multiply 7 by 1.
y = -11 + 7/3
Add -11 and 7.
y = -4/3
Move the negative in front of the fraction.
y = -4/3
Use the x and y values to form the ordered pair.
(1, -4/3)
Choose 2 to substitute in for the x in the ordered pair.
Remove parentheses.
y = -11/3 + 7(2)/3
Simplify -11/3 + 7(2)/3.
Combine the numerators over the common denominator.
y = -11/3 + 7(2)/3
Simplify the expression.
Multiply 7 by 2.
y = -11 + 14/3
Add -11 and 14.
y = 3/3
Divide 3 by 3,
y = 1
Use the x and y values to form the ordered pair.
(2, 1)
These are three possible solutions to the equation.
(0, -11/3), (1, -4/3), and (2,1)
Thanks,
Eddie
Determine whether the statement is true or false. If false, correct the right-hand side of the statement. 0 Question content area bottom Part 1 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The statement is true. B. The statement is false. The correct statement is enter your response here. (Simplify your answer.)
Based on the given statement of hy⁰ = 0, the answer is B. The statement is false. The correct statement is hy⁰ = 1.
Why is the mathematical statement wrong?The statement given is that hy⁰ = 0. This is false because of the mathematical rule that whenever a number or figure is raised to the power of 0, the result would be that the answer is 1.
For instance:
2 ⁰ = 1
56 ⁰ = 1
8676⁰ = 1
From hy ⁰ = 0, we take the value of y⁰:
y ⁰ = 1
If y ⁰ = 1, then it means that on the right hand side of the statement, we would have the expression h(1).
This therefore means that the equation hy⁰ = 0 is false because h(1) is h and so the correct statement is:
hy ⁰ = 1
Rest of the question is:
Determine whether the statement is true or false. If false, correct the right-hand side of the statement. hyº = 0
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3 + 51 x 1/10 + 9 x 1/100
Answer:
5.49
Step-by-step explanation:
3+ 51= 54
54 x 1/10= 5.4 + 9 x 1/100
5.4 + 0.09=
5.49
Can anyone help me with this?
Identify the correct box and whisker plot of the given data.
Given the data below.
[tex]\lbrace1,3,5,6,6,7,8,11,12\rbrace[/tex]The median of the data above is the middle number
[tex]median=6[/tex]The first quartile is:
[tex]\begin{gathered} 1,3,5,6 \\ Q1=\frac{3+5}{2}=\frac{8}{2}=4 \end{gathered}[/tex]The third quartile is:
[tex]\begin{gathered} 7,8,11,12 \\ Q3=\frac{8+11}{2}=\frac{19}{2}=9.5 \end{gathered}[/tex]The box and whisker plot for the data is:
The second option is correct.
1. **Gabriella and Lisbet are selling bracelets and earrings to make money for their summer vacation. The bracelets will cost $2 and earrings will cost $3. They want to make at least $500 and would like to make less than 50 bracelets to make a profit. Graph the solution set to the system of linear inequalities in the coordinate plane below. Label your axes and create a scale. a. Is it possible for Gabriella and Lisbet to make a profit? Justify your answer using your graph above.
Answer:
It is possible for Gabriella and Lisbet to make a profit
Explanation:
Let's call x the number of bracelets that they will make and y the number of earrings that they will make.
If the bracelets will cost $2 and the earring will cost $3, they will make:
2x + 3y
Then, this quantity should be at least $500, so:
2x + 3y ≥ 500
Additionally, they would like to make less than 50 bracelets, so:
x < 50
So, the system of inequalities is:
2x + 3y ≥ 500
x < 50
Now, to graph the system, we need to identify the lines that separate the regions. So, for x < 50, we get that the line is x = 50, a vertical line that passes through the point (0, 50).
For 2x + 3y ≥ 500, we need to identify two points that belong to the line
2x + 3y = 500 as (250, 0) and (100, 100)
So, the graph of the inequalities is:
Therefore, the solution of the system is the yellow region. Since there is a region in the graph, Gabriella and Lisbet can make a profit.
A rental car company charges $29 per day to rent a car and $0.05 for every mile driven. Santiago wants to rent a car, knowing that: He plans to drive 400 miles. He has at most $100 to spend. What is the maximum number of days that Santiago can rent the car while staying within his budget?
Answer: He can only go 2 days
Step-by-step explanation:
A store and a bank would both charge fees for
Answer:A returned check
Step-by-step explanation:
Answer: D. bouncing a check
Bouncing a check
When a check is deposited in a bank, or when it is written out to a store teller to ultimately deposit in the store bank, the funds are tracing back from an origin bank account. When the check bounces a fee is then charges by both the bank out of which the check is written (for non-sufficient funds) and by the payee. If the payee is a store they will often charge fees that are charged back to them by their bank of deposit."
Complete both transformations below.
Then enter the final coordinates of the figure.
(1,-3)
A
C (2,-5)
B
(5,-1)
A" ([?], [])
B" ([ ], [])
C" ([],[])
1) Reflect across y - axis
2) <4.5>
Answer:
A''(3, 2), B''(-1, 4), C''(2, 0)
Step-by-step explanation:
For the first step, negate the y coordinate.
For the second step, add 4 to the x coordinate and 5 to the y coordinate.
[tex]A(1,-3) \longrightarrow A'(-1, -3) \longrightarrow A''(3, 2) \\ \\ B(5,-1) \longrightarrow B'(-5,-1) \longrightarrow B''(-1, 4) \\ \\ C(2, -5) \longrightarrow C'(-2, -5) \longrightarrow C''(2, 0)[/tex]
Graph the function. Then state the domain and range. f(x) = 1/4x-2
The domain and the range of the function f(x) = 1/4x - 2 is the all set of real values
What is the domain of a function?The domain of the function is the set of input values of the graph
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the domain and the range?The function is given as
f(x) = 1/4x - 2
Next, we plot the graph of the function (see attachment)
From the graph, we can see that the graph is a linear graph
This means that the function has a domain and a range of all set of real values
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Kurt has pulled 15 marbles from a large bag, and 6 of them are brown. What is the experimental probability that the next marble selected from the bag will be brown? Simplify your answer and write it as a fraction or whole number. A. P(brown) = 1/5 B. P(brown) = 2/5 C. P(brown) = 1/2 D. P(brown) = 3/5
total marbles: 15
brown marbles: 6
Probability : brown marbles / total marbles = 6 /15 (simplify) = 2/5
After many studies, a researcher finds thatthe probability that a word-recognitionprogram correctly interprets a hand-writtenword is 10. How many words out of40 would the researcher expect theprogram to correctly interpret?
Given:
The probability that a word-recognition the program correctly interprets a hand-written word is:
[tex]=\frac{9}{10}[/tex]Find-:
How many words out of 40 would the researcher expect the program to correctly interpret?
Explanation-:
the probability that a word-recognition the program correctly interprets a hand-written word is:
[tex]=\frac{9}{10}[/tex]For 40 world is:
[tex]\begin{gathered} =\frac{9}{10}\times40 \\ \\ =9\times4 \\ \\ =36 \end{gathered}[/tex]So, there are 36 words.
5. Find the value of x for which ABCD must be a parallelogram.AB-9 - 6xX-30DC
Given:
We're a given figure ABCD
∠ADB = x - 30
∠DBC = -9 - 6x
To find:
The value of x for which ABCD must be a parallelogram.
Step-by-step solution:
For ABCD to be a parallelogram, Its Alternate angles (Z - angles) must be equal.
Thus,
∠ADB = ∠DBC
x - 30 = -9 - 6x
7x = 21
x = 3
Final answer:
For ABCD to be a parallelogram, The value of x should be equal to 3.
Problem 2: The area of a
rectangular desk is given
by the trinomial x²-7x-18.
What are the dimensions
of the desk? (10 points)
Answer: (x-9) and (x+2)
Step-by-step explanation:
You would first have to break the trinomial down into 2 factors.
Since there are two minuses in the trinomial, start off like this : (x- __) (x+__)
Now, what two numbers add to -7, and multiply to -18?
9 and 2, with one term being negative.
Since the 2nd term in the trinomial is a negative, there must be a number added that has a greater negative term than the other positive term, therefore, making 9 the negative term, since 2-9 is -7.
And -9 times 2 is -18.
Now fill in the blanks : (x-9)(x+2)
Since (x-9) and (x+2) are multiplied by each other, they are the dimensions of the desk, being L x W.
Now let's double check the factors:
(x-9)(x+2)
Distribute the terms.
x^2 +2x -9x -18
x^2-7x-18
There, hoped that helped :D
Solve the following equation for a. Be sure to take into account whether a letter is
capitalized or not.
D = Ga +3h³ a
[tex]a=\frac{D}{G+3h^{3}}[/tex]
Looking at the equation, we can see that “a” is a part of both terms. Therefore, we can factor it out. Then we divide to get “a” by itself.
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A new model is to be built to serve the towns of Sunnyvale and Gloomington, who’s centers are 6 miles apart. The developers want to locate the mall not more than 3 miles from the center of Sunnyvale and also not more than 5 miles from the center of Gloomington. Drawl a simple map showing Sunnyvale, Gloomington, and all potential locations for the new mall, based on the given information. Be sure to show the scale of your map. Explain how you determine do the possible locations for the mall.
See explanation below
Explanation:
We are told the centres of the two towns are 6miles apart.
This means the distance between Sunnyvale and Gloomington = 6 miles.
We will draw a line with a distance of 6cm to indicate their distance apart.
The two end points of the line will indicate the location of Sunnyvale and Gloomington respectively.
For the developers to locate the mall not more than 3 miles from the center of Sunnyvale, we will draw a circle which has radius of 3cm. This way the mall doesn't exceed 3 miles from Sunnyvale.
For the developers to locate the mall not more than 5 miles from the center of Gloomington, we will draw a circle which has radius of 5cm. This way the mall doesn't exceed 5 miles from Gloomington.
The scale of the drawing will be 1cm represent 1 mile
You can use a compass(drawing tool) to draw the circles. adjusting the legs to suit the measurement of each radius.
The area under the each of the circles are all the possible locations of the map. The location of the new mall cannot go beyond the area under circles but can be within it.
triangle IJK with vertices I(-9-8),J(-5-6),and K(-7-3) is drawn on the coordinate grid below. what is the area in square units of triangle IJK
Here, we want to calculate the area of the given triangle
Mathematically, the product of the height and base of a triangle divided by 2 gives its area
Now, as we can see the shape, while IJ represents the base, KJ represents the height
We need to calculate the distance between these points before we can get the area of the triangle
To get the distances between the points, we have to use the distance formula
We can proceed with this as follows;
[tex]\begin{gathered} D\text{ = }\sqrt[]{(_{}x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \text{For IJ} \\ (x_1,y_1)\text{ = (-9,-8)} \\ (x_2,y_2)\text{ = (-5,-6)} \\ |IJ|\text{ = }\sqrt[]{(-5+9)^2+(-6+8)^2} \\ |IJ|\text{ = }\sqrt[]{16\text{ + 4}} \\ |IJ|\text{ = }\sqrt[]{20} \\ \\ \text{For KJ} \\ (x_1,y_1)\text{ = (-7,-3)} \\ (x_2,y_2)\text{ = (-5,-6)} \\ |KJ|\text{ = }\sqrt[]{(-5+7)^2+(-6+3)^2} \\ |KJ|\text{ = }\sqrt[]{4+9} \\ |KJ|\text{ = }\sqrt[]{13} \end{gathered}[/tex]Thus, we have the area of the triangle as follows;
[tex]\begin{gathered} \text{Area = }\frac{1}{2}\times base\times height \\ \\ \text{Area = }\frac{1}{2}\times\sqrt[]{20}\times\sqrt[]{13\text{ }}=\frac{\sqrt[]{260}}{2}\text{ = }\frac{2\sqrt[]{65}}{2}\text{ = }\sqrt[]{65\text{ }}\text{ square units} \end{gathered}[/tex]dilate the triangle (2,3) , (-5,4) , (0,-12) with a scale factor of 2 centered from the origin
For us to be able to determine the new coordinates of the triangle after being dilated with a scale factor of 2 centered from the origin, multiply each x and y coordinate value by the scale factor of 2 to find the new coordinates.
We get,
A (2, 3) → A' (4, 6)
B (-5, 4) → B' (-10, 8)
C (0, -12) → C' (0, -24)
Let's now plot it in a graph,
For #5 - 7, using the given scale factor and center, dilate the following figures and state the new coordinates.
Given: A scale factor of 1/2 and center N of a figure is given.
Required: To dilate the given figure using the given scale factor and center.
Explanation: Dilation is a transformation, used to change the size of the given figure. If the value of dilation>1 then the new figure enlarges. If dilation<1 then the given figure contracts while a dilation=1 means that the new figure is of the same size.
Now here the center is given to be N. And the scaling factor is 1/2.
The coordinates of center N are (3,2). Point M is 2 units left and 4 units down from point N. Hence for dilation of a factor of 1/2, point M' will be 1 unit to the left and 2 units down from point N -
[tex]\begin{gathered} M^{\prime}=(3-1,2-2) \\ M^{\prime}=(2,0) \end{gathered}[/tex]Similarly, point O is 2 units to the right and 6 units down from point N. Hence for dilation of a factor of 1/2, point O' will be 1 unit to the right and 3 units down from point N.
[tex]\begin{gathered} O^{\prime}=(3+1,2-3) \\ =(4,-1) \end{gathered}[/tex]Final Answer: M'=(2,0)
O'=(4,-1)
find angle y If the opposite side is 12 and the adjacent side is 11mm
Answer:
answer is 47.49 because tan theta is equals to 12 / 11 which is 1.09091.
So tan-¹(1.09091) = 47.49
If Jenna saves $20 buying an item for 40 percent off the regular price, then what were the regular price and the sales price?
Solution
For this case we can create the following proportional rule:
[tex]\frac{20}{100-40}=\frac{x}{100}[/tex]For this case x = original price
Then solving for x we have:
[tex]x=100\cdot\frac{20}{60}=33.33[/tex]Then the original price is 33.33$
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YOU WILL GET 100 POINTS IF YOU HELP! QUESTION DOWN BELOW!!!!!
So, we know BC is parallel to EF and 1 is congruent to 3.
Angles between parallel lines have special relationships. The relationships between 2 and 3 is that they are Same-side Interior Angles. This means that angles on the same line, formed by parallel lines intersecting that line (and the angles are on the same side of their respective line) are congruent. So, 2 and 3 are congruent... But by the transitive property, if 1 = 3 and 3 = 2... 1 = 2! And if 1 = 2, they are also Same-side interior angles and thus, the lines they lie on are parallel! So, since 1 and 2 are congruent, AB is parallel to DE.
Answer:
See below.
Step-by-step explanation:
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
[tex]\begin{array}{c|c}\sf Statement & \sf Reason\\\cline{1-2} BC \parallel EF & \phantom{\dfrac11}\sf Given\\\\\angle 2=\angle 3 & \textsf{Corresponding Angles Postulate}\\\\\angle 1=\angle 3 & \sf Given\\\\\angle 1=\angle 2 & \textsf{Transitive property of equality}\\&(\angle 2=\angle 3 \; \textsf{and} \; \angle 1=\angle 3)\\\\AB \parallel DE & \textsf{Corresponding Angles Postulate}\\& \textsf{as} \;\angle 1=\angle 2\end{array}[/tex]
As DE intersects the two parallel lines BC and EF, ∠2 is congruent to ∠3 (corresponding angles postulate).
As ∠1 = ∠3 and ∠2 = ∠3, then ∠1 = ∠2 (transitive property of equality).
Therefore, as ∠1 and ∠2 are congruent, AB and DE must be parallel (BC is the transversal).
John Baxley borrowed $25,000 for one year. He borrowed some at 13% interest and the rest at 50% interest. At the end of the year, he owed $36,000 in interest how much did he borrow at each rate?
The amount borrowed at 13% interest is $20,945.95.
The amount borrowed at 50% interest is $4,054.05.
How much is borrowed at each rate?The first step is to formulate a system of equations:
a + b = $25,000 equation 1
0.13a + 0.5b = (36,000 - 25,000
0.13a + 0.5b =11,000 equation 2
Where:
a = amount borrowed at 13% interest
b = amount borrowed at 50% interest
Take the following steps to determine the value of b:
Multiply equation 1 by 0.13
0.13a + 0.13b = 3,250 equation 3
Subtract equation 3 from equation 2
7,750 = 0.37b
b = $20,945.95
a = $25,000 - $20,945.95 = $4,054.05
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When Andy Green broke the land speed record, his vehicle was traveling across a flat portion of the desert with a forward velocity of 341.11 m/s. How long would it take him at that velocity to travel 4.500 km?
Answer:
13.192 seconds
Step-by-step explanation:
You want to know the time to travel 4.500 km at a speed of 341.11 m/s.
Travel timeThe relation between time, speed, and distance is ...
time = distance/speed
time = (4500 m)/(341.11 m/s) ≈ 13.192 s
It would take Andy about 13.192 seconds to travel 4.500 km.
__
Additional comment
The distance of 4.500 km is rounded to the nearest meter, so may have an error of 0.5 meters. At 342.11 m/s, it takes about 1.47 ms to travel that distance. This suggests that timing to the nearest millisecond is consistent with the precision of the other numbers in the problem.
One could argue that speed is 5 significant figures, but distance is 4 significant figures. That suggests their ratio, time, is only accurate to 4 significant figures: 13.19 s. Analysis of the worst-case error in the ratio suggests that this reported value throws away some accuracy, so a better result is 13.192 s.