Number lines are significant because they depict numbers as they appear in daily life.
What is number line?
A number line is a representation of a graduated straight line in elementary mathematics that serves as a visual representation of the real numbers. It is assumed that every point on a number line corresponds to a real number, and that vice versa.
Research has revealed that number lines are crucial because they foster sound mental number sense and arithmetic procedures.
They assist in providing a mental approach for addition and subtraction. Number lines are crucial, we can all agree on that.
Number lines are significant because they depict numbers as they appear in daily life.
Primarily because they make it possible for negative integers to be represented in a meaningful fashion.
The ability to display all real numbers, even enigmatic irrational numbers such π, -π, √2, -√ 2, etc., was a secondary but no less significant result.
Hence, number lines are significant because they depict numbers as they appear in daily life.
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In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test
and their mean score is 67.7.
What is the mean score of all of these students together? Round to one decimal place.
mean of the scores of all the students.
The mean score of all the students is 79.5 and it is round off into one decimal place.
Mean
Mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given,
In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test and their mean score is 67.7.
Here we need to find the mean score of all students.
In order order to find the mean score, we have to calculate the total score of the students by multiplying the mean score by the number of students then we get,
=> 30 x 87.7 = 2631
Similarly, the total score for 21 students is,
=> 21 x 67.7 = 1421.7
So, the 51 students, cumulative score is
=> 2631 + 1421. 7 = 4052.7
Therefore, the mean score is calculated as,
=> 4052.7/51
=> 79.464
When we round off the value into one decimal place then we get
=> 79.5
Therefore, the mean value of all the students is 79.5.
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A particle moves with velocity dx/dt in the x-direction
and dy/dt in the y-direction at time t in seconds, where
dx/dt = 3t² and dy/dt = 12t.
Find the distance traveled by the particle from time
t=0 to t= 3.
Distance travelled by the particle from time t = 0 to t = 3 in x-direction and y-direction is 27 units and 54 units respectively.
How to get distance/displacement using velocity?
Velocity is defined as the rate of change of position or the rate of displacement.Velocity = dx/dt that is change in position x with respect to time t.Integration is anti derivative for any quantity. Hence to get displacement using velocity, integrate to with respect to 't' and substitute values of t accordingly.According to given data:
A particle moves with velocity (dx)/(dt) = 3t² in x- direction
and (dy)/(dt) = 12t in y-direction
Integrating both sides of these derivatives with respect to t
x= ∫3t² dt = (3t³)/3 + A = t³ + A
where A is integration constant
y= ∫12t d t = (12t²)/2 + B = 6t² + B
where B is integration constant
At t = 0 we get x = A and at t = 3 we get x = 3³ + A = 27 + A.
Therefore, the difference in position of a from t = 0 t = 3 is
27 + A - (0 + A) = 27 units.
Similarly,
At t = 0 , we get y = B and at t = 3 we get
y = 6 * 3² + B = 54 + B
Therefore, the difference in position of y from t = 0 tot t = 3 is
54 + B - (0 + B) = 54 units.
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The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft. What is the mean height of the low tides? (I need to show work.)
The mean height of the low tides is 1.21 ft
The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft
The mean of a sample is given by the formula =
summation of all observation / number of observation
mean = (x₁ + x₂ + x₃ + x₄)/ 4
mean = -0.22 + 2.64 - 0.22 + 2.64 / 4
mean = 4.48 / 4 = 1.21
Therefore, the mean height of the low tides is 1.21 ft
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Find the slope of the line
Answer:
-3
Step-by-step explanation:
we sure y2-y1/x2-x1 to find slope
6+6/-4+0
12/-4
-3 is the slope
Hopes this helps please mark brainliest
. You get an auto loan at 3.5% interest for 5 years; please answer the following.
A. You can afford a $250 per month car payment; how expensive a car can you afford?
B. You purchase a car for $8000 with a $2000 down payment, what are your monthly payments?
Using the monthly payment formula, it is found that:
A. You can afford a car at a price of $13,742.36.
B. The monthly payments are of $109.15.
What is the monthly payment formula?The monthly payments are given by the equation presented as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
The variables involved in the equation are listed and explained as follows:
P is the initial amount.r is the interest rate.n is the number of payments.For item a, the parameters are given as follows:
A = 250, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
Hence the maximum value of the car is obtained as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]250 = P\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
0.0181919241P = 250
P = 250/0.0181919241
P = $13,742.36
For item b, the parameters are given as follows:
P = 6000, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60
(P = 6000 as the 2000 of the down payment are already paid, hence not subjected to interest).
Hence the monthly payments are given as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 6000\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]
A = 6000 x 0.0181919241
A = $109.15.
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Are These acute obtuse or right
Hailey used math to describe design in nature:
the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals.
Math shows the world is designed, and that design is _______.
The math shows the world is designed, and that design is symmetry and spirals.
How is math found in nature What is the significance of mathematical patterns in nature?
Mathematics is seen in many beautiful patterns in nature, such as symmetry and spirals. Both are aesthetically appealing and proportional. Symmetry can be radial, where the lines of symmetry intersect a central point such as a daisy or a starfish.
Here,
If Hailey used math to describe the design in nature: the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals. The math shows the world is designed, and that design is symmetry and spirals.
Hence, the math shows the world is designed, and that design is symmetry and spirals.
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Find the coordinates of the point which divide the lines joining the following pairs of points in the given ratio
a. (5,8) and (-1,3) 2:3
b.(4,7) and (3,-2) 4:5
The coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio 2:3 is (8,4).
Using the section formula, if a point (x,y) divides the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio m:n, then
(x,y)=( (mx₂+nx₁)/m+n , (my₂+ny₁)/m+n )
Let the points be A(5,8) and B(-1, 3). Let a point P(x,y) divides AB in the ratio 2:3
Therefore, we have
P(x,y)=((2(-1) + 3x5)/(2+3) , (2(3) + 3x8)/(2+3))
P(x,y)=(2.6,6)
Hence,the coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio 2:3 is (8,4).
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At a carnival game, it cost Noah $12 to toss 30 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The table complete table that shows equivalent ratios is:
Toss Dollars
5 2
30 12
45 18
See image in the attachment that shows the points on a coordinate plane.
What are Equivalent Ratios?The ratios that give the same value when we compare them together are regarded as equivalent ratios.
For example, 2:3 is an equivalent ratio to 4:6, because 4/6 can be simplified as 2/3.
If it cost $12 to toss 30 rings, the ratio of dollars to number of toss would be: 12:30 = 2:5.
Let x = number of toss
Let y = amount in dollars
The equation that models the equivalent ratios can be written as y = 2/5x.
Therefore, when we have 2 dollars (y = 2):
2 = 2/5(x)
10 = 2x
10/2 = x
x = 5 toss
When we have 45 tosses (x = 45):
y = 2/5(45)
y = 18 dollars
The table of equivalent ratios would be:
Toss Dollars
5 2
30 12
45 18
The points, (5, 2), (30, 12), and (45, 18) are shown on the coordinate axes in the diagram below, where y = dollars, and x = toss.
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The statement 4 less than a number is given w
The equation representing the statement - "4 less than a number is given w" as -
[w] = x where x ∈ (- ∞, 4)
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have the following statement - "4 less than a number is given w".
Assume the number to be [x].
We can write the equation representing the statement -
"4 less than a number is given w" as a mathematical expression as -
[w] = x where x ∈ (- ∞, 4)
Therefore, the equation representing the statement - "4 less than a number is given w" as -
[w] = x where x ∈ (- ∞, 4)
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The production of a gold mine decreases by 5% per year.
What is the approximate half-life for the production decline?
Based on this approximate half-life and assuming that the
mine's current annual production is 5000 kilograms, about
what will its production be in 10 years?
Answer:d
Step-by-step explanation:d
If [tex]y = \frac{(1 + x)u}{(1 + x)v} [/tex]
Find dy/dx
The value of dy/dx is ( v du/dx - u dv/dx)/v²
From the question, we have
y = (1+x)u/(1+x)v
y = u/v
dy/dx = d/dx(u/v)
d/dx(u/v) = ( v du/dx - u dv/dx)/v²
Derivatives:
A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial. In calculus, a function's derivative measures how sensitively its output value changes in response to changes in its input value.
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I can determine if a function is linear or
nonlinear.
4. Determine if the table represents a
linear or nonlinear function.
Answer:
1st Table : Linear
2nd Table : Non-Linear
Step-by-step explanation:
To determine if the function is Linear or not , we find the change in y with a certain change in x
So for the 1st Table:
When x changes from x = 2 to x = 4 increased by 2
Then y changes from y = 3 to y = 0 decreases by 3
When x changes from x = 4 to x = 6 increased by 2
Then y changes from y = 0 to y = -3 decreases by 3
Since change in y is the same for the same change in x , Then the Function is Linear
So for the 2nd Table:
When x changes from x = 1 to x = 2 increased by 1
Then y changes from y = 1 to y = 4 increased by 3
When x changes from x = 2 to x = 3 increased by 1
Then y changes from y = 4 to y = 9 increased by 5
Since change in y is not the same for the same change in x , Then the Function is Non-Linear
Glad to Help
The lifetimes of batteries created by a company are normally distributed with a
mean of 105 hours and a standard deviation of 12 hours. What percentage of these batteries will last between 90.6 and 109.8 hours?
Answer:
84.6
Step-by-step explanation:
What transformation takes the graph of f(z) - 4z +9 to the graph of g (z) = 4x+7?
translation 2 units right
translation 2 units left
translation 2 units down
translation 2 units up
The linear function g(z) = 4 · z + 7 is the result of applying the transformation rule g(z) = f(z) - 2 (Translation two units down) on the linear function f(z) = 4 · z + 9 . (Correct choice: C)
What transformation rule is used to transform a given function?
In this problem we find a linear function that is modified into another linear function by a transformation rule. We need to find if the function is modified by a horizontal translation, a vertical translation or a combined translation, that is, a combination of horizontal and vertical translations.
Horizontal translation
g(x) = f(x - k), where k > 0 for a translation in + x direction.
Vertical translation
g(x) = f(x) + k, where k > 0 for a translation in + y direction.
After a quick inspection, we notice that linear function f(z) = 4 · z + 9 is transformed into g(z) = 4 · z + 7 by using vertical translation 2 units down. Then, we find the following transformation formula:
g(z) = f(z) - 2
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Find the focus and the directrix of the parabola with the equation y = - 1/12 (x - 4) 2. (A) Focus = (4, -1), directrix is y = -5 (B) Focus = (4,2), directrix is y = 5 (C) Focus = (4,1), directrix is y = -5 (D) Focus = (4, -1), directrix is y = 5
The focus of parabola is (4 , -1) and directrix is 5
The general equation of a parabola is: y = a(x-h)²+ k or x = a(y-k)² +h, where (h ,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.
Focus: The point (a, 0) is the focus of the parabola
Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola.
Given equation of parabola is :
y = - 1/12 (x - 4) - 2
Comparing it with standard equation,
h = 4
k = 2
a = -1/12
using Focus: (h, k+ (1/4a)) and Directrix: y = k - 1/4a)
=> focus = (4 , 2+(12/4×-1))
=> focus = (4 , 2-3)
=> focus = (4 , -1)
and directrix is : y = 2-(1/4×-1/12)
y = 2 + 12/4
y=2 + 3 => 5
So, the focus is (4,-1) and directrix is 5
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If y vaires directly with x and y= 12 when x= 15. What is the value of x when
y=16?
The value of x=20, according to the given question.
What is meant by equation?
A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.
According to the given data in the question,
We know that y varies directly with x like that,
y=kx..................(1)
y=12 when x=15.
Now, we have to find the value of x when y=16.
Then, putting the given values of x & y in the eq. (1), and determine the value of k.
12=k(15)
[tex]k=12/15\\k=4/5\\[/tex]
Now, putting the value of k in the second statement in eq.(1), where only y's value is given.
[tex]16=\frac{4}{5}x\\ x=16*\frac{5}{4} \\x=20[/tex]
Hence, the value of x=20.
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i bet u cant solve it
For the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.
As given in the question,
Given :
Pair of parallel lines are AG and BH.
CF is the transversal.
Transversal CF intersect line AG at point D and
Transversal CF intersect line BH at point E
Four pair of corresponding angles
Two pair of alternate interior angles
Corresponding pair of angles in the pair of parallel lines are congruent.
∠ADE ≅ ∠BEF
∠ADE and ∠BEF are corresponding angles.
Therefore, for the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.
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Please help! Select the equation that represents the following linear graph:
Jasenio is shooting target practice with a bow and arrow. His target is a paper rabbit that runs along a track. The track is 50 meters away from Jasenio and he estimates that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him. At what true bearing should Jasenio aim his bow and arrow?
a) 3.49°
b) 11.31°
c) 78.46°
d) 78.69°
The true bearing at which Jasenio should aim his bow and arrow is; b) 11.31°
How to apply Trigonometric Ratios?
We have different trigonometric ratios such as;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
We are told the track is 50 meters away from Jasenio and that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him.
This means that there will be a right angle triangle formed with the height as 50 m and the base length as 10m. Thus, by trigonometric ratios, we have;
tan θ = 10/50
where θ is the true bearing angle. Thus;
tan θ = 0.2
θ = tan⁻¹0.2
θ = 11.31°
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Lightest weight
750g
0.7kg
7.5kg
705g
7.05kg
Answer:
.7 kg
Step-by-step explanation:
1. Convert answers in grams into kilograms
1000g = 1 kg
750g = .75kg
705g = .705 kg
2. Find smallest number of kg
= .7 kg
Please help me complete this flowchart proof. The correct answer gets brainiest
The flowchart that is used to prove GR ║ F_K is presented as follows;
∠RND and ∠FDP are supplementary ⇒ ∠RND + ∠FDP = 180°
Given [tex]{}[/tex] Definition of supplementary
∠KDN ≅ ∠FDP [tex]{}[/tex] ⇒ ∠KDN = ∠FDP
Vertical angles are congruent[tex]{}[/tex] Definition of congruent angles
∠RND and ∠KDN are same side interior angles [tex]{}[/tex] ⇒∠RND + ∠KDN = 180°
Definition of same side interior angles[tex]{}[/tex] Substitution property
[tex]{}[/tex] GR ║ F_K
Same side interior angles formed between parallel lines that have a common transversal are supplementaryWhat are the relationships between the angles formed between parallel lines that have a common transversal?The relationships between the angles formed by a transversal and two parallel lines are;
Corresponding angles are congruentSame side interior angles are supplementaryLinear pair angles are supplementaryVertical angles are congruentAlternate interior angles are congruentAlternate exterior angles are congruentDefinition of congruency;
Two lines, shape or figure are said to be congruent if they have the same size and shape.
Supplementary angles;
Supplementary angles are angles that have a sum of 180°
Substitution property of equality
The substitution property sates that if an expression a = b, then the expression b can replace a in any equation and the equation will remain valid.
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reduce 12/16 to simplest terms
Answer: 3/4
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 12 and 16 is 4
Divide both the numerator and denominator by the GCD
12 ÷ 4
16 ÷ 4
Reduced fraction: 3/4
Therefore, 12/16 simplified to lowest terms is 3/4.
Answer:.
Step-by-step explanation:
76 points and brainlist
The length of a bacterial cell is about 3 x 10−6 m, and the length of an amoeba cell is about 4.5 x 10−4 m. How many times smaller is the bacterial cell than the amoeba cell? Write the final answer in scientific notation with the correct number of significant digits.
2 x 102
2 x 103
0.7 x 101
6.67 x 102
Answer:
d the last one I think
Step-by-step explanation:
I am not really sure
Answer:
D.) 6.67 X 10^2
Instructions: Show that the conjecture is false by finding a counterexample. Change the value of n below in order to make it a counterexample. "Two supplementary angles are not congruent."
The counterexample for "Two supplementary angles are not congruent." is
angle 100° and angle 80° are supplementary angels
angle 90° and angle 90° are supplementary angels
The instances show supplementary angles that are not congruent
What is counter examples?A specific situation that demonstrates that a statement is untrue is referred to as a counterexample.
Counterexamples provides instances that opposes the statement
In this case the two supplementary angles 100-and-80 and 90-and-90 are not congruent and hence a counterexample to the statement
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Need help with question 2b please
Answer:
20 mph
Step-by-step explanation:
If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph
Dylan has a bag of 1256 rubber balls to hand out as prizes at a town festival. There are 13 games at the festival. About how many rubber balls should he give each game?
Answer The answer is 96 but as a fraction 96 8/13
Step-by-step explanation: There are 1256 rubber bands and 13 games to distribute them according to the problem; therefore, to divide to give an equal amount per each group for each game, you would give out 96 rubber bands each time, so 96 is the answer or 96 8/13.
The graph below shows the daily low temperatures for one week in New Orleans, Louisiana. The shape of the temperature graph can be modeled by the quadratic function f (x) = 3x² 18x + 56, where 2 is the number of days starting Sunday, and f (2) is the temperature in Fahrenheit. Degrees Fahrenheit 60 50 40 30 20 10 0 - Sun. Mon. Tues Wed. Thu. Fri. Sat. a. Use the given quadratic function to approximate the temperature on Thursday. How does this approximation agree with the graph? b. Use the function and the quadratic formula to find when the temperature is 35 degrees Fahrenhait. (Hint: Set f (x) = 35 and solve.) Round the answer to one decimal place and interpret the decimal in terms of weekday and military time.
a. The numeric value at Thursday -> x = 4 is of 32 degrees, which agrees with the graph.
b. A numeric value of 35 degrees Fahrenheit is obtained on Monday and on Thursday, also agreeing with the graph.
How to obtain the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
In this problem, the function is defined as follows:
f(x) = 3x² - 18x + 56.
Giving the temperature in degrees Fahrenheit in x days after Sunday.
The day that represents Thursday is given by:
x = 4.
Hence the temperature is the numeric value of the function at x = 4, replacing both instances of x on the function by 4, hence:
f(4) = 3(4)² - 18(4) + 56 = 32 ºF.
Which agrees with the graph, as the Thursday's bar is a value slightly above 30, which can be interpreted as 32.
The numeric value is of 35 when:
3x² - 18x + 56 = 35
The solutions to the quadratic equation are:
x = 1.6, x = 4.4.
Hence the days are:
Monday and Thursday.
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Simplify: 3√50+ √24 - 2√72
A. 3√6 +2√2
B. 3√9+2√5
C. 3√2+2√6
D. 10√2+2√6
Answer:
Step-by-step explanation:
13+(-3)^2+4(-3)+1- {-10-(-6)}
_________________________
[4+5}/ [4^2-3^2(4-3)-8]+12
15/3=5
The probability that a vehicle entering the Lu-
ray Caverns has Canadian license plates is 0.12; the
probability that it is a camper is 0.28; and the proba-
bility that it is a camper with Canadian license plates
is 0.09. What is the probability that
The conditional probability that a camper entering the Luray Caverns has Canadian license Plates is given by:
0.3214 = 32.14%.
What is Conditional Probability?Conditional probability is the probability of one event happening, considering the outcome of a previous event. The formula is given by the rule presented as follows:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
The probabilities that compose the formula are listed as follows:
P(B|A) is the probability of the event B happening, given that the event A has already happened.[tex]P(A \cap B)[/tex] is the probability of both the events, A and B, happening.P(A) is the probability of the event A happening.The events in this problem are given as follows:
Event A: Camper.Event B: Canadian license plates.The probabilities are given as follows:
P(A) = 0.28, P(A and B) = 0.09.
Hence the conditional probability is obtained as follows:
P(B|A) = P(A and B)/P(A) = 0.09/0.28 = 0.3214 = 32.14%.
Missing InformationThe probability asked is that a camper entering the Luray Caverns has Canadian license Plates.
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