Answer: The probability of choosing a sophomore on the first draw is 125/512. Since the selection is random and without replacement, the probability of choosing another sophomore on the second draw is 124/511. Therefore, the probability of choosing two sophomores in a row is:
(125/512) x (124/511) = 0.0603 or approximately 0.06 (rounded to two decimal places).
Step-by-step explanation:
A bird flies from the bottom of a canyon that is 72 1/2 feet below sea level to a nest that is 719 2/5 feet above sea level. What is the difference in elevation between the bottom of the canyon and the bird's nest?
Answer:
The difference in elevation between the bottom of the canyon and the bird's nest is the sum of the depths, which is:
72 1/2 + 719 2/5
To add these two mixed numbers, we first convert them to improper fractions:
72 1/2 = 145/2
719 2/5 = (3595/5) + (2/5) = 3597/5
Now we can add them:
145/2 + 3597/5
To add fractions with different denominators, we need to find a common denominator. The smallest common multiple of 2 and 5 is 10, so we can rewrite the fractions with a denominator of 10:
145/2 × 5/5 = 725/10
3597/5 × 2/2 = 7194/10
Now we can add the fractions:
725/10 + 7194/10 = 7929/10
Finally, we can simplify the fraction and convert it back to a mixed number:
7929/10 = 792 9/10
Therefore, the difference in elevation between the bottom of the canyon and the bird's nest is 792 9/10 feet.
A rocket is launched from the top of a 200-foot tall cliff with an initial velocity of 120 feet per second. The height, h, of the rock at time t seconds after it was launched can be modeled by the equation h = -16t2 + 120t + 200. Once the rocket reaches its maximum height, how long will it take to reach the ground? Round to the nearest tenth of a second.
By answering the above question, we may infer that The rocket will thus equation touch down 2.5 seconds after it was fired (to the nearest tenth of a second).
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Hence, we may solve for t by setting the equation for h equal to 0:
[tex]-16t^2 + 120t + 200 = 0\\2t^2 - 15t - 25 = 0\\(-b \sqrt(b2 - 4ac)) / 2a[/tex]
where a=2, b=15, and c=25
[tex]t = (15 \sqrt(625)) / 2(2) (-(-15) \sqrt((-15)2 - 4(2)(-25))) / 4\st = (15 + 25) / 4[/tex]
T thus equals 10/2 or -5/2. Time cannot be negative, thus we may ignore the negative number.
The rocket will thus touch down 2.5 seconds after it was fired (to the nearest tenth of a second).
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(1 point) Find the angleαin radians between the vectors[−12] and [6−1]α=
The angle between the vectors "[−12] and [6−1]α" is approximately 2.03 radians.
To find the angle between the vectors, we can use the formula:
cos(α) = ([tex]V{1}[/tex] • [tex]V{2}[/tex]) / (||[tex]V{1}[/tex]|| ||[tex]V{2}[/tex]||)
Where v1 and v2 are the two vectors, and ||[tex]V{1}[/tex]|| and ||[tex]V{2}[/tex]|| are the magnitudes of the vectors.
For the given vectors:
[tex]V{1}[/tex] = [−1 2] and [tex]V{2}[/tex] = [6 −1]
[tex]V{1}[/tex]• v2 = (−1)(6) + (2)(−1) = −6 + −2 = −8
||[tex]V{1}[/tex]|| = √((-1)^2 + 2^2) = √(5)
||[tex]V{2}[/tex]|| = √(6^2 + (-1)^2) = √(37)
cos(α) = (−8) / (√(5) √(37)) = −8 / √(185)
α = cos^-1(−8 / √(185))
α ≈ 2.03 radians
Therefore, the angle between the vectors is approximately 2.03 radians.
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PLLLEASEEEEEE HELLLLPPPPPPPPPPPPPPPPPP
Answer: D, 912
Step-by-step explanation:
g(21) = 24 (21 + 17)
g(21) = 24 x 38
g(21) = 912 (Use your calculator for this part)
Slope intercept I need help
From the top of a cliff, the angle of depression of a boat on the sea is 60°. If the top of the cliff is 25m above the sea level, calculate the horizontal distance from the bottom of the cliff to the boat.
3. The bottom of a ramp is 15 feet from the entrance of a building. If the angle of the ramp is
about 3.2°, about how high does the ramp rise off the ground to the nearest inch?
The ramp rises about 10.4 inches off the ground to the nearest inch.
What is ramp ?A ramp is an inclined plane that connects two different levels, allowing people or objects to move between them with less force than if they had to be lifted vertically.
We can use trigonometry to solve this problem. Let's call the height of the ramp "h". Then we have:
tan(3.2°) = h/15
To solve for h, we can multiply both sides by 15:
h = 15 tan(3.2°)
Using a calculator, we get:
h ≈ 0.87 feet
To convert this to inches, we can multiply by 12:
h ≈ 10.4 inches
So, the ramp rises about 10.4 inches off the ground to the nearest inch.
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Andrew
collects coins
.
He collected a total of 275
coins
.
If 68
%
of the coins
he collected were foreign, how many other coins
did he collect?
Answer:
88
Step-by-step explanation:
METHOD 1:
Find 68% of 275:
275 * 0.68 = 187
Subtract 187 from the total:
275 - 187 = 88 coins
METHOD 2:
100% - 68% = 32%
Find 32% of total:
275 *0.32 = 88 coins
Consider the following inequality: |x+4|-1>=0 Step 1 of 2 : Solve the absolute value inequality and express the solution in interval notation and algebraic notation.
The solution of the absolute value inequality is (-∞,-5] U [-3,∞) in interval notation and x ≥ -3 or x ≤ -5 in algebraic notation.
Step 1: To solve the absolute value inequality, we need to isolate the absolute value expression on one side of the inequality. We can do this by adding 1 to both sides of the inequality:
|x + 4| ≥ 1
Step 2: Now, we can split the inequality into two separate inequalities:
x + 4 ≥ 1 and x + 4 ≤ -1
Step 3: Solve each inequality for x:
x ≥ -3 and x ≤ -5
Step 4: Express the solution in interval notation and algebraic notation. In interval notation, the solution is (-∞,-5] U [-3,∞). In algebraic notation, the solution is x ≥ -3 or x ≤ -5.
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Find a linear function h given h(−3)=−4 and h(−9)=−5. The linear function is h(x)= (Simpliky your answer. Use integers or fractions for any numbers in the espression)
To find a linear function h(x) given two points, we can use the formula for the slope of a line:
m = (y2 - y1) / (x2 - x1)
Where m is the slope, (x1, y1) and (x2, y2) are the two points.
In this case, the two points are (-3, -4) and (-9, -5). Plugging in the values into the formula, we get:
m = (-5 - (-4)) / (-9 - (-3))
m = (-1) / (-6)
m = 1/6
Now that we have the slope, we can use the point-slope form of a linear equation to find the function h(x):
y - y1 = m(x - x1)
Plugging in the slope and one of the points, we get:
y - (-4) = (1/6)(x - (-3))
y + 4 = (1/6)(x + 3)
y = (1/6)x + 3/6 - 4
y = (1/6)x - 21/6
Simplifying the equation, we get:
y = (1/6)x - 7/2
Therefore, the linear function h(x) is:
h(x) = (1/6)x - 7/2
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Its a screen shot
right down there its for math
Answer:
Step-by-step explanation:
2-Bs: 4 x 3.8 = 15.2 2 x 15.2 = 30.4 m²
2-Cs: 11.5 x 3.8 = 43.7 2 x 43.7 = 87.4 m²
Total S.A. = 92 + 30.4 + 87.4 = 209.8 m²
Answer: 2.98m squared i think im not sure im just guessing im still not fully awake yet bro.
Step-by-step explanation:
Name the property illustrated.
5(√3+2) = 5√3+10
Answer:
Distributive property
Step-by-step explanation:
In this problem, you are distributing the 5 to both the [tex]\sqrt{3}[/tex] and the 2. Therefore, the answer is the distributive property
Answer: Distributive property.
Step-by-step explanation: The initial terms are being multiplied by 5 into both terms and they are equivalent by the distributive properly.
Please Mark Brainliest!
Solve the following system of equations:
2x-6y+9z=-8
5x+y+2z=10
3x+y-8z = -28
(Please add an explanation for better understanding.)
I've been working on this for a week and I can't figure it out...
Answer:
This
Step-by-step explanation:
( x y z) = (-1,7,4) explanation is big
solve the absolute value equation or indicate that the equation
has no solution.
|2x-1|=9
The equation has two solutions:[tex]x=5[/tex] and [tex]x=-4[/tex].
To solve an absolute value equation, we need to consider both the positive and negative solutions. We can do this by setting up two separate equations and solving each one individually.
The first equation is:
[tex]2x-1 = 9[/tex]
We can solve for x by isolating the variable on one side of the equation:
[tex]2x = 10[/tex]
[tex]x = 5[/tex]
The second equation is:
[tex]2x-1 = -9[/tex]
We can also solve for [tex]x[/tex] in this equation:
[tex]2x = -8[/tex]
[tex]x = -4[/tex]
Therefore, the solution to the absolute value equation[tex]|2x-1|=9[/tex] is [tex]x=5[/tex] or [tex]x=-4[/tex].
In conclusion, the equation has two solutions: [tex]x=5[/tex] and [tex]x=-4[/tex].
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FOR THE FOLLOWING TABLE ANSWER THESE PROBABILITY QUESTIONS MATH(M) ENGLISH(E) HISTORY(H) BIOLOGY(B) TOTALS 15 22 13 18 68 FRESHMAN(F) SOPHOMORE(S) 14 20 29 16 79 18 15 23 22 78 JUNIOR(J) SENIOR(SE) 26 10 8 24 68 TOTALS 73 67 73 80 293 1. FIND P(MUF) = 2. FIND (B) = 3. FIND (E/)) = 4. FIND (ENS) 5. FIND (MUJUH) = FIND P(SEUM) = 7. FIND P(F/B) = 8. FIND P(AUB), IF P(A)=.4 AND P(B)= 35 AND P(A) AND P(B) ARE INDEPENDENT 9. IF YOU NEED TO PICK 5 NUMBERS OUT OF 30 TO WIN A LOTTERY AND ORDER DOES NOT MATTER WHAT IS YOUR CHANCE OF WINNING ON THE FIRST TRY 10. WHAT IF ORDER OF THE NUMBERS YOU CHOOSE MATTERS? WHAT IS THE PROBABILITY THEN? =
The probability of winning on the first try is 0.000003426 .
P(MUF) = P(M) + P(F) - P(M and F) = 73/293 + 79/293 - 14/293 = 138/293
P(B) = 80/293
P(E/S) = P(E and S)/P(S) = 20/293 / 78/293 = 20/78 = 10/39
P(ENS) = P(E and S and N) = 0 (since there is no N category in the table)
P(MUJUH) = P(M and J and H) = 0 (since there is no intersection of all three categories in the table)
P(SEUM) = P(SE and M) = 10/293
P(F/B) = P(F and B)/P(B)
=> 16/293 / 80/293
=> 16/80
=> 1/5
P(AUB) = P(A) + P(B) - P(A and B)
=> .4 + .35 - (.4 * .35)
=> .595
If order matters, the probability is
(5/30) * (4/29) * (3/28) * (2/27) * (1/26) * 5!
=> 0.00002056
The probability of winning on the first try is
(5/30) * (4/29) * (3/28) * (2/27) * (1/26)
=> 0.000003426
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I need help this due today
The required with the help of trig ratios we have,
1. x = 30.69
2. x =23.21
4. angle T = 61.42°
5. angle T = 28.5°
If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
1.
Apply the sine rule,
Sin21 = perpendicular/hypotenus
sin21 = 11 / x
x = 11/sin21
x = 30.69
Similarly,
2. x =23.21
4. angle T = 61.42°
5. angle T = 28.5°
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Rates and Unit Rates
Use ratios to solve.
3
-
Tyler reads page per minute.
4
What is the ratio of pages to minutes?
How many pages will he read in 16 minutes?
Tyler has to read 24 pages for homework.
How long will it take him to read 24 pages?help me pls
The ratio of pages to minutes is 3:4. If he read 16 minutes, then the number of pages is 12 pages. And Tyler has to read 24 pages for homework. Then the number of minutes is 32 minutes.
What is the ratio?The utilization of two or more additional numbers that compares is known as the ratio.
Tyler reads 3/4 pages per minute. Then the ratio of pages to minutes is given as,
Ratio = (3/4) / 1
Ratio = 3: 4
If he read 16 minutes, then the number of pages is calculated as,
⇒ (3/4) x 16
⇒ 3 x 4
⇒ 12 pages
Tyler has to read 24 pages for homework. Then the number of minutes is given as,
⇒ 24 / (3/4)
⇒ 24 x (4/3)
⇒ 8 x 4
⇒ 32 minutes
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3 = Problem 3. Given the vectors ū and ✓ find the vector w = 4ữ - 5 (in coordinates), and its magnitude | W |. Use exact values; assume mile as the length unit. (-1) 2 Problem 4. Let O be an angle in standard position, such that the point P(-15, 8) is on its terminal side. Find the exact values of all the six trigonometric functions of 0.
Given vectors ū = (u1, u2) and ✓ = (v1, v2), we can find vector w = 4ữ - 5✓ by using the formula:
w = (4u1 - 5v1, 4u2 - 5v2)
To find the magnitude of vector w, we can use the formula:
|w| = √((4u1 - 5v1)² + (4u2 - 5v2)²)
Since we do not have the exact values of u1, u2, v1, and v2, we cannot compute the exact values of w and |w|.
w = (4u1 - 5v1, 4u2 - 5v2), |w| = √((4u1 - 5v1)² + (4u2 - 5v2)²)
Problem 4:
Given the point P(-15, 8) on the terminal side of angle O in standard position, we can find the values of the six trigonometric functions of O using the following formulas:
sin O = y/r
cos O = x/r
tan O = y/x
csc O = r/y
sec O = r/x
cot O = x/y
Where x = -15, y = 8, and r = √(x² + y²) = √((-15)² + 8²) = √(225 + 64) = √289 = 17
Therefore, the exact values of the six trigonometric functions of O are:
sin O = 8/17
cos O = -15/17
tan O = -8/15
csc O = 17/8
sec O = -17/15
cot O = -15/8
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Convert these polar coordinates to rectangular coordinates. Make sure to show your work.
a.) (2, 3pi/2)
b.) (1, 5pi/6)
The rectangular coordinates of the polar coordinates are as follows:-
a) x = 0 and y = ( -2 )
b) x = ( -√3/2 ) and y = 1
How to convert these polar coordinates to rectangular coordinates?To convert these polar coordinates to rectangular coordinates, we calculate the following,
a) ( 2, 3π/2 ) :
r=2 ; θ = 3π/2
x = r * cosθ
x = 2 * cos( 3π/2 )
x = 2 * 0
Therefore, x = 0
y = r * sinθ
y = 2 * sin( 3π/2 )
y = 2 * ( -1 )
Therefore, y = ( -2 )
b) ( 1, 5π/6 ) :
r = 1 ; θ = 5π/6
x = r * cosθ
x = 1 * cos( 5π/6 )
x = 1 * ( -√3/2 )
Therefore, x = ( -√3/2 )
y = r * sinθ
y = 2 * sin( 5π/6 )
y = 2 * ( 1/2 )
Therefore, y = 1
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An economist is interested in testing the significance of the correlation between two variables. A sample of data of size 40 is collected and the sample correlation coefficient is 0.4165. What decision does the economist make, if the test is performed at the 5% level of significance?
a. The test statistic has the value 2.824 and hence the correlation is significant
b. The test statistic has the value 3.361 and hence the correlation is significant
c. The test statistic has the value 2.824 and hence the correlation is not significant
d. none of the above
The correct answer is Option c. The test statistic has the value 3.361 and hence the correlation is significant. Since the test statistic (2.824) is lower than the critical value (2.824), the correlation is not significant.
The sample correlation coefficient, r, estimates the population correlation coefficient, ρ. It indicates how closely a scattergram of x,y points cluster about a 45° straight line.
The test statistic has the value 2.824 and hence the correlation is not significant. To test the significance of the correlation, the economist needs to compare the sample correlation coefficient to the critical value of the correlation coefficient. In this case, the critical value of 0.4165 with a sample size of 40 and a 5% level of significance is 2.824.
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10 • e^3x=250
I need to show work
Therefore , the solution of the given problem of expressions comes out to be x = 1.0730 is roughly the answer to the equation 10*e(³ˣ) = 250.
What does an expression precisely mean?When variables are shifting, estimates should be created that mix joining, disabling, and instead of randomly dividing. They could answer a puzzle collectively, offer some information, and instead software. Formulas, elements, and mathematical operations like addition, subtraction, grouping, and combination are all found in a statement of truth. Words and sentences can both be evaluated and analysed.
Here,
In order to find x in the equation 10*e(3x) = 250, we can start by dividing both parts by 10 to isolate the exponential term:
=> e³ˣ = 25
The exponential can then be removed by taking the natural logarithm (ln) of both sides:
=> ln(e(³ˣ) = ln(25)
We can simplify the left half by using the fact that ln(ey) = y:
=> 3x = ln(25)
By multiplying both parts by 3, we can finally find the value of x:
=>x = (1/3) * ln(25)
We can use a computer to determine that the value of ln(25) is roughly 3.2189. Therefore:
=> x ≈ (1/3) * 3.2189
=> x ≈ 1.0730
So x = 1.0730 is roughly the answer to the equation 10*e(³ˣ) = 250.
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Can someone please help ?
Answer:
Height = 8
Volume = 48
Step-by-step explanation:
(4x4)x3 = 48
What is the volume of 9/5x2/3
The volume of 9/5x2/3x is 2/15.
What is volume?Volume is the amount of space an object or substance occupies or contains. It is measured in three-dimensional space and is often given in cubic units such as cubic centimeters, cubic meters, and cubic millimeters. Volume is an important concept in physics, chemistry, and other sciences, and is used to describe the size of all kinds of substances, from solids, liquids, and gases to particles and energy fields. Volume is also used to compare the relative sizes of different objects, and to measure the capacity of containers.
To calculate this, we first need to multiply 9/5 and 2/3 together. This gives us 18/15. Then, we multiply this by x. This gives us 2/15x. Therefore, the volume of 9/5x2/3x is 2/15.
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Find the geometric mean for 64 and 25
Answer:
40
Step-by-step explanation:
The geometric mean will equal the square root of the product of the two numbers.
√64 * √25
8 * 5 = 40
The ratio of raisins to al monds.
is 2:10.
What is the percent of the raisins in this
mix of raisins and almonds?
Answer:16.67%.
Step-by-step explanation:
The ratio of raisins to almonds is 2:10, which can be simplified to 1:5.
This means that for every 6 parts of the mix, 1 part is raisins.
To find the percentage of raisins in the mix, we need to divide the amount of raisins by the total amount of mix, and then multiply by 100 to convert to a percentage.
So if we let x be the total amount of mix (in any unit of measurement), then the amount of raisins is (1/6)x.
The percentage of raisins in the mix is:
[(1/6)x / x] x 100% = 16.67%
Therefore, the percent of the raisins in the mix is 16.67%.
What is the missing angel
The missing angle as labelled in the task content and required to be determined is; 33°.
What is the measure of the missing angle?It follows from the task content that the missing angle is to be determined from the task content.
By the use of trigonometric ratios;
The missing angle, x can be determined as follows;
tan (x) = 9.09 / 14
x = tan-¹ (9.09/14).
x = 32.995°
The missing angle is therefore; 33°.
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-7x + 6y = 34
7x+ 4y =-24
Answer:
x= -4
y=1
Step-by-step explanation:
-7x + 6y = 34
7x+ 4y =-24
You would add them up together
-7 +7x cancels out. 6y+4y = 10y
34+ (-)24 = 34 - 24 = 10
y= 1
substitute y
7x + 4 = -24
7x= -28
x=-4
Step-by-step explanation:
what is the question ?
to solve this system of 2 equating in 2 variables ?
if so, we start by adding both equations :
-7x + 6y = 34
7x + 4y = -24
----------------------
0 + 10y = 10
y = 1
with that we go into one of the original equations (it did not matter which one, I like the second better) :
7x + 4×1 = -24
7x + 4 = -24
7x = -28
x = -4
Set up (do not solve ) the partial fraction decomposition for (4x-3)/(x^(2)(x+3)(x^(2)+2x+9)(x^(2)+1)^(3)).
To find the values of these constants, we need to multiply both sides of the equation by the denominator of the original fraction and then equate the numerators. This will give us a system of equations that we can solve for the constants.
The partial fraction decomposition for the given fraction is:
(4x-3)/(x^(2)(x+3)(x^(2)+2x+9)(x^(2)+1)^(3)) = A/x + B/x^(2) + C/(x+3) + D/(x^(2)+2x+9) + E/(x^(2)+1) + F/(x^(2)+1)^(2) + G/(x^(2)+1)^(3)
Where A, B, C, D, E, F, and G are constants that need to be determined.
To find the values of these constants, we need to multiply both sides of the equation by the denominator of the original fraction and then equate the numerators. This will give us a system of equations that we can solve for the constants.
However, since the question only asks to set up the partial fraction decomposition, we do not need to solve for the constants at this time.
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A
radio transmission tower is 578 feet tall. A guy wire is to be
attached 6 feet from the top and is to make an angle of 20° with
the ground? How many feet long should the guy wire be? Round your
ans
The guy wire's length should be approximately 120.5 feet.
To find out, we can use trigonometry. The guy wire, the tower, and the ground form a right triangle, with the guy wire as the hypotenuse. We know the angle between the guy wire and the ground (20°), and we know the height of the tower (578 feet). We want to find the length of the guy wire. Using the trigonometric function tangent, we can set up the following equation:
tan(20°) = 578 / (guy wire length - 6)
Solving for the guy wire length, we get:
guy wire length = 578 / tan(20°) + 6
guy wire length ≈ 120.5 feet
Therefore, the guy wire should be approximately 120.5 feet long.
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Edgar and his older sisters, Anne and Maya, are going to visit their grandmother. Edgar is too young to drive, so Anne and Maya each drive the same amount of time to complete the 5-hour trip.
How long does each of Edgar's sisters drive?
Write your answer as a proper fraction or mixed number.
Anne and Maya drive for 2 1/2 hours.
What is mixed fraction?A mixed fraction is a combination of a whole number and a proper fraction. For example, 2 1/3 is a mixed fraction, where the whole number is 2 and the proper fraction is 1/3.
To convert an improper fraction into a mixed fraction, Divide the numerator by the denominator and write down the whole number result as the whole number part of the mixed fraction.
Write down the remainder as the numerator of the fractional part of the mixed fraction.
Here we have
Anne and Maya each drive the same amount of time to complete the 5-hour trip.
Let both of them be derived for 'x' hours
=> x + x = 5 hours
=> 2x = 5 hours
=> x = 5/2
Hence, Anne and Maya drive for 5/2 hours
Here 5/2 can be converted as 2 1/2
Therefore,
Anne and Maya drive for 2 1/2 hours.
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