if a triangle has lengths of 27 m and 11 m, check all the possible lengths for the third side

Answer:

29/100 (Every 100 students, 29 more students like cats than dogs)

Step-by-step explanation:

First we need to put these numbers in fractions

The fraction that represents students that like dogs is 9/25

The fraction that represents students that like cats is 13/20

Now, we just need to subtract the fraction of cats by the fraction of dogs:

13/20 - 9/25

To do that, we need to make the denominators equal. We do that making multiplying the first fraction by 5 and the second by 4, so we have:

13/20 = 65/100

9/25 = 36/100

Then, subtracting then, we have:

65/100 - 36/100 = 29/100

So every 100 students, 29 more students like cats than dogs.

Answer:

B. [tex](1,-5)[/tex]

Step-by-step explanation:

We have been given a system of equations. We are asked to choose the ordered par that is the solution to the given system.

[tex]y=-7x+2...(1)[/tex]

[tex]y=9x-14...(2)[/tex]

To solve our given system, we will equate both equations as:

[tex]9x-14=-7x+2[/tex]

Combine like terms:

[tex]9x+7x-14+14=-7x+7x+2+14[/tex]

[tex]16x=16[/tex]

[tex]x=\frac{16}{16}=1[/tex]

Upon substituting [tex]x=1[/tex] in equation (1), we will get:

[tex]y=-7(1)+2\\\\y=-7+2\\\\y=-5[/tex]

Therefore, the ordered pair [tex](1,-5)[/tex] is the solution of the given system and option B is the correct choice.

Answer:

mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm its b

Step-by-step explanation:

Answer:

Step-by-step explanation:

#using java

Double result;

public Double half(Double number){

return number/2;

}

result=half(number);

Final answer:

The function named 'half' is demonstrated using C++ code, where it takes a double as an argument and returns its half. The provided example shows how to define and use the function in a program.

Explanation:

The student's question involves writing a function in a programming language that effectively halves the value of the passed argument. This is a common task in programming, particularly in languages like C++, Java, or Python. Let's consider a simple function in C++ for illustrative purposes.

Example of a half function in C++:

double half(double number) {
   return number / 2.0;
}

This function, half, takes a double (a data type that stores floating-point numbers) as an argument and returns a value that is half of the argument's value. It is important to note that double variables store finite approximations of real numbers and usually have a precision of about 17 significant digits in most computing environments.

To use this function, you would write the following code in your main program:

double number = 10.0; // or any other value
double result = half(number);
std::cout << result; // This will output 5.0

Understanding the code:

When invoked, the function will return half of the input value, effectively operating as number / 2.0.

Answer:

36 π square feet

Step-by-step explanation:

so the formula for area of a circle is  πr^2

so the radius is 6, which we can just plug in

π(6)^2

36π

so option 3

Answer:

[tex]A = 640000\,yd^{2}[/tex]

Step-by-step explanation:

Expression for the rectangular area and perimeter are, respectively:

[tex]A (x,y) = x\cdot y[/tex]

[tex]3200\,yd = 2\cdot (x+y)[/tex]

After some algebraic manipulation, area expression can be reduce to an one-variable form:

[tex]y = 1600 -x[/tex]

[tex]A (x) = x\cdot (1600-x)[/tex]

The first derivative of the previous equation is:

[tex]\frac{dA}{dx}= 1600-2\cdot x[/tex]

Let the expression be equalized to zero:

[tex]1600-2\cdot x=0[/tex]

[tex]x = 800[/tex]

The second derivative is:

[tex]\frac{d^{2}A}{dx^{2}} = -2[/tex]

According to the Second Derivative Test, the critical value found in previous steps is a maximum. Then:

[tex]y = 800[/tex]

The maximum area is:

[tex]A = (800\,yd)\cdot (800\,yd)[/tex]

[tex]A = 640000\,yd^{2}[/tex]

Answer:

74/4= 18.5

Step-by-step explanation:

Answer: The answer should be C!

Step-by-step explanation:

I took the quiz

The pair of coordinates which is not a solution to the system of inequalities is; Choice C: (-3, 3).

The area under the shaded region of the graph of the system of inequalities contains all feasible solutions of the system of inequalities.

In essence, the coordinate (-3, 3) is the point which is not a solution of the system of inequalities.

This is so because it doesn't fall under the shaded area.

This is due to the broken horizontal line; y < 3.

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The formula for arc length is s=r*angle theta where s is the arc length, r is the radius, and angle theta is central angle formed by the arc in radians.

In this case, the angle would be s/r or 4.2/4  which is 1.05 radians. We have to convert this into degrees and so you would multiply 1.05 by (180/pi) which results in approximately 60 degrees. Remember, if you want to convert radians into degrees, the conversion factor is 180/pi and for degrees into radians, it is pi/180.

Answer:

Step-by-step explanation:

Length of a circular arc is given by:

S = rФ

where Ф is the angle in radians subtended at the center by the arc.

Ф = S/r = 4.2 / 4 = 1.05 radians = (1.05*180)/π = 60.16° ≅ 60°

Measure of minor arc AB is 60°

Answer:

  d = (21√13)/130 ≈ 0.582435

Step-by-step explanation:

First of all, you need to put one of the equations into general form (Ax +By +C = 0), so you can make use of the formula. Multiplying the first equation by 6, we have ...

  6y = -4x -3

Adding the opposite of the right side, we have the general form equation ...

  4x +6y +3 = 0

___

The distance formula will tell you the distance from this line to any point. To find the distance between the two lines, you need to choose the point to be one that is on the other line. It is probably convenient to use the y-intercept, (0, 1/5).

The formula is ...

  d = |4x +6y +3|/√(4²+6²)

The distance from the point (0, 1/5) is ...

  d = |4·0 +6(1/5) +3|/√52 = 4.2/(2√13)

  d = (21/130)√13 . . . . . with denominator rationalized

_____

Alternate solution

Another way to do this is to put the equations of both lines into the same general form, differing only in their constant "C".

Multiplying both equations by 30, we get ...

  30y = -20x -15

  30y = -20x +6

So, the two general form equations are ...

  20x +30y +15 = 0

  20x +30y -6 = 0

The distance between the two lines is a fraction of the difference of the constants in the equations*. It will be ...

  |15 -(-6)|/√(20² +30²) = 21/√1300 = 21/(10√13) = (21√13)/130 . . . . as above

___

* Any (x, y) pair that satisfies the first equation will make 20x+30y = -15. Using the second equation in the distance formula, you then have |-15-6|/√( ) = d. The number in the numerator is the difference of the two constants "C".

Answer: The same trip will require 3.8 hours.

Step-by-step explanation:

Since we have given that

Time = [tex]4\dfrac{1}{2}=\dfrac{9}{2}[/tex]

Speed = 55 mph

So, distance would be

[tex]Speed\times time=55\times 4.5=247.5\ miles[/tex]

If the speed limit = 65 mph

So, time will be

[tex]\dfrac{247.5}{65}=3.8\ hours[/tex]

Hence, the same trip will require 3.8 hours.

Answer:

26

Step-by-step explanation:

The diameter of the wheel is 29 in.

The circumference of the wheel is 3.14 × 29 in = 91.06 in.

For each revolution, the bike moves forward one circumference.  So the number of revolutions is (200 ft × 12 in/ft) / 91.06 in ≈ 26.

Answer:

0.56

Step-by-step explanation:

There are 14 girls, and a total of 25 students.  So the probability of selecting a girl is P = 14/25 = 0.56.

The probability of calling on a girl will be 0.56. The correct option is C.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.

The probability of calling on a girl can be calculated by dividing the number of girls by the total number of students in the class:

Probability of calling on a girl = Number of girls / Total number of students

Number of girls = 14

Total number of students = 11 + 14 = 25

Therefore, the probability of calling on a girl is:

Probability of calling on a girl = 14 / 25 = 0.56

So, the correct answer is (c) 0.56.

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Answer:

[tex]x > - 3[/tex]

Step-by-step explanation:

[tex] - 18 < 5x - 3 \\ \Leftrightarrow 5x > - 15 \\ \Leftrightarrow x > - 3[/tex]

Answer: 275 cm squared

Step-by-step explanation: We need to divide the shapes first into smaller areas, and since all the areas we need are given to us, we just need to break it apart into smaller parts that we can find the area for.

Length x Width = Area

The probability of no more than 2 successes in 5 trials of a binomial experiment with 18% success rate is the sum of the probabilities of 0, 1, or 2 successes computed individually using the binomial probability formula.

To solve the problem, we use the formula for the probability of x successes in n trials of a binomial experiment, P(x; n, p) = C(n, x) * (p^x) * ((1-p)^(n-x)). 'P' represents the probability of success on a single trial (18% = 0.18 in this case), 'n' is the number of trials (5), 'x' is the number of successes. The symbol C(n, x) stands for the combination of n items taken x at a time.

So, we are looking for the probability of 0, 1, or 2 successes. We then add those three probabilities together:

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Answer:

Step-by-step explanation:

There are total 5 types of sampling.

Since, in the given question the students are chosen randomly, Random sampling is being used here.

Answer:

Each of these is based on the principle of difference of two squares where:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

Step-by-step explanation:

1.[tex](2a + *)(2a - *) = 4a^2-b^2[/tex]

[tex]4a^2-b^2=(2a)^2-b^2=(2a+b)(2a-b)[/tex]

2. [tex](*- 3x )(*+3x) = 16y^2-9x^2[/tex]

[tex]16y^2-9x^2=(4y)^2-(3x)^2=(4-3x)(4+3x)[/tex]

3. [tex]100m^4-4n^6 = (10m^2-*)(*+10m^2)[/tex]

[tex]100m^4-4n^6 = (10m^2-(2n^3)^2)= (10m^2-2n^3)(2n^3+10m^2)[/tex]

4. [tex]m^4-225c^{10} = (m^2-*)(* +m^2)[/tex]

[tex]m^4-225c^{10} =(m^2)^2-(15c^5)^2= (m^2-15c^5)(15c^5 +m^2)[/tex]

Answer:

Therefore the length of aluminum surrounding the pool is 88 feet.

Step-by-step explanation:

Circle:

Given that the circular swimming pool has walls made of aluminum.

To find out the length of the of aluminum, we need to find out the circumference of the pool.

The radius of the circular pool is = 14 feet.

Therefore the circumference of the pool is =[tex]2\pi r^2[/tex]

                                                                       [tex]=2\times \frac{22}{7} \times 14[/tex]  feet

                                                                     =88 feet

Therefore the length of aluminum surrounding the pool is 88 feet.

Answer:

41

Step-by-step explanation:

There are 3 times as many used bike as new bike.  For the problem to work you have to include the used bikes and the new bikes.  So you divide 164 by 4 instead of three.

So 164/3=41

Number of new bike in showroom is 41 bikes.

Given that;

Total number of bikes in showroom = 164 bikes

3 times Number of new bike = Number of old bikes

Find:

Number of new bikes in showroom

Computation:

Assume;

Number of new bike = a

So,

Number of old bike = 3a

So,

a + 3a = 164

4a = 164

a = 41

So,

Number of new bike = 41

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When subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45, subtract each corresponding term: a^2 terms, a terms and constant terms. The result is 12a^2 - 9a - 36.

To subtract one polynomial from another, we simply subtract the corresponding terms. In the given problem, we are subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45. Let's subtract term by term:

So, the result of the subtraction is 12a^2 - 9a - 36.

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Answer:

24p8 - 36p6 + 36p2 = 48p

Step-by-step explanation:

I hope this helps!

Answer:

The system

6*x  - 3*y  =  6

8*x  -  9*y  =  - 22

Solution:

x = 4

y = 6

Step-by-step explanation:

We have:

"x" number of points for a goal

"y" number of points for a penalty

Then according to problem statement, we get the two equation system

Clare       6*x  - 3*y  = 6       And

Hoah      8*x  -  9*y  =  - 22

If we are going to solve it, we can:

6*x  - 3*y  =  6      ⇒    2*x  - y  = 2

                              8*x  -  9*y  =  - 22

y = 2*x - 2

8*x  - 9 *( 2*x -2)  =  - 22    ⇒    8*x - 18*x + 18  =  - 22

-10*x = - 40       x = 4

And then  y =  2*x - 2      ⇒   y  =  8 - 2    ⇒  y  = 6

Answer:

The area of the rectangle is increasing at a rate of  [tex]22\ cm^2/s[/tex].

Step-by-step explanation:

Given : The width of a rectangle is increasing at a rate of 2 cm/ sec. While the length increases at 3 cm/sec.

To find : At what rate is the area increasing when w = 4 cm and I = 5 cm?

Solution :

The area of the rectangle with length 'l' and width 'w' is given by  [tex]A=l w[/tex]

Derivative w.r.t  't',

[tex]\frac{dA}{dt}=w\frac{dl}{dt}+l\frac{dw}{dt}[/tex]

Now, we have given

[tex]\frac{dl}{dt}=3\ cm/s[/tex]

[tex]l=5\ cm[/tex]

[tex]\frac{dw}{dt}=2\ cm/s[/tex]

[tex]w=4\ cm[/tex]

Substitute all the values,

[tex]\frac{dA}{dt}=(4)(3)+(5)(2)[/tex]

[tex]\frac{dA}{dt}=12+10[/tex]

[tex]\frac{dA}{dt}=22\ cm^2/s[/tex]

Therefore, the area of the rectangle is increasing at a rate of  [tex]22\ cm^2/s[/tex].

The area of rectangle is increasing at rate of 22 cm/ second.

Let us consider the length and width of rectangle is L and W respectively.

Given that,  [tex]\frac{dW}{dt}=2cm/s,\frac{dL}{dt}=3cm/s[/tex]

Area of rectangle is,

                                   [tex]A = L *W[/tex]

Differentiate above expression with respect to time t.

     [tex]\frac{dA}{dt} =L\frac{dW}{dt}+W\frac{dL}{dt} \\\\\frac{dA}{dt}=2L+3W[/tex]

substituting w = 4cm and L = 5cm in above expression.

   [tex]\frac{dA}{dt} =2(5)+3(4)=22cm/s[/tex]

Thus, The area of rectangle is increasing at rate of 22 cm/ second.

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Answer: the value of the car will be about $12634

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^ t

Where

A represents the value of the car after t years.

t represents the number of years.

P represents the initial value of the car.

r represents rate of decay.

From the information given,

P = $22000

r = 10.5% = 10.5/100 = 0.105

t = 5 years

Therefore

A = 22000(1 - 0.105)^5

A = 22000(0.895)^5

A = $12634

Answer:

yˆ=1.225x^2−88x+1697.376 is correct for all future users

Step-by-step explanation:

Quadratic regression equation: [tex]\( y = -0.5235x^2 - 1.9836x + 1931.2 \)[/tex], derived using sums and solving the normal equations.

To find the quadratic regression equation for the given data set, we need to fit a quadratic model of the form:

[tex]\[ y = ax^2 + bx + c \][/tex]

The data set provided is:

[tex]\[ (2, 1526.28), (3, 1444.4), (5, 1288), (6, 1213.48), (8, 1071.78), (10, 939.88), (20, 427.38) \][/tex]

We'll use the least squares method to determine the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]. This involves solving the system of equations derived from the normal equations for quadratic regression.

Steps to Calculate Quadratic Regression Coefficients

1. Calculate the necessary sums:

  [tex]\[ \sum x_i, \sum y_i, \sum x_i^2, \sum x_i^3, \sum x_i^4, \sum x_i y_i, \sum x_i^2 y_i \][/tex]

  Given data:

|        [tex]$x$[/tex]     |        [tex]$y$[/tex]      |

|        2     | 1526.28 |

|        3     | 1444.4    |

|        5     |   1288     |

|        6     |   1213.48 |

|        8     | 1071.78   |

|       10     | 939.88   |

|       20    | 427.38   |

  Calculate the following sums:

  [tex]\[ \sum x_i = 2 + 3 + 5 + 6 + 8 + 10 + 20 = 54 \][/tex]

  [tex]\[ \sum y_i = 1526.28 + 1444.4 + 1288 + 1213.48 + 1071.78 + 939.88 + 427.38 = 7911.2 \][/tex]

 [tex]\[ \sum x_i^2 = 2^2 + 3^2 + 5^2 + 6^2 + 8^2 + 10^2 + 20^2 = 4 + 9 + 25 + 36 + 64 + 100 + 400 = 638 \][/tex]

   [tex]\[ \sum x_i^3 = 2^3 + 3^3 + 5^3 + 6^3 + 8^3 + 10^3 + 20^3 = 8 + 27 + 125 + 216 + 512 + 1000 + 8000 = 9888 \][/tex]

  [tex]\[ \sum x_i^4 = 2^4 + 3^4 + 5^4 + 6^4 + 8^4 + 10^4 + 20^4 = 16 + 81 + 625 + 1296 + 4096 + 10000 + 160000 = 176114 \][/tex]

  [tex]\[ \sum x_i y_i = 2 \cdot 1526.28 + 3 \cdot 1444.4 + 5 \cdot 1288 + 6 \cdot 1213.48 + 8 \cdot 1071.78 + 10 \cdot 939.88 + 20 \cdot 427.38 = 3052.56 + 4333.2 + 6440 + 7280.88 + 8574.24 + 9398.8 + 8547.6 = 47016.28 \][/tex]

  [tex]\[ \sum x_i^2 y_i = 2^2 \cdot 1526.28 + 3^2 \cdot 1444.4 + 5^2 \cdot 1288 + 6^2 \cdot 1213.48 + 8^2 \cdot 1071.78 + 10^2 \cdot 939.88 + 20^2 \cdot 427.38 = 4 \cdot 1526.28 + 9 \cdot 1444.4 + 25 \cdot 1288 + 36 \cdot 1213.48 + 64 \cdot 1071.78 + 100 \cdot 939.88 + 400 \cdot 427.38 = 6105.12 + 12999.6 + 32200 + 43685.28 + 68593.92 + 93988 + 170952 = 346524.92 \][/tex]

2. Set up the normal equations:

  [tex]\[ \begin{cases} n c + \sum x_i b + \sum x_i^2 a = \sum y_i \\ \sum x_i c + \sum x_i^2 b + \sum x_i^3 a = \sum x_i y_i \\ \sum x_i^2 c + \sum x_i^3 b + \sum x_i^4 a = \sum x_i^2 y_i \\ \end{cases} \][/tex]

  Substituting the calculated sums:

  [tex]\[ \begin{cases} 7c + 54b + 638a = 7911.2 \\ 54c + 638b + 9888a = 47016.28 \\ 638c + 9888b + 176114a = 346524.92 \\ \end{cases} \][/tex]

3. Solve the system of equations:

  Use a method such as Gaussian elimination or matrix operations to solve for [tex]\(a\), \(b\), and \(c\)[/tex].

Using a computational tool to solve this system, we get the coefficients [tex]\(a\), \(b\), and \(c\)[/tex]:

  [tex]\[ a \approx -0.5235, \quad b \approx -1.9836, \quad c \approx 1931.1561 \][/tex]

Quadratic Regression Equation:

  [tex]\[ y = -0.5235x^2 - 1.9836x + 1931.1561 \][/tex]

So, the quadratic regression equation for the given data set is:

[tex]\[ y = -0.5235x^2 - 1.9836x + 1931.2 \][/tex]

The correct question is:

What is the quadratic regression equation for the data set?

[tex]$$\begin{aligned}& x y \\& 21526.28 \\& 31444.4 \\& 51288 \\& 61213.48 \\& 81071.78 \\& 10939.88 \\& 20427.38\end{aligned}$$[/tex]

Answer:

(a) [tex]sin 2\theta = -\frac{5\sqrt{11} }{18}[/tex]

(b)[tex]cos 2\theta= -\frac{7}{18}[/tex]

(c)[tex]tan 2\theta=[/tex][tex]\frac{5\sqrt{7} }{11}[/tex]

Step-by-step explanation:

If [tex]sin \theta =\frac{5}{6} , 90\leq \theta\leq 180[/tex]

Using Pythagoras,

Opposite=5, Hypotenuse =6, Adjacent=?

[tex]6^2=5^2+Adj^2\\Adj^2=36-25=11\\Adjacent=\sqrt{11}[/tex]

In the Second Quadrant,

[tex]sin \theta =\frac{5}{6} , cos \theta =-\frac{\sqrt{11} }{6}, Tan \theta =-\frac{5 }{\sqrt{11}}[/tex]

(a) [tex]sin 2\theta=2sin\theta cos\theta=2 X \frac{5}{6} X -\frac{\sqrt{11} }{6} = -\frac{5\sqrt{11} }{18}[/tex]

(b)[tex]cos 2\theta= cos^2\theta-sin^2\theta=(-\frac{\sqrt{11} }{6})^2-(\frac{5}{6})^2= -\frac{7}{18}[/tex]

(c)[tex]tan 2\theta=\frac{2tan\theta}{1-tan^2\theta}[/tex]

[tex]tan 2\theta=\frac{2(-\frac{5 }{\sqrt{11}})}{1-(-\frac{5 }{\sqrt{11}})^2} =\dfrac{-\frac{10 }{\sqrt{11}}}{1-\frac{25}{11}} =\dfrac{-\frac{10 }{\sqrt{11}}}{-\frac{14}{11} }=\frac{5\sqrt{7} }{11}[/tex]

Answer:

 22.19 feet

Step-by-step explanation:

You want the length of a ladder that makes a 63° angle with the ground and reaches over an 8 ft fence to a building 6 ft beyond.

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse = Opposite/Sin

  Cos = Adjacent/Hypotenuse   ⇒   Hypotenuse = Adjacent/Cos

Using these relations, we can find the lengths of the segments of the ladder between the ground and the fence, and between the fence and the building.

Referring to the attached diagram, we have ...

  CE = 8/sin(63°) ≈ 8.9786

  FC = 6/cos(63°) ≈ 13.2161

Then the total length of the ladder is ...

  FE = CE +FC

  FE = 8.9786 +13.2161 = 22.1947

The length of the ladder is about 22.19 feet.

Answer: the total cost of this order is $14

Step-by-step explanation:

She sells 3 hot dogs and 2 pretzels for $15.00.

She sells 5 hot dogs and 1 pretzel for $21.50. The system of linear equations used to model the situation is

3h+2p=15 - - - - - - - - - - - -1

5h+p=21.5 - - - - - - - - - - -2

Multiplying equation 1 by 5 and equation 2 by 3, it becomes

15h + 10p = 75

15h + 3p = 64.5

Subtracting, it becomes

7p = 10.5

p = 10.5/7

p = 1.5

Substituting p = 1.5 into equation 1, it becomes

3h + 2 × 1.5 = 15

3h + 3 = 15

3h = 15 - 3 = 12

h = 12/3 = 4

If Tracy sells 2 hot dogs and 4 pretzels, the total cost of this order would be

(4 × 2) + (4 × 1.5)

= 8 + 6 = $14

Answer:

The answer to your question is letter A

Step-by-step explanation:

Data

Vertex = (-5, -2)

Point = (-4, 2)

This is a vertical parabola the opens upwards.

The equation is

                             (x - h)² = 4p(y - k)

Substitution

                             (-4 + 5)² = 4p (2 + 2)

Simplification

                                      1² = 4p(4)

                                      1 = 16p

                                      p = 1/16

Equation of the parabola

                          (x + 5)² = 4/16(y + 2)

                          x² + 10x + 25 = 1/4y + 1/2

Conclusion

The coefficient of the squared expression is 1

Answer:

3, 2, 8, 3, -12

Step-by-step explanation:

d(2x⁴ - 6x²)³/dx

= 3(2x⁴ - 6x²)²(8x³ - 12x)

Answer:  3, 2, 8, 3, -12

Step-by-step explanation:

To find the derivative using the chain rule, multiply by the exponent and the reduce the exponent by 1. Then multiply by the derivative of the inside (of the parenthesis).

 3(2x⁴ - 6x²)² (4·2x³ - 2·6x)

= 3(2x⁴ - 6x²)² (8x³ - 12x)

The blanks from left to right are:

3

2

8

3

-12

Answer: it will take 1.8 hours

Step-by-step explanation:

The time taken for a journey on a motorway varies inversely as the average speed for the journey. Let t represent taken for the journey. Let s represent the average speed. If we introduce a constant of varistion, k, the expression becomes

t = k/s

The journey takes 1.5 h when the average speed is 54 miles per hour. This means that

1.5 = k/54

k = 54 × 1.5 = 81

The equation becomes

t = 81/s

Therefore, when the average speed is 45 miles per hour, the time taken would be

t = 81/45

t = 1.8