write a math sequence for this problem! lilah and her little brother max went to the beach they dug 290 seashells and 645 rocks how many rocks and seashells did max and lilah collect in all?

The equivalent expression is $\boxed{4^{15} \cdot 5^{10}}$.

We can simplify the expression inside the parentheses first, using the rule that says when you raise a power to another power, you multiply the exponents:

$\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = \left(4^{3} \cdot 5^{2}\right)^{5}$

Now, we can use the rule that says when you raise a product to a power, you raise each factor to the power:

$\left(4^{3} \cdot 5^{2}\right)^{5} = 4^{3 \cdot 5} \cdot 5^{2 \cdot 5}$

Simplifying further:

$4^{3 \cdot 5} \cdot 5^{2 \cdot 5} = 4^{15} \cdot 5^{10}$

we can substitute this expression back into the original expression:

$\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = \left(4^{3} \cdot 5^{2}\right)^{5}$

To simplify this expression further, we can use the rule that says when you raise a product to a power, you raise each factor to the power:

$\left(4^{3} \cdot 5^{2}\right)^{5} = 4^{3 \cdot 5} \cdot 5^{2 \cdot 5}$

Simplifying the exponents, we get:

$4^{3 \cdot 5} \cdot 5^{2 \cdot 5} = 4^{15} \cdot 5^{10}$

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Expression[tex]58(8b+8)[/tex]simplifies to[tex]464b+464.[/tex]

Calculate the product of 58 and the quantity 8b + 8

The given expression is:

[tex]58(8b + 8)[/tex]

Multiplying 58 by 8b and 8, we get:

[tex]464b + 464[/tex]

Therefore, the answer is:

[tex]58(8b + 8) = 464b + 464[/tex]

To find the product of 58 and the quantity 8b + 8, we need to use the distributive property of multiplication over addition, which states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In this case, we can distribute 58 over 8b and 8, as follows:

[tex]58(8b + 8) = 58 × 8b + 58 × 8[/tex]

Multiplying 58 by 8b and 8 separately, we get:

[tex]58 × 8b = 464b[/tex]

[tex]58 × 8 = 464[/tex]

Adding the products, we get the final answer:

[tex]58(8b + 8) = 464b + 464[/tex]

Therefore, the expression [tex]58(8b + 8)[/tex]simplifies to[tex]464b + 464.[/tex]

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The solution of the system of equations is given by the ordered pairs [10, 0] and [8, -6].

In order to graphically solve the given system of equations on a coordinate plane, we would use an online graphing calculator to create a plot of the system of equations and then determine their point of intersection;

x² + y² = 100   ......equation 1.

3x - y = 30 ......equation 2.

Based on the graph shown in the image attached above, we can reasonably infer and logically deduce that the solution to this system of equations lies in both Quadrant I and Quadrant IV, and it is represented by this ordered pairs (10, 0) and (8, -6).

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The inequailty y < x + 3 would be true when x = -3 and all values of y are less than 0

From the question, we have the following parameters that can be used in our computation:

The statement that x = -3

The above value implies that we substitute -3 for x in an inequality and solve for the variable y

Take for instance, we have

y < x + 3

Substitute the known values in the above equation, so, we have the following representation

y < -3 + 3

Evaluate

y < 0

This means that the inequailty y < x + 3 would be true when x = -3 and all values of y are less than 0

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The Fourier series Using the complex form of f(x) is

f(x) = 1/2 + ∑[n=1, ∞] [2*(-1)^(n+k)/(nπ)]*sin(nπx), 2k-0.25 < x < 2k+0.25

where k is an integer.

To find the Fourier series of the function f(x) over the interval [-1, 1], we first note that f(x) is periodic with period T = 0.5. We can then write f(x) as a Fourier series of the form

f(x) = a0/2 + ∑[n=1, ∞] (ancos(nπx) + bnsin(nπx))

where

a0 = (1/T) ∫[0,T] f(x) dx

an = (2/T) ∫[0,T] f(x)*cos(nπx) dx

bn = (2/T) ∫[0,T] f(x)*sin(nπx) dx

Since f(x) = 0 for x < -0.25 and x > 0.25, we only need to consider the interval [-0.25, 0.25]. We can break this interval into subintervals of length 0.5 centered at integer values k

[-0.25, 0.25] = [-0.25, 0.25] ∩ [1.5, 2.5] ∪ [-0.25, 0.25] ∩ [0.5, 1.5] ∪ ... ∪ [-0.25, 0.25] ∩ [-1.5, -0.5]

For each subinterval, the Fourier coefficients can be calculated as follows

a0 = (1/0.5) ∫[-0.25, 0.25] f(x) dx = 1/2

an = (2/0.5) ∫[-0.25, 0.25] f(x)*cos(nπx) dx = 0

bn = (2/0.5) ∫[-0.25, 0.25] f(x)sin(nπx) dx = 2(-1)^k/(nπ)

Therefore, the Fourier series of f(x) is

f(x) = 1/2 + ∑[n=1, ∞] [2*(-1)^(n+k)/(nπ)]*sin(nπx), 2k-0.25 < x < 2k+0.25

where k is an integer.

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Check the picture below.

The slopes and y-intercept of a graph are two key components of the equation that describes the relationship between two variables.

The slope of a graph is the measure of how steeply the line is rising or falling. It is calculated by dividing the change in the y-axis by the change in the x-axis between two points on the line. A positive slope indicates that the line is rising, while a negative slope indicates that the line is falling.

The y-intercept of a graph is the point where the line crosses the y-axis. It is the value of y when x=0. The y-intercept is a fixed point on the line and is used to help determine the equation of the line.

Together, the slope and y-intercept of a graph can be used to write an equation in slope-intercept form, which is y=mx+b, where m is the slope and b is the y-intercept.

The function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20).

To answer this question, we need to identify the function that best models the number of game consoles sold in millions x years since 2010.

Option A can be simplified to g(x) = 30, which is a constant function. This means that it does not depend on the value of x and is not a good model for the number of game consoles sold over time.

Option B can be simplified to g(x) = 3x, which is a linear function. This means that the number of game consoles sold increases at a constant rate over time. This could be a good model for the number of game consoles sold, but we need to compare it to the other options.

Option C can be simplified to g(x) = 0.03x, which is also a linear function. However, the rate of increase is much slower than in option B. This is not a good model for the number of game consoles sold.

Option D can be simplified to g(x) = 300, which is a constant function like option A. Again, this is not a good model for the number of game consoles sold over time.

Therefore, the function that best models the number of game consoles sold in millions x years since 2010 is option B, g(x) = 0.15(20). This is a linear function that represents a constant rate of increase in the number of game consoles sold over time.

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complete question:

Based on this information, which function best models the number of game consoles

sold in millions x years since 2010?

A- g(x) = 0.15(20)^x

B- g(x) = 20(0.15)^x

C- g(x) = 20(1.5)^x

D- g(x) = 0.15(.2)^x

The statements are classified as follows:

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

8 is a low outlier, hence it is a value lower than the mean, meaning that the mean increases if we remove the observation of 8.

The range of a data-set is calculated as the difference between the highest value and the lowest value in the data-set, thus if we remove the low value of 8, the next low value is of 47, meaning that the range decreases.

The ordered data-set is given as follows:

8, 47, 48, 50, 51, 51.

The data-set has an even cardinality of 6, hence the median is calculated as the mean of the two middle elements as follows:

Median = (48 + 50)/2

Median = 49.

Removing 8, the data-set is given as follows:

47, 48, 50, 51, 51.

Hence the median increases, as it will be the middle value of 50.

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Replacing three repairers with a superworker would be cost-effective for the laundromat as the expected repair time would increase and lead to more downtime for the machines.

To determine if the laundromat should replace the three repairers with the superworker, we need to compare the expected repair time under each scenario.

With three repairers, the expected time to repair a machine is the sum of the expected time until a machine breaks down and the expected time for a repairer to fix it

E(time with three repairers) = 5 + 2.5/3 = 6.167 days.

With the superworker, the expected time to repair a machine is

E(time with superworker) = 5/6 = 0.833 days.

Therefore, on average, it takes much less time to repair a machine with the superworker than with three repairers. Since the salary of the superworker is equal to that of three repairers, the laundromat should replace the three repairers with the superworker. It is also more cost-effective.

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There are 24 three-digit numbers without repeating digits, and 64 three-digit numbers with repeating digits.

1) Pentru a alcătui numere de trei cifre în care cifrele să nu se repete, putem utiliza principiul combinatoric al permutărilor. Având la dispoziție cifrele 1, 2, 3 și 4, vom avea 4 posibilități pentru a alege prima cifră, 3 posibilități pentru a alege a doua cifră și 2 posibilități pentru a alege a treia cifră. Prin înmulțirea acestor numere, obținem:

4 * 3 * 2 = 24

Există deci 24 de numere de trei cifre în care cifrele nu se repetă, utilizând cifrele 1, 2, 3 și 4.

2) Pentru a alcătui numere de trei cifre în care cifrele se repetă, vom avea 4 posibilități pentru a alege oricare dintre cele trei cifre și anume 1, 2, 3 și 4. Prin urmare, avem:

4 * 4 * 4 = 64

Există 64 de numere de trei cifre în care cifrele se pot repeta, utilizând cifrele 1, 2, 3 și 4.

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a) The height of the tide at low tide is 3.7 feet.

b) The period of the function is 12 hours and it means that the tide goes through a full cycle of high tide.

c) The first time the tide reaches a height of 3 feet is therefore either 23.82 hours or 40.18 hours after high tide.

a. To find the height of the tide at low tide, we need to find the minimum value of the function f(x).

Since cos(π/6 x) has a maximum value of 1 and a minimum value of -1, the minimum value of the entire function occurs when cos(π/6 x) = -1.

This happens when π/6 x = π + 2nπ, where n is any integer.

Solving for x, we get x = 12 + 12n.

Substituting this value of x into the function, we get f(x) = 0 + 3.7 = 3.7 feet.

b. The period of the function is the time it takes for the function to complete one full cycle. Since the period of cos(π/6 x) is 2π/π/6 = 12 hours, the period of the entire function f(x) is also 12 hours. This means that the tide goes through a full cycle of high tide and low tide every 12 hours at this location.

c. To find the first time the tide reaches a height of 3 feet, we need to solve the equation 3 = 3.5 cos (π/6 x) + 3.7 for x.

Subtracting 3.7 from both sides and dividing by 3.5, we get cos(π/6 x) = -0.086.

Taking the inverse cosine of both sides, we get π/6 x = 1.67 + 2nπ or π/6 x = -1.67 + 2nπ, where n is any integer.

Solving for x, we get x = 40.18 + 24n or x = 23.82 + 24n.

The first time the tide reaches a height of 3 feet is therefore either 23.82 hours or 40.18 hours after high tide.

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The height of the cylindrical ornament is approximately 5.7 centimetres (option b).

To find the height of the cylindrical ornament given that 450 cubic centimetres of wood is used and the radius of the base is 5 centimetres, you can use the formula for the volume of a cylinder: V = π × radius² × height.

Step 1: Write down the given values.
Volume (V) = 450 cubic centimetres
Radius (r) = 5 centimetres

Step 2: Plug the given values into the formula.
450 = π × (5)² × height

Step 3: Solve for the height.
450 = π × 25 × height
450 = 78.54 × height

Step 4: Divide both sides by 78.54 to find the height.
height = 450 / 78.54
height ≈ 5.7 centimetres

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The volume of the given cone is 402.1 cubic feet if the slant height is 10ft and the length is 6ft.

To calculate the volume of a cone, the formula used is :

V = (1/3) * π * [tex]r^2[/tex] * h

Here, the radius is the unknown term. we need to calculate the radius of the cone. We can use the Pythagorean theorem to find the radius of the cone.

[tex]l^2 = r^2 + h^2[/tex]

[tex]10^2 = r^2 + 6^2[/tex]

[tex]r = \sqrt{(10^2 - 6^2)}[/tex]

radius = 8 ft

V = (1/3) *  π * [tex]r^2[/tex] * h

V = (1/3) * π *[tex]8^2[/tex] * 6

V = (1/3) * π * 384

V =  402.1 cubic feet

Therefore we can infer that the volume of the given cone is  402.1 cubic feet.

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The complete question is:

'Find the volume of this cone. Round to the nearest tenth.

slant height = 10ft

length = 6ft

So the angles that must be right angles are KER and ERI.

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex of the angle. The rays are usually denoted by the letters A and B, and the vertex is denoted by the letter V. The angle is denoted by the symbol ∠, followed by the letters of the rays with the vertex in between, such as ∠AVB. The measure of an angle is the amount of rotation needed to move one ray to coincide with the other ray, and is usually given in degrees or radians. Angles are used in many areas of mathematics and science, such as trigonometry, geometry, physics, and engineering. They are also used in everyday life, such as in navigation, construction, and design.

Here,

Since RE and RI are secants of the circle, we can use the Intersecting Secants Theorem to find the relationships between the angles in the diagram.

Angle ERK is half of the intercepted arc EIK, so we have m∠ERK = 1/2m(arc EIK).

Similarly, angle KRI is half of the intercepted arc KE, so we have m∠KRI = 1/2m(arc KE).

Angle REI is an exterior angle of triangle KIR, so we have m∠REI = m∠ERK + m∠KRI.

To determine which angles must be right angles, we need to look for cases where the intercepted arcs are semicircles, which have a measure of 180 degrees.

If arc EIK is a semicircle, then m(arc EIK) = 180 and m∠ERK = 1/2(180) = 90. Therefore, angle ERK is a right angle.

If arc KE is a semicircle, then m(arc KE) = 180 and m∠KRI = 1/2(180) = 90. Therefore, angle KRI is a right angle.

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The equation for the company's profit, P(x), is P(x) = 6.6x - 2,300, where x is the number of items sold.

To find the equation P(x) for the company's profit, we can first determine the slope (m) and the y-intercept (b) of the linear equation P(x) = mx + b.

1. Calculate the slope (m) using the given information:

m = (P2 - P1) / (x2 - x1)
m = ($30,700 - $24,100) / (5000 - 4000)
m = $6,600 / 1000
m = $6.6

2. Use one of the points to find the y-intercept (b):

P(x) = mx + b
$24,100 = $6.6(4000) + b
$24,100 = $26,400 + b
b = -$2,300

3. Write the equation for P(x):

P(x) = 6.6x - 2,300

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(a) A vector v parallel to the line of intersection L is v = <1, 1, -2>. (b) The cartesian equation of the plane is -7x + 10y - 3z = -1

(a) To find a vector v parallel to the line of intersection L, we need to take the cross product of the normal vectors to the two given planes. The normal vectors are the coefficients of x, y, and z in the equations of the planes.

In this case, the equations of the planes are:

x + y - 2z = 1

4x + y + 3z = 4

The normal vectors to these planes are <1, 1, -2> and <4, 1, 3>, respectively. Since the line of intersection is parallel to both planes, a vector parallel to the line must be perpendicular to both normal vectors.

We can find such a vector by taking the cross product of the two normal vectors, which gives us: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>

Therefore, a vector v = <1, 1, -2>.

(b) To find the equation of the plane through the point (2, -1, 3) and perpendicular to L, we need to find a normal vector to the plane that is also parallel to L.

We can find such a vector by taking the cross product of the normal vectors to the two given planes. The normal vectors are <1, 1, -2> and <4, 1, 3>, so the cross product is: <1, 1, -2> × <4, 1, 3> = <-7, 10, -3>

This vector is parallel to L, so it can serve as the normal vector to the desired plane. The equation of the plane can be written in point-normal form as: -7(x - 2) + 10(y + 1) - 3(z - 3) = 0

Simplifying, we get:

-7x + 10y - 3z = -1

Therefore, the cartesian equation of the plane is -7x + 10y - 3z = -1, and it passes through the point (2, -1, 3) and is perpendicular to the line of intersection between the given planes.

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Answer:

about 12.67 cm²

Step-by-step explanation:

The area of a sector of a circle is given by:

A = (θ/360) x πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.

In this case, we are given the central angle of the sector, which is 86.4 degrees, and the radius of the circle, which is 4.1 cm. Therefore, we can calculate the area of the sector formed by angle CBA as follows:

A = (86.4/360) x π(4.1)²

A ≈ 12.67 cm²

So, the area "about 12.67 cm²" is a possible area of the sector formed by angle CBA.

To determine if any of the other given areas are possible, we can calculate the central angle of each sector using the same formula as above, and then check if it matches the given angle of 86.4 degrees.

For the area "about 23.35 cm²":

23.35 = (θ/360) x π(4.1)²

θ ≈ 149.6 degrees

The central angle of this sector is approximately 149.6 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 23.35 cm²" is not a possible area of the sector formed by angle CBA.

For the area "about 3.09 cm²":

3.09 = (θ/360) x π(4.1)²

θ ≈ 19.16 degrees

The central angle of this sector is approximately 19.16 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 3.09 cm²" is not a possible area of the sector formed by angle CBA.

For the area "about 40.14 cm²":

40.14 = (θ/360) x π(4.1)²

θ ≈ 256.4 degrees

The central angle of this sector is approximately 256.4 degrees, which is not equal to the given angle of 86.4 degrees. Therefore, the area "about 40.14 cm²" is not a possible area of the sector formed by angle CBA.

Therefore, the only possible area of the sector formed by angle CBA is "about 12.67 cm²".

The radar beam moves at a pace of roughly 536.47 kilometers per hour as it scans the coastline.

Let A represent the location of the radar antenna and B represent the shoreline location that is closest to A. Let C represent the radar beam's current location on the coast and Ф represent the angle between the beam and the line AB. As a result, we obtain a right triangle ABC, where AB is equal to 4 km, and BC is the length at which the radar beam sweeps along the shore.

32 rev/min(2π/60 sec) = 3.36 radians/sec. BC = r(Ф) = (4 km)(π/4) = π km.

We may calculate the radar beam's speed down the shore by multiplying these two values:

(536.47 km/hr) = 10.54 km/sec or (3.36 rad/sec)(π km).

Hence, the of sweeping is 10.54 km/sec.

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The measurements from greatest to least would be ordered as follows:

First, we need to convert all the units to the same unit. Let's convert everything to inches, since that is the smallest unit.

6 yards = 6 x 3 = 18 feet

18 feet = 18 x 12 = 216 inches

2 1/2 feet = 2 x 12 + 6 = 30 inches

So now we have:

6 yards = 216 inches

2 1/2 feet = 30 inches

45 inches = 45 inches

Putting these in order from greatest to least, we have:

216 inches, 45 inches, 30 inches

Therefore, the measurements from greatest to least would be ordered as follows:

6 yards, 45 inches, 2 1/2 feet

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The full question is:
Put the measurements from greatest to least. 45 inches, 6 yards, and 2 1/2 feet

To find the values of f(a), f(a-1), and f(a+1) when f(x) = x^2 + 4x + 6, So, the values are:  f(a) = a^2 + 4a + 6, f(a-1) = a^2 + 6a + 3, f(a+1) = a^2 + 6a + 11.

we simply substitute the given values of a into the function.
1. f(a) = a^2 + 4a + 6
2. f(a-1) = (a-1)^2 + 4(a-1) + 6 = a^2 + 2a + 1 + 4a - 4 + 6 = a^2 + 6a + 3
3. f(a+1) = (a+1)^2 + 4(a+1) + 6 = a^2 + 2a + 1 + 4a + 4 + 6 = a^2 + 6a + 11
So, the values are:
1. f(a) = a^2 + 4a + 6
2. f(a-1) = a^2 + 6a + 3
3. f(a+1) = a^2 + 6a + 11

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Answer:

Step-by-step explanation:

to solve this question, we need to use the graph on the left to find the proportions of students who prefer each pasta dish, and then multiply those proportions by 400 to get the estimated number of students in the whole school who prefer each pasta dish. Then we need to plot those numbers on a bar graph with the pasta dishes on the horizontal axis and the number of students on the vertical axis. The graph below shows one possible way to create the bar graph:

We can see that the vertical axis is numbered from 0 to 120 in increments of 20. The bars show the estimated number of students who prefer each pasta dish, based on the sample of 16 students. For example, since 4 out of 16 students prefer spaghetti, we can estimate that 4/16 x 400 = 100 students in the whole school prefer spaghetti. Similarly, since 3 out of 16 students prefer lasagna, we can estimate that 3/16 x 400 = 75 students in the whole school prefer lasagna. We can repeat this process for the other pasta dishes and plot them on the graph.

✧☆*: .｡. Hope this helps, happy learning! (*✧×✧*) .｡.:*☆

The volume of the prism is 78 cubic feet.The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism.

In this case, the base of the prism is a right triangle with legs measuring 3 feet and 4 feet, so its area is (1/2)(3)(4) = 6 square feet. The height of the prism is 13 feet. Therefore, the volume of the prism is V = Bh = (6)(13) = 78 cubic feet.To understand this calculation, think of the prism as a stack of identical, parallel cross sections. Each cross section is a copy of the base, with an area of 6 square feet.

The height of each cross section is the same, and equal to the height of the prism, which is 13 feet. To find the total volume of the prism, we add up the volumes of all these cross sections, which is equal to the area of the base times the height of the prism.

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To find the length of BD in a parallelogram where BA = 5x + 5 and AD = 10x - 20, we use the fact that opposite sides of a parallelogram are equal in length. Therefore, BD = BA = 30.

Since it is a parallelogram, we know that opposite sides are equal. So, BD = BA = 5x + 5. To find the value of x, we can use the fact that AD is also equal to BD. So, we can set the two expressions for BD equal to each other

5x + 5 = 10x - 20

Simplifying and solving for x, we get

5x = 25

x = 5

Now we can substitute x back into the expression for BD to get the final answer

BD = 5x + 5 = 5(5) + 5 = 30

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The value of the volume of the cylinder is  706. 5 cm³

The formula for the volume of a cylinder is expressed as;

V = πr²h

Such that the parameters are;

Now, substitute the values into the formula, we get;

Volume, V = 3.14 × 5² × 9

Find the square value and substitute

Volume, V = 3.14 × 25 × 9

Multiply the values

volume, V = 706. 5 cm³

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The percentage of females who do not satisfy the minimum score requirement of 925 on the SAT-I test is 35.9%.

Calculating the z-score for the minimum score requirement:
z = (X - Mean) / Standard Deviation
z = (925 - 998) / 202
z = -73 / 202 ≈ -0.361

Now, using the z-score to find the percentage of females below the minimum score:
Since the z-score is -0.361, we can use a z-table (or an online calculator) to find the area to the left of this z-score, which represents the percentage of females who scored below 925. The area to the left of -0.361 is approximately 0.359.

3. Convert the area to a percentage:
Percentage = Area * 100
Percentage = 0.359 * 100 ≈ 35.9%

So, approximately 35.9% of females do not satisfy the minimum score requirement of 925 on the SAT-I test.

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The probability that she will select the two pink bean bags from the box on her first two attempts is approximately 2.2%.

To calculate the probability that she will select the two pink bean bags from the box on her first two attempts, we need to;
1. Determine the total number of bean bags in the box. There is one yellow, four blue, three red, and two pink bean bags, which makes a total of 1 + 4 + 3 + 2 = 10 bean bags.
2. Calculate the probability of selecting a pink bean bag on the first attempt. There are two pink bean bags out of 10, so the probability is 2/10 or 1/5.

3. After selecting one pink bean bag, there are now nine bean bags left in the box. Calculate the probability of selecting the second pink bean bag on the second attempt. Since there is only one pink bean bag left, the probability is 1/9.
4. To find the overall probability of selecting two pink bean bags in the first two attempts, multiply the probabilities from steps 2 and 3. So, the probability is (1/5) * (1/9) = 1/45.
5. Convert the fraction to a percentage by dividing the numerator by the denominator and multiplying by 100. (1/45) * 100 = 2.22% (rounded to the nearest tenth of a percent).

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The value of x is 48 km/hr.

How to solve for X

Total distance = 68 km

Total time = 50 minutes

First part:

Duration = 20 minutes

Speed = x km/hr

Second part:

Duration = 25 minutes

Speed = 2x km/hr

Third part:

Duration = 50 - (20 + 25) = 5 minutes

Speed = 3x km/hr

We can calculate the distance traveled in each part using the formula:

distance = speed × time

For the first part:

distance1 = x × (20/60) = (1/3)x (because 20 minutes = 1/3 hour)

For the second part:

distance2 = 2x × (25/60) = (5/6)x (because 25 minutes = 5/12 hour)

For the third part:

distance3 = 3x × (5/60) = (1/4)x (because 5 minutes = 1/12 hour)

Now, we know that the total distance is 68 km, so:

distance1 + distance2 + distance3 = 68

(1/3)x + (5/6)x + (1/4)x = 68

To solve for x, we'll first find a common denominator for the fractions, which is 12:

(4/12)x + (10/12)x + (3/12)x = 68

Now, add the fractions:

(4+10+3)/12 * x = 68

17/12 * x = 68

To isolate x, we'll multiply both sides by the reciprocal of the fraction (12/17):

x = 68 * (12/17)

x = 4 * 12

x = 48

So, the value of x is 48 km/hr.

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