Jose has scored 347 points on his math tests so far this semester. To get an A for the semester, he must score at least 403 points. Part 1 out of 2 Enter an inequality to find the minimum number of points he must score on the remaining tests in order to get an A. Let n represent the number of points Jose needs to score on the remaining tests.

Cloud storage is the storage option that has the ability to update itself regularly.

Unlike internal hard drives and flash drives, which require manual updates and data transfers, cloud storage services automatically synchronize and update your files across multiple devices. This feature ensures that you always have access to the most recent version of your data, without needing to perform manual updates.

Cloud storage services operate on remote servers managed by service providers, allowing users to store, share, and access their data from any device with internet access. This not only provides convenience but also offers enhanced data security and protection against data loss due to hardware failure or damage.

On the other hand, internal hard drives and flash drives are physical storage devices that store data locally. While they offer a certain level of convenience and portability, they lack the ability to automatically update or sync across multiple devices, making them less versatile compared to cloud storage.

In summary, cloud storage is the storage option with the ability to update itself regularly, providing users with convenience, enhanced security, and the ability to access their data from multiple devices. Meanwhile, internal hard drives and flash drives require manual updates and are limited in their capacity to sync data across devices.

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The scale of the map can be written as:

1cm to 20km

We want to find the distance that 1 cm in the map representes in the real world.

We know the relation:

3cm = 60km

We want to get a 1 in the left side, then we can divide both sides by 3 to get:

1cm = 60km/3

1cm = 20km

Then the scale of the map is 1cm to 20km

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Let's assume that the number of shirts that must be sold to cover the costs is x.

The revenue from selling x shirts is 12x dollars, and the total cost is the sum of the setup fee and the cost per shirt multiplied by the number of shirts, which is 65 + 7x dollars.

To break even, the revenue must be equal to the cost:

12x = 65 + 7x

Subtracting 7x from both sides:

5x = 65

Dividing both sides by 5:

x = 13

Therefore, the student council must sell 13 shirts to break even.

To find the total costs, we can substitute x = 13 into the expression for the total cost:

65 + 7x = 65 + 7(13) = 156

So the total costs will be $156.

Answer:

The student council's costs will be $146 and they need to sell 13 shirts to cover their costs.

Step-by-step explanation:

Let's call the number of shirts sold "x".

The revenue from selling x shirts at $12 each is:

The total cost of making x shirts is:

In order to break even (i.e. cover their costs), the revenue must equal the total cost:

[tex]\sf:\implies 12x = 7x + 65[/tex]

Solving for x:

[tex]\sf:\implies 5x = 65[/tex]

[tex]\sf:\implies \boxed{\bold{\:\:x = 13\:\:}}\:\:\:\green{\checkmark} [/tex]

Therefore, the student council must sell 13 shirts to break even.

To find the total costs, we can substitute x = 13 into the total cost equation:

[tex]\sf:\implies Total\: Cost = 7(13) + 65 = \boxed{\bold{\:\:\$146\:\:}}\:\:\:\green{\checkmark} [/tex]

So the student council's costs will be $146 and they need to sell 13 shirts to cover their costs.

There may be a difference on speed based on various factors

Though it would be reasonable to conclude that if it takes less time for a car to move 50 centimeters than 150 centimeters, they must be traveling faster; we do not know exactly when they did this and whether their speed changed accordingly.

Furthermore, it could have taken the same time covering both distances; thus leaving unanswered questions regarding their relative speeds.

Due to variables affecting car speed such as changes in terrain or obstacles in its path, we cannot accurately predict its speed without more information regarding these two runs.

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The function g(x, y) is defined as 15x^2 + 2y^2. To compute g(3,3), g(0,-2), and g(a,b), we substitute the given values into the function.

To find g(3,3), we substitute x = 3 and y = 3 into the function g(x, y) = 15x^2 + 2y^2:

g(3,3) = 15(3)^2 + 2(3)^2

g(3,3) = 135 + 18

g(3,3) = 153

To find g(0,-2), we substitute x = 0 and y = -2 into the function g(x, y) = 15x^2 + 2y^2:

g(0,-2) = 15(0)^2 + 2(-2)^2

g(0,-2) = 0 + 8

g(0,-2) = 8

To find g(a,b), we substitute x = a and y = b into the function g(x, y) = 15x^2 + 2y^2:

g(a,b) = 15a^2 + 2b^2

Note: The function g(a,b) cannot be simplified further without knowing the values of a and b.

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For the first question, to get the limit of the function lim (In V 4x2 + 6 - In x), we can use the property of logarithms that says ln(a) - ln(b) = ln(a/b). Applying this property to the given function, we get ln[(4x^2 + 6)/x]. Now we can simplify the expression by dividing both the numerator and the denominator by x. So we get ln(4x + 6/x), which can be rewritten as ln(4 + 6/x). Now we can take the limit as x approaches infinity. As x gets larger and larger, the 6/x term becomes smaller and smaller and approaches zero. So ln(4 + 6/x) approaches ln(4), and the final answer is A. In 2.

For the second question, to get the horizontal asymptote(s) of the function f(x) = 37€*, we can take the limit as x approaches infinity. As x gets larger and larger, the exponential term €* becomes larger and larger, approaching infinity. So the function approaches 37 times infinity, which is infinity. Therefore, there is no horizontal asymptote and the answer is D. none.
For the third question, the statement is false. The limit as x approaches infinity of 2^(ln(a)/ln(x)) is equal to infinity if a > 1 and is equal to zero if 0 < a < 1.

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To determine the range and sample standard deviation of tornadoes that touched down during each month of one year, we need to use the data in the table.

However, the table is not provided in the question.

Please provide the table with the number of tornadoes that touched down during each month of one year so I can help you with your question.
To determine the range and sample standard deviation of the number of tornadoes that touched down each month, you'll first need to provide the data in a table format.

Once you provide the data, I can help you calculate the range and sample standard deviation.

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Correct question:

Each​ year, tornadoes that touch down are recorded. The following table gives the number of tornadoes that touched down during each month of one year. Determine the range and sample standard deviation.

3 2 41 115 197 95

70 85 68 64 110 91

Range?

Sample Standard Deviation?

Answer:

39.27 square units

Step-by-step explanation:

In circle E with m∠DEF = 70∘ and DE=8, we want to find the area of sector DEF. To do this, we can use the formula for the area of a sector:

A_sector=1/2 r^2⋅

α

where r is the radius of the circle and α is the central angle in radians. In our case, r=8 and α=70 ∘ ⋅ π/180∘ = 7π/18 radians

Now, we can plug these values into the formula:

A_sector = 1/2(8^2) ⋅ 7π/18 = 32 ⋅ 7π/18 ≈ 39.27

So, the area of sector DEF is approximately 39.27 square units, rounded to the nearest hundredth.

The area of sector DEF in circle E is approximately 6.10 square units, rounded to the nearest hundredth.

To find the area of sector DEF in circle E, we need to use the formula for the area of a sector:

Area of sector = (Central angle / 360°) * π * r^2

where "Central angle" is the measure of angle DEF in degrees, "r" is the radius of the circle (DE in this case).

Given that m/DEF = 70° and DE = 8, we can calculate the area of sector DEF as follows:

Area of sector = (70° / 360°) * π * 8^2

Now, perform the calculations step by step:

Area of sector = (70/360) * π * 64

Area of sector = (7/36) * π * 64

Area of sector ≈ 3.14 * (7/36) * 64

Area of sector ≈ 3.14 * 1.9444

Area of sector ≈ 6.10 (rounded to two decimal places)

Therefore, the area of sector DEF in circle E is approximately 6.10 square units, rounded to the nearest hundredth.

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The confidence level for length of the thorax of 49 fruit fly males is  (0.7820 mm, 0.8188 mm).

Here the sample size (n=49), the sample mean (a=0.8004 mm), and the sample standard deviation (s=0.0782 mm), we can calculate the confidence interval as follows:

1. Determine the critical value (z-score) for a 90% confidence level. You can use a z-table or calculator to find the z-score, which is approximately 1.645.

2. Calculate the margin of error using the z-score, sample standard deviation, and sample size:
Margin of Error = z-score * (s / √n)
Margin of Error = 1.645 * (0.0782 / √49)
Margin of Error ≈ 0.0184 mm

3. Add and subtract the margin of error from the sample mean to obtain the confidence interval:
Lower Limit = a - Margin of Error = 0.8004 - 0.0184 ≈ 0.7820 mm
Upper Limit = a + Margin of Error = 0.8004 + 0.0184 ≈ 0.8188 mm

So, the 90% confidence interval for the true mean thorax length of a male fruit fly is approximately (0.7820 mm, 0.8188 mm). This means that we are 90% confident that the true mean thorax length of a male fruit fly falls within this range.

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Answer:

shape a is 20 cm squared

Step-by-step explanation:

shape a is a parallogram, A =b×h. 5x4=20

shape b is a trapezoid. The picture is cut off but here are the steps for you to solve. A=0.5h(base1+base2) count the number of squares on the top and bottom of the shape. I can see the top is 2, you will need to tfind the length of the bottom base.then count the height, how far to get from the bottom to top, here it is 4.

area=0.5*4(2+bottom base) simply and that's your answer! Don't forget your units

Answer:

Ф  Exponential.                                

Step-by-step explanation:

The most appropriate for tehe data shown is:

Ф  Exponential.                                          

...

Answer:

y = 10

Step-by-step explanation:

If y varies directly with x, and y=20 when x=-2, the best way to find y when x=-1 is to divide 20/-2, which equals -10.

Now cancel out -1 by dividing it by 1, and do the same with -10 by dividing it by 1 also. This equals 10, and that's your answer. Check the table I made below representing the problem. It should make it easier understand.

The measurement closest to the number of meters Chelsea sprinted is F) 109.1 yd.

To determine the number of meters Chelsea sprinted, we need to convert the distance she sprinted from yards to meters.

Given:

Chelsea sprinted 120 yards.

Conversion:

1 meter is approximately equal to 1.1 yards.

To convert yards to meters, we divide the distance in yards by the conversion factor:

120 yards / 1.1 yards/meter ≈ 109.1 meters.

Therefore, the measurement closest to the number of meters Chelsea sprinted is F) 109.1 yd.

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we need to find two numbers whose product is 110. Possible combinations include L = 10 feet and W = 11 feet or L = 11 feet and W = 10 feet. Therefore, the dimensions of the brick wall can be either 10 feet by 11 feet or 11 feet by 10 feet.

A brick wall can be shaped like a rectangular prism, and in this case, the wall needs to be 3 feet tall. With the builder having enough bricks for the wall to have a volume of 330 cubic feet, we can calculate the area of the base of the wall.

To find the base area, we can use the formula for the volume of a rectangular prism: Volume = Base Area × Height. In this situation, we know the volume (330 cubic feet) and the height (3 feet), so we can solve for the base area.

330 cubic feet = Base Area × 3 feet
Dividing both sides of the equation by 3, we get:
Base Area = 110 square feet

So, the base area of the brick wall that is shaped like a rectangular prism with a height of 3 feet and a volume of 330 cubic feet will be 110 square feet.

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Note that where the above statistics are give, the p-value is 0.04.

1st , we calculate the differences between the number of citations given in the day shift and afternoon shift for each day

Differences -  0, 6, 4, 6

The mean difference is  (m)  = (0 + 6 + 4 + 6) / 4 = 4

The sample standard deviation of the differences is    s = √ ([((0-4)² + (6-4)² + (4-4)² + (6-4)²)/3]) = 2.31

The standard error of the mean difference is  SE(m) = s / √(n) = 2.31 / √(4) = 1.155

The t-statistic is  t = (m - 0) / SE(m) = 4 / 1.155 = 3.4632034632

The paired t-test has n-1=3 degrees of freedom. We calcu0late the p-value associated with a t-statistic of 3.46 using a t-table or a t-distribution calculator with three degrees of freedom.

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Herbert will earn $63,417 for his tenth year of work which is calculated using compound interest formula.

After graduating from college, Herbert decided to join a new company. He agreed to a salary which will increase by 4.5% each year. This means that every year, Herbert's salary will increase by 4.5% of his previous year's salary. For example, if his salary in the first year is $50,000, his salary in the second year will be $52,250, and so on.

To find out Herbert's salary for his tenth year of work, we need to use compound interest formula. The formula is:

A = P(1 + r)ⁿ

Where:
A = Final amount (salary in the tenth year)
P = Initial amount (salary in the first year)
r = Annual interest rate (4.5%)
n = Number of years (10)

Substituting the values in the formula, we get:

A = $50,000(1 + 0.045)¹⁰
A = $63,417

Therefore, Herbert will earn $63,417 for his tenth year of work. It is important to note that the increase in salary is a result of compound interest, which means that the salary growth rate accelerates over time. This is a good incentive for Herbert to stay with the company and work hard.

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The trigonometric function equivalent to sec(-270) is -1.

The secant function is defined as the reciprocal of the cosine function, i.e., sec(x) = 1/cos(x). To find the value of sec(-270), we need to first find the cosine of -270 degrees. The cosine function has a period of 360 degrees, which means that cos(-270) is the same as cos(-270 + 360) = cos(90) = 0. Therefore, we have sec(-270) = 1/0, which is undefined.

However, we can determine the sign of sec(-270) by examining the quadrant in which the angle -270 degrees lies. Since -270 degrees is in the fourth quadrant, the cosine function is negative in that quadrant. Therefore, we can write sec(-270) = -1/0-, which is equivalent to -1. Hence, the trigonometric function equivalent to sec(-270) is -1.

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A theater can make at least $675 from ticket sales by selling at least 100 adult tickets and up to 50 child tickets.

To solve this problem, we can use a system of equations. Let's define:

- x as the number of adult tickets sold
- y as the number of child tickets sold

We know that:

- x + y ≤ 150 (due to the limit on seating)
- 12x + 7.5y ≥ 675 (they want to make at least $675)

We can solve this system of equations using substitution or elimination. Let's use elimination:

- Multiply the second equation by 2 to get rid of the decimals: 24x + 15y ≥ 1350
- Multiply the first equation by 15: 15x + 15y ≤ 2250
- Subtract the second equation from the first: 9x ≥ 900
- Divide both sides by 9: x ≥ 100

So they need to sell at least 100 adult tickets to make at least $675. Let's see if that's possible:

- If they sell 100 adult tickets, that leaves 50 tickets for children
- 100 adult tickets * $12 = $1200
- 50 child tickets * $7.50 = $375
- Total ticket sales = $1575 (more than $675)

So they can make at least $675 from ticket sales by selling at least 100 adult tickets and up to 50 child tickets.

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The landscaper needs to buy approximately 85.33 bags of topsoil to cover the whole garden.

The landscaper uses 4 bags of topsoil to cover 3/8 of the garden. To cover the whole garden, he would need:

First, we need to find how many bags of topsoil he needs per 1/8 of the garden:

4 bags / 3/8 of the garden = 32/3 bags of topsoil per 1 garden

Then, we can find the number of bags he needs for the whole garden:

32/3 bags * 8 = 256/3 bags or 85.33 bags (rounded to two decimal places)

Therefore, the landscaper needs to buy approximately 85.33 bags of topsoil to cover the whole garden.

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Discovering commonalities and variations among objects or people encountered daily is beneficial in several ways:

Decision-Making: Recognizing similarities and variations is key to making smart choices, such as selecting products or services based on their features, benefits, and drawbacks.

Problem Solve: Recognizing patterns and distinguishing features can assist with problem-solving by helping you pinpoint the causes of issues and create custom solutions.

Understanding commonalities and differences among people can enhance communication and relationships, enabling you to empathize with them, appreciate diverse viewpoints, and adjust your communication style appropriately.

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So the value of the integral ∫ dx/√(1-2x^2) over the interval [-1/√2, 1/√2] is (1/√2)π.
The value of the integral ∫ dx/√(1-2x^2) is given by:
∫ (1/√(1-2x^2)) dx = (1/2) * arcsin(√2 * x) + C
where C is the constant of integration.

The value of the integral ∫ dx/√(1-2x^2) is equal to the integral of the function 1/√(1-2x^2) with respect to x. This is an example of an integral that requires a trigonometric substitution to evaluate. Specifically, we can let x = sin(θ)/√2 and dx = cos(θ)/√2 dθ. Substituting these expressions into the integral yields:

∫ dx/√(1-2x^2) = ∫ (cos(θ)/√2) / √(1-2(sin(θ)/√2)^2) dθ

Simplifying the denominator gives:

√(1-2(sin(θ)/√2)^2) = √(1 - sin^2(θ)) = cos(θ)

Substituting this expression into the integral gives:

∫ dx/√(1-2x^2) = ∫ (cos(θ)/√2) / cos(θ) dθ = ∫ dθ/√2 = (1/√2)θ + C

To find the value of the integral, we need to substitute back in for x and evaluate at the limits of integration. If we are integrating over the interval [-1/√2, 1/√2], then:

(1/√2)θ evaluated from -π/4 to π/4 gives:

(1/√2)(π/4 + π/4) - (1/√2)(-π/4 - π/4) = (1/√2)π

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There were 19 teachers sitting in the school auditorium.

The question provides us with the total number of people present in the auditorium, which is 81. It also tells us that 19 of them were teachers. Therefore, the number of students present in the auditorium can be found by subtracting the number of teachers from the total number of people, which is 81 - 19 = 62.

Since the question only asks about the number of teachers present in the auditorium, the answer is simply 19. This is because the question already provides us with the information that there were 19 teachers present.

Alternatively, we can use algebra to solve the problem. Let x be the number of students present in the auditorium. Then, we can write an equation based on the total number of people in the auditorium: x + 19 = 81. Solving for x, we get x = 81 - 19 = 62. Therefore, the number of teachers present in the auditorium is 19.

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Cos(165) in terms of sine and cosine of an acute angle is -1 + 2sin^2(7.5).

We can use the trigonometric identity cos(180 - x) = -cos(x) to find cos(165) in terms of cosine of an acute angle.

Since 165 = 180 - 15, we have:

cos(165) = cos(180 - 15) = -cos(15)

To express cos(15) in terms of sine and cosine of an acute angle, we can use the following trigonometric identities:

sin(2x) = 2sin(x)cos(x) and cos(2x) = cos^2(x) - sin^2(x)

Let's take x = 7.5, which is half of 15 (the acute angle):

sin(15) = 2sin(7.5)cos(7.5)

cos(15) = cos^2(7.5) - sin^2(7.5)

Now, we can solve for cos(15):

cos(15) = cos^2(7.5) - sin^2(7.5)

= (1 - sin^2(7.5)) - sin^2(7.5)

= 1 - 2sin^2(7.5)

Therefore, we have:

cos(165) = -cos(15)

= -[1 - 2sin^2(7.5)]

= -1 + 2sin^2(7.5)

So, cos(165) in terms of sine and cosine of an acute angle is -1 + 2sin^2(7.5).

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The equation given in the solution is X(t) = (cos(4t) + C2sin(4t)). This equation represents the position of the mass at time t after the spring has been released with an initial velocity of 0. The terms "spring" and "stretch" indicate that Hooke's Law is being used to determine the spring constant k.

The term "velocity" is used to describe the initial velocity of the mass, which is given as 0. The position of the mass at time t is determined by the value of X(t), which is a function of time. Therefore, the position of the mass at any given time can be found by plugging in the value of t into the equation X(t) = (cos(4t) + C2sin(4t)).
Hi! Based on the information provided, you have a spring with a mass of 6 kg and a natural length of 0.3 m. A force of 38.4 N is required to stretch it to 0.7 m. The spring constant, k, is determined to be 96. The spring is then stretched to 0.7 m and released with an initial velocity of 0. To find the position of the mass at time t, you can use the equation:
x(t) = C1 * cos(4t) + C2 * sin(4t)

Given the initial condition x(0) = 0.4, we find that C1 = 0.4. The initial velocity x'(0) is 0, leading to the conclusion that C2 = 0. Therefore, the equation for the position of the mass at time t is:
x(t) = 0.4 * cos(4t)

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The total amount of the principal, interest, down payment, and fees described for Brooke's condominium is $1,154,091.59

The first step is to calculate the mortgage amount, which is the purchase price minus the down payment:

Mortgage amount = $413,600 - 9% of $413,600 = $376,576

Next, we need to calculate the total cost of the fees and charges:

Discount points = 1% of $376,576 = $3,766

Origination fee = 0.75% of $376,576 = $2,823.42

Documentary stamp tax on deed = $0.70 per $100 or portion thereof, so for $413,600 it would be:

$0.70 * ($413,600 / $100) = $2,895.20

Documentary stamp tax on mortgage = $0.35 per $100 or portion thereof, so for $376,576 it would be:

$0.35 * ($376,576 / $100) = $1,318.02

Brokerage fee = $175 + 5% of $376,576 = $19411.8

Intangible tax = 0.2% of $376,576 = $753.15

Now we can calculate the total cost of the principal and interest payments over the life of the mortgage. We'll use a mortgage calculator to do this, based on the mortgage amount, interest rate, and term:

Total mortgage payments = $2,244 * 12 months * 25 years = $673,200

Finally, we can add up all of these amounts to get the total cost of the principal, interest, down payment, and fees:

Total cost = Purchase price + Down payment + Mortgage payments + Discount points + Origination fee + Documentary stamp tax on deed + Documentary stamp tax on mortgage + Brokerage fee + Intangible tax

Total cost = $413,600 + $37,224 + $673,200 + $3,766 + $2,823.42 + $2,895.20 + $1,318.02 + $19,411.80 + $753.15

Total cost = $1,154,091.59

Therefore, we got a total cost of $1,154,091.59

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The ratio of the perimeters is 14/5, which simplifies to 70/25, which reduces to 14/5. So the answer is (d) 5/7.

Let's use the fact that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths. If we let the corresponding side lengths be a and b, then we have:

(area of first triangle)/(area of second triangle) = (a^2)/(b^2)

We are given that the areas of the two triangles are 50 cm^2 and 98 cm^2, respectively. Let's call the side lengths of the first triangle a1, a2, and a3, and the side lengths of the second triangle b1, b2, and b3. Then we have:

(50)/(98) = (a1a2)/(b1b2)

We don't know the actual values of a1, a2, b1, and b2, but we can find the ratio of their perimeters by adding up the side lengths of each triangle. Let's call the perimeters of the first and second triangles P1 and P2, respectively. Then we have:

P1 = a1 + a2 + a3

P2 = b1 + b2 + b3

Dividing P1 by P2, we get:

P1/P2 = (a1 + a2 + a3)/(b1 + b2 + b3)

We can rewrite the ratios of the side lengths using the equation we found earlier:

P1/P2 = [(a1a2)/(b1b2)]*[(a1 + a2 + a3)/(a1 + a2 + a3)]

P1/P2 = [(a1a2)/(b1b2)]*1

P1/P2 = (a1a2)/(b1b2)

We still don't know the values of a1, a2, b1, and b2, but we can eliminate them by using the equation we found earlier:

(50)/(98) = (a1a2)/(b1b2)

Simplifying this expression, we get:

(a1/a2) = sqrt((98/50)*(b1/b2))

We can use this to substitute for one of the ratios of side lengths in the equation for P1/P2:

P1/P2 = [(a1a2)/(b1b2)]*[(a1 + a2 + a3)/(a1 + a2 + a3)]

P1/P2 = [sqrt((98/50)(b1/b2))][(a1 + a2 + a3)/(a1 + a2 + a3)]

P1/P2 = sqrt((98/50)*(b1/b2))

Now we can substitute the given values to get:

P1/P2 = sqrt((98/50)(b1/b2)) = sqrt((98/50)(2/1)) = sqrt(196/50) = 14/5

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The average monthly exchange rate between the us dollar and the Australian dollar for 2018

A. The components of a time series of average monthly exchange rates include trend, seasonality, cyclical fluctuations, and random noise. The trend represents the long-term movement of the exchange rate, seasonality represents repeating patterns within a fixed period, cyclical fluctuations are changes due to economic cycles, and random noise consists of unpredictable fluctuations.

B. To smooth out the patterns that include everything the model learned, you can apply an exponential smoothing method with a chosen smoothing coefficient (alpha). A suitable coefficient could be 0.2, representing a balance between giving weight to recent data and considering the historical pattern. The decision on the coefficient depends on the specific characteristics of the data and the desired degree of smoothing.

C. To forecast the monthly exchange rate for 2020, you can apply various techniques, such as moving average, exponential smoothing, autoregressive integrated moving average (ARIMA), and machine learning-based methods. Each method has its advantages and limitations, and it's important to analyze the performance of each technique on historical data to choose the most appropriate method for forecasting.

D. Comparing the forecasting results of different techniques applied in part (C) requires measuring their accuracy using metrics like mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE). The technique with the lowest error values would be considered more accurate in predicting the monthly exchange rates. It is crucial to consider the data characteristics and the goals of the forecast when deciding on the most suitable technique.

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Answer: 64$

Step-by-step explanation:

The length of the hypotenuse of the right triangle is 15 cm.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Using this formula, we can calculate the length of the hypotenuse of a right triangle.

Given that the longer sides of the right triangle are 9 cm and 12 cm long, we can assume that one of these sides is the shorter side and the other is the longer side. Let's assume that the shorter side is 9 cm long and the longer side is 12 cm long.

Using the Pythagorean Theorem, we can calculate the length of the hypotenuse as follows:

Hypotenuse² = Shorter side² + Longer side²

Hypotenuse² = 9² + 12²

Hypotenuse² = 81 + 144

Hypotenuse² = 225

Taking the square root of both sides, we get:

Hypotenuse = √225

Hypotenuse = 15

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The length of CB is 3 unit.

In the given figure ;

By SAS property of similar of triangles,

ΔCED and ΔCAB are similar.

Therefore,

CE/CB = DE/AB = DC/AC

⇒ CE/CB = DC/AC

⇒ 2/CB = 2.4/3.6

⇒ CB = (3.6/2.4)X2 = 3

Hence CB = 3

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