A teacher had $57.72 in his checking account. He made a deposit of $209.54. Then he wrote a check for $72.00 and another check for $27.50. What is the new balance in his checking account?

Final answer:

The height of the cone is equal to the slant height plus 1.

Explanation:

To find the height of the cone, we can use the formula for the surface area of a cone: S = πr^2 + πrl, where r is the radius of the base and l is the slant height. Since the problem states that the surface area is equal to the volume, we can set S equal to V and solve for h, the height of the cone.

Here's the step-by-step calculation:

S = V

πr² + πrl = V

πr² + πrl = πr²h

πr² + πrl - πr²h = 0

Combine like terms: πr²(1 - h) + πrl = 0

Divide both sides by πr to solve for h: 1 - h + l = 0

Subtract l from both sides: 1 - h = -l

Subtract 1 from both sides: -h = -l - 1

Multiply both sides by -1 to solve for h: h = l + 1

So, the height of the cone is h = l + 1.

I hope that helps!

The other person is correct i just did the test

Answer:

Step-by-step explanation:

1) Make all the fractions have the same denominator.

- To do that you need to find the LCM (least common denominator) of 4, 9, and 7.

(look at image 1)

-Then apply the number you multiply the original denominator by to the original numerator

(look at image 2)

-Add the fractions together

(look at image 3)

0.075 m is 7.5 centimeters.

A unit conversion expresses the same property as a different unit of measurement.

Given that, convert 0.075 m into cm

We know that, 1 meter = 100 centimeters

0.075 meter = [(100) × 0.075] centimeter

0.075 meter = (100 × 0.075) centimeter

= (100 × 75/1000) centimeter

= (7500/1000) centimeter

= (75/10) centimeter

= 7.5 centimeter.

Hence, 0.075 m is 7.5 centimeters.

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A function can either be discrete or continuous, depending on the input values of the function

From the question, we understand that:

Notice that:

It is impossible to ask the contestant 1.5 questions

And base on the possible earnings, the contestant cannot earn $50.5 or number with decimal

When the data we are dealing with are non-decimal numbers, then the distribution is discrete

The domain and range

There are 5 possible questions to ask;

So, the domain is [0,5]

The contestant starts with $100.

So, the range is [0,100]

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Answer with explanation:

The equation, y=3 x,

y=Distance traveled

x =Total time

[tex]\frac{\text{Distance traveled}}{\text{Time}}=\frac{y}{x}=3\\\\ \frac{dy}{dx}={\text{Rate of change}}={\text{Velocity}}=3 {\text{unit of time}][/tex]

Also, in terms of straight line

Slope =3= uniform Velocity

Point (3,9) and (5,15) represents Distance traveled in 3 (unit of time) =9 unit ,and 15 unit=Distance traveled in 5 (Unit of time).

→Alonso is moving with uniform speed=3 (unit of time), as velocity remains constant in the entire process.

The graph of line y = 3x, y represents distance and x represents the time and the point (3,9) repersents the distance covered by Alonso's is 9 unit in 3 unit of time and the point (5,15) repersents the distance covered by Alonso's is 15 unit in 5 unit of time.

Given :

y = 3x , represents Alonso's walking speed.

If y = 3x represents Alonso's walking speed than y represents distance and x represent time. The graph of y = 3x is attached below.

The point (3,9) on the line (y = 3x) represent that at 3 unit of time the distance covered by Alonso's is 9 unit.

The ponit (5,15) on the line (y = 3x) represent that at 5 unit of time the distance covered by Alonso's is 15 unit.

Therefore, in the graph of line y = 3x, y represents distance and x represents the time and the point (3,9) repersents the distance covered by Alonso's is 9 unit in 3 unit of time and the point (5,15) repersents the distance covered by Alonso's is 15 unit in 5 unit of time.

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Consider the Set A = {X | X is an even whole number between 0 and 2 } = [tex]\Phi[/tex].

Since, whole numbers are the set of numbers starting from zero upto infinity.

Even numbers are the numbers which are exactly divisible by '2'.

So, we have to find the even whole number between 0 and 2.

Since, only '1' is a whole number between 0 and 2 which is not an even number as '1' is not divisible by '2'.

Therefore, there is no even whole number between 0 and 2.

So, this set is empty.

Therefore, A = { X | X is an even whole number between 0 and 2} =  [tex]\Phi[/tex]

The distance between the two airports is 252 miles

What is Speed?

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the distance between the two airports be = D

Now ,

Let the first airport be = A

Let the second airport be = B

And , the speed from Airport A to Airport B averaged = 280 mph

The speed from Airport B to Airport A averaged = 120 mph

The total time taken for the journey = 3 hours

So , the value of Time T = 3 hours

So , the equation will be

Time = Distance / Speed

Since , the distance between the airports remains the same on the journey,

Time = D/280 + D / 120

Substituting the values in the equation, we get

D/280 + D / 120 = 3

The LCM of 280 and 120 is 840 , so

( 3D + 7D ) / 840 = 3

On simplifying the equation , we get

Multiply by 840 on both sides of the equation , we get

10D = 2520

Divide by 10 on both sides of the equation , we get

D = 252 miles

Therefore , the value of distance D from the equation is 252 miles

Hence , The distance between the two airports is 252 miles

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Final answer:

By solving the equation 280t = 120(3 - t), we find that the time taken to fly to the city is 0.9 hours. Multiplying this by the speed of 280 mph, the distance between the two airports is determined to be 252 miles.

Explanation:

To find the distance between the two airports, we can use the formula distance = speed × time, but first, we need to find the time taken for each leg of the journey. Let t be the time (in hours) it takes for the plane to fly to the city at 280 mph. Hence, the time taken to return to the international airport at 120 mph will be 3 - t hours. We can establish the following equations based on this information:

To the city: 280t (since distance = 280 mph × t)

Returning: 120(3 - t) (since distance = 120 mph × (3 - t))

Since the distances are equal for both trips, we can set the equations equal to each other:

280t = 120(3 - t)

Solving for t, we get:

280t = 360 - 120t
400t = 360
t = 0.9

The time taken to fly to the city at 280 mph is 0.9 hours. Now we can find the distance:

Distance to the city = 280 mph × 0.9 h = 252 miles.

Therefore, the distance between the two airports is 252 miles.

Answer:

c = s + 4    

Step-by-step explanation:

We have given the Sal's and Carrie's ages. We need to represents the table below using equation.

Sal    =    3     5    8    13   15

Carrie =   7    9    12   17    19

Out of given options, equation (3) should be followed. We can proof it as :

c = s + 4

Putting one by one the ages of Sal in the above equation to get Carrie's age.

1. c = 3 + 4 = 7

2. c = 5 + 4 = 9

3. c = 8 + 4 = 12

4. c = 13 + 4 = 17

5. c = 15 + 4 = 19

Hence, the correct option is (c).

45 1/2 per cent as a fraction in simplest form is 91/200.

We need to write 45 1/2% as a fraction in the simplest form.

A fraction is in its simplest form when the top and bottom cannot be any smaller, while still being whole numbers.

To simplify a fraction: Divide the top and bottom by the greatest number that will divide both numbers exactly (they must stay whole numbers).

Now, 45 1/2% can be written as 45.5/100

Multiply both numerator and denominator by 10.

That is 455/1000

Now, 455/1000 = 91/200

Therefore, 45 1/2 per cent as a fraction in simplest form is 91/200.

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Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The number of ways in which the password can be formed is 7,893,600.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Given that a computer system password requires five characters, all lowercase letters (remember there are 26 letters), and all the letters must be different. Therefore, if a letter is used once it can not be used again.

For the first place available options = 26 letter

Now, one letter is only used therefore, there are only 25 options available for the next place.

For the Second place available options = 25 letter

Now, two letters are only used therefore, there are only 24options available for the next place.

For the third place available options = 24 letter

Now, three letters are only used therefore, there are only 23 options available for the next place.

For the fourth place available options = 23 letter

Now, the four letter are only used therefore, there are only 22 options available for the next place.

For the fifth place available options = 22 letter

Further, the number of ways in which the password can be formed is,

Number of ways = 26 × 25 × 24 × 23 × 22 = 7,893,600

Hence, the number of ways in which the password can be formed is 7,893,600.

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Final answer:

There are 789,360 different passwords that are possible.

Explanation:

To find the number of different passwords that are possible, we can consider the problem in a step-by-step manner.

To find the total number of possible passwords, we can multiply these choices together: 26 × 25 × 24 × 23 × 22 = 789,360.

Answer:

The correct option is:   $1.45 + $0.55x ≤ $35 ;  x ≤ 61 miles

Step-by-step explanation:

Suppose, the number of miles Ariel can travel [tex]=x[/tex]

The cab charges $1.45 for the flat fee and $0.55 for each mile. So, the total charges for [tex]x[/tex] miles [tex]=\$1.45+\$0.55x[/tex]

Given that, she has $35 to spend. That means, the total charges must be less than or equal to $35.

So, the inequality will be:   [tex]\$1.45+\$0.55x\leq \$35[/tex]

Solving the above inequality....

[tex]1.45+0.55x\leq 35\\ \\ 0.55x\leq 35-1.45\\ \\ 0.55x\leq 33.55\\ \\ x\leq \frac{33.55}{0.55}\\ \\ x\leq 61[/tex]

So, the number of miles Ariel can travel is 61 miles.