The high school dance team is learning a new routine to a song that lasts 3 minutes and 41 seconds, or 221 seconds total. Yesterday, they covered the first 45 seconds of the song at practice. They learn an average of 22 seconds of the dance in an hour. Let h represent the time, in hours, it will take the team to learn the entire dance. Which equation represents this situation, and how long will it take?

5/9 fraction of the bottle of cleaning solution will Calvin use to clean his entire bathroom.

A fraction is a numeral that represents a rational number.

Let a and b are two number, then their fraction can be represent as a/b.

Given that,

Calvin cleans 3/5 of his bathroom with 1/3 of a bottle of cleaning solution,

This implies that,

3/5 fraction of the whole bathroom takes 1/3 of the bottle

The entire bathroom will take= 1/3×5/3 = 5/9 of the bottle.

A 5/9 fraction will be used to clean the entire bathroom.

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To find the dimensions of an open rectangular tank that holds 4.5 m3 of liquid with minimal material, set the length as twice the breadth and use calculus optimization to derive the breadth, length, and height.

The student is asking for the dimensions of an open rectangular tank that can hold 4.5 m3 of liquid, where the length is twice the breadth, and the amount of material used should be minimal. To solve this, we will use optimization techniques often found in calculus.

Let the breadth be b, the length be l = 2b, and the height be h. The volume V of the tank is given by V = l \b \h = 4.5 m3. Therefore, 2b2h = 4.5.

The surface area A of the tank, which we need to minimize, is A = 2lh + 2bh + lb (since the top is open). Substituting l = 2b, we get A = 2(2b)h + 2bh + (2b)b.

From the volume equation, we can express h in terms of b, which is h = 4.5 / (2b2). Substituting this into the area equation and differentiating it with respect to b will give us a minimum. Finally, solving the equations will determine the breadth, from which we can find the length and height. By this process, we can find the dimensions with the least surface area.

The total cost of tickets for Marika and her three friends to attend a school play, with each ticket costing $5.75, is calculated using the distributive property to be $23.

The question asks to find the total cost of tickets for Marika and her three friends attending a school play, with each ticket costing $5.75, and to justify the answer using the distributive property.

To calculate the total cost, we can use the formula for the total cost which is the number of tickets times the cost of one ticket. In this case, Marika is buying tickets for herself and three friends, making it a total of 4 tickets.

Therefore, using the distributive property, the total cost can be calculated as 4 tickets × $5.75 per ticket.

Using the distributive property, we can represent this as:

(4 × $5) + (4 × $0.75) = $20 + $3 = $23

Thus, the total cost of the tickets is $23.

A. The total outcomes would simply be the product of the number of sides of the two dice, that is:

Total different outcomes = 6 * 6

Total different outcomes = 36

B. The combinations that both dice are even are:

2 – 2, 4 – 4, 6 – 6, 2 – 4, 2 – 6, 4 – 2, 4 – 6, 6 – 2, 6 – 4

So 9 combinations for Jenny

C. The combinations that at least one die is a 4 are:

4 – 4, 4 – 1, 4 – 2, 4 – 3, 4 – 5, 4 – 6, 1 – 4, 2 – 4, 3 – 4, 5 – 4, 6 - 4

So 11 combinations for Henry

D. The probability that jenny wins would simply be the ratio of the number of combinations for Jenny over the total number of combinations, that is:

P (Jenny) = 9 / 36 = 0.25 = 25%

So there is a 25% chance that Jenny will win.

E. The probability that Henry wins would simply be the ratio of the number of combinations for Henry over the total number of combinations, that is:

P (Henry) = 11 / 36 = 0.3056 = 30.56%

So there is a 30.56% chance that Jenny will win.

F. No the game is not fair because Henry has a higher chance of winning than Jenny. For it to be fair, they should have the same probability of winning.

G. We can see that there are actually combinations in which both Jenny and Henry would win. These are:

4 – 4, 4 – 2, 4 – 6, 2 – 4, 6 – 4

So there are 5 combinations in which both of them would win.

So the chance of being tie is:

P(tie) = 5 / 36 = 0.1389 = 13.89%

Hence a 13.89% chance of getting a tie

To convert a number from scientific notation to standard form, consider 1.5625 x 10^4. First, focus on the exponential number, which is 10^4. Multiply the base number, which is 10, by itself the number of times indicated by the exponent, which is four. You would do that like this:

10 x 10 x 10 x 10 = 10, 000

Plug the product -- which is 10,000 -- into the original equation to get this:

1.5625 x 10,000 = 15, 625

Therefore, the standard form of this number is 15,625.

For a number in expanded form, convert the number, using basic addition. For example, consider the expanded number 10,000 + 2000 + 100 + 10 + 9. Add up these numbers to get the standard form. Your equation would look like this:

10,000 + 2,000 + 100 + 10 + 9 = 12,119

Therefore, the standard form of the number is 12,119.

There are 22 boys in Billy's class of 40 students, which means that 55% of the students are boys.

To find the percent of students that are boys in Billy's class, we can start by calculating the number of boys. There are 40 students in total and 18 are girls. Therefore, the number of boys is 40 students minus 18 girls, which is 22 boys. Now, to calculate the percentage of boys, we use the formula:

Percentage = (Number of boys / Total number of students) × 100%

By inserting the numbers we have:

Percentage = (22 / 40) × 100%

Percentage = 0.55 × 100%

Percentage = 55%

So, 55% of the students in Billy's class are boys.

Answer:The third graph (left of the bottom) represents  [tex]y=\left \lceil x \right \rceil[/tex]over the domain 3≤x≤6.

Step-by-step explanation:

The Least Interger Function is represented by [tex]y=\left \lceil x \right \rceil[/tex].

The least integer function is a discontinuous function whose value at any number x is the smallest integer greater than of equal to x .It is denoted by  [tex]\left \lceil x \right \rceil[/tex].and It is also known as ceiling of x.  For example

[tex]\left \lceil3.4\right \rceil=4,\left \lceil5.6\right \rceil=6. \left \lceil4.4\right \rceil=5[/tex]

So the third graph (left of the bottom) represents  [tex]y=\left \lceil x \right \rceil[/tex]over the domain 3≤x≤6.

[we can see all the value of x starting from 3 pointed at y=3 and for x≤ 4 are converging to y=4 which is represented by solid dot  and so on ... ]

Final answer:

The electrician would take approximately 3 months to wire 55 houses at a rate of 4.5 houses per week.

Explanation:

An electrician can wire 4.5 houses per week.

To wire 55 houses at a rate of 4.5 houses per week, the electrician would take 55 / 4.5 = 12.22 weeks. As there are 4.5 weeks per month, dividing the total weeks by the weeks per month gives 12.22 / 4.5 = 2.72 months, which rounds up to 3 months.