(a) how many ways can the letters of the word minutes be arranged in a row? (b) how many ways can the letters of the word minutes be arranged in a row if m and i must remain next to each other as either mi or im? .

By solving a system of equations we conclude that Collen has 6 quarters, 4 dimes, and 2 nickels.

First, let's define the variables:

There are 12 coins, so:

x + y + z = 12

She has 2 dollars in total, so:

x*0.25 + y*0.05 + z*0.10 = 2

And she has 3 times as many quarters as nickels.

x = 3y

Then we can write the system of equations (or matrix, depending on how you like to see it):

x + y + z = 12

x*0.25 + y*0.05 + z*0.10 = 2

x - 3y = 0

To use the elimination method we just need to add/subtract these equations to remove variables.

If we subtract the third equation to the first one:

(x + y + z) - (x - 3y) = 12 - 0

4y + z = 12

Now we have two equations:

x*0.25 + y*0.05 + z*0.10 = 2

4y + z = 12

If we multiply the first one by 4:

x + y*0.20 + z*0.40 = 8

Subtracting the third eq:

x + y*0.20 + z*0.40 - (x - 3y) = 8 - 0

y*3.20 + z*0.40 = 8

Now the remaining equations are:

4y + z = 12

y*3.20 + z*0.40 = 8

On the top one, we can rewrite: z = 12 - 4y

Replacing that in the other equation:

y*3.20 + (12 - 4y)*0.40 = 8

Now we eliminated the variables x and z, so we can solve this for y:

y*1.60 + 4.8 = 8

y*1.60 = 3.2

y = 3.2/1.6 = 2

Now that we know the value of y, the values of x and z are:

x = 3y = 3*2 = 6

z  = 12 - 4y = 12 - 4*2 = 4

Then we conclude that Collen has 6 quarters, 4 dimes, and 2 nickels.

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

Therefore, the sum of the first 1234 terms of this sequence is 1234.

To find the sum of the first 1234 terms of the sequence consisting of 1's separated by blocks of 2's with n 2's in the nth block, we need to determine the number of blocks and the number of 1's in each block.

Let's examine the pattern of the sequence:

Block 1: 2's

= 1's

= 1 (1 2)

Block 2: 2's

= 2's

= 22 (1 22 1)

Block 3: 2's

= 3's

= 222 (1 222 1)

Block 4: 2's

= 4's

= 2222 (1 2222 1)

...

We observe that the number of 2's in each block is equal to the number of the block itself. So, in the nth block, there are n 2's.

Now, let's calculate the number of blocks required to reach the 1234th term:

To find the number of blocks, we need to determine the maximum block number before the 1234th term. We can calculate this by finding the sum of the series 1 + 2 + 3 + ... + n until the sum is greater than or equal to 1234.

The formula for the sum of the series 1 + 2 + 3 + ... + n is given by: S = (n/2)(n+1).

Let's solve this equation:

(n/2)(n+1) = 1234

\(n^2 + n - 2468 = 0\)

Using the quadratic formula:

n = (-1 + √(1 + 4*2468)) / 2

n ≈ 61.76

Since n must be a whole number, we take the ceiling of n, which gives us 62.

Therefore, there are 62 blocks in the sequence.

Next, let's calculate the number of 1's in each block:

In the nth block, there are n 2's. Since each 2 is separated by a 1, there are n + 1 terms in each block.

So, the number of 1's in each block is (n + 1) - n = 1.

Since there is always one 1 between two consecutive blocks, the total number of 1's in the sequence is equal to the number of blocks, which is 62.

Finally, let's calculate the sum of the first 1234 terms:

Each block has n + 1 terms, which gives us (n + 1) + (n + 1) + ... + (n + 1) (62 times).

Sum of (n + 1) repeated 62 times = 62(n + 1)

= 62 * 2

= 124.

In addition to the blocks, we have 1234 - 62 = 1172 remaining terms, which are all 1's.

So, the sum of the first 1234 terms is 62 + 1172 = 1234.

To know more about sequence,

https://brainly.com/question/20707381

#SPJ11

Answer:

the answer is 0/1

make the total number 1

because 1/2+3/8+1/8=1

1-1=0/1

Answer:

28 degrees

Step-by-step explanation:

A triangle is 180 degrees. 180-152=28.

Answer:

The third angle is 28 degrees

Step-by-step explanation:

A triangle has to add up to 180 degrees so just take 180 subtract your 152 from it and you'll have your answer!. (180 - 152 = 28) Hope this helps! :)

Answer:

20000000 + 8000000 +30000

Step-by-step explanation:

Answer:

There are three expanded form that we can do. Refer attachments given.

Answer:

The probability of hitting the circular area = P(H) = favorable area/ total area = Area of the circle / Area of the square

Step-by-step explanation:

= π/9

Answer:

2x - 6

Step-by-step explanation:

2(3 - x) - 12 + 4x =

6 - 2x - 12 + 4x =

-6 + 2x =

2x - 6

Answer:

this aint a question right?

Step-by-step explanation:

Answer:

24 will be your answer.

Step-by-step explanation:

Answer: 12.263 sqm

Step-by-step explanation:

1 square meter = 10.7639 square feet

132 square feet in meters would therefore be;

1 sqm : 10.7639 sqf

x sqm: 132 sqf

10.7639x sqm = 132sqf

x sqm = 132 / 10.7639

= 12.263 sqm

Step-by-step explanation:

y=14

y=1

thats the answer.

9514 1404 393

Answer:

  (d)  80y⁶ -10y³

Step-by-step explanation:

You only need to find the highest-degree term of the product to determine the correct answer choice.

That term is the product of the highest-degree terms of the factors:

  (-8y³)(-10y³) = 80y⁶

This matches choice D only.

a) The median number of hours per week these Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k is 5.75 hours.

The median is a central value or a middle value in a distribution. The number of values in a dataset is an important factor that determines the calculation of the median. It is a value that cuts the data set into two equal parts.

The data set consists of 20 Year 12 students. Sort the data in ascending order (or descending order) and find the middle value. Then, use the formula for calculating the median. 

a)The number of hours per week the Year 12 students spend doing homework is given as:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Arrange the data in ascending order:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Now count the data, which gives us 20 numbers. The middle value is the 10th and the 11th numbers, which are both 4.

So the median of the number of hours per week Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k can be found using the following formula:

100% - 10% = 90%

So, 90% of students study for k hours or less.

So, the value of k can be found using the median. The median value is 4 hours, and 90% of students are studying for k hours or less. Therefore, 10% of students study for more than k hours.

k = 10% more than the value of the 90th percentile value, which is given by: k = 5.5 + ((8-5.5)/10)*1 = 5.5 + 0.25 = 5.75 hours.

Therefore, 10% of Year 12 students spend more than 5.75 hours per week doing homework.

To know more about the "median": https://brainly.com/question/26177250

#SPJ11

In order to find the expected value of a probability distribution, you multiply each possible outcome by its corresponding probability and sum up the results. The expected value represents the average outcome you would expect to obtain if you repeated the experiment many times.

First, list all the possible outcomes and their associated probabilities. Then, multiply each outcome by its probability. Finally, add up all the products to find the expected value.

For example, let's consider a discrete probability distribution with outcomes x1, x2, ..., xn and their respective probabilities p1, p2, ..., pn. The expected value (E) is calculated as:

E = (x1 * p1) + (x2 * p2) + ... + (xn * pn)

Alternatively, if you have a continuous probability distribution, you need to integrate over the entire range of possible outcomes. In this case, the expected value is given by:

E = ∫(x * f(x)) dx

where f(x) is the probability density function.

The expected value provides a measure of the central tendency of the distribution and is often used in decision-making and statistical analysis.

To know more about expected value, refer here:

https://brainly.com/question/29068283#

#SPJ11

Answer:

Step-by-step explanation:

let y be the total charges

given that the hour is h

and the cost for raw material is r

therefore

1. The first hour of service call = $60

2. For each additional hour= 25h

 3. 30% over the cost of the materials.= 30/100*r=0.3r

total charges

y=60+25h+0.3r

therefore the expression is

y=60+25h+0.3r

The length of the rope that he needs to purchase if he makes two rounds of fence would be = 132m and at the cost of = Rs528

The perimeter of an object is defined as the total length of the boundary of that object. The perimeter of a circle can be calculated using the formula= 2πr

Where r = radio = Diameter/2 = 21/2 = 10.5m

π= 22/7

Perimeter = 2× 22/7 × 10.5

= 462/7 = 66

The length of the rope that he needs to purchase if he makes two rounds of fence would be = 2× 66 = 132m

If 1 meter = Rs4

132 meters = 132 × 4 = Rs528

Learn more about perimeter here:

https://brainly.com/question/25092270

#SPJ1

Answer: To determine the cost of Rob's lunch, we need to calculate the total amount he paid, including the cost of the meal and the tip.

Given that Carla's lunch cost $15 and the tip amount was $6, we can find the total amount Rob paid by dividing the tip amount by the tip percentage:

Total amount paid = Tip amount / (Tip percentage / 100)

In this case, the tip amount is $6 and the tip percentage is 20%.

Total amount paid = $6 / (20 / 100) = $6 / 0.20 = $30

So, Rob's total payment, including the cost of his lunch and the tip, was $30.

Since we know that Carla's lunch cost $15, we can subtract this amount from the total payment to find the cost of Rob's lunch:

Cost of Rob's lunch = Total amount paid - Carla's lunch cost = $30 - $15 = $15

Therefore, the cost of Rob's lunch was $15.

Ans .: Interval of one standard deviation from the mean = 63.5 to 90.5.

To find the interval of one standard deviation from the mean for this sample, we need to first calculate the mean and standard deviation.

The mean is found by adding up all the numbers in the sample and dividing by the total number of numbers:

(61 + 69 + 69 + 74 + 85 + 87 + 97) / 7 = 77

So the mean is 77.

To find the standard deviation, we need to calculate the variance first. The variance is found by subtracting each number in the sample from the mean, squaring the result, adding up all the squared results, and dividing by the total number of numbers:

((61-77)^2 + (69-77)^2 + (69-77)^2 + (74-77)^2 + (85-77)^2 + (87-77)^2 + (97-77)^2) / 7 = 183.43

So the variance is 183.43.

The standard deviation is the square root of the variance:

√183.43 ≈ 13.5

So the standard deviation is approximately 13.5.

To find the interval of one standard deviation from the mean, we need to subtract and add the standard deviation to the mean:

77 - 13.5 = 63.5

77 + 13.5 = 90.5

So the interval of one standard deviation from the mean for this sample is approximately 63.5 to 90.5.

We round the non-integer results to the nearest tenth, so the final answer is:

Interval of one standard deviation from the mean = 63.5 to 90.5.

Learn more about :

standard deviation : brainly.com/question/29808998

#SPJ11

The three types of consulting services that audit firms are now prohibited from providing to clients that are public companies are:

1. Bookkeeping services: Audit firms are prohibited from providing bookkeeping services to their audit clients. Bookkeeping involves the recording, organizing, and maintaining of financial transactions.

By prohibiting audit firms from providing bookkeeping services, it helps to ensure independence and objectivity in the audit process. This separation reduces the risk of potential conflicts of interest that could compromise the integrity of the audit.

2. Legal services: Audit firms are also prohibited from providing legal services to their audit clients. Legal services include activities such as drafting legal documents, providing legal advice, and representing clients in legal proceedings.

The prohibition on providing legal services aims to maintain independence and prevent any potential conflicts of interest that could arise if the audit firm were to also provide legal advice or services to the audited company.

3. Financial information systems design and implementation: Audit firms are further prohibited from designing and implementing financial information systems for their audit clients.

This involves the development and implementation of computerized systems that record and process financial data. The prohibition on providing financial information systems design and implementation services helps to avoid any potential bias or lack of objectivity in the audit process,

as the audit firm should remain independent and not be involved in the design and implementation of the systems they are auditing.

By prohibiting audit firms from providing these consulting services, it helps to ensure that the audit process is conducted objectively and independently, without any conflicts of interest.

This enhances the credibility and reliability of financial statements and promotes transparency and trust in the financial markets.

To know more about public companies refer here:

https://brainly.com/question/30957339

#SPJ11

If a business had sales of $4,000,000, and a margin of safety of 25%, the break-even point was is c. $1,000,000.

The margin of safety is the difference between the actual or expected sales and the break-even point. In this case, if the margin of safety is 25%, it means that the business is generating sales that are 25% higher than the break-even point.

To calculate the break-even point, we can use the following formula:

Break-even point = Fixed costs / Contribution margin ratio

The contribution margin ratio is the difference between the sales price and variable costs, divided by the sales price. We don't have enough information to calculate it directly, but we can use the margin of safety to estimate it.

If the margin of safety is 25%, it means that the contribution margin ratio is 25% of the sales price. So, the variable costs must be 75% of the sales price, and the contribution margin ratio is 25%/100% = 0.25.

We know that the sales are $4,000,000, but we don't know the fixed costs. However, we can use the break-even formula to solve for it:

$1,000,000 = Fixed costs / 0.25

Fixed costs = $250,000

Therefore, the break-even point is $250,000 / 0.25 = $1,000,000.

Based on the given information, the break-even point for the business with sales of $4,000,000 and a margin of safety of 25% is $1,000,000.

To know more about sales visit:

https://brainly.com/question/29436143

#SPJ11

The chi-square test for goodness of fit will produce a large value for chi-square under the circumstances where the observed frequencies significantly deviate from the expected frequencies based on the null hypothesis.

The chi-square test for goodness of fit is used to determine if there is a significant difference between the observed frequencies in a sample and the expected frequencies based on a specified distribution.

The test compares the observed frequencies in different categories or groups with the expected frequencies under the null hypothesis.

A large value for chi-square indicates a significant discrepancy between the observed and expected frequencies, suggesting that the null hypothesis is not supported.

This can occur in several circumstances.

First, if the sample size is large, even small differences between observed and expected frequencies can lead to a significant chi-square value.

Second, if there are substantial deviations between the observed and expected frequencies in one or more categories, the chi-square value will be large. This could indicate a lack of fit between the observed data and the expected distribution.

Additionally, if the assumptions of the chi-square test are violated, such as independence of observations or expected frequencies being sufficiently large, it can lead to inflated chi-square values.

These violations can distort the results and lead to a larger chi-square value.

In summary, the chi-square test for goodness of fit produces a large chi-square value when the observed frequencies significantly deviate from the expected frequencies, indicating a lack of fit between the observed data and the expected distribution.

Learn more about chi-square test here:

https://brainly.com/question/30760432

#SPJ11

ANSWER :

The height of the prism is h = 7 ft

The are of the base is B = 12 ft^2

The perimeter of the base is P = 18 ft

Fill in the formula. S = 2x12 + 18x7

The surface area of the triangular prism is 150 ft^2

EXPLANATION :

The given formula for the surface area is :

where B = Base area

P = perimeter of the bases

h = height of the prism

The height of the prism is h = 7 ft

The base is a triangle with dimensions of b = 8 ft and a height h = 3 ft

The area of a triangle is :

The are of the base is B = 12 ft^2

The perimeter of the base is 5 + 5 + 8 = 18 ft, so P = 18 ft

Substitute the results in the formula :

The null distribution is the sampling distribution of the test statistic if the null hypothesis.

In this scenario, the null hypothesis is assumed to be true, and the null distribution is the probability distribution of the test statistic under this assumption. This helps us determine the likelihood of observing a particular test statistic value if the null hypothesis were true, which is crucial for hypothesis testing.

Learn more about Probability: https://brainly.com/question/30034780

#SPJ11

Based on the balance on her account on October 25th, we can calculate that her balance on October 26th was a. $112.16

Any expenses that we make from our bank account reduces our bank balance. This means that Maggie's buying of gasoline and the dinner she went on will reduce her account balance.

Her new balance will therefore be:

= Beginning amount - Expenses

= 170.29 - 32.51 - 25.62

= $112.16

In conclusion, her balance on October 26th is $112.16

Find out more at https://brainly.com/question/13168057.

Answer:

A $112.16

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

a1 = 3

a2 = 3 + 2 = 5

a3 = 5 + 2 = 7

a4 = 7 + 2 = 9

The distance is  mathematically given as

D=1066.66667

The TIME function is included as part of Excel's Date and Time features. With the assistance of TIME, we are able to create a time by employing various components for the hours, minutes, and seconds.

While conducting financial analysis, it's possible that we'll need to date a report. Under these conditions, the TIME function may be used to convert a text string into a format that presents the time as a decimal representation of the seconds, minutes, and hours. Additionally, the function's capabilities include the ability to merge several values into a single time value.

formula= TIME (hour, minute, second)

distance = rate X time

D = RT

T = D/R

20 feet per second = 1200 feet per minute

16 feet per second = 960 feet per minute

(D/R) + 19 + (D/R) = 21

(D/R) + 19 + (D/R) = 21

(D/1200) + 19 + (D/960) = 21,

This is the equation we can use to find the distance from the flowerbed to the​ hive.

(D/1200) + (D/960) = 2

(D(1200)(960))/1200 + (D(1200)(960))/960 = 2(1200)960

960D + 1200D = 5(1200)960

2,160D = 2304000

D=1066.66667

To know more about time function, visit:

brainly.com/question/18724158

#SPJ1