mr.lim has a rectangle-shaped garden 24m long and 18 wide.he wants to plant trees on every side of the garden and to have them placed the same distance from each other.what is the least numbeer of trees he should plant?

The probability that exactly 6 patients is 2.0669, and the probability that at least 2 patients is 0.0017.

In large restaurants, an average of 3 out of every 5 customers ask for water with their meal. A random sample of 10 customers was selected. We need to estimate the probability that exactly 6 patients and at least 2 patients. The given situation is a binomial distribution since the experiment has only two outcomes, success or failure.

Here, Success is defined as requesting water with a meal, and failure as not requesting water with a meal. The probability of success is p = 3/5 = 0.6 and the probability of failure is q = 1 - p = 1 - 0.6 = 0.4. Let X be the number of patients requesting water with a meal out of 10 patients selected.

P(X = 6) = 10C6 (0.6) (0.4)⁴

= 210 × 0.31104 × 0.0256

= 2.0669P(X ≥ 2)

= P(X = 2) + P(X = 3) + .... + P(X = 10)P(X ≥ 2)

= 10C2 (0.6)² (0.4)⁸ + 10C3 (0.6)³ (0.4)⁷ + ..... + 10C10 (0.6)¹⁰ (0.4)⁰ P(X ≥ 2)

= 0.0022 + 0.0185 + 0.0881 + 0.2353 + 0.3454 + 0.2508 + 0.0986 + 0.0180 + 0.0016P(X ≥ 2)

= 1 - P(X < 2)P(X < 2) = P(X = 0) + P(X = 1)P(X < 2)

= 10C0 (0.6)⁰ (0.4)¹⁰ + 10C1 (0.6)¹ (0.4)⁹ P(X < 2)

= 0.0001 + 0.0016P(X < 2)

= 0.0017

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We can see here that the main difference between the teaching of data handling in Grade 5 and Grade 6 is the complexity of the concepts that are taught.

Data handling refers to the process of organizing, managing, and manipulating data in order to extract useful information and draw meaningful insights. It involves various tasks, including collecting, storing, cleaning, analyzing, and presenting data.

In Grade 5, students are introduced to basic concepts of data handling, such as collecting, organizing, and representing data. In Grade 6, students learn more complex concepts, such as analyzing and interpreting data, and using data to make decisions.

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Hello! :)

1/2x + 5 = 15

1/5x + 5 - 5 = 15 - 5 Subtract 5 from both sides

1/2x = 10

2 * (1/2x) = (2) * (10) Multiply both of the sides by 2

x = 20

Hope this answer helped you!

THEDIPER

Answer:

x = 20

Step-by-step explanation:

1/2 x 20/1 = 20/2 = 10

10 + 5 = 15

Hope this helps.

The area of the polygon is 37.81 units and the perimeter is 33.02 units.

The given points are in order, we have:

a(-3, 2)

f(2, -3)

b(0, 5)

c(3, 2)

d(5, 4)

e(7, 2)

g(0, -1)

Using the distance formula, we can find the lengths of the sides of the polygon. Then, we can add up the lengths of all the sides to find the perimeter of the polygon.

As per the shown figure,

Length of side fa = 7.07 units

Length of side ef = 7.07 units

Length of side de = 7.6 units

Length of side cd = 2.8 units

Length of side bc = 4.24 units

Length of side ab = 4.24 units

The perimeter of the polygon is:

= fa + ef + de + cd + bc + ab

= 7.07 + 7.07 + 7.6 + 2.8 + 4.24 + 4.24

= 33.02 units

The area of the polygon is:

= area of rectangle (1) + area of sqare (2)

= 7.07 × 4.24 + 2.8 × 2.8

= 37.81 units

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The graph is given below.

The area of the square TUVW is 9 square units.

We have,

The square TUVW with vertices

T = (-2, -4)
U = (-5, -4)

V = (-5, -1)

W = (-2, -1)

Now,

To find the area of the square TUVW, we need to find the length of its sides first.

Using the distance formula, we can find the length of TU:

TU = √((Ux - Tx)² + (Uy - Ty)²)

= √((-5 - (-2))² + (-4 - (-4))²)

= √(9)

= 3

Since TUVW is a square, all of its sides have the same length,

So UV = VW = WT = 3 as well.

The area of the square is the length of one side squared.

Area = side²

= 3²

= 9

Therefore,

The area of the square TUVW is 9 square units.

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Answer:

C

Step-by-step explanation:

After 14 days, you will have approximately $2.4414 invested in the stock market.

The amount you will have invested after 14 days can be calculated using the geometric sequence formula. The formula for the nth term of a geometric sequence is given by:

an = a1 x \(r^{(n-1)\)

Where:

an is the nth term,

a1 is the first term,

r is the common ratio, and

n is the number of terms.

In this case, the initial investment is $20,000, and each day the investment loses half of its value, which means the common ratio (r) is 1/2. We want to find the value after 14 days, so n = 14.

Substituting the given values into the formula, we have:

a14 = 20000 x\((1/2)^{(14-1)\)

a14 = 20000 x \((1/2)^{13\)

a14 = 20000 x (1/8192)

a14 ≈ 2.4414

Therefore, after 14 days, you will have approximately $2.4414 invested in the stock market.

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The amount you will have invested after 14 days is given as follows:

$2.44.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term of the sequence.

The parameters for this problem are given as follows:

\(a_1 = 20000, q = 0.5\)

Hence the amount after 14 days is given as follows:

\(a_{14} = 20000(0.5)^{13}\)

\(a_{14} = 2.44\)

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The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

According to the statement

we have to find that the number of ways are there to select the applicants who will be hired.

So, For this purpose, we know that the

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Here we use the combination.

And from the given information:

20 applicants from a pool of 90 applications will be hired.

And according to this the combination becomes:

\(C_{20} ^{90}\)

then solve it

\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)

\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)

Then after solve it

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)

Now open another factorial

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)

Now solve this then

\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).

So, The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

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Answer:

i dont know the answer but can i tell you what math is please dont get mad at me theres still someone who can give you the right answer

Step-by-step explanation:

Mental

Abuse

To

Humans

The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873

Let X shows the number of messages received per hour. The pdf of X is

\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)

Therefore, the probability that 5 messages are received in a single hour is

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)

(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is

\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)

(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is

\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)

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The monthly payment for a bank loan assuming a one-year repayment period and 13.5% interest is To calculate the monthly payment for a bank loan, we can use the formula:

Monthly payment = Total cost / Number of months

Given that the total cost is $1,800 and the repayment period is one year (12 months), we can substitute these values into the formula:

Monthly payment = $1,800 / 12 = $

Now, let's calculate the total cost for the bank loan:

Total cost = Monthly payment * Number of months

Total cost = $ * 12 = $

For the add-on method of interest calculation with a one-year repayment period and 11.5% interest, the monthly payment is $ (main answer).
The add-on method of interest calculation involves adding the interest to the principal amount and then dividing it by the number of months.

Given that the total cost is $1,800 and the repayment period is one year (12 months), we can calculate the interest as follows:

Interest = Total cost * Interest rate

Interest = $1,800 * 11.5% = $

Now, let's calculate the new principal amount:

New principal amount = Total cost + Interest

New principal amount = $1,800 + $ = $

Finally, we can calculate the monthly payment:

Monthly payment = New principal amount / Number of months

Monthly payment = $ / 12 = $

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Answer:

The volume is approximately 50 m^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h where r is the radius and h is the height

The radius is 1/2 of the diameter r = 8/2 = 4

V = pi ( 4)^2 (1)

V = 16 pi

Letting pi be approximated by 3.14

V = 3.14 * 16

V = 50.24

The volume is approximately 50 m^3

Answer:

Function with smallest zero  is:

f(x); (2, 0).

Step-by-step explanation:

f(x):

2x2 − 14x + 20 = 0

x^2 - 7x + 10 = 0

(x - 5)(x - 2) = 0

So the zeroes are (2, 0) and (5, 0)

g(x):

From the table:

when g(x) = 0, x =19 so its zero is (19, 0).

Using the above information, we can calculate the missing figures in the table and this is shown on the table attached.

For the "Shorts" row: It's given that 42 people were wearing shorts.

Therefore, the "Close-Toed Shoes" column in the "Shorts" row is also 42, and the "Total" column is the sum of open-toed and closed-toed shoes, which is 84.

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See text below

30 people surveyed were wearing open-toed shoes.

1/3 of the people with open-toed shoes were wearing

pants.

• 42 people were wearing shorts.

Twice as many people were wearing closed-toed shoes

than open-toed shoes.

Complete the table using the information given.

                   Open-Toed Shoes              Close-Toed Shoes         Total

Shorts                     -------                           ------                               --------

Pants                         ------                           ----------                            ------

Total                          ------                           ----------                            ---------

No, the determinant of a matrix can only be calculated for square matrices. A square matrix has an equal number of rows and columns, while a non-square matrix has a different number of rows and columns.

The determinant is a mathematical property that is defined for square matrices only. It is a scalar value that represents certain characteristics of the matrix. To calculate the determinant of a square matrix, you can use various methods such as expansion by minors, cofactor expansion, or using the properties of determinants.

For example, let's consider a 3x2 non-square matrix:

```

A = [[1, 2],

    [3, 4],

    [5, 6]]

```

Since A is a non-square matrix, we cannot calculate its determinant.

the determinant is a concept applicable only to square matrices. Non-square matrices do not have a determinant.

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Answer:

49.621

Step-by-step explanation:

If you need to show your work, just multiply 3,817 by 13 which equals 49,621. Then divide 49,621 by 10 three times to get 49.621

Answer:

b

Step-by-step explanation:

The statement about the data in the table is true is option b.  The data show a linear relationship because the rate of change is decreasing.

Since The table shows the air pressure left in the tire after each hour.

So as per the given table we can see the hours is increased and the air pressure is decreased.

So according to this, we can say that the option b is correct.

And, the rest of the options are wrong.

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From the diagram, we can see that

Answer:

Step-by-step explanation:

subtract 2 from both sides

Answer:

divide both sides by 3

Step-by-step explanation:

Answer:

Width

Step-by-step explanation:

As you need two widths and two lengths and as the length is shorter than the width by 10 it is - 20 to account for that. if the x was the length then it would add 20 instead

P(X ≤ 10) represents the probability that up to 10 apples in a basket of 100 are too small to sell.

To find the proportion of apples from the 2006 crop that were too small to sell, we need to calculate the probability that an apple weighs less than 130 grams. We can do this by using the standard normal distribution.

Proportion of apples too small to sell:

Let X be the weight of an apple from the crop. We are given that X follows a normal distribution with a mean of 173 grams and a standard deviation of 34 grams.

To find the proportion of apples weighing less than 130 grams, we need to calculate the cumulative distribution function (CDF) of the standard normal distribution up to the z-score corresponding to 130 grams.

First, we need to standardize the value of 130 grams using the formula:

z = (X - μ) / σ

where X is the value (130 grams), μ is the mean (173 grams), and σ is the standard deviation (34 grams).

z = (130 - 173) / 34 = -43 / 34 ≈ -1.2647

Using a standard normal distribution table or a calculator, we can find the CDF corresponding to this z-score. The CDF represents the proportion of values less than -1.2647 in the standard normal distribution.

Let P(Z < -1.2647) = p

The proportion of apples from the 2006 crop that were too small to sell is approximately p.

Probability of up to 10 apples too small to sell in a basket of 100 apples:

We can use the binomial distribution to calculate the probability of up to 10 apples being too small to sell in a basket of 100 apples.

Let X be the number of apples too small to sell in a basket of 100. The probability of a single apple being too small is p, as calculated in the previous step.

Using the binomial distribution formula, we can calculate the probability of X being less than or equal to 10:

P(X ≤ 10) = Σ (n choose x) * p^x * (1 - p)^(n - x)

where n is the number of trials (100), x is the number of successes (up to 10), and p is the probability of success (as calculated earlier).

This involves summing the probabilities for x = 0, 1, 2, ..., 10.

By calculating this probability, we can determine the likelihood of encountering up to 10 undersized apples in a picker's basket of 100 apples.

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Answer:

4 inches

Step-by-step explanation:

The surface area, A of a right square pyramid is given by :

A = a² + 2as

Where, s = height of each triangular surface = x

a = base edge of pyramid

Substituting values into the equation :

A = 84 in² ; a = 6 in ; Slant height, s = x

84 = 6² + 2(6 * x)

84 = 36 + 2(6x)

84 = 36 + 12x

84 - 36 = 12x

48 = 12x

48/12 = 12x / 12

4 = x

Hence, Slant height, x = 4 inches

Answer:

4 inches

Step-by-step explanation:

The surface area, A of a right square pyramid is given by :

A = a² + 2as

Where, s = height of each triangular surface = x

a = base edge of pyramid

Substituting values into the equation :

A = 84 in² ; a = 6 in ; Slant height, s = x

84 = 6² + 2(6 * x)

84 = 36 + 2(6x)

84 = 36 + 12x

84 - 36 = 12x

48 = 12x

48/12 = 12x / 12

4 = x

Hence, Slant height, x = 4 inches

Answer:

35

Step-by-step explanation:

70 minutes for 24 songs

70/2 minutes for 24/2 songs

35 minutes for 12 songs.

Answer:

35 minutes for 12 songs

Step-by-step explanation:

hope this helps

The optimal solution to the LP relaxation can be either smaller or larger than the optimal IP solution, but it can also provide a lower bound on the optimal IP solution value, and in some cases, it may be very close to the optimal IP solution value.

If both decision variables must be integer, then we are dealing with an Integer Programming (IP) problem. However, we can relax this constraint and solve the Linear Programming (LP) relaxation of the problem. The LP relaxation is solved by allowing the decision variables to take on non-integer values, which often results in a lower objective function value.

In this case, the LP relaxation of the problem will minimize the objective function z = 2x1 + 3x2, but the optimal solution may not be an integer solution. The LP relaxation solution can be either smaller or larger than the optimal IP solution. Therefore, the correct answer is b: "can be either smaller or larger than the optimal IP solution."

However, we can use the LP relaxation solution as a lower bound on the optimal IP solution value. Specifically, we can say that the optimal IP solution value is at least as large as the LP relaxation solution value. In other words, the LP relaxation solution value provides a lower bound on the optimal IP solution value.

Moreover, in some cases, the LP relaxation solution may be very close to the optimal IP solution value. Specifically, the LP relaxation solution may be within 5% of the optimal IP solution value. Therefore, answer choice a: "will be within 5% of the optimal IP solution value" is also a possibility.

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There are three journal entries to establish and record the reimbursement of the petty cash fund.

Here are the three journal entries to establish and record the reimbursement of the petty cash fund:

Journal Entry to Establish the Petty Cash Fund:

Date: 01/Aug

Account Debit Credit

Petty Cash Fund $127.30

Cash $127.30

(To establish the petty cash fund with $127.30 in cash)

Journal Entry to Reimburse the Fund at the End of the First Month:

Date: 31/Aug

Account Debit Credit

Petty Cash Fund $127.30

Computer Repairs Expense $33.65

Refreshments Expense $40.15

Office Supplies Expense $34.40

Cash $195.60

(To record the reimbursement of the petty cash fund at the end of the first month, including expenses for computer repairs, refreshments, and office supplies)

Journal Entry to Reimburse the Fund at the End of the Second Month:

Date: End of the second month (not specified in the information provided)

Account Debit Credit

Petty Cash Fund $XXX.XX

Expense Accounts $XXX.XX

Cash $XXX.XX

(To record the reimbursement of the petty cash fund at the end of the second month, including expenses incurred during that month. The specific amounts and expense accounts will depend on the transactions and amounts involved.)

Please note that the third journal entry is not provided in the given information, as the transactions after August 31 are not mentioned. Therefore, the entry for the end of the second month cannot be accurately determined without additional information.

Correct Question :

Cheque to reimburse the fund tor expenditures. There was $127.30 in cash in the fund. August 2 : Paid $33.65 for minor computer repairs. August 15: Paid $40.15 for refreshments for meetings. August 23 : Purchased ink for the office photocopier, $34.40, to be used this month. August 31: Hector Mendez sorted the petty cash receipts by accounts affected and exchanged them for a cheque to reimburse the fund for expenditures. However, there was $195.60 in cash in the fund. Prepare three journal entries: one to establish the petty cash fund, the second to record the reimbursement of the fund at the end of the first month, and the last to record the reimbursement of the fund at the end of the second month. Enter an appropriate description when entering the transactions in the journal. Dates must be entered in the format dd/mmm

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61 matchsticks need to make 20 squares.

Given,

From the figure,

Matchsticks are used to make the pattern.

To make these 4 squares, you need 13 matchsticks.

To find the how many matchsticks do you need to make 20 squares?

Now, According to the question:

Let the need matchsticks be 'n'

The number of the squares to make 1 square , you need 4 matchsticks,

and when you need to add one square, you need three more matchsticks .

So , we have to make  n no. of squares you need

4 + 3(n - 1) matchsticks     (n \(\geq\) )

= 4 + 3n - 3

= 1 + 3n

When, n = 20

1 + 3 x 20

= 61

Hence, 61 matchsticks need to make 20 squares.

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The probability that the first person picks a mango or a june plum or cashew pack is 0.84

From the question, we have the following parameters:

Start by calculating the total number of fruits

This is represented as

Total number of fruits = Mangoes + Cashew packs + June plums + Jamaican apples

Substitute the known values in the above equation

So, we have the following equation

Total number of fruits = 12 + 17 + 13 + 8

Evaluate the like terms

Total number of fruits = 50

The total number of mango,  june plum or cashew pack is

Selected fruit = Mangoes + Cashew packs + June plums

So, we have

Selected fruit = 12 + 17 + 13

Evaluate

Selected fruit = 42

The probability of picking any of these fruits is then calculated as

Probability (P) = Selected Fruit/Total number of fruits

So, we have

P = 42/50

Evaluate

P = 0.84

Hence, the value of the probability is 0.84

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If for the exam the high score was 98 points and low score was 53 points , then the approximate bin width for the data is 9 points but might round up width to 10 for easier interpretation .

The Class Width for the frequency distribution is defined as the difference between the upper or lower class limits for a consecutive classes in a bin frequency table .

the number of students in the class is = 50 students ,

the high score of the exam was = 98 points ,

the low score of the exam was = 53 points .

the number of bins(classes) = 5 .

the class width is = ( high score - low score)/number of classes ,

class width = (98 - 53)/5

= 45/5

= 9 points .

Therefore , the class width for the data is 9 points .

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The correct answer is option c. 35.3%. The annual percentage yield (apy) for money invested at the given annual rate of 3.5% compounded continuously is  35.3%.

The annual percentage yield (APY) is a measure of the total interest earned on an investment over a year, taking into account the effects of compounding.

To calculate the APY for an investment with continuous compounding, we use the formula:

\(APY = 100(e^r - 1)\),

where r is the annual interest rate expressed as a decimal.

In this case, the annual interest rate is 3.5%, which, when expressed as a decimal, is 0.035. Plugging this value into the APY formula, we get:

\(APY = 100(e^{0.035} - 1).\)

Using a calculator, we find that \(e^{0.035\) is approximately 1.03571. Substituting this value back into the APY formula, we get:

APY ≈ 100(1.03571 - 1) ≈ 3.571%.

Rounding this value to the nearest hundredth of a percent, we get 3.57%.

Among the given answer choices, option c. 35.3% is the closest to the calculated value.

Options a, b, and d are significantly different from the correct answer.

Therefore, option c. 35.3% is the most accurate representation of the APY for an investment with a 3.5% annual interest rate compounded continuously.

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