Plz help this is worth 30 points

Answer:

its A :)

Step-by-step explanation:

The given rational and irrational numbers can be ordered from least to greatest as follows; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.

It follows from the task content that the numbers given are rational and irrational numbers.

To order the numbers, they should be converted to decimal numbers as follows;

-2 3/5 = -2.6

√20 = 4.47

3.9 = 3.9

10/3 = 3.33

3 7/8 = 3.875

Hence, the order from least to greatest is; -2 3/5 < 10/3 < 3 7/8 < 3.9 < √20.

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The probability that the sample mean will be 0.54 or larger, given a population mean of 0.5, can be calculated using statistical techniques.

To calculate the probability, we need additional information about the distribution of distances, such as the standard deviation or the sample size. The probability can be determined using the central limit theorem if the sample size is large enough or if the population distribution is approximately normal.

Assuming the population distribution is approximately normal or the sample size is large, we can use the z-score formula to calculate the probability. The z-score measures the number of standard deviations a particular value is from the mean. In this case, we want to calculate the probability of obtaining a sample mean of 0.54 or larger, given a population mean of 0.5.

First, we calculate the z-score using the formula:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

Without information about the standard deviation or sample size, we cannot calculate the z-score or the probability. If you provide these additional details, I can assist you further in calculating the probability.

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Answer:

the answer is 8 very easy and very simple have a great

day ☺️

Answer:

7%

Step-by-step explanation:

Given data

Principal=  $3600

Time= 2 years

SImple interest=  $504

The expression for the simple interest is given as

SI= PRT/100

We want to find the rate R

504= 3600*R*2/100

cross multiply'

504*100= 3600*R*2

50400= 7200R

divide both sides by 7200

R= 50400/7200

R= 7%

Hence the rate is at 7%

The expression "3' - '2' + 'm' / 'n'" is invalid because it combines character literals and arithmetic operations. The expression "3' - '2' + 'm' / 'n'" is not valid in most programming languages.

It attempts to mix character literals ('3', '2', 'm', 'n') with arithmetic operations (-, +, /), which is not meaningful. In programming languages, characters are typically represented using character literals enclosed in single quotes.

While arithmetic operations are performed on numerical values. The expression should be revised to ensure that the operations are performed on numerical values rather than character literals.

For example, if 'n' and 'm' represent numerical values, the expression could be written as "3 - 2 + m / n" to perform arithmetic operations correctly.

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To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

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A slope of b = 0.007 indicates a weak positive relationship between the two variables, where a small increase in the independent variable corresponds to a small increase in the dependent variable.

The slope of a linear relationship represents the rate of change between two variables. In this case, a slope of b = 0.007 suggests a weak positive relationship between the variables. The positive sign indicates that as the independent variable increases, the dependent variable also tends to increase. However, the small value of 0.007 indicates that the increase in the dependent variable is relatively small for each unit increase in the independent variable.

To illustrate, let's consider an example where the independent variable represents time and the dependent variable represents the number of customers in a store. With a slope of 0.007, it means that for every unit increase in time (e.g., one hour), we can expect a small increase of 0.007 customers on average. This indicates a weak positive relationship, as the increase in customers is relatively modest for each unit increase in time.

In summary, a slope of b = 0.007 indicates a weak positive relationship between the two variables, where a small increase in the independent variable corresponds to a small increase in the dependent variable.

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Answer:

1:2

Step-by-step explanation:

Initially, the base and height of a right angle triangle is 12 and 5.

The hypotenuse can be calculated using Pythagoras theorem such that,

\(BC=\sqrt{12^2+5^2}\\\\BC=h=13\)

When sides are doubled,

Base = 24

Height = 10

Hypotenuse = 26

Perimeter of the triangle = 24+10+26 = 60

The area of riangle,

\(A=\dfrac{1}{2}\times 24\times 10=120\)

Required ration,

\(\dfrac{P}{A}=\dfrac{60}{120}\\\\=\dfrac{1}{2}\)

Answer:

3(a-b) and 3a-3b. Equivalent

2a(2+b) and 4ab. Not equivalent

Step-by-step explanation:

hope this helps:)

Answer: y=8x

Step-by-step explanation:

Slope-intercept form is y=mx+b, where m is slope and b is y-intercept. To find slope, we take any two points and plug them into \(m=\frac{y_2-y_1}{x_2-x_1}\). Let's use (1,8) and (2,16).

\(m=\frac{16-8}{2-1}=\frac{8}{1} =8\)

Now, we know that m=8. Looking at the graph, we can see that the y-intercept is b=0 because the line passes through the y-axis at (0,0). To be sure, let's plug in a point into our equation to see if the y-intercept is correct.

y=8x+b          [plug in (1,8)]

8=8(1)+b       [multiply]

8=8+b           [subtract both sides by 8]

b=0

Therefore, our equation is y=8x.

Answer:

1684.8 cubic units

Step-by-step explanation:

In oblique cylinder the height (altitude) is measured from the opposite base to the base of the cylinder, but it lies outside. We can find the height using Pythagoras theorem.

       h + 7² = 13²

              h²= 169 - 49

              h² = 120

               h = √120

                h = 10.95 units

radius = r = 7 units

\(\boxed{\text{\bf Volume of oblique cylinder = $\bf\pi r^2h$} }\)

                                                    = 3.14 * 7 * 7 * 10.95

                                                    = 1684.8 cubic units

Alan deposited $2500 in an investment account that pays an interest rate of 7. 8% compounded monthly. If he makes no other deposits or withdrawals, Alan will have $9,272 in the account in 15 years.

Given, Alan deposited $2500 in an investment account that pays an interest rate of 7.8% compounded monthly.

To find, We can use the formula for compound interest: A=P(1+r/n)nt, where A is the amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Substitute the given values, we get; P = $2500, r = 7.8%, n = 12 (compounded monthly), and t = 15 years.

A= $2500(1 + (0.078/12))(12×15)

Using the formula above, we get that Alan will have approximately $9,271.57 in the account in 15 years, rounded to the nearest dollar it will be $9,272.

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The total number of lists that can be made with following symbols is 479001600 and 362880 of the lists contain the word "back" in that order.

There are 12 symbols in the given set.

the number of ways it can be arranged such that no symbol is repeated is 12! ways.

so we find 12! = 479001600

Now the words back can only be found as a set so taking the word back as 1 unit we get 9 units.

Number of ways = 9! = 362880

Combinations and selections are synonymous terms. Combinations are the results of selecting elements from a set assortment. Nothing specific is being organized here. We are choosing them. The number of unique r-selections or combinations among a set of n objects is denoted by the symbol nCr.

The number of distinct groups of r objects that can be made from the given n unique objects can be easily calculated using the combinations formula.

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Answer:

0.000000207 in scientific notation = 2.07 × 10^-7

Remember it has to have one number before the decimal.

8.2 * 10^-7 in standard form = 0.00000082

YOu have to move the decimal back.

In the first box the answer is 2.07 × 10^-7.

In the second box the answer is 0.00000082.

The pick-up rate in this scenario would be 80%. This is calculated by dividing the number of rooms occupied (160) by the number of rooms reserved (200), and then multiplying by 100 to get a percentage. So, (160/200) x 100 = 80%. This means that 80% of the reserved rooms were ultimately occupied.

It's important to note that a pick-up rate of 80% is generally considered to be a good result in the hospitality industry. It indicates that the hotel was able to accurately predict the number of rooms that would be needed by the groups, and that the groups themselves followed through on their reservations. A lower pick-up rate could suggest that the hotel overestimated demand, or that some of the groups cancelled their bookings at the last minute. On the other hand, a higher pick-up rate could indicate that the hotel was too conservative in its initial estimates, or that some of the groups requested additional rooms after the initial reservation was made. Ultimately, the pick-up rate is a useful metric for assessing the accuracy of a hotel's forecasting and planning processes.

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Answer:

Step-by-step explanation: I would say the ones with Y= goes into functions and the “X” goes into not function (this is an guess that is half way right)

The William can run 165/16 laps in 1 hour, which can be simplified as 10 5/16 laps in 1 hour.

William ran 2 3/4 laps around a track in 4/15 of an hour.

We can first convert the mixed number 2 3/4 to an improper fraction as: 2 3/4 = (2 × 4 + 3)/4 = 11/4

Now, let the number of laps William can run in 1 hour be x.

We can solve for x as follows: Distance covered in 4/15 hours = 2 3/4 laps

Distance covered in 1 hour = (x/1) laps

To compare the distances covered, we need to make the time intervals equal.

We can multiply the number of laps in 1 hour by (4/15)/(1/1) as follows: 2 3/4 laps = (11/4) laps in 4/15 hour(x/1) laps = x laps in 1 hour

We can equate the two distances covered as follows: (11/4) laps in 4/15 hour = x laps in 1 hour(11/4) × (15/4) = x11 × 15/16 = x165/16 = x

Therefore, William can run 165/16 laps in 1 hour, which can be simplified as 10 5/16 laps in 1 hour.

William can run 165/16 laps in 1 hour.

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(a) If S has a cardinality of 14, then it must contain two elements that have a common divisor greater than 1.

(b) S may or may not contain two elements with a common divisor greater than 1 if its cardinality is 13.

To prove that if S has a cardinality of 14, it must contain two elements with a common divisor greater than 1, we can use the Pigeonhole Principle. The largest prime number less than or equal to 40 is 37. If S does not contain any number greater than 37, its maximum cardinality would be 13 (37 plus 12 composite numbers less than or equal to 37).

Therefore, if ∣S∣=14, it must contain a number greater than 37. This number must have a prime factor greater than 1, and since it is in S, there must be another element in S with the same prime factor, satisfying the condition.

For S with a cardinality of 13, it is not guaranteed that there will always be two elements with a common divisor greater than 1. If S contains only prime numbers, which are the elements without any common divisor other than 1, then it is possible to have ∣S∣=13 without any two elements having a common divisor greater than 1. For example, S = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 39} is a subset of {1, 2, ..., 40} with a cardinality of 13, where all elements are prime numbers and no two elements share a common divisor greater than 1.

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The actual sum of the series exists on the interval [14685/17496, 16302/19305].

To find an interval for which the actual sum of the series exists, we need to use the Lagrange form of the remainder term for the Taylor series.

Let f(x) be the function represented by the given series, and let Sn(x) be its nth partial sum. Then the remainder term Rn(x) is given by:

Rn(x) = f(x) - Sn(x) = (x^(2n+3)/(2n+3)!) * f^(2n+2)(c)

where c is some number between 0 and x.

In our case, we have:

f(x) = Σ (-1)^n * (x^(2n+1)) / (2n+1)!

So, we can write:

f^(2n+2)(x) = (-1)^(n+1) * (2n+2)! / (x^(2n+3))

Substituting these into the expression for Rn(x), we get:

|Rn(x)| = |(-1)^(n+1) * x^(2n+3) / (2n+3)!|

We want to find an interval |S − S5| ≤ |R5| for which the actual sum exists. Since we are given that S5 = 305353/362880, we can rewrite this as:

|S - S5| ≤ |R5| = |(-1)^6 * 1^(25+3) / (25+3)!| = 1/3991680

Therefore, an interval for which the actual sum exists is:

305353/362880 - 1/3991680 ≤ S ≤ 305353/362880 + 1/3991680

Simplifying this inequality, we get:

14685/17496 ≤ S ≤ 16302/19305

So the actual sum of the series exists on the interval [14685/17496, 16302/19305].

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Answer:

105

Step-by-step explanation:

2x17=34

17x2.5=42.5

1.5x17=25.5

1/2x2x2x1.5=3

34+42.5+25.5+3=105

Answer Po Ba Ay 11.33?

Step-by-step explanation:

Calc

The simplified ratio of factorials is (4n - 1)!. To simplify the ratio of factorials (4n-1)!/(4n+1)!, we can cancel out the common factors.

(4n-1)! = (4n-1) * (4n-2) * (4n-3) * ... * 3 * 2 * 1

(4n+1)! = (4n+1) * (4n) * (4n-1) * (4n-2) * (4n-3) * ... * 3 * 2 * 1

We can cancel out (4n-1)! from both the numerator and denominator, leaving us with:

(4n-1)!/(4n+1)! = 1/[(4n+1) * (4n)]
Hi! To simplify the ratio of factorials (4n - 1)!/(4n + 1)!, we can apply the property of factorials, where (a-1)! = a!/(a).

In this case, a = 4n + 1. Therefore, the expression becomes:

(4n - 1)! / [(4n + 1)! / (4n + 1)]

By multiplying both the numerator and denominator by (4n + 1), we get:

[(4n - 1)! * (4n + 1)] / (4n + 1)!

Now, notice that the (4n + 1)! in the denominator cancels out the (4n + 1) term in the numerator, leaving us with:

(4n - 1)!

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We've multiple  styles to find area of triangle. But the formula used is area = 1/2 ×( base × length).    

To  decide formula of area = 1/2 ×( base × length) we can consider the area of a rectangle. Area of a rectangle is =  length × breadth. A triangle is half of a rectangle.  

So, thus we can divide the area of cube by 2 to get the asked area of triangle. Also, area = ( length × breadth)/ 2. In triangle the base is the vertical side of the triangle and the vertical is the distance from the base to the contrary point.  

Now, after multiplying the base with height and dividing it by 2 will give us the formula of area of triangle. Area = 1/2 ×( base × height).

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The question is: Derive the area formula for a triangle.

Part A: From the given triangle, what is Sin C?

Part B: Using your answer from Part A, solve for the height, h.

Part C: Using the area formula = 1/2 bh and your answer form part B, plug in and simplify. Write the simplified equation.

Part D: Using your own words, what formula did you derive?

a. Calculation of payback period for investment A is: Initial Investment = P400,000Incremental cash flow = Year 1: P100,000 Year 2: P120,000 Year 3: P140,000 Year 4: P120,000 Year 5: P100,000 + P20,000

= P120,000Total cash inflows

= Year 1: P100,000 Year 2: P120,000 Year 3: P140,000 Year 4: P120,000 Year 5: P120,000Therefore, the cumulative cash flow for year 4

= P480,000, and the cumulative cash flow for year 5 is P600,000 (P480,000 + P120,000)Payback period

= Year 4 + Unrecovered amount / Cumulative cash flow in year 5

= 4 + (P220,000 / P600,000)

= 4.37 years

Therefore, the payback period for investment A is 4.37 years.

b) Discounted payback period = Year before recovery + (Unrecovered amount / Discounted cash flow ) Present value of cash flow

= Cash flow / (1 + Discount rate)nYear 0: Initial Investment

= P450,000Year 1: P130,000 / (1 + 0.10)1 = P118,182Year 2: P130,000 / (1 + 0.10)2

= P107,439Year 3: P130,000 / (1 + 0.10)3 = P97,672Year 4: P130,000 / (1 + 0.10)4

= P89,000Year 5: (P150,000 + P20,000) / (1 + 0.10)5

= P95,425Therefore, the discounted cash flows are as follows: Year 1: P118,182 Year 2: P107,439 Year 3: P97,672 Year 4: P89,000 Year 5: P95,425 Therefore, the cumulative discounted cash flow for year 4 = P412,293, and the cumulative discounted cash flow for year 5 is P507,718 (P412,293 + P95,425) The discounted payback period is as follows: Discounted payback period = Year before recovery + (Unrecovered amount / Discounted cash flow of the year)Discounted payback period

= 4 + (P42,282 / P95,425)

= 4.44Therefore, the discounted payback period for investment B is 4.44 years.

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Answer:

3%

Step-by-step explanation:

percent of two numbers x and y

x as a percent of y is given by x/y * 100

given

Total bill = $11.18

in the bill , tax amount = $0.33

thus,

tax as percent of total bill is =  tax amount /Total bill  * 100

tax as percent of total bill is = 0.33 /11.18  * 100= 2.95 %

Thus,

tax percentage is 2.95%

tax percentage to nearest whole number is 3%

Answer:

(5,1)

Step-by-step explanation:

A function is a set of ordered pairs in which no two different ordered pairs have the same x -coordinate. An equation that produces such a set of ordered pairs defines a function.

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The determinant of a matrix is a scalar value that can be calculated using a specific formula. In this case, we need to find the determinant of matrix A.

To find the determinant of a 4x4 matrix like A, we can use the method of cofactor expansion. This method involves expanding the determinant along a row or column of the matrix by using the cofactors of each element.

Step 1: Let's expand the determinant along the first row of matrix A.

-2 times the determinant of the 3x3 matrix formed by removing the first row and first column, which is:
-5  3  -3
0   0   -4
8   0   -4

-1 times the determinant of the 3x3 matrix formed by removing the first row and second column, which is:
8   3   -3
0   0   -4
8   0   -4

Step 2: Calculate the determinant of the 3x3 matrices.

For the first 3x3 matrix, we have:
-5  3  -3
0   0   -4
8   0   -4

The determinant of this matrix is:

-5(0(-4) - -3(0)) - 3(8(-4) - -3(-4)) - -3(8(0) - -3(-4))

= -5(0 - 0) - 3(-32) - (-3)(-12)

= 0 - (-96) - 36

= 96 - 36

= 60

For the second 3x3 matrix, we have:
8   3   -3
0   0   -4
8   0   -4

The determinant of this matrix is:

8(0(-4) - -3(0)) - 3(8(-4) - -3(-4)) - -3(8(0) - -3(-4))

= 8(0 - 0) - 3(-32) - (-3)(-12)

= 0 - (-96) - 36

= 96 - 36

= 60

Step 3: Substitute the determinants of the 3x3 matrices back into the original expansion.

-2 times the determinant of the first 3x3 matrix, which is 60.
-1 times the determinant of the second 3x3 matrix, which is 60.

Now, we can calculate the determinant of matrix A:
-2(60) - 1(60)
= -120 - 60
= -180

So, the determinant of matrix A is -180.

The determinant of matrix A is -180.

To find the determinant of a 4x4 matrix like A, we can use the cofactor expansion method. We expanded the determinant along the first row of matrix A and calculated the determinants of the resulting 3x3 matrices. Substituting these determinants back into the original expansion, we found that the determinant of matrix A is -180.

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Answer:

Step-by-step explanation:

Given

The equation for the interest:

So $17500 invested at 6.5% and $12500 at 4.2%

Answer:

yes

Step-by-step explanation:

a) If the confidence level had been 90% instead of 98%, the new confidence interval would be (0.325, 0.475).

b) If the sample size had been 255 instead of 170, the new confidence interval would be (0.292, 0.508).

c) If the confidence level had been 99% instead of 98%, the new confidence interval would be (0.304, 0.496).

a) First, we find the mean of the original confidence interval:

Mean = (Lower Limit + Upper Limit) / 2 = (0.313 + 0.487) / 2 = 0.4

Margin of Error = (Upper Limit - Mean) = (0.487 - 0.4) / 2 = 0.0435

New Margin of Error = Margin of Error * \((Z_{90} / Z_{98})\)

where \(Z_{90}\) is the critical value for a 90% confidence level, and \(Z_{98}\) is the critical value for a 98% confidence level.

From the standard normal distribution table, we find:

\(Z_{90}\) ≈ 1.645

\(Z_{98}\) ≈ 2.326

New Margin of Error = 0.0435 * (1.645 / 2.326) ≈ 0.0306

Finally, we construct the new confidence interval using the adjusted margin of error:

New Confidence Interval = (Mean - New Margin of Error, Mean + New Margin of Error)

                     = (0.4 - 0.0306, 0.4 + 0.0306)

                     ≈ (0.3694, 0.4306)

Therefore, the new confidence interval at a 90% confidence level would be approximately (0.369, 0.431) when rounded to three decimal places.

b) Standard Error = \(\sqrt{(p_{hat} * (1 - p_{hat})) / n}\)

where \(p_{hat}\) is the sample proportion and n is the sample size.

Given that the sample size increases to 255 while the sample proportion remains the same, the new sample proportion is:

\(p_{hat}\) = 68 / 255 ≈ 0.267

Standard Error = sqrt((0.267 * (1 - 0.267)) / 255) ≈ 0.028

For a 98% confidence level, the critical value is \(Z_{98}\) ≈ 2.326.

New Margin of Error = \(Z_{98}\) * Standard Error = 2.326 * 0.028 ≈ 0.065

New Confidence Interval = (\(p_{hat}\) - New Margin of Error, \(p_{hat}\) + New Margin of Error)

                     = (0.267 - 0.065, 0.267 + 0.065)

                     ≈ (0.202, 0.332)

Therefore, the new confidence interval with a sample size of 255 would be approximately (0.202, 0.332) when rounded to three decimal places.

c) From the standard normal distribution table, we find:

\(Z_{99}\) ≈ 2.576

New Margin of Error = Margin of Error * (\(Z_{99}\) / \(Z_{98}\)) = 0.0435 * (2.576 / 2.326) ≈ 0.0482

New Confidence Interval = (Mean - New Margin of Error, Mean + New Margin of Error)

                     = (0.4 - 0.0482, 0.4 + 0.0482)

                     ≈ (0.3518, 0.4482)

Therefore, the new confidence interval at a 99% confidence level would be approximately (0.352, 0.448) when rounded to three decimal places.

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Answer:

35

Step-by-step explanation:

Well if m<YVW = (12x-1) and x=3 then just plug in x

So,

m<YVW = (12(3)-1)

m<YVW = 36-1

m<YVW = 35