Mrs. Santos consumed 8.976 cubic meter. How much will she pay if a cubic meter of water costs Php 45.00?

The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines. The hotline is staffed for 16 hours a day.

To calculate the average number of calls in different time intervals and the probability of different events related to these calls.

Part 1:

a. 60-minute interval average number of calls: 400/16 = 25 calls

30-minute interval average number of calls: 25/2 = 12.5 calls

15-minute interval average number of calls: 12.5/2 = 6.25 calls

Part 2:

b. To find the probability of exactly 6 calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of exactly 6 calls in a 15-minute interval is:

P(6 calls) = (e^-6.25)*(6.25^6)/6! = 0.0686

c. To find the probability of no calls in a 15-minute interval, we can use the Poisson distribution formula. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of no calls in a 15-minute interval is:

P(0 calls) = e^-6.25 = 0.0047

d. To find the probability of at least two calls in a 15-minute interval, we can use the cumulative distribution function of the Poisson distribution. Let's assume that the average number of calls in a 15-minute interval is 6.25. Then, the probability of at least two calls in a 15-minute interval is:

P(X >= 2) = 1 - P(0 calls) - P(1 call) = 1 - 0.0047 - (e^-6.25)*(6.25^1)/1! = 0.9906

Thus, the average number of calls in a 60-minute interval is 25, in a 30-minute interval is 12.5, and in a 15-minute interval is 6.25. The probability of exactly 6 calls in a 15-minute interval is 0.0686, the probability of no calls in a 15-minute interval is 0.0047, and the probability of at least two calls in a 15-minute interval is 0.9906.

Learn more about Probability here brainly.com/question/11234923

#SPJ4

Answer:

The smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772 is 16.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}\)

\(\Delta = b^{2} - 4ac\)

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

n values from a normal distribution:

The mean is \(\mu n\) and the standard deviation is \(s = \sigma\sqrt{n}\)

A company manufactures a brand of lightbulb with a lifetime in months that is normally distributed with mean 3 and variance 1.

This means that \(\mu = 3, \sigma = \sqrt{1} = 1\)

For n bulbs:

The distribution for the sum of n bulds has \(\mu = 3n, \sigma = \sqrt{n}\)

What is the smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772?

We want that: \(S_{n} \geq 40 = 0.9772\).

This means that when X = 40, Z has a pvalue of 1 - 0.9772 = 0.0228, that is, when \(X = 40, Z = -2\). So

\(Z = \frac{X - \mu}{\sigma}\)

\(-2 = \frac{40 - 3n}{\sqrt{n}}\)

\(-2\sqrt{n} = 40 - 3n\)

\(3n - 2\sqrt{n} - 40 = 0\)

Using \(y = \sqrt{n}\)

\(3y^2 - 2y - 40 = 0\)

Which is a quadratic equation with \(a = 3, b = -2, y = -40\)

\(\Delta = b^{2} - 4ac = (-2)^2 - 4(3)(-40) = 484\)

\(y_{1} = \frac{-(-2) + \sqrt{484}}{2*3} = 4\)

\(y_{2} = \frac{-(-2) - \sqrt{484}}{2*3} = -...\)

Since y and n have both to be positive:

\(y = \sqrt{n}\)

\(\sqrt{n} = 4\)

\((\sqrt{n})^2 = 4^2\)

\(n = 16\)

The smallest number of bulbs to be purchased so that the succession of bulbs produces light for at least 40 months with probability at least 0.9772 is 16.

Answer

The polynomial is a 3rd degree polynomial

Explanation

Given the following expression

x^2 + 2x^3 - 4

Step 1: Re- arrange the expression

2x^3 + x^2 - 4

The highest power of x in the expression is 3

The highest degree is 3

Therefore, the polynomial is 3rd degree

Answer:

b

Step-by-step explanation:

45.72

Answer:

Step-by-step explanation:

Using the remainder theorem we get:

\(f(-2)=-5\),  \(f(1)=4\), and \(f(-1)=0\)

So we get

\(f(-2)=(-8)(p-1)+4p-2q+r=-5\)

                 \(-8p+8+4p-2q+r=-5\)

                              \(-4p-2q+r=-13\)  \((a)\)

\(f(1)=(p-1)+p+q+r=4\)

                       \(2p+q+r=5\)               \((b)\)

\(f(-1)=-(p-1)+p-q+r=0\)

                                 \(-q+r=-1\)    \((c)\)

We need to solve (a), (b) and (c) simultaneously to find p,q, and r.

from \((c)\)  \(r=q-1\). Sub this into (a) and (b):

\(-4p-2q+(q-1)=-13 \rightarrow -4p-q=-12\)    \((d)\)

      \(2p+q+(q-1)=5 \rightarrow q=3-p\)              \((e)\)

Sub (e) into (d) we get

\(-4p-(3-p)=-12 \rightarrow p=3\)

Sub \(p=3\) into \((e) \rightarrow q=0\)

Sub  \(p=3,q=0\) into \((c) \rightarrow r=-1\)

SOLUTION: \(p=3,q=0,r=-1\)    

So \(f(x)=2x^3+3x^2-1\)

by dividing (x+1) into f(x) we get  (I am not showing working for this division)

\(f(x)=(x+1)(2x^2+x-1)\)

\(\rightarrow f(x)=(x+1)(2x-1)(x+1)\)

Using the given coordinates we know that the area of the surface on which a student paints is 144 in².

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers, or coordinates.

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane.

The x-axis (horizontal) and y-axis are the two axes that make up a coordinate plane (vertical).

A square's area can be calculated using:

A = L²

We only need to determine the length of one side because a square's sides are all the same length.

The distance between the two vertices in this square, which serves as the side length, may be calculated as:

L = √[(x₂ - x₁)² + (y₂ - y₁)²]

But, since it is a square, we can use coordinate subtraction to obtain the side length, which is obtained by utilizing the first three coordinates:

Horizontal length = (6 + 6) = 12

Then;

Area = L² = 12² = 144 in²

Therefore, using the given coordinates we know that the area of the surface on which a student paints is 144 in².

Know more about coordinates here:

https://brainly.com/question/20362114

#SPJ1

Answer:

1.6

Step-by-step explanation:

5 times 1.6 is 8.

The correct answer is Graph 1: y = cos(x/4)Graph 2: y = cos(x/2)

Based on the given descriptions of the graphs and the patterns they follow, the correct pairs are:

Graph 1: y = cos(x/4) ⟶ This graph has a period of 8 units and matches the pattern described.Graph 2: y = cos(x/2) ⟶ This graph has a period of 4 units and matches the pattern described.

Graph 3: y = cos(x) ⟶ This graph has a period of 2π (or approximately 6.28 units) and matches the pattern described.

Graph 4: (Not used)

Graph 5: (Not used)

Please note that without visual representation, it's difficult to provide a definitive answer. The pairs are based on the descriptions provided and may vary depending on the actual shapes of the graphs.

Learn more about Graph here:

https://brainly.com/question/29538026

#SPJ8

The number of gallons of fruit drink is 118 gallons and the number of gallons of soda is 150 gallons.

The system of equations that represents the question is:

f + s = 168 equation 1

2.41f + 1.57s = (1.66 x 168)

2.41f + 1.57s = 278.88 equation 2

Where:

The elimination method would be used to determine the required values

Multiply equation 1 by 2.41

2.41f + 2.41s = 404.88 equation 3

Subtract equation 2 from equation 3

126 = 0.84s

s = 126 / 0.84

s = 150

Substitute for s in equation 1

f + 150 = 168

f = 168 - 150

f - 118 gallons

To learn more about system of equations, please check: brainly.com/question/25875552

#SPJ1

Answer:

15 years (180 months)

Step-by-step explanation:

turn it into months first

147

216

163

206

180

168

add them together, then divide by how many there are

1,080/6=180 months

180/12 =15

(a) Linda's monthly payment is approximately $578.80.

(b) If Linda pays the monthly payment each month for the full term, her total amount to repay the loan is approximately $55,660.80.

(c) If Linda pays the monthly payment each month for the full term, the total amount of interest she will pay is approximately $12,160.80.

Let's break down the calculation into the following steps:

(a) Monthly Payment Calculation:

To calculate the monthly payment, we can use the formula:

Monthly Payment = P × (r × (1 + r)ⁿ) / ((1 + r)ⁿ - 1)

Where:

P = Principal amount of the loan

r = Monthly interest rate (annual interest rate / 12)

n = Total number of monthly payments (number of years × 12)

Substituting the given values:

P = $43,500

Annual interest rate = 6.75%

r = 0.0675 / 12

n = 8 years × 12

Let's calculate the monthly payment:

r = 0.0675 / 12

= 0.005625

n = 8 × 12

= 96

Monthly Payment = $43,500 × (0.005625 × (1 + 0.005625)⁹⁶) / ((1 + 0.005625)⁹⁶ - 1)

Using a financial calculator or spreadsheet software, the monthly payment is approximately $578.80.

Total Amount Repaid Calculation:

The total amount repaid is equal to the monthly payment multiplied by the total number of payments (n).

Total Amount Repaid = Monthly Payment × n

Total Amount Repaid = $578.80 × 96

Using a financial calculator or spreadsheet software, the total amount repaid is approximately $55,660.80.

Total Interest Paid Calculation:

The total interest paid can be calculated by subtracting the principal amount (P) from the total amount repaid.

Total Interest Paid = Total Amount Repaid - P

Total Interest Paid = $55,660.80 - $43,500

Using a financial calculator or spreadsheet software, the total interest paid is approximately $12,160.80.

For similar questions on monthly payment

https://brainly.com/question/27926261

#SPJ11

On solving the provided question, we can say that  annual percentage yield (APY) in this situation, we need to take into account the effect of compounding. The formula for APY is: \(APY = (1 + APR/n)^{n - 1}\)

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

annual percentage yield (APY) in this situation, we need to take into account the effect of compounding. The formula for APY is:

\(APY = (1 + APR/n)^{n - 1}\)

where APR is the annual percentage rate, n is the number of compounding periods per year.

In this case, the APR is 2.65% and the compounding period is monthly, so n = 12 (number of months in a year). Plugging these values into the formula, we get:

\(APY = (1 + 0.0265/12)^12 - 1\\APY = 0.02692 or 2.692%\)

Therefore, the annual percentage yield (APY) for this bank account is 2.692%.

To know more about percentage visit:

https://brainly.com/question/28269290

#SPJ1

Answer:

C.

Step-by-step explanation:

To get a perpendicular line, the slope will be the opposite of what you currently have. You have a slope of 2, so the opposite reciprocal slope will be -1/2. Then, you use the equation y = mx+b and substitute (2,5) for the y and the x (2 for the x and 5 for the y). This is to solve for b. Then, you have your equation! Hope this helped.

Answer:

The next two numbers following:

431

141311

1114111321

311431131211

are:

132114132113111221

AND

11131221141113122113312211

Step-by-step explanation:

I shall explain the pattern below:

431 (just the digits 4, 3, and 1)

141311 (one 4 becomes 14, one 3 becomes 13, one 1 becomes 11 -> looking at each digit of the previous number, 431)

1114111321 (one 1 becomes 11, one 4 becomes 14, one 1 becomes 11, one three becomes 13, two consecutive 1s becomes 21 -> looking at each digit of the previous number, 141311)

311431131211 (three consecutive 1s becomes 31, one 4 becomes 14, 3 more consecutive 1s becomes 31, one 3 becomes 13, one 2 becomes 12, and one 1 becomes 11 -> looking at each digit of the previous number, 1114111321)

NEXT TWO NUMBERS:

one 3 (13), two consecutive 1s (21), one 4 (14), one 3 (13), two consecutive 1s (21), one 3 (13), one 1 (11), one 2 (12), two consecutive 1s (21)

that makes: 132114132113111221

one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 4 (14), one 1 (11), one 3 (13), one 2 (12), two consecutive 1s (21), one 3 (13), three consecutive 1s (31), two consecutive 2s (22), one 1 (11)

that makes: 11131221141113122113312211

The rule is that the next number is essentially the previous number with the number of times each digit appears consecutively before each digit of the previous number. I know that sounds convoluted. Hopefully it makes enough sense. Let me know if I should explain more fully.

I need to deposit $1558.41 to have $2000 in the account in 5 years.

What is compound interest?

The interest charged on a debt or deposit is known as compound interest. It is the idea that we use the most regularly. Compound interest is calculated for a sum based on both the principal and cumulative interest.

    ∴ Compound interest = P(1 + \(\frac{r}{100*12}\))ⁿ  (∵ for monthly interest)

        P = Principal

        r = rate of interest per month

        n = number of months

Given:

r = 5% per month

n = 5 years = 5*12 = 60 months

  CI = P (1+5/(12 * 100))⁶⁰

2000 = P(1.0041)⁶⁰

2000 = P(1.2834)

      P = 1558.41

Therefore, the amount required to deposit is 1558.41 dollars to get 2000 dollars after 5 years with 5 percent interest per month.

To know more about Compound interest visit:

brainly.com/question/14295570

#SPJ1

Answer:

550g

Step-by-step explanation:

total g in 1 kg is 1000

so 1000 - 550 =450

Based on the standard deviation, if your score was exactly one standard deviation below the mean then your score was 3.

When a score is said to be one standard deviation below or above the mean, then it means that they are in a range around the mean that is either the standard deviation added to the mean or subtracted from the mean.

The standard deviation of the survey results of self-reported mental wellness was 2. If you scored one standard deviation below the mean then your score was:

= Mean - Standard deviation from mean

= 5 - 2

= 3

In conclusion, your score was 3.

Find out more on standard deviation below the mean at https://brainly.com/question/15015716

#SPJ1

Answer:

\(x=\sqrt{24}\)

Step-by-step explanation:

2x^2+25=73

Subtract 25 from both sides:

2x^2=48

Divide both sides by 2:

x^2=24

Square both sides:

\(\sqrt{x^{2} } =\sqrt{24}\)

\(x=\sqrt{24}\)

Answer:

4/52 or 1/13 (simplified)

Step-by-step explanation:

There are 4 "10's" in a pack.

This means you have the chance to pick 4 10's.

So out of 52 cards, you can get 4.

4/52 -> Which can be simplified to 1/13.

This is the probability of getting a 10 (once) in a standard deck of cards.

The probability of drawing a 10 from a standard deck of 52 cards is 1/13.

Number of 10's in a standard deck of 52 cards  =4

Total cards =52

Probability is the measurement of the possibilities of events.

P(event) =Favorable outcomes/ Total possible outcomes

Here, Favorable outcomes =4

Total possible outcomes =52

P(10) =4/52

P(10) =1/13

So, the probability of drawing a 10 from a standard deck of 52 cards =1/13

Thus, the probability of drawing a 10 from a standard deck of 52 cards is 1/13

To get more about probability visit:

https://brainly.com/question/24756209

The greatest common divisor of 35x and 20y is 35x and 20y.

In the given question, if x and y are positive integers, then we have to find which of the following cannot be the greatest common divisor of 35x and 20y.

Since x and y are positive integer so 35x and 20y are also positive integer

Divisor of a positive integer cannot be more than that integer (for example integer 4 doesn't have a divisor more than 4, the largest divisor it has is 4 itself), so greatest common divisor of two positive integers 35x and 20y cannot  be more than 35x or 20y.

Hence, the greatest common divisor of 35x and 20y is 35x and 20y.

To learn more about greatest common divisor link is here

brainly.com/question/27962046

#SPJ4

Answer:

x=3, y=-6

Step-by-step explanation:

As you know there are many ways to solve this question! First is Subsitutuion, Second is Elimination, and Third is Graphing!

Let’s begin with our detailed answer:

As you know subsitution is solving for a variable and then it can be used as a variable substitution to figure out x and y.

So in our system of equations:

\(\left \ {3x+2y=-3}} \atop {9x+4y=3}} \right.\)

I will just take one equation and solve for x but it actually dosent matter which variable you subsitutue and solve for.

\(\left \ {3x+2y=-3}} \atop {9x+4y=3}} \right.\)

To eliminate this question we can divide the top part by -3:

\(\left \ {-9x-6y=9}} \atop {9x+4y=3}} \right.\)

Let‘s sum these system of equation and we get: \(y=-6\)

We can now insert y as -6 and solve for x:

\(3x-12=-3\)

\(x=3\)

So, \(x=3, y = -6\)

Answer:

(3, - 6 )

Step-by-step explanation:

3x + 2y = - 3 → (1)

9x + 4y = 3 → (2)

Multiplying (1) by - 3 and adding to (2) will eliminate the x- term

- 9x - 6y = 9 → (3)

Add (2) and (3) term by term to eliminate x

0 - 2y = 12

- 2y = 12 ( divide both sides by - 2 )

y = - 6

Substitute y = - 6 into either of the 2 equations and solve for x

Substituting into (1)

3x + 2(- 6) = - 3

3x - 12 = - 3 ( add 12 to both sides )

3x = 9 ( divide both sides by 3 )

x = 3

solution is (3, - 6 )

ANSWER

EXPLANATION

We want to convert 52 ounces to pounds (and ounces).

To convert from ounces to pounds, we have to multiply the mass in ounces by 0.0625. This implies that 52 oz is:

We want to write it in terms of whole numbers, so w have to convert the decimal part of the mass in piounds back to ounces. To do that, multiply by 16. This implies that 0.25 lb is:

Therefore, 52 oz is:

That is the answer.

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

For more such questions on cylinder

https://brainly.com/question/28247116

#SPJ8

Answer:

28.07°

Step-by-step explanation:

use SohCahToa

in this case we use tan^-1 to get the angle x°

tan^-1(8/15)=28.07248694

to the nearest hundredth

=28.07°

The relationship described by the equation 4y = 2x is proportional.

The relationship in the equation 4y = 2x is proportional. By simplifying the equation, we got that y = (1/2)x, which shows that y is directly proportional to x. In a proportional relationship, the ratio of y to x always remains constant.

In this scenerio, the constant of proportionality is 1/2. As x increases or decreases, y also increases or decreases by half of x.

So, the relationship between y and x in this equation is proportional, indicating that changes in x will result in corresponding proportional changes in y.

To know more about proportional:-

https://brainly.com/question/33460130

The question is:-

Is the relationship described by the equation 4y = 2x proportional or non-proportional?

Answer: 0.4337

Step-by-step explanation:

Let X represents the test results for a class that follow a normal distribution .

Given: Mean \(\mu=78\), Standard deviation  \(\sigma=36\)

Then, the probability that it is greater than 84 will be

\(P(X>84)=P(\dfrac{X-\mu}{\sigma}>\dfrac{84-78}{36})\\\\=P(Z>0.167)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.167)\\\\=1-0.5663=0.4337\ [\text{By p-value table}]\)

Hence, the required probability = 0.4337

Answer:

10

Step-by-step explanation:

Answer:

45:9

Step-by-step explanation:

Answer:

3/16

Step-by-step explanation:

In order to get the amount of water to fill a bin, we just divide the amount of water by the fraction of the bin it fills. This makes the unit of the resulting answer as gallons/bin or gallons per bin.

Answer:

\(The\) \(Answer\) \(Is:\) \(\frac{3}{9}\) \(&\)& \(\frac{5}{15}\)

Step-by-step explanation:

Divide by 4 , 2nd fraction Divide by 5:

3/4 ≠ 4/5

5/6 ≠ 6/5 We can already see it.

Divide by 3. . .

2/4 ≠ 3/4

Divide by 3 , 2nd fraction Divide by 5:

1/3 = 1/3 \(Perfect!\)

The answer is, \(\frac{3}{9}\) & \(\frac{5}{15}\)