​There is a total of 360 students and teachers ​​at a school.​​ A trip is organized and 65% of ​​the students and teachers bought ​​tickets to go on ​this trip.​​
(a)​ ​Work out how many ​of the students and teachers​​​ bought tickets to go on the trip​.
​The number of teachers,the number of male students and the number of female students ​​​​​who bought tickets ​​to go on the trip are in the ratios ​1:3:5 ​.
(b) ​Calculate the number of female students who bought tickets to go on the trip​​​​​.
​All the male students who bought tickets went on the trip ​​​but 4 of the female students ​​​who bought tickets did not go on the trip​​​.
(c) ​Find the ratio of the number of male students ​who went on the trip to the number of ​​female students who went on the trip​​​​.​​

Answers

Answer 1

Answer: Below :)

Step-by-step explanation:

(a) The percentage of students and teachers who bought tickets to go on the trip is 65%. So the number of students and teachers who bought tickets can be found by multiplying the total number of students and teachers by 65%:

65/100 x 360 = 234

Therefore, 234 students and teachers bought tickets to go on the trip.

(b) Let the number of teachers who bought tickets be x. Then the number of male students who bought tickets is 3x, and the number of female students who bought tickets is 5x.

The total number of students and teachers who bought tickets is:

x + 3x + 5x = 9x

We know that 234 students and teachers bought tickets, so we can set up the following equation:

9x = 234

Solving for x, we get:

x = 26

So the number of teachers who bought tickets is 26, the number of male students who bought tickets is 78 (3x), and the number of female students who bought tickets is 130 (5x).

However, 4 of the female students who bought tickets did not go on the trip, so the actual number of female students who went on the trip is:

130 - 4 = 126

(c) The ratio of the number of male students who went on the trip to the number of female students who went on the trip is:

78/126

Simplifying this ratio by dividing both numerator and denominator by 6, we get:

13/21

Therefore, the ratio of the number of male students who went on the trip to the number of female students who went on the trip is 13:21.


Related Questions

To purchase $13200 worth of machinery for her business, Nicole made a down payment of 1200 and took out a business loan for the rest. After 3 years of paying monthly payments of 365.07, she finally paid off the loan.


(a) What was the total amount Nicole ended up paying for the machinery (including the down payment and monthly payments)?

(b) How much interest did Nicole pay on the loan?

Answers

The answer of the given question based on the compound interest to find  total amount Nicole ended up paying for the machinery and the interest did Nicole pay on the loan is (A) the total amount Nicole ended up paying for the machinery is $14,342.52. (B) Nicole paid $2,342.52 in interest on the loan.

What is Compound interest?

Compound interest is type of interest that is calculated not only on initial principal amount but also on accumulated interest from previous periods. In other words,  interest earned in each period is added to  principal amount, and  interest for the next period is calculated on  new, larger principal amount.

Compound interest can be thought of as "interest on interest" and is used in many financial transactions, like loans, investments, and savings accounts.

(a) The total amount Nicole ended up paying for the machinery is the sum of her down payment and all of her monthly loan payments over the 3-year period. We can calculate this as follows:

Total amount paid = Down payment + (Monthly payment x Number of payments)

Total amount paid = 1200 + (365.07 x 36)

Total amount paid = 1200 + 13142.52

Total amount paid = $14,342.52

Therefore, the total amount Nicole ended up paying for the machinery is $14,342.52.

(b) To calculate how much interest Nicole paid on the loan, we first need to calculate the total amount of the loan. We can do this by subtracting her down payment from the total cost of the machinery:

Total loan amount = Total cost of machinery - Down payment

Total loan amount = $13,200 - $1,200

Total loan amount = $12,000

Next, we can calculate the total amount of interest paid over the 3-year period by subtracting the total loan amount from the total amount paid:

Total interest paid = Total amount paid - Total loan amount

Total interest paid = $14,342.52 - $12,000

Total interest paid = $2,342.52

Therefore, Nicole paid $2,342.52 in interest on the loan.

To know more about Principal visit:

https://brainly.com/question/2241772

#SPJ1

A random variable X follows the uniform distribution with a lower limit of 670 and an upper limit of 770.
a. Calculate the mean and the standard deviation for the distribution. (Round intermediate calculation for Standard deviation to 4 decimal places and final answer to 2 decimal places.)
Mean:
Standard deviation:
b. What is the probability that X is less than 710? (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
Probability:

Answers

a) The mean is 720 and the standard deviation for the distribution is approximately 28.87

b. The probability that X is less than 710 is 33%

a. To calculate the mean and standard deviation, we use the following formulas:

Mean (μ) = (lower limit + upper limit) / 2

Standard deviation (σ) = (upper limit - lower limit) / √12

Substituting the values, we get:

Mean (μ) = (670 + 770) / 2 = 720

Standard deviation (σ) = (770 - 670) / √12 ≈ 28.87

b. To find the probability that X is less than 710, we use the following formula:

Probability (X < 710) = (710 - lower limit) / (upper limit - lower limit)

Substituting the values, we get:

Probability (X < 710) = (710 - 670) / (770 - 670) ≈ 0.33

This means that there is a 33% chance that X will be less than 710.

To know more about standard deviation here

https://brainly.com/question/16555520

#SPJ4

ANSWER NEEDED IN 10 SEC

Answers

ignore the X since it is both 9 and just subtract 8-4 which you get 4 so your answer should be 4

Scenario #3:
Imagine you find a map with a scale of 1:63,360. On that map, you see your hiking destination is
seven inches from your current location.
(a) How far away is that in reality (in miles)?
(b) Explain how you arrived at this decision.
SHOW YOUR WORK! This includes the potential for partial value, if incorrect.

Answers

Answer:

7 miles

Step-by-step explanation:

Note there are 63,360 inches in a mile.

So, rewrite scale as 1 inch: 1 mile, where inch replaces the unit.

Therefore 7 inches: 7 miles.

Find the difference. 2.1 0.25 = ?

Answers

Answer: 1.85

Step-by-step explanation:

6TH GRADE MATH, PLS HELP. FIND SLOPE OF THE TABLE, TY

Answers

The slope of the table is -2.

bug s is slow and bug f is fast. both bugs start at 0 on a number line and move in the positive direction. the bugs leave 0 at the same time and move at constant speeds. four seconds later, f is at 12 and s is at 8. how many units apart are bugs f and s thirty seconds after leaving point 0.

Answers

After 30 seconds the bugs will be apart by (x -y) = 30 units

What is speed?

The speed of an object, aIso known as "v" in everyday speech and kinematics, is a scaIar quantity that measures how much its position changes over time or how much it changes per unit of time.

The distance traveIIed by an object during a time intervaI is equaI to the duration of the intervaI divided by the object's speed, with the instantaneous speed being the upper Iimit of the average speed as the intervaI's duration gets cIoser to zero. VeIocity differs from speed. Distance divided by time is the formuIa for measuring speed. A metre per second (m/s) is the metric unit of speed.

a) The speed of F is 12 units in 4 seconds, or 3 units per second.

x = 3t

The speed of S is 8 units in 4 seconds, or 2 units per second.

y = 2t

b) x-y = 3t -2t = t

After 30 seconds the bugs will be apart by (x -y) = 30 units

c) x - y = 100 = t

The bugs will be 100 units apart after 100 seconds.

To know more about speed ;

https://brainly.com/question/28224010

#SPJ1

The distance between bug f and bug s after 30 seconds is: distance = 90 - 60 = 30 units.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

When bug s and bug f leave point 0, they are initially at the same location, which is at position 0 on the number line. After four seconds, bug s has traveled a distance of 4v_s units from point 0, and bug f has traveled a distance of 4v_f units from point 0. We know that bug f has traveled 12 units in this time, so:

4v_f = 12

Solving for v_f, we get:

v_f = 3 units per second

Similarly, we know that bug s has traveled a distance of 8 units in four seconds, so:

4v_s = 8

Solving for v_s, we get:

v_s = 2 units per second

Now we can find out how far apart the bugs are after 30 seconds. Bug f has traveled a distance of 30v_f units from point 0, which is:

30v_f = 30 x 3 = 90 units

Similarly, bug s has traveled a distance of 30v_s units from point 0, which is:

30v_s = 30 x 2 = 60 units

Therefore, the distance between bug f and bug s after 30 seconds is:

distance = 90 - 60 = 30 units.

So the bugs are 30 units apart after 30 seconds.

To learn more about algebra from the given link:

https://brainly.com/question/24875240

#SPJ1

Suppose that the cost C, in dollars, of processing the exhaust gases at an industrial site to ensure that only p percent of the particulate pollution escapes is given by the equation shown below. C(p) = 7000(100− p) p (a) Find the rate of change of cost C with respect to the percent of particulate pollution that escapes when p = 5 (percent). (b) Write a sentence that explains the meaning of your answer in part (a).the cost would increase by the absolute value of this amount if 6% instead of 5% of the particulate pollution were allowed to escape.The cost would decrease by this amount if 4% instead of 5% of the particulate pollution were allowed to escape.The cost would decrease by the absolute value of this amount if 6% instead of 5% of the particulate pollution were allowed to escape.The cost would increase by this amount for each percent of the particulate pollution over 5% allowed to escape.

Answers

The rate of change of cost C with respect to the percent of particulate pollution that escapes when p = 5 (percent) is -190000.

We know that the cost C, in dollars, of processing the exhaust gases at an industrial site to ensure that only p percent of the particulate pollution escapes is given by the equation C(p) = 7000(100− p) p

we have to find the rate of change of cost C with respect to the percent of particulate pollution that escapes when p = 5 (percent)

a) c (p) = 7600 (100-p) / p

c (p) = 7600 [p(-1) - (100-p) (1)] / 2p

= 7600/2p = 760000/4

= -190000

therefore, the rate of change of cost C with respect to the percent of particulate pollution that escapes when p = 5 (percent) is -190000.

To learn more about rate, click here:

brainly.com/question/29781084

#SPJ4

PLEASE HURRY!!
Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle? Please show your work.

Answers

The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%

What is Conditional probability?

Conditional probability is the probability of an event occurring given that another event has occurred or is known to have occurred. It is denoted by P(A|B), which reads as "the probability of A given B."

The formula for conditional probability is:

P(A|B) = P(A and B) / P(B)

where P(A and B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.

The total number of Plastic #2 bottles is 8 (correctly placed) + 5 (incorrectly placed) = 13.

The total number of Plastic #4 bottles is 5 (correctly placed) + 2 (incorrectly placed) = 7.

The probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is given by:

(number of Plastic #4 bottles correctly placed) / (total number of bottles)

So the probability is:

5/20 = 1/4 = 0.25

Therefore, the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle is 0.25 or 25%.

To learn more about Conditional probability, visit the link:

https://brainly.com/question/10739997

#SPJ1

b. A kennel has 90 dogs in total, some are puppies and some are adult dogs. The ratio of puppies to adult dogs in a kennel is 1:4. What fraction of dogs are adults? Use this to work out how many adult dogs there are. See the examples on the formula sheet for this assessment.​

Answers

Answer:4/5 are adults. There are 72 adult dogs.

Step-by-step explanation:

Find the measures of angles 1 through 5 in the figure shown !

Answers

Answer:

55 degrees angles on a rights angle triangle. 1 and 3 they are equal cause they are vertical opp angles 55 degrees

Michelle is baking chocolate chip cookies and she wants to cut the recipe in half. If the recipe calls for 3 cups of flour, how much flour should Michelle
add to her cookie dough?
0 1 cups of flour
O 13 cups of flour
0 1² cups of flour
0 1 cups of flour

Answers

Answer:

1 1/2 or 3/2

Step-by-step explanation:

Cutting the recipe in half means multiplying each measurement by 1/2.

3 x 1/2 = 3/2 or 1 1/2

What is the area of the rhombus?

Answers

Answer:

36 units²

------------------------

As per given coordinates we can observe that the diagonals of the rhombus are horizontal and vertical.

The length of the diagonal is the difference of x-coordinates for the horizontal diagonal and the difference of y-coordinates for the vertical one.

The diagonals have the length:

4 - (-8) = 12 units, and-1 - (-7) = 6 units

The area of a rhombus is half the product of the diagonals, therefore the area of the given rhombus is:

A = 12*6/2 = 36 units²

The area οf the given rhοmbus is 22.5 square units. Tο find the area οf the rhοmbus, we need tο first find the length οf its diagοnals.

what is a rhοmbus?

A rhοmbus is a type οf quadrilateral that has fοur sides οf equal length. It is alsο knοwn as a diamοnd οr a lοzenge. In additiοn tο having equal sides, a rhοmbus alsο has οppοsite angles that are cοngruent (have the same measure). It is a special case οf a parallelοgram, as its οppοsite sides are parallel.

Tο find the area οf the rhοmbus, we need tο first find the length οf its diagοnals. We can dο this using the distance fοrmula:

[tex]\rm d_1 = \sqrt{((4 - (-2))^2 + (-4 - (-1))^2)} = \sqrt{(6^2 + (-3)^2)} = \sqrt{(45)[/tex]

[tex]\rm d_2 = \sqrt{((-8 - (-2))^2 + (-4 - (-7))^2)} = \sqrt{((-6)^2 + 3^2)} = \sqrt{(45)[/tex]

Now that we have the lengths of the diagonals, we can use the formula for the area of a rhombus:

Area = [tex]\rm (d_1 \times d_2) / 2 =\dfrac{ (\sqrt{(45)} \times \sqrt{(45)}}{2}[/tex]

= (45/2) square units

Therefore, the area of the given rhombus is 22.5 square units.

To learn more about rhombus from the given link:

https://brainly.com/question/27870968

#SPJ1

Suppose that Y1,Y2,Y3 denote a random sample from an exponential distribution with density funtion:
f(x) = (1/θ)e^-y/θf, y>0
Consider the following five estimators of θ:
θ(hat)1=Y1 ;
θ(hat)2= (Y1+Y2)/2
θ(hat)3= (Y1+2Y2)/3
θ(hat)4 = min(Y1,Y2,Y3)
θ(hat)5 = Y (bar)
a)Which of these estimators are unbiased and why?
b) Among the unbiased estimators, which has the smallest varienace?

Answers

Y1,Y2,Y3 denote a random sample from an exponential distribution with density funtion where θ(hat)1, θ(hat)2, θ(hat)3  and θ(hat)5 are unbiased. θ(hat)2 has the smallest variance among the unbiased estimators

To check for unbiasedness, we need to find the expected value of each estimator and see if it equals θ.

θ(hat)1 = Y1

E(θ(hat)1) = E(Y1) = θ

Thus, θ(hat)1 is an unbiased estimator.

θ(hat)2 = (Y1+Y2)/2

E(θ(hat)2) = E[(Y1+Y2)/2] = (1/2)[E(Y1) + E(Y2)] = θ

Thus, θ(hat)2 is an unbiased estimator.

θ(hat)3 = (Y1+2Y2)/3

E(θ(hat)3) = E[(Y1+2Y2)/3] = (1/3)[E(Y1) + 2E(Y2)] = θ

Thus, θ(hat)3 is an unbiased estimator.

θ(hat)4 = min(Y1,Y2,Y3)

For this estimator, we need to find the probability density function (pdf) of the minimum of the three random variables.

Let F_Y1_Y2_Y3 be the joint cumulative distribution function (cdf) of Y1,Y2,Y3, then the pdf of the minimum is given by:

f(θ(hat)4) = d/dy [F_Y1_Y2_Y3(y,y,y)] = 3(1/θ)e^-y/θf, y>0

E(θ(hat)4) = ∫0^∞ y(3/θ)e^-y/θ dy

= (3/θ) ∫0^∞ ye^-y/θ dy

Using integration by parts, we get:

= (3/θ) [θ + θ^2]

= 3θ + 3θ^2

Thus, θ(hat)4 is biased.

θ(hat)5 = Y (bar)

E(θ(hat)5) = E(Y (bar)) = E[(Y1+Y2+Y3)/3] = (1/3)[E(Y1) + E(Y2) + E(Y3)] = θ

Thus, θ(hat)5 is an unbiased estimator.

To compare the variances of the unbiased estimators, we need to compute their variances.

Var(θ(hat)1) = Var(Y1) = θ^2

Var(θ(hat)2) = Var[(Y1+Y2)/2] = (1/4)Var(Y1) + (1/4)Var(Y2) + (1/2)Cov(Y1,Y2)

Since Y1,Y2 are independent and identically distributed, Cov(Y1,Y2) = 0.

Thus, Var(θ(hat)2) = (1/4)θ^2 + (1/4)θ^2 = (1/2)θ^2

Var(θ(hat)3) = Var[(Y1+2Y2)/3] = (1/9)Var(Y1) + (4/9)Var(Y2) + (4/9)Cov(Y1,Y2)

Again, Cov(Y1,Y2) = 0, so Var(θ(hat)3) = (1/9)θ^2 + (4/9)θ^2 = (5/9)θ^2

Var(θ(hat)4) = Var(min(Y1,Y2,Y3))

Let X = min(Y1,Y2,Y3). Then,

F_X(x) = P(X ≤ x) = P(min(Y1,Y2,Y3) ≤ x)

= 1 - P(Y1 > x and Y2 > x and Y3 > x)

Since Y1,Y2,Y3 are independent,

= 1 - P(Y1 > x)P(Y2 > x)P(Y3 > x)

= 1 - (e^-x/θ)^3

Thus, the pdf of X is given by:

f_X(x) = d/dx[F_X(x)] = 3(e^-x/θ)^2 (1/θ)e^-x/θf, x>0

Using the formula for the variance of a continuous random variable, we get:

Var(θ(hat)4) = ∫0^∞ [x - E(θ(hat)4)]^2 f_X(x) dx

= ∫0^∞ [x - (3θ + 3θ^2)]^2 3(e^-x/θ)^2 (1/θ)e^-x/θf dx

= 6θ^2

Thus, Var(θ(hat)4) = 6θ^2.

Var(θ(hat)5) = Var(Y (bar)) = Var[(Y1+Y2+Y3)/3]

= (1/9)Var(Y1) + (1/9)Var(Y2) + (1/9)Var(Y3) + (2/9)Cov(Y1,Y2) + (2/9)Cov(Y1,Y3) + (2/9)Cov(Y2,Y3)

Since Y1,Y2,Y3 are independent, Cov(Yi,Yj) = 0 for i ≠ j.

Thus, Var(θ(hat)5) = (1/9)θ^2 + (1/9)θ^2 + (1/9)θ^2 = (1/3)θ^2.

Therefore, among the unbiased estimators, θ(hat)1, θ(hat)2, θ(hat)3, and θ(hat)5, the one with the smallest variance is θ(hat)2.

To know more about exponential distribution:

https://brainly.com/question/22692312

#SPJ4

Participant A did 120 jumping jacks in 10 minutes. Participant B did 140 jumping jacks in 14 minutes. Which participant had the greater jumping jack rate?​

Answers

Answer:  Participant A

Step-by-step explanation:

if you divide 120 by 10 you would get 12 jumping jacks per minute and if you divide 140 by 14 you would get 10 jumping jacks per minute

He has 2 pens. His friend gives him 2 more pens. How many pens he has?

Answers

Step-by-step explanation:

4 i guess... sry i m not good at maths

Graph the linear equation.
42 + 6y = -12
Plot two points on the line to graph the line.

Answers

The graph of the linear function 4x + 6y = -12 is given by the image presented at the end of the answer.

How to define a linear function?

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.

The function for this problem is given as follows:

4x + 6y = -12.

In slope-intercept form, the function is given as follows:

6y = -4x - 12.

y = -2x/3 - 2.

The slope and the intercept are given as follows:

Intercept of b = -2, meaning that when x = 0, y = -2.Slope of -2/3, meaning that when x decays by 3, y increases by two, hence the graph also passes through point (-3,0).

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Alexander and Rhiannon left school at the same time. Alexander travelled 14 km home at an average speed of 20 km/h. Rhiannon travelled 10 km home at an average speed of 24 km/h. a) Who arrived home earlier? b) How much earlier did this person arrive at home? Give your answer to the nearest minute. ​

Answers

Rhiannon arrived home approximately 17 minutes earlier than Alexander.

What is the average?

This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

According to the given information:

To solve this problem, we can use the formula:

time = distance / speed

a) The time it took Alexander to get home is:

time_Alexander = 14 km / 20 km/h = 0.7 hours

The time it took Rhiannon to get home is:

time_Rhiannon = 10 km / 24 km/h = 0.41667 hours

Since Rhiannon's time is smaller than Alexander's, Rhiannon arrived home earlier.

b) The time difference between their arrivals is:

time_difference = time_Alexander - time_Rhiannon = 0.7 hours - 0.41667 hours = 0.28333 hours

To convert this to minutes, we can multiply by 60:

time_difference_in_minutes = 0.28333 hours x 60 minutes/hour ≈ 17 minutes

Therefore, Rhiannon arrived home approximately 17 minutes earlier than Alexander.

To learn more about the average visit:

https://brainly.com/question/20118982

#SPJ1

can anyone help with this triangle question

Answers

The triangle's other leg, side B, measures 12 cm in length.

Are there 180 right triangles in all?

When one of the interior angles is 90 degrees, or a right angle, the triangle is said to be a right triangle. The three internal angles of a triangle add up to 180 degrees in a right triangle because one angle must always be 90 degrees and the other two must always total to 90 degrees (they are complementary).

We can observe that the given triangle is a right triangle because angle A's measure is 90 degrees. The hypotenuse, which is represented by the letter "c," is the side that is opposite the right angle. The legs are the other two sides, and they are indicated by "a" and "b".

We are told that the hypotenuse (side c) is 13 cm long and that one leg (side a) is 5 cm long. The length of the other leg must be determined (side b).

The Pythagorean theorem, which asserts that in a right triangle, can be used.

a² + b² = c²

Inputting the values provided yields:

5² + b² = 13²

25 + b² = 169

b² = 144

b = 12

To know more about triangle's visit:-

https://brainly.com/question/2773823

#SPJ1

Find the standard normal area for each of the following (LAB)Round answers to 4 decimals

Answers

The answer of the standard normal area for each of the following questions are given below respectively.

What is standard normal area?

Standard normal area refers to the area under the standard normal distribution curve, which is a normal distribution with a mean of 0 and a standard deviation of 1.

a. P(1.24<Z<2.14) = 0.0912

b. P(2.03 <Z<3.03) = 0.0484

c. P(-2.03 <Z<2.03) = 0.9542

d. P(Z > 0.53) = 0.2977

Note: The standard normal distribution is a continuous probability distribution with mean 0 and standard deviation 1. The area under the curve represents probabilities and can be calculated using a standard normal distribution table or a calculator with a normal distribution function.

To know more about probability distribution visit:

https://brainly.com/question/14210034

#SPJ1

I need help with this

Answers

Answer: D

Step-by-step explanation:

i think so

Let D be the disk with center the origin and radius a. What is the average distance from points in D to the origin?

Answers

Consider a disk D having center as origin and radius 'a', the average distance from point say ( r, θ) to the origin D to the origin is equals to the 2a/3.

The distance of a point to the origin is given by the function d(x, y) = √x²+ y². Denote the disk by D. To compute the average we need to evaluate the integral, for which we use polar coordinates, f(r, θ) = (1/area of region R)∬ f(r,θ)dA.

We have a disk D with center the origin (0,0) and radius 'a'. We have to determine the average distance from points in D to the origin. Since r is defined as the distance from the origin, the distance of any point (r,θ) from the origin is f(r,θ) = r

Integrating f over the region D, with limits r = 0 to a, and 0≤ θ≤2π , dA = r×dr×dθ

[tex]∬f(r,θ)dA = \int_{0}^{a} \int_{0}^{2π} r (rdr)dθ [/tex]

[tex]= \int_{0}^{2\pi} \int_{0}^{a} r^{2} drdθ = \int_{0}^{2\pi}[\frac{{r}^{3}}{3}]_{0}^{a}dθ[/tex]

[tex]= \int_{0}^{2π}[ \frac{a³}{3} ] dθ = \frac{{a}^{3}}{3} \int_{0}^{2π}dθ[/tex]

[tex]= \frac{a³}{3} [θ]_{0}^{2π} = 2\pi(\frac{a³}{3})[/tex]

Area of disk D with radius 'a' = πa²

So, the average distance from point ( r,θ) in D to the origin is = (1/area of region D)∬f(r,θ)dA

= (1/πa²)( 2πa³/3)

= 2a/3

Hence, required distance is 2a/3.

For more information about polar coordinates , visit :

https://brainly.com/question/29335657

#SPJ4

write the equation of a circle whose center is at latex: \left(-11,\:15\right) and whose radius is latex: 9 9 .

Answers

The equation of the circle with center at (-11, 15) and radius 9 is found to be x² + y² + 22x -30y + 337 = 0.

The center of the circle is located at the point (-11, 15). The radius of the circle is given to be 9.

Now, using the standard equation of the circle that has point (a, b) as center and r as the radius, we can write,

(x-a)² + (y-b)² = r²

Now, putting all the values,

(x-(-11))² + (y-15)² = (3)²

Solving further,

x² + 121 + 22x + y² + 225 - 30y = 9

x² + y² + 22x -30y + 337 = 0

So, the equation of the circle is found to be x² + y² + 22x -30y + 337 = 0.

To know more about equation of circle, visit,

https://brainly.com/question/1506955

#SPJ4

cyryl hikes a distance of 0.75 kilomiters in going to school every day draw a number line to show the distance ​

Answers

Answer:

Step-by-step explanation:

Sure! Here's a number line showing the distance of 0.75 kilometers:

0 -------------|-------------|------------- 0.75 km

The "0" on the left represents the starting point (such as home), and the "|---|" in the middle represents the distance of 0.75 kilometers to the destination (such as school).

Work out the probability of scoring a total of 4

Answers

Answer: 1/12

Step-by-step explanation:

Question 13 (2 points)
Suppose you flip a coin and then roll a die. You record your result. What is the
probability you flip heads or roll a 3?
1/2
3/4
7/12
1

Answers

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

we have 2 possible cases for the coin and 6 possible cases for the die.

so, we have 2×6 = 12 combined possible cases :

heads, 1

heads, 2

heads, 3

heads, 4

heads, 5

heads, 6

tails, 1

tails, 2

tails, 3

tails, 4

tails, 5

tails, 6

out of these 12 cases, which ones (how many) are desired ?

all first 6 plus (tails, 3) = 7 cases

so, the correct probability is

7/12

formally that is calculated :

1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12

the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.

A piece of wire 18cm long is bent to form a rectangle. If its length is x cm, obtain an expression for its area in terms of
* and hence calculate the dimensions of the rectangle with maximum area

Answers

Answer:

To form a rectangle, the piece of wire will have two sides of length x and two sides of length (18 - 2x)/2 = 9 - x. Therefore, the perimeter of the rectangle is given by:

2x + 2(9 - x) = 18 - 2x

The area of the rectangle is given by:

A = x(9 - x)

Expanding this expression, we get:

A = 9x - x^2

To find the dimensions of the rectangle with maximum area, we can differentiate the area expression with respect to x:

dA/dx = 9 - 2x

Setting this equal to zero to find the maximum:

9 - 2x = 0

x = 4.5

So, one side of the rectangle is x = 4.5 cm and the other side is (18 - 2x)/2 = 4.5 cm. Therefore, the dimensions of the rectangle with maximum area are 4.5 cm by 4.5 cm.

To calculate the maximum area, we can substitute x = 4.5 into the area expression:

A = 9(4.5) - (4.5)^2 = 20.25 cm^2

Step-by-step explanation:

For the given matrix A. find a 3 × 2 nonzero matrix B such that AB that any such matrix B must have rank 1. (Hint: The columns of B belong to the nullspace of A.] 0, Prove A= 13.421

Answers

The nullspace of matrix A found by solving the equation Ax=0. It is the nullspace of A is spanned by the vector [-2, 1, 0] and [0, -1, 1]. Any 3x2 matrix B that satisfies AB=0 belongs to the nullspace of A.

To find a 3×2 nonzero matrix B such that AB = 0, we need to find the nullspace of matrix A. The nullspace of a matrix A is the set of all vectors x such that Ax = 0.

Let's first write matrix A in row-echelon form:

1 2 1

0 -1 0

From this, we can see that the pivot variables are x1 and x2, and the free variable is x3. Thus, the general solution to Ax = 0 is given by:

x1 = -2x2 - x3

x2 = x2

x3 = x3

We can now write the columns of matrix B as:

[1, 0]

[-2, 1]

[0, -1]

To show that any such matrix B must have rank 1, we need to show that the columns of B are linearly dependent. Let's assume that B has rank 2. Then, the columns of B are linearly independent, and we can write:

c1[1, -2, 0] + c2[0, 1, -1] = [0, 0, 0]

where c1 and c2 are constants. This gives us the system of equations:

c1 = 0

-2c1 + c2 = 0

c2 = 0

which has only the trivial solution c1 = c2 = 0. This means that the columns of B are linearly dependent, and hence, any such matrix B must have rank 1.

To know more about Null space:

https://brainly.com/question/17215829

#SPJ4

_____The given question is incomplete, the complete question is given below:

For the given matrix A.= [1 2 1  1 1 1] find a 3 × 2 nonzero matrix B such that AB = 0 that any such matrix B must have rank 1. (Hint: The columns of B belong to the nullspace of A.] 0, Prove A= 13.421

please help I know its 9:35 PM I Just need help what this question2.1 × 1.6 =
21
10
×
16
10
= tenths × tenths my parents are gonna kill me help

Answers

The value of the expression 2.1 × 1.6 = 3.36.

What are decimals?

Decimals are a collection of numbers falling between integers on a number line. They are only an additional mathematical representation of fractions. Decimals allow us to express quantifiable quantities like length, weight, distance, money, etc. with more accuracy. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are shown to the right of the decimal point.

Given that the expression is: 2.1 × 1.6.

2.1 × 1.6 can be written as:

2.1 × 1.6 = 21/10 × 16/10

Multiply the numerator and denominator:

21/10 × 16/10 = 336/100

Covert the fraction into decimal:

336/100 = 3.36

Hence, the value of the expression 2.1 × 1.6 = 3.36.

Learn more about decimals here:

https://brainly.com/question/30958821

#SPJ1

n january 1,2020 flounder corportaion purchased 325 of the $1000 face value, 11%, 10-year bonds of Walters Inc. The bonds mature on January 1,2030 and pay interest annually beginning January 1, 2021. Flounder purchased bonds to yield 11%. How much did Flounder pay for the bonds?

Answers

Answer:

Step-by-step explanation:

To calculate how much Flounder paid for the bonds, we need to use the present value formula for a bond:

PV = C/(1+r)^1 + C/(1+r)^2 + ... + C/(1+r)^n + F/(1+r)^n

where PV is the present value, C is the annual coupon payment, r is the yield, n is the number of years, and F is the face value.

In this case, Flounder purchased 325 bonds with a face value of $1000 each, so the total face value of the bonds is:

325 * $1000 = $325,000

The coupon rate is 11%, which means that the annual coupon payment is:

0.11 * $1000 = $110

The bonds mature in 10 years, so n = 10. The yield is also 11%, so r = 0.11.

Using these values, we can calculate the present value of the bond:

PV = $110/(1+0.11)^1 + $110/(1+0.11)^2 + ... + $110/(1+0.11)^10 + $1000/(1+0.11)^10

PV = $110/(1.11)^1 + $110/(1.11)^2 + ... + $110/(1.11)^10 + $1000/(1.11)^10

PV = $110/1.11 + $110/(1.11)^2 + ... + $110/(1.11)^10 + $1000/(1.11)^10

PV = $110*(1-(1.11)^-10)/0.11 + $1000/(1.11)^10

PV = $750.98 + $314.23

PV = $1,065.21

Therefore, Flounder paid $1,065.21 for the 325 bonds of Walters Inc.

Other Questions
4. Circle the reason for each of the following manipulations used to simplify the product (8x)(3x).(8.3).(x-x)8x-3xcommutative or associative8.3.x-xcommutative or associative24xcommutative or exponent property Find the frequency w for which the particular solution to the differential equation dy dy 3 + dt + 3y iwt =e dt2 has the largest amplitude. You can assume a positive frequency w > 0. Probably the easiest way to do this is to find the particular solution in the form Aeiwt and then minimize the modulus of the denominator of A over all frequencies w. = 0 ? X 0% Try a new variant Correct answer W = 0.971825315808 .......??????????????? Which historical event discussed in the text was taking place in chicago that helped many jazz? which of these groups of particles has the greatest mass? which of these groups of particles has the greatest mass? a helium nucleus with two protons and two neutrons four electrons four individual protons if a stimulus was applied in the middle of a nerve roughly halfway between the cell body and the axon terminal, would the resulting action potentials travel only from the stimulus point to the axon terminal? Rae's unpaid credit card balance was $1,603. Her APR is 28.6%. What is her newbalance after she makes one new transaction for $51? Round answer to thehundredths place. If answer doesn't have a hundredths place then include a zero sothat it does. Use a word not a symbol for the units. a child who weighs 18kg is to receive motrin (ibuprofen) 8mg/kg by mouth every 4 hours as needed for pain. the label reads 100mg/5mls. how many milliliters will you administer? which of the following is not true about perception? group of answer choices it includes three stages explains how we can experience the same things but come away with different ideas it gives meanings to the things we notice in the world it impacts the way we see others but not ourselves which one of these defines an asset transformer? multiple choice question. an economic agent appointed to act on behalf of investors a financial institution which issues secondary securities to investors a corporation that repurchases outstanding shares of stock a financial institution that issues primary equity securities I will mark you brainiest!What is the length of AC in the given triangle?A) 126.6B) 99.6C) 66.9D) 57.1 What one person has the most significant influence on your life? essay response what is the vertex of h=-16t^2+29t+6 and its domain and range, and x and y axis? a hummingbird lives in a nest that is 5 meters high in a tree. the hummingbird flies 9 meters to get from its nest to a flower on the ground. how far is the flower from the base of the tree? if necessary, round to the nearest tenth. 6TH GRADE MATH PLS HELPPPP! TYSM Jamal sold hotdogs at a recent basketball game. Each hotdog sold for $3.50. In total, Jamsold $98 worth of hot dogs. Let n be the number of hotdogs that Jamal sold.Set up an equation that models the information given in this problem. this exercise stresses the relationships between the information recorded in a periodic inventory system and the basic elements of an income statement. each of the five lines represents a separate set of information. you are to fill in the missing amounts. (enter loss amounts as a negative number.) the purpose of a business impact analysis (bia) is to determine: a. the impact of a disaster b. the extent of damage in a disaster c. which business processes are the most critical d. which processes depend on it systems Please help me. !!!!!!!!!!! temperature decreasing is what causes the crystals to form on the wooden stick?