Local authority A has made a study of material being recycled per household following the introduction of a recycling scheme. Information from other local authorities that have introduced similar recycling schemes is that recycling material collected each week per household follows a normal distribution with mean 40kg and standard deviation of 15kg and is independent over households. It is considered reasonable to assume that the information from the other local authorities is applicable to local authority A.a. For a randomly selected household whose recycled material is collected by local authority A calculate the probability that the recycled material collected in a given week is less than 30kg. [4]b. A random sample of 100 households is taken and the sample mean recycled material collected per household is found. Calculate the probability that the sample mean recycled material collected in a given week is less than 30kg. [7]c. The sample mean recycled material of 100 households on a single street is taken and found to be 30kg. Why is this not necessarily overwhelming evidence that the recycling scheme of local authority A is not working as well as for other local authorities?d. To encourage increased recycling performance, local authority A introduces an extensive advertising campaign. Following the campaign, the authority collect a random sample of 1,000 households and find the sample mean recycled material is 41kg. Construct a 95% confidence interval for the mean amount of recycled material per household in local authority A, treating population standard deviation as known as 15kg. Is there statistically significant evidence of increased recycling following the campaign?

The circumference of the circle with radius 3 miles is 18.85 miles.

All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The following are some of the circle's crucial characteristics:

The radius of the circle is 3 miles

Circumference of the circle 2π(radius) = 2*π*3 = 18.85 miles.

To learn more about Circles refer to :

https://brainly.com/question/16125353

#SPJ4

"A music streaming service charges a flat monthly fee plus a per-song charge for each song downloaded. It cost $11 to download 2 songs during the month and $14 to download 8 songs during the month."

The equation in the form y = mx b for this function is:

y = (1/2)x + 10

To write an equation in the form y = mx + b for this function, we can use two sets of data points, (x, y), to find the slope (m) and the y-intercept (b) of the line.

Let x be the number of songs downloaded and y be the cost in dollars.

We can use the slope formula to find m:

Next, we can use one of the data points and the slope to find b:

Therefore, the equation of the line is:  y = (1/2)x + 10

This equation represents the cost y in dollars of downloading x number of songs, given the flat monthly fee and per song charge.

Complete Question:

"A music streaming service charges a flat monthly fee plus a per-song charge for each song downloaded. It cost $11 to download 2 songs during the month and $14 to download 8 songs during the month. Write an equation in the form y = mx + b for this function."

To know more about y = mx b equation, click on the link below:

brainly.com/question/16926983

#SPJ4

If 29 student tickets were sold, then all possible values for the number of adult tickets that the drama club must sell in order to meet the show's expenses are 54 and 55 .

the price for each student ticket is $4.50 and adult is $8 ;

The number of people auditorium can hold is = no more than 84 people ;

the number of children tickets sold is = 29 tickets ;

Let "x" be number of adult tickets sold.

The total revenue from ticket sales = $4.50×29 + $8×(x)

⇒ $130.5 + $8x.

The total revenue must be at least $560,

So , $130.5 + $8x ≥ $560.

Subtracting $130.5 from both sides, we get $8x ≥ $429.5   ;

Dividing both sides by 8, we get x ≥ 53.69    ;

Since the number of adult tickets sold must be an integer, the minimum number of adult tickets that must be sold is 54.

The maximum number of people allowed in the auditorium is 84, so the maximum number of adult tickets that can be sold is 84 - 29 = 55.

Therefore, the possible values for the number of adult tickets that must be sold are 54, 55.

The given question is incomplete , the complete question is

The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4.50 and each adult ticket sells for $8. The auditorium can hold no more than 84 people. The drama club must make at least $560 from ticket sales to cover the show's costs. If 29 student tickets were sold, determine all possible values for the number of adult tickets that the drama club must sell in order to meet the show's expenses.

Learn more about Tickets here

https://brainly.com/question/16481101

#SPJ4

The probability that a resident of this city who is 60 years old will survive until they are 80 will be 0.54 l.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur.

In this case, in the city of exactly 100,000 people, 90% can expect to live to (at least) age 60 and 60% can expect to live to (at least) age 80.

The probability that a resident of this city who is 60 years old will survive until they are 80 will be:

= 90% × 60%

= 0.54

Learn more about probability on

brainly.com/question/24756209

#SPJ1

The two integers required in the question are; 16 and 12

We are told that the sum of two positive integers is 28. Now, if the two integers are x and y, then we have;

x + y = 28   ------(1)

When the smaller integer is subtracted from three times the larger, the result is 36. Thus;

3x - y = 36  ------(2)

Add eq 1 and eq 2 to get;

4x = 64

x = 64/4

x = 16

16 + y = 28

y = 28 - 16

y = 12

Read more about Algebraic Word Problems at; https://brainly.com/question/21405634

#SPJ1

Original Equation:

[tex]\frac{3}{4} + x < \frac{1}{6}[/tex]

1) Subtract 3/4 from both sides:

[tex](\frac{3}{4}+x)-\frac{3}{4} < \frac{1}{6}-\frac{3}{4}[/tex]

2) Simplify:

[tex]x < \frac{1}{6}-\frac{3}{4}[/tex]

Find a common denominator for both fractions (I will use 12)

[tex]x < \frac{2}{12} -\frac{9}{12}[/tex]

Simplify:

[tex]x < \frac{-7}{12}[/tex]

We cannot simplify the expression anymore, therefore this is the answer!

The probability of getting at least 14 heads when flipping a fair coin 20 times is 0.25.

This can be calculated using the binomial distribution formula which states that the probability of obtaining exactly x successes in n trials is given by

P(x) = (n choose x) * p^x * (1-p)^(n-x),

where n is the total number of trials, p is the probability of success, and x is the number of successes.

For this problem, n=20, p=0.5, and x=14, so the probability of getting at least 14 heads is P(x) = (20 choose 14) * 0.5^14 * 0.5^6 = 0.25.

Learn more about probability:

https://brainly.com/question/13604758

#SPJ4

Answer:

x greater-than-or-equal-to negative 9.2

Step-by-step explanation:

Step by step in math notation here is what Marquis solved

Starting with -5.6 ≥ x + 3.6

Step 1

Step 2: Interpret the results

Since the question is asking only for the first step where the error was made, the rest of the actions taken have no relevance

The weight of gift is 5 pound extra with medium size of box.

In science and engineering, the weight of an object is the force acting on the object due to gravity.

Let the weight is W

The first company charged “$15 to ship a medium box, plus an additional $1 per pound”.

So, that the amount of certain weight is F =  $15 + $1*W

The second company charged “$10 to ship a medium box, plus an additional $2per pound”.

So, that the amount of certain weight is S  =  $10 + $2*W

The two shipping methods will cost the same amount

so that, F = S

$15 + $1*W = $10 + $2*W

$5  =  $1*W

W = 5 pound.

So that the weight of gift is 5 pound extra with medium size of box.

To learn more about weight of items visit:

brainly.com/question/28655978

#SPJ1

The quarter mile grounding rule for rural electric utilities for direct-buried jacketed distribution cables says that they must have at least 4 grounds per mile.

A utility cooperative is a specific kind of cooperative that is responsible for providing its members with a public utility, such as power, water, or telecommunications. Profits are either distributed to members as "patronage" or "capital credits," which are dividends paid on a member's investment in the cooperative, or they are reinvested for infrastructure. 

Every consumer is a shareholder and a member of the company. This means that, in contrast to investor-owned utilities where the amount of individual authority is determined by the number of shares held, all members have the same level of personal authority. Many utility cooperatives operate their business in accordance with a set of ideals based on the Rochdale Principles, just like cooperatives active in other industries.

Learn mor about Rural electric utilities:

https://brainly.com/question/1198789

#SPJ4

Answer:

Step-by-step explanation:

P = x

Answer:6

Step-by-step explanation:

On solving the provided question, we can say that here, the function is f(x) = 1/5(15^x) and growth factor is 15.

What is function?

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

For given question

the function is

f(x) = 1/5(15ˣ)

when f(x) = aˣ

then the growth factor of function = a

Then for f(x) = 1/5(15ˣ)

Growth factor = 15

Therefore the growth factor of function is 15.

To know more about function visit:

brainly.com/question/28193995

#SPJ1

A stratified random sample size is being used by Donald. He is segmenting the population into groups and choosing a representative sample of pupils from each category at random.

To examine the eating patterns of all pupils attending his school, Donald is utilising stratified random sampling. In this kind of sampling, the population is divided into strata, or groups, and a proportionate number of people from each category are randomly chosen to make up the sample. To make sure the sample is representative of the total community, Donald in this instance is grouping the pupils by grade level. Then he gathers information from the sample in order to make generalisations about the eating patterns of all the pupils enrolled in his school. A representative sample can be obtained and reliable population inferences can be made using stratified random sampling

Learn more about sample size here

https://brainly.com/question/25894237

#SPJ4

Answer:

90 is 150% of 60

OR

90 is 50% greater than 60

Step-by-step explanation:

To find the percentage increase between two values, the first step is to find the difference between the final and initial value.

Final value: 90cm

Initial value: 60cm

Difference = 90 - 60 = 30cm

Next, you need to divide the difference between the two values by the initial value.

30 / 60 = 0.5

Lastly, you need to take the value previously found and multiply it by 100 to convert it from a decimal to a percentage.

0.5 * 100 = 50%

This value will be your percentage increase.

If you want to know what percentage the final value is of the initial value, you can take the percentage you have and add 100% to it.

50% + 100% = 150%

If this answer helped you, please leave a thanks or a Brainliest!!!

Have a GREAT day!!!

Answer: 150%

Step-by-step explanation:

First, ask yourself what the difference between the two is: 90-60=30.

Secondly, 30 is 1/2 of 60. 1/2=50%.

You also need to add the hundred percent because we are adding 60 and 60 is 100% of 60. It increases by 50 and then 100. so 150%.

50% + 100% = 150%

Answer:

Step-by-step explanation:

sin(YZX)=opposite/hypotenuse

sin(YZX)=7.5/22.3

then apply sin inverse to find angle Z

Answer: 13.2%

Step-by-step explanation:

To find the percentage we need to use the formula: (original cost-new cost)/original cost *100

Plugging in the numbers: (38-33)/38*100=0.131578947368421*100=13.2%

The mean and median number of times a face will appear are 100 and 99.5. The mean and median face value of the 600 rolls of the die are 96.2 and 94.5

a) Mean number of appearances of each face = [tex]\frac{107+120+84+110+92+87}{6}[/tex]

                                                                             = 100

Median number of appearances of each face = Average of middle two values when arranged in ascending order

Ascending order: 84, 87, 92, 107, 110, 120

Average of middle two values = [tex]\frac{92+107}{2}[/tex]

                                                  = 99.5

b) Mean and Median face values of the 600 rolls of the die:

Mean = [tex]\frac{107\times1+120\times2+84\times3+110\times4+92\times5+87\times6}{21}[/tex]

         = [tex]\frac{2021}{21}[/tex]

         = 96.2

Median = [tex]\frac{92\times5+107}{2}[/tex]

            = [tex]\frac{567}{6}[/tex]

            = 94.5

The question is incomplete. The complete question is

"The following represents the outcomes of rolling a die 600 times

Face       1      2     3     4     5     6

Number 107 120  84  110   92   87

a. What are the mean and median numbers of appearances of each face?

b. What are the mean and median face values of the 600 rolls of the die?"

To learn more about Mean and Median here:

brainly.com/question/16970009

#SPJ4

The equation for your savings account can be represented as:

y = 50 + 10x

The equation for your friend's savings account can be represented as:

y = 25 + 10x

where x is the number of weeks and y is the total amount of money in the account.

The equation for the savings account can be determined by taking the initial amount of money and adding the weekly deposit over a certain number of weeks. The initial amount of money in your savings account is $50, and you plan to deposit $10 each week, so each week your balance will increase by $10.

Starting from the initial balance, after the first week, the balance will be $50 + $10 = $60. After the second week, the balance will be $60 + $10 = $70, and so on. We can represent this pattern using an equation:

y = 50 + 10x

where y is the balance after x number of weeks.

Similarly, for your friend's savings account, the initial balance is $25 and the weekly deposit is $10. So, each week the balance will increase by $10. Using the same pattern, the equation for your friend's savings account can be represented as:

y = 25 + 10x

where y is the balance after x number of weeks.

Learn more about Savings Account Equations here:

https://brainly.com/question/24995280

#SPJ4

The rule that describes the composition transformation that maps ABCD to A''B''C''D'' is;

''Translation of negative 6 units x, 1 units y composition reflection across the x-axis''.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

The given coordinates of parallelogram ABCD are;

⇒ (3, 5), (6, 5), (4, 1), (1, 1)

The coordinates of the parallelogram A'B'C'D' are;

⇒ A'(3, -5), B'(6, -5), C'(4, -1), D(1, -1)

The coordinates of the parallelogram A''B''C''D'' are;

⇒ D(-5, 0), C''(-2, 0), A''(-3, -4), B''(0, -4)

The image of the point (x, y), following a reflection about the x-axis is the point (x, -y).

And, The difference in the coordinates of the parallelogram ABCD and A'B'C'D' is the change in the sign of the y-coordinates

Therefore, the transformation that gives the parallelogram A'B'C'D' from the parallelogram ABCD is a reflection about the x-axis

Thus, The difference between the coordinates of the vertices of the parallelogram A'B'C'D' and the parallelogram A''B''C''D'', is a change in the x-value by (-6), and a change in the y-value by (+1)

Therefore, the parallelogram A''B''C''D'' can be obtained from parallelogram A'B'C'D', by a translation of -6 units (left) in the x-direction and a translation of 1 unit, x in the y-direction.

Which gives;

The composition transformation that maps the pre-image ABCD to the final image A''B''C''D'', (given that in a composition transformation, the transformation to the right is done first) are; which is the option;

''Translation of negative 6 units x, 1 units y composition reflection across the x-axis''.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

The probability that both the father and mother are current smokers is 0.12.

The probability that the mother is a current smoker is, 0.3 and the father is a current smoker is, 0.4.

The events are independent, the probability that both the events will occur is the multiplication of probability of individual events.

Therefore, the required probability is product of probability that mother is a current smoker with the probability that father is a current smoker.

P(Father and Mother are current smokers) = P(Father is a current smoker) × P(Mother is a current smoker)

P(Father and Mother are current smokers) = 0.4 × 0.3

P(Father and Mother are current smokers) = 0.12

The required probability is 0.12.

To know more about the speed, here

brainly.com/question/11234923

#SPJ4

Tomatoes are typically lighter than cucumbers since the mean weight for tomatoes is less than the mean weight for cucumbers.

Answer:

Lighter, less

Step-by-step explanation:

The mean is also known as the average. This means that it is the sum of all values divided by the total number. Therefore it is said that on average, tomatoes weigh less than cucumbers.

The number of feet away from the sprinkler where it could spread water would be the radius of the circle in which it is spraying.

The area of the circle is

[tex]\pi[/tex]r²=706.50

(3.14)r²=706.50

r²=706.50÷3.14

r²=225

Now, the square root will shift from LHS to RHS.

r=(225)²

r=15

Therefore, the sprinkler can spread the water 15 feet away .

Learn more about circle:

https://brainly.com/question/24375372

The needed temperature continues to decline at this pace in 2 hours -6°C, 5 hours -15°C, and half an hour -1.5°C.

A weather station on a mountaintop says that the temperature is now 0°C and has been dropping at a consistent pace of 3°C every hour.

We must discover,

What will the temperature be in 2 hours, 5 hours, and half an hour if it continues to plummet at current rate?

In response to the question,

A weather station on a mountaintop says that the temperature is now 0°C and has been dropping at a consistent pace of 3°C every hour.

The temperature drops by 3°C in one hour = 0 – 3 = -3°C

The temperature drops in two hours = (2)(-3°C) = -6°C

Temperature drop in 5 hours = (5)(-3°C) = -15°C

In half an hour, the temperature drops = (0.5)(-3°C) = -1.5°C.

As a result, the needed temperature continues to decline at this pace in 2 hours -6°C, 5 hours -15°C, and half an hour -1.5°C.

To learn more about temperature drops to refer:

https://brainly.com/question/29163891

#SPJ1

The required temperature will drop further at this rate in 2 hours at -6 °C, 5 hours at -15 °C, and 30 minutes at -1.5 °C.

A weather station on a mountaintop says that the temperature is now 0 °C and has been dropping at a consistent pace of 3 °C every hour.

A weather station is a place equipped with tools for measuring atmospheric conditions, gathering data for weather forecasts, and researching the weather and environment.

The temperature drops by 3 °C in one hour = 0 – 3 = -3 °C. The temperature drops in two hours = (2)(-3 °C) = -6 °C

Temperature drop in 5 hours = (5)(-3 °C) = -15 °C

In half an hour, the temperature drops = (0.5)(-3 °C) = -1.5 °C.

Therefore,  the needed temperature continues to decline at this pace in 2 hours -6 °C, 5 hours -15 °C, and half an hour -1.5 °C.

Learn more about weather station here:

https://brainly.com/question/26164593

#SPJ1

The measure of value of x for the given set of parallel lines is found as:

x = 34.

From the definition of  alternate exterior angles:

3x + 1 = 103°

3x = 103 - 1

3x = 102

x = 34

Thus, the measure of value of x for the given set of parallel lines is found as: x = 34.

To know more about the alternate exterior angles, here

https://brainly.com/question/26111088

#SPJ1

Answer:

40,28,16,4, -8,-20... keep going

Step-by-step explanation:

use 40-12, then 40-2*12, so forth

The value of k = −8 for which AB = BA.

[tex]A = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right][/tex]

[tex]B = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right][/tex]

Now,

[tex]AB = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right] \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right] = \left[\begin{array}{ccc}-7&18+3k\\2&-9-k\end{array}\right][/tex]

[tex]BA = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right] \left[\begin{array}{ccc}2&3\\-1&-1\end{array}\right] = \left[\begin{array}{ccc}-7&-6\\-6-k&-9-k\end{array}\right][/tex]

Thus, in order for AB = BA, we must have that

[tex]\left[\begin{array}{ccc}-7&18+3k\\2&-9-k\end{array}\right] = \left[\begin{array}{ccc}-7&-6\\-6-k&-9-k\end{array}\right][/tex]

Equate the values, and we get

18 + 3k = -6

3k = -6 - 18

3k = -24

k = -8

and 2 = -6 - k

k = -6 - 2

k = -8

Therefore we can say that it is easy to see that these equations are satisfied if and only if k = −8, and thus k = −8 is the (unique) value for which AB = BA.

--The given question is incomplete; the complete question is

"Let [tex]A = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right][/tex]. What value(s) of k, if any, will make AB = BA?"--

To know more about equations, here

https://brainly.com/question/22277991

#SPJ4

Answer: You should buy 7.5 pounds of pecan.

Step-by-step explanation: Each pecan pie needs 1.5 pounds each and 1.5 x 5 = 7.5

Answer:

2.5

Step-by-step explanation:

The minimum is the smallest value taken by the function.