a sanitation supervisor is interested in testing to see if the mean amount of garbage per bin is different from 50. in a random sample of 36 bins, the sample mean amount was 50.67 pounds and the sample standard deviation was 3.9 pounds. conduct the appropriate hypothesis test using a 0.01 level of significance. a) what are the appropriate null and alternative hypotheses?

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-4)}}} \implies \cfrac{2 +1}{8 +4} \implies \cfrac{ 3 }{ 12 } \implies \cfrac{1 }{ 4 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-1)}=\stackrel{m}{ \cfrac{1 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y +1 = \cfrac{1 }{ 4 } ( x +4) \\\\\\ y+1=\cfrac{1 }{ 4 }x+1\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 4 }x \end{array}}[/tex]

This is an example of stratified random sampling as the population is divided into two groups males and females and 200 samples are selected from each group.

Given that,

A researcher asks all 1000 employees to engage in a questionnaire survey to look at various areas of employee job satisfaction with the goal of selecting a sample of 200 males and 200 women.

A crucial element of the sampling method known as stratified random sampling is the division of a population into smaller subgroups known as strata

Therefore, the population is separated into two categories, males and females, and 200 samples are chosen from each group in this stratified random sampling example.

Learn more about stratified random sampling :

brainly.com/question/20692763

#SPJ4

3(y-9)

3y-27

Factorizing

3(y-9)

Marie did her homework in 8 hours.

Answer:

None of the above

Step-by-step explanation:

The speed of the tip of her shadow would be 5.714 ft/sec.  ft/sec.

let H, be the height of the pole = 20 ft.

h, be the height of the woman = 6 ft.

x, be the length of the woman's shadow,

and s, be the distance from the pole to the woman = 15

by using the equation of similar triangles,

[tex]\frac{H}{h} = \frac{(s+x)}{x}[/tex] or Hx = h(x+s)

differentiating, [tex]H\frac{dx}{dt} = h (\frac{ds}{dt} + \frac{dx}{dt} )[/tex]

[tex]20\frac{dx}{dt} = 6(4 + \frac{dx}{dt} ) = 24 + 6 \frac{dx}{dt}[/tex]

[tex]14\frac{dx}{dt} = 24[/tex],

[tex]\frac{dx}{dt} = \frac{24}{14}[/tex] ≈ 1.714 ft/sec, is how fast her shadow is lengthening.

the speed of the tip of her shadow would be the speed of shadow lengthening + speed of her traveling = 1.714 + 4 = 5.714 ft/sec.

thus, a street light is at the top of a 20 ft tall pole. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. the speed of the tip of her shadow would be 5.714 ft/sec.

know more about the speed of the shadow problems here: https://brainly.com/question/13316193

#SPJ4

The GCF of the expressions given as 70x³z and 45y⁴z² is 5z

From the question, we have the following expressions

70x^3z and 45y^4z^2

Rewrite the given expression as follows

This is represented using

70x³z and 45y⁴z²

Factor out z from the expression

So, we have the following representation

70x³ and 45y⁴z => Factored z

Factor out 5 from the expression

So, we have the following representation

14x³ and 9y⁴z => Factored 5z

So, we have

Factored = 5z

This represents the GCF

Hence, the GCF is 5z

Read more about GCF at

brainly.com/question/28552398

#SPJ1

Answer: Hence the answer is 27 square feet.

Please look at the images for more details.

Answer:

27 square feet

Step-by-step explanation:

Define the variables:

To increase a number by a certain percent, divide the percent by 100, add it to 1, then multiply the original number by this number.

If the length of the new flag is 20% greater than the length of the old flag:

[tex]\implies \textsf{Length}=\left(1+\dfrac{20}{100}\right) \timesl \times l=1.2l[/tex]

To decrease a number by a certain percent, divide the percent by 100, subtract it from 1, then multiply the original number by this number.

If the width of the new flag is 10% less than the width of the old flag:

[tex]\implies \textsf{Width}=\left(1-\dfrac{10}{100}\right) \times w =0.9w[/tex]

[tex]\boxed{\textsf{Area of a rectangle}=\sf width \times length}[/tex]

Therefore, given the area of the old flag is 25 ft²:

[tex]\implies wl=25[/tex]

To find the area of the new flag, substitute the expressions for width, length and wl into the formula for area of a rectangle:

[tex]\begin{aligned}\textsf{Area of new flag}&=\sf width \times length\\&=0.9w \times 1.2l\\&=0.9 \times 1.2 \times wl\\&=1.08 \times 25\\&=27\sf \;\; ft^2\end{aligned}[/tex]

Therefore, the area of the new flag is 27 square feet.

The stage that has the smallest percentage of prospects associated with the AIDA model is PlentyofFish implementing for its campaign is the action stage.

The AIDA Model (Attention, Interest, Desire, and Action) is an advertising effect model that identifies the stages that an individual goes through when purchasing a product or service.

The AIDA model is one of several models known as hierarchy of effects models or hierarchical models, all of which imply that when making a purchase decision, consumers go through a series of steps or stages.

An AIDA model entails the following steps:

Attention: The first step in marketing or advertising is to think about how to get consumers' attention.

Interest: Once a consumer is aware that a product or service exists, the company must work to increase the potential customer's level of interest.

Desire: Once the consumer is interested in the product or service, the goal is to make them want it.

Action: The ultimate goal of a marketing campaign is to motivate the recipient to take action and buy the product or service.

Learn more about AIDA model on;

https://brainly.com/question/13057677

#SPJ1

The range of the function is y ≥ -2 so , correct option is option c

Mathematical functions can be compared to vending machines. They provide some cans or biscuits in exchange for the money provided as input. Similar to this, functions take a set of input numbers and produce a set of results. One may argue that everything in actual life can be formulated and resolved with the aid of functions. It is impossible to avoid the fact that functions are of enormous importance in our daily lives. The mathematical model of almost everything in real life, from building design and architecture to mega skyscrapers, requires functions. One feature that can be used to describe a function is its domain and range.

The graph of the range of the given function is attached below .

learn more about range of a function here :

brainly.com/question/21027387

#SPJ13

Answer:

i have the similar question just radius is changed frm 12 to 20 cm..

hopefully this will help u ...^⁠_⁠^

Answer:

20°,70°

Step-by-step explanation:

X+y+90=180

X+y=90

20+y=90

y=70°

2x+180-40=180

2x=40

X=20°

The measures of angles of the triangle is x = 20° and y = 70°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

Now , let the side be represented as BD , which cuts AC at point D

And , the measure of BD = measure of DC ( given )

And , the measure of ∠ABC = 90°

The measure of ∠BDA = 40°

So , the measure of angle ∠BDC = 140° ( angles on a straight line )

Now , the measure of angle ∠DBC = measure of ∠BCD ( given )

So , the measure of x = ( 180 - 140 ) / 2

x = 20°

And , the measure of y = 180° - 40° - 70°

y = 70°

Hence , the angles of triangle are x = 20° and y = 70°

To learn more about triangles click :

https://brainly.com/question/16739377

#SPJ2

x= 4  is a number and five is at least half the difference of six and the same number.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.

Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.

Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.

According to our question-

learn more about unitary method click here:

brainly.com/question/24587372

#SPJ4

Answer:

False

Step-by-step explanation:

If is a real number and m and n are positive integers

The graph of the cosine function y = 3cos(4θ) - 1 is given by the image presented at the end of the answer.

The cosine function is defined by the rule presented as follows:

g(x) = acos(bx+c)+d.

The coefficients have the roles listed as follows:

In this problem, the definition of the function is:

y = 3cos(4θ) - 1

Considering the amplitude of 3 and the vertical shift of -1 the function will oscillate between:

-4 and 2.

(Without the vertical shift it would be between -3 and 3).

The period of the function will be as follows:

2π/b = 4

b = 2π/4

b = π/2.

Considering these features, the graph is given at the end of the answer.

A similar problem, also featuring cosine functions, is presented at brainly.com/question/28574324

#SPJ1

Answer: x=143

Step-by-step explanation: the ratio is 1:13 so 11*13=143

Answer: Don't take my word wait until someone else says something.

Step-by-step explanation: i think it is 134 or around that.

The height of the tree is 13.2 m.

What is proportional ?

 The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount.  

We can set up a proportion comparing the height of each object to the length of the shadow.

Then , [tex]\frac{h}{s}[/tex].

=> [tex]\frac{3.8}{1.3} = \frac{h}{4.5}[/tex]

=> h = [tex]\frac{3.8*4.5}{1.3}[/tex]

=> 13.2 m.

Hence the height of the tree is 13.2 m.

To learn more about proportional

https://brainly.com/question/870035

#SPJ1

11.25 percentage of the female students chose volleyball when 35 percent of the 80 kids in the group are girls.

Given that,

35 percent of the 80 kids in the group are girls. 9 of the female students selected volleyball as their preferred sport.

We have to find what percentage of the female students chose volleyball.

The total children's are 80.

The 35% are girls.

9 have selected the volleyball

So,

9/80

0.1125

The percent is

11.25%

Therefore, 11.25 percentage of the female students chose volleyball when 35 percent of the 80 kids in the group are girls.

To learn more about percentage visit: https://brainly.com/question/28269290

#SPJ1

The length of the chord used in this situation is approximately 40.54 ft.

To find the length of the chord used in the situation, we can use the formula for the chord length in a circular arc:

Chord length = 2√(r² - (r - h)²)

where r is the radius of the arc and h is the measure of the middle ordinate.

Given that the radius of the arc is 70 ft and the measure of the middle ordinate is 6 ft, we can substitute these values into the formula:

Chord length = 2√(70² - (70 - 6)²)

Chord length = 2√(4900 - 4489)

Chord length = 2√(411)

Chord length ≈ 2 * 20.27

Chord length ≈ 40.54 ft

Therefore, the length of the chord used in this situation is approximately 40.54 ft.

Learn more about the chords here:

https://brainly.com/question/15298662

#SPJ4

Answer:

c = 11.46 yd

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ c² = (8.1)² + (8.1)²

→ c² = 65.61 + 65.61

→ c² = 131.22

→ c = √131.22

→ [ c = 11.46 yd ]

Hence, value of c is 11.46 yd.

The relationship between variables p and q is given by p = kq. Also, the value of the variable p when q = 16 is 6 and when p = 2.4, the variable q is 6.4.

Mathematically, a proportional relationship can be represented with the following mathematical expression:

p = kq

Where:

Next, we would determine the constant of proportionality (k) as follows:

Constant of proportionality (k) = p/q

Constant of proportionality (k) = 4.5/12

Constant of proportionality (k) = 0.375.

When q = 16, the variable p is given by:

p = kq

p = 0.375 × 16

p = 6.

When p = 2.4, the variable q is given by:

q = p/k

q = 2.4/0.375

q = 6.4

Read more on proportionality here: brainly.com/question/12866878

#SPJ1

In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up. A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Given,

Ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards:

Through combination:

²⁴C₅

24!/51(24-5)!

Simplifying:

24!/5!(19!)

24 × 23× 22× 21× 20×19!/5! × 19!
24 × 23 × 22 × 21 × 20/ 5× 4 × 3 × 2 × 1

42504

In 42504 ways can 5 cards be drawn from a well-shuffled deck of 24 playing cards.

To learn more about combination, visit:

https://brainly.com/question/28720645

#SPJ4

Answer:

119.5

Step-by-step explanation:

Since supplementary is 180 degrees, 180-60.5=119.5

Answer:

Step-by-step explanation:

The number of fliers that he has not posted is 9

What is proportion?

Proportion can be defined as the mathematical comparison of two elements or numbers.

From the information given, we have that;

• Total number of fliers is 45

• First week, 1/3 of the floors were posted

• This week, 3/5 of the remaining were posted.

To determine the number of fliers remaining, we have that;

Remaining fliers for the First week

= 45 × 1/3

Multiply and find the quotient

= 15 fliers

Fliers remaining after the last week

= 15 × 3/5

Multiply and find the quotient

= 45/5

= 9 fliers

Thus, the number of fliers the he has not posted is 9

The number of green marbles removed from the bag is 3.

We will use the Formula of Probability:

In mathematics, the probability is defined as the ratio between the number of favorable outcomes and the total number of outcomes.

p(A) = n(A) / n(S)

p(A) is the probability of event A.

n(A) is the number of outcomes with respect to A.

n(S) is the total number of possible outcomes.

Given in the Question:

A bag contains 14 blue, 6 red, 12 green, and 8 purple marbles.

So the total number of marbles in the bag = 40

It is given that 25 marble are removed from the bag randomly

thus, the remaining marbles in the bag = 40 - 25 = 15

It is given that the probability of drawing a green marble from the bag after removing 25 marbles is 3/5.

So, for finding the number of green marbles in the bag after removing we can write,

n(A) = p(A) × n(S)

here, A is the event of drawing the number of green marbles and p(A) = 3/5 and  n(s) = 15 (after removing)

Thus, the number of green marbles in the bag after removing = 3/5 × 15

So, the number of green marbles left in the bag = 9

then, the green marbles removed from the bag = 12 - 9 = 3.

Therefore, only 3 green marbles are removed from the bag.

To Learn more about similar Probability Questions:

https://brainly.com/question/21898039

Answer:

1 carton

Step-by-step explanation:

3 (7/10)= 21/10

1/3 of 21/10= 7/10

7/10=1 carton

0.55 is the probability that a vacationer will visit at least one of these magnificent attractions.

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

50% of the vacationers going to toronto visit the CN tower= 0.5

40% visit skydome= 0.4

35% visit both=0.35

P( At lease one) = P(Toronto) + P(Skydome) - P(Both)

P( At lease one) = 0.4 + 0.5 - 0.35

P( At lease one)  = 0.55

learn more about probability here :

brainly.com/question/11234923

#SPJ4

Answer:

-64

Step-by-step explanation:

Start by moving everything to the left side making the equation equal 0. Then combine like terms.