A landscaper digs a rectangular region for a garden. The length is a one-digit whole number of meters. What is the least possible area? What is the greatest possible area?

Answer:

Figure b

Step-by-step explanation:

the sides are equal

Yes there is sufficient evidence that  the alternative hypothesis is;

bag filling machine works incorrectly at the 402 gram setting which is;

H_o ; μ ≠ 402

Null hypothesis; H_o ; μ = 402

Alternative hypothesis; H_o ; μ ≠ 402

The null hypothesis states that there is no difference in the test which is denoted by H_o. However, the sign of null hypothesis is denoted by the signs of = or ≥ or ≤.

Meanwhile, the alternative hypothesis is one that defers from the null hypothesis. This therefore implies a significant difference in the test. Thus, the signs of alternative hypothesis is denoted by; < or > or ≠.

Now, the question we have is a two tailed test. Thus;

The null hypothesis is;

bag filling machine works correctly at the 402 gram setting which is;

H_o ; μ = 402

The alternative hypothesis is;

bag filling machine works incorrectly at the 402 gram setting which is;

H_o ; μ ≠ 402

learn more about of hypothesis here

https://brainly.com/question/15720073

#SPJ4

The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.

Rectangular coordinates of a point is written like (x, y, z)

Cylindrical coordinates of a point  is written like (r, θ, z)

Spherical coordinates of a point is written like (p, θ, φ)

First talk about Rectangular vs Cylindrical.

x = rcosθ

y = rsinθ.

z = z

x^2 + y^2  = r^2

given rectangular coordinates as (2,2,-1)

x=2, y=2, z=-1.

r^2 = 4+4 = 8.

r = [tex]\sqrt{8}[/tex]

r = 2[tex]\sqrt{2}[/tex]

θ = [tex]tan \inv-1[/tex](y/x) = [tex]tan \inv-1[/tex](2/2) = [tex]tan -1[/tex](1) = 45° = 0.78rad .

z = -1.

So Cylindrical coordinates is (r,θ,z) = ([tex]\sqrt{8}[/tex],0.78,-1).

Now let's us talk about Rectangular vs Spherical Coordinates.

x =  pcosθsinφ.

y= psinθsinφ.

z = pcosφ.

p^2 =  x^2+y^2+z^2.

tanθ = y/x

cosφ = z/p = z/[tex]\sqrt{x^2+y^2+z^2}[/tex].

given rectangular coordinates as (2,2,-1)

x=2, y=2, z=-1.

p = [tex]\sqrt{x^2+y^2+z^2}[/tex] = [tex]\sqrt{2^2+2^2+(-1)^2}[/tex] = [tex]\sqrt{9}[/tex] = 3

θ = [tex]tan -1[/tex](y/x) =  0.78rad .

φ = [tex]cos -1[/tex](z/p) = [tex]cos -1[/tex](-1/3) = 1.91rad

So Spherical coordinates is (3, 0.78rad, 1.91rad).

The cylindrical and spherical coordinates of the point are ([tex]\sqrt{8}[/tex],0.78,-1),(3, 0.78rad, 1.91rad) respectively.

Given Question is incomplete, Complete Question here

The Rectangular Coordinates Of A Point Are (2,2,-1) Find The Cylindrical And Spherical Coordinates Of the Point,

To know more about cylindrical and spherical coordinates here.

https://brainly.com/question/4465072

#SPJ4

Answer:

12x² + 10xy + 2y²

Step-by-step explanation:

(3x + y)(4x + 2y) =

= 12x² + 6xy + 4xy + 2y²

= 12x² + 10xy + 2y²

12 inches in length and 3 inches in width when a rectangle's length is 4 inches longer than its width.

Given that,

A rectangle's length is 4 inches longer than its width. The area of rectangle is equal to 4 inches less than 2 times the perimeter of rectangle.

We have to find what is the length and width of rectangle.

We know that,

Let take length as l and width as w.

l=4w

Area of rectangle is l×w

Perimeter of rectangle is 2(l+w)

So,

l×w=2(2(l+w))-4

l×w=4(l+w)-4

Take l as 4w

4w×w=4(4w+w)-4

4w²=4(5w)-4

4w²=20w-4

4w²-20w+4=0

w²-5w+1=0

w=3

So,

l=4w

l=12

Therefore, 12 inches in length and 3 inches in width when a rectangle's length is 4 inches longer than its width.

To learn more about length visit: https://brainly.com/question/9387981

#SPJ4

Answer:

A. (18, 1)

Step-by-step explanation:

aₙ = 6aₙ₋₁ - 5aₙ₋₂ then the values for n≤3, then a₀ = 28; a₁ = -76 ; a₂ = -596 ; a₃ = -3196. The Sequence is 28, -76, -596, -3196.

How can the sequence's solution be found?

Given:

a₁ = -76 ; a₀ = 28

aₙ = 6aₙ₋₁ - 5aₙ₋₂

Then the arithmetic sequence is followed by:

a₂= 6a₂₋₁ - 5a₂₋₂

= 6a₁ - 5a₀

= 6(-76) - 5 (28)

= -456 - 140

a₂ = -596

a₃ = 6a₃₋₁ - 5a₃₋₂

= 6a₂ - 5a₁

= 6(-596) - 5(-76)

= - 3576 + 380

a₃ = -3196

The values for n≤3, then a₀ = 28; a₁ = -76 ; a₂ = -596 ; a₃ = -3196. The Sequence is 28, -76, -596, -3196.

To know more about Sequence check the below link:

https://brainly.com/question/7882626

#SPJ4

The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.

It is given that Kaori is taking a free-throw. H(d) models the basketball's height (in meters) at a horizontal distance of d meters from Kaori.

The given statement is H(R) = 4H.

Here we have H(R) instead of H(d) and it shows the height of basketball. So it clear that the height of basketball's is 4H because H(R)=4H at d = R

Since d represents the horizontal distance from Kaori, therefore the horizontal distance from Kaori is R.

Thus, Answer: The statement H(R)=4H means the height of ball is 4H meter at a horizontal distance of R meters from Kaori.

learn more about of models here

https://brainly.com/question/11339748

#SPJ4

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{w}~,~\stackrel{y_2}{-3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-7)}}}{\underset{run} {\underset{x_2}{w}-\underset{x_1}{(-4)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{\cfrac{1}{2}} \\\\\\ \cfrac{-3+7}{w+4}=\cfrac{1}{2}\implies \cfrac{4}{w+4}=\cfrac{1}{2}\implies 8=w+4\implies 4=w[/tex]

The angular velocity of a person standing on the equator is ω = 1.026 × 10⁻⁴ rad/s

Angular velocity is the number of revolution per second of an object.

Since a planet rotates through one complete revolution every 17 hours and since the axis of rotation is perpendicular to the equator, you can think of a person standing on the equator as standing on the edge of a disc that is rotating through one complete revolution every 17 hours. We thus require its angular velocity.

The angular velocity is given by ω = 2π/T where T = period of revolution

Since the planet rotates through one complete revolution every 17 hours, its period, T = 17 hours = 17 h × 60 min/h × 60 s/min = 61200 s

So, substituting the period into the equation for the angular velocity, we have

ω = 2π/T

ω = 2π/61200 s

ω = π/30600 s

ω = 0.0001026 rad/s

ω = 1.026 × 10⁻⁴ rad/s

So, the angular velocity is ω = 1.026 × 10⁻⁴ rad/s

Learn more about angular velocity here:

https://brainly.com/question/28155635

#SPJ1

The correct option regarding the heights of the trees include:

The range of the tree heights at Yard Works is greater than the range of the tree heights at The Grow Station. This was illustrated as:

(12 - 5) > (12 - 7)

7 > 5

The mean of tree heights at Yard Works is 8 feet.

The mean of tree height at The Grow Station is 9 feet.

The mean absolute deviation of the tree heights at both yards is 2.

Learn more about mean on:

https://brainly.com/question/10002748

#SPJ1

It takes 51.33 min or 6/7 hrs to travel upstream 4 km.

What is relative velocity?

it is the speed measured with respect to an observer whether he is moving or stationary and it might differ for different observers.

speed of boat = 7 km/hr

speed of river = r km/hr

speed upstream = 7-r km/hr

speed downstream = 7+r km/hr

time taken to go upstream 4 km = 4/(7-r)

time taken to go downstream 8 km = 8/(7+r)

as time taken is equal in both scenario:

4/(7-r) = 8/(7+r)

on solving we get:

r = 7/3 km/hr

put this value in time taken for upstream

4/(7-(7/3)) = 6/7 km/hr or 51.33 min

to learn more about relative speed:

https://brainly.com/question/29523095

#SPJ4

Using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.

Think about two trains that are traveling in the same direction and at the same pace.

Even though the tracks, buildings, and trees on either side of the track indicate that both trains are moving, to the observer of one train, the other train appears to be stationary.

The other train seems to be moving at a constant speed.

So, we know that:

Speed of boat = 7 km/hr

Speed of river = r km/hr

Now,

Speed upstream = 7-r km/hr

Speed downstream = 7+r km/hr

Time taken to go upstream 4 km = 4/(7-r)

Time taken to go downstream 8 km = 8/(7+r)

As the time taken is equal in both scenarios:

4/(7-r) = 8/(7+r)

On solving we get:

r = 7/3 km/hr

Put this value in time taken for upstream as follows:

4/(7-(7/3)) = 6/7 km/hr or 51.33 min

Therefore, using the relative velocity formula, we know that it takes 51.33 min or 6/7 hrs to travel upstream 4 km.

Learn more about relative speed here:

https://brainly.com/question/29523095

#SPJ4

The missing value if the point is a direct variation is -15

From the question, we have the following ordered pairs

(2, -6) and (5, y)

These ordered pairs are direct variation

A direct variation is represented as

k = y/x

This means that

y/5 = -6/2

Evaluate the quotient

y/5 = -3

Multiply both sides by 5

y = -15

Hence, the value of y is -15

Read more about direct variation at

https://brainly.com/question/6499629

#SPJ1

The population based on the information will be B. all internet users.

In statistics, a population is a group of similar items or events that are relevant to a particular question or experiment. A statistical population can be a group of existing objects or a hypothetical and potentially infinite group of objects conceived as an experience-based generalization.

A population is any complete group that shares at least one characteristic. Populations are more than just individuals. People, animals, businesses, buildings, motor vehicles, farms, objects, or events are examples of populations.

In this case, In an AOL survey of Internet there wwe'r 170,063 responses, and 63% answered "yes. The population is the internet users.

Learn more about population on:

https://brainly.com/question/24777420

#SPJ1

Answer:

Step-by-step explanation:

y = 2x - 1  

when you sub in 0 in x and -1 in y, the y-intercept is -1.

Step-by-step explanation:

 x    

 — -  6  = 0

 7    

Subtracting a whole from a fraction

Rewrite the whole as a fraction using  7  as the denominator :

        6          6 • 7

   6 =  —  =  —————

        1               7  

x - (6 • 7)                                x - 42

———————————  =  ——————

     7                                         7  

x - 42

 ——————  = 0

   7  

x-42

 ———— • 7 = 0 • 7

  7  

x-42  = 0

x = 42 Answer

To know more about solving;

https://brainly.com/question/11514947

The expression (8^(5))/(8^(-9)) is simplified to 8^14. Option 3

Index form of a number can simply be described as that number written in the form of an exponential expression.

The number can also be written as a single number which is raised to another number.

Some rules of indices to note;

Given that;

(8^(5))/(8^(-9))

Then, we have;

8^5-(-9)

8^5+9

Add the powers

8^14

Hence, the value is 8^14

Learn more about index forms here:

https://brainly.com/question/15361818

#SPJ1

Answer:

Domain: all real numbers

Step-by-step explanation:

The function is:

[tex] f(x) = \dfrac{2}{9}x^2 + 18x - 216 [/tex]

The domain of a function is the set of values of the x-coordinates of the points of the function.

In this function, there is no restriction on x, so the domain is all real numbers.

Answer:

n > 3

Step-by-step explanation:

2n - 5 > 1

Add 5 on both sides

2n > 6

Divide by two on both sides to isolate n

n > 3

The expected value of the random variable b is given as follows:

2.404 books.

The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.

From the histogram given by the image at the end of the answer, the distribution is given as follows:

Then the expected value of the random variable b is obtained as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.

The histogram is given by the image at the end of the answer.

More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440

#SPJ1

The slope of the line given the information in the table is 1.

The slope is found in linear functions. The slope measures the rate of change of the dependent variable with respect to the independent variable. In this question, the independent variable is x and the dependent variable is y.

Slope = change in the value of y / change in the value of x

Slope = (0 - - 1) / (1 - 0) = 1

Slope =  (1 - 0) / (2 - 1) = 1

Slope = (2 -1 ) / (3 - 2) = 1

Based on the value of the slope, it means that for every one percent change in the value of x, the value of y changes by 1%.

To learn more about slope, please check: https://brainly.com/question/3605446

#SPJ1

Answer:

Step-by-step explanation:

look at the x and axis and the irrational fractions and you should find your slope

Answer:

1/2

Step-by-step explanation:

-1(15+4-27)/16

Add 15 and 4 to get 19.

Now you have -1(19-27)/16

Subtract 27 from 19 to get −8.

-1(-8)/16

Reduce the fraction 16/−8 to lowest terms by extracting and canceling out 8.

-(-1/2)

Simplify

1/2

Answer:

1/2

Step-by-step explanation:

⁻¹⁽¹⁵⁺⁴⁻²⁷⁾⁄₁₆

Calculate:

-(15 + 4 - 27) / 16

-(19-27)/16

-(-8) / 16

= 8/16

Simplify:

= 1/2

By using the concept of compact set, it can be proved that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

What is compact set?

A set K is said to be compact if every open cover of K has a finite subcover.

Let K⊆Rn is compact  f:K→R is continuous, and ϵ>0

Let there exist [tex]x_n, y_n[/tex] ∈ K such that |f([tex]x_n[/tex])−f([tex]y_n[/tex])| > n∥[tex]x_n[/tex]−[tex]y_n[/tex]∥+ϵ,

Since K is compact there is a subsequence [tex]x_{nk}[/tex] and [tex]y_{nk}[/tex] of [tex]x_n, y_n[/tex] respectively such that [tex]x_{nk}[/tex] converges to x and [tex]y_{nk}[/tex] converges to y.

So,  |f([tex]x_{nk}[/tex])−f([tex]y_{nk}[/tex])| > [tex]n_k[/tex]∥[tex]x_{nk}[/tex]−[tex]y_{nk}[/tex]∥+ϵ,

Since f is continuous,

We can write

|f(x)−f(y)| > [tex]n_k[/tex]∥x - y∥+ϵ,

This is true for infinite many [tex]n_k[/tex]

So ||x - y|| = 0

|f(x) - f(y)| > ϵ, a contradiction since f is continuous

So,  there is a number A>0 such that

|f(x)−f(y)|≤A∥x−y∥+ϵ,∀x,y∈K.

To learn more about compact set, refer to the link-

https://brainly.com/question/17175854

#SPJ4

Based on this graph which shows the revenue, cost, and profit functions of a company, the way in which this company can become profitable is: C. by reducing its costs.

In Mathematics, a profit can be defined as a measure of the amount of money that is generated when the cost price is deducted from the selling price (revenue) of a good or service, which is usually provided by producers.

Mathematically, the profit made by an entrepreneur or business organization can be calculated by using this mathematical expression:

Profit = Revenue - Cost

In this scenario, the most effective and efficient way in which this company can become profitable is simply by reducing (lowering) its costs because it is incurring more cost than the amount of revenue it generates.

Read more on profit here: https://brainly.com/question/13849511

#SPJ1

Answer:

No Solution

Step-by-step explanation:

-1 is not equal to -5/3

Answer: the answer is 72

Step-by-step explanation:

if 50% of a number is 120 then that means its only half of that number so to find out the whole number multiply 120 by 2 which gives you the answer of 240

Now we need to determine 30% of 240 and the procedure explaining it as such

Step 1: In the given case Output Value is 240.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 240 = 100%.

Step 4: In the Same way, x = 30%.

Step 5: On dividing the pair of simple equations we got the equation as under

240 = 100% (1).

x = 30% (2).

(240%)/(x%) = 100/30

Step 6: Reciprocal of both the sides results in the following equation

x%/240% = 30/100

Step 7: Simplifying the above obtained equation further will tell what is 30% of 240

x = 72%

Therefore, 30% of 240 is 72

I hope this helps

Answer:

  72

Step-by-step explanation:

You want 30% of a number, given that 50% of it is 120, and 80% of it is 192.

The 30% you want will be the difference between 80% and 50%:

  80% -50% = 30%

  192 -120 = 72

30% of the same number is 72.

Answer:

if you have about an 85 now than you shouldn’t go below a b

Step-by-step explanation:

The mean of a data-set is given by the sum of the values of all observations in the data-set divided by the number of elements in the data-set.

In this problem, the data-set is given as follows:

910, 930, 965, 980, 1000, 1040, 1115, 1165, 1210.

Hence the mean is of:

M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1210)/9 = 1035.

After the change, the data-set is of:

910, 930, 965, 980, 1000, 1040, 1115, 1165, 1480.

Hence the mean will be of:

M = (910 + 930 + 965 + 980 + 1000 + 1040 + 1115 + 1165 + 1480)/9 = 1065.

Then the increase will be of:

1065 - 1035 = 30.

The median of a data-set is the middle element of the data-set, the value which:

The median is not affected by the values at the bounds of the distribution, such as 1210 and 1480 are in this distribution, hence it remains constant.

More can be learned about the mean and the median of a distribution at https://brainly.com/question/17631693

#SPJ1

Total number of people required is 3 to complete it in 57.33 days.

Basically in this proportion, two quantities generally follow the opposite trend of each other like if one is increasing other one is decreasing.

As an example, if the time  takes to run 10 m is inversely proportional to the speed you can run at - if you double your given speed, it takes you half as much long.

Initially,

Total People = 2

Total time taken = 86 minutes

Total time we have= 70 minutes

As people and time are inversely proportional to each other.

[tex]\frac{2}{3}[/tex] = [tex]\frac{x}{86}[/tex]

x = (86 × 2) / 3

x= 57.33

Hence, total number of people required is 3 to complete it in 57.33 days.

To know more about speed, time & distance, visit:

https://brainly.com/question/26862717

#SPJ4