A gardener has a circular garden, which he divides into four quadrants. He has four different kinds of flowers, and he wants to assign a flower to each quadrant, so that adjacent quadrants are not planted with the same kind of flower. (Also, the gardener can use the same flower more than once.) How many different gardens are possible?

Answers

Answer 1

Answer:

84

Explanation:

Call the quadrants I, II, III, and IV, counterclockwise, and the kinds of flowers A, B, C, and D.

Start by assigning a flower of kind A to quadrant I.

Then, quadrant II can have flower B, C, or D.

If it is B, then quadrant III can have either A, C, or D. If it is

If quadrant III has A, then quadrant IV can have either B, C, or D. That is 3 different gardens.

If quadrant III has C, then quadrant IV can have either B or D. That is 2 different gardens.

If quadrant III has D, then quadrant IV can either either B or C. That is 2 different gardens.

Those are all the possible different gardens if A is assigned to quadrant I and B is assigned to quadrant II: 3 + 2 + 2 = 7.

Working yet with A in quadrant I but assigning C to quadrant II, you can make the same reasoning as above to get other 7 gardens.

The same with A in quadrant I but D in quadrant II, other 7 different gardents.

In total, you find 7 × 3 = 21 different gardens when flowers of kind A are assingned to quadrant I.

Starting with a flower of kind B in quadrant I, there will be other 21 different gardens. The same for C and D. Then, in total, there are 4 × 21 = 84 different possible gardens.

Answer 2

Answer:

84

Step-by-step explanation:

Quadrants A and C either have the same kind of flower, or they have different flowers.

If quadrants A and C have the same kind of flower, there are 4 ways to choose this flower. There are then 3 ways to choose the flower for quadrant B, and 3 ways to choose the flower for quadrant D, so there are 4 x 3 x 3 = 36 possible ways in this case.

If quadrants A and C have different kinds of flowers, then there are 4 ways to choose the flower for quadrant A, then 3 ways to choose the flower for quadrant C. Then there are 2 ways to choose the flower for quadrant B, and 2 ways to choose the flower for quadrant D, so there are 4 x 3 x 2 x 2 = 48 possible ways in this case.

Therefore, there are a total of 36 + 48 = 84 ways to plant the flowers.


Related Questions

TV
A frog is sitting on the ground when he is scared by a big dog. His movement is modeled by
the equation h = -6t2 + 6t where h is the frog's height at any given time, t. How many
seconds until the frog is back on the ground?
2 seconds
1.5 seconds
3 seconds
1 second
0.5 seconds

Answers

Answer:

Step-by-step explanation:

Model of the frog jump is

h = -6t² + 6t

When will the frog be on the ground? The frog will be on the ground at h=0

Therefore,

0 = -6t² + 6t

Divide through by 6

0 = -t² + t

0 = t(-t + 1)

So, t = 0 OR. 0 = -t + 1

So, t = 0. OR. t = 1

So, we should note that, at t = 0, was when he wanted to lift of from the ground... So, t = 0 will be discarded

So, at t = 1 is when the frog is back to the ground.

It is like it starts from the ground at the 0 seconds and get backs to the ground at 1 seconds

I hope this helps!!!

Two of the sides of a right triangle are 8 and 6 units long. How long is the third side? Find all possible answers.

Answers

Answer:

10 units.

2√7 units.

- (or 5.29 units to the nearest hundredth)

Step-by-step explanation:

If the 2 sides are legs of the triangle ( that is they are at 90 degrees to each other) the third side, by Pythagoras  theorem:

=  √(6^2 + 8^2)

=  √100

= 10 units.

The other possibility is that 8 is the length of the hypotenuse, in which case

The third side

=  √(8^2 - 6^2)

=  √28

= 2√7 units.

a. The windows and door will not be painted. Calculate the area of the wall that will be painted

b. If a quart of Extra- thick exterior paint covers 30 Square feet, how many quarts must be purchased for the painting job? (SHOW WORK THANK YOU) (PICTURE IS ABOVE)

Answers

Given:

A rectangular wall with 2 windows and a 1 door.

To find:

The area of the wall and the amount of paint required to cover the wall.

Solution:

The area of the wall can be determined by subtracting the areas covered by the windows and the door from the area of the entire wall.

The entire wall has a length of 12 feet and a width of 8 feet.

The area of a rectangle [tex]=(l)(w).[/tex]

The area of a square [tex]= a^{2} .[/tex]

The entire wall's area [tex]= (12)(8)= 96[/tex] square feet.

The door has a length of 3 feet and a width of 6 feet.

The area of the door [tex]=(3)(6)=18[/tex] square feet.

The windows are in the shape of a square.

The side length of the windows is 2 feet.

The area of a window [tex]= 2^{2} =4[/tex] square feet.

The area of 2 windows [tex]= 2(4) = 8[/tex] square feet.

The area of the wall [tex]=96-18-8=70[/tex] square feet.

If a quart of extra-thick exterior paint covers 30 square feet, then 70 square feet will need;

The paint needed to cover 70 square feet [tex]= \frac{70}{30} = 2.333[/tex] quarts.

So the area of the wall was 70 square feet and 2.333 quarts of extra-thick exterior paint is required to cover the wall.

What is the area of a circle with a radius of 21 cm?

Answers

The area is 1,385,442


Hope that helps

Answer:

441[tex]\pi[/tex]

Step-by-step explanation:

What type of number is 0.25 over -0.25 whole number, intiger rational, irrational

Answers

[tex]\frac{0.25}{-0.25}[/tex] simplified will give us -1.

It's not a whole number, because it's negative. It isn't irrational because there is a determined answer. While it is rational, it more fits into integer - which is a less broad scope than rational.

Which expression shows a sum of four terms?

a. 4 + x + 4 + x
b. x4
c. 4(x + 4)
d. 4x

Answers

Answer:

a

Step-by-step explanation:

Answer:

I think c MAYBE dont quote me on it tho

Jaden collected 9 of the 12 hidden treasures in his video game. Write as a decimal.

Answers

Answer:

0.75

Step-by-step explanation:

9/12 equals 3/4 which is 0.75

Answer:

0.75

Step-by-step explanation:

First, you would need to convert it to a fraction for it says "of the", which is one of the key words to a fraction.

In fraction form it would look like this:

9/12

Now, if you remember, fractions are actually division; meaning this problem is also 9 divided by 12. So let's do that!

9 divided by 12 = 0.75.

You can also simplify the fraction; 9/12 is the same as 3/4, and you should know that 3/4 is the same as 0.75

Simplify: 3(5x+3x)+(x−8)

Thanks.

Answers

Answer:

=25x-8

hope this helps

-12 = 4 is equivalent to?

Answers

Answer:

no

Step-by-step explanation:

if you multiply 4 by -3 you get -12 tho

Calculate the volume of the rectangular prism.

Answers

Answer:

189 cm³

Step-by-step explanation:

V = lwh

V = 9*7*3

V = 189 cm³

Hope this helped! :)

Answer:

V =189 cm^3

Step-by-step explanation:

V = l*w*h

V = 3 cm* 9 cm * 7 cm

V =189 cm^3

What is the midpoint value of a data set, where the values are arranged in ascending or descending order?

A) Mode
B) Outlier
C) Median
D) Mean
E) Center of data

Answers

Answer:

Median

Step-by-step explanation:

Remember ...

Mean = Average

Median = Middle

Mode = Most (the number that appears most)

Final answer:

The midpoint value of a data set arranged in order is the median, which is the central value dividing the dataset into two halves.

Explanation:

The midpoint value of a data set, where the values are arranged in ascending or descending order, is known as the median. The median is the value that divides the dataset in half so that there are an equal number of values above and below it. In a dataset with an odd number of data points, the median is the middle value. For an even number of data points, the median is the average of the two central values. The mode is the most frequently occurring value in a set, while an outlier is an observation that is significantly different from the rest of the data. The mean represents the average of all values in the data set.

Choosing the appropriate measure of the center of data — whether mean, median, or mode — depends on the specific characteristics of the dataset, such as the presence of outliers and the distribution shape. The median is especially useful when the dataset contains outliers that may skew the mean.

115.9 rounded to the nearest hundred

Answers

Answer:

100

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

115.9 is closer to 100 then it is to 200, so round down to 100

What percent of 125 is 25?

Answers

Answer:

20%

Step-by-step explanation:

Step-by-step explanation:

When you check in percentage calculator the answer is 6.25

If two concentric circles have radii of 4 cm and 5 cm, how much longer, in cm, is the intercepted arc in the larger circle than an intercepted arc in the smaller circle for a central angle that is π2 radians?

Answers

Answer:

[tex]\dfrac{\pi}{2} cm[/tex]

Step-by-step explanation:

Given two concentric circles where:

Radius of the Larger Circle =5Radius of the smaller circle=4

Length of the intercepted arc for a central angle of [tex]\dfrac{\pi}{2} =\dfrac{\frac{\pi}{2} }{2\pi} X2\pi r=\dfrac{\pi r}{2}[/tex]

For the larger circle of radius 5cm, Length of the intercepted arc[tex]=\dfrac{5\pi}{2}[/tex]

For the smaller circle of radius 4cm, Length of the intercepted arc[tex]=\dfrac{4\pi}{2}[/tex]

Difference in Arc length

[tex]=\dfrac{5\pi}{2}-\dfrac{4\pi}{2}\\=\dfrac{\pi}{2} cm[/tex]

The difference in arc lengths between the two concentric circles for a central angle of π/2 radians is approximately 1.57 cm.

To compare the lengths of arcs intercepted by the same central angle in two concentric circles, we use the formula for arc length, which in a circle is a portion of its circumference that corresponds to the central angle. For a central angle π/2 radians, the arc length is given by (rθ), where r is the radius of the circle and θ is the central angle in radians.

For the smaller circle, the arc length is 4 cm × π/2 = 2π cm, and for the larger circle, it is 5 cm × π/2 = 2.5π cm. The difference in arc lengths is 2.5π cm - 2π cm = 0.5π cm. Using the approximate value of π as 3.14159, the difference in arc lengths is approximately 1.57 cm.

6) The length of a rectangle is 2 inches more than twice its width. Write an
equation relating the length of the rectangle to its width w. *

Answers

Answer:

2w + 2

Step-by-step explanation:

Width = w

Twice its width  = 2*w =2w

2 inches more than twice its width = 2w + 2

Length = 2w + 2


Round to the underlined place.

Answers

Answer:

158

Step-by-step explanation:

Evaluate the variable expression for x = 5, and enter your answer in the box
below.
6.(x- 9) - 5

Answers

The value of the variable expression 6.(x- 9) - 5 when x = 5 is -29.

To evaluate the variable expression for x = 5, we simply substitute 5 for x in the expression.

6.(x- 9) - 5 = 6.(5- 9) - 5

= 6.(-4) - 5

= -24 - 5

= -29

Therefore, the value of the variable expression 6.(x- 9) - 5 when x = 5 is -29.

For such more question on expression

https://brainly.com/question/1859113

#SPJ2

Find 1% of 100.
Find 5% of 100.
Find 12% of 100.

Answers

1% of 100 is 1.  

5% of 100 is 5.

12% of 100 is 12.

If you're going to ask an easy question, then please give me a thanks at least

1% = 1 5%=5 12%=12 it’s honestly easy

Imagine that you are eating at a restaurant with your friends. You and your best friend, Arabella, are seated at opposite ends of a large table, and
Arabella orders first. The probability that both you and Arabella end up ordering vegetable soup is in simpler terms, if the probability that you
order vegetable soup is P(A), and the probability that Arabella orders vegetable soup is PB), then is the probability of A and 8, or P(A and B).
The probability that you order vegetable soup given that you know that Arabella has ordered its P(
A B) = What is the probability that
Arabella orders vegetable soup?

Answers

Answer:

3/4

Step-by-step explanation:

Answer:

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

1/3 = (1/3)/P(B)

P(B)=3/4

Step-by-step explanation:

EDMENTUM

help me pls when was the game adopt me made

Answers

On April 11, 2020, Adopt Me! reached 1,615,085 concurrent Roblox players, making it the first and only game as of now to cross the 1 million concurrent players mark.

Answer:

On April 11, 2020

Step-by-step explanation:

I think sorry if i'm wrong

Joel biked 9 miles east and then 12 miles north. If he

biked back to his starting point using the most direct

route, how many miles would he ride all together?

Answers

Answer:

36 miles

Step-by-step explanation:

His entire journey, represented with a diagram, is in the shape of a right angle triangle.

We need to first find the hypotenuse of the triangle, then, add all the sides together:

hyp² = opp² + adj²

hyp² = 9² + 12²

hyp² = 81 + 144 = 225

Find the square root of both sides:

hyp = 15 miles

Therefore, adding the three sides together:

Total distance traveled = 9 + 12 + 15

Total distance traveled = 36 miles

He would ride 36 miles altogether.

Answer:

36

Step-by-step explanation:

A square box is 9 cm tall if you fill it 1/3 with water how much water did you use?

Answers

Answer:

3 cm

Step-by-step explanation:

Because 9 divided in 3 is 3 and if you used 1/3 it’s 3cm

help plzzzzz its hard

Answers

Answer:

Hehe Hopefully I'm the first one to help you

Step-by-step explanation:

Answer: I don't know....I'm here for emotional help cuz I'm also struggling in geo rn TwT. I relate to you so yea... Ily and I need more points to ask more questions about geo haha. Supporting you tho

Answer:

The surface area is 259.94 and the volume is 149.81

Step-by-step explanation:

What is not always true about 2 regular pentagons

Answers

Answer:

b

Step-by-step explanation:

The two regular pentagons could be differnt sizes, so they are not all congruent hope this helps :)

The answer is b!! I hope I helped

Please help!!! I NEED HELP!
A triangular pyramid has a triangular base with a height of 4 inches and a base length of 7 inches. The height of the pyramid is 6 inches. What is the volume of the pyramid in cubic inches?
(Recall the formula V = one-third B h.)
A. 14
B. 56
C. 28
D. 42

Answers

Answer:

the answer is 28

Step-by-step explanation:

i guessed ngl

Answer:

Bb 2ent option 28

Step-by-step explanation:

Megan has A quarters and B dimes with a total value of $1.95, where A and B are both counting numbers. How many different values of A can Megan have?

Answers

Answer: The number of quarters can be 1, 3, 5 or 7

Step-by-step explanation:

Megan has A quarters and B dimes.

The value of a quarter is $0.25 and the value of a dime is $0.10

Then we have that:

A*$0.25 + B*$0.10 = $1.95

We want to know the different possible values of A.

Now, it is usefull to see the different multilpes of 0.25 (this is the odd multyples of 0.25) we only care for the ones that have a 5 in the undredth place, becauses we only can ad multiple of $0.10, so the 5 in the undredth place needs to come from this

Then the possible values of A are the odd numbers such that A*0.25 is smaller than 1.95, let's do the math:

0.25*1 = 0.25 (here 1.95 - 0.25 = 1.70, then B = 1.70/0.10 = 17) the pair is B = 17 and A = 1

0.25*3 = 0.75 (here 1.95 - 75 = 1.20, then B = 1.20/0.10 = 12) the pair is B = 12 and A = 3.

0.25*5 = 1.25 (here 1.95 - 1.25 = 0.70, then B = 0.70/0.10 = 7) the pair is B = 7 and A = 5

0.25*7 = 1.75 (here 1.95 - 1.75 = 0.20, then b = 0.20/0.10 = 2) The pair is B = 2 and A = 7

Simplify the expression.

18a + 12x − 12a + 15x

A) 6a + 27x
B) 6a − 3x
C) 30a − 18x
D) −30 −3x

Answers

Answer:

6a+27x

it's simple math there is no work needed

Answer: A. 6a +27x

combine like terms

18a - 12a

12x + 15x

American Football: A quarterback throws a pass from the 12-yard line, 11 yards from the sideline. A wide receiver catches the pass on the 34-yard line, 40 yards from the same sideline. How long is the pass?

Answers

Answer:

36.4 yards

Step-by-step explanation:

The coordinates of origin is (12, 11) while coordinates of final landing is (34, 40)

Considering two points, x1, y1 and x2, y2, the distance between them is given by

[tex]d=\sqrt {(x2-x1)^{2}+(y2-y1)^{2}}[/tex]

Similarly, the distance between these two given points will be

[tex]d=\sqrt {(34-12)^{2}+(40-11)^{2}}\\d=36.4005494464026\approx 36.4 yd[/tex]

Therefore, the distance is 36.4 yards

A line parallel to $3x-7y = 65$ passes through the point $(7,4)$ and $(0,K)$. What is the value of K?

Answers

Answer:

1

Step-by-step explanation:

Hi, its you again lol.

I am in elementary btw.

I don't want to put the equation down.

Answer:

1

Step-by-step explanation:

AoPs Algebra ~ Graphing Multiple Lines Question

Show that 9^n can't end with 2 for any integer n.
Please tell me fast!

Answers

Answer:

i have no idea ask one of your dorm roomates.

Step-by-step explanation:

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