choose the correct equation for the function of the graph below.

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

5,874,589,152,000 mi.

Step-by-step explanation:

Answer:

x ≤ 2

Step-by-step explanation:

Expand

3x - 6 + x ≤ 2

Rearrange

4x ≤ 8

x ≤ 2

Answer:

x ≤ 2

Step-by-step explanation:

Step 1: Write inequality

3(x - 2) + x ≤ 2

Step 2: Solve for x

Here we see that any number less than or equal to 2 will work.

The given problem states that a bucket contains 512 gallons of water. Water spills from the bucket so that only 5 pints remain. We need to find out how many pints of water spill from the bucket. The first step towards the solution of the problem is to convert 512 gallons to pints, which is given below;

1 gallon = 8 pints512 gallons = 8 × 512 pints = 4096 pints. Now, we know that 5 pints of water are remaining after the spill. Hence, the total water that has spilled from the bucket would be;4096 - 5 = 4091 pints. Therefore, 4091 pints of water would have spilled from the bucket.

To solve the given problem, we need to convert gallons to pints, which is given below;1 gallon = 8 pints512 gallons = 8 × 512 pints = 4096 pints. Now, we know that only 5 pints of water remain in the bucket. Hence, we need to find out the total amount of water that has spilled from the bucket. To find out the total amount of water spilled, we need to subtract the remaining water from the initial water, which is given below;4096 - 5 = 4091 pints. Therefore, 4091 pints of water would have spilled from the bucket. Hence, t 4091 pints of water.

It can be concluded that if a bucket contains 512 gallons of water, and water spills from the bucket so that only 5 pints remain, then 4091 pints of water would have spilled from the bucket.

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The correct answers from the given lists are given as follows: Relation (a) a is (strictly) older than bA. irreflexiveB. asymmetricC. antisymmetricD. reflexiveE. transitive Relation (b) a and b have a common grandparentA.

irreflexiveB. antisymmetricC. symmetricD. reflexiveE. transitiveRelation (c) a has the same first name as bA. transitiveB. irreflexiveC. antisymmetricD. symmetricE. reflexiveRelation (d) a and b were born on the same dayA. transitiveB. reflexiveC. irreflexiveD. antisymmetricE. symmetric.

The given lists include different types of relations. Let's discuss the given relations one by one.(a) a is (strictly) older than b:This relation is irreflexive because a person can't be older than oneself. This relation is asymmetric because if a is older than b then it can't be possible that b is older than a.

This relation is antisymmetric because if a is older than b and b is older than a, then it means that a and b are the same person which is not possible. This relation is not reflexive because there is no one who is older than oneself. This relation is transitive because if a is older than b and b is older than c then a is also older than c.(b) a and b have a common grandparent:This relation is irreflexive because a person can't have a common grandparent with oneself. This relation is antisymmetric because if a has a common grandparent with b then it can't be possible that b has a common grandparent with a. This relation is symmetric because if a has a common grandparent with b then b also has a common grandparent with a. This relation is not reflexive because there is no one who has a common grandparent with oneself. This relation is transitive because if a has a common grandparent with b and b has a common grandparent with c then a also has a common grandparent with c.(c) a has the same first name as b:

This relation is transitive because if a has the same first name as b and b has the same first name as c then a has the same first name as c. This relation is irreflexive because a person can't have the same name as oneself. This relation is antisymmetric because if a has the same name as b then it can't be possible that b has the same name as a. This relation is symmetric because if a has the same name as b then b also has the same name as a. This relation is not reflexive because there is no one who has the same name as oneself.

(d) a and b were born on the same day: This relation is transitive because if a was born on the same day as b and b was born on the same day as c then a was born on the same day as c. This relation is reflexive because every person is born on the same day as oneself. This relation is irreflexive because no person is born on a different day than oneself. This relation is antisymmetric because if a was born on the same day as b then it can't be possible that b was born on the same day as a. This relation is symmetric because if a was born on the same day as b then b was also born on the same day as a.

The correct answers for each given relation are listed above.

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Answer:

x < -55

Step-by-step explanation:

Step 1: Convert word to math

85 - 3x > 250

Step 2: Solve for x

Here we see that any value smaller than -55 will work.

Answer:

(-b-81)/6=a

Step-by-step explanation:

3b−2a-17 = 4a+4b+64

3b-4b-17-64=4a+2a

-b-81=6a

(-b-81)/6=a

Bob could declare the pool was full of water at 6.00.Bob could declare the pool was full of water at 6.00 after Billy-Joe initially filled it and animals drank from it for a certain period.

From 13.00 to 23.00, Billy-Joe filled the pool with water at a rate of 3 gallons per hour for 10 hours, resulting in 3 gallons/hour * 10 hours = 30 gallons of water in the pool.

From 23.00 to 4.00, the combined drinking rate of the horses and the cow was 1 gallon per hour. Therefore, during this period, the water level decreased by 1 gallon/hour * 5 hours = 5 gallons.

At 4.00, Bob placed a second hose in the pool, which filled it at a rate of 2 gallons per hour.

Now let's calculate the remaining capacity of the pool after 4.00:

The initial capacity of the pool was 60 gallons.

From 13.00 to 23.00, 30 gallons were filled.

From 23.00 to 4.00, 5 gallons were consumed.

So, the remaining capacity is 60 gallons - 30 gallons - 5 gallons = 25 gallons.

With the second hose filling the pool at a rate of 2 gallons per hour, it would take 25 gallons / 2 gallons/hour = 12.5 hours to fill the remaining capacity.

Adding the time it took to reach 4.00, the total time needed to fill the pool would be 12.5 hours + 5 hours = 17.5 hours.

Therefore, Bob could declare the pool was full of water at 4.00 + 17.5 hours = 21.5 hours after 13.00, which is equal to 6.00.

Bob could declare the pool was full of water at 6.00 after Billy-Joe initially filled it and animals drank from it for a certain period.

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Answer: $48.03

Step-by-step explanation: I think

Answer:

$48.00 + $7.20 = $55.20.

Step-by-step explanation:

First, convert the 15% to an actual number that can be used in a calculation. For percents,this is always done by simply dividing the percent (in this case 15%) by 100%.So, the conversational term "15%" becomes 15% / 100% = 0.15 in terms of a real mathematical number.

Second, you need to find out what 15% of your $48 meal cost is.This is always done by multiplying 0.15 by $48.00, or

0.15 x $48.00=$7.20.

So, the amount of tip you are going to leave is $7.20.

This makes the total cost of your meal (to write on your charge slip or other payment)

hope this helped UwU

The area of the regular octagon is $\boxed{\frac{225}{2}}$ square centimeters, or $\boxed{112.5}$ square centimeters, rounded to one decimal place.

An octagon is an eight-sided polygon. An octagon with all sides congruent is called a regular octagon. Since AP = 10 cm and BC = 15 cm are given, and the octagon is regular,

we can find the area of the octagon.To find the area of the regular octagon, we can divide the octagon into 8 congruent isosceles triangles, each of which has an angle measure of 135 degrees.

First, let's find the length of the side of the regular octagon. Let "s" be the length of one side of the octagon, and let "r" be the radius of the circumscribed circle.

Then, we have:$$s^2 + s^2 = r^2$$$$2s^2 = r^2$$$$r = s\sqrt{2}$$Since the diameter of the circumscribed circle is BC = 15 cm,

we have:$$2r = 15$$$$s\sqrt{2} = \frac{15}{2}$$$$s = \frac{15}{2\sqrt{2}}$$

Now, let's find the area of one isosceles triangle. We can use the formula:$$\frac{1}{2}ab\sin C$$where a = b = s, and C = 135 degrees.

Then, we have:$$\frac{1}{2}(s)(s)\sin 135 = \frac{1}{2}s^2\frac{1}{\sqrt{2}} = \frac{s^2}{2\sqrt{2}}$$

Finally, the area of the regular octagon is given by:$$8\cdot \frac{s^2}{2\sqrt{2}} = \frac{4s^2\sqrt{2}}{2\sqrt{2}} = \boxed{2s^2}$$

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the probability of getting all heads after 7 tosses of a coin is 1/128, expressed as a simplified fraction or a decimal rounded to four decimal places is 0.0078.

When a coin is tossed, the probability of getting either heads or tails is 1/2. This probability remains constant regardless of the number of tosses.

In order to determine the probability of getting all heads after 7 tosses of a coin, we must calculate the probability of getting a head on each toss and multiply the individual probabilities together:

Probability of getting a head on the first toss = 1/2

Probability of getting a head on the second toss = 1/2

Probability of getting a head on the third toss = 1/2

Probability of getting a head on the fourth toss = 1/2

Probability of getting a head on the fifth toss = 1/2

Probability of getting a head on the sixth toss = 1/2

Probability of getting a head on the seventh toss = 1/2

The probability of getting all heads = (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) x (1/2) = 1/128

Therefore, the probability of getting all heads after 7 tosses of a coin is 1/128, expressed as a simplified fraction or a decimal rounded to four decimal places is 0.0078.

Answer: 0.0078

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The probability, to the nearest hundredth, that equal numbers of males and females are selected to go to Vancouver is approximately 0.43.

To determine the probability that equal numbers of males and females are selected to go to Vancouver, we need to calculate the number of ways to select 6 males and 6 females from the total pool of 7 males and 8 females.

The number of ways to select 6 males out of 7 is given by the combination formula:

C(7, 6) = 7! / (6!(7-6)!) = 7

Similarly, the number of ways to select 6 females out of 8 is:

C(8, 6) = 8! / (6!(8-6)!) = 28

Since we need to select equal numbers of males and females, we multiply the number of ways to select males and females together:

Total number of favorable outcomes = C(7, 6) * C(8, 6) = 7 * 28 = 196

Now, we need to calculate the total number of ways to select any 12 players from the total pool of 15 (7 males + 8 females):

Total number of possible outcomes = C(15, 12) = 15! / (12!(15-12)!) = 455

Finally, we can calculate the probability of selecting equal numbers of males and females by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes) = 196 / 455 ≈ 0.431

Therefore, the probability, to the nearest hundredth, that equal numbers of males and females are selected to go to Vancouver is approximately 0.43.

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Answer:

12 miles

Step-by-step explanation:

24 divided by 0.5 = 12

12 miles

Answer:

12 miles

The step-by-step explanation he went .5 a minute so every minute he went.5 he rode for 25 minutes so we multiply the two

Answer: The side length is tripled.

Step-by-step explanation: Area is length times width, or in the case of a square, s²

If the area is multiplied by 9, (that is 3²) it means the sides are 3 times as long.

16.5² = 272.25

(3)(16.5) = 49.5

49.5² = 2450.25

the same as 272.25 × 9

Triple the side length results in 9 times the area.

Answer:

4

Step-by-step explanation:

4 packs of 100, with 50 remaining

Answer:

$400

Step-by-step explanation:

150 + 300 = 450

450 - 50 = 400

Answer:

150+300=450 then 450-50=400

Step-by-step explanation:

I hope this is the right answer  ^-^

Answer:

Step-by-step explanation:

First, put -4x+y=7 into y=mx+b format

move -4x to the other side (or add 4x on both sides)

y=4x+7

now, parallel lines have the same slopes, but not the same y intercepts.

So, you already know the slope of your new line

y=4x+b

now we need to find b (y intercept)

take the point (4,-3) and put it into the equation above

-3=4(4)+b

-3=16+b

move 16 to the other side (or subtract 16)

-19=b

therefore the new line will be y=4x-19

Hope this helps!

Answer:  $53.13

Step-by-step explanation:

First find how much they spent on tax by multiplying 42.50 by 7%.

7% * 42.50 = 2.98    This means the tax amount was $2.98.

Next find the how much the tip was by multiplying 18% by 42.50.

18% * 42.50 = 7.65   This also means the tip was $7.65.

Now combine the cost of the dinner plus the cost of tax plus the cost of tip to find how much in total they spent.

42.50 + 7.65 + 2.98 =  53.13

The measures of the angles of the right triangle are 10 degrees, 80 degrees, and 90 degrees.

Let x be the measure of the smaller acute angle of the right triangle. Then the other acute angle is 8x. Since the sum of the measures of the angles of any triangle is 180 degrees, the measure of the right angle in this triangle is 90 degrees. Therefore, x + 8x + 90 = 1809x = 90x = 10. The measure of the smaller acute angle is 10 degrees, and the measure of the larger acute angle is 8 times this, or 80 degrees. The measure of the right angle is 90 degrees.

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Answer:

the second one Step-by-step explanation:

9514 1404 393

Answer:

  z = 3

Step-by-step explanation:

Add z/6 to both sides.

  z/6 +z/6 +6 = 7

  z/3 + 6 = 7

Subtract 6 from both sides.

  z/3 = 1

Multiply both sides by 3.

  z = 3

No, the gardener does not have enough fencing for the area of the garden to be 1300 square feet. The maximum possible area that can be achieved with 140 feet of fencing is given by the function A(w) = 70w - w^2. We need to find the width value (w) that corresponds to an area of 1300 square feet.

To determine if the gardener has enough fencing, we can set up an equation using the given function: 1300 = 70w - w^2. Rearranging this equation, we get w^2 - 70w + 1300 = 0.

By solving this quadratic equation, we find that the roots are w = 25 and w = 45. Since the width value (w) must be positive, we can conclude that the width of the garden cannot be 45 feet. Therefore, the gardener does not have enough fencing to create a garden with an area of 1300 square feet.

In summary, based on the given quadratic equation, the gardener cannot achieve an area of 1300 square feet with the available 140 feet of fencing. The maximum achievable area corresponds to a width of 25 feet.

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The number of unit cubes in each category is as follows:(a) Cubes painted red on only one face: 24 (b) Cubes painted red on two faces: 20 (c) Cubes painted red on three faces: 8 (d) Cubes without red paint on their faces: 12.

To solve this problem, let's analyze the different types of cubes based on the number of faces painted red.

(a) Cubes painted red on only one face:

On the big cube, there are 6 faces exposed to the outside. Each face consists of a 2x2 grid of unit cubes. Thus, each face has 4 unit cubes painted red.

Since there are 6 faces, the total number of unit cubes painted red on only one face is 6 * 4 = 24.

(b) Cubes painted red on two faces:

On the big cube, the corner unit cubes have two faces exposed to the outside, and each edge unit cube has three faces exposed. There are 8 corner unit cubes and 12 edge unit cubes in total. Therefore, the number of unit cubes painted red on two faces is 8 + 12 = 20.

(c) Cubes painted red on three faces:

On the big cube, there are 8 corner unit cubes, and each of these cubes has three faces exposed to the outside. Therefore, the number of unit cubes painted red on three faces is 8.

(d) Cubes without red paint on their faces:

To determine the number of unit cubes without red paint on their faces, we subtract the sum of the previous three categories from the total number of unit cubes, which is 64.

Number of cubes without red paint = 64 - (24 + 20 + 8) = 12.

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Answer:

x=c-g or x=-g+c

Step-by-step explanation:

Shoreline Park in Mountain View, California, has diligently maintained records of the number of visitors to the park ever since its establishment.

Shoreline Park, located in Mountain View, California, has implemented a comprehensive system to monitor and track the number of patrons visiting the park since it first opened. This proactive approach allows park management to gather data on the park's popularity and usage patterns, enabling them to make informed decisions regarding park maintenance, amenities, and future development plans. By closely monitoring the number of visitors, Shoreline Park can ensure that it meets the needs of the community and maintains a pleasant environment for everyone to enjoy.

Maintaining records of the number of patrons using the park serves multiple purposes. Firstly, it helps in understanding the park's peak times and off-peak periods, enabling park officials to allocate resources effectively and plan events or activities accordingly. It also aids in assessing the park's capacity and evaluating any potential overcrowding issues that may arise during busy periods. Additionally, tracking visitor numbers can assist in evaluating the success of marketing and promotional efforts aimed at attracting more people to the park. Overall, by keeping close tabs on the number of patrons using Shoreline Park, the park management can ensure that it remains a popular and well-utilized recreational space for the community while addressing any concerns or challenges that may arise.

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Answer:

C. 40

Step-by-step explanation:

.45x +6 = .3x + 12

.15x =6

.15x/.15=1 6/.15=40