The function p(x) is defined by p(x) = x3 - 4x2 - 9x - 36 where x E R.

Find the remainder when p(x) is divided by (x - 2).

It is given that the distance on the map is 8 inches.

It is also given that the map uses a scale of 2 inches=1 mile.

Hence the actual distance is given by:

The distance in real life is 4 miles.

Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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The value of "x" is the unknown number that, when multiplied by 12, gives a result of 72. By solving the equation, we find that the unknown number is 6.

Let's call the unknown number "x". The statement "When 12 is multiplied by a number, the result is 72" can be represented mathematically as:

12 * x = 72

This equation states that when we multiply 12 by the unknown number "x", we obtain a product of 72. To find the value of "x", we need to solve this equation.

To solve for "x", we can divide both sides of the equation by 12:

(12 * x) / 12 = 72 / 12

Simplifying, we have:

x = 6

Therefore, the equation that fits the given statement is:

12 * x = 72

Where "x" is equal to 6.

In this equation, the value of "x" is the unknown number that, when multiplied by 12, gives a result of 72. By solving the equation, we find that the unknown number is 6.

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Answer:

(x-1)^2=0#

Explanation:

#x^2-2x+1=0#

Let's start by subtracting #1# from both sides so that the #x# terms are isolated:

#x^2-2x=-1#

Now, let's compute #(b/2)^2# and add it to both sides of the equation:

#(b/2)^2=(-2/2)^2=1#

#x^2-2x+1=-1+1#

Let's factorize the left hand side and simplify:

#(x-1)(x-1)=0#

#(x-1)^2=0#

The total cost of fencing to David, based on the dimensions of the fence would be $ 996.

Since the area of a rectangle is length times width, the other side must be:

240 sq ft / 12 ft

= 20 ft

For the side along the street (12 feet), using the more expensive fencing ($18 per linear foot):

Cost = 12 ft x $18/ft

= $216

For the other three sides (two sides of 20 feet and one of 12 feet), using the less expensive fencing ($15 per linear foot):

Cost = (20 ft + 20 ft + 12 ft) x $15/ft

= 52 ft x $15/ft

= $780

So, the total cost for the fencing will be:

Total cost = Cost of expensive fencing + Cost of less expensive fencing

Total cost = $216 + $780

= $996

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Full question is:

David wants to install a fence fence around his garden. The garden is rectangular and has an area of 240 square feet. One side of the garden is along the street and is 12 feet long. For this side of the garden, David will use fencing that costs 18$ per linear foot. For the other three sides of the garden, David will use fencing that costs 15$ per linear foot.

There are many questions and problems for which efficient algorithms exist, but there are also many others for which no efficient algorithm is currently known, and some for which it has been proven that no algorithm can exist.

The field of computer science and mathematics known as computational complexity theory studies which problems can be solved by algorithms and how efficient those algorithms are. The theory classifies problems into different complexity classes based on the resources required to solve them, such as time, space, or the number of processors.

There are certain classes of problems for which efficient algorithms are known to exist. For example, sorting a list of numbers or searching for an item in a database can be done in polynomial time, which means that the time required to solve the problem grows at most as a polynomial function of the size of the input.

On the other hand, there are problems for which no efficient algorithm is currently known. One famous example is the traveling salesman problem, which asks for the shortest possible route that visits a set of cities and returns to the starting point. While algorithms exist to solve this problem, they have an exponential running time, meaning that the time required to solve the problem grows exponentially with the size of the input, making them infeasible for large inputs.

There are also problems for which it has been proven that no algorithm can exist that solves them efficiently. For example, the halting problem asks whether a given program will eventually stop or run forever. It has been proven that there is no algorithm that can solve this problem for all possible programs.

In summary, there are many questions and problems for which efficient algorithms exist, but there are also many others for which no efficient algorithm is currently known, and some for which it has been proven that no algorithm can exist.

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Answer:

<1=73

Step-by-step explanation:

All triangles add up to 180 degrees!

Add 20 and 87

20+87=107

Subtract 107 from 180

180-107=73

Hope this helps! :)

The correct answer is D. \(72 \pi\) \(units^{2}\)

Explanation:

The surface area refers to the sum of the area of all sides in a 3D shape such as a cube or cylinder. Additionally, the formula used to calculate the surface area varies with the shape. In the case of cylinders, the general formula is \(A = 2\pi r h + 2\pi r^{2}\). Moreover in this, the r represents the radius (measure from the center of a circle to any side), while the h represents height. Below, all the process is shown:

\(A = 2\pi r h + 2\pi r^{2}\)

\(A = 2\pi (8 x 3) + 2\pi 8^{2}\)

\(A = 2\pi 24 + 2\pi 64\)

\(A = 48\pi + 128\pi\)

\(A = 176\pi\)

In this point, you have the answer without solving \(\pi\) (3.1416). This makes option A the correct answer.

1/3 (n-1)=1/6 (3n-5)

= 7

Answer:

n equals 7

Step-by-step explanation:

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

The area of the regular octogon is 196.15 square inches.

For a regular octogon with apothem A and side length L, the area is given by:

area =(2*A*L) * (1 + √2)

Here we know that:

A = 7in

L = 5.8 in

Replacing these values in the area for the formula, we will get the area:

area = (2*7in*5.8in) * (1 + √2)

area = 196.15 in²

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Answer:

guy above me is wrigth. If you have any doubts see the picture.

Step-by-step explanation:

Hope it helps and mark as brailiest pleasee

Answer:

46

Step-by-step explanation:

Approximately 109 grams of protein would be consumed on a 2500 kcal daily diet, with 35% of the calories coming from proteins.

Protein intake is an important aspect of a healthy diet, as it plays a vital role in various bodily functions. To calculate the grams of protein consumed, we start by determining the total calorie intake and then find the proportion of calories that come from proteins. In this case, the daily diet consists of 2500 kcal. To find the protein calories, we multiply this by the percentage of calories from proteins, which is 35%. This gives us 0.35 * 2500 = 875 kcal from proteins.

Next, we need to convert these calories into grams of protein. Each gram of protein provides approximately 4 calories. Therefore, we divide the protein calories (875 kcal) by 4 to get the grams of protein consumed, which is 875 / 4 ≈ 218.75 grams. Rounding this to the nearest gram, the individual would consume approximately 219 grams of protein on a 2500 kcal daily diet with 35% of the calories coming from proteins.

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The slope of a graphed line that spans grid points (0, 2) and best represents the slope as -5 (1, -3)

A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).

given

If the line rises to the right, the slope has a positive sign. The slope of this line is negative since it descends to the right. (Removes options C and D)

The ratio of the vertical to horizontal distance between two sites determines the slope's magnitude. This line has a slope of rise/run = -5/1 = -5 because it descends five vertical squares for every square to the right.

-5 is the best way to describe the slope.

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Answer:

it would be the first one i think

Step-by-step explanation:

Answer:

Option C: between 2.75 and 3.0

Step-by-step explanation:

Maybe this might help somewhat.

Answer:

80

Step-by-step explanation:

the A and X are equal

Answer:

D

Step-by-step explanation:

I hope you get this right

Answer:

58.5 square feet

Step-by-step explanation:

PART 1

The exponential decay model is given to be:

where a is the initial value and r is the decay rate.

In the question, the initial value is 15,500 and drops at a rate of 3%. This means that we have the following parameters:

Therefore, the exponential model is gotten to be:

PART 2

The graph of the function is shown below:

At x = 8000, we have the time as shown below:

The time will be 21.7 years.

Answer:

1) m∠U = 90°

2) m∠C = 80°

Step-by-step explanation:

1) The given figure is a quadrilateral

The sum of the interior angles of  quadrilateral = 360°

∴ The sum of the interior angles of the given figure = 360°

Therefore, we have;

80° + 24·x + 4 + 6 + 21·x + 90° = 360°

80° + 45·x + 10  + 90° = 360°

x = (360°- (80° + 10° + 90°))/45 = 4

x = 4

m∠U = 6 + 21·x = 6 + 21 × 4 = 90

m∠U = 90°

2) The sum of the interior angles of the given quadrilateral = 360°

∴ 21·x + 6 + 20·x + 24·x + 4 + 21·x + 6 = 360°

86·x + 16 = 360°

x = (360° - 16°)/86 = 4

x = 4

m∠C = 20·x = 20 × 4 = 80

m∠C = 80°

3) In the figure, some angles are left out, therefore, more information on the remaining angles required

Answer:

10 ≥ 2(2.99) + 0.67b

10 ≥ 5.98 + 0.67b

4.02 ≥ 0.67b

6 ≥ b

David can buy 6 pounds of bananas at most.

Hope I helped <3

The common difference in the sequence 7, 12, 17, 22, 27,… is that the difference between two numbers increases by five in the ascending order.

A sequence can be referred to or considered as the set of observations, which usually consists of numbers arranged in such a way that they described a common characteristic between them. A sequence can be exhaustive or inclusive, depending upon the numbers being used in the continuity of the sequence. It can also be said that a sequence is a logical arrangement.

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Complete question

what is the common difference in the sequence 7, 12, 17, 22, 27, ...?

Answer:

37

Step-by-step explanation:

74*(-5+5+1/2)

74*(1/2)

37

Answer:

£22.40

Step-by-step explanation:

shorts: 10% off

jeans: 20% off

before discount:

jeans : shorts = 7:5

after discount:

shorts: £18

original price of shorts: £18/0.9 = £20

original price of jeans: j

j/20 = 7/5

5j = 7 × 20

j = 7 × 4

j = 28

original price of jeans: £28

sale price of jeans: £28 × 0.8 = £22.40

Answer:    £22.40

=========================================

Explanation:

The sale price of the shorts is £18

Let's say x is the original price of the shorts.

If there's a 10% discount, then you pay the remaining 90%

sale price = 90% of x = 0.90x

Set this equal to the 18 pounds and solve for x.

0.90x = 18

x = 18/0.90

x = 20

The shorts originally were £20.

The discount saves you 2 pounds.

---------------

Let y be the original price of the jeans before the discount.

The price ratio of jeans to shorts is 7:5. This is before the discount for both items.

So,

(jeans price)/(shorts price) = 7/5

y/20 = 7/5

5y = 20*7

5y = 140

y = 140/5

y = 28

The jeans were originally £28 before the discount.

---------------

Now apply the 20% price reduction for the jeans.

20% of 28 = 0.20*28 = 5.60

You save £5.60 and the sale price of the jeans is 28-5.60 = 22.40 pounds.

Or you can use this shortcut

80% of 28 = 0.80*28 = 22.40

This shortcut works because if you save 20%, then you pay the remaining 80%

The formula for the area of a regular pentagon is:

A = (1/2)Pa

where A is the area of the pentagon, P is the perimeter of the pentagon, and a is the apothem (the distance from the center of the pentagon to the midpoint of a side).

If the apothem of the pentagon is 3√2, then we need to know the perimeter of the pentagon in order to calculate its area.

Unfortunately, the apothem alone is not enough information to determine the perimeter of a pentagon. However, if we assume that the pentagon is regular, then we know that all of its sides and angles are equal, and we can use the following formula to find its perimeter:

P = 5s

where P is the perimeter and s is the length of a side.

To find the length of a side, we can use the fact that the apothem is perpendicular to a side and bisects it. This means that the triangle formed by the apothem, half a side, and the center of the pentagon is a right triangle. The hypotenuse of this triangle is the length of a side, and the legs are half a side and the apothem:

s/2 = 3√2

s = 6√2

Now we can use the equation for the perimeter of a pentagon:

P = 5s = 5(6√2) = 30√2

Finally, we can use the formula for the area of a regular pentagon:

A = (1/2)Pa = (1/2)(30√2)(3√2) = 45

Therefore, the area of the pentagon is 45 square units, assuming that it is a regular pentagon with an apothem of 3√2.

Answer:

no sorry

Step-by-step explanation:

To solve this problem, we can use a ratio proportion.
Let's assume that the store currently has x part-time workers and y full-time workers.
According to the problem, the ratio of part-time workers to full-time workers is 1:4. Therefore, we can write:
x/y = 1/4
Next, the problem states that if 5 part-time workers were hired, then the ratio would be 3:5. This means that the new ratio of part-time workers to full-time workers would be:
(x+5)/y = 3/5
Now we have two equations with two variables:
x/y = 1/4
(x+5)/y = 3/5
We can solve for x and y by cross-multiplying:
5x = y
15x + 75 = 12y
Substituting 5x for y in the second equation:
15x + 75 = 12(5x)
15x + 75 = 60x
60x - 15x = 75
45x = 75
x = 75/45 = 5/3
Since we can't have a fraction of a worker, we can round up to the nearest whole number.
Therefore, the store has 2 part-time workers and 10 full-time workers.
In summary, using the given ratios and information, we were able to solve for the number of part-time and full-time workers in the store.

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a. There are 66 ways to distribute the pens to 3 students.

b. There are 36 ways to distribute the pens to 3 students if every student must receive at least one pen.

c. There are 15 ways to distribute the pens to 3 students if every student must receive at least two pens.

d. There are 3 ways to distribute the pens to 3 students if every student must receive at least three pens.

(a) If there are no other conditions, the professor can give any number of pens to any student.

We can use the stars and bars method to calculate the number of ways to distribute the pens.

In this case, we have 10 pens and 3 students, which means we need to place 2 bars to divide the pens into 3 groups.

The number of ways to do this is given by:

\(${10+3-1 \choose 3-1} = {12 \choose 2} = 66$\)

Therefore, there are 66 ways to distribute the pens to 3 students.

(b) If every student must receive at least one pen, we can give one pen to each student first, and then distribute the remaining 7 pens using the stars and bars method.

In this case, we have 7 pens and 3 students, which means we need to place 2 bars to divide the pens into 3 groups.

The number of ways to do this is given by:

\(${7+3-1 \choose 3-1} = {9 \choose 2} = 36$\)

Therefore, there are 36 ways to distribute the pens to 3 students if every student must receive at least one pen.

(c) If every student must receive at least two pens, we can give two pens to each student first, and then distribute the remaining 4 pens using the stars and bars method.

In this case, we have 4 pens and 3 students, which means we need to place 2 bars to divide the pens into 3 groups.

The number of ways to do this is given by:

\(${4+3-1 \choose 3-1} = {6 \choose 2} = 15$\)

Therefore, there are 15 ways to distribute the pens to 3 students if every student must receive at least two pens.

(d) If every student must receive at least three pens, we can give three pens to each student first, and then distribute the remaining pen using the stars and bars method.

In this case, we have 1 pen and 3 students, which means we need to place 2 bars to divide the pen into 3 groups.

The number of ways to do this is given by:

\(${1+3-1 \choose 3-1} = {3 \choose 2} = 3$\)

Therefore, there are 3 ways to distribute the pens to 3 students if every student must receive at least three pens.

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Every time the same instrument is used for a measurement, it produces consistent results, which denotes: -reliability.

The degree to which a measurement tool produces consistent, repeatable estimates of what is believed to be a true score at the core.

The same set of people receives the same instrument again. The correlation between the results on the two instruments is what defines dependability. The scores ought to be comparable if the outcomes remain constant over time. How long to wait between the two administrations is the key to test-retest reliability.

Reliability is defined as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions.

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