For liner function f, f (2) = 0 and f (4) = -6.
Write function F in slope intercept form
How do you find the slope of the line when you have two points?

The best way of writing a prolog rule that gives you all the possible coin combinations adding to a dollar is using membership rules and arithmetic condition.

The Prolog interpreter warns that it can only find one occurrence of one or more variables, which is strange, since typically variables are used to perform unification, pass values from one predicate to another, etc.

Arithmetic in Prolog

In arithmetic expression, + - * / symbols are special type of infix operator, and these operators are also known as arithmetic operators. In Prolog, operators are used as predicates but here operators are functions and these operators return a numerical value.

Arithmetic expressions can include variables, numbers, operators, and arithmetic functions. These will be written in parentheses with their arguments. These will return numerical values just like the arithmetic operators.

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Using mathematical operation, the value of stock on Friday is $341.04

To find the value of the stock on Friday, the value of the stock on Monday is $24.42. Since he own 12 shares, we can multiply 12 by $24.42.

This can be done using a mathematical operation called multiplication.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

The value of the stock is 12 * 28.42 = 341.04

The stock value on Friday will $341.04

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If geometric sequence has a1= 5 and r = 3 then the A(n) will be; 5 × 3^(n-1)

There are three parameters which differentiate between which geometric sequence we're talking about. The first parameter is the initial value of the sequence. The second parameter is the quantity by which we multiply previous term to get the next term.

The General form of a geometric sequence:

[tex]A(n) = A_1 \times r^{(n-1)}[/tex]

If a1= 5 and r = 3 then

A(n) = 5 × 3^(n-1)

Therefore, If geometric sequence has a1= 5 and r = 3 then the A(n) will be; 5 × 3^(n-1)

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The number of times the point R ( 120° , P ) needs to be rotated so that the figure is mapped to itself is 3 times

What is Rotation?

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the number of rotation be = n

Let the point be R

Now , the coordinates of the point R is

R ( 120° , P )

Now , to map the figure onto itself it needs to rotate 360°

So ,the number of times 120° needs to rotate to reach 360° is calculated as

n x 120° = 360°

Divide by 120 on both sides , we get

n = 360 / 3

n = 3 times

Therefore , the value of n is 3

Hence ,  The number of times the point R ( 120° , P ) needs to be rotated so that the figure is mapped to itself is 3 times

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One or more of the mean differences are statistically significant, but not the precise location of the group differences.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, might be an independent variable.

Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.

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Answer: a

Step-by-step explanation:

Answer:

the answer is $6

Step-by-step explanation:

This is because there are 1000g in 1kg, so 500g is half of that and half of 12 is 6.

Answer:

  45 eggs

Step-by-step explanation:

You want to know the number of eggs left after 27 have been eaten from a supply of 6 crates having 12 eggs each.

If each of 6 crates had 12 eggs, the number of eggs bought was ...

  (6 crates) × (12 eggs/crate) = 72 eggs

If 27 of those 72 were eaten, the number remaining is ...

  72 -27 = 45

45 eggs are left.

Mia will pay a total of $4.5 for the shipping and handling of the t-shirt

From the question, we have the following parameters that can be used in our computation:

Cost of the shirt = $15

shipping and handling = 30%

The amount paid for the shipping and handling of the t-shirt can be calculated using the following equation

Amount paid = original price * + shipping and handling

Substitute the known values in the above equation, so, we have the following representation

Amount paid = 15 * 30%

Evaluate the products

Amount paid = 4.5

Hence, the amount paid is $4.5

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To be more certain that it captures the true value of the population proportion, a 95 % confidence interval must be larger than an 80 % confidence interval.

An area created using fixed-size samples of data from a population (sample space) that follows a certain probability distribution is known as a confidence interval. A selected population statistic is built into the interval with a specified probability. An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers. You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% chance of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval.

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Answer: I believe it is 2/12. tell me if I am wrong.

Step-by-step explanation: Hope this helps!

The dimensions of the box that minimize the total cost of materials used are:

L = W = 16 cm

H =  32 cm

What is the rectangular dimension?

Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth. A triangle's or an oval's interior likewise has two dimensions.

We have,

volume L* W * H = 512 cm³

sides of the box cost = 1 cent/cm²

top and bottom cost 2 cent/cm²

to find out

dimensions of the box that minimize the total cost of material use

we know here,

L* W * H = 512 cm³

where,

L is length and W is width and H is the height

so when we minimize the cost function

C( L, W, H ) = (1) 1 H ( L + W ) + (2) 1 L W

so put here H

substitute  [tex]H = \frac{512}{LW}[/tex] we get,

C(L, W) = 512([tex]\frac{1}{l}, \frac{1}{W}[/tex]) + 2LW

so

minimum cost will be when the two partial derivatives is 0

dC/dL = 2W - 512/L² = 0

so

dC/dW = 2L - 512/W² = 0

L =  256/W²

so

by solving the above equation we get

L = W = (256)⁻³ = 16cm

and

H = 512/16 = 32

H =  32 cm

Hence, the dimensions of the box that minimize the total cost of materials used are:

L = W = 16 cm

H =  32 cm

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The best prediction the price will do next is keep increasing.

What is stock price?

The price at which one share of a company would be purchased is known as the share price or stock price. A share's price is not constant; rather, it changes over time in response to market factors. It is likely to rise if the business is thought to be doing well or fall if it isn't living up to expectations.

A company's price rising more quickly indicates that investors are supporting the rally and that the stock will rise further.

On the other hand, a declining price trend with high volume suggests a possible downward trajectory. A high trade volume could also indicate a change in trend.

Hence, the best prediction the price will do next is keep increasing.

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98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.

What does a statistical random sampling entail?

P = x/n

= 89/168

= 0.53

α= 0.02

∴Zc = Zi - α/2

= 2.326

Now, C.I = P ± Zc * √[P(1-P)/n]

= 0.5 ± 2.326 * √[(0.53(1-0.53)) / 168

= (0.440, 0.619)

∴98% C.I. = 0.440 < P < 0.619

Hence, 98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.

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Answer:

The probability that marksman will hits the target at most 13 times is  27.92%.

The number of successes ("x") is the probability mass function for such binomial distribution.

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

We are interested in the likelihood that the target will be struck exactly five times, therefore the desired number of successes is five (i.e., x = 13).

P(X = 13) =  ¹⁵C₁₃. (0.89)¹³ (0.11)²

P(X = 13) = 0.2792

P(X = 13) = 27.92%

Thus, the probability that marksman will hits the target at most 13 times is  27.92%.

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Answer:

y = -x + 8

Step-by-step explanation:

x + y = 5

y = -x + 5

y = -x + b

0 = -(8) + b

b = 8

y = -x + 8

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The approximate distance from the sun to Earth is miles greater than the approximate distance from Earth to the moon by 9.276 × 10^7.

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers in the millions place after the decimal required to be represented in a simpler format.

In this case, the approximate distance from Earth to the moon is 240 thousand miles. This will be 2.4 × 10^5

The approximate distance from Earth to the sun is 93 million miles. This will be:

= 9.3 × 10^7

The difference will be:

= (9.3 × 10^7) - (2.4 × 10^5)

= 9.276 × 10^7

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The area of the polygons arranged in order of increasing Area is:

A polygon is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.

The area of the triangle is given as:

[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2

Where Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.

Hence given:

A(-4-3), B(1, -3), C(-1,2)

we have

[-4(-3-2) + (1(2-(-3)) + (-1(-2-(-3))]/2

= 24/2

= 12

Hence the area of the triangle is 12.

To calculate the area of the rectangle, we use the distance formula. The equation for this is given as:

d² = (x₂ - x₁)² + (y₂-y₁)²

Where (x₁, x₂) are the coordinates of the first point and

(y₁, y₂) are the coordinates of the second point.

Assuming that the vertices are labeled as follows:

A (7,9), B(6,9), C(6,5), D(7,5), then

AB² = (6-7)² + (9-9)²
AB² = 1 + 0

AB = 1

BC² = (6-6)² + (5-9)²

BC² = 0² + -4²

BC = 4

CD² = (7-6)² +(5-5)²

CD² = 1² + 0²

CD = 1

DA² = (7-7)² + (9-5)²

DA² = 0² +4²

DA = 4

From the above, we can tell as is typical of a rectangle, that AB = CDand BC = DA

Since the Area of the rectangle is AB x CD OR BC x DA

The area of the rectangle =

4 x 1 = 4

Using the distance methods we can also arrive at the length of the sides of the square.

Since the area of a square is given as L² we only need the lenght one one side.

Hence,

AB = 3.60555

Hence the area of the square =

3.60555²

= 12.9999908025

Area of the square [tex]\approx[/tex] 13.

Thus the polygons arranged in order of increasing area are:

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Answer:

c. -24

Step-by-step explanation:

f(3) means the y value where x = 3, therefore f(3) = -24

Answer: =3x+6

Step-by-step explanation:

Answer: Quadrant 1, y-axis

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, Amelia thinks of a number that is a factor of both 18 and 12. This number is odd, so it can't be a whole number. Next, Amelia has to find the largest number that is a factor of both 18 and her chosen number. This number is 36.

Answer:

  3

Step-by-step explanation:

You want the largest odd factor of both 18 and 12.

The greatest common divisor of both 18 and 12 is 6:

  18 = 3·6

  12 = 2·6

This is an even factor, which has two factors: 2 and 3. Only 3 is an odd factor of both 18 and 12.

The largest odd factor of both 18 and 12 is 3.

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Answer:

Its the second one

Step-by-step explanation:

.

The margin of error for the population proportion is ± 3.39%

Error is the difference between a genuine value and an estimate, or approximate, representation of that value in practical mathematics. The discrepancy between the mean of the complete population and the mean of a sample taken from that population is a frequent example in statistics.

Given that A survey of factories in five northeastern states found that 10% of the 300 workers surveyed were satisfied with the benefits offered by their employers

i.e. sample size n =300

Sample proportion p = 0.10

q=1-p=0.9

[tex]\sqrt{} \frac{pq}{n}[/tex] = [tex]\sqrt{\frac{0.1*0.9}{300} }[/tex]

Standard error ≈ 0.01732

Margin of error at 95% would be

1.96*std error

= 0.0339=3.39%

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A linear problem is always convex, because anything linear is convex.

What is linear programming?

A mathematical model whose requirements are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming.

A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.

Every linear function has a concave shape. However, only convex polygons (possible sets of linear programs) exist.

A linear problem is always convex, because anything linear is convex.

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The Central Limit Theorem establishes that the sampling distribution of the sample means with size n can be roughly equivalent to a normal distribution with mean and standard deviation for a normally distributed random variable X, with mean and standard deviation.

The Central Limit Theorem can also be used with skewed variables if n is at least 30.The mean of the sampling distribution of sample means is p for a proportion p in a sapling of size n, and the standard deviation is s=root of p(1-p)/n.This issue involves that:(A) Determine the sample proportion's sampling distribution's mean.The Central Limit Theorem states that 0.85

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Answer:

Step-by-step explanation:

(3x-2)(3x+1)

Answer:

(3x - 2)(3x + 1)

Step-by-step explanation:

9x^2 - 3x - 2 = 9x^ 2 - 6x  + 3x - 2 =

=3x(3x - 2) + (3x - 2) = (3x - 2)(3x + 1)