Given that f(x) = x² − 8x + 12 and g(x) = x − 2, find (ƒ – g)(x) and express
the result as a polynomial in simplest form.

The probabilities are given as follows:

1. a. Exactly one hits the target: 7/20.

1. b. At least one hits the target: 31/40.

2. Health insurance is chosen: 0.57 = 57%.

The outcomes with exactly one person hitting the target are given as follows:

Hence the probability is obtained as follows:

p = 3/5 x 3/4 x 1/2 + 1/4 x 2/5 x 1/2 + 1/2 x 3/4 x 1/2

p = 9/40 + 2/40 + 3/40

p = 14/40

p = 7/20.

The probability that none hits the target is of:

3/5 x 3/4 x 1/2 = 9/40.

Hence the probability of at least one hitting is of:

1 - 9/40 = 40/40 - 9/40 = 31/40.

The percentages associated with health insurance are given as follows:

Hence:

p = 0.45 x 0.4 + 0.65 x 0.6

p = 0.57.

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There are 3d + 6 seeds is going to​ plant.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

Val is going to plant d vegetable seeds in one garden and 2d+6 vegetable seeds in another.

Hence, The total vegetable seeds to plant is,

⇒ d + (2d + 6)

⇒ d + 2d + 6

⇒ 3d + 6

Thus, The total vegetable seeds to plant is, (3d + 6)

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Answer:

the answer to this question is 12

Answer:

Step-by-step explanation:

In the diagram there are two vertex A & B

Let us assume the 3rd vertex  to be C

AB is the hypotenuse which is 8

AC is the adjacent side which is 6

CB is the opposite side. Let us assume it to be x for now

[tex]hypotenuse^{2} = opposite^{2} +adjacent^{2}[/tex]

[tex]8^{2} =x^{2}+6^{2} \\64=x^{2} +36\\x^{2} =64-36=28\\x=2 \sqrt{7}[/tex]

sinA=CB/AB = 2[tex]\sqrt{7[/tex] /8

CosA=AC/AB=6/8

TanA=sinA/CosA=CB/AC=2[tex]\sqrt{7}[/tex]/6

Similarly,

CosecA=1/SinA

SecA=1/CosA

CotA=1/TanA

The area of the region between x = 0 and x = 2 of the curve y = 2x² - 4x is given as follows:

2.64 square units.

The area of a curve y = f(x) between an interval from x = a to x = b is obtained by the definite integral of f(x) from x = a to x = b.

The curve in this problem is given as follows:

y = 2x² - 4x.

The integral is given as follows:

I(x) = 0.67x³ - 2x².

The bounds are given as follows:

x = 0 and x = 2.

Applying the Fundamental Theorem of Calculus, the definite integral is given as follows:

A = |I(2) - I(0)|.

A = |0.67(2)³ - 2(2)²|

A = 2.64 square units.

The shaded region is between x = 0 and x = 2.

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Answer:

diving board has a length of 20 feet and a width of 2 feet

Step-by-step explanation:

diving board has a length of 20 feet and a width of 2 feet

Area = length (l) x width (w)

lw = 40

Perimeter = 2l + 2w

we can solve for 'l' and have:

l = 40/w

now substitute 40/w in for 'l' in the perimeter formula to get:

2(40/w) + 2w = 44

distribute through by 2 to get:

80w + 2w² = 44w

we can create the quadratic equation:  2w²-44w + 80 = 0

we can factor out a 2 to get:

2(w² - 22w + 40) = 0

2(w-20)(w-2) = 0

w = 20 and 2

The probability of winning, assuming optimal play, is m/n, where m and n are relatively prime integers. Then 100m + n is 11.

To find the probability of winning assuming optimal play, we need to find the probability that we choose the correct box after we know what is in the other box. Let X be the event that the gemstone is in box B1. Then P(X) = 1/10.

After Auntie Hall opens a box, the probability of X changes. Let Y be the event that the opened box contains yoghurt. Then P(Y) = 2/3.

Given Y, the probability of X changes to P(X | Y) = P(X) / (P(X) + P(X complement given Y)). We can use Bayes' theorem:

P(X | Y) = P(Y | X) × P(X) / P(Y)

Since the box that Auntie Hall opens is selected randomly, P(Y | X) = 2/3 for each X complement. Thus,

P(X | Y) = 1/10 × 2/3 / (2/3) = 1/10

The probability of winning is the same regardless of whether we switch boxes or not, so the probability of winning is 1/10.

So, 100m + n = 100 × 1/10 + 1 = 11, and the answer is 100m + n = 100 × 1/10 + 1 = 11.

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The corresponding point for the transformed function are:

Ordered pair (-4, -9).

Ordered pair (-2, 0).

Ordered pair (1, 12).

Ordered pair (3, 36).

In order to determine the corresponding point for the transformed function, we would have to substitute the given value of x (x-value) into the transformed function and then evaluate.

When the x-value = -4, the corresponding point for the transformed function is:

y = -3f(x + 2)

y = -3f(-4 + 2)

y = -3f(-2)

y = -3(3)

y = -9.

When the x-value = -2, the corresponding point for the transformed function is:

y = -3f(x + 2)

y = -3f(-2 + 2)

y = -3f(0)

y = 0

When the x-value = 1, the corresponding point for the transformed function is:

y = -3f(x + 2)

y = -3f(1 + 2)

y = -3f(3)

y = -3(-4)

y = 12.

When the x-value = 3, the corresponding point for the transformed function is:

y = -3f(x + 2)

y = -3f(3 + 2)

y = -3f(5)

y = 36

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The range is the set of all real numbers greater than zero.

It is clear that from the figure the exponential function never become zero and it is always positive.

The range is the set of all real numbers greater than zero.  


Real numbers are used to measure quantities that change over time, such as size and time.. They are distinguished from imaginary numbers by the word real, which involves the symbol I or Square root of 1.

Complex numbers. Positive and negative integers are included in the real numbers. an exponential function is a relationship of the form
y = axes, with the independent variable x ranging across the entire real  number line as the exponent of a positive number.

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Two right triangles are similar by angle-angle similarity if they share an acute angle measure. The triangles' corresponding side length ratios will be equal.

The triangle's characteristics are: A triangle's (of all varieties) total sum of angles is 180°. The length of a triangle's two longest sides added together is longer than the third side. Similar to this, the length of the third side of a triangle's third side is shorter than the difference between its two sides.

Given,

[tex]\frac{AC'}{AC}=\frac{AB'}{AB} \\\\\frac{6}{AC}=\frac{10}{4}\\\\ AC= 8.4[/tex]

The measure of AC is 6 cm.

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True, line y = -4x passes through the origin of coordinates.

Graph of the line is attached below.

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

Given equation of the line,

y = -4x

Line passes through the origin

So, Coordinates of the origin (0, 0) should satisfy the above equation.

0 = -4(0)

0 = 0

LHS = RHS

Hence, line y=-4x pass through the origin of coordinates.

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To form an isosceles triangle Jefferson should plot the third point at (4,2).

Any triangle with two sides that have the same length is said to be an isosceles triangle. If the two sides of a triangle are congruent, then the angle across from them must likewise be, according to the theorem that explains the isosceles triangle. As a result, the two angles of an isosceles triangle that are on opposite sides with equal numbers are equal in size.

Given, Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph.

the given points are,

(-2,-4) (4,-4)

Let, x₁ = -2, y₁ = -4

x₂ = 4, y₂ = -4

distance between (-2,-4) (4,-4) is given as,

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(4 - -2)² + (-4 - -4)²]

= √[(4 + 2)² + (-4+ 4)²]

= √[(6)² + (0)²]

= √[(6)²

= 6

now verifying with other options,

1). For points (-2, -9),

Distance between (-2, -4) and (-2, -9) = √[(-2 + 2)² + (-4 + 9)²] = √5

Similarly, distance between (4, -4) and (-2, -9) = √[(4 +2)² + (-4 + 9)²] = √61

side is not equal. So the triangle is not isosceles.

2). For a point (3, 1),

Distance between (3, 1) and (-2, -4) = √[(3 + 2)² + (1 +  4)²] = 5√2

Distance between (3, 1) and (4, -4) = √[(3 - 4)² + (1 +  4)²] = 26

side is not equal. So the triangle is not isosceles.

3). For a point (-2,0),

Distance between (-2, 0) and (-2, -4) = √[(-2 + 2)² + (-4 + 0)²] = 4

Distance between (-2, 0) and (4, -4) = √[(-2 - 4)² + (0 + 4)²] = 2√13

side is not equal. So the triangle is not isosceles.

4). For a point (4, 2),

Distance between (4, 2) and (-2, -4) = √[(4 + 2)² + (2 + 4)²] = 6√2

Distance between (4, 2) and (4, -4) = √[(4 - 2)² + (2 + 4)²] = 6

Sides are equal so the triangle formed is an isosceles triangle.

Therefore, the third coordinate is (4, 2).

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The complete question is,

Jefferson is plotting the vertices of an isosceles right triangle on a coordinate graph. He has plotted the two points shown. Where should he plot the third point?

The point is on the graph is (-2,-4) (4,-4)

The options is

(-2,-9)

(3,1)

(-2,0)

(4,2)

The value of C is; 1/3 for the probability density function f(x)=cx , 0<x<2.

The probability density function is a function of a continuous random variable, whose integral across an interval gives the probability that the value of the variable lies within the same interval.

Given that the function

f(x)={cx} ,at 0, 0≤x≤2

Here, we can see that the value of x is varies as 0,1,2

So, at 0,1,2 the value of the function is;

f(1) = c

f(2) = 2c

Thus, the probability density function is given as:

Summition f(x) = f(1) + f(2)

f(x) =c + 2c = 1

3c = 1

c = 1/3

Therefore, the value of C is 1/3

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Salut/Hello!

Answer:
The Mandelbrot set is the set of values  [tex]c[/tex] in the complex plane for which the orbit of the critical point [tex]z = 0[/tex] under iteration of the quadratic map
[tex]z_{n+1} = z_{n}^{2} + c[/tex] remains bounded.

I hope it was helpful! :]

Answer:

A Mandelbrot set is a mathematical set of points in the complex plane, the boundary of which forms a fractal shape. The set is composed of all complex numbers c for which the complex-valued iterative equation zn+1 = zn2 + c does not tend to infinity as n tends to infinity. The set is named after the mathematician Benoit Mandelbrot, who studied it in the 1970s and is considered to be one of the most famous and studied fractal shapes in mathematics.

The solid formed by a given net is cylinder.

What is Three dimensional shape?

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The net has two circles and one rectangle.

The net of a cylinder is formed of two circles, with one attached to each end of a rectangle.

A cylinder is a 3D shape with a circular cross section and a curved surface. It has no straight edges

Hence, the solid formed by a given net is cylinder.

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When a number is divided by 4, the available remainders are 0, 1, 2, and 3. A number divided by 4 has a residue as a result.

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.

It may exceed or fall short of the quotient. For instance, the result of 41 divided by 7 is 5 and the remaining is 6.

Division of Euclid Given positive integers a and b, the lemma or Euclid division procedure claims that there are unique integers q and r satisfying

a = bq + r, 0 ≤ r < b.

By Euclid's division lemma

If we divide any number a by 4 we get

a= 4q + r where 0 ≤ r < 4

So, the value of r can be  0, 1, 2, 3

So, when a number is divided by 4, the available remainders are 0, 1, 2, and 3.

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On solving the provided question, we can say that the ratio of the short leg to the hypotenuse in the right triangle is 1;2

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

the ratio of the short leg to the hypotenuse in the right triangle is

1;2

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Answer: 30inches

Step-by-step explanation:

P=5a

a=side length

P=5(6)

5*6=30

Answer:

Step-by-step explanation:

set the months as X

base on the question information, we have

35X + 100 ≤ 485

then we can have

35x ≤ 485 -100

35x≤385

x≤385/35

x≤11

thus, we can say, the total month is 11 months the parents will pay for the phone

The arc of length π/6 on the unit circle can be visualized as one-sixth of a full circle with a radius of 1 unit. The unit circle is defined as a circle with a radius of 1 unit centered at the origin (0, 0) in a coordinate plane.

What does the mathematical term "arc" mean?

An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference. A curve contains an arc.

To locate the point on the unit circle that corresponds to the end of the arc, we can use the concept of polar coordinates. In polar coordinates, a point on the unit circle is defined by its distance from the origin (r) and its angle with the positive x-axis (θ), as shown in the diagram below.

[diagram here]

For the arc of length π/6 on the unit circle, the angle θ is π/6 and the distance from the origin (r) is 1 unit.

Therefore, the point on the unit circle that corresponds to the end of the arc can be represented in rectangular coordinates as (r * cos(θ), r * sin(θ)), where cos(θ) and sin(θ) are the cosine and sine of the angle θ, respectively.

Substituting the values for r and θ, we have:

x = 1 * cos(π/6) = sqrt(3) / 2

y = 1 * sin(π/6) = 1/2

So, the point on the unit circle that corresponds to the end of the arc of length π/6 is (sqrt(3) / 2, 1/2).

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The degrees of freedom for a one-sample t test with 2,822 U.S. adults in the sample is 2821.

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The truth about the position of the student scuba diving using absolute value concept is;

D. The student is 3.75 ft below sea level, and the absolute value is 3.75 ft.

The absolute value (or modulus) | x | of a real number x is defined as the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.

Thus, if negative 3.75 is marked on the number line, from the given options, we can say that if we apply the definition above that |-3.75| = 3.75ft below the sea level

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Answer:

VU = 15, SU = 21.21 or 15[tex]\sqrt{2}[/tex], TV = 21.21 or 15[tex]\sqrt{2}[/tex], and SW = 10.6 or [tex]\frac{15\sqrt{2} }{2}[/tex].

Step-by-step explanation:

VU = 15 by the properties of a square.

To find SU and TV we need to use the rule: the diagonal for a square of side length s is: (√2)s

Then the diagonals for our square are: TV = SU = (√2)*15 = 21.2

SW is just the diagonal divided by 2, so SW = 10.6

The other answers are in radical form, but you can put either the number or radical version.

The monthly payment on the principal is $33.22

A monthly payment is a regular installment made by a borrower to a lender in order to pay off a debt over a period of time. It is typically used to repay loans such as mortgages, car loans, or personal loans, and is usually calculated based on the loan's interest rate, principal amount, and loan term (the number of months over which the loan will be repaid).

The formula of monthly payment is given as;

The formula for calculating the monthly payment on a loan is:

M = P * (r(1 + r)^n) / ((1 + r)^n - 1)

Where:

M = monthly payment

P = the principal amount of the loan = $1500

r = the monthly interest rate (expressed as a decimal) = 11.8%

n = the number of payments (in months) = 60 months

Substituting the values into the formula;

Monthly Payment = $ 33.22

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Complete Question:

A music company offers a loan to buy a drum set for $1500. The simple interest is 11.8% and the loan will be paid in equal monthly payments for 5

years. What is the monthly payment?

Answer:

In spherical geometry, the sum of the angles of a triangle is always greater than 180 degrees. The formula for this is:

x + y + z > 180 degrees

where x, y, and z are the angles of the triangle.

The formula for the area of a triangle in spherical geometry is given by:

A = R^2 * (θ1 + θ2 + θ3 - π)

Where A is the area of the triangle, R is the radius of the sphere, θ1, θ2, θ3 are the angles of the triangle in radians, and π is the constant pi.

It's important to note that this formula is based on the triangle's spherical excess which is the amount by which the sum of the triangle's angles exceeds 180 degrees.

a) The inequality is,

⇒  x + y + z > 180°

b) Area of spherical ΔXYZ is,

⇒ A = r²  (α + β + у - pi),

where, r is the radius of the sphere and α, β, and y are the angles of the triangle in radians.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, the sum of the angles of a triangle is greater than 180 degrees.

Hence, The actual sum of the angles is given by;

x + y + z = π + A,

where A is the area of the triangle measured in radians.

And, As for the formula for the area of a triangle in spherical geometry, it is given by the formula;

⇒ A = r²  (α + β + у - pi),

where, r is the radius of the sphere and α, β, and y are the angles of the triangle in radians.

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Answer:

here

let ABC is triangle

SO

The resultant normal force at point D along the x-direction is [tex]F_D_x=0[/tex] and  the resultant shear force at point D along the y-direction is [tex]F_D_y=154.29N[/tex]

Consider the equilibrium of the shaft.

Resolve the forces along the y-direction.

[tex]R_A_y+R_B_y=200+200+80+80R_A_y+R_B_y=560-----(1)[/tex]

Take moments about point B and about the z-axis:

[tex]R_A_y*1.4=2*100*0.7+2*80*0.4\\\\R_A_y=245.71[/tex]

Substitute the above value in equation (1).

[tex]245.71+R_B_y=560\\\\R_B_y=314.29N[/tex]

Resolve the forces along the z-direction.

[tex]R_A_z+R_B_z=385+385R_A_z+R_B_z=770-----(2)[/tex]

Take moments about point B and about the y-axis:

[tex]R_A_z*1.4=2*385*1.1\\\\R_A_z=605N[/tex]

Substitute the above value in equation (2).

[tex]605+R_B_z=770\\\\R_B_z=165N[/tex]

a) The resultant normal force at point D along the x-direction is

[tex]F_D_x=0[/tex]  

b) The resultant shear force at point D along the y-direction is

[tex]F_D_y-R_B_y+2*80=0\\\\F_D_y-314.29+160=0\\F_D_y=154.29N[/tex]

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Answer:

Step-by-step explanation:

u cant explain it