Is (x - 2) a factor of f(x) = x3 - 2x2 + 2x + 3? Explain your reasoning.

Answer:

Step-by-step explanation:

The probability that airline b detected it will be 0.22.

The probability that airline B detected the weapon can be calculated using Bayes' Theorem, which states that:

P(airline B detected the weapon | weapon detected) = P(weapon detected | airline B detected the weapon) * P(airline B) / P(weapon detected)

where P(airline B) is the prior probability that a passenger was serviced by airline B (30%) and P(weapon detected) is the total probability that a weapon was detected (sum of the probabilities that a weapon was detected by each airline).

The numerator can be calculated as P(weapon detected | airline B detected the weapon) * P(airline B) = 0.5 * 0.3 = 0.15.

The denominator can be calculated as the sum of the probabilities that a weapon was detected by each airline, weighted by their respective prior probabilities:

P(weapon detected) = P(weapon detected | airline A detected the weapon) * P(airline A) + P(weapon detected | airline B detected the weapon) * P(airline B) + P(weapon detected | airline C detected the weapon) * P(airline C)

= 0.9 * 0.5 + 0.5 * 0.3 + 0.4 * 0.2

= 0.45 + 0.15 + 0.08

= 0.68

Finally, the answer is P(airline B detected the weapon | weapon detected) = 0.15 / 0.68 = 0.22.

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Answer: the measure of arc A B is 180°.

Step-by-step explanation:

mArc A B = mArc B O + mArc O A Because line segments B D and A C are diameters, they are also chords of the circle and therefore bisect each other. This means that angle A O C and angle B O C both measure x.

A radius drawn to cut angle C O C into 2 equal angle measures of x, it means that angle C O C measure 2x. So, arcs A O and B O are also equal.

Since angle A O C and angle B O C both measure x, and arcs A O and B O are equal, it means that mArc A B = mArc B O + mArc O A = x + x = 2x

As angle C O C measure 2x, and x angle measures are equal to each other. It means that x = (2x)/2 = x = angle C O C/2 = (180°)/2 = 90°

So, mArc A B = 2x = 2(90°) = 180°

Therefore, the measure of arc A B is 180°.

There are 69300 possible ways of selecting six bottles randomly with two bottles of each variety.

Probability is a branch of mathematics concerned with numerical descriptions of how likely an event is to occur or how likely a statement is to be true. In the given question, we have to select 6 bottles randomly with two bottles of each variety,

= ¹⁰C₂× ⁸C₂ × ¹¹C₂

¹⁰C₂= [1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 × 10] / [(1 × 2)(1 × 2 × 3 × 4 × 5 × 6 × 7 × 8)]

= 90/2

= 45

Similarly,  ⁸C₂  = 28

In the same way ¹¹C₂= 55

= ¹⁰C₂× ⁸C₂× ¹¹C₂

= 45 × 28 × 55

= 69300

Therefore, there are 69300 possible ways of selecting 6 bottles with two bottles of each variety.

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Answer: if your account has more liquidity

Answer:

О  B.  more

Step-by-step explanation:

You can access your funds easier if ypur account has more liquidity.

...

The difference quotient is equal to -3a2h, which simplifies to -3a2 divided by h.  This is the slope of the line tangent to the graph of f(x) = -x3 at the point (a, -a3).

The difference quotient is a way to approximate the slope of the line tangent to the graph of a given function. To calculate the difference quotient for f(x) = -x3, we can use the formula f(a h) − f(a) h. Plugging in values for f(a) and f(a h), we get -a3 - (-(a+h)3) / h. We can simplify this expression by multiplying out the parentheses: -a3 + (a3 + 3a2h + 3ah2 + h3) / h. We can then combine like terms and cancel out the h's to get -3a2h / h, which simplifies to -3a2 / h. This is the difference quotient for f(x) = -x3 at the point (a, -a3).

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The product is equivalent to $72 and its unit is $

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

The rate,

8hx$9/h

In simple words,

$9 per hour for 8 hours.

Now, for 1 hour, the cost is $9.

Therefore, for 8 hours,

It can be written as -

x = 9 x 8

x = $72

Hence, the product is equivalent to $72.

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Answer:

y = 12

Step-by-step explanation:

I believe that you can use the geometric mean theorem to solve for y

y is the geometric mean of the segments of the hypotenuse, so

24/y = y/6

simplify using means and extremes property: y^2 = 144

simplify: y=12

Answer:

1/6

Step-by-step explanation:

1-1/2 = 1/2

night = x

1/2 - x = 1/3

3/6 - x = 2/6

so x = 1/6

Answer:

The first side = 2x = 2(4) = 8 cm

The second side = 5x = 5(4) = 20 cm

The third side = 8x = 8(4) = 32 cm

Step-by-step explanation:

We can use the fact that the ratio of the sides of the triangle is 2:5:8 and the perimeter of the triangle is 60 cm to find the length of each side of the triangle.

First, we can use the ratio to find the ratio of the perimeter to the sides of the triangle: 2:5:8. Since the perimeter is 60 cm, we can set up the following equation:

2x + 5x + 8x = 60

where x represents the length of one side of the triangle in cm.

We can then simplify the equation:

15x = 60

To find the value of x, we can divide both sides of the equation by 15:

x = 4

So each side of the triangle is 4 cm long.

Therefore,

The first side = 2x = 2(4) = 8 cm

The second side = 5x = 5(4) = 20 cm

The third side = 8x = 8(4) = 32 cm

Therefore, the smaller part = 41.29 and the greater part = 57 - 41.29 = 15.71.

Let the smaller part be x.

Then, the greater part = 57 - x

According to the question,

1/2 (57-x) = 11 + 1/5x

Solve for x:

1/2 (57-x) - 1/5x = 11

7/10 (57-x) = 11

7/10 (57-x) - 11 = 0

7/10 (57-x) = 11

57-x = 11 * (10/7)

57-x = 15.71

x = 57 - 15.71

x = 41.29

The equation for this problem is:

x + y = 57

1/2 x = 11 + 1/5 y

y = 57 - x

1/2 x = 11 + 1/5 (57 - x)

2x = 11 + 57 - 5x

7x = 68

x = 68/7

x = 9.71

y = 57 - x

y = 57 - 9.71

y = 47.29

Therefore, the two parts of 57 are 9.71 and 47.29.

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The total number of text messages Connor sent last month is 171 text messages.

Number text messages Jonah sent = 73

Number of text messages Connor sent = x

So,

1/3x + 16 = 73

Subtract 16 from both sides

1/3x = 73 - 16

1/3x = 57

divide both sides by 1/3

x = 57 ÷ 1/3

multiply by the reciprocal of 1/3

x = 57 × 3/1

x = 171 text messages

Therefore, last month, Connor sent 171 text messages.

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The linear charge density of a thin wire bent into a circle remains constant, due to the fact that the linear charge density is determined by the number of electrons in the wire and the length of the wire.

Linear charge density refers to the amount of charge per unit length of a charged object.

In the case of a thin wire bent into a circle, the linear charge density remains constant despite the change in shape.

The reason for this is that the linear charge density is determined by the number of electrons in the wire and the length of the wire.

When the wire is bent into a circle, the length of the wire remains constant, while the number of electrons remains the same. As a result, the linear charge density remains constant.

It is important to note that the total charge in the wire changes when it is bent into a circle. The total charge is equal to the product of the linear charge density and the circumference of the wire.

So, while the linear charge density remains constant, the total charge in the wire increases as the wire is bent into a circle.

Complete Question:

What is the linear charge density of a thin wire bent into a circle (or ring) of radius if the total charge on the wire is constant?

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The unit vector that has an angle θ= 2π/3 with the positive x-axis can be represented in component form as: (x, y) = (-1/2, √3/2).

The unit vector that makes an angle θ= 2π/3 with the positive x-axis can be represented as a vector in the form of (x, y) components. To solve for the components of this vector, we must use trigonometric functions. Using the trigonometric function SOH-CAH-TOA, we will solve for the components of the unit vector.

The x-component of the vector can be found using the SOH CAH TOA formula and the angle θ= 2π/3:

x-component = cos(2π/3)

Plugging in the angle yields: x-component = cos(2π/3) = -1/2

The y-component of the vector can be found using the SOH CAH TOA formula and the angle θ= 2π/3:

y-component = sin(2π/3)

Plugging in the angle yields: y-component = sin(2π/3) = √3/2

Therefore, the unit vector that has an angle θ= 2π/3 with the positive x-axis can be represented in component form as: (x, y) = (-1/2, √3/2).

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"Your question is incomplete, probably the complete question/missing part is:"

Find the component form of the vector: the unit vector that makes an angle theta=2pi/3 with the positive x-axis.

Answer:

see explanation

Step-by-step explanation:

3

(f + g)(x)

= f(x) + g(x)

= 2x² - 4x - 5 + 3x - 13 ← collect like terms

= 2x² - x - 18

4

(f - g)(x)

= f(x) - g(x)

= 2x² - 4x - 5 - (3x - 13) ← distribute parenthesis by - 1

= 2x² - 4x - 5 - 3x + 13 ← collect like terms

= 2x² - 7x + 8

The approximate surface area of a cone is 204 inches².

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

We have,

The surface area of a cone is πr (r + √(h² + r²) )

Now,

Diameter = 10 inches

Radius = 5 inches

Slant height = 8 inches

Now,

The surface area of a cone is πr (r + √(h² + r²) )

Slant height = √(h² + r²) = 8 inches

So,

= πr (r + √(h² + r²) )

= π x 5 (5 + 8)

= 3.14 x 5 x 13

= 204 inches²

Thus,

The surface area of a cone is 204 inches².

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The approximate surface area of the cone is 227 square inches.

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 diameter of a cone's circular base measures 10 inches

Radius of cone is 5 inches.

Slant height = 8 inches

A=πr(r+√h²+r²)

A=3.14×5(5+√64+25)

A=3.14×5(5+√89)

A=3.14×5(5+9.43)

A=3.14×5(14.43)

A=226.61

Hence, the approximate surface area of the cone is 227 square inches.

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Answer:

5

Step-by-step explanation:

Hope it helps! =D

Step-by-step explanation:

for % problems always try to identify explicitly 100% and/or 1%.

everything else can be easily calculated out of that.

we need to find a 15% increase. of what ? that is the 100% in question.

so,

100% = 50

1% = 100%/100 = 50/100 = 0.5

15% = 1% × 15 = 0.5 × 15 = 7.5

so, 50 + 15% = 50 + 7.5 = 57.5

now, we could simply round (as a half-person or student does not make any sense).

the problem with the rounding is the small number of students overall.

if we round normally, we get 58 students.

but that are 8 students more, and 8 students are (remember, 1% = 0.5)

8/0.5 = 16%

if we round down, we get 57 students.

but that are 7 students more, and 7 students are

7/0.5 = 14%

so, every rounding to "whole students" actuality changes the % significantly.

there is no way to have 15% more students given the small number of students. only 14% more or 16% more.

if you need to give a number, do the normal rounding : 58.

but many greetings to your teacher with my additional comments.

FYI

once you understand the principle behind the % calculation, there are shortcuts to the calculations by combining 2 steps into 1 step :

x% of y is

y×x/100

or

y×0.x

in our case

50×0.15 = 7.5

x% added to y is

y×1.x

in our case

50×1.15 = 57.5

because

50 + 0.15×50 = (1 + 0.15)×50 = 1.15×50 = 57.5

The general solution of the given differential equation is y = sin x + c. cos x

What is Equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

cos (x) dy/dx +sin (x) y =1

now, divide with cos x on both the sides

cos(x)/cos x dy/dx + sinx.y/cos x = 1/cos x

dy /dx + sinx/cosx .y = 1/cos x

= dy/dx +tanxy =secx

the above equation is linear differentiation equation in y

so, now integrating factor

IF= secx

now the solution is

y secx = (secx .secxdx+c)

y secx = (sec[tex]x^{2}[/tex]dx+c)

= y* secx = tanx+c

y = 1/secx(tanx+c)

y = cos x (tanx+c)

we know that, tanx = sinx/cosx

y = cosx(sinx/cosx +c)

y = cos x .sinx/cosx +cosx (c)

Solution of the given differential equation y = sin x + c. cos x

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Step-by-step explanation:

a =

[tex] \frac{1}{6} [/tex]

The measure of∠SAU = 92°,

SV  = 22, ∠SBV = 18°.

A triangle is a three-sided polygon because it has three edges and three vertices. The most important attribute of a triangle is that the sum of its internal angles to 180 degrees. This quality is referred to as the angle sum property of triangles.

Given  a triangle ABC

and AV, BV, and CV are angle bisectors,

TV = 22 and CV = 27

∠TCU = 52°, ∠SAV = 46°

A: to find ∠SAU,

as we know angle bisector divides an angle into two equal parts,

so ∠SAV = ∠VAU = 46°

∠SAU = ∠SAV + ∠VAU

∠SAU =  46 + 46 = 92°

B: to find ∠SBV,

we have ∠SAU =  92° and ∠TCU = 52°

from angle sum property,

∠SAU + ∠TCU +  ∠SBT = 180°

∠SBT + 92 + 52 = 180

∠SBT = 180 - 92 - 52

∠SBT = 36°

so  ∠SBV = ∠BVT = ∠SBT/2 (due to angle bisector)

∠SBV = ∠BVT = 36/2

∠SBV = ∠BVT = 18°

C: to find SV,

since V is the incenter, Due to the junction point of the central axis being the center of the triangle's inscribed circle, this point will be equally spaced from each of the triangle's sides.

so TV = UV = SV  = 22

Hence ∠SAU = 92°,

SV  = 22,

∠SBV = 18°

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Answer: C; $5 for 40 ounces

Step-by-step explanation: To find the lowest cereal amounts, we need to find the unit price. To find the unit price, you ALWAYS divide the price by the amount. In this case, we need to divide the money by the ounces. So, the prices for each (in cents) are:

[tex]\frac{3.20}{20} = 0.16[/tex]

[tex]\frac{4.50}{25} = 0.18[/tex]

[tex]\frac{5}{40}[/tex] ≈ 0.13 (0.125)

So, the decimals are the prices (in cents) and the last one was 0.125, but we need to round up to the nearest cent. This would be $0.13. This makes the 40 ounces of cereal for $5 the cheapest of the 3 deals. I hope this helped!

For dy/dt = (1 + t^2)/ (3y - y^2), the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point if y ≠ 0 and y ≠ 3.

The hypotheses of Theorem 2.4.2 state that for the initial value problem

dy/dt = f(t, y), y(t₀) = y₀

to have a unique solution in some interval t₀ - h < t < t₀ + h within α < t < β, provided that:

f and its partial derivative with respect to y, ∂f/∂y, are continuous in a rectangle α < t < β, γ < y < δ that contains (t₀, y₀).

To determine if the hypotheses are satisfied for the given differential equation we need to check if f and ∂f/∂y are continuous in a rectangle that contains the initial point (t₀, y₀). If they are, then the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point.

dy/dt = (1 + t^2)/ (3y - y^2)

dy/ dt = (1 + t^2)/ y(3 - y)

So dy/dt is not continuous at y = 0 and y = 3.

So the hypotheses of Theorem 2.4.2 are satisfied, and a unique solution exists in some interval around the initial point if y ≠ 0 and y ≠ 3.

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Answer:

A linear equation in two variables is an equation of the form ax + by + c = 0 where a, b, c ∈ R, a, and b ≠ 0. A system of linear equations that has no solution is called an inconsistent pair of linear equations.

The exact value for the tangent of 240° is -0.422618261740699.  The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side of a right triangle. In order to calculate the tangent of 240°, first, find the ratio of the length of the opposite side to the length of the adjacent side. Then, use a calculator to convert the ratio into a decimal. To do this, simply divide the length of the opposite side by the length of the adjacent side. The decimal that is produced is the exact value for the tangent of 240°. In this case, the value is -0.422618261740699.

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South Carolina can produce 26x26x10x10x10 = 676,000 different license plates with the configuration digit, letter, digit, letter, digit, digit.

Permutations are arrangements of objects in a specific order. For example, if you have the letters A, B, and C, the possible permutations are ABC, ACB, BAC, BCA, CAB, and CBA. Permutations are often used to calculate the total number of possible combinations for a given set of objects, as each permutation is a unique combination. For example, if you have three letters and three digits, the total number of permutations is 26x10x10x26x26x10 = 17576000.

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A) The change in entropy of the ice is 0.346 kJ/K.

B) The change in entropy of the stone slab is -1.257 kJ/K.

C) The total change in entropy of the system is -0.911 kJ/K.

Part A:

The change in entropy of the ice can be calculated using the formula:

ΔS_ice = Q_ice / T

where Q_ice is the heat transferred to the ice and T is the temperature at which the heat transfer occurs.

In this case, the ice is absorbing heat from the stone slab until it reaches thermal equilibrium.

The amount of heat transferred can be calculated using the formula:

Q_ice = m_ice c_ice ΔT

where, m_ice is the mass of the ice, c_ice is the specific heat of ice, and ΔT is the change in temperature of the ice.

Since the ice is initially at -10∘C and the final temperature is 0∘C (the melting point of ice), ΔT is 10∘C.

Substituting these values into the equations, we get:

Q_ice = (4.5 kg) (2100 J/kg⋅K) (10 K)

          = 94.5 kJ

ΔS_ice = Q_ice / T = (94.5 kJ) / (273 K)

           = 0.346 kJ/K

Therefore, the change in entropy of the ice is 0.346 kJ/K.

Part B:

The change in entropy of the stone slab can be calculated using the same formula as before:

ΔS_stone = Q_stone / T

where, Q_stone is the heat transferred to the stone and T is the temperature at which the heat transfer occurs.

In this case, the stone is losing heat to the ice until both reach thermal equilibrium.

The amount of heat transferred can be calculated using the same formula as before:

Q_stone = m_stone c_stone ΔT

where m_stone is the mass of the stone slab, c_stone is the specific heat of the stone, and ΔT is the change in temperature of the stone.

Since the stone slab is initially at +10∘C and the final temperature is 0∘C, ΔT is 10∘C.

Substituting these values into the equations, we get:

Q_stone = -(4.5 kg) (790 J/kg⋅K) (10 K) = -355.5 kJ

ΔS_stone = Q_stone / T = (-355.5 kJ) / (283 K) = -1.257 kJ/K

Therefore, the change in entropy of the stone slab is -1.257 kJ/K.

Part C:

The total change in entropy of the system can be calculated by adding the changes in entropy of the ice and the stone slab:

ΔS_tot = ΔS_ice + ΔS_stone

Substituting the values we calculated earlier, we get:

ΔS_tot = 0.346 kJ/K + (-1.257 kJ/K) = -0.911 kJ/K

Therefore, the total change in entropy of the system is -0.911 kJ/K.

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The equivalent value of sin{D} is -

sin{D} = √13/10.

Given is a right angled triangle.

In the given right angle triangle, we can use the Pythagoras theorem as -

{FD}² = {√13}² + {√87}²

{FD}² = 13 + 87

{FD}² = 100

FD = 10

So, we can write that -

sin{D} = √13/10

Therefore, the equivalent value of sin{D} is -

sin{D} = √13/10.

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The average of these two values is the final answer:

d = (7.5 + 3.38) / 2 = 5.44 km, rounded to the nearest kilometre, the distance is 5 km.

To determine the distance from station A to the balloon, you can use the tangent function. The formula is: d = h / tan(angle of elevation), where d is the distance, h is the height of the balloon, and angle of elevation is the angle between the line of sight from the observer to the balloon and the horizontal.

Using the first angle of elevation (57°), we can calculate the distance as:

d = h / tan(57°) = h / 1.998 = 15 / 1.998 = 7.5 km

Using the second angle of elevation (83°), we can calculate the distance as:

d = h / tan(83°) = h / 4.398 = 15 / 4.398 = 3.38 km

The average of these two values is the final answer:

d = (7.5 + 3.38) / 2 = 5.44 km, rounded to the nearest kilometre, the distance is 5 km.

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The probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

[tex]P(C)[/tex] [tex]=P(C \mid G) P(G)+P(C \mid G c) P(G c)[/tex] = (1) (0.6) + (0.2) (0.4) =0.68

This is then used to update the inspector's belief in the suspect's guilt posterior to discovering that the suspect does have that characteristic.

[tex]$$\begin{aligned}& P(G \mid C)=(P(G) P(C \mid G)) / P(C) \\& =\frac{1(0.6)}{0.68} \\& =0.882\end{aligned}$$[/tex]

Therefore, the probability that the inspector in-charge is convinced that the suspect is guilty given he/she has brown hair is 0.882.

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