HELP ME WITH THIS QUESTION PLESE!!​

Answer:

[tex]3x^{3}[/tex] - [tex]11x^{2}[/tex] + 10x - 2

Step-by-step explanation:

Helping in  the name of Jesus.

William will have £309.40 at the end of 3 years.

To calculate the amount of money William will have at the end of 3 years, we need to use the formula for simple interest:

Simple Interest = Principal x Rate x Time

Where:

Principal is the amount of money invested

Rate is the interest rate

Time is the duration of the investment

In this case, William invests £280, the interest rate is 3.5%, and the duration of the investment is 3 years. Plugging these values into the formula, we get:

Simple Interest = £280 x 0.035 x 3

Simple Interest = £29.40

This means that William will earn £29.40 in interest over the 3-year period. To calculate the total amount of money he will have at the end of the 3 years, we simply add the interest to the principal:

Total amount = Principal + Simple Interest

Total amount = £280 + £29.40

Total amount = £309.40

Therefore, William will have £309.40 at the end of 3 years.

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The general solution to the linear system is: (x1) = (17/4 - 3/4 x4 - 2 x2) (x2) = (-11/4 + 5/4 x4) (x3) = (10/7 - 2/7 x4) (x4) = (x4)

The general solution to the linear system can be found by using matrix row operations to reduce the system to a simpler form. After reducing the matrix, we can express the solution as a column vector and identify the free variables.

First, we can use the first equation to eliminate the x1 term from the other equations. We can multiply the first equation by 2 and subtract it from the second equation, and multiply the first equation by -1 and add it to the third equation.

This gives us the following system:

(-1 2 1 1) (x1) (-3)
( 0 -7 -3 -4) (x2) ( 8 )
( 0 -3 -1 -2) (x3) ( 2 )
(x4)

Next, we can use the second equation to eliminate the x2 term from the third equation. We can multiply the second equation by -3/7 and add it to the third equation.

This gives us the following system:

(-1 2 1 1) (x1) (-3)
( 0 -7 -3 -4) (x2) ( 8 )
( 0 0 4/7 2/7) (x3) (-10/7)
(x4)

Finally, we can use the third equation to eliminate the x3 term from the first and second equations. We can multiply the third equation by -7/4 and add it to the first equation, and multiply the third equation by 3/4 and add it to the second equation.

This gives us the following system:

(-1 2 0 3/4) (x1) (-17/4)
( 0 -7 0 -5/4) (x2) ( 11/4 )
( 0 0 4/7 2/7) (x3) (-10/7)
(x4)

Now we can express the solution as a column vector:

(x1) = (17/4 - 3/4 x4 - 2 x2)
(x2) = (-11/4 + 5/4 x4)
(x3) = (10/7 - 2/7 x4)
(x4) = (x4)

The free variables are x2 and x4, since they can take on any value and the other variables are expressed in terms of them.

So the general solution to the linear system is:

(x1) = (17/4 - 3/4 x4 - 2 x2)
(x2) = (-11/4 + 5/4 x4)
(x3) = (10/7 - 2/7 x4)
(x4) = (x4)

And the free variables are x2 and x4.

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A non-zero, 2 x 2 matrix that satisfies the given conditions is

A = [ -1 0 ; 0 2 ].

The determinant of A is -2.

For each row, the first entry is -1 and the sum of the entries is -1 + 0 = 0, and for each column the first entry is -1 and the sum of the entries is -1 + 2 = 1.

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The required probability of rainfall duration falls for at least 2 hours, at most 3 hours and between 2 and 3 hours is given by  0.5896, 0.6808, and 0.2704 respectively.

Rainfall duration at Toronto Pearson International Airport follows,

An exponential distribution with a mean value of 2.725 hours

Probability that the duration of a particular rainfall event is at least 2 hours is,

Probability that the rainfall duration is greater than or equal to 2 hours.

Let X be the duration of a rainfall event,

P(X ≥ 2) = 1 - P(X < 2)

The cumulative distribution function (CDF) of an exponential distribution with mean value λ is,

F(x) = 1 - e^(-λx)

Substituting λ = 1/2.725 (since the mean value is 2.725 hours) and x = 2,

P(X < 2)

= F(2)

= 1 - e^(-1/2.725 × 2)

≈ 0.4104

Probability that the duration of a particular rainfall event is at least 2 hours is,

P(X ≥ 2)

= 1 - P(X < 2)

≈ 0.5896

Probability that the duration of a particular rainfall event is at most 3 hours,

Probability that the rainfall duration is less than or equal to 3 hours.

Using the CDF of the exponential distribution,

P(X ≤ 3)

= F(3)

= 1 - e^(-1/2.725 × 3)

≈ 0.6808

Probability that the duration of a particular rainfall event is at most 3 hours is approximately 0.6808.

Probability that the duration of a particular rainfall event is between 2 and 3 hours,

Probability that the rainfall duration is greater than or equal to 2 hours and less than or equal to 3 hours.

P(2 ≤ X ≤ 3)

= P(X ≤ 3) - P(X < 2)

= F(3) - F(2)

= e^(-1/2.725 × 2) - e^(-1/2.725 × 3)

≈ 0.2704

Probability that the duration of a particular rainfall event is between 2 and 3 hours is approximately 0.2704.

Therefore , the probability that the duration of rainfall is at least 2 hours, at most 3 hours and between 2 and 3 hours is equals to  0.5896, 0.6808, and 0.2704 respectively.

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The Slope of line is 10

the equation of line is y = 10x + 4.

The equation of a line is a formula that describes the relationship between the x and y coordinates of points on the line. The most commonly used form of the equation of a line is the slope-intercept form: y = mx + b

First make a chart for x and y values from the given graph;

Study time in hours (x) =  60    75    70     80    90    80   100   95   100

Grade % (y) =                       1       1       2       2      2       3      3      4      4

We know that the line equation, y = mx + b

Slope (m) = [tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]

Take any two values from chart, (2, 80) and (4, 100)

Put the values then, m = [tex]\frac{100-80}{4-2}} = \frac{20}{2} = 10[/tex]

m = 10

Therefore, the Slope of line is 10.

So, equation for (2, 80) is: y = mx + b

80 = 10 × 2 + b

b = 4

put the values in above line equation; y = 10x + 4

Therefore, the equation of line is y = 10x + 4

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If 6 is a zero of the function f(x), it means that the point (6,0) lies on the graph of the function, and f(6) = 0.

What is function ?

In mathematics, a function is a rule or a mapping that associates each element of a given set (called the domain) to a unique element in another set (called the codomain or range). In other words, a function is a relationship between two sets of numbers, where each input value from the domain corresponds to exactly one output value in the range.

If 6 is a zero of the function f(x), it means that when x = 6, f(x) = 0. In other words, the point (6,0) lies on the graph of the function f(x).

The value of f(6) can be found by substituting x = 6 into the function. Since f(x) = 0 when x = 6, we have:

f(6) = 0

This means that the output of the function when x = 6 is zero. Geometrically, this means that the graph of the function crosses the x-axis at x = 6. The x-axis is the line where the y-coordinate is zero, so when the graph of the function crosses the x-axis, the y-coordinate of the point of intersection is zero.

Knowing that 6 is a zero of the function f(x) can be useful for a variety of applications. For example, if the function represents the position of an object as a function of time, and the object is at position 6 at some time t, then we know that the object will be at rest at that time. Similarly, if the function represents the temperature of a system as a function of some other variable, and the temperature is zero when that variable is 6, then we know that the system is at a critical point when that variable takes the value of 6.

In summary, if 6 is a zero of the function f(x), it means that the point (6,0) lies on the graph of the function, and f(6) = 0. This information can be useful for understanding the behavior of the function and making predictions about its properties.

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Your complete question is :-If 6 is a zero of the function f(x), f(6)

The four pairs of x and y values are   (-2,1) (-1,0.5) (0,2) (1,3.5)

To find four pairs of x and y values that satisfy the equation y = 1.5x + 2, we can simply choose four values of x and then calculate the corresponding values of y.

Let's choose x = -2, -1, 0, and 1. Then we can calculate the corresponding values of y as follows:

When x = -2:

y = 1.5(-2) + 2

y = -1 + 2

y = 1

So one pair of x and y values that satisfy the equation is (-2, 1).

When x = -1:

y = 1.5(-1) + 2

y = -1.5 + 2

y = 0.5

So another pair of x and y values that satisfy the equation is (-1, 0.5).

When x = 0:

y = 1.5(0) + 2

y = 2

So another pair of x and y values that satisfy the equation is (0, 2).

When x = 1:

y = 1.5(1) + 2

y = 1.5 + 2

y = 3.5

So the final pair of x and y values that satisfy the equation is (1, 3.5).

    |

    |

    |

    |

    |

    |

    |

-----+-----+-----+-----+-----+-----+

    |     |     |     |     |     |

   (-2,1) (-1,0.5) (0,2) (1,3.5)

Note that these points all lie on the same line, which is the graph of the equation y = 1.5x + 2.

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An interest rate οf apprοximately 2.08% cοmpοunded mοnthly wοuld result in a final amοunt οf $8000 frοm an initial investment οf $6000 οver 10 years.

An algebraic expressiοn is a cοmbinatiοn οf variables, cοnstants, and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. It can cοntain οne οr mοre terms, and each term can have οne οr mοre variables raised tο pοwers οr multiplied by cοnstants.

The fοrmula fοr cοmpοund interest is:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where A is the final amοunt, P is the principal (initial investment), r is the interest rate, n is the number οf times the interest is cοmpοunded per year, and t is the time in years.

In this prοblem, we want tο find the interest rate that will result in a final amοunt οf $8000 frοm an initial investment οf $6000 οver 10 years with mοnthly cοmpοunding.

Since the interest is cοmpοunded mοnthly, we have n = 12, and t = 10*12 = 120.

We can plug in the given values and sοlve fοr r:

[tex]8000 = 6000(1 + r/12)^{(12*10)[/tex]

Simplifying:

[tex](1 + r/12)^{120} = 4/3[/tex]

Taking the natural lοgarithm οf bοth sides:

120 ln(1 + r/12) = ln(4/3)

Dividing by 120:

ln(1 + r/12) = ln(4/3) / 120

Taking the expοnential οf bοth sides:

[tex]1 + r/12 = e^{(ln(4/3) / 120)}[/tex]

Subtracting 1 and multiplying by 12:

[tex]r = 12(e^{(ln(4/3)} / 120) - 1)[/tex]

Using a calculatοr, we find:

r ≈ 2.08%

Therefοre, an interest rate οf apprοximately 2.08% cοmpοunded mοnthly wοuld result in a final amοunt οf $8000 frοm an initial investment οf $6000 οver 10 years.

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The surface area of a prism where the base=5 height=3 length=2 is 62 square units.

We must first calculate the area of each aspect of a prism before adding them together to determine its surface area.

The size of each base face is as follows because the base is a rectangle:

Area of base equals length times breadth, which is 5 times 3 square units.

Since there are two basis faces, the base faces' combined area is:

The base faces' total size is 2 x 15 square units.

The front and rear faces of the prism are also rectangles with length 2 and height 3 due to its rectangular shape. The region of each front or rear face is therefore:

Area of front/back visage equals length times height, which equals 2 times 3 square units = 2*3 = 6 square units

Since there are two front/back faces, their combined size is as follows:

Front and rear faces' combined area is 2 x 6 = 12 square units.

Last but not least, the two lateral faces are rectangles as well, measuring 2 and 5. The region of each side face is thus:

Area of the side wall = length x height = 2 x 5 = 10 square units

Since there are two side faces, the side faces' combined size is:

The total square footage of the side sides is 2 x 10 = 20 square units.

We add up the areas of all the faces to determine the overall surface area:

Total surface area is calculated as follows: 30 + 12 + 20 = 62 square units for the foundation faces, front/back faces, and side faces.

As a result, the provided prism has a surface area of 62 square units.

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The sample of drawing two balls from the bag containing four balls of different colours (R, B, Y and W) is the set of all possible outcomes of selecting two balls from the bag, which has a probability of 1/6  for each outcome.

The possible outcomes include (R,B), (R,Y), (R,W), (B,Y), (B,W) and (Y,W). Each outcome has an equal probability of occurring. For example, the probability of drawing a red ball (R) and a blue ball (B) from the bag is P(R,B) = 1/6.

To calculate the probability of drawing any two balls from the bag, we can use the combination formula nCr, which is used to find the number of combinations of selecting r items from a set of n items. In this case, the number of items (n) is 4 (R,B,Y and W) and the number of items to be selected (r) is 2.

Therefore, the total number of possible combinations of selecting two balls from the bag is:

nCr = 4C2 = 4! / (2! (4 - 2)!) = 6. The probability of drawing any two balls from the bag is 1/6.

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Answer:

AE AND AD

Step-by-step explanation:

The unknown values in the triangles are:

H = 88°

h ≈ 3.35

g ≈ 7.25

What is the law of sines?

The law of sine or the sine law states the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To find the unknown value of H, we can use the fact that the sum of the angles in a triangle is 180 degrees. We have:

∠F + ∠G + ∠H = 180°

25 + 67 + ∠H = 180°

∠H = 180 - 25 - 67

∠H = 88°

Therefore, the unknown value of H is 88°.

To find the unknown values of h and g, we can use the law of sines, which states that in any triangle ABC:

a/sin(A) = b/sin(B) = c/sin(C)

Let's use this formula to find the values of h and g:

h/sin(25) = 7/sin(67) (using angle G and side GH)

h = (7/sin(67)) * sin(25)

h ≈ 3.35

g/sin(88) = 7/sin(67) (using angle G and side GH)

g = (7/sin(67)) * sin(88)

g ≈ 7.25

Therefore, the unknown values in the triangles are:

H = 88°

h ≈ 3.35

g ≈ 7.25

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The carrier will charge you for shipping based on the item's weight or dimensional weight. Weight-based pricing is simple, meaning the heavier the package, the higher the shipping costs. The dimensional weight price is based on the length, height and weight of the box.

Shopping costs are part of the main production costs (labor and services) of a given store; these costs are allocated to the main costs of the corresponding manufactured item through the normal apportionment system.

E-commerce business owners need to know exactly how much shipping will be incurred for each sale for a number of reasons. First of all, it will have a direct impact on your profitability. If you don't know how much you're paying to ship to your customers, you won't have an accurate picture of your profits.

The second and most important reason is that you can provide your customers with accurate estimates. Charges may vary depending on package size and type of freight being shipped. You must ensure that accurate information is provided to customers on the checkout page. It could damage your company's goodwill if customers find out they were quoted differently and charged differently.

Costly hassles are cited as the top reason for shopping cart abandonment. There are many ways to reduce dropouts, and managing shipping costs is one of them. Here are some stats to give you a better idea:

1. 45% of shoppers abandoned their cart when they realized their order value was not eligible for free shipping.

2. 52% of shoppers added more items in cart because they want to be free Shipping.

3. 56% of shoppers are willing to pay for shipping when they think their order is too cheap to discount based on shipping alone.

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a. The proportion of people who did not have a heart attack is 98.7%.

b. The proportion of people who had a heart attack who took the placebo is 64.6%.

The overall number of persons who avoided having a heart attack is equal to the sum of the number of patients who took aspirin and avoided having one, as well as the number of patients who received a placebo. Therefore:

The total without a heart attack is equal to 10,845 plus 10,933 or 21,778.

The percentage of individuals who did not experience a heart attack is: 21,778 / 22,071 ≈ 0.987

Hence, 98.7% of the patients did not get a heart attack.

So, approximately 98.7% of the patients did not have a heart attack.

b. To get the percentage of patients who both took the placebo and experienced a heart attack, we must divide the total number of patients who experienced heart attacks by the number of patients who took the placebo:

189/293 = 0.646 people who took a placebo and experienced a heart attack

Thus, almost 64.6% of those who experienced a heart attack received the placebo.

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The expression of the statement is (27 - 3) / 4

Given the statement:

divide the difference of 27 and 3 by 4

The difference of 27 and 3 is 27 - 3 = 24.

To divide this by 4, we can use the expression:

(27 - 3) / 4

This expression represents the statement "divide the difference of 27 and 3 by 4".

We can simplify the expression by performing the subtraction first:

(27 - 3) / 4 = 24 / 4 = 6

So the result of "divide the difference of 27 and 3 by 4" is 6.

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1. The solution to the differential equation is: y*√(x2+1) = (1/2)x2 + 25

2. The solution to the differential equation is: -1/6ln(e^(6u+7t)) = u + 2

1. Solve the separable differential equation:
9x-4y√(x2+1) dy/dx=0
Subject to the initial condition:  y(0)=5

Solution:
Separating the variables, we have:
dy/√(x2+1)= (9x/4y)dx

Integrating both sides, we get:
∫dy/√(x2+1)= ∫(9x/4y)dx

On the left side, we have:
y*√(x2+1) = (1/2)x2 + C

On the right side, we have:
ln(y) = (9/4)ln(x) + C

Equating the two expressions, we get:
y*√(x2+1) = (1/2)x2 + (9/4)ln(x)

Substituting the initial condition, y(0)=5, we get:
5*√(02+1) = (1/2)02 + (9/4)ln(0)

Solving for C, we get:
C = 25

Therefore, the solution to the differential equation is:
y*√(x2+1) = (1/2)x2 + 25

2. Solve the separable differential equation for u:
du/dt = e^(6u+7t)
Use the following initial condition: u(0)=2

Solution:
Separating the variables, we have:
du/e^(6u+7t) = dt

Integrating both sides, we get:
-1/6∫du/e^(6u+7t) = ∫dt

On the left side, we have:
-1/6ln(e^(6u+7t)) = t + C

On the right side, we have:
u = C

Equating the two expressions, we get:
-1/6ln(e^(6u+7t)) = u + C

Substituting the initial condition, u(0)=2, we get:
-1/6ln(e^(62+7(0))) = 2 + C

Solving for C, we get:
C = 2

Therefore, the solution to the differential equation is:
-1/6ln(e^(6u+7t)) = u + 2

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The equation of CD is 3y- 2x = -5 in given question. Thus, option C is correct.

Equatiοns are mathematical statements cοntaining twο algebraic expressiοns οn bοth sides οf an 'equal tο (=)' sign. It shοws the relatiοnship οf equality between the expressiοn written οn the left side with the expressiοn written οn the right side. In every equatiοn in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equatiοns can be sοlved tο find the value οf an unknοwn variable representing an unknοwn quantity. If there is nο 'equal tο' symbοl in the statement, it means it is nοt an equatiοn.

We can conclude that C=(4;1)

Slope of AB= (3-1)(4-1)=2/3

The equation of CD is

y-1= 2/3(x-4)

=> 3y - 3=2x-8

=> 3y- 2x = -5

Thus, Option C is correct.

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Complete question:

Part of the graph representing an electrical signal is shown. The voltage rises steadily from an initial value (A) to a maximum value (B). It then drops instantly to the initial value (C) and repeats such that ab || cd and bc and de are vertical. If A = (1, 1) and B = (4, 3), what is the equation of cd?

systematic sampling

The sampling method being used in the given scenario is a systematic sampling method.What is screening?Screening is defined as the procedure for identifying and diagnosing certain medical conditions. Screening tests may be medical examinations or diagnostic procedures that are performed on people who do not have any symptoms, but who may be at risk of developing certain illnesses or diseases. The objective of screening is to detect the condition at an early stage so that treatment can be initiated, reducing morbidity and mortality. The following terms are used to define different sampling methods:Census Stratified Systematic Simple Random ClusterSystematic Sampling Method:Systematic sampling is a statistical method for selecting samples from a population. It is used when the population is too large to be surveyed in its entirety, and a representative sample must be chosen. The systematic sampling technique involves selecting every nth individual in the population to form a sample, where n is a predetermined number. For example, every 10th person, every 100th person, and so on may be selected as a sample member. In this way, the sample is chosen in a systematic manner. Therefore, in the given scenario, the screening method being used is a systematic sampling method.

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Answer: 63.2 dollars.

Step-by-step explanation: take 79 and divide it by 100 = .79

.79*20= 15.8

79-15.8= 63.3

Based on the above, Nico needs 22 feet of fence to enclose the play area.

To find the total length of fence needed, we need to calculate the perimeter of the rectangular play area.

The perimeter is the sum of the lengths of all four sides.

For a rectangle, the opposite sides have the same length. In this case, the opposite sides are both 7 feet long, and the other two opposite sides are both 4 feet long.

So, the perimeter is:

P = 2(7 ft) + 2(4 ft)

P = 14 ft + 8 ft

P = 22 ft

Therefore, Nico needs 22 feet of fence to surround the rectangular play area.

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Lateral Area = 40 ×20 = 800 cm².

Area is a measure of the size of a two-dimensional region. It is defined as the amount of two-dimensional space an object or shape occupies. It can be measured in different units, such as square feet, meters, kilometers, and acres. Area is an important concept in mathematics, especially geometry, and can be used to calculate the perimeter, circumference, and volume of a shape. It is also used in physics to measure pressure, force, and work.

The lateral area of a triangular prism with a height of 20 centimetres (cm) and base being a right triangle with side lengths of 8cm, 15cm and 17cm can be calculated as follows:

1. Calculate the area of the triangle using Heron's formula:

A = √(s × (s-a) × (s-b) × (s-c)),

where a, b, c are the sides of the triangle and s is the semiperimeter of the triangle.

In this case,

s = (8 + 15 + 17) / 2 = 15

A = √(15 × (15-8) × (15 - 15) × (15-17))

A = √(15 ×7 × 0 × -2)

A = √-210

A = Not defined

2. Calculate the lateral area of the prism using the formula:

Lateral Area = Perimeter of the base × Height

In this case,

Perimeter of the base = 8 + 15 + 17 = 40

Lateral Area = 40 ×20 = 800 cm²

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The area of the region bounded by the parabola and the tangent line is given by A = 27 units²

The area bounded by curves refers to the region enclosed between two curves on a graph. It represents the area that is enclosed or trapped between the two curves.

The area of the curve is determined by the integral of the difference of the curves over a particular interval or boundary conditions.

Given data ,

To find the area of the region bounded by the parabola y = 3x², the tangent line to this parabola at (3, 27), and the x-axis, we need to determine the points of intersection of these curves and calculate the area between them.

The equation of the tangent line to the parabola at (3, 27).

The derivative of the parabola y = 3x² is given by:

y' = 6x

The slope of the tangent line at (3, 27) is equal to the value of the derivative at x = 3:

m = y'(3) = 6(3) = 18

So, the equation of the tangent line is:

y - 27 = 18(x - 3)

y = 18x - 27

Now, the points of intersection between the parabola and the tangent line.

3x² = 18x - 27

Simplifying, we have:

3x² - 18x + 27 = 0

Dividing the equation by 3, we get:

x² - 6x + 9 = 0

This is a perfect square trinomial that can be factored as:

(x - 3)² = 0

So, the only solution is x = 3.

Now, the area between the curves by integrating the difference between the two functions from x = 0 to x = 3:

A = ∫[0, 3] (3x² - (18x - 27)) dx

Simplifying, we have:

A = ∫[0, 3] (3x² - 18x + 27) dx

Integrating term by term, we get:

A = [x³ - 9x² + 27x] evaluated from 0 to 3

Evaluating the integral at the limits, we have:

A = (3³ - 9(3)² + 27(3)) - (0³ - 9(0)² + 27(0))

A = (27 - 81 + 81) - (0 - 0 + 0)

A = 27 units²

Hence , the area of the region bounded by the parabola y = 3x^2, the tangent line at (3, 27), and the x-axis is 27 square units.

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The given information is:

P(C1) = 0.9 (probability that C1 functions properly on any given day)

P(C2) = 0.8 (probability that C2 functions properly on any given day)

P(C2|C1') = 0.4 (probability that C2 fails given that C1 fails)

P(C2|C1) = P(C2∩C1)/P(C1) = (P(C1) * P(C2))/P(C1) = P(C2) = 0.8

P(system functional) = P(C1∩C2) = P(C1) * P(C2) = 0.9 * 0.8 = 0.72

P(C1|system fails) = P(C1∩system fails)/P(system fails) = P(C1∩C2')/P(C1'∪C2') = P(C1) * P(C2'|C1)/P(C1'∪C2') = (0.9 * 0.2)/(1-0.72) = 0.18/0.28 = 0.6429

Therefore, the answers are:

(a) 0.8

(b) 0.72

(c) 0.6429

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When the cylinder's radius is quadrupled, its capacity is 360 cm3.. The new radius is 12 cm and the height is still 5 cm.

The volume of a cylinder is calculated by multiplying the area of its base (πr²) by its height (h). When the radius of the cylinder is tripled, the new radius would be 12 cm and the height would still be 5 cm. Therefore, the new volume of the cylinder is calculated by multiplying the area of its base (π x (12 cm)²) by its height (5 cm). This results in 360π cm³. To calculate this in a more simplified form, 120π cm³ (which is the original volume) can be multiplied by 3, since the radius is tripled. The result of this multiplication will be the same as 360π cm³. This demonstrates that the volume of the cylinder when its radius is tripled is 360π cm³.

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The centerline (X) is 76.2143°F,

The upper control limit (UCL) is 76.6763, and

The lower control limit (LCL) is 75.7523°F.

Thus, option C is correct.

To construct a cantrol chart for the process mean, we need ta find the centerline (X), the upper control limit (UCL), and the lawer control limit (LCL). We can use the formula:

X = Grand Mean

UCL = X + A2 * R

LCL = X - A2 * R

where A2 is a constant factor based on the sample size (n) and R is the mean range.

From the given data, we can calculate:

Grand Mean (X) = (77.4 + 75.5 + 76.1 + 76.8 + 75.2 + 75.9 + 76.7 + 75.6 + 76.2 + 77.1) / 10 = 76.2143°F

Mean Range (R) = 1.5°F

Sample Size (n) = 10

We can look up the value of A2 for n = 10 in a statistical table or use a calculator to find A2 = 0.577.

Now we can calculate the control limits:

UCL = 76.2143 + 0.577 * 1.5 = 76.6763°F

LCL = 76.2143 - 0.577 * 1.5 = 75.7523°F

Therefore, the centerline (X) is 76.2143°F,

the upper control limit (UCL) is 76.6763, and

the lower control limit (LCL) is 75.7523°F.

We can use these values to construct a control chart for the process mean and monitor the temperatures on the floor to ensure they are within acceptable limits.

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Answer:

Yes it is C

Step-by-step explanation:

The length of PR is approximately 30.08 feet.

What is Pythagorean theorem ?

The Pythagorean theorem is a fundamental concept in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In other words, if we have a right triangle with legs (or shorter sides) of length a and b, and a hypotenuse (longest side) of length c, then:

[tex]c^2 = a^2 + b^2[/tex]

According to the question:
Since ∆HIJ ~ ∆RQP, we know that the ratio of corresponding sides is 4:3. Let's set up a proportion:

HI/JH = RP/PQ

Substituting the values we know:

HI/12 = RP/PQ

We want to find PR, which is the sum of RP and PQ. We can use the Pythagorean theorem to find PQ, since we know that ∆RQP is a right triangle:

[tex]PQ^2 = RP^2 + RQ^2[/tex]

[tex]PQ^2 = (3/4)HI^2 + (4/4)HI^2[/tex](substituting HI/JH = 4/3)

[tex]PQ^2 = (7/4)HI^2[/tex]

[tex]PQ = HI\sqrt{7/4} = HI(\sqrt{7})/2[/tex]

Substituting this value into the original equation:

HI/12 = RP/(HI(√7)/2)

Simplifying:

[tex]RP = HI^2/(2 (12 ) \sqrt{7}/2)[/tex]

[tex]RP = HI^2/(12\sqrt{7})[/tex]

Substituting the given value of JH = 12 ft.

[tex]RP = 12^2/(12\sqrt{7}) = 12/\sqrt{7} \approx 4.555 ft[/tex]

Therefore, PR = RP + PQ:

[tex]PR = 12/\sqrt{7} + 12(\sqrt{7})/2 \approx 30.08 ft[/tex]

So the length of PR is approximately 30.08 feet.

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Answer:

9 ft

Step-by-step explanation:

Keep it simple, but correct :)

Answer:

The value of the tan 75 degrees is given as 3.7320508.

Step-by-step explanation: