Find the equation for the plane through the points Po(5,5,2), Qo(-4,0,-2), and Ro(-4,-1,1).
Using a coefficient of - 19 for x, the equation of the plane is

The total surface area is 3994ft sq.

Suppose the base of the pyramid has length = l units, and width = w units.

Surface area of rectangular prism = 2lb +2lh+2bh

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]

is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

Given;

Length= 32ft

Breadth= 21ft

Height= 25ft

Now,

Surface area of rectangular prism = 2lb +2lh+2bh

=2*32*21+2*32*25+2*21*25

=1344+1600+1050

=3994

Therefore, the area will be 3994ft sq.

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True, the classic tradeoff between "guns and butter" states that when a society spends more on national defense, it has less to spend on consumer goods to raise the standard of living.

The production possibility curve, which illustrates the concept of opportunity cost, has a famous economic example known as the "guns-and-butter" curve. One must decide how much of each good to create in a hypothetical economy with only two goods.

An economy must decrease its production of butter (food) as it increases its production of firearms (military spending), and vice versa. According to the guns-and-butter curve, you can only acquire something if you offer something else in exchange.

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The value of x is 17. The solution has been obtained using mid-point theorem of triangle.

What is mid-point theorem of triangle?

The midpoint theorem states, "The line segment of a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of its length."

Let the triangle be ABC and the line dividing it be PQ

We are given AP = PB and AQ = QC

Now, as per mid-point theorem, PQ is parallel to BC and is also half of its length as the two sides are equal.

Therefore,

x= 34/2

x=17

Hence, the value of x is 17.

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In the given expression, t-2 (t+5) is incorrect. The correct expression is (t-2)(t+5) = t² + 3t - 10. The error in the original expression is that it is not using the distributive property. The correct way to find the product is by using either distributive property or FOIL method.

The expression (t-2)(t+5) is the product of two binomials. To find the product, we use the distributive property and the FOIL method. The distributive property states that for any two binomials (a+b)(c+d) = ac + ad + bc + bd.

The FOIL method stands for "first, outer, inner, last", and is a mnemonic for the distributive property. To use the FOIL method, we take the first term from the first binomial, the second term from the second binomial, the second term from the first binomial, and the last term from the second binomial.

In your original expression, the error is that there is no operator between the two binomials (t-2) and (t+5), which makes it unclear whether you are trying to multiply them or not. To correct this, you need to add the multiplication operator () between the two binomials, so it becomes (t-2)(t+5).

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Expanding and simplifying the expression gives:

(3x - 2)² = 9x² - 12x + 4

Here we want to expand and simplify the expression below:

(3x - 2)²

First let's expand that, we can rewrite this as:

(3x - 2)² = (3x - 2)*(3x - 2)

We can distribute that product to get:

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

Now we can keep simplifying this to get:

(3x)*(3x) + (3x)*(-2) + (-2)*(3x) + (-2)*(-2) = 9x² - 6x - 6x + 4

9x² - 6x - 6x + 4 = 9x² - 12x + 4

The simplified expression is:

9x² - 12x + 4

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The Work done by a person is 24 x 103 J.

Force ratio is the ratio of two forces. It is often used in the context of mechanics, where a force is the product of mass and acceleration, and is measured in newtons (N).

Velocity ratio, on the other hand, is the ratio of two velocities. It is also used in mechanics and is measured in meters per second (m/s).

Force ratio and velocity ratio are closely related, as they are both used to measure mechanical properties of an object.

Force ratio is used to measure the ratio of two forces acting on an object, while velocity ratio is used to measure the ratio of two velocities.

Both force ratio and velocity ratio can be used to analyze the movement of an object, as well as its response to external forces.

Force ratio and velocity ratio are important concepts in mechanics, as they can help to analyze the dynamics of an object and its behavior over time.

Let M.A. = F1 and V.R. = F2

E = M.A. x 100% V.R.

Substituting the given values,

E = 80 = F1 x 100% F2

Work done by a person = Force x Displacement

= F1 x F2 x 200 kg x 3.0 m

= (80 x 100%) x 200 kg x 3.0 m

= (8 x 103) N x 3.0 m

= 24 x 103 J

Work done by a person = 24 x 103 J

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Answer:

Step-by-step explanation:

49255-1674.67=47580.33

Answer:

Step-by-step explanation:

a. No, he can't buy 12 packs of baseball cards because 12 packs * $1.70/pack = $20.40, which is more than $20.

b. Yes, he can buy 30 packs of gum because 30 packs * $0.60/pack = $18.00, which is less than or equal to $20.

c. He will still have $6.75 after he buys 5 packs of bouncy balls because $20.00 - (5 packs * $3.15/pack) = $20.00 - $15.75 = $6.75

In the table you provided, you can see the cost of different numbers of packs of baseball cards, gum and bouncy balls. This can help Dante to decide how much to spend on each item and how much he will save.

An imperfectly elastic ball is projected with the velocity [tex]\sqrt{gh}[/tex]  at an angle α with the horizontal, so that it strikes a vertical wall distant c from the point of projection, and returns to the point of projection.

Then, The Time of flight (T) =   [tex]\frac{2c}{ \sqrt{gh cosa } }[/tex]                

When a ball is projected with the velocity [tex]\sqrt{gh}[/tex]  at an angle α with the horizontal, it follows a parabolic path.

The ball will have a horizontal component of velocity (Vx) =  [tex]\sqrt{gh cosa}[/tex] , and a vertical component of velocity (Vy) = [tex]\sqrt{ghsina}[/tex] .

The ball will travel a horizontal distance equal to c before reaching the wall. The total time of flight (T) for the ball is equal to the time it takes the ball to reach the wall plus the time it takes for the ball to return to the point of projection.

The time it takes for the ball to reach the wall is equal  [tex]\frac{c}{vx}[/tex] , and the time it takes for the ball to return to the point of projection is also equal  [tex]\frac{c}{vx}[/tex].

Since the horizontal component of velocity (Vx) is equal to  [tex]\sqrt{gh cosa}[/tex] ,

the total time of flight (T) is equal to  [tex]\frac{2c}{ \sqrt{gh cosa } }[/tex] .

The correct question is:

An imperfectly elastic ball is projected with velocity √gh at an angle α with the horizontal, so that it strikes a vertical wall distant c from the point of projection, and returns to the point of projection. Then the time of flight is equal to?

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The distance between two cities, A and B is 1884 miles. The solution has been obtained using the concept of arc of circle.

What is arc of circle?

A circle's arc is referred to as a section or portion of its circumference. A chord of a circle is a straight line that can be created by joining the arc's two ends. A semicircular arc is one whose length is exactly half that of the circle.

We are given that the angle is 27° and radius is 4000 miles

We know that circumference of circle = 2πr

So,

C=2*3.14*4000

C= 25120

Now, to find the length of arc AB,

⇒Arc length = (27° × 25120)/360°

⇒Arc length = 1884

Hence, the distance between two cities, A and B is 1884 miles.

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The complete question is attached below.

Answer:

See below for proof.

Step-by-step explanation:

[tex]\large\boxed{\begin{minipage}{4 cm}\underline{Exponent Rules}\\\\$\sqrt[n]{a}=a^{\frac{1}{n}}$\\\\$(a^b)^c=a^{bc}$\\\end{minipage}}[/tex]

Given functions:

[tex]\begin{cases}f(x) = x^3 + 7\\g(x) = \sqrt[3]{x-7}\end{cases}[/tex]

The composite function f[g(x)] means to substitute the function g(x) in place of the x in function f(x):

[tex]\begin{aligned}f[g(x)]&=[g(x)]^3+7\\&=(\sqrt[3]{x-7})^3+7\\&=((x-7)^\frac{1}{3})^3+7\\&=(x-7)^\frac{3}{3}+7\\&=(x-7)^1+7\\&=x-7+7\\&=x\end{aligned}[/tex]

The composite function g[f(x)] means to substitute the function f(x) in place of the x in function g(x):

[tex]\begin{aligned}g[f(x)]&=\sqrt[3]{f(x)-7}\\&=\sqrt[3]{(x^3+7)-7}\\&=\sqrt[3]{x^3+7-7}\\&=\sqrt[3]{x^3}\\&=(x^3)^{\frac{1}{3}\\&=x^{\frac{3}{3}\\&=x^1\\&=x\end{aligned}[/tex]

Hence proving that the functions are inverses by showing that f(g(x))= x and g(f(x)) = x.

The answer to this question is -12x+20

The indicated side of the triangle of side a = 14 and side b =12.12.

The concept that will be used here is trigonometry. Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

From the triangle, of the side a which is the hypothenus:

sin(θ)=opposite/hypothenus

but the angle (θ)

sin30= 7/hypothenus

hypothenus *sin30=7

hypothenus=7/sin30

hypothenus =  a=14

Then we can do that For b:

cos(θ)=b/hypothenus

but hypothenus =14

cos30= b/14

b=14*cos30

b= 12.12

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complete question:

Find the indicated side of the

triangle.

a

30°

b

b = [?][]

A ratio scale is used for measurements that have both a meaningful zero point and also an equal interval between each point. An ordinal scale is used for measurements that rank order items from highest to lowest. A nominal scale is used for measurements that have categories without any order. An interval scale is used for measurements that have an equal interval between each point but do not have a meaningful zero point.

A ratio scale is used for measurements that have both a meaningful zero point and also an equal interval between each point. It is often used for measurements that involve numbers, such as temperature or length. An ordinal scale is used for measurements that rank order items from highest to lowest. This type of measurement can be used to classify student performance on an exam, such as with letter grades (A, B, C, D, and E). A nominal scale is used for measurements that have categories without any order. This is typically used for measurements that involve assigning names or labels to categories, such as gender or ethnicity. An interval scale is used for measurements that have an equal interval between each point but do not have a meaningful zero point. This type of measurement is often used for measurements that involve numbers, such as temperature or time. In this example of classifying student performance on an exam, the ordinal scale is the most appropriate measurement to use.

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The equation is incorrectly written by the student to find the third side of the triangle.

The right triangle states that if one of the angles of a triangle is a right angle - 90º, the triangle is called a right-angled triangle or a right triangle.

(Hypotenuse)² = (Base)² + (Altitude)²

If the two sides are right angle triangle is 5 units and 13 units and the equation is  5²+13²=c² then the value of c is

c=√25+169

c=13.92 and 13.92 is not an integer number.

so, the equation written by the student to find the third side is incorrect.

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The differential equation that best models the growth rate of the rabbit population with respect to time t, where k is a constant is option D) [tex]\frac{dP}{dT}=KP(2400-P)[/tex].

A differential equation is an equation that relates a function and its derivatives to some independent variables. The solution to a differential equation is a function that satisfies the equation and is often used to model physical processes.

Differential equations come in many forms, including ordinary differential equations (ODEs) and partial differential equations (PDEs).

For the population in function of the time, is:

[tex]\frac{dP}{dT}[/tex]

The population P of rabbits on a small island grows at a rate that is jointly proportional to the size of the rabbit population and the difference between the rabbit population and the carrying capacity of the population

Carrying capacity is 2400.

This means that the differential equation is kP(size of the population multiplied by the constant) multiplied by 2400 - P(difference between the population and the carrying capacity).

=> [tex]\frac{dP}{dT}=KP(2400-P)[/tex]

Therefore, The differential equation that best models the growth rate of the rabbit population with respect to time t, where k is a constant is option D) [tex]\frac{dP}{dT}=KP(2400-P)[/tex].

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The value of the angles that are in the triangle will be 97°, 51° and 32°.

The first thing to note before solving the question is that the sum of the total angles that are in a triangle is 180°.

In this case, it should be noted that the angles that are given are represented by variables. Therefore, we'll add them together and equate them to 180°. This will be:

18x + 7 + 8x + 11 + 6x + 2 = 180

32x + 20 = 180

Collect the like terms

32x = 180 - 20

32x = 160

Divide

x = 160 / 32

x = 5

First angle = 18x + 7

= 18(5) + 7

= 97°

Second angle = 8x + 11

= 8(5) + 11

= 51°

Third angle = 6x + 2

= 6(5) + 2

= 32°

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For a positive angle, the rotation from the initial side to the terminal side takes place in a counter clockwise where as for a negative angle, the rotation takes place in a clockwise.

In math the term angle is defined as a figure in which two rays emerge from a common point and this is called the vertex of the angle and the two rays forming the angle are called its arms or sides.

Here we have to know that the angle which is greater than 180 degrees but less than 360 degrees is called a reflex angle.

Here we need to find the missing term in the given statement.

According to the definition of angle we have know that the rotation is measured from the initial side to the terminal side of the angle.

If it has Positive angles result from counterclockwise rotation, and negative angles result from clockwise rotation.

Here we have know that the angle with its initial side on the x‐axis is said to be in standard position.

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If the terminal point determined by t is in the given quadrant.sin(t), cos(t);  sin(t)= -cos(t) in Quadrant II.

In Quadrant II, the sine function is positive and the cosine function is negative. The sine and cosine functions are related by the Pythagorean identity, which states that sin^2(t) + cos^2(t) = 1.

Since the sine is positive and the cosine is negative in Quadrant II, we can square the sine function and subtract it from 1 to get:

1 - sin^2(t) = cos^2(t)

We can then take the square root of both sides to get:

cos(t) = sqrt(1 - sin^2(t))

And since the cosine is negative in Quadrant II, we can then multiply the equation by -1 to get:

sin(t) = -cos(t)

This equation is only valid in Quadrant II.

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False. A persuasive speech is a type of public speaking that attempts to convince the audience to adopt a certain viewpoint or take a specific action.

While there are often competing perspectives on issues, a persuasive speech is not the most appropriate way to address them. Instead, a better approach to discussing issues with competing perspectives is to use an informative speech. An informative speech provides an unbiased overview of the issue, presenting both sides fairly and objectively. This allows the audience to develop their own opinion on the matter based on the facts presented. Although a persuasive speech may be used to present a particular point of view, informative speeches are the best tool for discussing issues with multiple perspectives.

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The equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 is Y= 11/14 xz^2.

The concept that will be used here is variation.

since Y varies jointly with respect to z^2 and x  the we will introduce K which is the proportionality constant, then we have:

Y= Kxz^2.

The we can introduce Y, x and z  to solve for the single unknown and have the answer for the equation of variation.

231=K (6) (7^2)

231=6*49*K

231=(K*294)

231/294=K.

K = 11/14

We can  have Y= 11/14 xz^2 which is the equation of variation.

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complete question:

Find an equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 the equation of varation is y

He travels 2.5 times as farther on Monday than on Tuesday.

The ratio between the distances is obtained applying the proportions in the context of this problem, as the Monday's distance is divided by the Tuesday's distance.

It gives how much farther he traveled on Monday than on Tuesday.

Then the ratio is given as follows:

(5/6)/(1/3) = 15/6 = 2.5.

(the ratio between two amounts is obtained dividing the two amounts).

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The answer are assuming the information provided, such as cost per visit, co-payments, admission charge etc . The total cost of the Franklin family is $1,865 + $3,650 + $22,025 = $27,540.

Sharon Wilson

a. The amount she paid for the deductible is $2,000.

b. In total co-payments, she paid $9 * $35 + $10 * $50 + $15 * $95 + $2 * $5 + $3 * $10 = $1,085 for physician and specialist visits, physical therapy and pharmacy co-payments.

c. In hospital charges, she paid $240 + $54,860 = $55,100.

d. In total costs, she paid $2,000 + $1,085 + $55,100 = $58,185.

The Franklin family

a. They paid $17 * $75 + $9 * $100 + $4 * $90 = $1,865 for physician and specialist visits and physical therapy.

b. They paid $2 * $1,500 + $350 = $3,650 for emergency room visits and ambulance fees.

c. They paid $350 + $21,675 = $22,025 in hospital charges.

d. The total cost of the Franklin family is $1,865 + $3,650 + $22,025 = $27,540.

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The required statistical parameters has been computed as follows:

Range = 17.

Standard deviation, SD = 6.87.

Mathematically, the range of a data set can be calculated by using this formula;

Range = Highest number - Lowest number

Range = 25 - 8

Range = 17.

Mathematically, the mean for these set of data would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 11 + 8 + 5 + 11 + 25

F(x) = 60.

Mean = 60/5

Mean = 12

Next, we would calculate the standard deviation by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × (11 - 12)² + (8 - 12)² + (5 - 12)² + (11 - 12)² + (25 - 12)²)

SD = √(1/5 × (1 + 16 + 49 + 1 + 169)

SD = √(1/5 × 236)

Standard deviation, SD = 6.87.

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The percentage increase in the average price of the piano is 40%.

What is the percentage increase?

To calculate the percentage increase, we use the following formula:

Percentage increase = (New value - Old value) / Old value x 100

In this case, the old value is the average price of the piano in 1991 ($12,500), and the new value is the average price of the piano in 2013 ($17,500). So, we can substitute these values into the formula:

Percentage increase = (17,500 - 12,500) / 12,500 x 100 = 40%

Hence, the percentage increase in the average price of the piano is 40%.

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Based on proportion, the amount of investment to have an annual interest of $150 at a 5% annual rate is $3,000.

The annual interest is the amount that is paid or received for accepting or giving credit.

The annual interest can be computed as the product of the annual percentage rate and the principal.

Where information for the interest rate and amount is available, the principal is the reciprocal of the interest and rate.

The annual interest rate = 5%

The annual interest (in dollars) = $150

Proportionately, $150 = 5%; therefore, 100%  of $150 = $3,000 ($150/5%)

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The area of the parallelogram is equal to: D. 4 over 25 square foot.

Mathematically, the area of a parallelogram can be calculated by using this formula:

Area of a parallelogram = b × h

Where:

Based on the information provided above, the actual base of the parallelogram is given by:

Actual base of parallelogram = 3/5 - 1/5

Actual base of parallelogram = 2/5 foot.

Substituting the given parameters into the area of a parallelogram formula, we have the following;

Area of a parallelogram = 2/5 × 2/5

Area of a parallelogram = 4/25 square foot.

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Answer:

C. [tex]f(0)=f(2)[/tex]

Step-by-step explanation:

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

The function is not differentiable over [0, 2]. Therefore, the option B is the correct answer.

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

The given function is f(x)=x³/3 over [0, 2].

Here, f(0)= 2 and f(2)=2. Hence, according to the Rolle's theorem there should be at least one x for which f'(x)=0.

Now, f'(x)= 3x²/3

0=3x²/3

3x²=0

x²=0

x=0

Therefore, the option B is the correct answer.

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The simple interest rate for Mikhail's investment to grow to $11,500.00 in 20 years is solved to be 10.13%

The rate for the simple interest tis calculated using the formula for simple interest.

The formula is stated as

Simple interest = Principal *  time *  rate / 100

In the problem the give data include

principal = $3,800.00

rate = ?

time = 20 years

simple interest =  $11,500.00 - $3,800.00 = $7700

plugging in the values

Simple interest = Principal *  time *  rate / 100

7700 = 3800 * 20 * r / 100

7700 * 100 = 3800 * 20 * r

770 000 / (3800 * 20 ) = r

r = 10.13%

The interest rate is 10.13%

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The percent relative average deviation for the data set is 0.30%.

((20.96 - 20.89) + (20.85 - 20.89) + (20.92 - 20.89)) / 3 / 20.89 * 100 = 0.30%

The percent relative average deviation for the given data set can be calculated by first finding the absolute differences between each value and the mean (20.89) then adding those differences together. Once the differences are added, divide that by the mean and multiply by 100. This will give you the percent relative average deviation, which in this case is 0.30%.

The percent relative average deviation for the data set is 0.30%.

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