The following data includes the year, make, model, mileage (in thousands of miles) and asking price (in US dollars) for each of 13 used Honda Odyssey minivans. The data was collected from the Web site of the Seattle P-I on April 25, 2005.
year make model mileage price
2004 Honda Odyssey EXL 20 26900
2004 Honda Odyssey EX 21 23000
2002 Honda Odyssey 33 17500
2002 Honda Odyssey 41 18999
2001 Honda Odyssey EX 43 17200
2001 Honda Odyssey EX 67 18995
2000 Honda Odyssey LX 46 13900
2000 Honda Odyssey EX 72 15250
2000 Honda Odyssey EX 82 13200
2000 Honda Odyssey 99 11000
1999 Honda Odyssey 71 13900
1998 Honda Odyssey 85 8350
1995 Honda Odyssey EX 100 5800
Compute the correlation between age (in years) and price for these minivans. (Assume the correlation conditions have been satisfied and round your answer to the nearest 0.001.)

The instantaneous rate of change of a function at a point is given by the derivative of the function at that point.

The instantaneous rate of change of a function at a particular point x is equal to its derivative at that point. To find the derivative of the function g(x) = 3/x, we can use differentiation rules.

the function g(x) = 3/x describes the relationship between x and 3/x. The derivative of this function, which is -3/x^2, gives us the instantaneous rate of change at any given value of x.

The derivative of g(x) is given by:

d/dx (3/x) = -3/x^2

The derivative at a given x tells us exactly how quickly the value of the function is increasing at that particular x.

So, the instantaneous rate of change of g(x) at a point x is given by -3/x^2.

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Quadrilateral ABCD is congruent to quadrilateral A'B'C'D'. Therefore, the correct answer option is: a. Congruent.

In Mathematics, a transformation can be defined as the movement of a point from its original (actual) position to a final (new) location such as the following:

In Mathematics, a translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

In conclusion, we can reasonably infer and logically deduce that quadrilateral ABCD and quadrilateral A'B'C'D' are congruent because quadrilateral ABCD was translated to form quadrilateral A'B'C'D'.

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Complete Question:

Fill in the blank in the sentence given below.

Quadrilateral ABCD is _____ to quadrilateral A'B'C'D'.

a. Congruent

b. Similar

c. Neither

Answer:0.794

Step-by-step explanation:

Answer:

the answer would be 0.794. but hundredths would be 0.79

hope this helped!

Step-by-step explanation:

The length of the third side of the given right triangle is 6.32.

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”. The formula for the same is;

c² = a² + b², where a, b, c are sides of a right triangle.

Given that, a right triangle, with two sides 7 and 3, since, the figure is unavailable, let us assume that 7 is the hypotenuse and 3 is the other side, let the unknown side be x,

According to the Pythagoras theorem,

7² = 3² + x²

x² = 7² - 3²

x² = 49-9

x² = 40

x = √40

x = 6.32

Hence, the length of the third side of the given right triangle is 6.32.

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In this case, 2x - 2 < g(x) < x^2 + 2x - 3 for all x in some interval.

The Sandwich Theorem states that if f(x) < g(x) < h(x) for all x in an interval, then g must have a value that is equal to either f or h at some point in that interval.

In this case, 2x - 2 < g(x) < x^2 + 2x - 3 for all x in some interval.

Hence, there exists a constant c such that g(c) = x^2 + 2x - 3.

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Given that2x - 2 < g(x) < x^2 + 2x - 3, use the Sandwich Theorem to prove that there exists a constant c such that g(c) = x^2 + 2x - 3.

The equation of the profit function is P(x) = 269x - 4x^2 - 128

The profit function P(x) can be found by subtracting the cost function C(x) from the revenue function R(x), where R(x) = p * x:

So, we have

P(x) = R(x) - C(x)

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

P(x) = (285 - 4x) * x - (128 + 16x)

So, we have

P(x) = 285x - 4x^2 - 128 - 16x

Evaluate the like terms

P(x) = 269x - 4x^2 - 128

To find the profit for making and selling 3 million fans, we substitute x = 3 into the profit function P(x):

P(3) = 269(3) - 4(3)^2 - 128

P(3) = 643

For other number of fans, we have

P(5) = 269(5) - 4(5)^2 - 128

P(5) = 1117

P(9) = 269(9) - 4(9)^2 - 128

P(9) = 1969

P(12) = 269(12) - 4(12)^2 - 128

P(12) = 2524

Hence, the profits are 643, 1117, 1969 and 2524

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Answer: 20

Step-by-step explanation:

6 (1/2) + 17

3 + 17 = 20

Answer:

20

Step-by-step explanation:

6(1/2) + 17

6(1/2) = 3

3 + 17 = 20

JL is MK congruent by CPCT.

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Given that, a figure, in which JK ≅ ML, ∠ JKL ≅ ∠ MLK,

We need to prove, JL ≅ MK,

The proof of the same is follows;

     STATEMENT                                                                     REASON

1) JK ≅ ML                                                                                  Given

2) ∠ JKL ≅ ∠ MLK                                                                      Given

3) KL ≅ KL                                                                          Reflexive property

4) Δ JKL ≅ Δ MLK                                                                   By SSA rule

5) JL ≅ MK                                                                                By CPCT

Hence, we get JL is MK congruent by CPCT.

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Answer:

5/13 chance of getting blue marble

Step-by-step explanation:

5+6+2=13

5 blue marbles so

5/13

The probability of drawing two blue card is 1/16

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Probability = sample space / total outcome

The total number of cards = 12

number of blue cards = 3

Probability of drawing blue card = 3/12

= 1/4

Since the blue card is replaced,

the probability to draw blue card in the second draw is 3/12 = 1/4

probability of drawing two blue cards = 1/4× 1/4

= 1/16

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well, the actual cost of it was 12.5% of 45 less, hmmm what's 12.5% of 45?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{12.5\% of 45}}{\left( \cfrac{12.5}{100} \right)45} ~~ \approx ~~ 5.63~\hfill \stackrel{45~~ - ~~5.63}{\approx\text{\LARGE 39.37}}[/tex]

Answer:

Step-by-step explanation:

58

The linear equation that represents the given literal problem is  3x+12= 28.50 (letter D) and Ava pays $5.5 (letter B)  for each pumpkin.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=9x+5. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=9 and b=5.

The exercise presents two questions, before solving them, you should convert the given text information into equations.

Data question

     1) Question 1

     Here you should write a linear equation that represents the given problem. Thus, you can write

    3x+12= 28.50

    Since 3x represents the payment of pumpkins and the value 12 is the difference between the total of Ava´s money and the total cost of pumpkins.  

    Therefore, the answer to question 1 is the letter D ( 3x+12= 28.50)

   2) Question 2

As you know the equation that represents the problem, for solving this question you need to find the value of x.

    3x+12= 28.50

     3x=28.5-12

    3x=16.5

      x=16.5/3

      x=5.5 (letter B)

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Answer: x = 15

Step-by-step explanation:

Use the Pythagorean theorem

The factors of the quadratic function  p(x) is equal to

(x + 5 + √(65)/2)(x - 5 + √(65)/2).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, The zeros of the quadratic function p(x) = x² - 5x - 10 are,

(5 + √(65)/2, 5 - √(65)/2).

Therefore, The factors of p(x) = [x + (5 + √(65)/2)][x + (5 - √(65)/2)]

p(x) = (x + 5 + √(65)/2)(x - 5 + √(65)/2).

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Answer:

In order in which the boxes appear:

[tex]\boxed{a\sqrt{2}}[/tex]

[tex]\boxed{a\sqrt{2}}[/tex]

[tex]\boxed{a\sqrt{2}}[/tex]

Step-by-step explanation:

At any coordinate (x , y) the distance from the origin (0, 0) is computed by the distance (Pythagorean formula) as:

d = [tex]\sqrt{x^2+y^2}[/tex]

Since x = y = a for both ants, the distance is

[tex]d = \sqrt{a^2+a^2}\\\\d = \sqrt{2a^2}\\\\d = \sqrt{a^2}\cdot \sqrt{2}\\\\d = a\sqrt{2}[/tex]

It does not matter whether both coordinates are positive or both negative since we are taking the squares of the coordinates and distance is always positive

The required area of the given triangle is given as 15 cm².

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

To calculate the area of a triangle with its vertices A(2, 5), B(3, -1), and C(-2, -1),

Evaluate the absolute value of the expression 1/2
= 1/2|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|

Substitute the value in the above expression
= 1/2|2(-1 + 1) + 3(-1 - 5) -2(5 + 1)|
= 1/2[30]
= 15 cm²

Thus, the required area of the given triangle is given as 15 cm².

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The general form of the equation of the hyperbola with the given information is [tex]9x^2 - 16y^2 - 36x + 160y - 508 = 0[/tex]. The equation can be determined by first finding the center of the hyperbola, which is (2, 5), and the distance between the foci, which is 4.

The general form of the equation of a hyperbola can be determined from the given information. The vertices of the hyperbola are given as (-2, 5) and (6, 5). The foci of the hyperbola are given as (-3, 5) and (7, 5). The first step in finding the equation of the hyperbola is to determine the center of the hyperbola. The center of the hyperbola can be calculated by taking the average of the x-coordinates of the vertices and then the average of the y-coordinates of the vertices. The center of the hyperbola is then (2, 5). The distance between the foci of the hyperbola is 4. This distance can be calculated by subtracting the x-coordinates of the foci and then subtracting the y-coordinates of the foci. The standard equation for a hyperbola can then be formed by substituting the center coordinates and the distance between the foci into the equation. The resulting equation is [tex]9x^2 - 16y^2 - 36x + 160y - 508 = 0[/tex]. This equation is the general form of the equation of the hyperbola with the given

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Answer:

ksjsvsbsvsdjsjsbwbwbwbwushs

Hey, for this type of question, go on desmos it a calculator. but I hope this is right. Sorry if wrong

So Isaiah has a total of 6 gallons of paint and each bookcases takes 1/3 gallon. How many bookcases can he paint?

Alright to solve this problem, we can simply take the total gallons of paint Isaiah has and divide that by 1/3

So 6 divided by 1/3 should give us the answer.

But how do we divide fractions? Remember this useful tip for all throughout your school life when you don't have a calculator: Keep, Change, Flip

Keep the first fraction, change the sign to a multiplication sign, and flip the second fraction.

This should give us 6 x 3/1 or 3, which is 18.

Isiah will be able to paint 18 bookcases.

Hope this helped!

The advantages of bar charts over pie charts while graphing the given data are discussed below.

A bar chart or bar graph is a visual representation of categorical data that uses rectangular bars with heights or lengths proportional to the values they represent. The possibility of a bar plot, both vertical and horizontal, exists. Vertical bar graphs are also referred to as column charts.

A circular statistical image known as a pie chart uses slices to represent numerical proportions. Each slice's arc length in a pie chart varies depending on the amount it represents.

Any numbers can be chosen for the numeric value axis in a bar chart.

Pie charts can only be used if the sum of the various parts equals a meaningful whole because they are intended to illustrate how each portion contributes to the whole.

Hence bar chart is more advantageous over pie chart when more information is to be presented through charts.

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The height of the vase is 45 inches. To the nearest tenth of an inch, this is 45.0 inches.

A hyperbola is a type of conic section that is the result of intersecting a right circular cone with a plane that is perpendicular to one of its sides, and is oblique to the other. It is defined by two curves that are mirror images of each other and are each a set of all points such that the difference of their distances from two fixed points, called the foci, is a constant value.

A hyperbola can be represented in standard form as an equation, where the x and y terms are squared and the constant terms have opposite signs. It can also be graphed in the coordinate plane, where it appears as a set of two open curves, each going off to infinity in opposite directions.

The height of the vase can be found by using the formula for the height of a hyperbolic paraboloid, which is given by:

h = e × c × √(1 + (2a/c)²)

where h is the height of the vase, e is the eccentricity, a is the width at the narrowest point (4 inches), and c is the average width of the opening and base (6 inches).

Plugging in the values, we get:

h = 2.5 × 6 × sqrt(1 + (2 × 4 / 6)²)

h = 2.5 × 6 × sqrt(1 + (2 × 2)²)

h = 2.5 × 6 × sqrt(1 + 8)

h = 2.5 × 6 × sqrt(9)

h = 2.5 × 6 × 3

h = 45

The height of the vase is 45 inches. To the nearest tenth of an inch, this is 45.0 inches.

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The lowest score for the normally distribution with mean 72 and standard deviation 8 is equal to 82.

Mean of the normally distributed data 'μ' = 72

Standard deviation 'σ ' = 8

Lowest score with 10% ( 90percentile )

z = InvNorm(0.90)

 = 1.28

Let 'X' be the lowest score for the normal distribution

z = ( X - μ ) / σ

Substitute the values we get,

⇒ 1.28 = ( X - 72 ) / 8

⇒ X - 72 = 1.28 × 8

⇒ X = 10.24 + 72

⇒ X = 82.24

⇒ X = 82 ( round to an integer )

Therefore, the lowest score for normally distribution which will place manage on 90th percentile with given mean and standard deviation is equal to 82.

The above question is incomplete, the complete question is:

Scores on a management aptitude examination are normally distributed with a mean of 72 and a standard deviation of 8.we want to find the lowest score that will place a manager in the top 10% (90th percentile) of the distribution. Your answer is Please round to an integer number.

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The exact value of is x  [tex]e^{4}[/tex] - 6/5 and the value of x will be 9.720.

What is exponential?

The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

a) In(5x + 6) = 4 exact value decimal approximation XE

ln (5x+6) = [tex]e^{4}[/tex]

5x = [tex]e^{4}[/tex] - 6

x =  [tex]e^{4}[/tex] - 6/5

5x = e^-6 x = 5 (r) x = 9.720

Hence, The exact value of is x  [tex]e^{4}[/tex] - 6/5 and the value of x will be 9.720.

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a)  If the tank is initially full, it will take  14.31 min. long to  tank to empty

b) If the height of the water is initially 10 feet, it will take 1.67 min for the tank to empty.

For the first case, we  have the differential  equation governing the height of the water, where the volume of a cone  is  V= 1/3 πr^2h by the similar triangles  we can conclude that  what the  value  will be  for the height, the cone  shape will always have the same relation  with the  radius of the water r/h=8/20⟹r=2/5h⟹r^22=4/25h^2, so V= 4/75πh^3, we will  take the derivative of the  height  of with respect to time t

dV/dt=4/25πh2 dh/dt, now converting into inches  we get  :

dV/dt=−cAh√2gh=−3/5(π(1/6)^2)√64h=−24π/5⋅36 √h=−2π/15√h.

now adding  both the  equations of   dV/dt,

425πh^2dhdt=−2π15√h⟹dhdt=−56h−3/2.

since the tank is empty m  it will happen in at h=0, so for the value of t  we will solve for h(t). after  solving  this differential equation using  the separation of  variables : dh h^3/2=−5/6dt, after  integration of both sides, we get: 25h5/2=−5/6t+C0⟹h5/2=−25/12t+C, since  here the intial height is  20 feet , so h(0)=20, Therefore  20^5/2=−25/12(0)+C⟹C=20^5/2, so h(t)=(−25/12t+20^5/2)^2/5.so  when  h  will be 0 , then −25/12t+20^5/2=0⟺25/12t=205/2⟺t=12/25 20^5/2≃858.65 s=14.31 min.

For the second case, the relationship between the height and radius is different, here the angle between the side of the tank and the vertical is  30 degrees, and the ratio of the radius and height of the tank is √3:1, which is also the ratio of height and radius of the water.  

1/√3=r/h⟹r=h/√3⟹r^2=h^2/3.

V=1/3πr^2h=π/9h^3, to solve it  we need to for dVdt, to  find the height and  rate of  change of height :dV/dt=π/3h^2dhdt here c is 0.6 and Ah=1/9π, dVdt=−35⋅19π⋅8√h, adding up those equations we get dV/dt, we have   π/3h^2dh/dt=−8π/15√h⟹dh/dt=−8/5h^−3/2,  now apply the separation of variables:

h^3/2dh=−8/5dt⟹2/5h^5/2=−8/5t+C, here the initial was at t=0, h is 11, C will be 2/5 11^5/2, therefore h(t)=−8/5t+2/5 11^5/2, so the time when the tank is empty will be  0=−8/5t+2/5 11^5/2⟺85t=25 11^5/2⟺t=1/4 11^5/2= 100.33 s=1.67 min.

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Suppose water is leaking from a tank through a circular hole of area at its bottom. When water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to , where is an empirical constant.

A tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom.

a) Suppose the tank is high and has radius and the circular hole has radius . The differential equation governing the height h in feet of water leaking from a tank after t seconds is . In this model, friction and contraction of the water at the hole are taken into account with , and is taken to be . See the figure below. If the tank is initially full, how long will it take the tank to empty? (Round your answer to two decimal places.)

b) Suppose the tank has a vertex angle of and the circular hole has radius . Determine the differential equation governing the height h of water. Use and If the height of the water is initially , how long will it take the tank to empty? (Round your answer to two decimal places.)

The height of the school is given by the equation H = 13.274 m

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the height of the building be represented as ED = H

Let the distance of mirror from the building be CD = 11.15 m

The distance walked extra from the mirror CB = 1.05 m

The distance of Fawzia's eyes to the ground AB = 1.25 m

Now , let the triangles be represented as ΔABC and ΔCED ,

where both the triangles are similar and have a common angle

So , the corresponding sides of similar triangles are in the same ratio

And , ED / AB = CD / CB

Substituting the values in the equation , we get

ED / 1.25 = 11.15 / 1.05

Multiplying by 1.25 on both sides of the equation , we get

The height of the school building ED = ( 11.15 x 1.25 ) / 1.05

On simplifying the equation , we get

The height of the school building ED = 13.2738 m

Hence , the height of the school is 13.274 m

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Answer:x=8

Step-by-step explanation:

The interior angles of a triangle add up to 180 so

2x+39 + 2x+70 + x+31 = 180

2x + 2x +x=180-39-70-31

5x= 40

x=40/5

x=8

x+31 is in there because one of the int angles of the triangles is congruent with the angle of x+31

Answer:0.628571428571- or 63% and in fraction form it would be 5/8

Step-by-step explanation:

Answer: 22/35 (Result in decimals: 0.62)

Step-by-step explanation:

13/15 - 5/21

= 13 x 7/15 x 7 - 5 x 5/21 x 5

= 91/105 - 25/105

= 91 - 25/105

= 66/105

= 66 divided by 3 / 105 divided by 3

= 22/35