Madame Pickney has a rather extensive art collection and the overall value of her collection has been increasing each year. Three years ago, her collection was worth $600,000. Two years ago, the value of the collection was $690,000 and last year, the collection was valued at $793,500.

Assume that the rate at which Madame Pickney’s art collection’s value increase remains the same as it has been for the last three years. The value of the art collection can be represented by a geometric sequence. The value of the collection three years ago is considered the first term in the sequence.

What explicit rule can be used to determine the value of her art collection n years after that?

Answer:

(7, - 4) and r = 7

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x - 7)² + (y + 4)² = 49 ← is in standard form

with (h, k) = (7, - 4 ) and r = [tex]\sqrt{49}[/tex] = 7

Answer:

-0.00348

Step-by-step explanation:

x          y           xy        [tex]x^2[/tex]                        [tex]y^2[/tex]

0        8            0             0                      64

1        7.5         7.5           1                  56.25    

2        6          12            4                    36

2       5.5          11            4                   30.25

3       5.5          16.5        9                   30.25

3        4            12            9                     16

4       3             12           16                     9

5       3             15           25                   9

6      2.5         15            36                  6.25

Now [tex]\sum x=0+1+2+2+3+3+4+5+6=26[/tex]

[tex]\sum y=8+7.5+6+5.5+5.5+4+3+3+2.5=45[/tex]

[tex]\sum (xy)=0+7.5+12+11+16.5+12+12+15+15=101[/tex]

[tex]\sum x^2=0+1+4+4+9+9+16+25+36=104[/tex]

[tex]\sum y^2=64+56.25+36+30.25+30.25+16+9+9+6.25=257[/tex]

N = number of pairs of scores = 9

Formula :[tex]r =\frac{N\sum(xy)-\sum x \sum y}{(N \sum x^2 -(\sum x)^2)(N \sum y^2 -(\sum y)^2)}[/tex]

Substitute the values.

[tex]r =\frac{9(101)-(26 \times 45)}{(9 (104) -(26)^2)(9(257) -(45)^2)}[/tex]

[tex]r =-0.00348[/tex]

Hence the correlation coefficient is -0.00348

The value of Correlation coefficient is -0.00348.

A correlation coefficient denotes the strength of the relation between two variables of a function.

The formula for correlation coefficient is

[tex]\rm r = \dfrac{ N \sum (xy) - \sum x \sum y}{(N \sum x^2- (\sum x)^2)(N\sum y^2 - (\sum y)^2}[/tex]

The data is

x y

0 8

1 7.5

2 6

2 5.5

3 5.5

3 4

4 3

5 3

6 2.5

the value of ∑x = 26

∑y = 45

∑(xy) = 101

∑x² = 104

∑y² = 257

N =  Total frequency = 9

The value of r is obtained by substitution of value in the equation.

r = -0.00348

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Answer:

[tex]\boxed{70^\circ}[/tex]

Step-by-step explanation:

Step 1. Calculate θ

[tex]\begin{array}{rcll}70^{\circ} + \theta + 60^{\circ} & = & 180^{\circ} & \text{Angles of straight line}\\130^{^{\circ}} + \theta & = & 180^{\circ}} & \\\theta & = & 50^{\circ} & \\\end{array}[/tex]

Step 2. Calculate x

[tex]\begin{array}{rcll}60^{\circ} + \theta + x & = & 180^{\circ} & \text{Interior angles of triangle}\\60^{\circ} + 50^{\circ} + x & = & 180^{\circ} &\\110^{^{\circ}} + x& = & 180^{\circ} & \\\\x & = & \boxed{70^\circ} & \\\end{array}[/tex]

Answer:

25

Step-by-step explanation:

The book is 420 pages long and he reads 45 pages so he has 375 pages left.

The will read equal amounts during the next 15 days so 375 ÷ 15 = 25

George reads 45 pages each day

According to the problem,

Number of pages left after reading 45 pages = (420 - 45) = 375

So number of pages he read per day = 375/15 = 25

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ANSWER

B. 24 sq. units.

EXPLANATION

The area of a triangle is calculated using the formula:

[tex]Area = \frac{1}{2} \times AB \times BC[/tex]

From the graph ,

AB=3--3=6 units.

BC=3--5=8 units

We substitute the values into the formula to get,

[tex]Area = \frac{1}{2} \times 6 \times 8 = 24sq. \: units[/tex]

The correct answer is B

Answer:

A)SAS

Step-by-step explanation:

The tick marks represent which sides of the triangles are congruent, while the arc represents which angles are congruent.

Since the arc is in between the sides that are congruent therefore the postulate is Side Angle Side

Without visual or informational context, the congruence criteria between the pairs of triangles cannot be determined. It's essential to know specific details about the triangles to apply congruence criteria like Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Angle-Angle-Side (AAS). However, with no further details, the answer is 'D. None'.

To determine which criterion for triangle congruence can be used to prove that the pair of triangles are equal, we first need to examine the triangles. SAS refers to Side-Angle-Side, which is when two sides and the included angle of one triangle is congruent to two sides and the included angle of another triangle. ASA refers to Angle-Side-Angle, which is when two angles and the included side of one triangle is congruent to two angles and the included side of another triangle. AAS refers to Angle-Angle-Side, which is when two angles and a non-included side of one triangle is congruent to two angles and a non-included side of another triangle. So, without a visual or further information about the triangles, we cannot directly apply any particular congruence criteria and the answer would be 'D. none'. However, with more information, the pair of triangles can possibly be proven congruent using either SAS, ASA, or AAS methods.

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Answer:

Step-by-step explanation:

All other things being equal, spinner A is fine. It is a fair spinner.

Spinner B is not fair. Players 1 and 3 have only 1 number each. Player 2 on the other hand, has 2 numbers that work for him. If player 2 puts in two dollars and players 1 and 3 one dollar each, that should even up the odds. Now you want it just to be fair. So I think player 2 has to put up 2 dollars and players 1 and 3 each put up one. The pot is 4 dollars each time it is played.

Spinner 3 is not fair either. Player one has 2 chances. Player 2 has 3 chances and player 3 has but one chance. There are 6 chances in all. Player 1 should put up 2 dollars to play player 1 should put up 3 dollars and player 1 should put up 1 dollar.

The answer to this question is:

y = -2x - 1

Answer:

all but the second statement are correct

Step-by-step explanation:

The n roots of unity are evenly spaced around a circle of radius 1 in the complex plane. One of the roots is always 1. If n is even, -1 will also be a root.

Answer:

The correct answer option is ST.

Step-by-step explanation:

We are given a figure of a right angled triangle and we are to determine whether which of the given segments is the projection of QT on RT.

We know that:

QT = QS + ST

Therefore, on RT, ST is the projection of QT since it comes mid way from Q to T.

So the correct answer option is ST.

Answer:

ST is the projection of QT on RT

Step-by-step explanation:

To Find : What segment is the projection of QT on RT?

Solution:

We are supposed to find the projection of QT

In the projection

We draw a perpendicular on RT with point Q

So, Perpendicular on RT is QS

So, ST is the projection of QT on RT

So, Option B is true

Hence ST is the projection of QT on RT

The r value is a number between -1 and +1.

For a negative value, the closer to -1 it would be a strong negative, if it is closer to 0, it would be a strong negative.

-0.31 is closer to 0 than -1, so it would have a strong negative association.

Answer:

The current at t = 0 is

[tex]I (0) = 2[/tex] units of current

Step-by-step explanation:

If the current flowing through an electric circuit is defined as the derivative of the charge as a function of time and we have the equation of the charge as a function of time, then, to find the equation of the current, we derive the equation of the charge.

[tex]q (t) = 3t ^ 2 + 2t-5[/tex]

[tex]\frac{dq(t)}{dt} = 3 (2) t ^ {2-1} +2t ^ {1-1} -0[/tex]

Simplifying the expression we have:

[tex]\frac{dq(t)}{dt} = 6t + 2t ^0\\\\\frac{dq(t)}{dt} = 6t + 2 = I (t)[/tex]

Finally, the equation that defines the current of this circuit as a function of time is:

[tex]I (t) = 6t +2[/tex]

Now to find the current at t = 0 we make [tex]I (t = 0)[/tex]

[tex]I (0) = 6 * 0 +2[/tex]

[tex]I (0) = 2[/tex] units of current

Answer:

g(x) has an axis of symmetry at x = 3.

g(x) is shifted right 3 units from the graph of f(x)

g(x) is shifted up 4 units from the graph of f(x).

Step-by-step explanation:

The parent function is:

[tex]f(x)=x^2[/tex]

The transformed function is [tex]g(x)=-x^2+6x-5[/tex].

This new function can be rewritten in the vertex form as:

[tex]g(x)=-(x-3)^2+4[/tex]

This function is obtained by shifting the parent function 3 units right and 4 units up.

The axis of symmetry is x=3;(x=h) and h=3.

There is no horizontal stretch or compression.

The new function is however reflected in the x-axis

Step-by-step explanation:

on edge its A,C,D :)

Answer:

  97π m² ≈ 304.7 m²

Step-by-step explanation:

The area of a circle is given by the formula ...

  A = πr²

The sum of the areas of the two circles is ...

  A = π(9 m)² + π(4 m)² = π(81 +16) m²

  = 97π m² ≈ 304.7 m²

Answer: Option D

Step-by-step explanation:

You know that the ratio between the radii of the two sphere is 3:5. Knowing this fact, you can calculate the ratio of their volume with this procedure:

[tex]ratio\ volume=\frac{3^3}{5^3}[/tex]

You need to remember that:

[tex]a^3=a*a*a[/tex]

 Then, you can rewrite it as:

[tex]ratio\ volume=\frac{3*3*3}{5*5*5}[/tex]

Finally, you get the the ratio of the volumes of the spheres is:

[tex]ratio\ volume=\frac{27}{125}[/tex] or 27:125

This matches with the option D.

Answer:

The ratio of their volumes is 27 : 125

Step-by-step explanation:

Points to remember

Volume of sphere V = 4/3(πr³)

Where r is the radius of sphere

To find the ratio of volume of spheres

It is given that,  the ratio between the radii of the two sphere is 3:5

V₁ =  4/3(πr₁³)  =  4/3(π3³) and

V₂ =  4/3(πr₂³) =  4/3(π5³)

V₁/V₂ = 4/3(π3³)/4/3(π5³)

 = 3³/5³ = 27/125

Therefore  the ratio of their volumes = 27 : 125

First we pick the equation. Let's say we pick first one. From it we express y.

[tex]-5x+y=-2\Longrightarrow y=-2+5x[/tex]

Then we use this y and plug it in instead of y in the second equation.

[tex]-3x+6(-2+5x)=-12[/tex]

Now just solve for x.

[tex]

-3x-12+30x=-12 \\

-3x=-30x \\

\underline{x=10}

[/tex]

We plug this x in the first equation.

[tex]-5\cdot10+y=-2[/tex]

And solve for y.

[tex]

-50+y=-2 \\

\underline{y=48}

[/tex]

So the solution to the equation is geometrically a point P which lies on the intersection of the two lines.

[tex]\boxed{P(10,48)}[/tex]

Hope this helps.

r3t40

The area of a circle is

[tex]a = r {}^{2} \pi[/tex]

So we get

[tex]a = 2.5 {}^{2} \pi[/tex]

so we get 19.6 rounded to the nearest tenth

Now we subtract that from the area of the square which is 25

We get 5.4

So the answer shoild be 5.4ft

Hopefully this is correct and helps you!

Answer:

5.4 ft²

Step-by-step explanation:

The area of the yellow region = area of square - area of circle

area of square = 5² = 25

note that the diameter of the circle = 5, thus radius = 2.5

area of circle = π × 2.5² = 6.25π

yellow region = 25 - 6.25π ≈ 5.4 ft²

Answer:

okay

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the equation, 72t represents the initial upwards velocity and 5 represents the initial launching height.  The leading term represents the pull of gravity on the object in the English system of measurement.

So the first question says the initial height is 5 feet.  TRUE

The second question says the initial vertical velocity is -72.  FALSE (it's positive 72 ft/sec)

The third question says that the object will hit the ground after approximately 4.57 seconds.  TRUE.  Find this by setting the h(t) on the left equal to 0, since this is the height at any time during the flight.  When h(t) = 0, that means that there is NO height, which means the object is on the ground.  Set the equation equal to 0 and factor to find t.  Putting that into the quadratic formula gives you t values of -.068 and 4.57.  Since the 2 things in math that will NEVER EVER be negative are distances and time, we can safely disregard the negative t value and go with t = 4.57.

The fourth question says that after t = 3 seconds, the object is 173 feet high.  FALSE.  Find this by subbing in a 3 for every t in the equation.

[tex]h(3)=-16(3)^2+72(3)+5[/tex]

This gives you that h(3) = 77 feet

The last question says that at t = 0, h(t) = 0.  FALSE again.  Sub in a 0 for every t in the equation, and you get h(0) = 5, which is the initial launching height.

Answer:

The initial height is 5 feet.

The object will hit the ground after approximately 4.57 seconds.

A & C

Step-by-step explanation

An object is launched into the air. The projectile motion of the object can be modeled using the function h(t) = -16t^2 + 72t + 5, where t is the time in seconds since the launch and h(t) represents the height in feet of the object after t seconds

General equation is

V_0 is the initial velocity

h_0 is the initial height

From the given equation , the initial height is 5 feet

Initial velocity is +72 feet / sec

When the onbject hits the ground, the height becomes 0

So we plug in 0 for h(t) and solve for t

USe quadratic formula to solve for t

a=-16, b= 72, c= 5

t= -0.06  and t= 4.568

The object will hit the ground after approximately 4.57 seconds.

To find out the height after 3 seconds, plug in 3 for t

At t=0 , h(0) = 5

Answer:

the slope is 1/2

Work:

if the x-coordinate is two times the y-coordinate, that means you are going up one over two each time

slope= y2-y1/x2-x1

so you can pick two points, like (2, 1) and (4,2) and use the formula

slope= 2-1/4-2= 1/2

Answer:

a. an = -1 • 4^(n - 1)

Step-by-step explanation:

It's easy see that each term is multiplied by 4 to get the next term, so the common ratio will be 4, that reduces the choices to answers A and B (since C and D use -1 as common ratio).  Also, normally a geometric progression uses "n-1", so we'll first try with A to see if it works.

a1 = (-1) * 4^0 = -1 * 1 = -1

a2 = (-1) * 4^1 = -1 * 4 = -4

a3 = (-1) * 4^2 = -1 * 16 = -16

Yes, it works... so the answer is an = -1 • 4^(n - 1)

A relative minimum = −36 , relative maximum = 64

Answer:

A

Step-by-step explanation:

The relative minimum is where the curve changes directions from down to up.  The relative maximum is where the curve changes direction from up to down.

In the interval [-4, 4], there are two relative minimums: y=-36.  And there is one relative maximum: y=64.

Answer A.

Answer:

132 deg

Step-by-step explanation:

from diagram, if lines m and n are parallel, then angle 3 = angle 7 and angle 4 = 132deg

The measure of angle 4 depends on its relationship to other angles in the diagram. If angle 4 is an alternate interior angle to another angle whose measure we know, it would share that measure.

To find the measure of angle 4 given that lines m and n are parallel, we need to understand a concept in geometry called alternate interior angles. According to this concept, when a line (called a transversal) intersects two parallel lines, the pairs of alternate interior angles it forms are equal. So, if angle 4 is an alternate interior angle to another angle whose measure we know, we can say that the measure of angle 4 is equal to that angle. Therefore, without knowing the measure of the corresponding angle, we can't provide a definitive measure for angle 4.

To make this more concrete, let's imagine we have a situation where lines m and n are parallel and line t is a transversal. We know the measure of angle 3 (on line m and intersected by t) is 75 degrees. If angle 4 is on line n and forms a Z shape with angle 3 (making them alternate interior angles), the measure of angle 4 would also be 75 degrees.

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Answer:

The Answer is multiple choice and the answer is B. Only B.

Step-by-step explanation:

The Answer is multiple choice and the answer is B.

We have given that,

St. Louis, Missouri, and Washington, D.C.

Have very similar latitudes. (Latitude measures how far north or south a place is, which in turn affects the temperature.)

The latitude is specified by degrees, starting from 0° and ending up with 90° to both sides of the equator, making latitudes Northern and Southern.

The box plots below show the daily high temperatures (in degrees Celsius) that were recorded during July 201320132013 in each city.

The pieces of the information that can be gathered from these box plots are option is B.

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Answer:

helloooooooooooooooooooo

Answer:

52

Step-by-step explanation:

add add add add add add adddaddd addda

The inscribed angle is half that of the arc it comprises. The measure of both the angle is 52°.

we know that the inscribed angle is half that of the arc it comprises.

Here, the arc that the inscribed angles comprise is the same.

2(3m+2)° = (4m+20)°

Solve for m

6m + 4 = 4m + 20

6m - 4m = 20 - 4

2m = 16

m = 8

To find the measure of the angle

(4m+20)°= 4(8) + 20 = 52°

2(3m+2)° = 2(26) = 52

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I think that the first choice is the correct one

Answer:

Step-by-step explanation:

2

With 6 unit cubes, it is possible to form 4 distinct rectangular prisms: 1x1x6, 1x2x3, 1x3x2, and 2x3x1.

The subject here is combinatorial mathematics focusing specifically on the construction of geometric shapes with a limited number of unit cubes. With 6 unit cubes, Donald can make 4 different rectangular prisms:1x1x6, 1x2x3, 1x3x2, and 2x3x1, each dimension representing length, width, and height in units. Here, the number of ways to arrange the cubes depends on unique combination of dimensions that respect the given total volume (i.e., number of unit cubes), which is 6 in this case.

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Answer:

4,810

Step-by-step explanation:

$10 per ticket times 741 people (10 * 741) is 7,410, then subtract the cost to produce the play, 7,410 - 2600 = 4,810.