1. Find the sum of the first six terms of the geometric sequence for which a2 = 0.7 and a3 = 0.49.


A. Rewrite using radicals.


B. Rewrite using rational exponents.

the next two terms in the sequence would be 12 and 17.

Step-by-step explanation:

Answer:

188.33

Step-by-step explanation:

113 = .6n  Divide both sides by .6

188.33 = n  Rounded to the nearest hundredth.

Helping in the name of Jesus.

The mapping of the function f(x) given as 3x⁴ - 4x³ + 3x² - 5x - 3 is define at; -3, f(-3) = 390 and at 4, f(4) = 537

A function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers

For x = -3;

f(-3) = 3(-3)⁴ - 4(-3)³ + 3(-3)² - 5(-3) - 3

f(-3) = 3(81) + 4(27) + 3(9) + 15 - 3

f(-3) = 243 + 108 + 27 + 15 - 3

f(-3) = 390

For x = 4;

f(4) = 3(4)⁴ - 4(4)³ + 3(4)² - 5(4) - 3

f(4) = 3(256) - 4(64) + 3(16) - 20 - 3

f(4) = 768 - 256 + 48 - 20 - 3

f(4) = 537

Therefore, for the mapping of the function f(x) = 3x⁴ - 4x³ + 3x² - 5x - 3 for the values of x: -3 and 4 we have the results 390 and 537.

After the mathematical calculations, we can see that the value of z = 5 - 15i.

To simplify, let's square the complex number (2 - i):

[tex](2 - i)^2 = 2^2 - 2i + 2i - i^2 = 4 - 4i - 1 = 3 - 4i.[/tex]

Divide the complex number (7 - 4i) by (2 + i):

The approach we will take involves multiplying the top and bottom of the equation by the complex conjugate of the denominator.

[tex](7 - 4i) * (2 - i) / (2 + i) * (2 - i) = (14 - 7i - 8i + 4i^2) / (4 + 1) = (14 - 15i + 4(-1)) / 5[/tex]

= (10 - 15i) / 5

= 2 - 3i.

We have to minus 8i:

[tex](3 - 4i) + (2 - 3i) - 8i = 5 - 7i - 8i = 5 - 15i.[/tex]

Therefore, z = 5 - 15i.

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There will be no sugar left after the transfer.

Given are two containers in the shape of a rectangular prism and the second one is a composite solid of rectangular prism and a triangular prism,

We need to compare the volume of both prisms,

For the volume of the composite solid we will add the volume of both solids = 1/2 × base area × height + length × width × height

= 1/2 × 300 × 8 + 12 × 12 × 25

= 1200 + 3600

= 4800 cm³

Now the volume of the old container (rectangular prism - the blue one) = length × width × height = 30 × 20 × 8 = 4800 cm³

Since the volume of both old and new container is same, so there will be no sugar left after the transfer.

Hence there will be no sugar left after the transfer.

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After transformation, we will have the point as  (3, 5).  

A rotation is  described as a type of transformation which is a turn and that turns the figure in either a clockwise or counterclockwise direction.

The rotation does not alter the shape.

When we Rotate (4,-1) 90° anticlockwise centered at the origin yields the point (1, 4).

We next transform the point (1, 4) two units to the right and 1 unit up results in the point (3, 5).

We can also rotate 90° clockwise that would result in some different point on this coordinate system. We will also have some 2D figures like a triangle or a rectangle instead of a straight line

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Answer:

So 98 adult tickets were sold.

Step-by-step explanation:

Let's use a system of equations to solve the problem.

Let x be the number of child tickets sold and y be the number of adult tickets sold. Then we have:

x + y = 176 (equation 1)

5.10x + 8.20y = 1201.40 (equation 2)

We can solve for x by isolating y in equation 1 and substituting into equation 2:

y = 176 - x (from equation 1)

5.10x + 8.20(176 - x) = 1201.40 (substitute into equation 2)

5.10x + 1443.20 - 8.20x = 1201.40

-3.10x = -241.80

x = 78

Therefore, 78 child tickets were sold that day. We can find the number of adult tickets by substituting x into equation 1:

78 + y = 176

y = 98

So 98 adult tickets were sold.

Answer:

  8.68 cm²

Step-by-step explanation:

You want the increase in surface area of a box with length and width 13 cm and 8.7 cm when the height is increased from 30 cm by 0.2 cm.

The increase in area is effectively the lateral area of the prism whose length and width are the same, but whose height is 0.2 cm. That is ...

  A = Ph = 2(L+W)h

  A = 2(13 cm +8.7 cm)(0.2 cm) = 8.68 cm²

The surface area increases by 8.68 cm².

We can find the total area of the box with the different dimensions, then subtract the original area from the increased area.

  A = 2(LW +H(L+W))

  A1 = 2(13·8.7 +30(13 +8.7)) = 1528.2 cm²

  A2 = 2(13·8.7 +30.2(13 +8.7)) = 1536.88 cm²

The increase in area is 1536.88 -1528.2 = 8.68 cm².

We prefer the first solution, as it requires a lot less arithmetic.

<95141404393>

Answer:

76%

Step-by-step explanation:

57/75

(57 X 100)/ 75

5700/75

1900/25

76/1

76

It is not a polynomial function because polynomial functions have non-negative integer exponents, and the exponent in this function is -10, which is a negative integer.

The function f(x)=12x^-10 is a power function because it can be written in the form f(x)=kx^n where n is a negative integer. Specifically, this function can be written as f(x)=12/x^10.
Function f(x) = 12x^(-10), this function is a power function.
A power function has the form f(x) = kx^n, where k and n are constants. In this case, k = 12 and n = -10. Since the function fits the power function definition, it is a power function.
It is not a polynomial function because polynomial functions have non-negative integer exponents, and the exponent in this function is -10, which is a negative integer.

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It will take Adrian 16 full months to save enough money for the electric keyboard.

- Price of the keyboard (with tax) at Macelli's: $2,400
- Adrian's monthly savings: $150
We need to find how long it will take Adrian to save for the keyboard. To do this, we'll divide the total cost of the keyboard by his monthly savings and round up to the nearest full month.
Step 1: Divide the total cost by monthly savings.
Time (in months) = (Total Cost) / (Monthly Savings) = ($2,400) / ($150)
Step 2: Calculate the result.
Time (in months) = 16
So, it will take Adrian 16 full months to save enough money for the electric keyboard.

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The area of the trapezoid is 104 square yards

As given a table was made by Veronica which is in the shape of a trapezoid.

twice as long as the table's width

Let us find the area of the trapezoid by the given data and formula of trapezoid

The length of the bottom base is x= 16 yd.

Area A=(a+b)h/2

a=10 yd

b=16 yd

h =8 yd

Substitute the values of a, b and h in the area of trapezoid

Area =1/2(10+16)8

=208/2

=104 square yards

Hence, the area of the trapezoid is 104 square yards

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Answer: 149

Step-by-step explanation: 15 17 19 21

23 25 27 29 31 33 35 37 39 41

43 45 47 49 51 53 55 57 59 61

63 65 67 69 71 73 75 77 79 81

83 85 87 89 91 93 95 97 99 101

103 105 107 109 111 113 115 117 119 121

123 125 127 129 131 133 135 137 139 141

143 145 147 149 151 153 155 157 159 161

163 165 167 169 171 173 175 177 179 181

183 185 187 189 191 193 195 197 199 201

203 205 207 209 211 213 215 217 219 221

223 225 227 229 231 233 235 237 239 241

243 245 247 249 251 253 255 257 259 261

263 265 267 269 271 273 275 277 279 281

283 285 287 289 291 293 295 297 299 301

303 305 307 309 311 313 315 317 319 321

323 325 327 329 331 333

1) According to Denis' article "The Definition of Neotraditionism," his encounter with a painting by Maurice Denis himself.

2) In his book "Concerning the Spiritual in Art," Kandinsky expressed his belief that art should go beyond mere representation of the physical world and instead aim to express the spiritual and emotional aspects of human experience.

3) In Part II, About Painting, VI: The Language of Form and Color of "Concerning the Spiritual in Art," Kandinsky wrote: "Color is a power which directly influences the soul.

Denis was influenced to write the first non-objective statement because of the limitations of representational art.

1) According to Denis' article "The Definition of Neotraditionism," his encounter with a painting by Maurice Denis himself, which featured a landscape that was "no longer a transcription of nature, but a creation" (Denis, 1914), influenced him to write the first non-objective statement.

This painting by Denis challenged the traditional notions of art as mere representation of nature, and instead presented a new idea of art as a creative act in its own right.

2) In his book "Concerning the Spiritual in Art," Kandinsky expressed his belief that art should go beyond mere representation of the physical world and instead aim to express the spiritual and emotional aspects of human experience. He wrote that "the artist must be blind to distinction between 'recognized' or 'unrecognized' conventions of form, deaf to the transitory teaching and demands of his particular age.

He must watch only the trend of the inner need, and hearken to its words alone" (Kandinsky, 1977, p. 8). This suggests that Kandinsky was motivated by a desire to break away from the conventional artistic norms of his time and create something that was more true to his own personal vision and inner creative impulses.

3) In Part II, About Painting, VI: The Language of Form and Color of "Concerning the Spiritual in Art," Kandinsky wrote: "Color is a power which directly influences the soul. Color is the keyboard, the eyes are the hammers, the soul is the piano with many strings. The artist is the hand that plays, touching one key or another purposively, to cause vibrations in the soul" (Kandinsky, 1977, p. 72).

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The step function evaluated in x = 1.4 gives the outcome y = 1, thus, the correct option is the first one.

The step function, written as:

f(x) = [x]

Is a function that rounds down the value of x to the nearest whole number.

So, for any input that we give to that function, the output will be equal to the number before the decimal point.

If we evaluate this function in x = 1.4, then we will round to the number before the decimal point, thus the outcome is y = 1.

Then we will get:

f(1.4) = [1.4] = 1

The correct option will be the first one.

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[tex]6 + 3 = 9 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]

a) The equation representing the total area of the pool and the pool deck is: A = (x + 25)(x + 9).

b) The area equation in standard form is A = x² + 34x + 225.

c) The vertex form is A = (x + 17)²- 289

d) The x-intercepts is (-4, 0).

a) The equation representing the total area of the pool and the pool deck is: A = (x + 25)(x + 9).

b) Re-writing the area equation in standard form using the FOIL method:

A = x² + 9x + 25x + 225

A = x² + 34x + 225

c) Re-writing the equation from part b in vertex form by completing the square:

A = (x + 17)²- 289

d) The vertex of the parabola is (-17, -289).

The x-intercepts can be found by setting A = 0:

(x + 17)² - 289 = 0

(x + 17)² = 289

x + 17 = ±17

x = -34, 0 (x-intercepts)

The y-intercept is found by setting x = 0:

A = (0 + 17)² - 289

A = 0 (y-intercept)

e) The graph of the parabola is a downward-opening parabola with vertex (-17, -289).

f) In this problem, only positive values of x make sense because the dimensions of the pool and deck cannot be negative.

g) The point on the graph that shows a total area that includes the pool but not the pool deck is the vertex (-17, -289).

h) When x = 6 yards, the total area of the pool and deck can be calculated by substituting x = 6 into the equation:

A = (6 + 17)² - 289

A = 23² - 289

A = 529 - 289

A = 240 square yards

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the total number of posts needed is, 56

Since, we know that the area of the horse corral is 10,000 square feet.

So, it is a square corral, we can find the length of each side by taking the square root of the area, which is 100 feet.

Now, For the total number of posts needed, we need to calculate the perimeter of the corral.

Since there are four sides of equal length, the perimeter of the corral is 4 times the length of one side.

Therefore, the total perimeter is 400 feet.

Now, we need to find the number of posts needed.

We know that each post is placed 10 feet apart along the sides of the corral.

Since there are 4 sides, we need 3 intervals of 10 ft between each post, which gives us a total of 4 posts for every 30 feet of fencing.

Therefore, the total number of posts needed is,

= (400 / 30) x 4 + 4

= 56 posts.

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Step-by-step explanation:

it says in the headline here : "college".

really ???

this is basic triangle calculation.

the yellow (shaded) area is the total area of the large triangle minus the area of the small (white) triangle.

both area right-angled triangles, so their areas are simple :

leg1 × leg2 / 2

the area of the full large yellow triangle is therefore

31.6 × 33.1 / 2 = 522.98 in²

the area of the small white triangle is

17.1 × 17.9 / 2 = 153.045 in²

that means the shaded area alone is

522.98 - 153.045 = 369.935 in² ≈ 369.94 in²

The measures of each of the arcs are: 16. m(MN) = 72°; 17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 193°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°; 24. m(PRN) = 265°; 25. m(MQN) = 288°.

Recall that in a circle, the measure of an intercepted arc is always the same or equal to the measure of the central angle it subtends.

Therefore, we have:

16. m(MN) = 72° (based on the vertical angles and inscribed angle theorems).

17. arc NQR is an half circle, therefore:

m(NQR) = 180°

18. m(NQ) = 180 - 72 = 108°

19. m(MRP) = 180 + (180 - 72 - 95)

m(MRP) = 193°

20. m(QR) = 72°

21. m(MR) = 180 - 72 = 108°

22. m(QMR) = 360 - 72

m(QMR) = 288°

23. m(PQ) = 180 - 72 - 95

m(PQ) = 13°

24. m(PRN) = 360 - 95

m(PRN) = 265°

25. m(MQN) = 360 - 72

m(MQN) = 288°

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Answer:

29658

Step-by-step explanation:

N =  A (1 + increase) ^n

Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.

N = 28337 (1 + 0.0153)^3

= 28337 (1.0153)^3

= 29658 to nearest number

The value of x is given as follows:

x = 76º.

To obtain the value of x, we must consider that the sum of the internal angle measures of a triangle is of 180º.

The internal angles of the triangle in this problem are given as follows:

Considering that the sum of the measures is of 180º, the value of x is obtained as follows:

48 + 56 + x = 180

x = 180 - (48 + 56)

x = 76º.

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The axis of symmetry of the given quadratic function f(x) = -(x - 2)(x + 4) is x = -1.

Given the function in the question:

f(x) = -(x - 2)(x + 4)

To find the axis of symmetry, first expand  quadratic function f(x) = -(x - 2)(x + 4).

f(x) = -(x - 2)(x + 4)

f(x) = (-x + 2)(x + 4)

f(x) = -x(x + 4) + 2( x + 4 )

f(x) = -x² - 4x + 2x + 8

Collect and add like terms

f(x) = -x² - 2x + 8

To find the axis of symmetry, we can use the formula:

x = -b/2a

Where a = -1 and b = -2.

Substituting these values, we get:

x = -(-2) / 2(-1)

Simplify

x = 2 / -2

x = -1

Therefore, the the axis of symmetry is x = -1.

Option D) x = -1 is the correct answer.

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The calculated height of the prism​ is 5 inches

from the question, we have the following parameters that can be used in our computation:

Volume = 45 cubic inches

Base = square

The height of the prism​ is calculated as

Volume = Base length² * Height

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

Base length² * Height = 45

So, we have

Base length² * Height = 3² * 5

This means that

Base length = 3

Height = 5

Hence, the height of the prism​ is 5 inches

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An exponential equation that best fit the data above is [tex]y = 535.02(1.15)^x[/tex]

a = 535.02

b = 1.15.

In this scenario, the x-values (x) would be plotted on the x-axis of the scatter plot while the y-values (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the x-values (x) and y-values (y), the exponential equation and the correlation coefficient are given by:

[tex]y = 535.02(1.15)^x[/tex]

Correlation coefficient, r = 0.9973006 ≈ 1.0

In conclusion, we can logically deduce that there is a strong correlation between the data because the correlation coefficient (r) is is greater than 0.7;

0.7＜|r| ≤ 1.0   (strong correlation)

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The student's chances of answering all five questions correctly are 7/64.

This is an example of a binomial distribution, where each question has a probability of 1/2 of being answered correctly and there are 8 independent trials.

The probability mass function for a binomial distribution is:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the number of trials, p is the probability of success, and k is the number of successes.

In this case, n = 8, p = 1/2, and we want to find P(X = 5).

P(X = 5) = (8 choose 5) * (1/2)^5 * (1/2)^(8-5)

P(X = 5) = (8 choose 5) * (1/2)^8

Using the formula for combinations, (n choose k) = n! / (k! * (n-k)!) we get:

P(X = 5) = (8! / (5! * 3!)) * (1/2)^8

P(X = 5) = 56 * 1/256

P(X = 5) = 7/64

Therefore, the probability of the student getting 5 questions correct is 7/64.

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The given matrix has no solution. Therefore, option A is the correct answer.

From the given matrix,

[tex]\left[\begin{array}{ccc}1&1&-4\\-2&-1&6\\-5&-3&16\end{array}\right]\left[\begin{array}{ccc}x\\y\\x\end{array}\right] = \left[\begin{array}{ccc}6\\-10\\-26\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}x+y-4z\\-2x-y+6z\\-5x-3y+16z\end{array}\right] =\left[\begin{array}{ccc}6\\-10\\-26\end{array}\right][/tex]

x+y-4z=6  -------(i)

-2x-y+6z=-10 ---------(ii)

-5x-3y+16z=-26 ---------(iii)

Multiply equation (i) by 2, we get 2x+2y-8z=12 ---------(iv)

Add equation (ii) and (iv), we get

-2x-y+6z+2x+2y-8z=-10+12

y-2z=2 ---------(v)

Multiply equation (i) by 5, we get

5x+5y-20z=30 ---------(vi)

Add equation (vi) from (iii), we get

5x+5y-20z+(-5x-3y+16z)=30-26

5x+5y-20z-5x-3y+16z=4

2y-4z=4

y-2z=2 ---------(vii)

From equation (vi) and (vii), we understood the matrix has no solution

Therefore, option A is the correct answer.

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The inverse of function f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.So, the correct option is D.

To find the inverse of a function, we switch the x and y variables and solve for y. So, if f(x) = -2, we have:
x = -2
y = f(x) = -2
Switching x and y, we get:
x = f¯¹(y)
y = -2
Solving for f¯¹(y), we get:
f¯¹(y) = 2y + 3
Therefore, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
To find the inverse of a function, we need to swap the input (x) and output (f(x)), and then solve for the new input. Given f(x) = -2, let's find the inverse:
1. Swap the input and output: x = -2
2. Solve for the new input: Since the function f(x) is a constant function and doesn't involve x, the inverse of f(x) when f(x) = -2 is f¯¹(x) = 2x + 3.
Therefore, Option D is the correct inverse of f(x).

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