which statement is true? a. the graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g. b. the graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g. c. the graph of

The sum of the first 6 terms of the geometric sequence 3, -6, 12, -24, ... is -3.

The first 6 terms of the geometric sequence 3, -6, 12, -24, ... can be calculated using the formula for the nth term of a geometric sequence:

[tex]a_n = a_1 * r^{(n-1)}[/tex]

where a_1 is the first term, a_n is the nth term, r is the common ratio, and n is the term number.

For the given sequence, a_1 = 3 and r = -2, so the first 6 terms can be calculated as follows:

[tex]a_2 = 3 * (-2)^{(2-1)} = -6\\a_3 = 3 * (-2)^{(3-1)} = 12\\a_4 = 3 * (-2)^{(4-1)} = -24\\a_5 = 3 * (-2)^{(5-1)} = 48\\a_6 = 3 * (-2)^{(6-1)} = -96\\[/tex]

The sum of the first 6 terms will be = 3 - 6 + 12 - 24 + 48 - 96 = -3

A geometric sequence is a number sequence in which the ratio of any two consecutive terms is always the same.

A geometric sequence has the following general form: a, ar, ar^2, ar^3,...,

where an is the first term of the sequence and r is the common ratio, which is a fixed number that represents the factor by which each term is multiplied to get the next term.

The formula for calculating the nth term of a geometric sequence is:

a_n = a * r(n-1) where n is the term number.

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Sandra's last year salary was $24500

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Sandra saves 10% of her salary for retirement. This year her salary was $1,000 more than in the previous year, and she saved $5,000.

Let her previous salary be x, then according to question,

10% of x + 10% of 1000+x = 5000

x / 10 + (1000+x) / 10 = 5000

x + 1000 + x = 50000

2x = 49000

x = 24500

Hence, Sandra's last year salary was $24500

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If three bulbs are randomly selected, the probability that a) exactly 2 are 23 watts is 0.136, the probability that b) all are of the same type is 0.542 and c) there will be one bulb of each type is 0.244.

Here we have been given that out of 23 bulbs,

8 are 13 watt

9 are 18 watt

6 are 23 watt

now if three bulbs are randomly selected out of these, it can be done in

²³C₃ ways

a)

There are 6, 23 watts, and 17 bulbs that are not 23 watts.

Hence they can be chosen in

⁶C₂ X ¹⁷C₁ ways

Therefore the probability to get exactly 2 23 watt bulbs is

[⁶C₂ X ¹⁷C₁]/²³C₃

= [6 X 5 X 17 X 3 X 2]/[2 X 23 X 22 X 21]

= [3 X 5 X 17]/[23 X 11 X 7]

= 240/1771

= 0.136

b)

The probability that all three bulbs are of the same type will have three cases. Hence they can be selected in

⁸C₃ + ⁹C₃ + ⁶C₃ ways

Hence the probability will be

[⁸C₃ + ⁹C₃ + ⁶C₃]/²³C₃

= [(8 X 7 X 6) + (9 X 8 X 7) + (6 X 5 X 4)](3 X 2)/[23 X 22 X 21]

=  [(8 X 7 X 6) + (9 X 8 X 7) + (6 X 5 X 4)]/[23 X 11 X 7]

= [336 + 504 + 120]/1771

= 960/1771

= 0.542

c)

The probability to select one bulb of each type will be

[8 X 9 X 6]/²³C₃

= [8 X 9 X 6]/[23 X 11 X 7]

= 432/1771

= 0.244

d) Now if at least 6 bulbs need to be examined, hence

the probability will be 1 - probability that we need to check (1, 2, 3, 4, 5)

= 1 - (¹⁷C₀/23 + ¹⁷C₁/²³C₂ + ¹⁷C₂/²³C₃ + ¹⁷C₃/²³C₄ + ¹⁷C₄/²³C₅)

= 1 - (1/23 + 17/253 + 136/1771 + 136/1771 + 340/4807)

= 0.66

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Complete Question

A box in a supply room contains 23 compact fluorescent lightbulbs, of which 8 are rated 13-watt, 9 are rated 18-watt, and 6 are rated 23-watt. suppose that three of these bulbs are randomly selected. (round your answers to three decimal places.)

(a) What is the probability that exactly two of the selected bulbs are rated 23-watt?

(b) What is the probability that all three of the bulbs have the same rating?

(c) What is the probability that one bulb of each type is selected?

(d) If bulbs are selected one by one until a 23-watt bulb is obtained, what is the probability that it is necessary to examine at least 6 bulbs?

Fitness increases with energy intake rate was an assumption varied by Lima, Valone, & Caraco (1985) in their model of squirrel food carrying

Now, According to the question:

A parameter is used to describe the entire population being studied. For example, we want to know the average length of a butterfly. This is a parameter because it is states something about the entire population of butterflies.

Fitness increases with energy intake rate varied by Lima, Valone and Caraco (1985) in their model of squirrel food carrying.

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The given question is incomplete, complete question is:

Mathematical models allow researchers to make different predictions by varying assumptions. Which of the following parameters was an assumption varied by Lima, Valone, & Caraco (1985) in their model of squirrel food carrying?

A correct answer is an option (C); both statements together are sufficient.

Although k < n, no details are given about the value of k or n; not sufficient.

Since the median of the numbers in the list is 10 and there are 5 numbers in the list, 10 is one of these 5 numbers. Hence, n = 10 or k = 10. If n = 10, then the value of n has been decided. However, if k = 10, then n can be any number that is 10 or less, so the value of n cannot be found out; not sufficient.

Taking (1) and (2) together, if k < n and the median of the list are 10, then 12 and 17 are to the right of the median and the list in ascending order is either 6, k, n, 12, 17 or k, 6, n, 12, 17. In this case, n is the middle number, and since the median is 10, n = 10.

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The complete question is:

Given the list k, n, 12, 6, 17, What is the value of n in the list above?

(1) k < n

(2) The median of the numbers in the list is 10.

Which option is correct?

A) Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.

B) Statement (2) alone is sufficient, but Statement (1) alone is not sufficient.

C) Both statements together are sufficient, but neither statement alone is sufficient.

D) Each statement alone is sufficient.

One system of quadratic equations that has solutions of (-3, -3) and (3, -3) is:

x^2 + y^2 = 18

x + y = 0

You can check that for x = -3 and y = -3, the left-hand side of both equations is equal to the right-hand side, and the same is true for x = 3 and y = -3.

The parabola opens up, Axis of symmetry = 5, The quadratic have two solutions, x = 2 and x = 8 and And the vertex is a minimum.

Any geometric shape is divided into two equal halves by the symmetry. For a quadratic equation in standard form, y = ax2 + bx + c, the axis of symmetry formula is given as x = -b/2a. The equation is x = h if the parabola is in vertex form, which is y = a(x-h)2 + k.

Axis of symmetry = -b / 2a

x = 10 / 2(1)

x = 5

As axis of symmetry is x = 5,

the parabola opens up

Given the equation is y = x² - 10x + 16

factorizing the equation,

x² - 10x + 16

x² - 8x - 2x + 16

x(x - 8) -2(x - 8)

(x - 2)(x - 8)

x = 2 or x = 8

There are 2 solutions of parabola.

From the given equation,

x² - 10x + 16

Using completing squares method,

⇒ x² - 10x + 16 + 25 - 25

⇒ (x - 5)² - 9

The value of vertex (h, k) = (5,-9)

The vertex is minimum.

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If you roll a standard number cube, the times you will roll a number less than 5 if you roll a standard number cube 250 times is 167

Given that this is a cube since there are three faces with numbers less than 5 (1, 2, and 3)

The result of multiplying the probability by the number of rolls is the expected number of rolls that will be fewer than 5. The number cube is being rolled 250 times.

we would have 2 / 3 * 250

= 166.66667

this is approximately 167

Hence the number of times that we would predict for the number is 167 times.

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Answer:

330 approximately.

Step-by-step explanation:

The percentage lying between 2 standard deviations is 95%.

So we have 348 * 0.95 = 330 approximately.

The probability of a student completing the final examination in less than 65 minutes is 13.45%.

The time it takes to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes and a standard deviation of 12 minutes. This can be expressed mathematically as X~N(77, 12).

The probability of a student completing the final examination in less than 65 minutes can be calculated by using the Z-score formula:

Z = (x - μ) / σ

Where x = 65 minutes, μ = 77 minutes, and σ = 12 minutes.

Plugging these values into the formula, we get:

Z = (65 - 77) / 12 = -1.17

Using a Z-score table, we can find the probability of a student completing the final examination in less than 65 minutes, which is equal to 0.1345, or 13.45%. Therefore, the probability of a student completing the final examination in less than 65 minutes is 13.45%.

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Complete question :What is the probability of a student taking 90 minutes or less to finish the exam?

Answer: B: 15

Step-by-step explanation: I hope this helps!

Answer:

Step-by-step explanation:

a. To find the percentage of the weight limit that 33 pounds is, we can use the following formula:

(Weight / Weight Limit) x 100 = Percentage

So, for 33 pounds:

(33 / 60) x 100 = 55%

b. To find the percentage of the weight limit that 114 pounds is:

(114 / 60) x 100 = 190%

c. To find what weight is 95% of the limit, we can use the following formula:

Weight Limit x (Percentage / 100) = Weight

So, for 95%:

60 x (95 / 100) = 57 pounds

Therefore, 95% of the weight limit is 57 pounds.

The standard deviation of the sampling distribution of the mean is d)3.75; the distribution is approximately Normal.

According to the Central Limit Theorem, when the sample size is large enough (typically n > 30), the sampling distribution of the mean will be approximately normal, regardless of the shape of the population distribution.

In this case, the sample size is 16, which is larger than 30, so we can assume that the sampling distribution of the mean is approximately normal.

The standard deviation of the sampling distribution of the mean (also known as the standard error) is given by:

σm = σ/ √n

where σ is the population standard deviation and n is the sample size.

Plugging in the given values:

σm = 15/ √16 = 15/4 = 3.75

So the standard deviation of the sampling distribution of the mean for the student's sample is 3.75 minutes.

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The amounts of each fruit that Anna bought is given as follows:

The variables for the system of equations are given as follows:

She buys a total of 14 pounds, hence:

x + y + z = 14.

She buys twice the amount of bananas as grapes, hence:

x = 2y.

She buys 2 more pounds of apples than grapes, hence:

z = 2 + y.

Then the amount of grapes can be obtained as follows:

x + y + z = 14.

2y + y + 2 + y = 14

4y = 12

y = 3 pounds.

Then the remaining amounts are given as follows:

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The little cubes can be possible to remove in number of 18 cubes maximum.

What is cube ?

A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only regular hexahedron and is one of the five Platonic solids.

The original surface area is (3x3) x 6 = 54 units.

A unit cube has 6 units of area, so we need 9 cubes.

Remove all the cubes except the original eight corners and the center cube.

The 3×3×3 cube has a surface area of 6×3×3 square units. Taking the 27 smaller units and connecting them to form a single entity, the maximum exposed surface area per cube is 6 square units. If nine of these are connected vertex to vertex in any shape then the objective is achieved. So a maximum of 18 of the small cubes can be removed.

Hence , The little cubes can be possible to remove in number of 18 cubes maximum.

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The trigonometric equation has the following roots: x₁ = ± i · π, x₂ = π / 6 ± i · π, where i are integers. (Correct choice: D)

Trigonometric equations are equations that involve trigonometric functions. Trigonometric functions are periodic trascendent functions. In this problem we must determine the roots of a trigonometric equations by means of algebra properties and trigonometric formulas:

3 · tan² x = √3 · tan x

3 · tan² x - √3 · tan x = 0

tan x · (3 · tan x - √3) = 0

The roots of the equation are tan x = 0 or tan x = √3 / 3, whose angles are: x₁ = ± i · π, x₂ = π / 6 ± i · π, where i are integers.

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Average rate of change is the change in the function per unit in a given interval. The average rate of change from x = 5 to x = 7  is -4.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, The graph of y = f(x)

See attachment for the points on f(x) that links x = 5 to x = 7

The line segment is represented by a green line

To determine the average rate of change using the line segment; we have the following values.

When x = 5: y = 8

When x = 7: y = 0

So, the average rate of change (m) is:

m = Δy/Δx

Where:

Δy = y₂ - y₁

Δy = 0- 8

Δy = -8

Δx = x₂ - x₁

Δx = 7 -5

Δx = 2

So, we have:

m = Δy/Δx

m = -8/2

m = -4

Hence, the average rate of change from  x = 5 to x = 7  is -4

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Complete question:

Answer:

8

Step-by-step explanation:

so first you need to add by the fraction of 10 the the BASS of eletro power of 10¬ then you add the μ3 that is how you get 8

Therefore, the starting value of the house was £724,492.37 (rounded to two decimal places).

A fraction is a mathematical expression that represents a part of a whole. It is expressed as two numbers separated by a line or a slash, with the number on top called the numerator and the number on the bottom called the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of parts in the whole. Fractions can be used to represent quantities such as lengths, distances, time, weight, and many other things in the real world. They are an important concept in mathematics and are used in a wide range of applications, from basic arithmetic to advanced calculus and beyond.

Here,

Let's denote the starting value of the house by x.

After the first year, the value increased by 9%, so the value became 1.09x.

After the second year, the new value decreased by 4%, so the value became 0.96(1.09x) = 1.0464x.

We know that this final value is £758,640, so we can set up an equation and solve for x:

1.0464x = 758640

x = 758640 / 1.0464

x ≈ 724492.37

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250 adults and 195 children swam at the public pool on that day.

What is the system of linear equations?

A system of linear equations is a set of two or more equations that contain two or more variables. The goal is to find the values of the variables that will satisfy all of the equations in the system.

This is a system of equations problem. We can start by using two variables, x for the number of children and y for the number of adults, and then set up two equations based on the information given.

The first equation is for the total number of people: x + y = 445

The second equation is for the total amount of money collected: 1.75x + 2.5y = 964.75

We can now use the first equation to solve for one of the variables in terms of the other, and then substitute that expression into the second equation.

x + y = 445

x = 445 - y

Now we substitute x = 445 - y into the second equation

1.75(445 - y) + 2.5y = 964.75

after solving this equation we get

y = 250

x = 195

Hence, 250 adults and 195 children swam at the public pool on that day.

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During the first eighteen years of his rule, he spent most of his time defending his nation against attacks from Egypt, Italy, and the Mahdists.

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The equation with an infinite number of solutions is 12x-x+8+3x=14x+8.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

12x-x+8+3x=14x+8

The equation so that it has infinitely many solution is 12x-x+8+3x=14x+8.

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Answer:

Step-by-step explanation:

46

Answer: y=1.25

Step-by-step explanation:

First things first you have to find what is in the bracket things (i don’t know what it’s called) So 3 - 7 is -4y but since it’s absolute it’s going to be 4y.

So now you’ve got 4y - 10 = -5. Your going to want to eliminate 10 so, subtract 10 to both sides giving you 4y = -5

Lastly to get y by itself you need to divide it by its self so, 4y divided by 4. Do it to both sides. This gives you…

Y = 1.25

The coordinates of the end points of the segment after the reflection over the x-axis are given as follows:

A'(-2,-3) and B'(2,-1).

The drawing is given by the image presented at the end of the answer.

The rule for a reflection over the x-axis is given as follows:

(x,y) -> (x, -y).

Meaning that the x-coordinate remains constant, while the y-coordinate is exchanged.

Hence, changing the signal of the y-coordinate, the endpoints after the reflection are given as follows:

A'(-2,-3) and B'(2,-1).

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The rotation of the image given 180° clockwise around the point (-2, 1) gives the image in the second option.

Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.

The coordinates of the given image are :

(-1, 1), (-2, 1), (-1, 4) and (-2, 4).

Point of rotation is (-2, 1).

The points are not rotated around the origin.

To make it seem like around the origin, subtract the point of rotation from the points.

So the new points are :

(1, 0), (0, 0), (1, 3) and (0, 3)

Now rotate the image with the new coordinates around the origin 180° clockwise.

Rotation is -180°, which is equivalent to rotation of 180° counterclockwise.

Coordinates (x, y) when rotated 180° clockwise becomes (-x, -y).

New coordinates after rotation about origin are :

(-1, 0), (0, 0), (-1, -3) and (0, -3).

Now add the point of rotation (-2, 1) again.

Points are :

(-3, 1), (-2, 1), (-3, -2) and (-2, -2).

Image with these points is the second option.

Hence the required image is the second option.

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The maximum and minimum number of hikers from the given frequency table are 17 and 4 respectively.

What is a frequency table?

One approach to display data is in a frequency table. To summarise bigger collections of data, the data are organised and counted. You can examine the distribution of the data across various values using a frequency table.

From the given frequency table, we can see that

Between 0 and 5 miles, there are 3 hikers

Between 5 and 10 miles, there are 4 hikers

Between 10 and 15 miles, there are 7 hikers

Between 15 and 20 miles, there are 6 hikers

Between 20 and 25 miles, there is only 1 hiker.

So the maximum number of hikers between 8 miles and 19 miles is the total number of hikers between 5 and 20 miles = 4 + 7 + 6 = 17

The minimum number of hikers who could have walked between 8 miles and 19 miles is 4 hikers.

Therefore the maximum and minimum number of hikers from the given frequency table are 17 and 4 respectively.

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The point of intersection will be the x, and y coordinates where the two lines cross.

To determine the point(s) of intersection algebraically, we need to find the solutions of the system of equations:

y = x² - x + 1

We can re-arrange the equation to solve for x:

x² - x + 1 - y = 0

We can then use the quadratic formula to find the solutions:

x = (1 ± √(1 - 4(1)(-y)))/2

x = (1 ± √(1 + 4y))/2

Now we can substitute values for y to find the x-coordinates of the points of intersection.

To verify the results, we can use a graphing utility to graph both equations and visually see where they intersect.

The point of intersection will be the x, and y coordinates where the two lines cross.

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By taking a quotient we will see that the percent is 24%.

The percent will be given by the quotient between the number of cars that have a speed above the speed limit, and the total number of cars (and we multiply that by 100%)

There are 25 cars in total, and 6 of these have a speed above the speed limit, then the percent is:

p = (6/25)*100% = 24%

So 24 percent of the cars are travelling above the speed limit.

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The expressions using only addition are (a) 4x + (-7y) + (-5z) + 6 and (a) -3x + (-8y) + (-4) + (-8/7z)

Expression 1

From the question, we have the following expression that can be used in our computation:

4x - 7y - 5z + 6

When represented using only addition, we have

4x + (-7y) + (-5z) + 6

Expression 2

From the question, we have the following expression that can be used in our computation:

-3x - 8y - 4 - 8/7z

When represented using only addition, we have

-3x + (-8y) + (-4) + (-8/7z)

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