Zeno has to go a distance, d, to get to his destination. He claims he can never get there because he has to travel half that distance d, then half of half of distance d, and so on. He says that he has to do an infinite number of tasks and that it is impossible. Use an infinite geometric series to help Zeno. Identify a1 and r to form the infinite geometric series that represents the problem.

Answer:

Option D

Step-by-step explanation:

The given function is

[tex]f(x)=4|x|[/tex]

It is given that the graph of g(x) is obtained by reflecting the graph of f(x)=4|x| over the x-axis.

If a figure reflected across x-axis, then the rule of reflection is

[tex](x,y)\rightarrow (x,-y)[/tex]

Using the above rule, if the given function reflected across x-axis, then g(x)=-f(x).

[tex]g(x)=-(4|x|)[/tex]

[tex]g(x)=-4|x|[/tex]

The equation g(x)=-4|x| describes g(x).

Therefore, the correct option is D.

A unit test for the function addInventory() can be written in JavaScript using Jest. The test checks that the quantity of red sweaters increases correctly after calling addInventory(). If the test fails, an error message will be shown.

Based on the information given, you can create a unit test in many programming languages. Here we are going to illustrate with JavaScript and use the Jest testing framework.

Firstly, let's name the unit test file as redSweater.test.js. In this file, we call the addInventory() of the redSweater object with sweaterShipment as parameter.  Note that addInventory() is a method that increases the quantity of red sweaters in inventory by a certain amount provided by sweaterShipment.

Here is a sample unit test for your needs:

const redSweater = require('./redSweater'); // path to your redSweater.js file

test('addInventory() unit test', () => {

let initialQty = 10;

redSweater.qty = initialQty;

let shipmentQty = 50;

redSweater.addInventory(shipmentQty);

expect(redSweater.qty).toBe(initialQty + shipmentQty);

});

This script tests that the quantity of red sweaters increases correctly after calling the addInventory() method. If the quantity is not correct after the method call, the test will fail and show an error message.

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Answer:  The correct option is (B) 5.

Step-by-step explanation:  We are given to find the distance between the points (2, 5) and (6, 8).

We will be using the following formula :

DISTANCE FORMULA :  The distance between the points (a, b) and (c, d) is given by

[tex]D=\sqrt{(c-a)^2+(d-b)^2}.[/tex]

Therefore, the distance between the points (2, 5) and (6, 8) is given by

[tex]D\\\\=\sqrt{(6-2)^2+(8-5)^2}\\\\=\sqrt{4^2+3^2}\\\\=\sqrt{16+9}\\\\=\sqrt{25}\\\\=5.[/tex]

Thus, the required distance between the given points is 5 units.

Option (B) is CORRECT.

To get an average earnings of $1,000 for all nine salespeople, the ninth salesperson needs to earn $2,450.

The subject of this question is mathematics, specifically statistics, and it involves the concept of 'mean' or 'average'. To find out what the ninth person needs to earn to keep the average earn of $1,000, we first need to calculate the total earnings of all nine people. Since the average earnings of a salesperson is $1,000, we multiply $1,000 by 9, which gives us $9,000. Then we need to subtract the sum of the earnings of the first eight salespeople from $9,000 to find out the earnings of the ninth person.  

Here is the breakdown with the given figures:

So, the ninth person would need to earn $2,450 for the average earnings to remain at $1,000.

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The sample mean for the given 90% confidence interval (65, 77) is 71. The margin of error is 6. The sample standard deviation cannot be specifically calculated without the t-value, but presuming a common t-value for such datasets (1.96), it approximates to 3.072.

The subject at hand pertains to confidence intervals and basic statistics calculations. Given a 90% confidence interval of (65, 77), we can find the sample mean by adding the two limits and dividing by 2. So (65 + 77) / 2 equals 71.

The margin of error for the confidence interval is calculated by subtracting the sample mean from the upper limit. That gives us 77 - 71 equals 6.

Unfortunately, without knowing the value of the t-statistic, we can't calculate the sample standard deviation, as it's calculated via the formula: standard deviation = margin of error / (t-value/sqrt(sample size)). But, usually, for a sample size of 25 observations and a 90% confidence level, the t-value is about 1.96. Using that assumed t-value, the standard deviation calculation gives us 6/(1.96/sqrt(25)) equals approximately 3.072.

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Answer:

Yes, the number is correct.

Step-by-step explanation:

The cost of a hamburger is $2.50.

Each additional hamburger cost $2.00.

Sully wrote this explicit rule to explain the sequence of costs:

[tex]f(n) = 2+2.5(n-1)[/tex]

Using the rule, he found the cost of 12 hamburgers to be 29.50.

Lets check by putting n = 12.

[tex]f(12) = 2+2.5(12-1)[/tex]

= [tex]2+2.5(11)[/tex]

=  [tex]2+27.5 [/tex]

= $29.50

So, yes Sully is correct.

To find the area of the surface above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.

To find the area of the surface that lies above the given rectangle, we need to determine the intersection of the cylinder with the plane of the rectangle. The equation of the cylinder is y^2+z^2=9, and the vertices of the rectangle are (0,0), (4,0), (0,2), and (4,2). At the x=0 and x=4 cross sections, we can see that the y-coordinate ranges from 0 to 2 and the z-coordinate ranges from -3 to 3. Therefore, the surface area above the rectangle is equal to the area of the rectangle multiplied by the range of the z-coordinate.

The area of the rectangle is (4-0)(2-0) = 8 square units. The range of the z-coordinate is -3 to 3, so the surface area above the rectangle is 8 * (3 - (-3)) = 48 square units.

The real square roots of 0.0625 are -0.25 and 0.25, as both of these numbers squared equal 0.0625.

The student has asked to find all the real square roots of 0.0625. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we're looking for a number which, when squared, equals 0.0625.

To find this, we can recognize that the square root of 0.0625 could be thought of in fraction form as the square root of 625/10000, which simplifies to the square root of 625 divided by the square root of 10000. This reduces to 25/100 because 625 is a perfect square (25 * 25) and 10000 is also a perfect square (100 * 100). Therefore, the principal square root of 0.0625 is 0.25.

However, since every positive number has two square roots, one positive and one negative, and because the square of both -0.25 and 0.25 gives 0.0625, we conclude that the real square roots of 0.0625 are -0.25 and 0.25.

There are two kinds of real numbers in mathematics, one is rational number and other is irrational number. Out of given options, π and √20 are irrational number. Therefore option A, D are correct option

Real numbers that can not be written in the form of fraction is called irrational number. Real number that can be written in form of fraction is called rational number.

In option (1)  π is an irrational number as it contains infinite decimals when we divide 22 by 7

In option (2)  1.33 is a fixed number so it can be written in fractions so this number is rational number

In option (3) √196, it is square root of 14 so it can be written in fraction so it is rational number.

In option (4) √20  is an irrational number as on finding its square root there will be infinite decimals so it cannot be written in form of fraction

Therefore π and √20 are irrational number.  Therefore option A, D are correct option

To know more about irrational number, here:

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-5.25, -5.09, 1.002

hopes this help please mark me as brainliest. :)

Final answer:

The largest area for a rectangle with a fixed perimeter of 168 feet is achieved by a square, and the dimensions of that square are 42 feet by 42 feet.

Explanation:

To find the dimensions of a rectangle with the largest area given a fixed perimeter, we need to understand that the rectangle with the largest area for a given perimeter is a square.

In this problem, the perimeter is 168 feet, which can be expressed by the formula 2l + 2w = 168, where l is the length and w is the width of the rectangle. Knowing that a square has all four sides equal, we simply divide the perimeter by 4 to get the side length, which gives us l = w = 168/4 = 42 feet.

Therefore, the dimensions of the rectangle with the largest area, which in this case is a square, are 42 feet by 42 feet.

Answer:

9 full pieces.

Step-by-step explanation:

In order to solve this we have to divide the total feets of wood that Jessie has, by the size of the pieces that Jessie needs:

[tex]\frac{8}{\frac{7}{8} }\\\frac{\frac{8}{1} }{\frac{7}{8} }\\\frac{8*8}{7*1}\\\frac{64}{7} =9.14[/tex]

Since Jessie will be able to cut 9.14 pieces of wood, he will have only 9 full pieces, so the total amount of pieces that he would be able to cut will be 9.

To find the probability of not drawing a blue marble from the bag, one must divide the number of non-blue marbles by the total number of marbles, resulting in a probability of 3/4

The question asks to find the probability of not drawing a blue marble from a bag that contains 8 red marbles, 3 blue marbles, and 1 green marble. The total number of marbles is 8 + 3 + 1 = 12. The probability of not drawing a blue marble (P(not blue)) is the number of marbles that are not blue divided by the total number of marbles. This is (8 red + 1 green) / 12 total marbles. Calculated, the probability is 9/12, which simplifies to 3/4