by how much must the sample size n be increased if the width of the ci (7.5) is to be halved? if the sample size is increased by a factor of 25, what effect will this have on the width of the interval? justify your assertions.

The sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1.

The formula for the sum of an infinite geometric series when |x| < 1 is given as:

S = a/(1-r)

We have a = 1 and r = x/1.

S = 1/(1-x) + 2x/(1-x)² + 3x²/(1-x)³ + 4x³/(1-x)⁴ + ...

we multiply both sides of this equation by (1-x)²,

S(1-x)² = (1-x) + 2x + 3x²(1-x) + 4x³(1-x)² + ...

S(1-x)² = 1 + x + x² + x³ + ...    eqn (1)

Using the formula for the sum of an infinite geometric series when |x| < 1, we have:

1/(1-x) = 1 + x + x² + x³ + ...

Substituting this into equation (1), we get:

S(1-x)² = 1/(1-x)

S = 1/[(1-x)²]

In conclusion, the sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1

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The equation in slope-intercept form that describes the relationship in the graph is: y = -20x + 100.

An equation is a mathematical statement that shows the equality between two expressions. It contains one or more variables, and the values of these variables can be solved for to make the equation true. An equation can be represented using symbols, numbers, and operators such as addition, subtraction, multiplication, division, and exponents. Equations are used in many fields of mathematics and science, and they are a fundamental tool for solving problems and making predictions.

Here,

Part A:

The equation in slope-intercept form that describes the relationship in the graph is:

y = -20x + 100

Part B:

To determine the equation, we need to find the slope of the line passing through the two given points.

Slope, m = (change in y) / (change in x)

m = (0 - 100) / (5 - 0)

m = -20

The y-intercept can be found by substituting the slope and any point on the line into the slope-intercept form of the equation:

y = mx + b

100 = (-20)(0) + b

b = 100

Therefore, the equation in slope-intercept form is:

y = -20x + 100

Part C:

In the given situation, the slope represents the rate of decrease in the percentage of battery remaining per hour. The negative value indicates that the percentage of battery remaining decreases over time, and the magnitude of the slope (-20) indicates that the battery percentage decreases by 20% per hour.

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Answer: 2.8%

Step-by-step explanation: 2.8%

£80 :))

According to the given statement, the government is held accountable by the citizens. Citizens are the ones who elect the government and, thus, have the power to hold it accountable. This is a fundamental principle of democracy that ensures that those in power are serving the people's interests.In a democratic society, the government is accountable to the people.

This means that citizens have the right to hold elected officials accountable for their actions. This is achieved through various means such as free and fair elections, the rule of law, and the right to free speech and expression.Government officials are elected to serve the people and carry out their wishes. This means that they must be transparent and open to criticism. They must be willing to listen to citizens' concerns and take action to address them. This is why democratic societies have mechanisms in place to ensure that citizens can hold their government accountable, such as a free press and independent judiciary.In conclusion, citizens are the ones who hold the government accountable in a democratic society. They have the power to elect officials and the right to criticize them if they are not serving their interests. This ensures that those in power are always acting in the best interests of the people.

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Answer:

꧁. ꧂

Step-by-step explanation:

꧁. ꧂꧁. ꧂

In order to have a potential value of $12,000 at a simple rate of interest of 8.0% after 6 years, the current value you must invest is therefore approximately $8,108.11.

A formula called Simple Interest (S.I.) is used to determine how much interest will be charged on a certain principal sum of money at a specific interest rate. For instance, if a person borrows Rs. 5000 for two years at a rate of 10 p.a., they will be compelled to pay S.I. on the whole amount borrowed during those two years.

For simple interest, use the formula:

A = P(1 + rt)

where r is the interest rate, t is the amount of time in years, A represents the future value, P is indeed the present value, and so on.

This formula can be changed to account for P:

P = A / (1 + rt)

By entering the specified values, we obtain:

P = 12,000 / (1 + 0.08 x 6)

P = 12,000 / 1.48

P = $8,108.11

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The constant of proportionality is the cost per unit. In this case, it can be calculated by dividing the cost of 1 motorcycle by the number of motorcycles.

Unit is an individual item or segment of a larger whole. It is used to measure or quantify different elements or entities, including physical objects, abstract concepts, and even people. In mathematics, a unit is a number or quantity that is equal to one. In the physical sciences, a unit is a standard amount of a certain quantity, such as a kilogram or an hour. In economics, a unit is a measure of a certain commodity or factor of production, such as labor or capital.

Constant of Proportionality = Cost per Motorcycle = 4,590 / 1 = 4,590

Using this constant of proportionality, we can complete the table as follows:

Number of Motorcycles

Cost

Manufactured

0

1

3

8

15

$

$0.00

$4,590.00

$13,770.00

$36,720.00

$68,850.00

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The constant of proportionality is 4,080.00. Using this constant, we can calculate the cost for each number of motorcycles.

A constant is a quantity or value that remains unchanged over time. It is a fixed value that does not vary and is unaffected by external influences. Constants are used in mathematics, physics, chemistry, and other sciences to represent a fixed value.

Number of Motorcycles
Cost
Manufactured
0
1
3
8
15
$
$0.00
$4,590.00
$12,240.00
$22,950.00
25
$37,275.00
The constant of proportionality is the rate of increase in cost as the number of motorcycles manufactured increases. This can be calculated by dividing the cost of each number of motorcycles by the number of motorcycles.
For example, when 1 motorcycle is manufactured, the cost is $4,590.00, so the constant of proportionality is $4,590.00 / 1 = $4,590.00.
When 3 motorcycles are manufactured, the cost is $12,240.00, so the constant of proportionality is $12,240.00 / 3 = $4,080.00.
Therefore, the constant of proportionality is 4,080.00. Using this constant, we can calculate the cost for each number of motorcycles.

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The percentage of adults who planned to file their taxes electronically is approximately 63%.

A random telephone survey of 1,051 adults (aged 18 and older) was conducted by an online tax preparation and e-filing service. The survey results showed that 664 of those surveyed planned to file their taxes electronically.

Total number of adults surveyed = 1,051

Number of adults who planned to file their taxes electronically = 664

Percentage of adults who planned to file their taxes electronically is;

= (Number of adults who planned to file their taxes electronically / Total number of adults surveyed) x 100%

=(664/1051) x 100%

= 63.16 %

Therefore, the percentage of adults who planned to file their taxes electronically is approximately 63%.

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Answer:50

Step-by-step

Answer:

Answer is D

Step-by-step explanation:

The absolute value is the distance between a number and zero. The distance between −50 and 0 is 50

There can be any angles  like vertical, linear pair, supplemenatry which can be shown in the following figure.

(a) One pair of vertical angles:

Vertical angles are formed by the intersection of two lines. They are opposite to each other and are congruent. For example, in the following diagram, ∠1 and ∠6 are a pair of vertical angles, and ∠3 and ∠8 are another pair of vertical angles.

b) one pair of angles that form a linear pair:

A linear pair is formed by  pair of adjacent angles whose non-adjacent sides form a line.

In the figure the linear pair will be ∠4 and ∠8.Beacause they are adjacent angles whose non adjacent sides form a line.

c)one pair of angles that are supplementary:

Two are said to be supplementary if they add up to be 180 degrees.

So in the figure ∠4 and ∠8 can be supplementary and also ∠1 and ∠5 can be supplementary.

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Answer:

4,320

Step-by-step explanation:

answer is 4,320

9x2x3x8x2x5

Answer:

66 km²

Step-by-step explanation:

To solve this, you should find the area of the rectangle as if it were complete and then subtract the area of the missing section.

Step one: Finding the area of the big rectangle

A =  length x width

A = 9 x 8

A = 72 km²

Step two: Find the area of the smaller rectangle

A = 2 x 3 = 6 km²

Step three: Subtract the area of the small rectangle from the area of the big rectangle

72 - 6 = 66

Answer:

90°

Step-by-step explanation:

Each angle measures 90°

Hope has 6 nickels (x) and 10 quarters (x + 4).

How many of each coin Hope has if she has 4 more quarters than nickels and they have a combined value of 280 cents. To solve this problem, we can use algebraic equations.

Let's assume the number of nickels Hope has is x. Then, the number of quarters she has would be x + 4.

Now, we need to find the total value of the coins. Each nickel is worth 5 cents, so the total value of nickels is 5x cents. Similarly, each quarter is worth 25 cents, so the total value of quarters is 25(x + 4) cents. The combined value of the coins is 280 cents, so we can set up an equation:

5x + 25(x + 4) = 280

Simplify and solve for x:

5x + 25x + 100 = 280
30x = 180
x = 6

Therefore, Hope has 6 nickels (x) and 10 quarters (x + 4).

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Answer:

Step-by-step explanation:

To find the percentage of the original amount that Dylan has remaining on his gift card, we can divide the remaining amount by the original amount and then multiply by 100 to express it as a percentage.

The original amount on the gift card was $20.00, and the remaining amount is $0.06, so the percentage of the original amount that Dylan has remaining on his gift card is:

($0.06 ÷ $20.00) x 100% =

0.003 x 100% =

0.3%

Therefore, Dylan has 0.3% of the original amount remaining on his gift card.

The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 22.21 and the sum of squares due to error (sse) is 6.89 will be 15.32.

To find the Sum of Squares due to Regression (SSR), we use the formula:

SST = SSR + SSE

Rearranging the equation to obtain SSR, we get:

SSR = SST - SSE

[tex]$\begin{aligned}SSR&= SST - SSE \\&= 22.21 - 6.89 \\&= 15.32\end{aligned}$[/tex]

Therefore, the value of the Sum of Squares due to Regression (SSR) is 15.32, given the Total Sum of Squares (SST) is 22.21 and the Sum of Squares due to Error (SSE) is 6.89.

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Answer:

Step-by-step explanation:

asdfasdf

Answer: x is equal to 1

Step-by-step explanation:

The values as per similarity of traingles is x=4 and y=10.

Since ABC and DEF are similar triangles, their corresponding sides are proportional.

That is,

AB/DE = AC/EF = BC/DF

Substituting the given values, we get:

9/6 = 18/10 = (4x-1)/y

Simplifying this expression, we can solve for x and y:

9/6 = (4x-1)/y

Cross-multiplying, we get:

27y = 6(4x-1)

27y = 24x - 6

Substituting y = 10/3, we get:

(27)(10/3) = 24x - 6

90 = 24x - 6

96 = 24x

x = 4

Therefore, the value of x is 4.

9/6 = (4x-1)/y

Substituting x = 4, we get:

9/6 = (4(4)-1)/y

9/6 = 15/y

Cross-multiplying, we get:

9y = 90

y = 10

Therefore, the value of y is 10.

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There is only one possible triangle that can be drawn with one angle measuring 30 deg and another measuring 110°. This is because all triangles have a sum of 180° for the three angles.

Triangle is a three-sided polygon with three straight sides that intersect at three vertices. It is one of the basic shapes in geometry, and is considered to be a building block of other shapes. Triangles can be classified according to their sides, angles, and area. The most common types of triangles are equilateral, isosceles, and scalene triangles, which are classified according to the length of their sides. Triangles can also be classified according to their angles, as acute, right, and obtuse triangles, which are classified according to the size of their angles. Additionally, the area of a triangle is determined by its base, height, and side lengths.

Therefore if one angle is 30° and the other is 110°, the third angle must be 40° for the triangle to be valid.

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False. For two triangles to be similar, the angles must be equal. The angles of the two triangles given do not match, so the triangles are not similar.

An angle is a geometrical figure that is formed by two lines or rays that have a common endpoint. It is a measure of the amount of turn between the two lines or rays. Angles are typically measured in degrees, with a full angle measuring 360 degrees. Angles can also be measured in radians, with a full angle measuring 2π radians. Angles are used in math and science to describe position and orientation. Common examples of angles include right angles, acute angles, obtuse angles, and straight angles. Angles can be used to calculate the area of polygons, measure the slope of a line, and determine the force of friction.

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Complete Question:
A triangle has angles that measure 45° and 65°. A second triangle has angles that measure 110° and 30°. These two triangles are similar. O True O False

The area of the half-dollar coin with a diameter of 1.2 inches is greater.

Both the given objects have a circular shape with a different diameter.

One of the objects is made up of two separate quarters of a circle, each with a diameter of 1 inch.

On the other hand, the second object is one half-dollar coin with a diameter of 1.2 inches.

We will use the formula of the area of a circle that is : A = πr²

Where A is the area of the circle.

π is the constant value (3.14)

r is the radius of the circle.

Let's calculate the area of 2 quarters each with a diameter of 1 inch.

The radius will be half of the diameter.

So, the radius is 1/2 inch for each quarter of the circle.

A = πr²A = π × (1/2)²A = π × 1/4A = 0.7854 square inches.

The total area of both quarters will be = 2 × 0.7854 square inches

The total area of both quarters = 1.5708 square inches

Now, let's calculate the area of the half-dollar coin with a diameter of 1.2 inches.

The radius will be half of the diameter.

The radius of the half-dollar coin = 1.2 / 2 = 0.6 inch

A = πr²A

  = π × 0.6²A

  = π × 0.36A

  = 1.1318 square inches

The half-dollar coin has a greater area as compared to the two quarters of a circle.

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On his journey to his room, Eugene first found a few pieces of paper before discovering three more. Let's assume that he began with x bits of paper. Eugene started with  [tex]3[/tex] pieces of paper.

Eugene started with some pieces of paper, and then he found 3 more on his way to his room. So, let's say he started with x pieces of paper.

After finding the 3 more pieces, he had a total of   [tex]x + 3[/tex] pieces of paper.

He then cut each piece of paper in half, which means he doubled the number of pieces of paper. So, he ended up with  [tex]2 \times (x + 3) = 2x + 6[/tex]  half-pieces of paper.

We're given that he had 12 half-pieces of paper in the end, so we can set up the equation:

[tex]2x + 6 = 12[/tex]

Solving for x, we get:

[tex]2x = 6[/tex]

[tex]x = 3[/tex]

Therefore, Eugene started with 3 pieces of paper.

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answer: 10

step by step explanation:

this is not a textbook way but

4:5 means 4/5 and we know that the numbers will be equal to this number so we can multiply the number 4/5*2/2 so we will get 8/10

8/10=4/5

and 8*10=80

so 1st no. is 8 and 2nd is 10

10>8

Answer:

greater number is 10

Step-by-step explanation:

the ratio of the 2 numbers = 4 : 5 = 4x : 5x ( x is a multiplier )

their product is 80 , that is

4x × 5x = 80

20x² = 80 ( divide both sides by 20 )

x² = 4 ( take square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

then greater number = 5x = 5 × 2 = 10

If one of the 619 residents is selected at random, the probability they have experienced delays is 70.6%.

To find the probability that a randomly selected Salinas resident has experienced significant traffic delays within the last month, we need to use the formula for probability:

Probability = Number of favorable outcomes / Total number of outcomes

In this case, the favorable outcome is the number of residents who have experienced significant traffic delays, which is 437. The total number of outcomes is the total number of residents surveyed, which is 619. Therefore, the probability is:

Probability = 437 / 619 ≈ 0.706

This means that there is a 70.6% chance that a randomly selected Salinas resident has experienced significant traffic delays within the last month, based on the given survey results.

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The unit digit of the given sum [tex]1998^{1999}-1999^{1998}[/tex] is one according to the one's place of 8 and 9 powers.

Here, we need to find the unit digit of [tex]1998^{1999}[/tex] :

8 power of any dight will give us the unit digit of 8, 4, 2 and 6.

Here 8 has power 9.

Then the unit place of the sum will be equal to 2.

Similarly, we need to find the sum of other one.

Other sum: [tex]1999^{1998}[/tex]

9 power of 8

9 power of odd numbers will give 9 as unit digit.

9 power of even numbers will give 1 as unit digit.

Here, we have 8 as power the, we will get the unit digit as 1.

Now we need to simplify the sum.

Unit digit of  [tex]1998^{1999}-1999^{1998}[/tex] is equal to 2 - 1 = 1.

The unit digit of the given sum [tex]1998^{1999}-1999^{1998}[/tex] is one.

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The probability that Arianna will lose a turn is impossible.

In probability, impossible events have a probability of 0. This means that there is no chance that the event will occur. In this case, the probability that Arianna will lose a turn on her next turn is 0, which means that it is impossible for her to lose a turn.

In probability theory, the term "probability" refers to the likelihood of an event occurring. It is typically expressed as a value between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

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The area of the given shape is 22 square tiles. The given shape consists of two rectangles and a square.

To find the area of the shape, we need to find the area of each of these three shapes and then add them up.

First, we can see that the length of the longer rectangle is 6 tiles and the width is 2 tiles. Therefore, the area of this rectangle is 6 × 2 = 12 tiles.

Next, the length of the shorter rectangle is 3 tiles and the width is 2 tiles. Thus, the area of this rectangle is 3 × 2 = 6 tiles.

Finally, the square has a side length of 2 tiles, so its area is 2 × 2 = 4 tiles.

Adding up the areas of the three shapes, we get 12 + 6 + 4 = 22 tiles.

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Answer:

The balanced equation that represents an endothermic reaction is:

2 CH4 (g) + 2 O2 (g) → 2 CO2 (g) + 2 H2O (g)

This is because the reactants (CH4 and O2) have a higher bond energy than the products (CO2 and H2O), meaning that energy must be absorbed in order to break the bonds and form the products. As a result, the reaction is endothermic.

When using the empirical rule and you have a mean of 10 and a standard deviation of 1, approximately 68% of values fall between 9 and 11.

The empirical rule is also known as the three-sigma rule, which states that the values under a normal distribution curve are given by:

Approximately 68% of values fall within one standard deviation from the mean

Approximately 95% of values fall within two standard deviations from the mean

Approximately 99.7% of values fall within three standard deviations from the mean

To solve the problem, we have to calculate how many standard deviations the given values are from the mean:

Lower value = 9Mean = 10

Upper value = 11

Standard deviation = 1

Now, calculate the z-scores:

Lower z-score = (9 - 10) / 1 = -1

Upper z-score = (11 - 10) / 1 = 1

The values between 9 and 11 are within one standard deviation from the mean, so we use the first part of the empirical rule:

Approximately 68% of values fall within one standard deviation from the mean

Therefore, approximately 68% of the values fall between 9 and 11.

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