the sum of a certain infinite geometric series is $2$. the sum of the squares of all the terms is $3$. find the common ratio.

The required two column proof is explained below.

When a set of three points 1, 2 and 3 are arranged on a straight path, then a betweenness relationship holds that the addition of segments joining points 1 to 2, and 2 to 3 is the same as segment 1 to 3.

These points divide the line segment joining 1 to 3 into parts.

Considering the given guide, the two column proof required is explained thus:

     STATEMENT                                          REASON

1. BC = EF                                                   Given

2, AC = AB + BC                                        Betweenness

3. AC > BC                                                 Part of a line segment

4. AC > EF                                                  Addition property of a segment

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A photo of a woman standing between two long rows of sewing machines in a factory. The factory owners relied on skilled workers to run the machines. Thus, option b is correct.

The manufacturing system's key advantages were lower costs for the business and increased worker productivity. The factory administration had direct control over the workers, allowing for regular monitoring of their output. Resources may be used more efficiently if they are shared across several employees.

First, equipment hastened the production of goods. This is because a machine might perform routine tasks skillfully and dependably. The ability of equipment to decrease the number of people required to complete a task is its second advantage. They were able to avoid paying employees by doing this, which allowed them to save money.

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The complete question is-

The photo shows a woman watching a row of machines in a factory. A photo of a woman standing between two long rows of sewing machines in a factory. what advantages did machinery provide for factory owners?

a. machines could do the work faster than skilled workers by hand.

b. factory owners relied on skilled workers to run the machines.

c. the machines produced a better product than skilled workers by hand.

d. factory owners needed more unskilled workers to run the machines.

Answer:

see below

Step-by-step explanation:

4 brothers in total, each saves 17 per week, in 3 weeks

314+(17*4)*3 =518

yes they do have enough

How many weeks will it take for them to save enough $ to buy the gift

515 = x *(17*4) + 314

How much each of them must save per week to have enough?

515= 3(x*4) +314

Step-by-step explanation:

Multiplying the kites by 2 then adding 20

For 4 kites, 4 times 2 is 8. Adding 20 is 28

For 7 kites, 7 times 2 is 14. Adding 20 is 34

For 10 kites, 10 times 2 is 20. Adding 20 is 40

For the equation we have to multiply kites purchased by 2, so 2x. They also said to add 20, making it 2x + 20. Doing this will get the total cost, which they indicate as y

Equation; y = 2x + 20

The probability of the sixth child being born as a boy is 0.5 or 50%. It is irrespective to the five boys born previously.

Since probability of a girl or boy being born is 50%,

Probability of Girl being born, P(G) = ½

Probability of boy being born, P(B) = ½

When one is calculating the probability of any one of the two events occurring or both evens have a chance of occurring, considering the events are non-mutually exclusive, the rule of addition is used.

Rule of addition: P(A or B)= P(A) + P(B) –P(A+B)

Where P(A)- probability that event A takes place

P(B)- Probability that event B takes place

P(A+B)-  probability of both events taking place.

In this case, both events cannot take place simultaneously, i.e., they are mutually exclusive, hence,

P(G or B)= ½ + ½ = 2/4 = ½ = 0.5.

Therefore, Probability of boy being born is 0.5

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The value of z that corresponds to 68% of the observations falling below is 0.84, and the value of z that corresponds to 75% of the observations falling above is 1.15.

A. To find the value of z that corresponds to 68% of the observations falling below, we can use the z-score formula. The z-score formula is z = (x-μ)/σ, where x is the value we are looking for, μ is the mean of the normal distribution, and σ is the standard deviation. Using this formula and a standard normal table, we can find that the value of z is 0.84. This means that 68% of the observations fall below z = 0.84. We can sketch a standard normal curve with this value of z marked on the axis by drawing a bell-shaped curve with the value of 0.84 marked on the x-axis.

B. To find the value of z that corresponds to 75% of the observations falling above, we can use the same formula and a standard normal table. We can find that the value of z is 1.15. This means that 75% of the observations fall above z = 1.15. We can sketch a standard normal curve with this value of z marked on the axis by drawing a bell-shaped curve with the value of 1.15 marked on the x-axis.

The value of z that corresponds to 68% of the observations falling below is 0.84, and the value of z that corresponds to 75% of the observations falling above is 1.15.

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Integers between, but not including, 20 and 30 have a prime factorization with exactly 3 factors is 0 integers.

To find the integers between 20 and 30 with a prime factorization with exactly 3 factors that are not 1, we can start by listing out all the prime numbers up to 30.

The prime numbers up to 30 are 2, 3, 5, 7, 11, 13, 17, 19, and 23.

Next, we can list out all the integers that have exactly 3 factors in their prime factorization that are not 1. This can be done by finding all the products of exactly 3 primes. For example, the product of

2 * 3 * 5 = 30 has 3 prime factors.

However, 30 is not between 20 and 30, so we need to find another example.

The product of 2 * 3 * 7 = 42 is not between 20 and 30 either, so we need to keep finding examples until we find one that falls between 20 and 30.

The product of 2 * 5 * 7 = 70 is too large, but the product of 2 * 3 * 5 = 30 is between 20 and 30, so we have found one example.

We can continue this process to find all the examples and count how many there are. In this case, there is only 1 example, so the answer is 1.

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The scale factor for the given dilation transformation is 1/3

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Given that, a triangle ABC is being dilated to form a new triangle A'B'C'

We are asked to the scale factor,

The length of sides of triangle ABC is 6 units

And, length of sides of triangle A'B'C' is 2 units,

Since, the figure id shrinking, therefore, the dilation is a reduction, and scale factor must be less than 1,

Scale factor = 2/6

= 1/3

Hence, the scale factor for the given dilation transformation is 1/3

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The a) mean of the sample means is equal to the population mean.

This is because the mean of all of the sample means is a measure of the center of all of the samples, which is the same as the center of the population. This can be shown by calculating the arithmetic mean of the sample means.

The arithmetic mean of the sample means is calculated by summing the means and dividing by the number of samples. Since the sum of all the sample means is the same as the sum of the population, the mean of the sample means must also be equal to the population mean.

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20. The sample mean is an unbiased estimator for the population mean. This means: (a) The sample mean always equals the population mean. (b) The average sample mean, over all possible samples, equals the population mean. (c) The sample mean is always very close to the population mean. (d) The sample mean will only vary a little from the population mean. (e) The sample mean has a normal distribution.

the Image of Point C(-5, 3) under a rotation 90° clockwise about the origin followed by a reflection about the x-axis will be  C'(3, -5).

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given A triangle BCD that has rotated clockwise 90° about the origin and then reflected about the x-axis.

Rule of reflection and rotation a point:

Rotation about 90° : (x, y) → For clockwise (y, -x) For counterclockwise (x, y)

Reflection about x-axis : (x, y) => (x, -y)

For point C (-5, 3):

After Rotation 90 about origin clockwise:

As per the rule mentioned above

C(-5, 3) => C" (3, 5)

After reflection about the x-axis:

As per the rule mentioned above

C" (3, 5) => C'(3, -5)

therefore, the Image of Point C  under a rotation 90° clockwise about the origin followed by a reflection about the x-axis will be  C'(3, -5).

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A property which is represented by the equation above is

The Associative Property of Addition states that when three (3) numbers are added, the end result would always be the same regardless of the way the numbers are grouped.

Generally speaking, the Associative Property of Addition allows the addends to be re-grouped without causing a change in the result, output, or outcome.

By applying the Associative Property of Addition, we have the following;

1/3 + (2/3 + 1/7) = (1/3 + 2/3) + 1/7

8/7 = 8/7

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The required match of the sentence to the correct vocabulary has been shown below.

In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.

Here,

1. If x is not a rational number, it must be a(n) irrational number.

2. 0.7 is a rational number.

3. x is a terminating decimal, so it must also be a rational number.

4. A decimal that ends in zero is a terminating decimal.

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Answer:

Blue paint = %90, Red Paint = 10%

Step-by-step explanation:

Out of 100, blue takes up more of the equation. It's 7/8's of the equation while there's only a quarter for red paint, making this equation, Blue > Red, aka, 90 > 10

90 > 10 = 90% of blue paint and 10% of red paint

Answer: 315

Step-by-step explanation:

(45 * 6) + 45

Since there are 45 pins and each takes 6 minutes, then you multiply those 2 first, and then each pin takes 1 minute each, so add 45 to your last answer, which will be your final answer of 315. :)

Answer:

315 minutes

Step-by-step explanation:

We know

One pin requires 6 minutes, with 1 minute per pin for placing stock in the lathe, which means 7 minutes to machine 1 pin.

7 times 45 = 315 minutes

So, it will take 315 minutes to machine 45 pins

The probability that a bottle passes inspection and does not have a flaw is 0.9598067.

Let P(f) = 0.0002 be the probability of a bottle having a flaw, and P(s|f) = 0.993 be the probability of a bottle failing the inspection given that it has a flaw. Also, let P(s|~f) = 0.96 be the probability of a bottle passing the inspection given that it does not have a flaw. We want to find P(~f|s).

We can use Bayes' Theorem to find P(~f|s):

P(~f|s) = P(s|~f) * P(~f) / P(s)

P(s) = P(s|f) * P(f) + P(s|~f) * P(~f)

P(s) = 0.993 * 0.0002 + 0.96 * (1 - 0.0002)

P(s) = 0.0001986

P(~f|s) = 0.96 * (1 - 0.0002) / 0.0001986

P(~f|s) = 0.9598067

Therefore, the probability that a bottle passes inspection and does not have a flaw is 0.9598067.

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b.

because if you use math it tells you b

As a general rule of data ; a class is represented by Lower Limit to Upper Limit. So, by comparison. Lower Limit = 40 and Upper Limit - 60

The lower limit of the first class

The attached histogram has overlapping interval, and the intervals are:

40 to 60, 60 to 80, 80 to 100, and so on....

The first class data here is:

40 to 60

As a general rule; a class is represented by Lower Limit to Upper Limit.

So, by comparison.

Lower Limit = 40

Upper Limit - 60

and hence limit can also be calculated by checking the continuity of a function

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The distribution appears to be approximately bell-shaped and symmetric. The majority of the data falls between 40 and 80 units of hand grip strength, with the highest frequency occurring around 60 units.

The data appears to be unimodal, with a single clear peak in the middle. The distribution does not appear to be skewed to the left or right.

Overall, the distribution appears to be relatively normal, with the majority of the data falling within one or two standard deviations of the mean. This suggests that the data is relatively normally distributed and that the mean and standard deviation would be appropriate measures of central tendency and variability, respectively.

Overall, the histogram suggests that the data is relatively normally distributed. This means that the mean and standard deviation would be appropriate measures of central tendency and variability, respectively. Additionally, because the distribution appears to be relatively symmetrical, the median would also be a reasonable measure of central tendency.

It is worth noting that the histogram provides a visual representation of the data, but it does not provide exact measures of central tendency or variability. Therefore, to make any quantitative inferences about the data, it would be necessary to calculate these statistics based on the raw data.

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Data was collected on hand grip strength of adults. the histogram below summarizes the data. which statement is true about the distribution of the data shown in the graph?

A. There m have been a mistake made n data collection because the distribution should be bell shaped.

B. The graph is useless because it is bimodal

C. The graph shows that two different groups may have been combined into one collection

D. The best estimate of typical grip strength is 90 pounds because it is in the center of the distribution

Answer:

Step-by-step explanation:Find the GCD (or HCF) of numerator and denominator GCD of 2 and 3 is 1

Divide both the numerator and denominator by the GCD 2 ÷ 1 3 ÷ 1

Reduced fraction: 2 3 Therefore, 2/3 simplified to lowest terms is 2/3.

After 4 hours, the distance between Jasmine and Ron is increasing at a rate of 54 mi/h.

To find the rate at which the distance between Jasmine and Ron is increasing after four hours, we need to use the Pythagorean theorem to find the hypotenuse of the right triangle formed by the distance between them and their respective speeds.

The distance between them after 4 hours is given by the square root of the sum of the squares of their respective distances traveled:

[tex]\sqrt{((42 * 4)^2 + (56 * 4)^2)}[/tex]

The rate at which this distance is increasing is equal to the magnitude of the velocity vector of their relative motion, which can be found using the hypotenuse formula:

[tex]\sqrt{(42^2 + 56^2)} = \sqrt{(2916) }= 54 mi/h[/tex]

So, after 4 hours, the distance between Jasmine and Ron is increasing at a rate of 54 mi/h.

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The number of possible orderings of appointments is 720.

The number of possible orderings of appointments can be calculated using the formula n!/(n-r)! where n is the number of teaching assistants (7) and r is the number of appointments (7). Therefore, the total number of possible orderings of appointments is 5040.

To explain this formula, we can think of it in terms of permutations. A permutation is an arrangement of a set of items in a specific order. In this case, the set of items are the 7 teaching assistants (4 men and 3 women). The number of possible permutations (orderings) of these 7 teaching assistants is 7!. This is because there are 7 possible choices for the first appointment, 6 for the second, 5 for the third, and so on. This simplifies to 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.

However, since each appointment is a unique one-time meeting, the order in which the teaching assistants are appointed does not matter, so the number of possible orderings of appointments is reduced to 7!/7 = 5040/7 = 720.

Therefore, in this case, the number of possible orderings of appointments is 720.

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The expression that represents the length of the rectangular computer chip is 14ab².

A rectangle is a quadrilateral with opposite sides equal to each other and opposite sides parallel to each other.

Therefore, the area of the rectangular computer chip is 112a²b³ square microns. The expression that represents the length of the rectangular computer chip can be represented as follows:

Area of the rectangular computer chips = lw

where

Therefore,

w = 8ab microns

Hence,

Area of the rectangular computer chips =112a²b³

112a²b³  = 8ab × length

Therefore, let's divide both sides of the equation by 8ab

length = 112a²b³  / 8ab

length of the rectangular computer chip = 14ab²

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Answer:A linear model is appropriate because the scatterplot shows a strong, positive linear relationship.

Step-by-step explanation:

600 cactus wren nests the experimenter would expect to be in the entire 200-acre preserve.

To estimate the number of cactus wren nests in the entire 200-acre preserve, we can use the ratio of the area surveyed to the number of nests found.

Let's call the number of nests in the entire 200-acre preserve "N".

The ratio of the area surveyed to the number of nests found is:

2 acres / 6 nests = 200 acres / N nests

We can use this ratio to find the number of nests in the entire 200-acre preserve:

N nests = 200 acres * (6 nests / 2 acres)

N nests = 200 * 3

N nests = 600

So the experimenter would expect to find approximately 600 cactus wren nests in the entire 200-acre preserve, assuming that the habitat is fairly uniform.

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The value of the expression correct to 1 decimal place is P = 1.3.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

The given expression is, P = (t - w)/y.

Where, t = 9.7 correct to 1 decimal place, w = 5.9 correct to 1 decimal place

and y = 3 correct to 1 significant figure.

Therefore, P = (9.7 - 5.9)/3.

P = 3.8/3.

P = 1.26 or P = 1.3.

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The decimal with the bar is 4.1[tex]\over6[/tex].

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

25/6

= 4.16666666

6 is the repeating number so we put the bar on 6.

= 4.1[tex]\over6[/tex]

Thus,

The decimal is 4.1[tex]\over6[/tex].

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The slope of the given points is [tex]\frac{2}{5}[/tex] or 0.4.

Let (-7, 5) be ordered pair 1.

Let (-2, 7) be tordered pair 2.

Since point (-7, 5) is ordered pair 1: [tex]x_{1} =-7[/tex] and [tex]y_{1} =5[/tex].

Since point (-2, 7) is ordered pair 2: [tex]x_{2} =-2[/tex] and [tex]y_{2} =7[/tex]

Formula: [tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

Substitute the variables in the formula by the identified coordinates in step 2 and calculate.

[tex]m=\frac{(7)-(5) }{(-2) -(-7) }=\frac{7-5}{-2+7}=\frac{2}{5}[/tex]

The slope of the given points is [tex]\frac{2}{5}[/tex].

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Answer: 2/5

Step-by-step explanation:

(-7,5) (-2,7)

change in y           2

------------------    =  -----

change in x           5

The probability that a roll chosen at random and utilized by the manufacturer has problems is 0.032.

Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics. Probability is a mathematical representation of the likelihood or potential that an event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%. Probability, in its simplest form, gauges the likelihood that something will happen. When we are unsure of how an event will turn out, we might talk about the likelihood of different outcomes. The study of events susceptible to probability is known as statistics.

So, the probability

[tex]=\frac{80}{100}*0.03+\frac{20}{100}*0.04\\=0.8*0.03+0.2*0.04\\=0.024+0.008\\=0.032[/tex]

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a) The y - intercept of the graph is, 20.

b) The slope of the line is, - 4

c) The equation of line is, y = - 4x + 20

d) The cost of 3 comics = $8.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

We have to given that;

The graph shows a linear relationship between x and y, where x represents the number of comic books, all at the same price, Priya buys at the store, and y represents the amount of money (in dollars) Priya has after buying the comic books.

Now, By the graph;

Let two points on the graph are (5, 0) and (0, 20).

Since, The equation of line passes through the points (5, 0) and (0, 20).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (20 - 0) / (0 - 5)

m = 20 / - 5

m = - 4

Thus, The equation of line with slope - 4 is,

⇒ y - 0 = - 4 (x - 5)

⇒ y = - 4x + 20

Thus, The y - intercept of the graph = 20

Now, When Priya buy 3 comics, then the cost of comics are,

⇒ y = - 4x + 20

⇒ y = - 4 × 3 + 20

⇒ y = -12 + 20

⇒ y = $8

Thus, We get;

a) The y - intercept of the graph is, 20.

b) The slope of the line is, - 4

c) The equation of line is, y = - 4x + 20

d) The cost of 3 comics = $8.

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The solution is, a. Climate change takes place at a constant rate over time.

Climate is the long-term weather pattern in a region, typically averaged over 30 years. More rigorously, it is the mean and variability of meteorological variables over a time spanning from months to millions of years.

here, we have,

A climate can be define as the average state of the everyday weather condition which remain probably stable for a period of 30 years. It is measured by various parameters like atmospheric pressure, temperature and humidity.

so,

On the basis of the above description, a.Climate change takes place at a constant rate over time. is the correct option.

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