A simple random sample of 31 observations was taken from a large population that has a mean of 5.2 and a standard deviation of 1.1. From the sample, the average was calculated to be 5 and the standard deviation was computed as 0.92. The number 1.1 in this scenario is a

1.738 kg of coffee are required to produce 200 cups of coffee.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal.

Now it is given that,

1 pound of coffee yield 50 cups.

Since 1 pound = 0.4535 kg

Therefore, 0.4535 kg of coffee yield 50 cups.

Let x be the kgs of coffee that yields 200 cups of coffee.

Thus by proportion we can write,

0.4345 / 50 = x / 200

By cross multiplication we get,

50 x = 0.4345 * 200

⇒ 50x = 86.9

⇒ x = 86.9 / 50

⇒ x = 1.738 kgs

which is the required amount of coffee need to yield 200 cups.

Thus, 1.738 kg of coffee are required to produce 200 cups of coffee.

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The recommended rule to sequence the jobs for minimum flow time is the EDD (Earliest Due Date) rule.

The EDD rule prioritizes jobs based on their due dates, where jobs with earlier due dates are given higher priority. By sequencing the jobs in order of their due dates, the goal is to minimize the total flow time, which is the sum of the time it takes to complete each job.

In this case, applying the EDD rule, the sequence of jobs would be as follows:

D (Due on Friday 10th June)

F (Due on Tuesday 14th June)

E (Due on Wednesday 15th June)

C (Due on Friday 17th June)

G (Due on Thursday 16th June)

H (Due on Saturday 18th June)

A (Due on Monday 13th June)

B (Due on Monday 20th June)

By following the EDD rule, we aim to complete the jobs with earlier due dates first, minimizing the flow time and ensuring timely delivery of the orders.

Therefore, the recommended rule for sequencing the jobs in this scenario is the EDD (Earliest Due Date) rule.

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The population mean (μ) is estimated to be: μ = 18 minutes

In this problem, we are given a sample of 81 people who waited in line for a rollercoaster at an amusement park. We are also given the sample mean (18 minutes) and the sample standard deviation (0.5 minutes).

To estimate the population mean (μ), we use the sample mean (18 minutes). Since the sample mean is a good estimate of the population mean, the estimated population mean (μ) is 18 minutes.

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The expected population mean () is: = 18 minutes.

Additionally, the sample mean (18 minutes) and sample standard variation are provided (0.5 minutes).

We use the sample mean to determine the population mean (). (18 minutes). The expected population mean () is 18 minutes because the sample mean is a reliable indicator of the population mean.

Answer:

The price of 1 marker is $3

Step-by-step explanation:

15/5 = 3

Answer:

5 markers cost $6.55 :)

The coordinates of point B on the triangle after the dilation is (8, 12)

The given parameters are:

Triangle coordinates = A(1, 1), B(2, 3) and C(4, 1)

The scale factor of dilation is given as

Scale factor = 4

Mathematically, this transformation can be represented as

(x, y) = 4(x, y)

So, we have

(x, y) = (4x, 4y)

When represented as a function, we have

Image = 4 * Point

Substitute the points in the equation Image = 4 * Point

So, we have the following equation

Image = 4 * [A(1, 1), B(2, 3) and C(4, 1)]

For point B, we  have

B' = 4 * (2. 3)

Evaluate the product

B' = (8, 12)

Hence, the image is (8, 12)

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Answer: 8,12

Step-by-step explanation: I’m always right

To round 59° to four decimal places, we use the following formula:

Rounded Value = round(59°, 4)

Rounded Value = 59.0000°

The probability of event E c is P(Ec) = 1 - P(E) = 1 - 0.32 = 0.68. This is the simplified answer.

To explain further, the probability is a measure of the likelihood of an event occurring, given a set of circumstances. It is expressed as a number between 0 and 1, with 0 indicating that an event cannot happen, and 1 indicating that an event is certain. In this case, the probability of event E is 0.32. This means that, given the specified circumstances, event E is 32% likely to occur.

The probability of event E c is the probability of event E not occurring. This is calculated by subtracting the probability of event E from 1. So, in this example, the probability of event E c is 1 - 0.32 = 0.68. This means that, given the specified circumstances, event E c is 68% likely to occur.

Overall, the probability of event E c, given that P (E)=0.32, is 0.68.

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Answer:

Arithmetic is a branch of mathematics that consists of the study of numbers, especially concerning the properties of the traditional operations on them - addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Answer:

The arithmetic mean is the simplest and most widely used measure of a mean, or average. It simply involves taking the sum of a group of numbers, then dividing that sum by the count of the numbers used in the series.

Step-by-step explanation:

9514 1404 393

Answer:

  (x, y) = (-2.5, -4)

Step-by-step explanation:

Since you are given an expression for y, it is convenient to substitute that into the second equation.

  2x -3(6x +11) = 7

  2x -18x -33 = 7

  -16x = 40 . . . . . . add 33

  x = -40/16 = -2.5

Using the equation for y, we find ...

  y = 6(-2.5) +11 = -15 +11 = -4

The solution is (x, y) = (-2.5, -4).

Answer:

Step-by-step explanation:

\(\frac{-3x}{2}\) = 5

multiply both sides by 2

2 ( \(\frac{-3x}{2}\) = 5 )

-3x = 10

divide both sides by  \(\frac{-1}{3}\)

\(\frac{-1}{3}\) ( -3x = 10 )

x = \(\frac{-10}{3}\)

got it?

Answer:

x = -10/3

Step-by-step explanation:

2(-3x/2) = (5)2

-3x = 10

-----    ---

-3     -3

x = -10/3

Answer: 1 7/16

Step-by-step explanation: If you look at a ruler 1 7/8 is just a little behind 1 7/16 while 1 3/4 is far behind. Also 2 1/8 is past where the green line stops.

Answer:

option 1) 1 7/8"

Step-by-step explanation:

its clearly visible that the green line covers 1 unit completely.

but it stops before it can reach 2 units.

check the attachment

it will be at a distance of 1/ 2 units from the "unit 1".

( since 1 and 2 are 1 unit apart their mid point will lie exactly at rhe center that is 1/ 2 = 0.5)

since the "mid point" is at a distance of 0.5 units from "unit 2", second mid point will be at a distance of (1/ 2)/ 2 = 1/ 4 units from "mid point".

since they're 1/ 4 units apart the third mid point will be (1/ 4)/2 units away from "second mid point"

and this is where the green line stops!

we got these points now well just add them up, to get the distance of required point from unit 1.

1/ 2 + 1/ 4 + 1/ 8

= 7/ 8

and this is in centimeters so add a " after it

1 7/ 8"

that is option 1.

Answer:

y = - 5x + 48

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 5x + 1 ← is in slope- intercept form

with slope m = - 5

Parallel lines have equal slopes, thus

y = - 5x + c ← is the partial equation

To find c substitute (9, 3) into the partial equation

3 = - 45 + c ⇒ c = 3 + 45 = 48

y = - 5x + 48 ← equation of parallel line

Answer:

SAS

Step-by-step explanation:

The triangles are similar by SAS. Two side lengths are given, and we know that vertical angles are congruent.

It is not SSS because we do not know the side lengths of FG and BC.

It is not AA because we do not know two angle measurements.

Answer:

if you can tell me what this ^means i can help you

Answer:

Table A

Step-by-step explanation:

None of the numbers in the x values are repeating

b) h = \(tan \theta\)  x 17 is the required equation.

c) The height of the streetlight is 20.4 ft.

The height of the person is 6 ft.

The distance at which the person is standing from the streetlight = 12 ft.

The distance at which the person's shadow appears = 5ft.

a) Hence, we can make the following diagram.

The right triangle below gives a visual representation of the problem. It shows the known quantities and a variable 'h' to indicate the height of the streetlight.

b) Let's now find an equation trigonometric function involving the unknown quantity 'h'.

from the below diagram, we can say that,

\(tan \theta\) = h/base

base= 12+5=17

hence we have, \(tan \theta\) = h/17

h = \(tan \theta\)  x 17 is the required equation.

c) Now we have to find the height of the streetlight.

firstly let's find the value of \(\theta\),

\(\theta\) = tan 6/5.

\(tan^{-1}\)(6/5) = 50.2°

hence, tan 50.2 = h/17

                   1.20 = h/17

                         h= 1.20 x 17

                         h= 20.4 ft.

Hence, the height of the streetlight is 20.4 ft.

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The Fahrenheit temperature of 100°C is 212°F. So, we can put the given Celsius temperature in the above formula:F = 9/5(100) + 32F = 180 + 32F = 212°FTherefore, the Fahrenheit temperature of 100°C is 212°F.

Given, Celsius temperature c = 100°FTo find Fahrenheit temperature, we can use the formula:F = 9/5C + 32Put the given Celsius temperature into the formula:F = 9/5(100) + 32F = 180 + 32F = 212°F. Therefore, the Fahrenheit temperature of 100°C is 212°F.

We know that the formula for converting Celsius to Fahrenheit is given by:F = 9/5C + 32Where, F is the temperature in Fahrenheit and C is the temperature in Celsius.Water boils at 100°C. So, we need to find the Fahrenheit temperature when Celsius temperature is 100°F.So, we can put the given Celsius temperature in the above formula:F = 9/5(100) + 32F = 180 + 32F = 212°FTherefore, the Fahrenheit temperature of 100°C is 212°F.

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Answer:

5

Step-by-step explanation:

To find the prime factorization of a number, start by dividing the number by each prime number that you can divide by as many times as possible, starting with the smallest prime number and moving up. Then move on to the next prime number. The last division must give a quotient of 1. Then the prime factorization is the product of all the prime factors you divided the number by.

Here's how you use this method with 180.

Here are the first 10 prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Start by trying to divide by 2. 180 is divisible by 2.

180/2 = 90       90 is divisible by 2.

90/2 = 45         45 is not divisible by 2, so now try 3.

45/3 = 15          15 is divisible by 3.

15/3 = 5            5 is prime, so it is divisible by 5.

5/5 = 1              The divisors in bold are the prime factors of 180.

180 = 2 × 2 × 3 × 3 × 5

180 = 2² × 3² × 5

Answer: 5

Answer:

5

Step-by-step explanation:

180

/\

2 90

/\

9 10

/\ /\

3 3 2 5

180 = 2 × 3 × 3 × 2 × 5

2² × 3² × 5

NOTE: The numbers underlined in the factor tree are prime numbers.

Also, 2²is 4 (2 × 2)

3² is 9 (3 × 3)

4 × 9 = 36

36 × 5 = 180

The image of the transformation is added as an attachment

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

The figure

From the figure, we can see that

The horizontal line is the axis of rotation

Using the above as a guide, we have the following:

The image of the transformation would be a reflection of the original figure on the other axis

See attachment for the image of the transformation

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Answer:

49/12 or 4 1/12 or 4.083 (all the same answer in different forms)

Step-by-step explanation:

2m-14m+49=0

-12m+49=0

-12m+-49

m=49/12

Answer: m=7

Step-by-step-explanation:

m^2-14m+49=0

(m-7)^2=0

m-7=0

m=7      

Substituting the values we found, the vector V becomes: V = (34 * cos(120°)) * i + (34 * sin(120°)) * j. To find the horizontal and vertical components of a vector given its length and direction, and write the vector in terms of the vectors i and j, we can use trigonometry.

Let's denote the vector as V and its horizontal component as Vx and vertical component as Vy. Given:

||V|| = 34 (length of the vector)

θ = 120° (direction of the vector)

To find Vx, we can use the formula Vx = ||V|| * cos(θ).

Vx = 34 * cos(120°).To find Vy, we can use the formula Vy = ||V|| * sin(θ).

Vy = 34 * sin(120°).

Now, to write the vector V in terms of the vectors i and j, we can express it as V = Vx * i + Vy * j.

Substituting the values we found, the vector V becomes:

V = (34 * cos(120°)) * i + (34 * sin(120°)) * j.

Please note that in this expression, i represents the unit vector in the horizontal direction, and j represents the unit vector in the vertical direction.

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The distribution A must has a smaller standard deviation. So, option C is correct.

Normal usually refers to the word "normal" in normal distribution.

The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from mean, its chances decrease.

If we've got a normal distribution, then we can convert it to a standard normal distribution and its values will give us the z score.

If we have

\(X \sim N(\mu, \sigma)\)

(X is following a normal distribution with mean and standard deviation )

then it can be converted to a standard normal distribution as

\(Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)\)

Normal curve A has a wider distribution than Normal curve B.

The distribution A must has a smaller standard deviation.

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The coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point on the directed line segment that partitions it into a ratio of 1 to 3, we can use the concept of section formula.

The section formula states that if we have two points A(x₁, y₁) and B(x₂, y₂) dividing a line segment in the ratio of m₁ : m₂, then the coordinates of the dividing point P are given by:

Px = (m₁ * x₂ + m₂ * x₁) / (m₁ + m₂)

Py = (m₁ * y₂ + m₂ * y₁) / (m₁ + m₂)

In this case, the ratio is 1:3, which means m₁ = 1 and m₂ = 3. The given points are A(6, 2) and B(8, -10). Substituting these values into the formula, we can calculate the coordinates of the dividing point P:

Px = (1 * 8 + 3 * 6) / (1 + 3) = 7

Py = (1 * -10 + 3 * 2) / (1 + 3) = -2/2 = -1

Therefore, the coordinates of the point that divides the line segment from (6, 2) to (8, -10) into a ratio of 1 to 3 are (7, -1).

To find the coordinates of the point that divides the line segment between (6, 2) and (8, -10) in a 1:3 ratio, we can use the section formula. Applying the formula, where m₁ is 1 and m₂ is 3, the point P(x, y) can be determined.

By substituting the values into the formula, the x-coordinate is calculated as (1 * 8 + 3 * 6) / (1 + 3) = 7, and the y-coordinate is (1 * -10 + 3 * 2) / (1 + 3) = -1. Thus, the coordinates of the point that partitions the line segment into a ratio of 1 to 3 are (7, -1).

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Given:

Modeling: Slope intercept equation of a line

To find:

The slope intercept equation of a line.

Solution:

The slope intercept equation of a line is defined as:

\(y=mx+b\)

Where, m is the slope and b is the y-intercept.

It means the line intersects the y-axis at (0,b).

For example: The slope of a line is 2 and its y-intercept is 1, then the slope intercept of the line is:

\(y=2x+1\)

Therefore, the slope intercept form of a line is \(y=mx+b\), where m is the slope and b is the y-intercept.

For the function transformation form of f(x), \(g(x) = a f(\frac{1}{b} x - h) + k \), we are replacing variable a by 2, result will in the transformation displayed in the above graph. So, option(d) is right one.

A transformation is an another way to a parent function's graph. There are serval formulas for distinct rules of transformation. If consider transformation function of f(x) is g(x) = f(x - h) + k,

We have a function f(x) = 2cos(x), that is cosine function and g(x) is it's transform function. Here, \(g(x) = a f(\frac{1}{b} x - h) + k \), now see the graph carefully.

Thus, for g(x) in above graph, there are no horizontal and vertical translation. So, h = k = 0. Also, the graphs are not reflected on both axes. However, notice that the graph of g(x) is just the vertical stretched version of f(x). The values of g(x) are twice that of f(x). Therefore, the factor a must be twice, a = 2. Hence, we replace a by 2.

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Complete question:

The above graph of shows f(x) = 2cos(x) and transform g(x). For the transformation rule in the form , g(x) = a f( 1/b x - h) + k

replacing which variable with what number will result in the transformation displayed in the graph?

a) b is replacing by 1/2

b) k is replacing by -1/2

c) h is replacing by -2

d) a is replacing by 2

The value of the test statistic is 6.51.

The test statistic for this problem can be calculated using the formula:

z = (p - P) / √(P * (1 - P) / n)

Where p is the sample proportion (0.67 in this case), P is the hypothesized population proportion (we don't know this value, so we assume it to be 0.5 for a two-tailed test), n is the sample size (380), and z is the standard normal distribution value corresponding to the level of significance.

Plugging in the values, we get:

z = (0.67 - 0.5) / √(0.5 * (1 - 0.5) / 380) = 6.51

So the value of the test statistic is 6.51.

The test statistic is a measure of how far the sample proportion deviates from the hypothesized population proportion under the null hypothesis. In this case, we assume that the population proportion is 0.5 (since we have no reason to believe otherwise), and we calculate the probability of observing a sample proportion of 0.67 or greater assuming this null hypothesis is true.

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Answer:

x = 5

Step-by-step explanation:

the radius (centre to edge) is the same right around the circle.

so that means that distance O to left edge of line that is 24 long = 13.

draw a line from O to top left end of 24 line. label that left end A. also, where the vertical line from O meets the 24 line, call that B.  notice how OAB has just become a right-angled triangle?

we can see that AB = 12.

we have a right-angled triangle.

x is the length OB.

OB² = 13² - 12²

      = 169 - 144

      = 25

OB = √25 = 5.

OB = x = 5

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{x = - 4}}}}}\)

Step-by-step explanation:

\( \sf{3x - 5 = 2x - 9}\)

Move 2x to left hand side and change it's sign

⇒\( \sf{3x - 2x - 5 = - 9}\)

Move 5 to right hand side and change it's sign

⇒\( \sf{3x - 2x = - 9 + 5}\)

Collect like terms

⇒\( \sf{x = - 9 + 5}\)

Calculate

⇒\( \sf{x = - 4}\)

Hope I helped!

Best regards!!

The correct statements are:

b. The population variances for each of the cells should be equal (i.e., there is homogeneity of variance).

c. The populations from which the samples are taken for a two-way ANOVA must be distributed normally.

In a two-way ANOVA, there are several assumptions that need to be met for valid statistical inference. Two of these assumptions are the equality of population variances and the normal distribution of populations.

b. The assumption of homogeneity of variance states that the population variances for each combination of levels of the two factors in a two-way ANOVA should be equal. Violation of this assumption can lead to biased results and affect the validity of the statistical test.

c. The assumption of normality states that the populations from which the samples are taken should follow a normal distribution. This assumption is important because the validity of the F-test used in ANOVA is based on the assumption of normality. Departures from normality can impact the accuracy and reliability of the results.

a. The statement in option (a) is not true. The two-way ANOVA is not robust to violations of the assumptions of sampling from normal distributions and homogeneity of variance, even if the samples are of equal size. Violations of these assumptions can lead to inaccurate and unreliable results.

d. The statement in option (d) is also not true. If the assumptions of a two-way ANOVA are violated, it does not necessarily mean that the researcher should conduct two separate one-way ANOVAs. There are alternative non-parametric tests or robust ANOVA methods that can be used in such cases. The choice of appropriate statistical analysis depends on the nature of the data and the specific research question.

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