a box of a dozen donuts contains 5 glazed, 3 blueberry, and 4 chocolate donuts. what is the probability that you randomly choose a chocolate donut from the box? state your answer as a reduced fraction.

We have:

ab = bc (hypothetical)

so the triangle ABC is isosceles at B

we have: bd is the height of the triangle ABC, so BD is perpendicular to AB

Consider the triangle ABD and the right triangle ACD have:

AB = BC (hypothesis)

BD is the common edge

So the triangle ABD = triangle ACD (hypotenuse - acute angle)

hence the angle ABD = angle ACD

Mr. David Miller, a statistician, is interested in selecting a sample. He want to give equal probability to each population unit to be selected in the sample. This method is called option (a) simple random sampling

Simple random sampling is a method of selecting a sample from a population where each unit has an equal chance of being selected. This means that every member of the population has the same probability of being chosen for the sample, making it a fair and unbiased method of sampling.

The process involves selecting units at random, without any specific order or pattern. Simple random sampling is commonly used in research studies to obtain representative samples from a population, as it ensures that the sample is a true reflection of the population and reduces the risk of bias or error in the findings.

Therefore, the correct option is (a) simple random sampling

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The logarithm statement can be written as

log₃9 = log 9/ log 3

log₉ 3 = log 3/log 9

log₂ 8 = log 8/ log 2

log₈2 = log 2/ log 8

What is a logarithm?

The power to which a number must be raised in order to obtain other values is referred to as a logarithm. The easiest way to express large numbers is this way. Numerous significant characteristics of a logarithm demonstrate that addition and subtraction logarithms can also be written as multiplication and division of logarithms.

"The exponent by which b must be raised to yield an is the logarithm of a positive real number a with respect to base b, a positive real number not equal to 1"

Given logarithm are log₃9, log₉ 3, log₂ 8, log₈2.

Apply the formula \(log_ab\) = log b/log a:

log₃9 = log 9/ log 3

log₉ 3 = log 3/log 9

log₂ 8 = log 8/ log 2

log₈2 = log 2/ log 8

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The likelihood of each utility function representing actual investor preferences varies based on different factors such as risk aversion, wealth accumulation, and personal preferences.

Utility function (a) U(W) = \(W^2\) represents a preference for increasing wealth at an increasing rate, indicating risk aversion and a desire for wealth accumulation. This is a commonly observed preference among investors.

Utility function (b) U(W) = 1/W represents a preference for wealth preservation and risk aversion. It implies that the marginal utility of wealth decreases as wealth increases, which aligns with the concept of diminishing marginal utility.

Utility function (c) U(W) = -W represents a preference for taking on risk and potentially incurring losses. This utility function implies a risk-seeking behavior, which is less common among investors who typically aim to maximize their wealth.

Utility function (d) U(W) = W represents a preference for increasing wealth linearly. This utility function suggests a risk-neutral attitude where investors are indifferent to risk and aim to maximize their wealth without considering risk factors.

Utility function (e) U(W) = ln(W) represents a preference for wealth accumulation, but with a decreasing marginal utility. This logarithmic utility function reflects risk aversion and diminishing sensitivity to changes in wealth.

Utility function (f) U(W) = \(W^(1-γ)\)/(1-γ), with γ = 2, represents risk-neutral behavior. However, the likelihood of this utility function representing actual investor preferences depends on the specific value of γ chosen. If γ is different from 2, it may represent risk aversion or risk-seeking behavior.

Overall, utility functions (a), (b), (d), and (e) are more likely to align with actual investor preferences due to their consistency with risk aversion and wealth accumulation. Utility function (c) represents a less common risk-seeking behavior, and utility function (f) depends on the chosen value of γ, making it less likely to represent typical investor preferences.

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(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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The task requires analyzing a list of departments and performing several tasks related to relationship codes, activity relationship diagrams, reason codes, a worksheet, and a dimensionless block diagram.

We need to consider the number of departments. Since we have 7 departments listed, the number of relationship codes can be calculated using the formula: (n * (n-1)) / 2, where n is the number of departments.

Substituting the value of n = 7, we get:

Relationship Codes = (7 * (7-1)) / 2

= (7 * 6) / 2

= 42 / 2

= 21

Therefore, there will be 21 relationship codes in the chart.

Create an activity relationship diagram:

An activity relationship diagram visually represents the relationships between departments. Here is a basic diagram representing the given departments:

Receiving --+

           +-- Assembly & Shipping -- Offices

Fabrication--+

           +-- Painting -- Stores

Restrooms & Lockers

Populate the diagram with codes for all the relationships:

To populate the diagram with codes, we can assign a unique code to each relationship. Here's an example of assigning codes to the relationships in the diagram:

Receiving (R) --+

               +-- Assembly & Shipping (AS) -- Offices (O)

Fabrication (F)--+

               +-- Painting (P) -- Stores (S)

Restrooms & Lockers (RL)

What is the percentage of codes in each category? Does it follow the standard percentages?

To determine the percentage of codes in each category, we need to count the number of codes in each category and calculate the percentage relative to the total number of codes (21).

In this case, we have the following categories and their respective codes:

Production: R, F, AS, P (4 codes)

Administration: O, S (2 codes)

Support: RL (1 code)

Percentage of Production codes = (4 / 21) * 100 ≈ 19.05%

Percentage of Administration codes = (2 / 21) * 100 ≈ 9.52%

Percentage of Support codes = (1 / 21) * 100 ≈ 4.76%

These percentages do not necessarily follow any standard percentages. The distribution of codes among categories can vary depending on the specific organization or context.

Provide at least 3 reason codes for the chart:

Reason codes are used to provide explanations or justifications for the relationships depicted in the chart. Here are three example reason codes for the given chart:

R01: Receiving department receives raw materials and supplies from external sources.

AS01: Assembly & Shipping department assembles products and prepares them for shipment.

O01: Offices department provides administrative support and management functions for the organization.

Create a worksheet to assist in the creation of the dimensionless block diagram:

Here's an example of a worksheet that can assist in creating the dimensionless block diagram:

Relationship Code From Department To Department

R Receiving Fabrication

F Fabrication Painting

AS Assembly & Shipping Offices

P Painting Stores

RL Restrooms & Lockers -

O Offices -

S Stores -

This worksheet lists the relationship codes along with the corresponding "From" and "To" departments.

Create a dimensionless block diagram for your data B. Show the flow through the dimensionless block diagram:

A dimensionless block diagram represents the flow of activities or information between different departments. Here's an example of a dimensionless block diagram based on the given data:

Receiving --> Fabrication --> Painting --> Stores

                  |

                  v

        Assembly & Shipping --> Offices

                  |

                  v

       Restrooms & Lockers

The arrows indicate the flow of activities or information from one department to another.

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The surface area of the composite figure is 217.28yd²

The volume of the composite figure is 141.12yd³

A composite figure can be defines as a shape created with two or more basic shapes.

The composite figure consist of a triangular prism and cuboid

The surface area of the cuboid =2(lh+lb+bh)

= 2 ( 4.8×2.8 + 8× 2.8 + 4.8×8)

= 2( 13.44+22.40+38.4)

= 2(74.24)

= 148.48yd²

The surface area of the prism = 2B+ph

Base area = 1/2 × 3×8 = 12

The perimeter = 3+8+5 = 16

SA = 2×12+ 16×2.8

SA = 24+44.8

SA = 68.8yd²

the surface area of the composite figure = 148.48+68.8 = 217.28yd²

The volume of the cuboid = 4.8× 2.8 × 8 = 107.52yd³

Volume of the prism = base area × height = 12×2.8 = 33.6yd³

Therefore the volume of composite figure= 107.52+33.6 = 141.12 yd³

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Answer:

4.5

Step-by-step explanation:

Answer:

4.5 (Rounded to the nearest tenth)

Step-by-step explanation:

\(\sqrt{20} =4.472135955........\\\)

Rounded to the nearest tenth: 4.5 because you would round up

Answer:

452km

Step-by-step explanation:

Answer:

Given any initial point (x, y), a reflection across the y-axis means the y-coordinate remains the same but the sign of the x-coordinate changes. Therefore, the coordinate expression that gives the coordinates of the point after a reflection across the y-axis is (-x, y).

Step-by-step explanation:

I ctrl c ctrl v the answer so thats it

The new coordinates of the point across the y-axis would be  (-x, y) if the initial point was at (x, y).

Reflection across the y-axis is defined as reflecting a point across they = x,  the x-coordinate, and y-coordinate places, the line y = -x is the coordinates (-x, y).

Any initial point (x, y) will result in a reflection across the y-axis, which will result in the y-coordinate being the same while the sign of the x-coordinate changes.

As a result, the coordinate expression that provides the point's coordinates following a reflection over the y-axis is (-x, y).

Therefore, the new coordinates of the point across the y-axis would be  (-x, y) if the initial point was at (x, y).

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The measurement of the other angles of the quadrilateral are 60 and 200 degrees.

A quadrilateral is a polygon with 4 sides. The sum of angles in a quadrilateral is 360 degrees.

Therefore, the quadrilateral has two angles measuring 60 degrees and 40 degrees and the others are at a ratio of 3 : 10.

Let's find the other angles measurements.

Hence,

360 - 60 - 40 = 260 degrees

This means the other two angles are 260 degrees.

Therefore,

first angle = 3 / 13 × 260

first angle =  780 / 13

first angle = 60 degrees

second angle = 260 - 60 = 200 degrees

Therefore, the angles are 60 and 200 degrees.

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The dilation factor for the question should be 1/2 as per options

So

dilated lengths are

Option D

Answer:

D

Step-by-step explanation:

Figure A is dilated by a scale factor of 1/2.

Hence, new dimensions will be :

⇒ 1/2 × 2 = 1 inch

⇒ 1/2 × 4 = 2 inches

⇒ 1/2 × 1 = 0.5 inch

⇒ 1/2 × 5 = 2.5 inches

Option D has the right dimensions

Answer:

3 and -2

Step-by-step explanation:

3 + (-2) = 3 - 2 = 1

3 * -2 = -6

I assume you're asking to solve for the n-th term in the sequence, \(a_n\).

From the given recursive rule,

\(a_n = a_{n-1} + 2 \implies a_{n-1} = a_{n-2} + 2\)

and by substitution,

\(\implies a_n = a_{n-2} + 2\times2\)

Similarly,

\(a_n = a_{n-1} + 2 \implies a_{n-2} = a_{n-3} + 2\)

\(\implies a_n = a_{n-3} + 3\times2\)

The pattern continues, so that we can write the n-th term in terms of the 1st one:

\(a_n = a_1 + (n-1)\times2 \implies a_n = 10 + 2(n-1) = \boxed{2n+8}\)

So the first few terms of the sequence are

{10, 12, 14, 16, 18, 20, …}

Answer:

135 meters/90 seconds

Step-by-step explanation:

Kathy swims 45 meters in 30 seconds. Divide 90 with 30:

90 seconds/30 seconds = 3 seconds/1 seconds.

Multiply 45 meters with 3 to get the amount she swam in 90 seconds:

45 x 3 = 135

135 meters is your answer.

~

Answer:

9.73  cm to 2 DP

Step-by-step explanation:

Total of the  lengths involved = 7*9.4 +  5*10.2

= 116.8 cm

So the mean of the 12 fingers

= 116.8/12

= 9.73  cm to 2 DP.

(a*) The relation defined as a∼b if there is a book that both students have borrowed is likely to be an equivalence relation.

(b*) The relation defined as a∼b if both students have borrowed exactly the same books is also likely to be an equivalence relation.

(a*) Reflexivity: For any student a, there will be a book that they have borrowed (themselves), so the relation is reflexive.

Symmetry: If student a has borrowed a book that student b has borrowed, then student b also has borrowed that book. Hence, the relation is symmetric.

Transitivity: If student a has borrowed a book that student b has borrowed, and student b has borrowed a book that student c has borrowed, then it implies that student a has borrowed a book that student c has borrowed. Therefore, the relation is transitive.

(b*) Reflexivity: Each student has borrowed the exact same books as themselves, so the relation is reflexive.

Symmetry: If student a has borrowed exactly the same books as student b, then it implies that student b has borrowed exactly the same books as student a. Hence, the relation is symmetric.

Transitivity: If student a has borrowed exactly the same books as student b, and student b has borrowed exactly the same books as student c, then it follows that student a has borrowed exactly the same books as student c. Therefore, the relation is transitive.

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Answer:

2x^3+17x^2+44x+36

Step-by-step explanation:

(X+2)(X+2)

X^2+2x+2x+4

X^2+4x+4(2x+9)

2x^3+9x^2+8x^2+36x+8x+36

2x^3+17x^2+44x+36

Hopes this help please mark brainliest

The null and alternative hypothesis for testing to see if there is a relatonsip between age and opinion for the question asked by gallup is Divorce Opinions and Gender I.

We introduce the results of a

May 2010 Gallup poll of 1029 US adults. When asked if they view divorce as “morally acceptable”,

71% of the men and 67% of the women in the sample responded yes. In the test for a difference in

proportions, a randomization distribution gives a p-value of 0.165. Does this indicate a significant

Solution

If we use a 5% significance level, the p-value of 0.165 is not less than α = 0.05 so we would not

reject H0 : pf = pm. This means the data do not show significant evidence of a difference in the

proportions of men and women that view divorce as “morally acceptable”

Solution

(a) The p-value (0.003) is small so the decision is to reject H0 and conclude that the mean recall

for sleep (¯xs = 15.25) is different from the mean recall for caffeine (¯xc = 12.25). Since the mean

for the sleep group is higher than the mean for the caffeine group, we have sufficient evidence to

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Step-by-step explanation:

large is 3 times larger than medium.

2 1/4 × 3 = 6 3/4

large is 6 times larger than small.

1 1/8 × 6 = 6 6/8 = 6 3/4

medium is 2 times larger than small.

1 1/8 × 2 = 2 2/8 = 2 1/4

Answer:

yes (5,9) is a solution to the system of inequalities

Step-by-step explanation:

5+9= 14

14>12 - this statement ends up being true

2(5)-9

10-9=1

1<4- this statement also ends up being true

Answer:

20 and 55

Step-by-step explanation:

You subtract 35 from 75 to remove the difference between the two numbers.

Then you divide 40 by 2 to get 20 as one of the numbers. Then you add 35 to one of the 20's to get 55.

There is no sufficient evidence at the 0.05 level of significance that the percentage is not 58%.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given percentage = 98%

alpha = 0.05

First we will design the null hypothesis.

null hypothesis: p greater than or equal to 0.58

and alternate hypothesis: p is less than to 0.58

The null hypothesis shows that 58% or more readers owns a Rolls Royce.

The alternative hypothesis shows less than 58% of the readers own a rolls Royce.

Thus, the null hypothesis is selected.

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Driving a personal car would be the most cost-effective mode of transportation for this commute, with a total daily cost of approximately $4.60 ($3.60 for gas + $1 for travel time).

Based on the given information, the most cost-effective mode of transportation for this commute would be to drive a personal car. Taking public transportation or carpooling may be more environmentally friendly options, but they may not save as much money as driving alone.

Assuming an average speed of 60 miles per hour on the highway, the commute would take approximately 20 minutes each way, or 40 minutes round-trip. This means the total cost of travel time for each workday would be $40 ($60/hour x 2/3 hour).

Using a cost calculator such as GasBuddy, we can estimate that the cost of driving 20 miles per day (round-trip) would be around $3.60 per day, assuming an average fuel efficiency of 25 miles per gallon and a gasoline price of $2.50 per gallon.

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Answer: 10%

Step-by-step explanation: R20 = 100

Therefore R1 = 100%÷ R20 = 5%. The difference between R22 and R20 is R2, therefore the increase in % is R2×5%=10%.

Answer:

+10%

Step-by-step explanation:

i got it right on edge

Answer:

can you send a more clear photo its quite blurry

From the figure, angle ACB anf angle BCD are complementary, that is,

∠ACB + ∠BCD = 90°

Replacing with data

61° + ∠BCD = 90°

∠BCD = 90° - 61°

∠BCD = 29°

From the picture, angle BCD and angle FCE are vertical angles, then they are congruent, which means that:

∠FCE = ∠BCD = 29°

Angle FCA is a right angle, that is, ∠FCA = 90°. Therefore:

∠FCE + ∠FCA = ∠ACE

29° + 90° = ∠ACE

119° = ∠ACE

Answer:

44.4% according to A P E X

Step-by-step explanation:

A P E X