A farmer keeps cows and pigs on his farm.
The ratio of cows to pigs on the farm is 2:3
(a) What percentage of the animals on the farm are cows?
(b) What percentage of the animals on the farm are pigs?

Answers

Answer 1

So, 40% of the animals on the farm are cows, whereas 60% are pigs.

What is percent?

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.

Here,

(a) On the farm, the cow-to-pig ratio is 2:3, which means that for every 5 animals, there are 2 cows and 3 pigs. To get the percentage, divide the number of cows by the total number of animals and multiply by 100. As a result, the farm's cow proportion is:

(2 / (2 + 3)) * 100 = 40%

(b) To find the percentage of pigs on the farm, we can use the same method as for the cows. The percentage of pigs on the farm is:

(3 / (2 + 3)) * 100 = 60%

So, 40% of the animals on the farm are cows, and 60% of the animals are pigs.

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Related Questions

1. Simplify the following expression. (84x + 82y) - (14x + 38y)

Answers

Answer:

70x+44y

Step-by-step explanation:

step 1: distribute

84x+82y−(14x+38y)

84x+82y−14x−38y

step 2: combine like terms

84x+82y−14x−38y

84+82−14−38

70x+44y

Please Help!!! Will mark brainliest!

Answers

Answer:

4th

Step-by-step explanation:

first is over y-axis and the linear translation: 6 horizontal and -5 vertical

PLS PLS ANWSer ASAP ITS GRADED I NEEd at least

Answers

Answer:

The third angle is 60

Step-by-step explanation:

The interior angle of a triangle is equal to the 180 minus the exterior angle.

[tex]180-80=100[/tex]

So one of the interior angles is equal to 100

All of the interior angles of a triangle add up to 180

[tex]180=100+20+x[/tex]

[tex]x=60[/tex]

9. the scenario in problem 14 generates an extraneous solution. neither solution makes a denominator equal zero. why can we not use both solutions?

Answers

An extraneous solution is not part of the solution set because it is not valid in the original problem context and may not satisfy the problem's constraints.

The scenario in problem 14 generates an extraneous solution because it is a solution obtained by squaring both sides of an equation, which can lead to extraneous solutions. These extraneous solutions may not satisfy the original equation, and hence, cannot be considered as a valid solution. To determine if a solution is extraneous, we must check if it satisfies the original equation. If it does not, then it is considered extraneous and should not be used.

In other words, an extraneous solution is an extraneous or unintended answer that is obtained as a result of an error in the solution method, but it may not satisfy the original equation or problem. This can occur when using algebraic methods that involve squaring, square roots, or other operations that can cause the equation to change in such a way that some solutions are no longer valid. To ensure that a solution is valid, it is always important to check that the solution satisfies the original equation, and not just the simplified or transformed equation.

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when you solve a system of equations (i.e. two equations with two variables each), what possible form(s) could the solution take

Answers

The solution to a system of equations can take the form of a single ordered pair (x, y) that satisfies both equations, or it can take the form of "no solution" if the equations are inconsistent, or it can take the form of "infinitely many solutions" if the equations are dependent.

After 16 years in an account with a 4.8% annual interest rate compounded continuously, an investment is worth a total of $38,744.77. What is the value of the principal investment? Round the answer to the nearest penny.
$18,068.73
$20,676.04
$17,975.25
$20,769.52

Answers

$18021 is value of the principal investment

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Given that after 16 years in an account with a 4.8% annual interest rate compounded continuously an investment is worth a total of $38,744.77

We have to find the value of the principal investment

[tex]A=Pe^{rt}[/tex]

Where P is the principal amount, r is rate of interest and A is total amount.

[tex]38744.77=Pe^{0.048(16)}[/tex]

[tex]38744.77=Pe^{0.768}[/tex]

38744.77=2.15P

Divide both sides by 2.15

18021=P

Hence, $18021 is value of the principal investment

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Answer:

its the 1st option

Step-by-step explanation:

i jus took the test

eventually, the markov chain will end up in state 2. what is the probability that when the process moves into state 2, it does so from state 1?

Answers

For the markov chain will end up in state 2, the probability that when the process moves into state 2, it does so from state 1 will be calculated as:

Let,

[tex]\tau = \min\{n: X_{n+1}= 2\}[/tex]

Now,

[tex]p_{i,j} = P(X_{\tau}=i|X_{0}=j)[/tex]

We can observe that,

[tex]p_{0,0} = P(X_{\tau}=0|X_{0}=0) = \sum_{k=0}^{2}{P(X_{\tau}=0,X_{1}=k|X_{0}=0)} [/tex]

[tex]=\sum_{k=0}^{2}{P(X_{1}=k|X_{0}=0)P(X_{\tau}=0|X_{1}=k,X_{0}=0)}[/tex]

A Markov chain or Markov process is a stochastic model that depicts a series of potential events where each event's likelihood is solely determined by the state it reached in the previous event. This can be thought of colloquially as, "What happens next depends only on the situation right now. Discrete-time Markov chains (DTMC) are produced by a countably infinite sequence where the chain changes state at distinct time steps. A continuous-time Markov chain (CTMC) is a continuous-time process. It bears the name Andrey Markov after the Russian mathematician. As statistical representations of processes in the real world, Markov chains have numerous uses.

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5 cm
3 cm
7 cm
What is the surface area, in cm², of the figure shown above?

Answers

142 centimeters squared

Find the volume of the cone, height = 11cm radius = 6cm

Answers

Therefore , the solution of the given problem of volume comes out to be volume of cone is  132π cm³.

Describe volume.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two examples of cubic units are cm3 and in3. The amount of matter in a thing is measured by its mass, on the other hand. The weight of an object is typically converted into mass quantities like pounds and kilograms.

Here,

Given :

=>height = 11cm

=> radius = 6cm

Volume of cone :

=> 1/3πr²h

=> 1/3*π * 36 * 11

=> 132π cm³

Thus , volume of cone is  132π cm³

Therefore , the solution of the given problem of volume comes out to be volume of cone is  132π cm³.

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(3^3-6.8)divided by 7

Answers

Answer:

Yurrrr Tha answer to your question is 2.8

Step-by-step explanation:

now tha full Answer is 2.88571429

but hope this help and hope you pass type xhii

which of the following illustrates the abuse of respondents in marketing research? multiple choice selling unnecessary or unwarranted research services having friends and relatives fill out surveys not using the designated sample of respondents but rather anyone who is conveniently available to complete a survey not providing the promised incentive for completing interviews or questionnaires revealing one's clients to the respondents

Answers

An illustrates the abuse of respondents in marketing research is :

Not providing the promised incentive for completing interviews or questionnaires.

Definition of Marketing Research

The world organization body, the American Marketing Association (AMA), conveys the definition of marketing research is a function that connects customers, consumers, or the general public with marketers through information used to identify marketing problems and opportunities.

Meanwhile, Philip Kotler defines marketing research as the systematic design, collection, analysis, and reporting of data or findings that are relevant to a particular marketing situation faced by a company.

Simply put, marketing research is the identification, collection, analysis, and presentation of systematic and objective information to help companies make decisions related to problem solutions and find opportunities in the marketing process.

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a random sample of 100 kernels is taken from a population in hardy-weinberg equilibrium. it is found that 9 kernels are yellow, and 91 kernels are purple. what is the frequency of the yellow allele in this population?

Answers

100 kernels are randomly selected from a population that is in Hardy-Weinberg equilibrium. 9 yellow kernels and 91 purple kernels are discovered. In this population, the yellow allele is 0.09 times more common.

Both citizens who are physically present in a country or who are temporarily away from it, as well as all foreigners who have permanently emigrated to that country, are included in the phrase "people." This indicator represents the population of a particular area. Growth rates are used to describe the differences in population that occur each year as a result of births, deaths, and net migration. In 2022, Russia had the highest population density in Europe—144.7 people per square mile. In terms of population size, Turkey came in second with 85 million people, followed by Germany with 83.4 million, the United Kingdom with 67.4 million, and France with 65.6 million. Vatican City has a population of just over 800, making it the world's least populous country. Vatican City is the smallest totally sovereign nation-state in the world.

The  frequency is 9/10 or 0.09

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HELP TIIMED PLEASE HELP
what is the solution of x+4/2x-1 <0


The answer choices are a.) -4 <= x <= 1/2 b.) -4 < x <= 1/2 c.)-4<= x < 1/2 d.) -4 < x < 1/2

Answers

The solution to the inequality is x < -4

How to determine the solution to the inequality

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

x+4/2x-1 < 0

Multiply both sides of the inequality

So, we have the following representation

x + 4 < 0

Subtract 4 from both sides of the expression

So, we have the following representation

x < -4

Hence, the solution is x < -4

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Use the two-way frequency table to complete the relative frequency table. Drag the numbers into the boxes.

Answers

According to the information, it can be inferred that the percentages are from left to right and from top to bottom the following: 27, 21, 49, 37, 14, 51, 64, 36, 100.

How to find the percentage that each value is equivalent to?

Based on the information in the upper box, we must find the percentage to which each of the values in the lower box is equivalent. To find these percentages we must perform the following mathematical procedure:

1. We must make the rule of three in which the total equals 100%, then we must multiply each of the values in the upper box by one hundred and then divide it by 70.

With the previous procedure we will have the possibility of finding all the values as shown in the table below.

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draw similar rectangles that are in the ratio of 2/3. What is the ratio of the areas of the rectangles you drew.

Answers

The ratio of the areas of the rectangles will be 4:9.

What is the similarity?

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

We know that the sides cannot be the same because it is a rectangle, therefore there is a width and length.

For the width, which is the shortest side, we will keep the radius as it is, that is, for rectangle 1 it will be 2 and for rectangle 2 it will be 3.

For the length, which is the longest side, we multiply the radius by two, which means that rectangle 1 will be 4 (2 x 2) and for rectangle 2 it would be 6 (2 x 3)

If we calculate the area it would be:

Rectangle 1:

2 x 4 = 8

Rectangle 2:

3 x 6 = 18

This means that the radius is 8/18 = 4/9

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The distance a bus travels varies directly with time as shown in the table.



Time (h), x Distance (mi), y
1.5 93.75
3 187.5
4.5 281.25
6 375


Write the constant variation and the mph

Answers

The constant variation rate is given as follows:

62.5 miles per hour.

What is a proportional relationship?

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

Hence we can solve for the constant as follows:

k = y/x.

In the context of this problem, the constant variation rate is the constant of the proportional relationship, obtained dividing one output by it's respective input, hence:

k = 375/6

k = 62.5 miles per hour.

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Need help with trigonometry, please explain each step.

Answers

The ceiling for this problem is given as follows:

450 m.

What are the trigonometric ratios?

The three trigonometric ratios are defined as follows:

Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.

The parameters for this problem are given as follows:

Part of ceiling of x.Adjacent side of 150 m.Angle of 71.5º.

Hence the value of x is obtained as follows:

tan(71.5º) = x/150

x = 150 x tangent of 71.5 degrees

x = 448.3 m.

Adding 1.7 m, the ceiling is obtained as follows:

448.3 + 1.7 = 450 m.

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Deion is in the business of manufacturing phones. He pays a cost of $50 per phone produced for materials and labor and also must pay a daily fixed cost of $200 to rent the building and equipment. Make a table of values and then write an equation for � , C, in terms of � , p, representing total cost, in dollars, of producing � p phones in a given day.

Answers

C = 200 + 50p is the equation represents the total cost, in dollars, of producing p phones in a given day.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

Given that Deion pays a cost of $50 per phone produced for materials and labor.

Deon also must pay a daily fixed cost of $200 to rent the building and equipment.

C = 200 + 50p

The above equation represents the total cost, in dollars, of producing p phones in a given day.

Number of phones (p) Total cost (C)

0                                   200

1                                   250

2                                  300

3                                   350

Hence, C = 200 + 50p is the equation represents the total cost, in dollars, of producing p phones in a given day.

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if the polynomial is divided by (x+4), the quotient is x^2-x+8, and the remainder is -6. Find the original polynomial

Answers

The original polynomial is x^3 - x^2 + 8x + 26.

How to find the original polynomial

The division of a polynomial by a linear factor (x + 4) can be reversed by multiplication:

f(x) = (x^2 - x + 8) * (x + 4) + (-6)

Expanding the product on the right-hand side, we get:

f(x) = x^3 - x^2 + 8x + 32 - 6

f(x) = x^3 - x^2 + 8x + 26

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HELP pls will mark you the brainliest

Answers

From the given graph solution of lines is (32, 5).

What is a linear system of equations?

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

In the give graph two lines intersect at (32, 6).

Here, 32 represents the number of kites and 6 represents the total cost.

Therefore, from the given graph solution of lines is (32, 5).

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a rectangular bin 4 feet long, 3 feet wide, and 2 feet high is solidly packed with bricks whose dimensions are 8 inches by 4 inches by 2 inches. the number of bricks in the bin is

Answers

In the trash can, there are 648 bricks. when the measurements are 8 by 4 by 2 The right response is so (C).

This same total mass of a three-dimensional shape is referred to as its porous structure. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. The cuboid's length, width, and height can also be labeled, and indeed the surface area (SA) can indeed be calculated using the equation SA=2lw+2lh+2hw.

Based on this equation, surface area is equivalent to two times overall combination of width and length, two times its products of length and height, and two times the ratio of both height and width.

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You and your sister are saving money from your allowances. You have $25 and you save $3 each week. Your sister has $40 and she saves $2 each week. In how weeks, you and your sister will have the same amount of money; and at the time, you both will have how much?

Answers

Answer:

15 weeks

Step-by-step explanation:

1 write an equation fore each

you                    sister

y=25+3x            y=40+2x    

y is total money and x is weeks

we want to find when they have the same amount of  total money we set them equal to echother

25+3x=40+2x

-2x             -2x

25+x=40

-25      -25

x=15

you will have the same amount as yore sister in 15 weeks

Answer:

see below

Step-by-step explanation:

you: 25 +$3 /week * x weeks

sis: 40 + 2/week * x weeks

they have to equal to each other

so 25 + 3x = 40 +2x

move x around & simplify

so x = 15

total 25+3*15 = 25+45 = 70

8. A Caribbean resort has a nightly limbo contest on the beach. Participants must be less than 64 inches tall. The distribution of heights of adult American men is approximately normal with mean 69 inches and standard deviation 2.5 inches. a. What percent of adult American males could enter this contest? b. How tall would a man have to be for his height to be in the top 15% of this distribution of adult American men?​

Answers

The percent of adult American males could enter this contest is 2.23%

What does "normal" describe in statistics?

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

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

We solve using z score formula

z = (x-μ)/σ,

where, x is the raw score = < 64 inches

μ is the population mean = 69

σ is the population standard deviation = 2.5

Here Participants must be less than 64 inches tall.

For x < 64 inches

z = 64 - 69/2.5

z = -2

Probability value from Z-Table:

P(x<64) = 0.02275

Converting to percentage;

= 0.02275 × 100

= 2.275%

Approximately = 2.23%

The participants must be less than 64 inches tall to participate in this limbo contest, the percent of adult American males thag could enter this contest is 2.23%

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Which length and width are possible dimensions for the garden?

Answers

The length and width are possible dimensions for the garden is l = 20 ft; w = 10 ft.

Square & Rectangle

The characteristics of a square and a rectangle in a flat shape are very different. Although both are rectangular, the nature and characteristics of these two buildings are different.

The difference between a square and a rectangle can be seen from the properties they have. These properties are also characteristics of squares and rectangles. For this reason, if we want to mention the difference between the two wakes, then we must know their characteristics.

Your question is incomplete but most probably your full question was:

Which length and width are possible dimensions for the garden?

l = 20 ft; w = 5 ft

l = 20 ft; w = 10 ft

l = 60 ft; w = 20 ft

l = 55 ft; w = 30 ft

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The level of significance in hypothesis testing is the probability of:A. Accepting a true null hypothesisB. Accepting a false null hypothesisC. Rejecting a true null hypothesisD. None of these alternatives is correct

Answers

The correct option C. Rejecting a true null hypothesis, is the probability in  significance level in hypothesis testing.

Explain about the null hypothesis significance testing?

By testing an experimental component against a no effect or even no relationship hypothesis based on a specific observation, NHST is a statistical inference technique.

The idea that there is no influence on the population is known as the null hypothesis. We may refuse the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect with in population (p ).In the biological, biomedical, and social sciences, null hypothesis significance testing (NHST) continues to be the statistical technique of choice for presenting evidence of an effect.

Thus, the likelihood of rejecting a valid null hypothesis determines the significance level in hypothesis testing.

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Which graph below does not represent a function of x? A B 5432 1 0 1 2 3 4 5 S43N 5 y 2 -5 -4 -3 -2 -1 0 -1 -2 24EN -4 -5 1 2 3 4 5 C D 5 3 2 0 1 2 3 4 5 5 737 7 4 2 1 -5-4-3 -2 -10 -1 N345 -2 -4 -5 DU 1 2 3 4 5​

Answers

The graph that represents the compound inequality –3 < n < 1 is option C.

What is inequality?

The two sides of a mathematical equation having an inequality must be equal. We compare two values via inequality rather than equations. The equal sign is replaced by the signs less than (or less than or equal to), greater than (or greater than or equal to), or not equal to.

The straight line from -3 to 1 with a hollow circle at the -3 point and the 1 point serves as the graph for the compound inequality -3 n 1. This is because n can only have values larger than -3, excluding -3, and less than -1, excluding -1, according to the symbol.

Therefore, the graph that represents the compound inequality –3 < n < 1 is option C.

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5. Rewrite each of the following in simplest form by combining like terms.
(b) -2n+10n
(c) 8y-14y
(a) 9x+14x
CONS
(d) -6w-11w

Answers

(B) 8n  (C) -6y (A) 23x  (D) -17w

Evaluation:

B. 10 + (-2) is the same as 10 - 2, the answer is 8.

C. 8 - 14 could be rewritten as -14 + 8, depending on which is easier to comprehend. The answer is -6

A. 9 + 14 = 23.

D. -6 - 11 is the same as -11 + (-6), which is -17.

Cheers,

qxxi

What is the lateral surface area of the triangular prism shown below?





150 cm2




40 cm 2

190 cm2



170 cm2

Answers

The area of the triangular prism is calculated as; 170 cm²

How to find the Lateral Surface Area of the Prism?

The given triangular prism when broken down is made up of;

2 triangles (top and bottom)

2 side rectangles

1 back rectangle

Formula for area of triangle = ¹/₂ * base * height

Formula for area of rectangle = length * width

Thus;

Area of trapezoid = 2(¹/₂ * 5 * 4) + 3(10 * 5)

Area = 20 + 150

Area = 170 cm²

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A management dilemma defines the research question.True or False

Answers

A management conundrum is an issue or difficulty that a manager faces that necessitates a choice. This difficulty or challenge frequently defines the study question and motivates researchers to conduct research to discover a solution that is the given statement is true.

What is research?

Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Mathematics research is the long-term, open-ended investigation of a series of connected mathematical issues, the answers to which connect to and build upon one another. Because students always come up with new questions to ask based on their observations, problems are open-ended. Student research also has the following characteristics: Students create questions, tactics, and outcomes that are, at least for them, unique. Students employ the same broad techniques as research mathematicians. They go through data collection, visualization, abstraction, conjecture, and proof cycles.

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(1 point) a vertical right-circular cylindrical tank measures 7 ft high and 6 ft in diameter. it is full of kerosene weighing 51.2 pounds per cubic feet. how much work does it take to pump the kerosene to the level of the top of the tank?

Answers

Work done to pump the kerosene is equal to W = 126106 ft-lbs

"Information available from the question"

Height of the cylinder = 7 ft.

Diameter of cylinder = 8 ft.

Radius of the cylinder = 4 ft

Weight of the kerosene = 51.2 lb/ft³

Calculating the volume of cylinder for dy height

dV = π r² dy

dV = π 4² dy

dV = 16π dy

Force acting on the cylinder

dF = W x dV

dF = 51.2 x 16πdy...….(1)

We know

Work done = Force x displacement

Displacement = 7 - y

dW = 51.2 x 16πdy x (7 - y)

Now, integrating both side

[tex]\int\limits dW = \int\limits^7_0 {819.2\pi(7-y) } \, dy[/tex]

[tex]W = [819.2\pi (7-y)^2]^0_7[/tex]

By solving, we get

W = 126106 ft-lbs

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13. what observational evidence do you have to support that combustion is a chemical change? an appropriate answer requires a minimum of two pieces of evidence. there is observational evidence that have to support that combustion is a chemical change. burning steel wheel, candle, sulfur, splint, results in the formation of new chemical. Use prime factorization to find greatest common factorof the moninomial18xy, 12x TRUE/FALSE. when working with a spreadsheet, data analysts can use the where function to locate specific characters in a string. What does a botanist study? WHAT is it!!??!??!HELLPPP MEEE PLSSSS a(n) outcome (not an event) of flipping a coin is heads. to determine if a probability distribution is valid, make sure that all probabilities are between 0% and 100% and the sum of all is 100%. the ratio of the ways to succeed to all possible ways that something can occur is also known as probability . to find out how many ways a multi-step process can be completed, use the . what proofreading techniques should you use for both routine and complex documents? check all that apply. meera needs to remove a gun from a crime scene to take it to the lab. what is the best way for her to complete this process? Which of the following is an example of using a descendant selector to configure the anchor tags within the nav element? a. nav. a b. a nav c. nav a d. a#na a data analyst is studying weather data. they write the following code chunk: bias(actual temp, predicted temp) what will this code chunk calculate? 1 point the total average of the values the minimum difference between the actual and predicted values the maximum difference between the actual and predicted values the average difference between the actual and predicted values 4 over 5 divided by 3 over 4 Doeringers research suggests that Japanese managers pay ______________ attention to values and ____________ attention to business performance. the three dates related to a cash dividend include all of the following: (you may select more than one answer. single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. any boxes left with a question mark will be automatically graded as incorrect.) check all that apply date of declarationunanswered date of paymentunanswered date of issuanceunanswered date of recordunanswered date of payable T/F - REM sleep begins about 90 minutes after sleep begins. two parallel conducting plates are connected to a constant voltage source of 27 kv. if the plates are separated by 18 cm, what is the magnitude of the electric field generated by the plates? bautista corporation reported pretax book income of $1,510,000. included in the computation were favorable temporary differences of $237,500, unfavorable temporary differences of $88,500, and favorable permanent differences of $197,000. compute the company's current income tax expense or benefit. determine the molality of a solution of water dissolved in ethanol for which the mole fraction of water is 0.492. A spinner with 12 equally sized slices has 5 blue slices and 7 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red slice? Write your answer as a fraction in simplest form. frederick taylor believed that workers should do which of the following? provide labor create solutions increase productivity solve problems the client asks the nurse to explain the difference between arteriosclerosis and atherosclerosis. which is the best explanation the nurse can give to the client? select all the statements that are true about operating system roles. group of answer choices the os creates a layer of abstraction between the user/application and the hardware. the modern os allows multiple applications to co-exist in memory and run at the same time. the os mediates requests with differing programs/users. the os ensures that any error an application encounters does not affect other running applications. the os helps users share the same resource when possible. the os takes requests from multiple users and processes them in an order specified by the device. the os keeps copies of recently used information to improve system performance.