Write a polynomial f(x) that satisfies the given conditions. Polynomial of lowest degree with zero of -5/3( multiplicity 2) and 1/6( multiplicity 1) and with f(0)=50

Answers

Answer 1

The polynomial of lowest degree that satisfies the given conditions is f(x) = -108(x + 5/3)^2(x - 1/6).

To find the polynomial f(x), we start by using the zero-factor property of polynomials. Since we are given that -5/3 is a zero of multiplicity 2, we know that the polynomial must contain the factor (x + 5/3)^2. Similarly, since 1/6 is a zero of multiplicity 1, we know that the polynomial must contain the factor (x - 1/6). Thus, a possible polynomial that satisfies the given conditions is:

f(x) = a(x + 5/3)^2(x - 1/6)

where a is a constant that we need to determine. To find a, we use the fact that f(0) = 50:

f(0) = a(5/3)^2(-1/6) = 50

Simplifying this equation, we get:

-25a/54 = 50

Multiplying both sides by -54/25, we get:

a = -108

Thus, the polynomial of lowest degree that satisfies the given conditions is:

f(x) = -108(x + 5/3)^2(x - 1/6).

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Related Questions

Water is flowing at the rate of 50m^3/min into a holding tank shaped like an cone, sitting vertex down. The tank's base diameter is 40m and a height of 10m.
A.) Write an expression for the rate of change of water level with respect to time, in terms of h ( the waters height in the tank).
B.) Assume that, at t=0, the tank of water is empty. Find the water level, h as a function of the time t.
C.) What is the rate of change of the radius of the cone with respect to time when the water is 8 meters deep?

Answers

A.) The rate of change of the water level with respect to time is (1/4) times the rate of change of the radius with respect to time. B.) The water level h as a function of time t is given by the equation h = 50t. C.) The rate of change of the radius of the cone with respect to time when the water is 8 meters deep is 200.

A.) To find the rate of change of the water level with respect to time, we need to use similar triangles. Let's denote the water level as h (the height of the water in the tank) and let's denote the radius of the water surface as r.

Since the tank is in the shape of a cone, we know that the ratio of the change in radius to the change in height is constant. Therefore, we can write:

(r/40) = (h/10)

To find the rate of change of the water level with respect to time (dh/dt), we differentiate both sides of the equation with respect to time:

(d(r/40)/dt) = (d(h/10)/dt)

Now, let's express the rate of change of the radius with respect to time (dr/dt) in terms of the rate of change of the water level with respect to time:

(dr/dt) = (40/10) * (dh/dt)

Simplifying this expression, we get:

(dr/dt) = 4 * (dh/dt)

Therefore, the rate of change of the water level with respect to time (dh/dt) is (1/4) times the rate of change of the radius with respect to time (dr/dt).

B.) To find the water level h as a function of time t, we need to integrate the rate of change of the water level with respect to time (dh/dt) over time. Since water is flowing into the tank at a constant rate of 50m^3/min, we can write:

dh/dt = 50

Integrating both sides with respect to time, we get:

∫dh = ∫50 dt

h = 50t + C

Since we are given that the tank is initially empty at t = 0, we can substitute h = 0 and t = 0 into the equation:

0 = 50(0) + C

C = 0

Therefore, the equation for the water level h as a function of time t is:

h = 50t

C.) To find the rate of change of the radius of the cone with respect to time when the water is 8 meters deep (h = 8), we can use the relationship we derived earlier:

(dr/dt) = 4 * (dh/dt)

We know that the rate of change of the water level with respect to time is dh/dt = 50. Substituting this into the equation, we get:

(dr/dt) = 4 * 50

(dr/dt) = 200

Therefore, the rate of change of the radius of the cone with respect to time when the water is 8 meters deep is 200.

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fill in the missing number: 0,1,1,2,3,5,8,13,-,34,55

Answers

The missing number of the series is 21.

The given sequence appears to follow the pattern of the Fibonacci sequence, where each number is the sum of the two preceding numbers. The Fibonacci sequence starts with 0 and 1, and each subsequent number is obtained by adding the two previous numbers.

Using this pattern, we can determine the missing number in the sequence.

0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55

Looking at the pattern, we can see that the missing number is obtained by adding 8 and 13, which gives us 21.

Therefore, the completed sequence is:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.

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The missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55 is 21.

To find the missing number in the sequence 0, 1, 1, 2, 3, 5, 8, 13, -, 34, 55, we can observe that each number is the sum of the two preceding numbers. This pattern is known as the Fibonacci sequence.

The Fibonacci sequence starts with 0 and 1. To generate the next number, we add the two preceding numbers: 0 + 1 = 1. Continuing this pattern, we get:

011235813213455

Therefore, the missing number in the sequence is 21.

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Indra worked overtime for 8 hours last week. Her regular hourly wage is $7.50. Her overtime rate is 1.5 times her regular wage. How much did she earn in overtime?

Answers

Answer:90 dollar’s

Step-by-step explanation:7.5x1.5=11.25x8=90

If you were constructing a 99% confidence interval of the population mean based on a sample of n=30 where the standard deviation of the sample S=0.05, the critical value of t will be 2.7564 2.4922 2.7969

Answers

The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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jeremy and robin like to collect nickles. Jeremy has n nickels, and Robin has 55 nickels together they have a total of 100 nickels.
Write an equation to describe this situaton

Answers

Jeremy has 45 nickels and Robin has 55 - 45 = 10 nickels.

What is the algebraic equations?

An algebraic equation is a mathematical statement that shows the equality between two expressions, typically with one or more variables.

Let x be the number of nickels Jeremy has. Then, the number of nickels that Robin has is 55 - x.

The total number of nickels they have together is 100, so we can write:

x + (55 - x) = 100

Simplifying the expression, we get:

55 = 100 - x

x = 45

Hence, Jeremy has 45 nickels and Robin has 55 - 45 = 10 nickels.

The equation to describe this situation is:

n = 45

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In a population that is normally distributed with mean 75 and standard deviation 3, the bottom 80% of the values are those less than
.

Answers

The bottom 80% of the values are those less than approximately 72.48.

The bottom 80% of the values are those less than--------?

We can use the Z-score formula to find the cutoff value for the bottom 80% of the distribution. The Z-score formula is:

Z = (X - μ) / σ

where Z is the standardized score, X is the raw score, μ is the mean, and σ is the standard deviation.

To find the cutoff value for the bottom 80% of the distribution, we need to find the Z-score that corresponds to the 20th percentile, which is the value below which 80% of the values lie. We can look up this Z-score in a standard normal table, or use a calculator.

Using a standard normal table, we find that the Z-score corresponding to the 20th percentile is approximately -0.84. Substituting the given values into the Z-score formula and solving for X, we get:

-0.84 = (X - 75) / 3

-2.52 = X - 75

X = 72.48

Therefore, the bottom 80% of the values are those less than approximately 72.48.

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Howard wants to use multiplication to solve {w} = 5 \div \dfrac15w=5÷ 5 1 ​ w, equals, 5, divided by, start fraction, 1, divided by, 5, end fraction.

Answers

The multiplication equation that Howard can use is 5=1/5*w

The equations that involve the multiplication operation are known as multiplication equations. These calculations can be found in everyday life and business, as well as in math examinations and quizzes. When we compute how many hours we worked in a week to determine if our paycheck is proper, we come across multiplication equations. So, what exactly is a multiplication calculation? Our multiplication equation for determining the number of hours worked may look like this: 12x = 480.

W=5÷1/5

Multiply both sides by 1/5

(1/5)w=5÷1/5(1/5)

(1/5)w=5×5/1(1/5)

1/5*w=25/1 * 1/5

1/5*w=25/5

1/5*w=5

It can also be written as

5=1/5*w

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Your question is incomplete, but most probably the complete question was:

Howard wants to use multiplication to solve w=5 divided by 1/5 Which multiplication equation can Howard use?

A:5*1/5=w

B:1/5*5=w

C:5=1/5*w

a three-digit integer contains one of each of the digits , , and . what is the probability that the integer is divisible by ?

Answers

The numbers that end in 5 are divisible are 5, and the probability of choosing those numbers is \(\frac{1}{3}\)

As per the given data the integers are 1, 3, 5

The three digit numbers are 135, 153, 351, 315, 513, 531.

Total possible outcomes are 6.

A number is divisible by 5 only if the units digit is 0 or 5

The integers is divisible by 5 are 135 and 315.

Number of favorable outcomes are 2.

The numbers that end in 5 are divisible are 5, and the probability of choosing those numbers is \(\frac{2}{6}\)

\(=\frac{1}{3}\)

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Circle the outliers in the following scatter plots. -5 15 10 L 5 5 -5 10 15 4 3 2 2 3 4 5 - 60 7

Answers

The outliers in the following scatterplots need to be circled:--5, 15-60

The points (-5,15) and (-60,7) are outliers.

An outlier is a value that lies outside (is smaller or larger) than most other values in a given data set. An outlier may represent a unique event or error. When examining scatterplots, outliers are the values that appear to be farthest from the trend line. Outliers are labeled as "L" in scatterplots. To answer this question, the outliers in the following scatterplots need to be circled:

--5, 15-60

The points (-5,15) and (-60,7) are outliers.

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As part of a quality-control program, 3 batteries from a box of 15 is chosen at random for testing. In how many ways can this test batch be chosen?a) 455 b) 3 c) 2,730d) 45 e) 6

Answers

This test batch can be chosen is 455 ways. (Option A).

The problem is asking for the number of ways to choose 3 batteries out of a box of 15.

This is a combination problem and the number of ways to choose k items out of a set of n items, without regard to the order of selection, is given by the binomial coefficient:

C(n,k) = n!/(k!(n-k)!)

where ! denotes factorial.

So in this case, we have:

C(15,3) = 15!/(3!(15-3)!) = 151413/(321) = 455

So, the answer is 455.

Therefore, This test batch can be chosen is 455 ways. (Option A).

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Which of the following are equal to 16?

Which of the following are equal to 16?

Answers

Answer:

the answer is A. 256

Step-by-step explanation:

256

16^2

=16

A farmhouse shelters 10 animals, some are pigs, and some are ducks. Altogether there are 36 legs. How many pigs are there

Answers

Answer:

8 Pigs.

Step-by-step explanation:

~ P = the number of pig

~ D = the number of ducks

p + d = 10

  4p + 2d = 36

4(10 - d) + 2d = 36

40 - 4d + 2d = 36

40 - 2d = 36

-40       = -40

    -2d = -4

    -2      -2

        d = 2 ducks

p + d = 10

p + 2 = 10

   Therefore, 8 pigs. :)) hope this helped you :))

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 125.2-cm and a standard deviation of 2.3-cm. For shipment, 25 steel rods are bundled together.Find the probability that the average length of a randomly selected bundle of steel rods is less than 124.5-cm.P(M < 124.5-cm) =Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answers

The probability that the average length of a randomly selected bundle of steel rods is less than 124.5-cm i.e.,

P(M < 124.5-cm) is 0.0603..

We have Given that,

The lengths of the steel rods are Normally distributed.

mean of distribution (μ) = 125.2

standard deviation (σ) = 2.3

Sample size (n) = 25

Standard error = σ/√n = 2.3 /√25 = 0.46

convert to P(z < ???) using transformation to z-statistic which is N(0,1):

P(z < (M - population mean)/(standard deviation/square root(sample size))

P(M < 124.5 ) = P[(M - μ ) /σ /√n < ( 124.5 - 125.2 ) /0.46 ]

= P( z < -1.522 )

Using z table,

= 0.0603

Probability = 0.0603

Hence, the Z-score is -1.52 and the required probability is 0.0603

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Work out the value of x?​

Work out the value of x?

Answers

Using angle theorems the value of x = 67.5°

What are angle theorems?

Angle theorems are rules that govern the properties of angles.

Given that we have the figure and we desire to find angle x, we proceed as folllows.

Now, we notice that one angle is a right angle and it is equal to 90°.

Also, we notice that all the angles meet at the same point.

So, we have that

x + 3x + 90° = 360° (sum of angles at a point)

Solving for x, we have that

x + 3x + 90° = 360°

4x + 90° = 360°

4x = 360° - 90°

4x = 270°

x = 270°/4

x = 67.5°

So, the value of x = 67.5°

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The table lists the number of members at a local gym for selected years, where year I represents 2002, year 3 represents 2004, and soon.Year* y = number of members2002 1382004 3532006 573802008 720109100Use the ordered pairs (5,73) and (7,80) to find the equation of a line that approximates the data. Express your answer in slope-intercept form. (If necessary, round the slope to the nearest hundredth and the y-intercept to the nearest whole number.)

The table lists the number of members at a local gym for selected years, where year I represents 2002,

Answers

ANSWER

y = 3.5x + 56

EXPLANATION

The slope of a line passing through points (x1, y1) and (x2, y2) is,

\(m=\frac{y_2-y_1_{}}{x_2-x_1}\)

And the slope-intercept form of the equation of a line is,

\(y=mx+b\)

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

In this problem, we have to use points (5, 73) and (7, 80) to find the equation of the line. First, we can find the slope,

\(m=\frac{80-73}{7-5}=\frac{7}{2}\)

For now, the equation is,

\(y=\frac{7}{2}x+b\)

We have to find the y-intercept, by replacing x and y for the coordinates of one of the given points,

\(80=\frac{7}{2}\cdot7+b\)

And solve for b,

\(80=\frac{49}{2}+b\)\(b=80-\frac{49}{2}=\frac{160-49}{2}=\frac{111}{2}\)

The equation is,

\(y=\frac{7}{2}x+\frac{111}{2}\)

The slope as a decimal is 3.5 and the y-intercept, rounded to the nearest whole number is 56, so the equation is y = 3.5x + 56

Solve for f please I need help

Solve for f please I need help

Answers

Answer:

See Below

Step-by-step explanation:

Isolate f

h =  4 + f

-4   -4

h - 4 = f

Or  f = h-4

Which statement correctly compares the function shown on this graph with
the function ya 2x - 52

Answers

answer: 2(x-26)

explaintion: using a graph with the root 26,0 and a vertical intercept of 0, -52 your answer is y=2x-52

question in photo, pls answer and explain! giving brainliest

question in photo, pls answer and explain! giving brainliest

Answers

Answer:

Step-by-step explanation:

4(x-3)^2 = 80

4x-12^2= 80              --- (distribute)

4x+144= 80          --- ( why a positive 144 because a (-) * a (-) = a (+)

4x =  (80-144)      --- ( subtract -144 from +144(do it on both sides)

4x = -64    --- (divide both sides by 4)

x= -16

Answer:

2√5 +3

Step-by-step explanation:

Isolate x:

4(x-3)^2 = 80

Divide both sides by 4.

(x-3)^2 = 20

Then take the square root of each side.

(x-3) = √20

Add 3 to each side.

x = √20 + 3

√20 can be rewritten as 2√5.

x = 2√5 + 3

Compute the mean cost of repair. Select the correct choice below and, if necessary, fill in the answer box to complete
your choice, please help and explain

Compute the mean cost of repair. Select the correct choice below and, if necessary, fill in the answer

Answers

The Mean is 391.75, the Median is 441, and no mode.

What is a mean median and mode?

The mean is the average of a set of numbers, calculated by adding all the numbers together and dividing by the number of items in the set. The median is the middle value in a set of numbers, or the average of the two middle values if the set has an even number of items. The mode is the most frequently occurring value in a set of numbers.

Data:  ​$436​, ​$403​, ​$479​, and ​$249.

Mean = SUm of all observation / total no. of observations.

Mean = 436 + 403 + 479 + 249 / 4.

Mean = 391.75

No. of terms n = 4(even)

Median = (n/2+(n/2 + 1)) / 2

Median = 403 + 479 / 2

Median = 441.

Mode is the value repeating the more no. of times

So, there is no mode.

Hence, the Mean is 391.75, the Median is 441, and no mode.

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Simplify this expression.
–6w + (–8.3) + 1.5+ (–7w)

Answers

The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.

What is the simplified form of the expression?

Given the expression in the question;

-6w + (–8.3) + 1.5+ (–7w)

To simplify, first remove the parenthesis

Note that;

- × + = -- × - = ++ × + = +

-6w + × - 8.3 + 1.5 + × - 7w

-6w - 8.3 + 1.5 - 7w

Next collect and add like terms

-6w - 7w - 8.3 + 1.5

Add -6w and -7w

-13w - 8.3 + 1.5

Add -8.3 and 1.5

-13w - 6.8

Therefore, -13w - 6.8 is the simplified form.

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Cho sells kakigori, a Japanese frozen dessert flavored with sweet syrup, at a street stand.
The scatter plot shows the daily high temperature and the number of servings of kakigori
Cho sells each day for 12 days. Based on a line of best fit for the data, about how many
servings of kakigori will Cho sell on a day when the high temperature is 29° Celsius?
Number of Servings Sold
115
110
105
100
95
90
85
80
75
70
65
60
55
50
0
18 19 20 21 22 23 24 25 26 27 28 29 30
Temperature (°C)
94
101
88
111

Answers

We can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.

Based on the line of best fit for the data, we can estimate the number of servings of kakigori Cho will sell on a day when the high temperature is 29° Celsius.

From the scatter plot, we can see that the line of best fit is increasing as the temperature increases.

By estimating the value on the line of best fit for the temperature of 29° Celsius, we can approximate the number of servings sold. Based on the scatter plot, it appears that the number of servings sold is around 100 when the temperature is 29° Celsius.

Therefore, we can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.

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What are not changed after a rotation

Answers

Answer: b

Step-by-step explanation:

In the figure, angle D measures 71° and angle G measures 37°. What is the measurement of angle A?

Answers

Answer:

No u

Step-by-step explanation:

Answer : M{A}=72

This is a triangle, meaning the total degree will be 180.

what type of military equipment have the u.s. and germany been in the news for sending as aid to ukraine?A. CentiB. MiliC. MikroD. Nano

Answers

Germany and the US are sending tanks to Ukraine as a show of support for the government in Kyiv, with Germany sending 14 Leopard 2 tanks & the US delivering 31 Abrams in the coming months.

The rationale behind this military aid is to demonstrate solidarity with Ukraine in its ongoing conflict with Russia & to bolster its military capabilities in the face of aggression. This move is seen as a signal to Russia that the international community will not tolerate further military incursions into Ukrainian territory and is committed to supporting Ukraine's sovereignty & territorial integrity. It is also hoped that this aid will help stabilize the situation in Ukraine and bring about a peaceful resolution to the conflict.

Centi, mili, micro and nano are not types of military equipment. Centi, mili, micro and nano are units of measurement used in the metric system.

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please help- provid explanation if possible! <3

please help- provid explanation if possible! &lt;3

Answers

Answer:

Exponential

Step-by-step explanation:

The rate of change is exponential.

please help me with my guided practice ​

please help me with my guided practice

Answers

The answer is bc if you add them all together

Answer:

b

Step-by-step explanation:

you have to add the 3 numbers together to get 170

Which one is correct? int i = 3.0; float f = 4.5; byte b = 123456789; double d = 123456789; boolean b = 1;
double d = 123456789;

Answers

The correct statement is: double d = 123456789

In the given statements:

1. int i = 3.0; - This is incorrect because a decimal value (3.0) cannot be assigned directly to an integer variable. It should be assigned to a floating-point type variable instead.

2. float f = 4.5; - This is correct as a floating-point value (4.5) can be assigned to a float variable.

3. byte b = 123456789; - This is incorrect because the value 123456789 is outside the range of a byte (-128 to 127). It should be assigned to a data type with a larger range, such as into or long.

4. double d = 123456789; - This is correct as the value 123456789 can be assigned to a double variable.

5. boolean b = 1; - This is incorrect because the value 1 cannot be directly assigned to a boolean variable. It should be assigned with either true or false.

Among the given statements, the correct one is "double d = 123456789;", as it assigns the value 123456789 to a double variable.

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andreas höring and thomas peternell. algebraic integrability of foliations with numerically trivial canonical bundle

Answers

Andreas Höring and Thomas Peternell have made significant contributions to the study of algebraic integrability of foliations with numerically trivial canonical bundle.

Andreas Höring and Thomas Peternell are mathematicians who have made significant contributions to the study of algebraic integrability of foliations with numerically trivial canonical bundle.

Algebraic integrability refers to the property of a foliation (a geometric structure defined on a manifold) to have certain algebraic properties. In particular, it relates to the existence of rational functions that preserve the foliation structure.

A foliation is said to have a numerically trivial canonical bundle if the line bundle associated with the canonical divisor of the foliation has degree zero on every curve. The canonical bundle is a fundamental object in algebraic geometry that captures the intrinsic geometry of a variety.

Höring and Peternell have studied the algebraic integrability of foliations with numerically trivial canonical bundle from various perspectives. They have investigated the existence and properties of meromorphic first integrals, which are rational functions that preserve the foliation. These integrals play a crucial role in understanding the dynamics of the foliation.



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Complete question:

Aandreas höring and thomas peternell. algebraic integrability of foliations with numerically trivial canonical bundle. prove that the the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical bundle.

how many ways can rudy choose 5 pizza toppings from a menu of 20 toppings if each topping can only be chosen once?

Answers

20x19x18x17x16
Each time she can choose one less type of toppings.

Let's say someone is conducting research on whether people in the community would attend a pride parade. Even though the population in the community is 95% straight and 5% lesbian, gay, or some other queer identity, the researchers decide it would be best to have a sample that includes 50% straight and 50% LGBTQ+ respondents. This would be what type of sampling?
A. Disproportionate stratified sampling
B. Availability sampling
C. Snowball sampling
D. Simple random sampling

Answers

The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."

A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.

B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.

C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.

D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.

Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.

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