a data set consists of 145 observations that range from 56 to 490. what size class interval would you recommend? (round up to the next whole number.)

The technique used by a researcher to estimate the characteristics of an entire population based on sample measures is called "sampling."

Sampling is the process of identifying the group from whom you will gather data for your research. For example, if you want to know what students think at your institution, you may poll 100 of them. In statistics, sampling allows you to test a hypothesis about a population's characteristics.

Probability Sampling methods are further subdivided into simple random sampling, systematic sampling, stratified sampling, and clustered sampling.

In a research project, sampling is the selection of a subset of the population of interest. In the great majority of research activities, involvement of an entire population of interest is not possible, hence data gathering is reliant on a smaller group.

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Step-by-step explanation:

y² - 100

= y² - 10²

Now by using formula:

[tex]a { \\ }^{2} - {b}^{2} = (a - b)(a + b)[/tex]

= (y - 10)(y + 10)

The probability of two friends meeting at the station 0.28.

To calculate the probability of the two friends meeting at the station, we need to find the overlap in their arrival times, which is between 7:00 and 7:05 in the morning. This overlap represents the time window where they both arrive at the station and can meet. Given that they both arrive between 7:00 and 7:20 in the morning with a uniform distribution, the probability of one of them arriving in the overlap time window is 5/20.

Thus, the probability of both friends arriving in this time window and meeting at the station is the product of these probabilities, which is (5/20) * (5/20) = 0.28.

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Answer:

2x − 1 = 1 + 2x

Step-by-step explanation:

A.

1 + 2x = 1

2x = =0

x = 0

1 solution, x = 0.

B.

1 + 2x = 2x + 1

1 = 1

Infinite number of solutions, all real numbers.

C.

2x − 1 = 1 + 2x

0 = 2

No solution

D.

2x − 1 = −1 + 2x

-1 = -1

Infinite number of solutions, all real numbers.

The solution of the equation  2x + 1 = 9 is 4.

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

The given equation is 2x + 1 = 9

Two times of x plus one equal to nine

To solve this we have to isolate the x term.

Subtract 1 from both sides

2x=8

Divide both sides by 2

x=4

Hence, the solution of the equation  2x + 1 = 9 is 4.

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The image of a point (-6, 3) after a translation right 5 units and down 3 units is

The transformation rule for translation right 5 units and down 3 units is

(x, y) → (x + 5, y - 3)

Applying the rule to the point (-6, 3)

(-6, 3) → (-6 + 5, 3 - 3) → (-1,, 0)

hence the translation results to create an image of (-1, 0)

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Answer: 7:4

Step-by-step explanation:

To simplify the ratio 14:8, we find the greatest common divisor of 14 and 8, and then we divide 14 and 8 by the greatest common divisor.

The greatest common divisor that you can use to simplify 14:8 is 2. This means the answer to the ratio 14:8 simplified is:

7:4

The population of the bacteria colony in 52 minutes is 16,000.

The bacteria colony grows at an exponential rate. An exponential equation can be described as an equation with exponents. The exponent is usually a variable.

The general form of exponential equation is f(x) = [tex]e^{x}[/tex]

Where:

The equation that can be used to determine the population in 52 minutes is:

FV = P(2^(t/13)

Where:

FV = 1,000(2^52/13)

= 1,000 x (2^4)

= 16,000

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Answer:The first two

Step-by-step explanation: To solve the problem you would

5(x+3)=25

x+3=5

-3     -3

x=2

The troop leader can use the two variables of preference (hiking or swimming) as the row and column headings of the table.

In mathematics, independent and dependent variables are values that vary in relation to one another. The dependent variable is dependent on the independent variable, which means that if the value of the independent variable changes, so will the dependent variable.

The troop leader can utilize the two variable categories (hiking or swimming) as the table's row and column headings.

The number of members who prefer each activity can be recorded in the cells of the table to show the distribution of preferences within each troop and the comparison between the two troops.

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Answer:

point form (1,3) equation form: x=1, y=3

Step-by-step explanation:

yw!! :)

Answer: x = 1

Step-by-step explanation: we know what y equals so all we have to do is plug that in into the other equation! if confused, look at attached image.

The system of inequalities on the graph is:

y ≤ 2

y > 2x - 4

Here we have the graph of a system of inequalites.

First, we can see a solid horizontal line, such that the shaded region is below that line, then one of the two inequalities will be:

y ≤ 2

And then we have a dashed line with a slope of 2 and an y-intercept of -4, this time the region above the line is shaded.

y > 2x - 4

Then the system of inequalities on the graph is:

y ≤ 2

y > 2x - 4

I can notice that this system does not appear on the options, so there may be a mistake in the options.

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Solving a linear equation we will see that the measures of the angles are:

∠1 = = 6°

∠2  = 84°

We can see that we have a right angle (this is a 90° angle) and it is divided in the angles ∠1 and ∠2.

Then we can write:

∠1 + ∠2 = 90°

And we know that:

∠1 = x - 8

∠2 =  6x

Then we can write the linear equation:

x - 8 + 6x = 90

We can solve that for x toget:

x - 8 + 6x = 90

7x = 90 + 8

x = 98/7 = 14

Then the measures of the angles are:

∠1 = x - 8 = 14 - 8 = 6°

∠2 =  6x = 6*14 = 84°

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If 7 slices of pizza is divided into equally sized pieces for 4 people then the fraction will be [tex]\frac{7}{32}[/tex] of original pizza.

Total number of people to share the pizza = 4

Total number of slices in the pizza =8

number of slices left = 7

so the fraction of pizza now is [tex]\frac{7}{8}[/tex]

the plan is to slice the 7 slices further into equally sized pieces so that everyone can each have an equal amount of pizza.

Therefore   [tex]\frac{7}{8}[/tex] would be divided by 4

The fraction each person will get of original pizza

=  [tex]\frac{7}{8}[/tex] ×[tex]\frac{1}{4}[/tex]

=  [tex]\frac{7}{32}[/tex]

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There are 127 subsets of {1,2,3,4,5,6,7} that do not contain two consecutive integers, including the empty set.

Each number in the set {1,2,3,4,5,6,7} can either be included or not included in a subset.

So, the number of subsets of this set is:

However, we need to exclude the subsets that contain two consecutive numbers, such as {2,3} or {5,6}. This can be achieved by considering each number as the starting point of a subset and appending it with a number of non-consecutive numbers that can follow.

For example, if 1 is the starting point, the next numbers can only be 3, 4, 5, 6, or 7. Hence, the number of subsets starting from 1 is 5.

By repeating this process for each number in the set, we obtain a total of 5555551 = 127 subsets.

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The probability that no two members of the family are assigned to the same station is 2/9.

From the information given, the probability that all three family members are assigned to the same station will be:

= 3 × (1/3) ³

= 1/9

Now, the probability that at most two family members are allocate to the same station will be:

= 1 - 1/9

= 8/9.

The total number of outcomes for the experiment is 3^3 = 27.

The number of outcomes in which no two members of the family are assigned to the same station is 3! = 6.

Therefore, the probability that no two members of the family are assigned to the same station is 6/27 = 2/9.

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Yes, it is true that  [tex]x^{2}[/tex] + 3x - 1  is a factorization of [tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 3x + 1.

Let us factorize the equation,

     [tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 3x + 1

  => [tex]x^{4}[/tex] - 2[tex]x^{2}[/tex] + 1 - 3x + 3[tex]x^{3}[/tex]

Let's construct a complete square using the terms provided:

=>[tex](x^{2}) ^{2}[/tex]- 2 × [tex]x^{2}[/tex] × 1 + [tex]1^{2}[/tex] + 3[tex]x^{3}[/tex] - 3

=> [tex](x^{2} - 1)^{2}[/tex] + 3[tex]x^{3}[/tex] - 3x

After completing the above calculation, take the common 3x from 3x^3 - 3x.

 =>[tex](x^{2} - 1)^{2}[/tex] + 3x([tex]x^{2}[/tex] - 1)

 =>([tex]x^{2}[/tex] - 1) ( ([tex]x^{2}[/tex] - 1)+ 3x )

 =>([tex]x^{2}[/tex] - 1) ([tex]x^{2}[/tex] + 3x - 1)

Hence, ([tex]x^{2}[/tex] - 1) and ([tex]x^{2}[/tex] + 3x - 1) are two factors of the

equation   [tex]x^{4}[/tex] + 3[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 3x + 1.

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(a) In this case, the men and women alternate, so we can treat them as two separate groups. There are n! ways to seat the n men in the first n seats and n! ways to seat the n women in the next n seats.

So, there are a total of (n!) ^2 ways to seat the n married couples.

(b) In this case, every woman must be next to her husband. We can treat each married couple as a single entity and seat them in (n!) ways.

So, there are n! ways to seat the n married couples around the table in this case.

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The solution of the system of linear equation is x = 5 and y = 3.

A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."

The given system of linear equations is:

3x-2y=9......(1)

y=2x-7........(2)

Substituting the value of y in equation 1 we have:

3x-2y=9

3x - 2(2x - 7) = 9

3x- 4x + 14 = 9

-x = -5

x = 5

Substitute the value of x in equation 2:

y = 2(5) - 7

y = 10 - 7

y = 3

Hence, the solution of the system of linear equation is x = 5 and y = 3.

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The first number is 12.5, and the second number is -3.25.

Let x be the first number, and y be the second number.

2x + 23 = 2y

y - 19 = 2x

Subtracting the second equation from the first:

24 = y

Substituting 24 for y in the first equation:

2x + 23 = 48

2x = 25

x = 12.5

Substituting 12.5 for x in the second equation:

12.5 - 19 = 2y

2y = -6.5

y = -3.25

The first number is 12.5, and the second number is -3.25.

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The trigonometric expression that has a value of three-fourths is; tan (x)

The basic trigonometric ratios are;

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

sec x = 1/cos x

csc x = 1/sin x

cot x = 1/tan x

Thus;

If csc x = 5/3, it means that;

sin x = 3/5

By trigonometric ratios, we know that;

cos x = 4/5 and tan x = 3/4

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Answer:

y = 7x + 60

Step-by-step explanation:

Ron gets paid 7 dollars an hour, this is our constant, since we don't know how many hours he works per day, it can be represented as "x":

7x

He starts his job receiving 60 dollars for his first day:

7x + 60

Of course this needs the outcome "y":

[y = 7x + 60]

The correct answer is option (B). The answer is  one is quantitative and two are categorical.

Given that,

A student quizzed his or her peers about their height, birth month, and relationship status. what proportion of these variables are categorical and what proportion are quantitative.

To find : How many variables are quantitative and categorical ?

A variable where the data indicate the amounts is referred to be a quantitative variable (e.g. height, age). Any variable where the data represent groupings is referred to as categoric variable.

Any trait that cant be quantified is referred to as categorical variable (also known as a qualitative variable). Nominal or ordinal categorical variables are also acceptable.

Therefore, option is the appropriate response (B). One is a quantitative response, and two is a categorical one.

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Answer:

no

Step-by-step explanation:

5:2 =35:14

7:3 = 35 :15

Answer: no

Step-by-step explanation:

They are both in the smallest form that they can me at.

The ratio of two thirds to four is given as follows:

1 : 6.

The ratio between two amounts a and b is obtained applying a proportion.

A proportion is applied because the ratio is given by the division of the amount a by the amount b.

The parameters for this problem are given as follows:

Hence the ratio of two thirds and four is calculated as follows:

(2/3)/4 = 2/3 x 1/4 = 2/12 = 1/6.

In ratio notation, it is given as follows:

1 : 6.

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Estimators like the hatBS.gif have a sampling distribution because of the following reasons, according to the given sources:

Individuals respond differently to incentives, leading to the difference in values of Y across random samples.

In real life, we typically get to sample many times, leading to the difference in values of Y across samples .

Economics not being a precise science is not mentioned as a reason for the sampling distribution of estimators like hatBS.gif.Estimators are statistical methods used to calculate the values of population parameters based on a sample of data. They are a key tool for making inferences about a population from a sample. An estimator is a function that takes the sample data as input and produces an estimate of the population parameter.

There are two types of estimators: point estimators and interval estimators. Point estimators provide a single estimate of the population parameter, while interval estimators provide a range of values that are likely to contain the population parameter.

The quality of an estimator is measured by its accuracy and precision. An accurate estimator is one that produces estimates that are close to the true population parameter, while a precise estimator is one that produces estimates that are consistently close to each other. There are various methods for selecting the best estimator for a given situation, including mean squared error, bias, and confidence intervals.

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Step-by-step explanation:

Given

Opp=8

Adj=6

Hyp=10

Answer

1)Sin<A=Opp/Hyp

8/10=4/5... Yes

2)Cos<A=Opp/Adj

8/6=4/3... No

Given

Opp=6

Adj= 8

Hyp= 10

Answer

1)Sin<B= Opp/Hyp

6/10=3/5... No

2)Cos<B= Opp/Adj

6/8=3/4... No

Answer:

figure 2

Step-by-step explanation:

A rhombus is a flat shape with four equal straight sides. All sides have equal length and it looks like a diamond. It is a special type of a parallelogram whose opposite sides are equal.

Answer: figure 2 only but if the third image is a square thenits 2 and 3 cause I can't see the third very well

Step-by-step explanation:

The true statement about b is b = p + q, and about c is c = p*q.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given a quadratic function, x² + bx + c

and factors of equation is (x + p)(x + q)

for any quadratic equation, the product of factors is equal to the product of a and c,

here a = 1 and c = c

c = p*q,

and the sum of factors is equal to b,

b = p + q.

Hence options A and C are correct.

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