a researcher studies language development by selecting a sample of two-year-old children and giving them a language skill test. each year for the next two years, the children are brought back and tested again. the researcher plans to compare the children's scores at age two, age three, and age four. this study is an example of a(n) .

The probability of the product of the given expressions is in the form of x² - (by)² is equal to 1/6.

As given in the question,

Given four expressions are:

( x + y ) , ( x + 5y ) , ( x - y ) and ( 5x - y )

Product of any two expression to have two degree expressions :

( x + y )( x + 5y ) = x² + 6xy + 5y²

( x + y )( x - y ) = x ² - y²

( x + y )( 5x - y ) = 5x² + 4xy -y²

( x + 5y )( x - y ) = x² + 4xy -5y²

( x + 5y )( 5x - y ) = 5x² + 24xy -5y²

(x - y) ( 5x - y) = 5x² - 6xy + y²

Total number of possible outcome of the product with degree 2 = 6

Favourable outcomes in the form of x² - ( by )² is x² - y² = x² -(1y)²

Here b = 1 is an integer.

Number of favourable outcomes = 1

Required probability = 1/6

Therefore, the probability of the product in the form of x² - ( by )² is equal to 1/6.

The complete question is:

If two of the four expressions x + y, x + 5y, x – y, and 5x – y are chosen at random, what is the probability that their product will be of the form of x2 – (by)2, where b is an integer?

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On solving tthe question, we got by double integration [tex]\int\limits^0_1 \int\limits^1_2{100x^2+49y^2} \, dx dy = x(\frac{100x^2 + 147y^2}{3} )[/tex]

A function in two variables over a region in R2, or the real number plane, is referred to in mathematics as a double integral. It is possible to write the double integral of a function of two variables, such as f(x, y), over a rectangular region as follows:  ∬ R f ( x , y ) d A = ∬ R f ( x , y ) d x d y.

g[tex]\int\limits^0_1 \int\limits^1_2{100x^2+49y^2} \, dx dy \\ At first,\\ \int\limits^{} \,100x^2 dx = 100\int\limits^ {} \,x^2 dx \\ \int\limits^ {} \,x^2 dx = \frac{x^3}{3} \\[/tex]

[tex]the result - \frac{100x^3}{3}\\ now,\\\int\limits \, 49y^2dx = 49xy^2\\\\result - \frac{100x^3}{3} + 49xy^2\\\\On simplyfing-\\[/tex]

[tex]x(\frac{100x^2 + 147y^2}{3} )[/tex]

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For the given statement option C  increase, wider and decrease , narrower is correct.

What is confidence interval?

A confidence interval is computed at a designated confidence level; the  95% confidence level is most common, but other levels, such as 90% or  99%, are sometimes used.

When constructing a confidence interval, if the level of confidence increases, the margin of error must Increase and the confidence interval will be Wider.

Hence  Increase; wider is the correct answer.

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The distance between the point H= (−9, 0) and J= (−1,−8) in the coordinate plane is 8√2 units.

For the stated question-

Distance formula;

d = √(x2 -x1)² + (y2 - y1)²

H(x1, y1) = (−9, 0)

and J(x2, y2) = (−1,−8)

Put the values;

HJ = √(-1 + 9)² + (-8 - 0)²

HJ = √(64 + 64)

HJ = 8√2

Thus, the distance between the point H= (−9, 0) and J= (−1,−8) in the coordinate plane is 8√2 units.

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The given statement is True.

What is the Null Hypothesis?

The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is possible to determine the probability that the null hypothesis is correct using statistical tests.

True. In a non-directional significance test of a correlation, the null hypothesis states that the population correlation is zero.

Hence, The given statement is True.

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The histogram's best summary is option (D), "there are a total of 12 snacks with the same amount of sugar."

While bar charts show categorical variables, histograms show quantitative or numerical data.

The majority of the time, a histogram's numerical data will be continuous (having infinite values).

It would be ridiculous to try and show all possible values of a continuous variable along an axis.

So, the y-axis displays the number of snacks.

The x-axis displays how much sugar is in each snack.

The histogram's first column reveals that 2 snacks each contain between 220 and 224 mg of sugar.

The second column reveals that around 3 snacks have 224–228 mg of sugar.

The third column reveals that 8 snacks range in sugar content from 228 to 232 mg.

Twelve snacks are identified in the fourth column as having between 232 and 236 mg of sugar.

Twelve snacks are identified in the fourth column as having between 232 and 236 mg of sugar.

The fifth column reveals that 11 snacks range in sugar content from 236 to 240 mg.

Three snacks are shown to contain between 240 and 244 mg of sugar in the sixth column.

According to the seventh column, 2 snacks contain 244–248 mg of sugar.

The total number of observations is 41 nibbles, or 2+3+8+12+11+3+2.

So, the best statement that describes the histogram is "The most snacks with the same quantity of sugar are 12 in total."

Therefore, the histogram's best summary is option (D), "there are a total of 12 snacks with the same amount of sugar."

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Complete question:
Data were collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. Which statement best describes the meaning of one of the bars in the histogram?

2

4

6

8

10

12

amount of sugar (mg)

220

224

228

232

236

240

244

248

Frequency

a. 2 snacks have about 226 mg of sugar.

b. 226 snacks have 2 mg of sugar.

c. 226 snacks have between 224 and 228 mg of sugar.

d. The largest number of snacks have 12 mg of sugar

Physical attractiveness determined whether college freshmen who had been randomly paired for a welcome week dance liked each other.

Samples with natural or matched couplings are known as paired samples (sometimes referred to as dependent samples). This results in the creation of a data set where each data point from one sample is uniquely linked with a data point from the other sample. In statistics, paired data, also known as ordered pairs, refers to two variables in a population's individuals that are linked together to ascertain their association. We refer to two datasets that are identical in length and in which each observation can be "paired" with an observation from the other dataset as having "paired data." Each observation in one dataset must only be paired with one observation in the other dataset in order for the two datasets to be paired.

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Answer:g(-8)=-62

Step-by-step explanation:

8x+2=-62. minus 2 to both sides

8x=-64.  divide both sides by 8 to isolate x of the left

x=-8.   final answer

g(-8)=-62

Answer:

13/16

Step-by-step explanation:

Answer: 4x - 1

Step-by-step explanation:

Answer:

4x-2

Step-by-step explanation:

i did it

1.15 percentile of people would be expected to score 115 or more

What is Standard Deviation?

A standard deviation (or σ) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.

Solution:

Mean = 100

Standard Deviation = 13

To solve the given problem we need to calculate the Z - Score

Z = X - Mean / Standard Deviation

P(X > 115)

Z = 115 - 100 / 13

Z = 15 / 13

Z = 1.15 Percentile

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Answer:

a. El auto pesado ganará, ya que debido a su mayor masa tendrá una mayor fuerza de arrastre.

b. El auto ligero se detendrá en menos tiempo, debido a que su masa es menor, lo cual significa que tendrá una menor resistencia al movimiento.

Step-by-step explanation:

The solution to this question is  27 units the perimeter of kite OBDE.

The perimeter of a shape is the entire length of the shape's boundary as used in geometry. A form's perimeter can be calculated by adding the lengths of all of its sides and edges. In order to calculate it, linear distances such as centimeters, meters, inches, or feet are used.

Here

This is because 15x15 =225

8x8 = 64

225+64=289 and

the square root of 289 is 17 and that is the diameter of the circle and the hypotenuse of the triangle and since the kite has two congruent sides which are both radii or  can be written as half of a diameter times two would be the same as the length of the diameter which is17+the two bottom sides (which are both 5 and 5 )

So 5+ 5 = 10 and

10 + 17 =27 or the perimeter of the kite.

Therefore ,the perimeter of kite OBDE is 27 units.

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After a dilation by a scale factor of (3/2) the vertices are A'(- 3, - 3), B'(6, - 3) and

(3/2, 3/2).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

A triangle has coordinates A(- 2, - 2), B(4, - 2) and C(1, 1).

After a dilation by a scale factor of (3/2) it will be A'(- 3, - 3), B'(6, - 3) and

(3/2, 3/2).

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The null hypothesis for the sample data set is given by H₀ : μ = 2 and the alternate hypothesis for the data is H₁ : μ > 2 .

a)H₀ : μ = 2

H₁ : μ > 2

We cannot reject the null hypothesis and conclude that no significant evidence exists to confirm that the mean tree-planting time differs from two hours.

Given :

X = 23.71,17.79, 29.87,18.78,28.76

b)Sample mean, x = Σx / n = 22/10 = 2.2

c) Standard deviation, s = 0.516

H0 : μ = 2

H1 : μ > 2

Test statistic :

(x - μ) ÷ (s/√(n))

n = 10

d) Test statistic :

=(2.2 - 2) ÷ (0.516/√(10))

=0.2 / 0.1631735

Test statistic = 1.23

Using the P-value from T-score we get the degrees of freedom:

df

= n - 1

= 10 - 1

= 9

P-value (1.23, 9) = 0.1249

e) Since, P-value > α ; We fail to reject the null and conclude that no significant evidence exists to support that mean tree-planting time differs from two.

A hypothesis is thetheory put up to explain a phenomenon. If a hypothesis cannot be tested by the scientific method, it cannot be referred to as a scientific hypothesis.

Scientific theories frequently start with historical observations that can't be adequately explained by the body of knowledge at this time. A hypothesis is a tested assertion regarding the relationship between two or more variables in the scientific area or a theory put out to explain an observed phenomena.

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Answer:

-4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

g(x) tells us what the variable is and what variable should be replaced with a value.

g(1) tells us the value that will replace x.

Plug in 1 to the equation:

-5(1) + 1 = g(1)    (multiply)

-5 + 1 = g(1)       (combine like terms)

-4 = g(1)

Therefore, g(1) is equal to -4

Answer: x > -3

Steps:

5x > -15                       Bring 5 to the other side (multiplication ---> division)

x > -15/5                      Divide

x > -3

The solution of the inequality 5x > -15 after solving the inequality expression is x > -3.

Given an inequality expression:

5x > -15

It is required to find the value of x after solving the expression.

In order to solve this, it is required to isolate the value of the variable, in this case, x, on one side and the constant terms on the other side.

In order to isolate the variable:

Divide both sides by 5.

x > [tex]\frac{-15}{5}[/tex]

x > -3

Hence, the solution of the inequality expression is x > -3.

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There is a 1 in 4 probability, or 25%, that the envelope will contain just one letter with the proper address.

Tanya wrote four distinct letters that she was going to send to four different addresses. She prepared an envelope with the correct address for each letter. The probability that only 1 letter will be placed into the envelope with the correct address if the 4 letters are randomly placed into the 4 envelopes is

1 in 4, or 25%

(4c4/4c1).

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The total number of schools such that 35% of it is 105 will be 300.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.

Suppose the total number of students is x.

35% of x = 105

(35/100)x = 105

x = 105(100/35)

x = 300 students

Hence "The total number of schools such that 35% of it is 105 will be 300".

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the best approximation of the percent of scores that fell between 58.9 and 75.1 is 4.

The mathematical average of a group of two or more numbers is called the mean. There are two different sorts of means that can be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.

Find the difference between these two figures and the mean, divide it by the standard deviation of 5.4, and you will know how many standard deviations 75.1 and 61.5 are above and below the mean:

(75.1−64.3)/5.4

=2sd

According to the empirical rule, 95% of data are within two standard deviations of the mean.

So, the answer is 4.

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In a periodic review system when an order is placed  every 14 days, the uncertainty period is 22 days.

Lead time is the time that passes from the start to the conclusion.  It helps in measuring the time taken to complete a project. It varies from industry to industry.

It is normally calculated as:

Lead time = processing time + post-processing time.

Given,

lead time = 8 days

Order place date = 14 days

uncertainty period  = order date + lead time

uncertainty period = 14 + 8 = 22 days

So, we can say that in a periodic review system when an order is placed  every 14 days, the uncertainty period will be 22 days.

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Answer:

Step-by-step explanation:

11. First option

12. 5p+4 > 14

> symbol is greater than and has an open circle, going right

Answer:

--------------------------

The graph indicates the inequality n ≤ 1, since highlighted part is to the left from the 1 and there is a closed circle.

Double both sides to get 2n:

And add 5 to both sides to get 7:

This is matching the option A.

The graph indicates the inequality p > 2, since highlighted part is to the right from the 2 and there is a open circle.

Multiply both sides by 5 to get 5p:

Add 4 to both sides to get 14:

This is matching the option A.

113 % = 1893per capacity

Step-by-step explanation:

first you have to calculate the 113 feet with its equation then calculate the quation with the number 69 divisible by it then divide it and your answer is there

The number of ways to contain 2 black card and 3 red cards are 84,500.

What is card deck?

A piece of specially made card stock, heavy paper, thin cardboard, plastic-coated paper, cotton-paper blend, or thin plastic that has been imprinted with distinctive motifs is what is known as a playing card. Each card frequently has a finish on the front and reverse to make handling simpler.

There are 26 red card and 26 black card in a 52 card deck.

We have to find the number of ways contain 2 black card and 3 red cards.

Initial black card: 26 options

Secondly black card: 25 options

First caution: 26 options

Second warning: 25 options

Three red cards: 24 options

A total of,

26 x 25 x 26 x 25 x 24 = 10,140,000.

But since all orders are equal, we divide by the number of orders for a five card hand:

5 x 4 x 3 x 2 x 1 = 5! = 120

So,

10,40,000 / 120 = 84,500.

Hence, the number of ways to contain 2 black card and 3 red cards are 84,500.

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Answer:

  12 feet

Step-by-step explanation:

You want the length of the side of a square with a diagonal length of 12√2.

The diagonal of a square is the hypotenuse of a right triangle with equal-length sides. Such an isosceles right triangle has side lengths in the ratio ...

  1 : 1 : √2

That is, the hypotenuse is √2 times the side length.

The given hypotenuse is 12√2, so the side length is 12.

Each side of the bedroom is 12 feet.

Answer:

b) P(mean weight > 176) = 1 - P(mean weight ≤ 176) = 1 - 0.9332 = 0.0668

c) P(mean weight > 176) = 1 - P(mean weight ≤ 176) = 1 - 0.9997 = 0.0003

LSD training is  type of interval training consists of overhead squats, front squats, and romanian deadlifts

Whats the definition for intervals?

in·​ter·​val ˈin-tər-vəl. plural intervals. : a space of time between events or states. a two-month interval between medical treatments. There were long intervals during the game in which nothing exciting happened

The area of focus of the Single Leg Romanian Deadlift is the back of the individuals legs and hips. By engaging in this activity, a person is getting a great workout for his or her glutes, hamstrings, lats. It requires the person to lift one leg directly beside the balance leg and then bend from waist to slowly reach hand toward the toes of the balance leg.

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The algebraic expression for the number of eggs he collected initially in terms of b and c would be 12c + b.

What is an algebraic expression?

In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.).

The total number of eggs he collected =  12c + b.

Because 12 eggs are a dozen multiplied by unknown, you get a multiple of twelve then you add your broken eggs for the total.

Hence, the algebraic expression for the number of eggs he collected initially in terms of b and c would be 12c + b.

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