a scientist randomly divided a group of 100 lab rats into two groups of 50. one group was fed regular rat chow while the other was fed the same amount of rat chow with added ddt (an insecticide). both groups were housed in the same room with the same environmental conditions. at the end of the experiment, rats were weighed and the mean difference was calculated. what is the independent variable?

Step-by-step explanation:

3.

[tex]( \frac{25 + 3}{0.5} ) - 16.4 \div 4[/tex]

6.

[tex]56 - 4.1[/tex]

The number of sides is 72 sides

A polygon can be defined as a plane figure that is known by a finite number of straight line segments that are joined to form a closed polygonal chain.

To determine the number of sides in a polygon given the exterior angle value, we have make use of the formula;

360 degrees/ divide the exterior angle given

Now, substitute we have to substitute the value, we get;

360/5

Divide the values, we get;

72  sides

Hence, the number is 72

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Answer:

1st box = 2/3

2nd box = 16/3

==============================================

Work Shown for the 1st box

2/3 = x/1

x = 2/3

There's not much in terms of steps

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

Another approach for the 1st box

2/x = 3/1

2*1 = x*3

2 = 3x

x = 2/3

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

Work Shown for the 2nd box

2/3 = x/8

2*8 = 3*x ... cross multiplying

16 = 3x

x = 16/3

Optionally this can be converted into a mixed number

16/3 = (15+1)/3

16/3 = 15/3 + 1/3

16/3 = 5 + 1/3

16/3 = 5 & 1/3

If  the length of AB is the same as the length of DC, AC = 9, and

DE = 4, the length of DC is 6 units.

Since DE is parallel to AB and AC = 9, then we can use alternate interior angles to find the length of DC.

Using alternate interior angles, we have:

∠DAC = ∠EAB (Since they are alternate interior angles of two parallel lines)

And from the diagram, we have:

∠DAC = 90° (Since AC is perpendicular to DC)

∠EAB = 90° (Since AB and DE are parallel)

So, we have two right angles, ∠DAC = ∠EAB.

Let find the length of DC:

DC^2 = AC × DE

DC^2 = 9× 4

DC^2 = 36

DC = √36

DC = 6

Therefore, the length of DC is 6 units.

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The probability of selecting exactly one defective calculator out of the 6 sent to the local high school is 0.29166.

The probability of selecting exactly one defective calculator out of the 6 sent to the local high school can be calculated using the binomial probability formula. The binomial probability formula is [tex]P(x) = nCx * p^x * q^(n-x)[/tex]. For this problem, n = 6 (the number of calculators sent to the local high school), x = 1 (the number of defective calculators selected), p = 4/12 (the probability of selecting a defective calculator from the shipment of 12 calculators), and q = 8/12 (the probability of selecting a non-defective calculator from the shipment of 12 calculators). Plugging these values into the formula gives [tex]P(x) = 6C1 * 4/12^1 * 8/12^5[/tex], which simplifies to 0.29166. This means that the probability of selecting exactly one defective calculator out of the 6 sent to the local high school is 0.29166.

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The measure of the two angles will be x > 25° and y = 180° - x°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The two lines are parallel and the third line is a transversal line.

If one angle is greater than 25°. Then the other angle is given as,

Let the angles be 'x' and 'y'. Then angles are supplementary angles. Then the inequality is given as,

x > 25°               ...1

x + y = 180°

y = 180° - x       ...2

From equations 1 and 2, then we have

y = 180° - x

The measure of the two angles will be x > 25° and y = 180° - x°.

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Answer:

Below

Step-by-step explanation:

Just count the number of results on the Right

        that have at least two heads = 11

  out of 16 combos      =   11/16 = .6875

The length of QS is obtained as follows:

QS = 28.

The length of QS is obtained applying the proportions in the context of the problem.

The ratio of the side lengths is given as follows:

PQ : QR : RS = 3 : 3 : 1.

The ratio of the side lengths can be simplified as follows:

PQ : QS = 3:4.

Which means that QS is equals to 4/(4 + 3) = 4/7 of the length of segment PS.

The segment PS has a length of 49 units, hence the length of segment PS is given as follows:

PS = 4/7 x 49

PS = 28 units.

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Multicollinearity occurs when independent variables in a regression model are correlated.

Multicollinearity is a statistical concept that describes the correlation of several independent variables in a model. If the correlation coefficient between two variables is +/- 1.0, they are considered perfectly collinear. When independent variables are multicollinear, statistical inferences are less reliable.
Multicollinearity is a problem because it undermines an independent variable's statistical significance. Other things being equal, the larger a regression coefficient's standard error, the less likely it is that this coefficient will be statistically significant.
When two or more predictors in a regression model are moderately or highly correlated with one another, multicollinearity exists. Unfortunately, it can wreak havoc on our analysis, limiting the research conclusions we can draw.

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The probability that x is greater than 75 from a normal distribution with a mean of 100 and a standard deviation of 10 is 0.9151.

The formula for calculating the probability that x is greater than 75 from a normal distribution with a mean of 100 and a standard deviation of 10 is P(x>75)=1-P(x<75). The probability can be calculated using the cumulative distribution function of the normal distribution. The cumulative distribution function of the normal distribution is given by

F(x)=1/2[1+erf((x-mean)/(standard deviation*sqrt(2))]

Where erf is the error function defined by erf(x)=2/sqrt(pi)*∫x^0 e^-t^2 dt

Therefore, the probability that x is greater than 75 is

P(x>75)=1-1/2[1+erf((75-100)/(10*sqrt(2))]

=1-1/2[1+erf(-1.25)]

=1-1/2[1-0.1151]

=0.9151

The probability that x is greater than 75 from a normal distribution with a mean of 100 and a standard deviation of 10 is 0.9151.

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Connection between normal probabilities and empirical rule links to an external site probability is 0.95 probability is 0.02.

The parts from a supplier in an average  have a mean value  of 31.8 inches and a standard deviation value  of 2.4 inches. Probability is 0.02, which is inconsistent with the.

Probability is basically the chances of something happening . The theoretical probability is the form of probability that is  based on the reasoning behind probability. For example, if a coin is tossed than the theoretical probability of the chance or outcome of getting a head will be ½.

Probability is the branch of mathematics that basically deal for outcome of something or the chances of getting the favorable outcome four main types of probability exist: classical, empirical, subjective and axiomatic.

Probabilities always range between 0 and 1. The formula to find the  probability can be expressed as: Probability =Favorable number of Outcomes / Total Number of Outcomes. or. P(A) = f / N.

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The graph of the linear function y = -1/3x + 8 is given by the image presented at the end of the answer.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The function for this problem is defined as follows:

y = -x/3 + 8.

Meaning that:

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Russia has 33 nuclear reactors, which puts it in the top 10 countries in the world with the most nuclear reactors. This puts Russia in the 99th percentile, meaning that 99% of countries have fewer nuclear reactors than Russia.

The 99th percentile is a very high ranking, and it indicates that Russia has a large number of nuclear reactors compared to other countries. This is a testament to the country's commitment to nuclear energy, and it is a sign of the country's technological and economic power.

Overall, Russia has 33 nuclear reactors, which puts it in the 99th percentile. This is a very high ranking, and it shows that Russia is one of the most powerful countries in the world when it comes to nuclear energy. This is a testament to the country's commitment to nuclear energy, and it is a sign of its commitment to sustainability.

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The material needed to fix the Rectangular side of tent was 150 sq. ft.

What are Solids?

Solids are 3-D shapes which are extension of 2-D figures. Solids are nothing just some 2-D figures which have some height of their own.

There are various solids like- cube, cuboid, cylinder, prism, sphere, cone , etc.

3-D solids have height so they don't have perimeter but they have total surface area and volume.

We can obtain a solid by the rotation of an appropriate 2-D figures.

Now for the given question:

The ripped side of the tent is a rectangular figure with length 15 ft and breadth 10 ft.

Material required to repair the ripped part of tent = Area of the rectangle of the ripped side of the tent.

Area of rectangle = length × breadth

                             = 15 × 10

                             = 150 sq. ft.

Hence, Material required to fix the ripped tent is 150 sq. ft.

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The solution is (6, 32) and it means that the total cost of 6 kites from 2 different businesses is $32.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

From the graph of two lines,

The intersection point is the solution to the two lines system of equations.

Now,

The intersection point = (6, 32)

This means,

x = 6 and y = 32

x = number of kites

y = total cost of the kites

Thus,

The solution is (6, 32).

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The solution is Option B.

The pressure at the ocean's surface is given by the equation A = 14.7 pounds per square inches

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

P = 14.7 + ( f/22.5 )   be equation (1)

where P is the total pressure in pounds per inch²

And , f is the height in feet below the ocean's surface

Now , pressure at the ocean's surface is when f = 0

Substitute the value of f = 0 in equation (1) , we get

P = 14.7 + ( 0/22.5 )

On simplifying the equation , we get

P = 14.7 pounds/inch²

Hence , the equation is P = 14.7 pounds/inch²

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The number of fish that were between 30 cm and 40 cm long is equal to 0.8.

In Mathematics, a histogram can be defined as a type of chart that is used to graphically represent a group of data points (statistical information) into user-specified ranges through the use of rectangles or rectangular bars.

Based on the information provided in the histogram (see attachment), the number of fish that were between 30 centimeters and 40 centimeters long can be calculated based on the frequency density as follows;

Number of fish = 1/5 × 4

Number of fish = 0.2 × 4

Number of fish = 0.8

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Answer:

The list that has the angles of AABC in order from smallest to largest is: ZC, ZA, ZB

The measure of the angles of the triangle in order from smallest to largest is ∠C , ∠A , ∠B

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

if a² + b² = c² , it is a right triangle

if a² + b² < c² , it is an obtuse triangle

if a² + b² > c² , it is an acute triangle

Given data ,

Let the triangle be represented as ΔABC

And , In AABC, AB= 7, BC= 8, and AC=9

We can use the Law of Cosines to determine the size of each angle in AABC:

cos A = (b^2 + c^2 - a^2) / (2bc)

cos B = (a^2 + c^2 - b^2) / (2ac)

cos C = (a^2 + b^2 - c^2) / (2ab)

Plugging in the values of a = 9, b = 7, and c = 8, we get:

cos A = (7² + 8² - 9²) / (2 x 7 x 8) = 39/112

cos B = (9² + 8² - 7²) / (2 x 9 x 8) = 17/18

cos C = (9² + 7² - 8²) / (2 x 9 x 7) = 5/14

Taking the inverse cosine of each value gives:

A = cos^-1(39/112) ≈ 62.02°

B = cos^-1(17/18) ≈ 26.56°

C = cos^-1(5/14) ≈ 91.42°

And , the longest side in a triangle is always opposite the largest angle, and the shortest side is opposite the smallest angle and ∠C , ∠A , ∠B

Hence , the triangle is solved

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Based on the given parallelogram, we find that:

Remember that:

11. It was given that:

∠B = 4x - 5

∠D = 3x + 10

∠B?

∠C?

Since ∠B and ∠D are opposite angles, then ∠B and ∠D are congruent.

∠B = ∠D

4x - 5 = 3x + 10

x = 15

∠B = 4x - 5

∠B = 4(15) - 5

∠B = 60 - 5

∠B = 55°

∠B and ∠C are adjacent angles, then ∠B and ∠C are supplementary.

∠B + ∠C = 180°

55° + ∠C = 180°

∠C = 125°

12. ∠B = 53°

∠B and ∠D are opposite angles and congruent; then:

∠B = ∠D = 53°

∠A and ∠C are opposite angles and congruent; then:

∠A = ∠C

∠B and ∠A are adjacent angles and supplementary; then:

∠A + ∠B = 180°

∠A + 53° = 180°

∠A = 127°

∠C = 127°

13. ∠A = 3∠B

∠A and ∠B are adjacent angles and supplementary; then:

∠A + ∠B = 180°

3∠B + ∠B = 180°

4∠B = 180°

∠B = 45°

∠A = 3∠B

∠A = 3(45°)

∠A = 135°

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Answer: 25

It could also be 31 though.

The range and interquartile range of the data set 2, 4, 7, 8, 16, 19, 21 are 19 and 8 respectively.

The range of a data set is the difference between the maximum and the minimum values. In other words, the range is the difference of the highest value and the lowest value of a data set.

Therefore, let's find the range of the data sets. Firstly, let's arrange the data sets in ascending order as follows:

2, 4, 7, 8, 16, 19, 21

range = 21 - 2

range = 19

Let's find the interquartile range of the data set.

The interquartile range is the range of values that resides in the middle of the scores.

Hence,

interquartile range = 8

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Answer: They make the same amount of money

Step-by-step explanation:

Divide 36 by 4

Divide 63 by 7

You get 9 each time.

Answer:

They make the same amount of money

Divide 36 by 4

Divide 63 by 7

You get 9 each time.

Step-by-step explanation:

pls, tell me if wrong have a good day/night<3

For the function g(x) the changes are mentioned as -

"Slope becomes (-a) from (a) and the y - intercept becomes {-(b + 1)} from b".

In mathematics, the inverse function of a function f is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective.

Given is the function -

g(x) = - f(x) - 1

Since the function g(x) is not given, we can assume -

f(x) = ax + b                           .... Eq { 1 }

Now -

g(x) = - f(x) - 1

So, we can write -

g(x) = - (ax + b) - 1

g(x) = - ax - b - 1

g(x) = - ax + {-(b + 1)}                                        ... Eq { 2 }

So, we can see that -

Slope becomes (-a) from (a) and the y - intercept becomes {-(b + 1)} from b.

Hence, for the function g(x) the changes are mentioned as -

"Slope becomes (-a) from (a) and the y - intercept becomes {-(b + 1)} from b".

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Answer: $925.93

Step-by-step explanation:

See image:

The correct answer is option (A). The answer is metes and bounds.

Given that,

Despite being antiquated, the most adaptable method of defining land, capable of characterizing even the most atypical of parcels, may be summed up as a very exact, compass-directed stroll around a parcel's boundaries.

To find : This approach is frequently known as ?

Metes and bounds are limits of  piece of a land that may be located on its natural features. Metes and bounds markers are frequently employed in a land's "legal description." Legal description, which is recorded with the land's deed, is the geographical description of a piece of land that pinpoints its exact location.

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a) The probability that all three family members are assigned to the same station is  1/27.

b) The probability that at most two family members are assigned to the same station is 11/27.

c) The probability that every family member is assigned to a different station is 2/9.

For (a), there is only one way for all three family members to be assigned to the same station, and there are 3 stations, so the probability is 1/3^3 = 1/27.

For (b), there are three ways for two family members to be assigned to the same station, either A and B, B and C, or A and C. The probability of two family members being assigned to the same station is (1/3)^2 (2/3). There are three ways for this to occur, so the probability is (3) (1/9) (2/3) = 2/3. There is also one way for all three family members to be assigned to the same station, so the probability is (1/3)^3 = 1/27. Adding these two probabilities gives 11/27.

For (c), there are 3! = 6 permutations for the family members to be assigned to different stations. Each family member can be assigned to any of the 3 stations, so the probability is (3!) (1/3)^3 = (6) (1/27) = 2/9.

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Complete Question:

A family consisting of three persons-A, B, and C-goes to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the clinic once and is assigned at random to a station. The experiment consists of recording the station number for each member. Suppose that any incoming individual is equally likely to be assigned to any of the three stations irrespective of where other individuals have been assigned. What is the probability that (a) All three family members are assigned to the same station? (Round your answer to three decimal places.) (Ne Responseberse ssigd tah ni sation number tor each (b) At most two family members are assigned to the same station? (Round your answer to three decimal places.)  (c) Every family member is assigned to a different station? (Round your answer to three decimal places.)

5/45 = 1/9 represents the probability of the best-case scenario. 40/45 = 8/9 represents the probability of the worst-case scenario.

When two socks from the same pair are missing, the likelihood of the best-case scenario increases. As a result, all four pairs of socks are present. Now, 10C2 = 45 gives the total number of possible methods to choose 2 socks from a total of 5 x 2 = 10 socks. The probability of choosing one pair of socks from five pairs is equal to the number of ways to choose two socks from a pool of ten socks, and this is provided by the formula 5C1 = 5.  given by 5 / 45 = 1 / 9. The worst case situation is when they are not from the same pair of socks. As a result, all three pairs of socks are present. Now, 10C2 = 45 gives the total number of possible methods to choose 2 socks from a total of 5 x 2 = 10 socks. 10C2 - 5C1 = 45 - 5 = 40 is the number of ways to choose two socks from a group of ten so that they are not from the same pair.  given that by 40 / 45 = 8 / 9

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The expression of the area of the barrel is 14π(h + 7)

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

The DIAMETER of the barrel is 14.

This means that the radius is 7 units

The area of the barrel is calculated as

Area = 2πr(h + r)

Substitute the known values in the above equation, so, we have the following representation

Area = 2π * 7(h + 7)

Evaluate

Area = 14π(h + 7)

Hence, the area is 14π(h + 7)

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