East Middle’s football team has 20.9 liters of sports drink on the field during the game. Each player receives the same amount of sports drink.

If East Middle’s football team consists of 22 players, how much sports drink, in liters, does each player receive?

(Write the answer as a decimal to the nearest hundredth.)

The probability that none are mechanical engineering majors is 0.51.

The number of students who are not mechanical engineering majors is 100 - 49 = 51. The probability of choosing a student who is not a mechanical engineering major in one draw is 51/100. The probability of choosing five students in a row who are not mechanical engineering majors is (51/100)^5. Thus, the answer is (51/100)^5 = 0.1517816.

Probability refers to potential. From 0 to 1 is used to express the value. To determine how likely an event is to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment. The complete number of possibilities that can occur should be known before calculating the likelihood that a certain event will occur.

The complete question is:-

In a class of 100 students, 30 are computer science majors, 49 are mechaincal engineering majors, 13 are civil engineers and the rest are general engineering majors. Assume students only have one major.Suppose five students from the class are chosen at random what is the probability none are mechanical engineering majors?My info I know: The mechanical engineers account for 49% of the students, making 51% not mechanical engineers? Do I take five out of the 51, so 0.05 X 0.51?

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The equation that represents the total amount of kites for a given number will be y = 2x + 20.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The rate of the kite is $2 per kite and the shipping charge is $20.

Let 'x' be the number of kites and 'y' be the total amount. Then we have

y = 2x + 20

Then the table is completed below.

Number of kites      Total amount

         0                             20

          1                             22

         4                             28

         7                             34

        10                            40

The equation that represents the total amount of kites for a given number will be y = 2x + 20.

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Answer:

21

Step-by-step explanation:

We can use Pythagorean theorem a^2 + b^2 = c^2

a = 20

b = x

c = 29

20^2+b^2=29^2

resulting our b value being 21

The standard deviation of the sample proportions (i.e., the standard error of the proportion) is 10.5.

The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.

n = 525

Population Proportion(p) = 0.3

q = 1 - 0.3

q = 0.7

σ = √npq

σ = √(525 × 0.3 × 0.7)

σ = √110.25

σ = 10.5

So The standard deviation of the sample proportions = σ/n

The standard deviation of the sample proportions = 10.5/525

The standard deviation of the sample proportions = 0.02

The standard deviation of the sample proportions = 2%

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The complete question is:

Random samples of size 525 are taken from an infinite population whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

a.0.0004

b.0.2100

c.0.3000

d.0.0200

Answer:

19.6666666667

Step-by-step explanation:

To find the mean of the data set, we will simply take the average of the data as:  Mean= 345+340+400+625/ 4=  427.5

So we have mean as, 427.5

Now we have to calculate the variance of the data.

As we know, for variance we take the difference of each value from mean, take its square and then average of all.

345-427.5 = -82.5

340-427.5 =-87.5

400-427.5 = -27.5

625-427.5 =197.5

Now

Variance=σ2 =(-82.5)^2 + (-87.5)^2 + (-27.5)^2+ (197.5)^2 /4  

σ2=6806.25+7656.25+756.25+39006.25/4

σ2=13556.25

So, the variance is 13556.2

Now we have to calculate the Standard deviation (S.D) of the data.

And the Standard Deviation is just the square root of Variance, so:

σ = √13556.25

σ =116.43

So, the Standard deviation of the data is 116.4

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Answer:

150

Step-by-step explanation:

(5)(5)=25

(25)(5)=125

add: =150

[tex]5\times5+25\times5[/tex]

[tex]5\times5=25\\25\times5=125[/tex]

[tex]25+125[/tex]

[tex]=\fbox{150}[/tex]

The wechsler intelligence scale has a mean of 100 and a standard deviation of 15.  the z score that corresponds to an iq score of 115 is 1.

To calculate the Z score, you subtract the mean from the score and divide it by the standard deviation. In this case, 115-100=15, and 15/15=1.  A Z score of 1 indicates that the score is one standard deviation above the mean. This means that a score of 115 is higher than 84% of the population. It is in the top 16% of scores.

This score is considered to be in the high average range on the Wechsler Intelligence Scale.  The Z score can be interpreted in a variety of ways. It can be used to compare scores or to see how far a score is from the mean. It also can be used to compare scores across different tests. For example, a Z score of 1 on the Wechsler Intelligence Scale could be compared to a Z score of 1 on another test to see how the scores compare.

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The expression as a terminating decimal is 0.2499999....

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

-4/-16

Evaluate the expression by dividing 4 and 16 by 4

So, we have the following representation

1/4

Next, we divide 1 by 4

This gives

0.25

As a repeating decimal, we have

0.2499999....

Hence, the solution is 0.2499999....

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To answer this question, you cannot do it all at once. Since the percentage will change every year because of how percents work, you must do seven calculations for each of the seven decades.

To decrease a number by 6%, you multiply it by 0.94, which is the same as finding 94% of that number, as you have taken 60% away.

1. 1200*0.94 = 1128

2. 1128*0.94 = 1060.32

3. 1060.32*0.94 = 996.7008

4. 996.7008*0.94 = 936.898752

5. 936.898752*0.94 = 880.68482688

6. 880.68482688*0.94 = 827.843737267

7. 827.843737267*0.94 = 778.173113031

You probably don't need 9 decimal places, so we can round to 778.17.

After seven decades, the mountain will be 778.17 meters.

The larger cup can hold 144.51 in³ more water than the smaller cup.

The volume of a cone of radius r and height h is given by one third of the multiplication of pi = 3.14 by the radius squared by the height, hence:

V = 3.14r²h/3

V = 1.0472r²h.

For the smaller cup, the dimensions are r = 2 in and h = 3 in, hence the volume is given as follows:

V = 1.0472 x 2² x 3

V = 12.57 in³.

For the larger cup, the dimensions are r = 5 in and h = 6 in, hence the volume is given as follows:

V = 1.0472 x 5² x 6

V = 157.08 in³.

Then the difference is of:

157.08 - 12.57 = 144.51 in³.

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The value of {x} would be 11.872.

Cosine of the angle is defined as the ratio of base and hypotenuse. Mathematically -

cosθ = (base)/(hypotenuse)

Given is a right angled triangle as shown in the figure.

We can write the value of {x} as -

cos{32} = x/14

{x} = 14 cos (32)

{x} = 14 x 0.848

{x} = 11.872

Therefore, the value of {x} would be 11.872.

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Expanded form of the expression - 1/3 (y - x) is,

⇒ - 1/3y + 1/3x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ - 1/3 (y - x)

Now, We can expand the expression as;

⇒ - 1/3 (y - x)

⇒ - 1/3 × y - 1/3 × - x

⇒ - 1/3y + 1/3x

Thus, Expanded form of the expression - 1/3 (y - x) is,

⇒ - 1/3y + 1/3x

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The outside factor of the average property price of the local neighborhood would bias bexp in a positive direction.

This is because an increase in average property price will increase the value of the dependent variable (bexp). If the average property price of the local neighborhood increases, it will likely lead to an increase in the value of bexp.

This is because the increase in average property price will lead to an increase in the value of properties in the local neighborhood, which will in turn increase the value of bexp. Therefore, an increase in the average property price of the local neighborhood will lead to an increase in the value of bexp.

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The value of x based on the information given in the triangle will be 11.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.

It should be noted that based on the information given, the value of x will be calculated thus:

24 / x + 5 = 54 / 36

Cross multiply

24 / x + 5 = 3 / 2

3(x + 5) = 24 × 2

3x + 15 = 48

Collect the like terms

3x = 48 - 15

3x = 33

Divide

x = 33 / 3

x = 11

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Stratified Random Sampling is used when dividing a population into subgroups so that a random sample from each subgroup can be collected. (option 3)

Stratified Random Sampling is a type of probability sampling where the population is divided into subgroups (or strata) based on some important characteristic. The purpose of stratifying the population is to ensure that each subgroup is represented in the sample, so that the results of the study can be more accurately generalized to the larger population.

After dividing the population into strata, a random sample is selected from each stratum. This approach is used when there is heterogeneity within the population and it is important to ensure that each subgroup is adequately represented in the sample. This method can result in a more precise estimate of population parameters compared to simple random sampling, as it ensures that each subgroup is proportionately represented in the sample.

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Complete Question:

when dividing a population into subgroups so that a random sample from each subgroup can be collected, what type of sampling is used?

Therefore , the solution of the given problem of unitary method comes out to be $1.5 one apple cost.

To finish a work using the unitary strategy, multiply the quantity by two after computing the size of a small slice. The unit variable technique, which is just an expression, helps to distinguish a coded item from a specific group or collection of groups. For example, 40 pens would cost Rs. 400 (or $1.01 or 400 pounds). There is a chance that one nation will have complete control over the technique used to do this. Almost all living things have a unique trait.

Here,
Given :

=> 3 pound bag of apples cost $16

=> 8 apples in a pound

So,

In 3 pounds there are 3*8 = 24 apples

=> 24/16

=> 12/8

=> 3/2

=> 1.5

Therefore , the solution of the given problem of unitary method comes out to be $1.5 one apple cost.

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The expression which is equivalent to 3x² - 10x - 8 is (x - 4)(3x + 2).

The correct answer option is option C

3x² - 10x - 8

check all that applies:

(3x - 2)(x - 4)

= 3x² - 12x - 2x + 8

= 3x² - 14x + 8

(3x - 4)(x - 2)

= 3x² - 6x - 4x + 8

= 3x² - 10x + 8

(x - 4)(3x + 2)

open parenthesis

= 3x² + 2x - 12x - 8

= 3x² - 10x - 8

(3x - 4)(x + 2)

= 3x² + 6x - 4x - 8.

collect like terms

= 3x² + 2x - 8

Therefore, (x - 4)(3x + 2) is equivalent to the expression 3x² - 10x - 8

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The expression for the perimeter of the triangle is 6x + 15 units.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

Given that, an art class is making a mural for their school which has a triangle drawn in the middle.

Let x represent the bottom of the triangle.

One side if the triangle is 12 more than four times the length of the bottom of the triangle, hence:

Length of the side = 4x + 12

The last side is 3 more than the bottom of the triangle, hence:

Length of the side = x + 3

Perimeter of the triangle = x + (4x + 12) + (x + 3)

Perimeter = 6x + 15 units

Therefore, the expression for the perimeter of the triangle is 6x + 15 units.

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Answer:

(- 1, 1 )

Step-by-step explanation:

the solution to a system of equations given graphically is at the point of intersection of the lines.

the lines intersect at (- 1, 1 ) , then

the solution is (- 1, 1 )

The probability that it will have distinct even digits is 6/1000.

The first digit can take on 5 values (0,2,4,6,8).

The second digit could take on 4 values (one less than 5 to be unique).

The third digit could take on 3 values (two less than 5 to be unique).

So that makes,

N=5.4.3

N=60

P= 60/1000

P=3/50

So there are 60 unique three digit even numbers.

There are 1000 possible outcomes.

Probability and statistics are two fundamental concepts in mathematics. Probability is about the probability of an event, whereas statistics are about how different techniques are used to process different data.

Probability and statistics allow us to process complex data in a very understandable way.

Probability is one of the most popular topics in statistics. The reason is that this one theory is often used when trying to predict something. For example, figuring out what comes out of a random series of events. For simplicity, probability is also called chance or probability. 

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The probability that the hand contains exactly 3 face cards is 0.1503.

Combinations of 7 cards out of a choice of 52.

52!/(45! *7!)= 52*51*50*49*48*47*46/7*6*5*4*3*2 = 133,784,560

Combinations of 3 face cards out of 12

12*11*10/3*2 = 220

Combinations of 4 non-face cards out of 40

40*39*38*37/4*3*2 = 91,390

Combinations of 5 face cards and 2 non-face cards

220 * 91,390 = 20,105,800

So the probability is 20,105,800/133,784,560 or 0.1503

Probability theory is the theory used to model uncertainty. Probability value o events show how likely it is the event will occur with an interval of values between zero up to one. However, probability theory can only used for events that have information that complete.

For events that have no information complete can be represented by imprecise probability. One model of imprecise probability is the set-valued probability. Probability worth the set is the non-empty set with every the elements are the results of the probability selector mapping.

Then a set-valued measure is constructed which is constructed by set-valued probabilities.

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We need to calculate the total  of the rectangular prism and divide it with the volume of single 1/3 cubes to get the number of cubes. It takes almost 25 cubes to fill the rectangular prism of given dimension.

The rectangular prism has 2.5 m length, 5 m tall and 0.75 m wide.

The total volume of the rectangular prism will be 2.5 m × 5 m × 0.75 m = 8.25 m³.

The volume of single cube will be (1/3) m³ = 0.33 m³

Now to find the number of cubes to fill the rectangular prism, we can divide the volume of the prism with the volume of single cube.

8.25 m³ / 0.33 m³ = 25 cubes.

It takes almost 25 cubes to fill the rectangular prism of dimension 2.5 m length, 5 m tall and 0.75 m wide.

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Taking into account the definition of a system of linear equations, Celia has 58 coins in her bank, 13 dimes and 45 quarters.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

In the systems of equations, the values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

So, the system of equations to be solved is

d + q= 58

0.10d + 0.25q= 12.55

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, Isolating the variable "d" from the first equation, we obtain:

d= 58 -q

Substituting in the second equation you get:

0.10× (58-q) + 0.25q= 12.55

Solving:

0.10×58 - 0.10q + 0.25q= 12.55

5.8 - 0.10q + 0.25q= 12.55

- 0.10q + 0.25q= 12.55 -5.8

0.15q= 6.75

q= 6.75÷ 0.15

q= 45

Remembering that d=58 - q, you get:

d= 58 - 45

d= 13

Finally, she has 13 dimes and 45 quarters.

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The equation of the linear function in slope intercept form is;

y = -0.5x + (-5)

The equation of a line in slope intercept form is expressed as;

y = mx + c

where;

m is slope

c is y-intercept

From the given table, we can see that the slope is;

m = (y2 - y1)/(x2 - x1)

m = (-4.5 - (-4))/(-1 - (-2))

m = -0.5/1

m = -0.5

At x = 0, y = -5 and so the y-intercept is -5. Thus the equation is;

y = -0.5x + (-5)

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According to the graph, it can be inferred that the average height of the students is 63 inches.

To find the height of the seventh grade soccer players we must analyze the graph. In this case we have a height range from 60 inches to 65 inches. However, we do not know what the individual heights of each of the players are.

In the graph, an intermediate line is also shown in the height segment that signifies the average height of soccer players. In this case it would be 63 inches. Based on the above, the average height would be 63 inches.

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Answer:

O up to the left, down to the right

Step-by-step explanation:

See attached graph.  As x becomes negative, x^3 will always be negative.  But the minus sign in -x^3 mean it will go in the positive direction as x gets smaller (below 0).  The same logic tells us that when x is positive, the -x^3 term will always be negative,  As x increases, the term -x^3 rapidly decreases.

The probability of the sample having a average gas mileage between 27 and 29 miles per gallon will be 0.0116.

What is a normal distribution?

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

In 2015, new cars had an average fuel efficiency of 27.9 miles per gallon with a standard deviation of 6.8 miles per gallon. a sample of 30 new cars is taken.

Then the probability the sample has a mean gas mileage between 27 and 29 miles per gallon will be

The value of the z-score at x = 27, we have average as

The value of the z-score at x = 29, we have

z= 0.16

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The perimeter of the playground is 92 meters

The figure is added as an attachment

To calculate the perimeter, we simply add the side lengths of the playground

i.e. Perimeter = Sum of side lengths

Using the above as a guide, we have the following:

Perimeter = 10 + 14 + 10 + 10 + 6 + 6 + 6 + 14 + 6 + 10

Evaluate the like terms

Perimeter = 92

Hence, the perimeter is 92 meters

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