An experiment consists of 8 independent trials where the probability of success on each trial is 3 8. Find the probability of obtaining the following. Round answers to the nearest ten-thousandth. 13. Exactly 3 successes. 14. Exactly 6 successes.

The length of a human's femur, x, and the length of a human's humerus, Y would ,positive correlation.

A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.

A scale from + 1 to -1 is used to calculate the correlation coefficient. Either + 1 or -1 represents a variable's complete connection with another. The correlation is positive when one variable rises as the other rises; it is negative when one variable falls as the other rises.

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The greatest common factor being 12, the difference between the two values is 12.

What is GCD?

The greatest common divisor (GCD) from mathematics is the largest positive integer that splits each of two or more non-zero integers.

The symbol gcd stands for the greatest common divisor of the two integers x and y.

For instance, gcd(8,12)=4 is the GCD of the numbers 8 and 12.

According to the given question:

The greatest common factor of 48 and z, some unknown positive integer, is 12. There are two possible values for z between 10 and 30.

Now there are only two numbers between 10 and 30 which has a factor of 12.

The numbers are 12 and 24.

Hence the difference between these two numbers is 24 - 12 = 12

Therefore the required value is 12.

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Answer:

4x+28

4 multiplied by x is just 4x and 4x7 is 28

The distance, in feet, on Main Street between First Avenue and Canal Street, using relations in a right triangle, is of:

319.25 ft.

The situation is represented by a right triangle, hence the three trigonometric measures are defined as follows:

From the image given at the end of the answer, the parameters are given as follows:

Hence the distance of the Main Street is found using the sine of the angle of 70º, as follows:

sin(70º) = 300/x

x = 300/sin(70º)

x = 319.25 ft.

The right triangle is given by the image shown at the end of the answer.

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Answer:

Step-by-step explanation:

it depends on the vaiable you choose to cancel out first. For example, if I had two equations:

-12x+9y=7

9x-12y=6

if you wanted first eliminate the x values, then you distribute a certain number to either equation that will cause the x values to cancel (one being negative, and the other being positive)

The number of songs that were originally on the player is 41.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this situation, a DJ added 20 more songs to his MP3 player, making the total more than 61. The number of songs will be the subtraction of the value.

This will be:

= 61 - 20

= 41

The original songs are 41.

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Your answer is 8.

[tex]2x2x2=8[/tex]

If she records the liquid volume using milliliter and deciliter, then the deciliter gives more precise measure

The total capacity = 3 gallon

Convert the gallon to milliliter

We know

1 gallon = 3.785 ml

The total capacity in milliliter = The total capacity × 3.785

Substitute the values in the equation

= 3 × 3.785

= 11.355 milliliter

Convert the gallon to deciliter

We know,
1 gallon = 37.854 deciliter

Total capacity in deciliter = The total capacity × 37.854

Substitute the values in the equation

= 3 × 37.854

= 113.562 deciliter

Here deciliter is much smaller than millimeter

Therefore, deciliter gives more precise measure

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The value of x is 35 and the value of y is 82.

In geometry, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

Given that the three angles of the triangle are 40, 2x and y-12. The value of x and y will be calculated as,

2x = y-12

2x + y-12 + 40 = 180

2x + y =180-40+12

2x + y = 152

2x - y = -12

___________

4x = 140

x = 35

y = 2x + 12

y = 2 x 35 + 12

y = 82

Therefore, the value of x is 35 and the value of y is 82.

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28.9641 ≤ x-bar(t) ≤ 39.0359.

Knowing that we have 10 different values of speed, the size of the sample is 10; n=10. Therefore, this sample is considered statistically small because n < 30.

Arithmetic mean= (Sum of all values) / (Amount of values)

x-bar= (340) / (10)

x-bar= 34.0000.

x-bar= arithmetic mean.

We're going to use the Microsoft Excel tool for the standard deviation for samples (check attached image 1).

Standard deviation for samples (s)= 7.0396.

Check attached image 2.

σ(x-bar)= 2.2261.

α is the error that the confidence interval will have. Given a 95% confidence level, we know that the error is 5%; Error= 1 - Confidence.

α/2= 5%/2= 0.05/2= 0.025.

You can either use the probability tables or the Microsoft Excel tools to find the inverse of a t-student distribution for this α/2 value (check attached image 3).

In this case we use the t-student distribution instead of the normal distribution because the sample size is small and the standard deviation of the population is unknown.

T-student value= -2.2622

Absolute t value= 2.2622.

Check attached image 4 to see the formulas.

Lower limit = (34) - (2.2622*2.2261) = 28.9641

Upper limit = (34) + (2.2622*2.2261) = 39.0359

28.9641 ≤ x-bar(t) ≤ 39.0359

This result means that the value of speed could be any value between 28.9641 and 39.0359, including, with a 95% confidence level. There's a 5% chance that a newly measured value of speed is outside this interval.

The required reciprocal of 3 would be 1/3.

The reciprocal of a number multiplied by a number is 1.

The coefficient of the inverse of the function f(x)=nx is the reciprocal of a number n. A function's inverse is the function with its points flipped.

The reciprocal of a number is the same as its multiplicative inverse.

(The multiplying opposite) It is the number 'turned upside down.

The product of a number and its reciprocal is always 1

So in this case, we can write 3 as: 3/1

The reciprocal is 1/3.

Therefore, the required reciprocal of 3 would be 1/3.

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1/3 Answer:

this is a random answer

Step-by-step explanation:

Using mathematical operations, we know that 1,099ft² of cement would be needed.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.

Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are collectively referred to as PEMDAS.

So, square feet of cement needed:

A: 60' x 7' = 420SF.

90' x 7' = 630SF on side B.

Keep in mind that the corner is 49 SF (7'x7') in size.

The three components are added together as follows:

1,099 square feet = 420SF + 630SF + 49SF.

Therefore, using mathematical operations, we know that 1,099ft² of cement would be needed.

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Answer:

x < -8

Step-by-step explanation:

1. Subtract 5 from both sides

-4x + 5 > 37

-4x + 5 - 5 > 37 - 5

2. Simplify

Subtract the numbers:

-4x + 5 - 5 > 37 - 5

-4x > 37 - 5

Subtract the numbers:

-4x > 37 - 5

-4x > 32

3. Divide both sides by the same factor, and flip the relation because the factor is negative

-4x > 32

[tex]\frac{-4x}{-4}[/tex] < [tex]\frac{32}{-4}[/tex]

4. Simplify

Cancel terms that are in both the numerator and denominator:

[tex]\frac{-4x}{-4}[/tex] < [tex]\frac{32}{-4}[/tex]

x < [tex]\frac{32}{-4}[/tex]

Divide the numbers:

x < [tex]\frac{32}{-4}[/tex]

x < -8

Solution:

x < -8

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Answer:

x < - 8

Step-by-step explanation:

-4x + 5 > 37

-4x > 37 - 5

-4x > 32  ( now I have to divide by -4 )

-4x > 32 / -4

x < - 8

x has to be smaller than -8 for example ( -9 or - 10 )

demonstration: -4 * (-9) + 5 > 37

36 + 5 > 37

41 > 37

Using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.

What is line of best fit?

Line of best fit refers to the "a line through a scatter plot of data points that best expresses relationship between those points". Lines of best fit is used to describe data and predict data where the new data will appear. Examples for lines of best fit is 'Least square method'.

Two variables are said to be correlated or to have a correlation coefficient when "changes in the value of one variable produce changes in the variable of the other variable."

In order to find the correlation between two variables on a graph, the question asks for the line of best fit and correlation coefficient.

Only when there is a linear correlation between the variables—that is, when the relationship between the variables is linear on a graph—does the correlation coefficient hold true.

Variation in "x" on the graph leads to variation in "y." Variation in "y" on the graph results in variation in "x." The variables "x" and "y" are jointly dependent on the graph.

The correlation coefficient between two variables on the graph is calculated in this manner.

Hence, using line of best fit and correlation coefficient, the correlation coefficient of determination represent the percentage of data that is closest to the lines of best fit.

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After 10 years the population growth will be 3054, if the population doubles after every 17 years.

A mathematical function with the form f (x) = ae^x is an exponential function. "x" is a variable, and "a" is a constant that serves as the function's base and must be greater than 0. The transcendental number e, or roughly 2.71828, is the base for exponential functions that is most frequently used.

Growth rate = 100% in 17 years

  In 1 year = 5.88% growth

Initial population = P₀ = 1725

Time = 17 years

So, after 10 years population

        P= P₀ ( 1 + [tex]\frac{r}{100}[/tex])^t

           = 1725 ( 1 + 5.88/100 )^10

           =≈ 1725 * 1.77

           =≈ 3054

Hence, the population growth after 10 years at the rate of 5.88 % would be 3054.

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A ball must be fast rolled is 185.2cm/sec, according to the question.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have the given information:

Table height = h = 70cm

Distance = s = 70cm

g = 9.8[tex]ms^{-1}[/tex]

Now, we have to find the time of falling,

[tex]t=\sqrt{\frac{2h}{g} }=0.378c[/tex]

Horizontal velocity,

[tex]v=\frac{s}{t}=\frac{70cm}{0.378s}=185.2cm/s[/tex]

Therefore, the required answer is 185.2cm/sec.

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The distance between two points (4, 0) and (2, -9) is √85 units in the simplest radical form.

The length of the line segment connecting two points in a plane is defined as the distance between them. The formula for calculating the distance between two points is commonly presented as √(x₂-x₁)²+(y₂-y₁)².

Distances in geometry are usually positive, unless when the points coincide. We consider two points A(a, b) and B to obtain the formula for the distance between two points in the plane (c, d).

The given two points are (4, 0), (2, -9).

Distance between two points is given by,

Distance=√(x₂-x₁)²+(y₂-y₁)²

Where x₁, x₂, y₁, y₂ are the points.

So, the distance between (4, 0) and (2, -9)

=√(2-4)²+(-9-0)²

=√4+81

=√85 units

Therefore, the distance between two points (4, 0) and (2, -9) is √85 units in the simplest radical form.

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A triangle is a plane figure that consists of three sides and three internal angles. Thus m&lt;FHG is [tex]122^{o}[/tex].

A triangle is a family of polygon which is bounded by three straight sides, thus forming three internal angles. The sum of the internal angles of a trigon is [tex]180^{o}[/tex]. While exterior angles are angles which are outside the edges of a triangle.

From the given question;&lt;IGH = &lt;BGD = 42°   (vertically opposite angles)&lt;HIG = 180 - &lt;CIH         = 180 - 100&lt;GIH = [tex]80^{o}[/tex]

Thus, we can conclude that;&lt;IGH + &lt;GIH + &lt;GHI =   [tex]180^{o}[/tex]42 + 80 + &lt;GHI =  [tex]180^{o}[/tex]&lt;GHI =  [tex]180^{o}[/tex] - 122         = 58&lt;GHI = [tex]58^{o}[/tex]So that;m&lt;FHG

=  [tex]180^{o}[/tex] - M&lt;GHI             =  [tex]180^{o}[/tex] - 58            

= [tex]122^{o}[/tex]m&lt;FHG

= [tex]122^{o}[/tex]

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Answer:

5 people total including Mark. So, 4 friends.

Step-by-step explanation:

$67 total - $22 concession stands

$45 spent on tickets

45/$9per ticket

5 tickets were purch

An equation to represent this situation is 16x - 5 = 14x + 1. The value of x is equal to 3.

The perimeters of the rectangle and triangle are equal to 43 units.

Mathematically, the perimeter of a rectangle can be calculated by using this equation;

P = 2(L + W)

Where:

An equation for the perimeter of this rectangle is given by:

P = 2[(5x - 2) + (3x - 0.5)]

P = 2(8x - 2.5)

P = 16x - 5.

Mathematically, the perimeter of a triangle can be calculated by using this equation:

P = a + b + c

Where:

P = (2x + 3) + (2x + 3) + (10x - 5)

P = 14x + 1

Since the perimeter of both geometric figures are the same, we can calculate the value of x as follows:

16x - 5 = 14x + 1

2x = 6

x = 3

For the perimeter of this rectangle, we have:

P = 16x - 5.

P = 16(3) - 5.

P = 43 units.

For the perimeter of this triangle, we have:

P = 14x + 1.

P = 14(3) + 1.

P = 43 units.

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The value of f(0) is f(0) = 3 and the value of f(-4) is f(-4) = 1

From the question, we are to determine the value of the given functions

The functions are

f(0) and f(-4)

First, we will determine the value of f(0)

Since 0 ≥ -2, we will use the function

f(x) = x² + 2x + 3

Thus,

f(0) = (0)² + 2(0) + 3

f(0) = 0 + 0 + 3

f(0) = 3

Now, we will determine the value of f(-4)

Since -4 < -2, we will use the function

f(x) = x + 5

Thus,

f(-4) = -4 + 5

f(-4) = 1

Hence, f(0) = 3 and f(-4) = 1

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Gregory has 10 ways to choose 3 boxes of cereal.

What do you mean by purchase?

A corporation or organization uses the purchasing process to buy products or services in order to achieve its objectives. Although many organizations make an effort to establish standards for the purchasing process, procedures can differ significantly between organizations.

According to data in the given question,

We have :

The purchase of 3 boxes and the store has 5 different varieties of munchie brand cereal.

The order in which the boxes of cereal are chosen is not important as Gregory can randomly choose any 3 different varieties. So, this is a combination problem.

Use the combination formula:

[tex]_nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

Putting n=5 (5 different varieties) and r=3 (3 different varieties). So, the number of ways Gregory choose 3 boxes of cereal is:

[tex]_{5}C_3=\dfrac{5!}{3!(5-3)!}=\dfrac{5!}{3!2!}= \frac{5.4.3.2.1}{3.2.1.2.1} _{5}C_3=\dfrac{5\cdot 4}{2\cdot 1}=10[/tex]

Therefore, the required answer is 10 ways.

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The number of people needed will be approx 65.

Margin of error = Critical value x Standard deviation for the population.

Margin of error = Critical value x Standard error of the sample.

Given, Margin of error (m) = 0.08

          z (at 80% confidence level)=1.282

Sample size(n) = (z/m)^2 p (1-p)

In order to find the sample size, we must know the value of proportion.

The value of proportion is missing so, in the absence of proportion, we will consider it as 0.5.

p = 0.5

∴ Sample size = (z/m)^2 p (1-p)

                       = (1.282/0.08)^2 × 0.5 × (1-0.5)

                       = 65

Inferential statistics is a statistical method that deduces from a small but representative sample the characteristics of a bigger population. In other words, it allows the researcher to make assumptions about a wider group, using a smaller portion of that group as a guideline.

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A car travels 500/3 meters in 2 seconds.

What is speed?

The speed at which an object's location changes in any direction. The distance traveled in relation to the time it took to travel that distance is how speed is defined. Given that it just has a direction and no magnitude, speed is a scalar number.

Here, we have

Speed of car  = 100 KM/ hour

1 km= 1000m

1 hour = 3600 seconds

Let's find the speed of the car in Meters/second

Speed of car in m/sec = 100*1000 m/3600 second

Here we have taken 1000 for km and 3600 for an hour

Speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second

Speed of car in m/sec = 250/9  m per sec

We know that

Distance = speed*time

Speed = 250/9  m per sec

Time = 2 second

Distance = 250/9 * 2 meters = 500/3 meters

Hence, a car travels 500/3 meters in 2 seconds.

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Answer: When multiplying a whole number by a PROPER fraction (always less then 1), the product is always less than a whole number. So yes, i agree with jenny when using proper fractions.

The values of the functions defined in the piecewise function are f(0) = 5 and f(-4) = 11

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

f(x) = | x + 5                 x < -2

         x² + 2x + 3        x ≥ -2

Evaluating the function f(0)

In this function, we have the x value to be

x = 0

This x value is at the domain x < -2

So, we make use of

f(x) = x + 5

Substitute 0 for x in f(x) = x + 5

f(0) = 0 + 5

Evaluate

f(0) = 5

Evaluating the function f(-4)

In this function, we have the x value to be

x = -4

This x value is at the domain x ≥ -2

So, we make use of

f(x) = x² + 2x + 3

Substitute -4 for x in f(x) = x² + 2x + 3

f(-4) = (-4)² + 2(-4) + 3

Evaluate

f(-4) = 11

Hence, the value of f(-4) is 11

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Answer:

4/45

Step-by-step explanation:

Answer:

can u see when i do this????

Step-by-step explanation:

Answer:

ypotheses:

H0: μ = 2000

H1: μ < 2000

Claim: The average number of acres in the State Park is less than 2000.

Critical Value (s): -1.645 (z-score)

Acceptance Region: z < -1.645

Rejection Region: z ≥ -1.645

Test Value: z = -3.537

Conclusion: Since -3.537 is less than -1.645, we reject the null hypothesis and accept the alternate view. There is enough evidence to support the claim that the average number of acres in the State Park is less than 2000.

Step-by-step explanation:

So when parent population is right-skewed and the sample size is small, the percentage of intervals that include population mean is (above, below, equal to) 0.95 when building 95% confidence intervals for said mean.

A confidence level of both the CI refers to the likelihood that its confidence interval contains the actual population mean value.

Thus, when parent population is right-skewed and the sample size is small, the percentage of intervals that include population mean is (above, below, equal to) 0.95 when building 95% confidence intervals for said mean.

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