let d be the difference in the number of puzzles solved by two randomly selected subjects in a five-minute period. what's the standard deviation

The experimental probability of 2.5% is less than the theoretical probability of 16.67%.

What is the experimental probability?

The experimental probability of an event occurring is the number of times that it occurred when the experiment was conducted as a fraction of the total number of times the experiment was conducted.

The experimental probability of landing on 5 is the number of times that 5 was rolled divided by the total number of rolls. So, for Katie, the experimental probability of landing on 5 is:

(number of times 5 was rolled) / (total number of rolls) = 5/200 = 0.025 or 2.5%

This experimental probability, 2.5%, is the probability that Katie obtained from rolling the number cube 200 times.

The theoretical probability of landing on 5, assuming the cube is fair, is the number of ways to land on 5 divided by the total number of possible outcomes. Since a fair number cube has 6 faces numbered 1 to 6, the theoretical probability of landing on 5 is 1/6 or about 16.67%.

Hence, the experimental probability of 2.5% is less than the theoretical probability of 16.67%. This might be due to the fact that 200 rolls is not a large number to get accurate results. With more rolls, the experimental probability should get closer to the theoretical probability.

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The lower bound for a 95% confidence interval for the average length of the entire population of fish is 65.492.

Let the sample mean be ( x ) = 66.7

Standard deviation for the given sample be = s = 8.5

random sample of 190 fish is collected from the ocean so ( n )= 190

Confidence level be 95% so the Z-score be 1.959 ≈ 1.96.

By using the formula ,

x ± [tex]Z\frac{s}{\sqrt{n} }[/tex]

= 66.7 ± 1.96 (8.5/√190)

= 66.7 ± 1.208

where 1.208 indicates margin error (E).

So upper bound be 66.7 + 1.208 = 67.908

and lower bound be 66.7 - 1.208 = 65.492.

95% of samples contain the population mean (μ) within the confidence interval x ± E.

"A confidence interval is the range of values, obtained from sample statistics, that is likely to include the value of an unknown population parameter," according to the definition.

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The Average snowfall in Boston is 44.6 inches

Average is a single value that is taken as prototypically of a set or list of numbers. Depending on the context the average might have statistically different meanings like median or mode.

Average= sum of observation/number of observations

The temperature in january=32.8

the temperature in february= 56.4

∴Average= 32.8+56.4/2

=89.2/2

=44.6

Therefore, the Average snowfall in Boston over this period is 44.6 inches.

Some properties of average are:

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Answer:

5 2/10

Step-by-step explanation:

5.2 = 5 + 0.2 = 5 + 2/10 = 5 2/10

Answer: 5 2/10

The equation y = a[tex]x^2[/tex] + bx + c is in factored form when it is written as:

y = a(x - r(1))(x - r(2))

A quadratic expression that is the product of two factors, each of which is a linear expression, is referred to as having a "factored form."

When an equation is in factored form, it can be expanded to recreate it in standard form by multiplying out the components. The act of factoring involves summarizing the parts of a given integer or algebraic expression.

The equation y = a[tex]x^2[/tex] + bx + c is in factored form when it is written as:

y = a(x - r(1))(x - r(2))

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The other ratio equivalent to (3, 5) will be (9, 15).

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Given that, Cory is reading a graph of equivalent ratios. If 1 of the ratios is represented as 3,5 which could be another ratio

In the given options,

a) (6, 8) = 3, 4

b) (8, 6) = 4, 3

c) (9, 15) = 3, 5

Since, (9, 15) = 3, 5

Hence, the equivalent ratio will be (9, 15).

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The angle of 135 degrees is an obtuse angle.

An angle is a space shared by two rays that are joined at the same vertex. We can find different types of angles according to their amplitude.

If the amplitude is larger than 90º (90 degrees) and less than 180º (180 degrees) that tells us that it is an obtuse angle.

An obtuse angle is also defined as an angle that is formed when a ray rotates between 90º and 180º around a point.

Visually, this angle is more than a quarter of a circle but less than half of a circle. So, if we divide a circle into four parts, an obtuse angle will always occupy between 1/4 and 1/2 of a circle.

Thus, the angle of 135 degrees is an obtuse angle.

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Answer:

(3, 9 )

Step-by-step explanation:

x + y = 12 → (1)

y = 3x → (2)

substitute y = 3x into (1)

x + 3x = 12

4x = 12 ( divide both sides by 4 )

x = 3

substitute x = 3 into (2) and solve for y

y = 3x = 3 × 3 = 9

solution is (3, 9 )

On using subtraction it can be seen that Simone needs more 8 inches space in her room to fit the chest beside the bed. So, the chest cannot fit in Simone's room with the measurements of room = 100 inches and bed  = 74 inches.

What is subtraction?

The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).

The measurement for Simone's room is, a = 100 inches.

The measurement for Simone's bed is, b = 74 inches.

The amount of space left in Simone's room = a - b.

Using the arithmetic operation of subtraction -

= 100 - 74

= 26

Hence, 26 inches of space is left in Simone's room.

The measurement for chest that Simone wants to fit in her room next to bed is 85 centimeters.

To convert 85 cm to inches divide the length by 2.5 -

Using the arithmetic operation of division -

85/2.5 = 34

Hence, the measurement of the chest in inches is 34 inches.

26 < 34

Using the arithmetic operation of subtraction -

34 - 26 = 8

So, Simone has 26 inches space left and the size of chest is 34 inches, which cannot be fitted in the room.

Therefore, Simone cannot fit the chest in her room.

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I'm not aware of any concrete information to support the assertion that New Yorkers travel less than 12,200 miles per year on average.

The average number of miles driven can vary significantly based on a number of variables, including population density, demography of urban and rural areas, transportation infrastructure, and individual preferences.

The availability of alternate modes of transportation, changes in fuel prices, and changes in the general state of the economy can all have an impact on data on average miles driven.

It's impossible to say for sure whether the typical amount of miles driven in New York is less than 12,200 without access to particular data or a research.

However, because sample data can be influenced by bias and other kinds of inaccuracy, if this statistic was obtained from a sample of data, it might not correctly reflect the general average for the entire state.

A thorough and representative study would need to be carried out to precisely establish the typical amount of miles travelled in New York.

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An independent system is a system that does not interact with its environment or any other system. A dependent system, on the other hand, is a system that interacts with its environment or other systems. In other words, the behavior of a dependent system is affected by external factors, whereas the behavior of an independent system is not.

Independent systems are self-sufficient and don't rely on external factors to function or operate. They can function and make decisions on their own without being affected by anything else. For example, a calculator is an independent system, it performs mathematical operations on its own and does not depend on anything else to work.

On the other hand, dependent systems are not self-sufficient and rely on external factors to function or operate. They are affected by and interact with their environment, and their behavior is influenced by external factors. For example, a car is a dependent system, it needs gasoline to run and is affected by the road conditions, traffic, and weather.

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A) Evaluate f(0)

f(0) = 6*0 - 4 = -4

What does a math function mean?

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

B) Evaluate f(2)

f(2) = 6*2 - 4 = 8

C) Evaluate f(-2)

f(-2) = 6*(-2) - 4 = -12

D) Evaluate f(4)

f(4) = 6*4 - 4 = 20

E) Evaluate f(-3)

f(-3) = 6*(-3) - 4 = -16

Note: In the given function, x is replaced by z, so in order to evaluate the function for the given values of x, we need to replace x with z.

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Answer:Pr(4.19 ≤ X ≤ 4.81)

Step-by-step explanation:

First of all, let's calculate the mean;

x¯ = (4.3 + 5.1 + 3.9 + 4.5 + 4.4 + 4.9 + 5.0 + 4.7 + 4.1 + 4.6 + 4.4 + 4.3 + 4.8 + 4.4 + 4.2 + 4.5 + 4.4)/17

x¯ = 76.5/17

x¯ = 4.5

We are given standard deviation; s = 0.31

Now, z-value for a 68% Confidence interval is 1

Range in which the data falls is;

Range = x¯ ± zs

Range = 4.5 ± (1 × 0.31)

Range is;

Pr[(4.5 - 0.31) ≤ X ≤ (4.5 + 0.31)]

Pr(4.19 ≤ X ≤ 4.81)

The answer of 10 more than 23 is 33.

The answer of 10 more than 23 is 33 which can be derived using simple mathematical calculations.

To find 10 more than 23, you can add 10 to the original number 23.

10 + 23 = 33

It's a simple arithmetic operation where you add a specific number, in this case 10, to the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 10 more than 23 is 33.

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The missing sides in the triangle is 2

If leg an is the missing side, change the equation such that an is on one side and compute the square root of that number: a = √(c² - b²)

Leg b is equal to (c2 - a2) if leg b is unknown.

The formula for a missing hypotenuse is c = (a2 + b2).

When given the length of one side, multiply it by 2 to determine the length of the hypotenuse. You can get the side lengths of a triangle with sides of 45°, 45°, and 90° by simply dividing the hypotenuse by 2.

c = (a2 + b2) = 8

here

[tex]2a^{2}[/tex] =8

[tex]a^{2}[/tex] = 8/2 =4

a = [tex]\sqrt{4} = 2[/tex]

The missing sides in the triangle is 2

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The inverse of the function f(x) = 2x + 1 is [tex]f^{-1}[/tex](x) = [tex]\frac{x-1}{2}[/tex]

Let y=f(x)

x=[tex]f^{-1}[/tex](y)

Given, f(x)=2x+1

y=2x+1

2x=y−1

x=[tex]\frac{y-1}{2}[/tex]

[tex]f^{-1}[/tex] (y)=[tex]\frac{y-1}{2}[/tex]

Replace y by x, we get,

[tex]f^{-1}[/tex](x)=[tex]\frac{x-1}{2}[/tex]

This is the inverse of function.

A function that can reverse into another function is known as an inverse function or anti function. In other words, if any function "f" takes x to y, then the inverse of that function will take y to x. When a function is written as "f" or "F," its inverse is written as "[tex]f^{-1}[/tex]" or "[tex]F^{-1}[/tex]." Here, (-1) should not be confused with an exponent or a reciprocal.

Inverse functions f and g result in f(x) = y if and only if g(y) = x.

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What is the inverse of the function f(x) = 2x + 1?

If no two men are to sit next to each other, there are 144 ways to arrange four men and four women at a round table.

Combinations are mathematical operations that count how many possible combinations there are for a given set of components, regardless of the order in which they were chosen. One can choose the components of combos in any order.

First, arrange the four women so that there is a free seat between each pair of them at the round table. These four women can be seated at the round table in 3 different ways, for a total of 6 possible arrangements. This is written as 3! = 6.

Then, the four vacant seats will be occupied by the four men and this is written as ⁴P₄=4!=24. Then, the required number of ways to seat the two men who are not adjacent to each other is 6×24=144 ways.

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Answer:

28/10

Step-by-step explanation:

To find out scale factor, you need to divide both sides which means

7/2.5 is 2.8 and if we turn that into a fraction we get 28/10

Answer:

  y = a · (x -(h +√(-k/a))) · (x -(h -√(-k/a))) . . . . . . from y = a(x -h)² +k

Step-by-step explanation:

You want to know how to write an equation in intercept form from vertex form.

"Intercept form" of the equation of a parabola is the factored form. The x-intercepts are the values of x that make the factors zero. This form can be found from vertex for by solving for the x-intercepts—the values of x where y=0.

The vertex form equation is ...

  y = a(x -h)² +k . . . . . . . vertex (h, k)

Solving for x when y=0, we have ...

  0 = a(x -h)² +k

  -k/a = (x -h)² . . . . . . . subtract k and divide by 'a'

  ±√(-k/a) = x -h . . . . . take the square root

  x = h ±√(-k/a) . . . . . add h

These are the x-intercepts.

To write the equation in intercept form, we use these values to form factors of the quadratic. Each x-intercept (p) corresponds to a factor (x-p). The factors are multiplied by 'a' to keep the same vertical scaling of the graph that the original function had.

  y = a · (x -(h +√(-k/a))) · (x -(h -√(-k/a))) . . . . . . intercept form

The reflexive, symmetric, transitive, additional, and multiplication characteristics are the five algebraic qualities of equality.

The reflexive property states that a = a for every real integer.

For any two real numbers, a and b, the symmetric condition is that if a = b, then b = a.

For each real number, a, b, and c, the transitive property states that if a = b and b = c, then a = c.

For every real integer a, b, and c, if a = b, then a + c = b + c. This is known as the addition property of equality.

The equality's multiplication property states that if any real integer, a, b, and c, are equal, then a * c is equal to b * c.

These features serve as the basis for algebraic manipulation and are employed in the decomposition of expressions and the solution of equations.

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Answer:

x = 22, y = -13

Step-by-step explanation:

4x + 3y = 49

- x - 2y = 4

x + 2y = -4

4x + 8y = -16

Subtract both equations,

5y = -65

y = -13

x - 26 = -4

x = 22

Cheers

The Total weekly revenue of Mae Ling is 570$ with a five percentage commission.  

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Mae Ling earns a weekly salary of $355 plus a 5.0% commission on sales at a gift shop.

Since she sold $4,300 worth of merchandise

Her commission would be = 4300 * 5%

Commission = 4300 * 5/100

Commission = 215$

Her total salary = commission + weekly wage

Her total salary = 215 + 355 = 570

Therefore, the Total weekly salary of Mae Ling is 570$ with a 5 percent commission.

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The initial cost, which is zero, is 4.25 less than the plotted value of the stock, which is 4.25. So, "The stock is equation  4.25 less than the initial value, and the absolute value is 4.25" is the right response.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Based on the information provided, a vertical number line with tick marks every half unit starts at minus 7 and goes all the way up to 0. The number line displays the value of the negative 4.25.

The initial cost, which is zero, is 4.25 less than the plotted value of the stock, which is 4.25. So, "The stock is 4.25 less than the initial value, and the absolute value is 4.25" is the right response.

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What is the rational expression?

A rational expression is an expression of the form (p(x))/(q(x)) where p(x) and q(x) are polynomials. The expression is called a rational expression because it is the ratio of two polynomials.

A rational expression that is equal to the given expression when x doesn't equal 2 or -3 is:

5x / (x+3)

This is obtained by canceling the common factor of (x-2) in the numerator and the denominator of the original expression. Note that, this is only true when x doesn't equal 2 or -3, because the original expression is not defined when x = 2 or x = -3, as it would result in a division by zero.

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The given rational expression can be simplified by canceling out the common factor of (x-2) in the numerator and denominator, which results in the following simplified rational expression:

5/(x+3)

A rational expression is an expression of the form (p(x))/(q(x)) where p(x) and q(x) are polynomials. The expression is called a rational expression because it is the ratio of two polynomials.

A rational expression that is equal to the given expression when x doesn't equal 2 or -3 is:

5x / (x+3)

This is obtained by canceling the common factor of (x-2) in the numerator and the denominator of the original expression. Note that, this is only true when x doesn't equal 2 or -3, because the original expression is not defined when x = 2 or x = -3, as it would result in a division by zero.

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Line 'b' is perpendicular to line 'a'. Then the slope of line 'b' is 5/4.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are given below.

(7, 10) and (2, 14)

The slope of the line 'a' is given as,

m = (14 - 10) / (2 - 7)

m = - 4 / 5

Line 'b' is perpendicular to line 'a'. Then the slope of the line 'b' is given as,

Slope = - 1 / m

Slope = - 1 / (-4/5)

Slope = 5/4

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The difference of the given fractions lie between 0 and 1/2

A proper fraction is a fraction which has its numerator value less than the denominator. For example, ⅔, 6/7, 8/9, etc. are proper fractions.

Given here: 7/8-6/11= 77-48 /88

                                =0.32 or 8/25

but  0<0.32<1/2<1

Hence, the difference of the given fractions lie between 0 and 1/2

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The value of the expression is 4/25.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is,

-16/25 - (-12/15)

Two negatives become positive.

-16/25 - (-12/15) = (-16/25) + (12/15)

Doing the cross multiplication,

-16/25 - (-12/15) = [(-16 × 15) + (12 × 25)] / [25 × 15]

                         = 60 / 375

                         = 12/75

                         = 4/25

Hence we get the resulting value as 4/25.

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The interest rate is 5%.

It is the interest calculated on the principal at a given rate for a time period.

The formula for simple interest is,

SI = PRT/100.

Where P is the principal, R is the rate and T is the time.

We have,

P = $4000

T = 5

SI = $1000

Now,

SI = PRT/100

Substitute the values.

1000 = (4000 x R x 5)/100

1000 = 200R

Divide 200 into both sides.

R = 1000/200

R = 5%

Thus,

The rate of 5%.

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Two ordered pairs of the equation -x+6y=8

are (0, 4/3) and (-8, 0).

Here we want to find an ordered pair for the given equation:

-x + 6y = 8

To find an ordered point we just need to evaluate the equation in any value of x or y that we want.

For example, if we use x = 0 we will get:

-0 + 6y = 8

6y = 8

y = 8/6

y = 4/3

So we have the ordered pair (0, 4/3)

And if we evaluate in y = 0, we willg et:

-x + 6*0 = 8

-x = 8

x = -8

We have the point (-8, 0)

So these are two examples of ordered pairs of the equation.

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