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What does the notation below indicate?

Expected value of the mean = 50 (the population mean)

The expected value of the mean for a sample size of 4 from a population with a mean of 50 and a standard deviation of 12 can be calculated using the central limit theorem.

According to the central limit theorem, the expected value of the mean of a sample from a population approaches the population mean as the sample size increases. In other words, as the sample size becomes larger, the sample mean becomes a more accurate estimate of the population mean.

In this case, the expected value of the mean of a sample of 4 from a population with a mean of 50 and a standard deviation of 12 can be calculated as follows:

Expected value of the mean = 50 (the population mean)

It is important to note that the expected value of the mean is equal to the population mean, regardless of the sample size. The central limit theorem states that the sample mean approaches the population mean as the sample size increases, but for a sample size of 4, the expected value of the mean is still equal to the population mean.

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Probability that the system works is approximately 0.9841.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Let the three events be C₁, C₂ and C₃.

Probability that computer 1 works = P(C₁) = 0.65

Probability that computer 1 does not work = P(C₁') = 1 - 0.65 = 0.35

Probability that computer 2 works = P(C₂) = 0.65

Probability that computer 2 does not work = P(C₂') = 1 - 0.65 = 0.35

Probability that computer 3 works = P(C₃) = 0.87

Probability that computer 3 does not work = P(C₃') = 1 - 0.87 = 0.13

Let the event that at least one of the computer is working is S.

P(S) = 1 - P(no computer is working)

P(no computer is working) = P(C₁' ∩ C₂' ∩ C₃')

We have the operations of the computers are independent of each other.

P(C₁' ∩ C₂' ∩ C₃') = P(C₁') × P(C₂') × P(C₃')

                            = 0.35 × 0.35 × 0.13

                            = 0.015925

P(no computer is working) = 0.015925

P(S) = 1 - 0.015925

      = 0.984075 ≈ 0.9841

Hence the required probability is 0.9841.

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Answer:

A

Step-by-step explanation:

[tex]4\leq x < 4[/tex]

Focusing on the left end of the graph, the x value corresponding to the graph is -4. The circle present at this end of the graph is coloured in, which indicates that -4 is included in the domain.

Focusing on the right end of the graph, the x value corresponding to the graph is 4. The circle present at this end of the graph is NOT coloured in, which indicates that 4 is NOT included in the domain.

This suggests that a gas's pressure decreases as its volume increases. Similar to this, a gas's pressure rises as its volume decreases. The balloon's expansion for the given implies that its volume grows. Boyle's law predicts that its pressure will decrease as a result.

In other words, as the atmospheric gas exerts less pressure on the surface of the balloon, the interior gas expands until the internal and external pressures are equal. This is why weather balloons grow larger as they ascend through the atmosphere to lower pressure regions because the volume of the gas has increased.

You can observe Avogadro's Law whenever you blow up a balloon. By inflating the balloon, you can add moles of gas, which increases the balloon's volume.

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The exponential function r=(0.88)^4t can be written as r=(1-0.12)^4t.

What are exponential functions?

An exponential function is a Mathematical function in the form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Now,

given exponential function is r(r) = (0.88)^4t

we can rewrite its as  r=(1-0.12)^4t. to find whether it is increasing or decaying. As the - sign shows decrement.

hence,

             Given exponential function is decaying in nature..

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A population includes all elements or objects of interest in a study, whereas a sample is a subset of the population used to gain insights into the characteristics of the population.

The following statement is True.

A variable is a trait that can be measured and has several values. Variables include height, age, income, province or country of birth, school grades, and kind of dwelling. Variables can be divided into two types: category and numeric.

A "sampling frame" is a list of all population items to be researched. Probability and nonprobability are the two primary types of sampling methodologies. A simple random sample is a sample drawn from the population in which every member has an equal probability of being chosen.

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Answer:

92

Step-by-step explanation:

We first do 12x7 which equals to 84

Then we add 8 which equals to 92

The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Given expression,

7 raised to the power 2 divided by 7 raised to the power 3

7 ^ 2 / 7 ^ 3

The value of a ^ m / a ^ n  = a ^ m-n

= 7 ^ (2-3)

= 7 ^ ( -1)

= 1 / 7 .

Therefore, The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7

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The equation that represents the second step of solution process is 12x-3+27=-24. Thus, option A is correct.

The simplex method is a widely used linear programming methodology for addressing optimization problems. These problems typically involve a function and a number of constraints that are stated as inequalities.

Step 1: 3(4x-1)+27=-24

Step 2: 12x-3+27=-24

Step 3: 12x+24=-24

Step 4: 12x=-48

Step 5: x=-4

A. 12x-3+27=-24.

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The union of two subspaces of V is a subspace of V if and only if one of the subspaces of v is contained in the other

Let [tex]$V_1, V_2$[/tex] be the two subspaces of V. Suppose [tex]$V_1 \cup V_2$[/tex] is a subspace of V.

Then if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then we must have [tex]$x_1 \in V_1 \cup V_2$[/tex] and[tex]$x_2 \in V_1 \cup V_2$[/tex] so that we must have [tex]$x_1+x_2 \in V_1 \cup V_2$[/tex].

If and only if one of the subspaces is contained in the other, the union of the two subspaces is a subspace.

But this by definition means [tex]$x_1+x_2 \in V_1$[/tex] or [tex]$x_1+x_2 \in V_2$[/tex]. Either way, by the existence of additive inverses and the closure properties for the subspaces we have:

[tex]\left(x_1+x_2\right)+\left(-x_1\right) \in V_1[/tex]

Or

[tex]\left(x_1+x_2\right)+\left(-x_2\right) \in V_2[/tex]

By the associative/commutative properties, we have:

[tex]x_2 \in V_1 \text {, or, } x_2 \in V_1[/tex]

Thus we have shown if [tex]$x_1 \in V_1$[/tex] and [tex]$x_2 \in V_2$[/tex] then [tex]$x_1 \in V_2$[/tex] or [tex]$x_2 \in V_1$[/tex]. If [tex]$x_1 \in V_2$[/tex] for all [tex]$x_1 \in V_1$[/tex] then we have [tex]$V_1 \subseteq V_2$[/tex]. If [tex]$x_2 \in V_1$[/tex] for all [tex]$x_2 \in V_2$[/tex] then [tex]$V_2 \subseteq V_1$[/tex]. In either case, we see one subspace is a subset of the other.

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The length of the unknown side or, the length of AC = 22.62.

To calculate the length of the unknown side in a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides or, in familiar algebraic notation, a2 + b2 = c2.

In this Question, side AC is the hypotenuse, so we can use the Pythagorean theorem to find the length of side AC:

AC^2 = AB^2 + BC^2

We know that AB = 12 and BC = 19, so we can substitute these values into the equation:

AC^2 = 12^2 + 19^2

AC^2 = 144 + 361

AC^2 = 505

To find the length of AC, we can take the square root of 505:

AC = √505

Rounded to two decimal places, the length of AC = 22.62.

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Mercury, gallium, and caesium often have low melting points, except gold. The only liquid metal with a 38 °C melting temperature is mercury.

They have high melting and boiling points because melting and boiling require a lot of energy to break through the strong metallic connections present in a metal's massive structure.

Brass: 930 °C (1710 °F) Aluminium Bronze*: 1027-1038 °C (1881-1900 °F) Chromium: 1860 °C (3380 °F) Copper: 1084 °C (1983 °F).

In general, aluminium is an easy metal to melt, and it is easy to get your hands on.  To make aluminum metal shapes, many people melt discarded soda cans made of aluminum. The aluminum should be heated until it melts completely.

Therefore, the melting or boiling point will be higher the more energy is required. Varying metals have different melting and boiling points because the force of attraction between the metal ions differs between them.

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By assuming that the taxpayer has $100,000 as his income on the completed Form 1040, the total tax that the employee is responsible for paying will be: $17,836.

A tax bracket is a range of incomes that are taxed at a specific rate. Tax brackets are part of a progressive tax system, which means that tax rates increase progressively as an individual's income increases. Low-income taxpayers pay relatively low tax rates, while higher-income taxpayers pay higher rates.

In 2022, for example, a single filer with taxable income of $100,000 will pay $17,836 in taxes, representing an average tax rate of 18%. However, your marginal tax rate or tax bracket is 24%. As a result, the total tax that the employee is responsible for is $17,836.

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[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-16})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{(-16)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{8}}} \implies \cfrac{5 +16}{-7} \implies \cfrac{ 21 }{ -7 } \implies - 3[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-16)}=\stackrel{m}{- 3}(x-\stackrel{x_1}{8}) \implies y +16 = - 3 ( x -8) \\\\\\ y+16=-3x+24\implies {\Large \begin{array}{llll} y=-3x+8 \end{array}}[/tex]

The rule shows the input and output of the reflection is, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.

And, The new coordinate of A' = (- 5, - 1)

Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.

We have to given that;

Parallelogram ABCD is shown. A is at (-5, 1), B is at (-4, 3). C is at (-1, 3) . D is at (-2, 1).

We know that;

When a point is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.

And, The reflection of point (x, y) across the x-axis is (x, -y).

Hence, The new coordinate of A' is,

⇒ (- 5, 1) = (- 5, - 1)

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By concept of linear equations, The number of birds is 14 and number of lions is 17.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Let no. of birds=x and no. of lions=y

Given heads=31

and feet=96

Therefore, the equations will be

             x+y=31 and 2x+4y=96

from given equations x=14 and y=17.

Hence,

           The number of birds is 14 and number of lions is 17.

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The equation of the parabolas are

y = (x - 2)(x + 2)

y = (x - 2)(x + 2) -4

The graph is attached below.

What is a coordinate grid?

Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis. The origin is the location where the x- and y-axes intersect.

Assume the x-intercepts are 2 and -2.

The equation of a parabola whose x-intercepts a and b is y = (x-a)(x-b)

The equation of a parabola is

y = (x-2)(x-(-2))

y = x² - 4 .....(i)

The vertex of the parabola is (0,4).

The parabola's maximum or minimum value is the vertex's y-coordinate.

Thus replace - 4 with -8 of equation (i)

y = x² - 8

Puttin x = 0 in equations (i) and (ii)

y(0) = -4

y(0) = -8

Puttin x = 1 in equations (i) and (ii)

y(1) = -3

y(1) = -7

Puttin x = -1 in equations (i) and (ii)

y(-1) = -3

y(-1) = -7

The points on y = x² - 4 are (0,-4), (1,-3), and (-1,-3).

The points on y = x² - 8 are (0,-8), (1,-7), and (-1,-7).

Plot the points and join them.  

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The comparison of the fractions are

15/24 < 16/24, 3/18 < 4/18 and 14/24 <15/24

Fraction 1

Here, we have

5/8 and 2/3

The LCM of 8 and 3 is 24

So, the pair is

15/24 and 16/24

When compared, we have

15/24 < 16/24

Fraction 2

Here, we have

1/6 and 2/9

The LCM of 6 and 9 is 18

So, the pair is

3/18 and 4/18

When compared, we have

3/18 < 4/18

Fraction 3

Here, we have

7/12 and 5/8

The LCM of 12 and 8 is 24

So, the pair is

14/24 and 15/24

When compared, we have

14/24 <15/24

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Answer:

let the two numbers be x and y.

Given ,

[tex] \underline{\underline{\frac{x}{y} = \frac{3}{5}}} \\ [/tex]

To find - ratio of squares of the two numbers.

[tex]\longrightarrow \: \frac{ {x}^{2} }{ {y}^{2} } = ( \frac{ {3}^{2} }{ {5}^{2} } ) \\ \\ \longrightarrow \: \boxed{\frac{ {x}^{2} }{ {y}^{2} } = \frac{9}{25} }[/tex]

Therefore ,

[tex] \underline{\underline{ratio \: of \: the \: squares \: of \: two \: numbers \: = \: 9 \: : \: 25}} [/tex]

hope helpful! :)

Answer:

[tex]y = 10.5[/tex]

Step-by-step explanation:

[tex]\frac{5}{4} y = 13\\[/tex]

We transpose

[tex]y =\frac{13X4}{5}[/tex]

[tex]y = \frac{52}{5}[/tex]

[tex]y = 10.5[/tex]

The predicted egg production in 2001 is given as follows:

65.6 billion.

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

y = mx + b.

In which:

The production in 1995 was of 52.7, hence the intercept b is given as follows:

b = 52.7.

In 4 years, the production increased to 61.3, hence the slope m is given as follows:

m = (61.3 - 52.7)/4

m = 2.15.

Hence the function is of:

y = 2.15x + 52.7.

2001 is 6 years,hence the estimate is given as follows:

y = 2.15(6) + 52.7

y = 65.6 billion.

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The number of ordered pairs $(x,y)$ of positive integers that satisfy the equation would be 480.

We only count one ordered pair by substituting 2 for 60 in this case. We count four ordered pairs by doing with 4.

We got 7 pairings from 6 people. I add 8 to get 12, thus. the difference between neighboring phrases by moving on and doing so (1,3,3,5,5,...).

We believe that if 2n were substituted for 60, we would find 1+3+3+5+5+7+7.... where n words will be present.

So, 1+3+3+5+5... 29+29+31 = 16*30 = 480 is our response.

The number of ordered pairs $(x,y)$ of positive integers that satisfy the equation would be 480.

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The full question:

Find the number of ordered pairs $(x,y)$ of positive integers that satisfy the following equation

The degrees of freedom equals 7.

The test statistic will be 2.55

The critical value will be 1.89.

From the information, they randomly sample 20 individuals and administer a 30 item true or false psychological test designed to measure depression and the scores that are greater than 20 indicate significant levels of depression.

The degree of freedom will be:

= n - 1

= 8 - 1

= 7

The test statistic will be:

= 22.25 - 20 /2.49 ✓8

= 2.55

The critical value will be 1.89.

Based on the information, it should be noted that we will fail to reject the null hypothesis.

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Answer:

[tex]y \: = 2cos \: ( \frac{\pi}{5} x) - 3[/tex]

The value of y is 1446.38.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

y = 601 [tex](1.05)^{18}[/tex]

Now,

y = 601 x 2.4066192336911

y = 1446.3781

y = 1446.38

Thus,

y = 1446.38

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The exact values of each trigonometric function are 4/5, 3/5, 4/3, 5/4, 5/3, and 3/4.

Given, the terminal side of contains the point p(9, 12).

Each trigonometric function must have an exact value, which we must determine.

A line segment drawn from the origin to the point should have a length of r.

r = √x2 + y2

Here, x = 9 and y = 12

r = √(9)2 + (12)2

= √81 + 144

= √225

r = 15

sin θ = y/r = 12/15 = 4/5

cos θ =x/r = 9/15 = 3/5

tan θ = y/x = 12/9 = 4/3

cosec θ = 1/sin θ = 5/4

sec θ = 1/cos θ = 5/3

cot θ = 1/tan θ = 3/4

Consequently, each trigonometric function's precise values are 4/5, 3/5, 4/3, 5/4, 5/3, and 3/4.

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The full question:

The point p(9, 12) is on the terminal side of θ. Find the exact values of each trigonometric function.

Six categories of integers based on their ones digit are:

The cases when sum or difference of the pair is divisible by 10:

Therefore, no matter which seven integers we choose, there is always a pair that meets the condition.

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53 is the value of the 99% of the time.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center

Given, Let X represent the lifetime in months of a battery, and someone claims that X~N(50,25). We wish to investigate the claim, so 16 batteries are life-tested and the average survival times of the 16 batteries are Comput.

μ = 50

σ² = 25

n = 16

So, the Population standard deviation

σ² = 25

σ = 5

To find the value 99% of the time

The z-score will be

P(z <Z) = 0.999

P(z < 2.326) = 0.999

Z = 2.326

To find a z score corresponding to a known probability, select fx, Statistical, NORMSINV, and enter the total area to the left of the given value.

Now we determine the z-score using the z-score formula

x = μ + (Z *σ  / √n)

x = 53

Therefore, the value of 99% of the time is 53.

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Complete question:

The area of the rectangular garden can be calculated as follows: 57 m * 42 m = 2406 m^2.

The ornamental fence with a width of 60 cm has a width of 0.6 m. If the fence is planted inside the perimeter of the garden, the length of the garden will decrease by 2 * 0.6 m = 1.2 m and the width of the garden will decrease by 2 * 0.6 m = 1.2 m.

So, the new length and width of the garden will be 57 m - 1.2 m = 55.8 m and 42 m - 1.2 m = 40.8 m, respectively.

The new area of the garden can be calculated as follows: 55.8 m * 40.8 m = 2270.784 m^2.

Finally, the decrease in area can be calculated as follows: 2406 m^2 - 2270.784 m^2 = 35.216 m^2.

Therefore, the area of the garden will decrease by 35.216 m^2.

Answer:

The width of the ornamental fence is 60 cm, which is equal to 60/100 = 0.6 meters.

The total length of the ornamental fence that will be planted inside the perimeter of the rectangular garden is 2 * (57 m + 42 m) = 2 * 99 m = 198 m.

The decrease in the area of the garden due to the ornamental fence is 0.6 m * 198 m = 118.8 m^2.