Let S be the universal set, where:
S={1,2,3,...,23,24,25}
Let sets A and B be subsets of S, where:

The central limit theorem states that the distribution of the sample mean will be approximately normal if the sample size is sufficiently large.

Specifically, the  central limit theorem states that if the sample size (n) is greater than or equal to 30, then the sample mean (X) will be approximately normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n). Mathematically X~N(μ, σ/√n)

For example, if a population has a mean of 10 and a standard deviation of 2, then a sample of size 30 taken from that population will have a sample mean (X) that is approximately normally distributed with a mean of 10 and a standard deviation of 2/√30, or 0.6.

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Answer:

it should be true because sum of 3 interior angle of a triangle is 180 degree

Answer:

True.

Step-by-step explanation:

A triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle.

Answer: (-3, -1)

Step-by-step explanation:

First, we can use the first equation to solve for one variable in terms of the other.

y = -2x - 7

Next, we can substitute this expression for y into the second equation:

2y - x = 1

2(-2x - 7) - x = 1

Simplifying:

-4x - 14 - x = 1

-5x - 14 = 1

-5x = 15

x = -3

Now that we have the value of x, we can substitute it back into either of the original equations to find y. Using the first equation:

y = -2(-3) - 7

y = 6 - 7

y = -1

Therefore, the ordered pair that satisfies both equations is (-3, -1).

Answer: (-3,-1)

Explanation Step By Step

The area of a sector is a region bounded by two radii of a circle and an arc between is  (320/9) π sq. units.

Radius is a straight line segment that connects the center of a circle or sphere to any point on its circumference or surface, respectively. In other words, it is the distance from the center of the circle or sphere to any point on its edge or surface.

The given sector is EFG = 128°.

The area of a sector is a region bounded by two radii of a circle and an arc between them.

A = (θ/360) × πr²

Where:

The fraction (θ/360) represents the fraction of the entire circle that the sector occupies. Multiplying this fraction by the total area of the circle (πr²) gives the area of the sector.

Use the formula for the area of a sector with the central angle in degrees:

A = (n/360) × πr²

From the given figure, n = 128 and r = 10

A = (128/360) × π(10)²

  = (320/9) π sq. units.

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This is true, of course. The collection of any and all finite sequence of X's elements, along with the concatenation operation, is referred to as the free fuzzy set F over a set .

The sentence xA denotes that x is an element of a set A since the symbol denotes set membership and meaning "is an element of". In those other words, x belongs to the group of (potentially many) items in set A.

What do math components consist of?

Components are also the components that constitute a set. A shared characteristic of the items can define a set. For instance, the set is the collection E of positive roughly equal numbers. Furthermore, F is a semigroup, since the operation of concatenation is associative: if  and  are elements of F, then Finally, F is a free semigroup over , which means that every element of F can be written uniquely as a product of elements of .

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Using triple angle formula the evaluation of the trigonometric identity cos(2a) are 1 and 1/2.

We can use the trigonometric identity cos(2a) = 1 - 2sin^2(a) to evaluate cos(2a), but first we need to find the value of sin(a) from the given equation.

Given: sin(3a) = 2sin(a)

We can expand sin(3a) using the triple angle formula:

[tex]sin(3a) = 3sin(a) - 4sin^3(a)[/tex]

Substituting the given equation into this, we get:

[tex]2sin(a) = 3sin(a) - 4sin^3(a)[/tex]

Simplifying, we can rearrange to get:

[tex]4sin^3(a) - sin(a) = 0[/tex]

Factorizing, we get:

[tex]sin(a)(4sin^2(a) - 1) = 0[/tex]

So, either sin(a) = 0 or 4sin^2(a) - 1 = 0.

If sin(a) = 0, then

[tex]cos(a) = \±1\\cos(2a) = cos^2(a) = 1.[/tex]

If 4sin^2(a) - 1 = 0, then we can solve for sin(a) to get:

[tex]sin(a) = \±\sqrt{(1/4)} = \±1/2[/tex]

If sin(a) = 1/2, then

[tex]cos(a) = \sqrt{(1 - sin^2(a))} = \sqrt{(1 - 1/4)} = \sqrt{3/2}[/tex]

Using the identity cos(2a) = 1 - 2sin^2(a), we can then calculate:

[tex]cos(2a) = 1 - 2sin^2(a) = 1 - 2(1/4) = 1/2[/tex]

If sin(a) = -1/2, then cos(a) = -√3/2, and using the same identity we get:

[tex]cos(2a) = 1 - 2sin^2(a) = 1 - 2(1/4) = 1/2[/tex]

So, we have two possible values for cos(2a): 1 and 1/2.

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Answer: D. As x → -∞, y → -∞.

Step-by-step explanation:

The graph shows the function approaching negative infinity on the x-axis (left side).  When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.

A function declaration specifies the return data type, name of the function, and the parameter variable(s).

In programming, a function declaration is a statement that specifies the characteristics of a function. It includes the name of the function, the return data type (if any), and the parameter variable(s) (if any) that the function expects to receive as input. The declaration is used to inform the compiler or interpreter about the existence and behavior of the function, so that it can be called from other parts of the program. The function's actual implementation or definition is typically written separately from the declaration. By separating the declaration and implementation of a function, programs can be more modular and easier to maintain.

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Answer:

x = 18

Step-by-step explanation:

Alternate exterior angles are congruent.  Set the equations equal to each other and solve for x.

7x + 11 = 10x - 43  Subtract 7 x from both sides

7x - 7x + 11 = 10x - 7x - 43

11 = 3x - 43  Add 3 to both sides

11 + 43 = 3x -43 + 43

54 = 3x  Divide both sides by 3

[tex]\frac{54}{3}[/tex] = [tex]\frac{3x}{3}[/tex]

18 = x

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

First, we need to find the median of each series.

For series a, the median is:

(3680 + 3682)/2 = 3681

For series b, the median is:

(382 + 408)/2 = 395

Next, we calculate the deviation of each value from its respective median:

For series a:

|3487 - 3681| = 194

|4572 - 3681| = 891

|4124 - 3681| = 443

|3682 - 3681| = 1

|5624 - 3681| = 1943

|4388 - 3681| = 707

|3680 - 3681| = 1

|4308 - 3681| = 627

For series b:

|487 - 395| = 92

|508 - 395| = 113

|620 - 395| = 225

|382 - 395| = 13

|408 - 395| = 13

|266 - 395| = 129

|186 - 395| = 209

|218 - 395| = 177

Then, we calculate the mean deviation for each series by adding up the absolute deviations and dividing by the number of values:

For series a:

Mean deviation = (194 + 891 + 443 + 1 + 1943 + 707 + 1 + 627)/8

= 682.5

For series b:

Mean deviation = (92 + 113 + 225 + 13 + 13 + 129 + 209 + 177)/8

= 115.5

Comparing the two mean deviations, we see that series a has a larger mean deviation than series b. This indicates that series a has more variability than series b.

Answer:

the coordinate of C is 10.5, and the distance between A and C is 10.5 - 5 = 5.5, and the distance between B and C is 15 - 10.5 = 4.5.

Step-by-step explanation:

If C is 2 units closer to B than it is to A, then we can find the distance between A and C and between B and C by using the distance formula:

Distance between two points (x1, y1) and (x2, y2) = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Let x be the coordinate of C. Then, the distance between A and C is x - 5, and the distance between B and C is 15 - x. We know that the distance between B and C is 2 units greater than the distance between A and C, so we can set up an equation:

15 - x = 2 + (x - 5)

Simplifying and solving for x, we get:

15 - x = 2 + x - 5

18 - x = x - 3

2x = 21

x = 10.5

Therefore, the coordinate of C is 10.5, and the distance between A and C is 10.5 - 5 = 5.5, and the distance between B and C is 15 - 10.5 = 4.5.

Therefore , the solution of the given problem of probability comes out to be (B) Verifying that an event's chance is 0.05 or less is the right response.

The primary goal of a procedure's criteria-based methods is to calculate the probability that a statement is true or that a specific occurrence will occur. Any number range from 0 to 1, where 0 usually represents the likelihood of something happening and 1 typically represents an amount of confidence, can be used to represent chance. A probability illustration displays the possibility that a specific event will take place.

Here,

Several techniques can be used to determine whether it is reasonable to infer that sample data come from a population with a normally distributed population, including:

A. Recognizing anomalies

B. Verifying that an event's probability is 0.05 or lower C.

Examining a histogram visually to see if it approximately resembles a bell shape

D. Creating a normal quantile plot, a type of graph.

Option B is invalid because it doesn't reveal anything about how the sample data are distributed.

The threshold for statistical significance is the chance of an event being 0.05 or less, but it has no bearing on the distribution's shape.

As a result, (B) Verifying that an event's chance is 0.05 or less is the right response.

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Answer:

See below, please.

Step-by-step explanation:

The rise of democracy has had a significant impact on the African continent, with many countries transitioning from authoritarian rule to democratic governance since the 1990s. For example, South Africa emerged from decades of apartheid and transitioned to democracy in 1994, with the election of Nelson Mandela as the country's first black president. Similarly, in Ghana, the return to multiparty democracy in 1992 after years of military rule led to the establishment of a more stable political system.

The impact of democracy has not been uniform across Africa, with some countries experiencing significant challenges in their democratic transitions. For instance, in Zimbabwe, President Robert Mugabe, who came to power after independence in 1980, held on to power for over three decades through rigged elections and suppression of political opposition. It wasn't until a military coup in 2017 that he was forced to step down.

Despite the challenges, democracy has brought about some significant improvements on the African continent. With democratic governance, there has been a greater emphasis on human rights, the rule of law, and good governance. Free and fair elections have become the norm in many African countries, and citizens have become more involved in the political process, leading to greater accountability from leaders.

The rise of democracy in Africa has had both positive and negative impacts, but overall it has contributed to the establishment of more accountable and transparent governance systems. With democratic institutions in place, African nations are better positioned to address the political and socio-economic challenges that they face.

Step-by-step explanation:

my previous answer assumed we need a kind of average change rate.

but it seems you need the immediate change rate ?

or what ? the question does not specify.

I would appreciate if you would leave a comment, when you find that my answer is seemingly not matching some expected answers.

so, let's try now the immediate change rate (as I have no information to go - I have also no information about what you are currently learning in your class, and if you do already derivatives or not, so, this might be now above your learning level ...) :

again, the area between the inner circle and the outer square is

A = As - Ac = s² - pi×r²

where s is the square's side length, and r is the radius of the circle.

the immediate change rate of that area is the sum of first derivatives of A based on both used variables multiplied by their individual change rates :

dA/dt = dAs/ds × ds/dt - dAc/dr × dr/dt

and this is then calculated for the given data point (s = 16, r = 3) and the individual change rates of the variables (ds/dt = 2 meters/minute, dr/dt = 1 meter/minute).

so, we have

dA/dt = 2s × 2 - 2×pi×r × 1

as (s²)' = 2s, (pi×r²)' = 2×pi×r

dA(16, 3)/dt = 2×16×2 - 2×pi×3×1 = 64 - 6pi =

= 45.15044408... meters²/minute ≈

≈ 45.15 meters²/minute

so, you see, for a curved function (not a line) there has to be a difference between the average change rate between 2 points and the immediate change rate directly at a point.

I hope this works now for you.

and here now the original answer for an average change rate :

right now the radius is 3 m, and the square side lengths are 16 m.

1 minute ago the radius was 2 m, and the square side lengths were 14 m.

the area between the circle and the square is always the area of the square minus the area of the circle.

these areas are right now

circle : pi×3² = 9pi m²

square : 16² = 256 m²

area between = 256 - 9pi = 227.7256661... m²

these areas were one minute ago

circle : pi×2² = 4pi m²

square : 14² = 196 m²

area between = 196 - 4pi = 183.4336294... m²

the change rate of the area between the circle and the square is

227.7256661... - 183.4336294... = 44.29203673... m² per minute

The weighted average length of a nail from the carpenter's box is 3.5 centimeters.

Different from calculating the average, the weighted average implies considering the frequency or abundance percentage. Now, to calculate the average weighted we will need to multiply the length of each type of nail by the abundance and finally, we will need to add the results obtained. The process is shown below:

Short nail: 2.5 cm x 70.5%= 1.7625 cm

Medium nail: 5.0 cm x (19% = 0.95 cm

Long nail: 7.5 cm x 10.5% = 0.7875 cm

1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm

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Answer:

Step-by-step explanation:

Let weight of fourth parcel be x

Mean = Sum of all values/total number of values.

8.5 = 7.7 + 7.6 + 8.2 + x/4

8.5 = 23.5 + x/4

8.5 × 4 = 23.5 + x

34 = 23.5 + x

34 - 23.5 = x

10.5 = x

Therefore, weight of the fourth parcel will be 10.5 kg

Answer:

What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←​

Step-by-step explanation:

To map the point (4, -7) to (7, 4) by a rotation centered about the origin, we need to find the angle of rotation and direction.

We can start by finding the vector from the origin to (4, -7), which is <4, -7>. We want to rotate this vector to the vector from the origin to (7, 4), which is <7, 4>.

To do this, we need to find the angle between these two vectors. Using the dot product, we have:

<4, -7> · <7, 4> = (4)(7) + (-7)(4) = 0

Since the dot product is zero, we know that the two vectors are orthogonal, and the angle between them is 90 degrees.

To map (4, -7) to (7, 4) with a 90-degree rotation counterclockwise, we can use the matrix:

[0 -1]

[1 0]

Multiplying this matrix by the vector <4, -7>, we get:

[0 -1] [4] = [-7]

[1 0] [-7] [ 4]

which corresponds to the point (-7, 4). This matches our desired endpoint, so the answer is 90° counterclockwise.

Answer:

90° counterclockwise

Step-by-step explanation:

I am not sure if the picture helps or not.  I am trying to show that I traced the point (4,-7).  Then I have a plus sign at (0,0).  I start rotating the tracing paper counterclockwise until  I get to the point (7,4).  I needed to turn one turn of the plus sign.  That would be 90°

Helping in the name of Jesus.

The plane travels a distance of 11710 feet from point A to point B.

Why are trig ratios important?

As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

The figure representing the situation is given below.

From triangle AOC,

tan 19° = AC / OC

tan 19° = 7425 / OC

OC = 7425 / tan 19°

OC = 21563.77 feet

Similarly for triangle BOD,

tan 37° = BD / OD

tan 37° = 7425 / OD

OD = 7425 / tan 37°

     = 9853.31 feet

AB = CD

    = OC - OD

    = 21563.77 feet - 9853.31 feet

    = 11,710.46 feet

    ≈ 11710 feet

Hence the distance plane travelled from point A to point B is 11710 feet.

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The graph that matches the piecewise function, f(x) = √(x + 5), if x < -2, f(x) = |x + 1| if -2 ≤ x ≤ 2, and f(x) = (x - 2)² if x > 2 is the graph in the third option.

A piecewise function is a function is a function that consists of two or more subfunctions each of which are applied, based on the specific interval of the input variable.

The intervals of the piecewise function are;

f(x) = √(x + 5) if x < -2

f(x) = |x + 1| -2 ≤ x ≤ 2

f(x) = (x - 2)² if x > 2

The graph of the piecewise function is a three piece graph which consists of the graph of f(x) = √(x + 5), for x values less than -2, f(x) = |x + 1|, for x-values in the interval -2 ≤ x ≤ 2 and the graph of f(x) = (x - 2)²

The <-2, symbol indicates the presence of an open circle in the graph of f(x) = √(x + 5) at x = -2

The interval -2 ≤ x ≤ 2 for the function f(x) = |x + 1| indicates that the graph of f(x) = |x + 1| in the interval -2 ≤ x ≤ 2, consists of closed circles at x = -2 and x = 2.

The interval, x > 2, for the function, f(x) = (x - 2)², indicates that the presence of an open circle in the graph of f(x) = (x - 2)² at x = 2.

The correct option for the graph of the piecewise function is therefore the third option.

Please find the attached the graph of the piecewise function created with MS Excel

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Answer:

D 20

Step-by-step explanation:

Let's call the integer we're looking for "x". We know that 18% of x is greater than 3.5, so we can write the inequality:

0.18x > 3.5

To solve for x, we can divide both sides by 0.18:

x > 3.5 ÷ 0.18

x > 19.44

We want the smallest possible integer that satisfies this inequality, which is 20. So the answer is D) 20.

Answer:

graph Z , Horizontal Shift

Step-by-step explanation:

Got it right on edmentum.

Answer:

arc length = 2.2π inches

Step-by-step explanation:

arc length is calculated as

length = circumference of circle × fraction of circle

           = 2πr × [tex]\frac{22}{360}[/tex] ( r is the radius )

           = 2π × 18 × [tex]\frac{22}{360}[/tex] ( cancel 18 and 360 by 18 )

          = 2π × [tex]\frac{22}{20}[/tex]

        = [tex]\frac{44}{20}[/tex] π

       = 2.2π inches

Answer:

82

Step-by-step explanation:

3, 6, 11, 18, 27, 38, 51  , Next term 51 in the sequence is nth term .

What does math sequence mean?

An arrangement of numbers in a specific order is referred to as a sequence. The sum of the components of a sequence, on the other hand, is what is referred to as a series.

SEQUENCE    3,6,11,18,27...

  the series follows the odd counting.

for example:

we have odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, etc.

now

    3 + 3 = 6

    6 + 5 = 11

we can see adding odd numbers in a series results in the solution of the proceeding number of series.

similarly,

    11 + 7 = 18

     18 + 9 = 27

      27 + 11 = 38

now adding 13 to 38 according to the series will result in the next number.

     38 + 13  = 51

hence, 51 is the next number in the series.

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Answer:

[tex]y=-\frac{1}{4}x+5[/tex]

Step-by-step explanation:

Given the point (8,3) and slope of 4, we can write an equation in point-slope form.

We know that any line perpendicular to another line has a opposite reciprocal. The opposite reciprocal of 4 is [tex]-\frac{1}{4}[/tex].

Now, to write this in point slope form.

Point slope formula:

[tex]y-y_1=m(x-x_1)[/tex]

New equation:

[tex]y-3=-\frac{1}{4}(x-8)[/tex]

Simplify:

[tex]y=-\frac{1}{4}x+5[/tex]

Here is the equation :)

Hi!
The percent change is 15%.
Hope this helps!

~~~PicklePoppers~~~

Step-by-step explanation:

The formula to calculate the value of the account after t years, with principal P and annual percentage rate (APR) r compounded n times per year, is given by:

A = P(1 + r/n)^(nt)

In this case, P = $690, r = 0.022 (2.2% expressed as a decimal), n = 4 (compounded quarterly), and t is the number of years.

So the function to calculate the value of the account after t years is:

A(t) = 690(1 + 0.022/4)^(4t)

Simplifying and rounding to four decimal places, we get:

A(t) = 690(1.0055)^4t

To find the annual percentage yield (APY), we use the formula:

APY = (1 + r/n)^n - 1

In this case, r = 0.022 and n = 4, so:

APY = (1 + 0.022/4)^4 - 1

= 0.022321

Multiplying by 100 and rounding to two decimal places, we get an APY of 2.23%.

The volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis is (16/3)π cubic units.

To find the volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis, we use the formula:

V = ∫[a,b] πr²dy

where a and b are the limits of integration in the y-direction, r is the radius of the circular cross-sections perpendicular to the y-axis, and V is the volume of the solid.

First, we need to find the equation of the curve that is generated when we rotate y = 4 - 2x² around the y-axis. To do this, we use the formula for the equation of a curve generated by revolving y = f(x) around the y-axis, which is:

x² + y² = r²

where r is the distance from the y-axis to the curve at any point (x, y).

Substituting y = 4 - 2x² into this formula, we get:

x² + (4 - 2x²) = r²

Simplifying, we get:

r² = 4 - x²

Therefore, the radius of the circular cross-sections perpendicular to the y-axis is given by:

r = √(4 - x²)

Now, we can integrate πr²dy from y = 0 to y = 2:

V = ∫[0,2] π(√(4 - x²))²dy

V = ∫[0,2] π(4 - x²)dy

V = π∫[0,2] (4y - y²)dy

V = π(2y² - (1/3)y³)∣[0,2]

V = π(8 - (8/3))

V = (16/3)π

Therefore, the volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis is (16/3)π cubic units.

b. To find the volume of the solid generated by revolving the region enclosed by the curves x = √y+9, x = 0, and y = 1 through 360° about the y-axis, we use the same formula as in part (a):

V = ∫[a,b] πr²dy

where a and b are the limits of integration in the y-direction, r is the radius of the circular cross-sections perpendicular to the y-axis, and V is the volume of the solid.

First, we need to solve the equation x = √y+9 for y in terms of x:

x = √y+9

x² = y + 9

y = x² - 9

Next, we need to find the equation of the curve that is generated when we rotate y = x² - 9 around the y-axis. Using the same formula as in part (a), we get:

r = x

Now, we can integrate πr²dy from y = 1 to y = 10 (since x = 0 when y = 1 and x = 3 when y = 10):

V = ∫[1,10] π(x²)²dy

V = π∫[1,10] x⁴dy

V = π(1/5)x⁵∣[0,3]

V = π(243/5)

Therefore, the volume of the solid generated by revolving the region.

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Step-by-step explanation:

There are many possible solutions to this problem, but one possible set of values for P, Q, R, S, T, and U is:

P = 2

Q = 5

R = 1

S = 8

T = 9

U = 9

With these values, we have:

PQR = 251

STU = 156

And the sum of PQR and STU is indeed 407.