for positive integers n. which elements of this sequence are divisible by 5? what about 13? are any elements of this sequence divisible by 65

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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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.

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.

Rounding to four decimal places, the answer is 0.8926. So the probability that at least one of the ten college students has not taken a mathematics course is approximately 0.8926.

what is probability?

Probability is a measure of the likelihood or chance that a particular event will occur. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability that a college student has taken a mathematics course is 0.80. Therefore, the probability that a student has not taken a mathematics course is

1 - 0.80 = 0.20.

The probability that at least one of ten college students has not taken a mathematics course can be found using the complement rule. That is, the probability that at least one student has not taken a mathematics course is equal to one minus the probability that all ten students have taken a mathematics course.

The probability that all ten students have taken a mathematics course is:

0.80¹⁰ = 0.1074

Therefore, the probability that at least one student has not taken a mathematics course is:

1 - 0.1074 = 0.8926

Therefore, Rounding to four decimal places, the answer is 0.8926. So the probability that at least one of the ten college students has not taken a mathematics course is approximately 0.8926.

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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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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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The value of the variable, x, obtained using the formula for the perimeter of a sector of a circle is; x = 6 cm

A sector of a circle is the region of the circle that has two radii of the circle and the arc between the two radii as the boundary of the region.

The perimeter of a sector of a circle can be obtained using the formula;

Perimeter = 2·r + (θ/360°) × (2·π·r)

The radius of sector OAD, r = 6 cm

Therefore;

The perimeter of sector OAD = 2 × 6 + (50/360) × 2 × π × 6 = 12 + 5·π/3

The perimeter of sector OBC = 2 × The perimeter of sector OAD

Therefore;

The perimeter of sector OBC = 2 × (12 + 5·π/3) = 24 + 10·π/3

Which indicates;

The perimeter of sector OBC = 2  × (6 + x) + (50/360) × 2 × π  × (6 + x)

2  × (6 + x) + (50/360) × 2 × π  × (6 + x) = (5·π·x + 30·π + 36·x + 216)/18

24 + 10·π/3 = (5·π·x + 30·π + 36·x + 216)/18

432 + 60·π = 5·π·x + 30·π + 36·x + 216

432 - 216 + 60·π - 30·π  = x·(5·π + 36)

216 + 30·π = x·(5·π + 36)

6 × (5·π + 36 ) = x·(5·π + 36)

x·(5·π + 36) = 6 × (5·π + 36 )

x = 6 × (5·π + 36 )/(5·π + 36 ) = 6

x = 6 cm

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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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The function g(t) is defined as:

g(t) = 1/√(16-t^2)

The function is continuous for all values of t that satisfy the following conditions:

The denominator is non-zero:

The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].

There are no vertical asymptotes:

The function does not have any vertical asymptotes, because the denominator is always positive.

Thus, the function g(t) is continuous on the interval [-4,4].

Answer:

Step-by-step explanation:

2

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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Answer:

graph Z , Horizontal Shift

Step-by-step explanation:

Got it right on edmentum.

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.

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.

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.

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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Answer:

A = 32

Step-by-step explanation:

A= (a+b divided by 2) mulitiplied by height

a = 6

b = 2+6+2 = 10

h = 4

a+b = 6 + 10= 16

16 divided by 2 = 8

8 x 4 = 32

Therefore, the area is 32.

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

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

~~~PicklePoppers~~~

The approximate volume of a human head is 4000 cubic centimeter.

A sphere is simply a geometrical object that is a three-dimensional analogue to a two-dimensional circle.

The circumference of a sphere is given by the formula:

C = 2πr

Where r is the radius of the sphere. In this case, we are given that the circumference of the sphere (which approximates the human head) is 60 cm, so:

60 cm = 2πr

Solve for r

r = 60/2π

r = 30/π

The volume of a sphere is given by the formula:

V = (4/3)πr³.

Substituting the value we found for r, we get:

V = (4/3) × π × ( 30/π )³

V = (4/3) × π × ( 30/π )³

V = 3647.566 cm³

V = 4000 cm³

Therefore, the volume to the nearest 1,000 cubic cm is 4000 cm³.

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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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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%.

Answer:

82

Step-by-step explanation:

Yes, the apparent under representation of Hispanics on the jury duty calls into question the fairness of the jury selection system, as the results of the hypothesis test suggest that the system may be systematically excluding Hispanics.

To determine whether the apparent underrepresentation of Hispanics on the jury selection system is statistically significant and calls into question its fairness, we need to perform a hypothesis test.

First, we set up the null hypothesis, which is the assumption that there is no difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool. That is, the proportion of Hispanics in the jury pool is expected to be equal to 19%.

The alternative hypothesis is that there is a difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool.

We can use a one-tailed z-test to test the null hypothesis, where the test statistic is calculated as:

z = (p - P) / sqrt(P(1-P)/n)

where p is the proportion of Hispanics in the jury pool, P is the proportion of Hispanics in the county population (0.19), and n is the sample size (72).

Plugging in the values, we get

z = (9/72 - 0.19) / sqrt(0.19*(1-0.19)/72) = -2.39

Assuming a significance level of 0.05, we compare the calculated z-value with the critical z-value of -1.645 (obtained from a standard normal distribution table). Since the calculated z-value is less than the critical z-value, we reject the null hypothesis and conclude that the proportion of Hispanics in the jury pool is significantly different from the proportion of Hispanics in the county population.

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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:

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

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.

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.