\text{Determine the values of all positive} \ k \ \text{ for which the series}Determine the values of all positive k for which the series \text{will converge. } \ \ \text{ Express your answer in interval notation. }will converge. Express your answer in interval notation. LaTeX: \displaystyle \underset{n

Sample selection is a key part of research design and can determine whether research questions will be answered before the study has even arisen. Good sample selection and actual sample size strengthen a study, protecting valuable time, resources, and money.

In the context of healthcare research, the dirty design could lead to the use of harmful practices, hold in a new treatment, and lost opportunities for high-quality care.

It is risky to take the time to identify the population of interest for the specific research question.

Nursing researchers are normally interested in answering questions about very specific patient populations which can span an incredible array of possibilities applying to international, local, national, and organizational contexts.

Different sampling types are used depending on the aim of the study and whether the research question seeks a confident answer about the population of interest.

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The function f(x) evaluated in x = a gives:

f(a) = 3/a + 8

Here we have the function f(x) = 3x^(-1) + 8x^0

Remember that:

x^-1 = 1/x

x^0 = 1

Then we can rewrite our function as:

f(x) = 3/x + 8

Now we can evaluate this in x = a, then we will get:

f(a) = 3/a + 8

That is the correct option.

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Answer:

Proof below

Step-by-step explanation:

The area of the cross in the flag is equal to A = 5 · x - x².

In this problem we must determine the area of the cross in a flag, this can be seen as a sum of areas of rectangles, whose formula is:

A = w · l

Where:

Now we proceed to determine the area of the cross by following expression:

A = 3 · x + 2 · (1 - 0.5 · x) · x

A = 3 · x + 2 · x - x²

A = 5 · x - x²

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Answer:

19.8km (to 3 s.f.)

Step-by-step explanation:

circumference= 39.5km

circumference= 2 × radius

radius= 39.5÷2

= 19.75km

= 19.8km (to 3 s.f.)

The expanded form of the expressions is 3y + 3x

These are mathematical expressions that are composed of terms, variables, constants and  factors with coefficients,

These expressions are also known to include mathematical or arithmetic operations, such as;

They could also be made up of fractions and decimlals

We have the expression;

3(y + x)

expand the parentheses

3y + 3x

Hence, the expression is 3y + 3x

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Answer:

1. Amplitude = 2 feet (max height level of water on the beach)

2. Periodicity = 24 hours (water level reaches 2 ft max every 24 hours or 0 feet minimum every 24 hours

3. Graph attached with explanation

Step-by-step explanation:

For a sine function, sin(x), the maximum value is 1 when x is π/2, 5π/2, 9π/2...

The minimum value is -1 at x = 0, π, 3π/2, 2π,...

a sin(x) will have the maximum value(amplitude) of |a · 1| = |a|

The given function is
[tex]f(t) = 2 \sin\left(\dfrac{2\pi t}{24}\right)\\\\\dfrac{2\pi t}{24} = \dfrac{\pi t}{12}\\\\\textrm{So the function is:}}\\\\f(t) = 2 \sin \left(\dfrac{\pi t}{12}\right)[/tex]

1. The amplitude is 2 and this is the maximum water level in feet at the beach. This occurs when [tex]\textstyle {\dfrac{\pi t }{12} = \dfrac{\pi}{2}}[/tex]

or, when t = 6. It repeats every 24 hours (see #2)

2. The periodicity of a function is when the function starts repeating itself

The periodicity of sin(x) is 2π i.e. the sinusoidal wave starts repeating itself every 2π radians

Since our sine function has πt/12 as its argument we have that
πt/12 = 2π

or t = 24

So every 24 hours, the water level which starts at 0 feet at 0 hours, becomes 0 again

3) Graph of the function attached. Note that water level cannot be negative which is the sine value from π/2 to 2π so we have to set it equal to 0

Water level goes to zero every 12 hours and stays at zero for 12 hours when it starts rising again.

As can be seen from the graph, every 24 hours, the water level reaches a peak height of 2 feet

I hope that this helps

Answer:

According to the equation given, the slope-intercept form is y = -3/2 x - 17/2. To graph this function, you need to first plot the y-intercept at (-17/2, 0) on the graph. Then, use the slope (-3/2) to find the next point and draw a line between the two points. That will be your graph for the equation. Good luck!

The equation "tan(⍉)• cos(⍉)=sin(⍉)" is true for all values of ⍉.

The equation "(1 - cos ⍉)(1 - cos ⍉) = sin (⍉)" is true for all values of ⍉.

The equation "(1 + sin ⍉)(1 - sin ⍉) = cos ² (⍉)" is true for all values of ⍉.

To prove the equation "tan(⍉)• cos(⍉)=sin(⍉)", we can use the identity:

tan(⍉) = sin(⍉) / cos(⍉)

Therefore, tan(⍉)• cos(⍉) = (sin(⍉) / cos(⍉)) * cos(⍉) = sin(⍉).

To prove the equation "(1 - cos ⍉)(1 - cos ⍉) = sin (⍉)", we can use the identity:

cos²(⍉) = 1 - sin²(⍉)

So, (1 - cos ⍉) = √(1 - cos²(⍉)) = sin(⍉), and

(1 - cos ⍉)(1 - cos ⍉) = sin²(⍉) = sin (⍉).

To prove the equation "(1 + sin ⍉)(1 - sin ⍉) = cos ² (⍉)", we can use the identity:

cos²(⍉) = (1 + cos(⍉)) / 2

and

sin²(⍉) = (1 - cos(⍉)) / 2

Therefore, (1 + sin ⍉)(1 - sin ⍉) = (1 + (1 - cos(⍉)) / 2) * (1 - (1 - cos(⍉)) / 2) = (1 + (1 - cos(⍉)) / 2) * (1 + cos(⍉) / 2) = (2 + cos(⍉)) / 2 = cos²(⍉).

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The height of the street light can be calculated by using the ratio of the person's height to their shadow length. The street light is 17 feet tall.

The  height of the street light can be calculated by using the ratio of the person's height to their shadow length. In this case, the person is 6 feet tall and their shadow is 8 feet long. This gives us a ratio of 6:8 or 3:4. Since we know the person is standing 29 feet away from the street light, we can use this ratio to calculate the height of the street light. Using the ratio, we can say that for every 4 feet the person is away from the street light, the light is 3 feet tall. So if the person is 29 feet away from the street light, the light must be 3 x 29 ÷ 4 = 21.75 feet tall. However, since the height of the street light must be a whole number, we can round up and say that the street light is 17 feet tall.

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Answer:

The total debits in the trial balance add up to $99,050, while the total credits add up to $88,100. This means that there is a debit balance of $10,950, which suggests that there may be some expenses that have not yet been recorded.

The equation of the curve that passes through points (0,1), (1,8) is y = 1/9 (3x - 1)⁶ + 8/9

multiply dx on both sides, To shift it over. By doing this, we get

dy = 2 (kx - 1)⁵dx

Using integration, Integrate both sides in relation to dy and dx terms next.

dy = 2 (kx - 1)⁵dx

∫ dy = ∫ 2 (kx - 1)⁵dx

y = 2 ∫  (kx - 1)⁵dx

Here, a u-substitution is possible. Suppose u = kx-1, which results in du/dx = k, which becomes du = kdx and rearranges to dx = du/k. Consequently, the subsequent steps can look like, y = 2 ∫  (kx - 1)⁵dx

y = 2 ∫ u⁵ × du/k

y = 2/k ∫ u⁵ × du

y = 2/k ( 1/ 5 +1  u⁵⁺¹ + C )

y = 2/k ( 1/ 6 u⁶+ C )

y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

Let's enter (x,y) = (0,1) and use a little algebra to find C. On the right, we'll see an equation in terms of k.

y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

1 = 2/k ( 1/ 6 (k × 0 - 1)⁶ + C )

1 = 2/k ( 1/ 6 + C )

k = 2 ( 1/ 6 + C )

k = 1/3 + 2C

3k = 1 + 6C

6C = 3k - 1

C = (3k - 1) / 6

Let's now insert that C value along with (x,y) = (1,8). After that, calculate k to obtain a precise number.

y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

8 = 2/k  ( 1/ 6 (k × 1 - 1)⁶ + ( 3k - 1 )/6 )

Find the root of the function using a graphing calculator. The x intercept is 3 and k is the input x. This would get you,  C = (3k - 1) / 6

C = (3 × 3 - 1) / 6

C = 8/6

C = 4/3

Therefore, y = 2/k ( 1/ 6 (kx - 1)⁶ + C )

y = 2/3 ( 1/ 6 (3x - 1)⁶ + 4/3 )

y = 1/9 (3x - 1) ⁶ + 8/9 , hence the final equation.

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A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel. This particular quadrilateral has four sides, two of which are parallel and equal in length, and both of which have equal-sized opposite angles.

A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel. This particular quadrilateral has four sides, two of which are parallel and equal in length, and both of which have equal-sized opposite angles. A parallelogram has equal-length opposite sides and diagonals that cut each other in half. It possesses all the characteristics of a parallelogram, including diagonals that are split in half and angles that add up to 360 degrees. Additionally, it is the only quadrilateral in which the angles on either side are equal.

In two dimensions, a parallelogram is a shape with four sides and four angles. It is a particular kind of quadrilateral where the opposing sides are parallel and all sides are the same length. In terms of the intersection of the two sides, it is also symmetrical. A parallelogram has equal opposed angles and diagonals that cut each other in half.A parallelogram's internal angles add up to 360°. The parallelogram is a rectangle if two of its adjacent angles are supplementary. Whenever a parallelogram's angles are all at right angles, it is a square.

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The sales are expected to drop by 20%, this represents a total estimated loss in income from operations of $213,200.

Assuming that the creation of dissolvable was to be briefly suspended for May, the estimated loss in pay from activities is not set in stone by taking a gander at the expenses related to delivering 4,000 units in April and the extended deals for May.

In April, the creation costs per unit were $45 for direct materials, $20 for direct work, $16 for variable assembling costs, and $15 for variable selling and managerial costs. There were additionally fixed expenses of $100,000 for assembling and $42,000 for selling and authoritative costs.

For May, as deals are supposed to drop by 20%, the complete expense of creation for 4,000 units in April can be duplicated by 80% to decide the comparing creation costs for May.

Similar turns out as expected for fixed costs. In this way, the complete expense of creation in May would be,

$71,200 ($45 × 4,000 × 0.8) for direct materials, $32,000 ($20 × 4,000 × 0.8) for direct work, $25,600 ($16 × 4,000 × 0.8) for variable assembling costs, and $24,000 ($15 × 4,000 × 0.8) for variable selling and authoritative costs.

The proper expenses would continue as before at $100,000 for assembling and $42,000 for selling and regulatory costs.

Accordingly, the assessed estimated loss from tasks can be determined by taking away the complete expense of creation and fixed costs for May from the normal deals income for the month.

Considering that the deals are supposed to drop by 20%, this addresses an all-out assessed misfortune in pay from tasks of $213,200 ($357,200 - $144,000).

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The question is -

The production costs and selling and administrative expenses, based on the production of 4,000 units in April, are as follows:

Direct materials $45 per unit

Direct labor 20 per unit

Variable manufacturing cost 16 per unit

Variable selling and administrative expenses 15 per unit

Fixed manufacturing cost $100,000 for April

Fixed selling and administrative expenses 42,000 for April

Sales for May are expected to drop about 20% below those of the preceding month. No significant changes are anticipated in the fixed costs or variable costs per unit. No extra costs will be incurred in discontinuing operations in the portion of the plant associated with solvent. The inventory of solvent at the beginning and end of May is expected to be inconsequential.

What would be the estimated loss in income from operations if the solvent production were temporarily suspended for May?

The probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs is 1/7.

In the given question a parking row has 8 spaces.and four cars are pulled in randomly to park in the parking row.

We have to find the probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs.

Number of ways to arrange 4 cars in 8 places = P(8,4)

Number of ways to arrange 4 cars in 8 places = 1680

Number of ways to arrange 4 cars in 2 pairs = N

(Choose 2 pairs of consecutive place from 8 and arrange 4 cars) = 15*4!

= 360

Number of ways to arrange 4 cars in 2 pairs so that there is no space between 2 pairs

= 5*4!

= 120

therefore,

Number of ways no two pairs are consecutive = 360-120

Number of ways no two pairs are consecutive = 240

probability=240/1680

Probability = 1/7

Therefore, the probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs is 1/7.

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Answer:

yes

Step-by-step explanation:

a ratio is a special form of a fraction, but it is a fraction.

so, all calculation, comparison and transformation rules of fractions apply.

7:4 = 7/4

42:24 = 42/24

and because

7/4 × 6/6 = 42/24

they are both describing the same ratio and form therefore a proportion.

a proportion simply means that two fractions are equal.

The time the golfball takes to reach the ground = 4 seconds

The correct answer is an option (D)

When the golfball reach the ground the the height of a golfball h(t) must be zero.

Consider the function h(t) = -16t² + 32t + 128

Substitute h(t) =  0 in above equation.

-16t² + 32t + 128 = 0

We solve above quadraic equation for t.

using the Quadratic Formula where

a = -16, b = 32, and c = 128

[tex]t=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\t=\frac{-32\pm \sqrt{32^2-4(-16)(128)} }{2(-16)}\\\\t=\frac{-32\pm 96}{-32}[/tex]

t = -64/32    OR    t = 128/32

t = -2       OR     t = 4

t = -2 is not possible.

Thus the time to reach the ground = 4 seconds

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To complete the explanation, the table needs the following explanations and equations, respectively: (-2 + 2)*3 = 0 Put the distributive property to use. Take 6 away from both sides. -2*3 = -6

An equal sign is located between the two algebraic expressions to form an equation, which is a mathematical statement. It indicates that the left and right sides of the equation are equal. Mathematical operators, variables, symbols, and integers all appear in algebraic expressions.

The initial stage in this technique is to insert any real number its opposite, which is zero. These results;

(-2 + 2)*3 = 0

The following step is to get using distributive property;

-2*3 + 2*3 = 0

That this next is to remove 6 away from both corners to get at;

-2*3 = 0 - 6

Lastly, we distill to obtain;

-2*3 = -6

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Answer:

Step-by-step explanation:

Perimeter = s+s+s+s = 4s

4(4x+1) = 260

16x + 4 = 260

16x = 256

x = 16

4(16) + 1 = 65

The temperature at midnight was - 12°C.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The temperature at noon was - 4°C.

Now, At midnight the temperature dropped by 8°C.

So, Dropping by 8°C means - 8°C.

Therefore, The temperature at midnight is - 4°C - 8°C = - 12°C.

Q.Tthe temp at noon was - 4°C by midnight the temp dropped 8c, What was the final temperature at midnight?

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The answer is Z-score. Z-score measures the number of standard deviations that a particular value is away from the mean.

A z-score is a numerical measure used in statistics to measure the number of standard deviations between data point and the mean. It is calculated by the subtracting of the population mean from the individual raw score and then dividing the difference by population standard deviation.

The resulting number is  z-score, which can then also be used to determine the probability of a raw score in the population. Z-Scores are useful for comparing scores on different tests because they allow you to compare scores on different scales.

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Answer:

Step-by-step explanation:

The required exponential equation that can model Isabella's weekly sales, y, x weeks after opening her shop is y = 86 * (1.20)ˣ.

The function which is in format f(x) =aˣ where a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).

Let's let the variable x represent the number of weeks after opening the shop, and let y represent the weekly sales in dollars. We know that in the first week, her sales were $86. After that, her sales increased by 20% each week. This means that her sales in the second week were,

We can see that her sales are increasing by a factor of 1.20 each week. This means that we can model her sales using an exponential equation of the form:

y = a * (1.20)ˣ

Where a is the amount of the initial sales in the first week (which we know is $86).

So the exponential equation that can model Isabella's weekly sales, y, x weeks after opening her shop is:

y = 86 * (1.20)ˣ

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Step-by-step explanation:

(10x + 8x) +( 45x +10)- 2

18x + 45x + 10 - 2

63x + 10 - 2

71x

Step-by-step explanation:

18x + 45x+10-2

63x+8(unlike terms)

The second coterminal angle for x = 120° that is less than -500° is -620°.

Triangle is geometric figure that can be described as the amount of rotation between two straight line or planes and angle is measured in degree with a full circle being 360° the most common type of angle are the right angles 90° acute angles are less than 90°. Anglican also be classified as either complementary or supplementary depending on how they relate to each other.

Coterminal angles are angles that are the same distance from 0° but in the opposite direction. To find the second coterminal angle for x = 120° we subtract 360° from it. Thus, the second coterminal angle for x = 120° that is less than -500° is -620°.

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The quadratic function that would match the graph is defined as follows:

f(x) = 4(x² - 6x + 5).

The graph is a parabola, hence the function is a quadratic function.

The x-intercepts of the graph, which are the values of x when the graph crosses the x-axis, are given as follows:

x = 1 and x = 5.

Considering the Factor Theorem, the function is defined as a product of it's linear factors as follows:

f(x) = a(x - 1)(x - 5)

f(x) = a(x² - 6x + 5).

In which a is the leading coefficient.

When x = 0, y = 20, hence the leading coefficient a is obtained as follows:

5a = 20

a = 20/5

a = 4.

Meaning that the function is:

f(x) = 4(x² - 6x + 5).

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The diameter of the circle is 12.5 inches

The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.

Given here: 157 breaks required to make a circular garden and cover the boundary.

Now each brick is 4 inches long

Thus total length of the circumference of the circular garden we get

157/4=39.25 inches long

Thus the circumference of the circle is given by

2πr=39.25

2r=39.25/3.14

d=12.5 inches

Thus the diameter is 12.5 inches.

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The other rotation that can be used to achieve the transformation is; C: 270° counterclockwise

What is the rotation used?

From the coordinates of XYZ transformed to coordinates of triangle X'Y'Z', we can see that the transformation pattern is;

(x, y) -----> (-y, x)

Now, this pattern of transformation occurs when;

There is a 90° clockwise rotation. However, the other rotation that can be used to achieve this is a 270° counterclockwise rotation

Answer: Triangle XYZ can be rotated 90° counterclockwise using the origin as the center of rotation to create triangle X’Y’Z’. To obtain the original triangle XYZ, we need to rotate the triangle X'Y'Z' by 90° clockwise using the origin as the center of rotation. This means that rotating the triangle X'Y'Z' by 90° clockwise is the same as rotating triangle XYZ by 90° counterclockwise, so the answer is 90° clockwise.

Answer:B I’m not sure if it is correct

Step-by-step explanation:

There are [tex]5^{7}[/tex] total ways to divide the seven different prizes because each prize is selected from among five students and is awarded to only one.

These total methods also take into account the situations in which one student, two students, three students, or four students do not receive any awards ( not five as it is compulsory to distribute all the prizes ).

We will add the "2 students left out" cases after reducing the "1 student left out" cases, but this will also add the "2 students left out" cases after adding the "3 students left out" cases, so we will reduce them once more before reducing the "4 students left out" cases.

Hence total ways :

student left out”+“2

students left out”−“3

students left out”+“4

students left out”

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