are these equivalent
10-2x -2x10

Answer:

27.18

Step-by-step explanation:

Firstly, you must label the triangle.

r- opposite

13.85- adjacent

We know that tan θ = opposite/ adjacent so we substitute our numbers into the equation.

tan (63) = r/13.85

Then, times 13.85 on both sides so we only have our unknown on one side.

(x13.85)  tan(63)= r/13.85   (x13.85)

r= tan (63) x 13.85

r=27.18

:)

Answer: So that means the answer is $112.5

Step-by-step explanation:Percent of Discount is 80%. Sale Price is $90. The original price,. = 90 x 100 / 80. = 9000/80. = 112.5. Therefore, $112.5 is the original price.

YES THIS IS RIGHT!!!!

Joe aura 35 pommes.

40-5=35

Answer:

B. Isosceles right triangle

C. Quadrilateral

D. Parallelogram

Step-by-step explanation:

Answer:

The geometric figures that could describe how the garden might look are B. Isosceles right triangle and C. Quadrilateral.

Therefore, the function that matches the mosquito counts is'(w) = 8([tex]1.5^{w}[/tex]).

by the question.

To determine which function matches the mosquito counts, we can plot the given data points on a graph and see which function fits the curve. Here are the counts for the first few weeks:

Week Mosquito Count

0 8

1 20

2 50

3 125

4 312

Plotting these points on a graph with weeks on the x-axis and mosquito count on the y-axis, we get:

mosquito graph

Looking at the graph, we can see that the curve increases rapidly and seems to be exponential. This rule out option A (which is linear), leaving us with options B, C, and D.

To determine which of these options matches the data, we can try plugging in the week numbers and seeing which one gives us values close to the actual counts. We can also use a calculator or graphing technology to help us with this.

Option B gives us the following mosquito counts for the first five weeks:

Week Mosquito Count

0            8

1         19.5

2        47.25

3       114.19

4       276.32

Option C   gives us:

Week Mosquito Count

0       8

1        12

2       18

3       27

4       40.5

Option D is not a function of mosquito counts with weeks as the input variable, so we can rule it out.

Comparing the values from options B and C to the actual counts, we can see that option C is the closest match.

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Answer:

143°

When solving angle problems, make sure to label the other angles (even the ones that are not asked) and use them to relate to each other to find the answer.

The weight of the package is 56 using arithmetic operations.

Mathematicians use multiplication to calculate the product of two or more integers. It is a fundamental operation in mathematics that is frequently used in everyday living. When we need to combine sets of similar sizes, we use multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are compounded are referred to as the factors. Repeated adding of the same number is made easier by multiplying the numbers.

let weight of package be= x

x*5/7=40

x=(40*7)/5

x=56

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Answer:

b ≈ 12.1

Step-by-step explanation:

using the tangent ratio in the right triangle

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{7}[/tex] ( multiply both sides by 7 )

7 × tan60° = b , then

b ≈ 12.1 ( to the nearest tenth )

Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.

The time taken by Meredith to file 70% of the 10 reports given, given that each report takes an average of 75 minutes is 6 hours, 30 minutes. Therefore, the correct option is B. 6 hours, 30 minutes. How long will it take Meredith to file 70% of 10 reports, given that each report takes an average of 75 minutes to file?

Here, the total number of reports = 10

Average time to file one report = 75 minutes

To find out the time taken to file 70% of 10 reports, we will need to multiply the average time taken to file one report by the number of reports to be filed, which is 7 in this case:

75 × 7 = 525 minutes

We have calculated the time it will take Meredith to file 7 reports. Now, to convert this time to hours and minutes, we divide the total minutes by 60 to get the hours and then find out the remainder for the minutes:

525 ÷ 60 = 8 hours 45 minutes

Therefore, Meredith will take 8 hours 45 minutes to file 70% of the 10 reports given.

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Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

Average temperature is calculated as (Monday's temperature plus Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature)/Total days.

Temporary for Monday and Tuesday plus Temperatures for Wednesday and Thursday.

The sum of the temperatures for Monday, Tuesday, Wednesday, and Thursday is equal.

As stated, the 6.5 degree average for the days of Tuesday, Wednesday, Thursday, and Friday.

using the formula no.

Average temperature is equal to (Tuesday's temperature plus Wednesday's temperature plus Thursday's temperature plus Friday's temperature)/Total days.

Thus, Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature.

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the complete question is

Write a positive or negative number to represent each change in the high temperature.

1. Tuesday’s high temperature was 4 degrees less than Monday’s high temperature. ?

2. Wednesday’s high temperature was 3.5 degrees less than Tuesday’s high temperature. ?

3. Thursday’s high temperature was 6.5 degrees more than Wednesday’s high temperature. ?

4. Friday’s high temperature was 2 degrees less than Thursday’s high temperature. ?

The probability that a randomly selected component is shorter than 7 inches long is approximately 25.14%.

We are given that the lengths of components produced by the automatic press are normally distributed with a mean of 8 inches and a standard deviation of 1.5 inches.

We need to find the probability that a randomly selected component is shorter than 7 inches long.

We can use the standard normal distribution to find this probability. We first need to convert the length of 7 inches to a z-score:

z = (7 - 8) / 1.5 = -0.67

Using a standard normal distribution table or calculator, we can find the area to the left of this z-score, which represents the probability that a randomly selected component is shorter than 7 inches long:

P(z < -0.67) = 0.2514

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Answer:

The given equation is in vertex form y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. Comparing the given equation with the vertex form, we have a = -3, h = -3 and k = 4.

Since a = -3 < 0, the parabola opens downwards and has a maximum point.

To find the maximum value of y, we need to evaluate y at the x-coordinate of the vertex:

x = -3

y = -3(-3+3)^2 + 4 = 4

Therefore, the parabola y = -3(x+3)2 + 4 contains a maximum point and the maximum value of y is 4.

Hence, the answer is option C

Answer:

C)  Maximum point; 4

Step-by-step explanation:

Given parabola:

[tex]y=-3(x+3)^2+4[/tex]

The given parabola is in vertex form:

[tex]\boxed{y = a(x - h)^2 + k}[/tex]

where:

By comparing the given equation with the vertex form, we can see that:

As a < 0, the parabola opens downwards. Therefore, the vertex of the parabola is a maximum point.

The vertex of the parabola is (h, k) = (-3, 4).

Therefore, the maximum value of y is 4, which occurs at x = -3.

Answer:

Step-by-step explanation:

Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:

999n = 727272

To solve for "n", we divide both sides by 999:

n = 727272/999

Using a calculator or long division, we get:

n ≈ 728.56

Therefore, each pizza has approximately 728 slices.

Answer:

Step-by-step explanation: In the problem, they tell us that

dL / dt = 7 cm/s (the rate at which the length is changing) and

dw / dt = 8 cm/s (the rate at which the width is changing)

Want dA/dt (the rate at which the area is changing) when L = 7 cm and w = 5 cm

The equation for the area of a rectangle is:

A = L·w, so will need the product rule when taking the derivative.

dA/dt = L (dw/dt) + w (dL/dt)

Now just plug in all of the given numbers:

dA/dt = (7)(7) + (5)(8) = 49+40 = 89  cm²/s

Given that a 0.625 kg basketball is dropped from a height of 3 meters straight down. The coefficient of restitution between the ball and the ground is e = 0.87. At 0.15 seconds after the basketball is dropped, a 58.5-gram tennis ball is dropped from the same 3-meter height straight onto the basketball. If the coefficient of restitution between the tennis ball and the basketball is e = 0.9,

    determine how high the tennis ball bounces above the ground after the collision. Neglect the size of the balls.

The balls meet at a height of 0.5073 m above the ground. Hence the height that the tennis ball bounces above the ground is to be calculated.

Given that the coefficient of restitution between the ball and the ground is e = 0.87The coefficient of restitution between the tennis ball and the basketball is e = 0.9

The coefficient of restitution(e) is defined as the ratio of the relative velocity of separation and relative velocity of approach between two objects.

When a ball falls from height, it gains potential energy.

Potential energy (PE) = mghWhere, m = mass of the object, g = acceleration due to gravity, h = height

PE of Basketball = mgh= 0.625 kg * 9.81 m/s² * 3 m= 18.4 Joules

Initial kinetic energy (KE) = PE of Basketball

KE of Basketball = 18.4 J

Let the velocity of the basketball before collision be u1 and the velocity of the tennis ball before collision be u2. After the collision, let the velocity of the basketball be v1 and the velocity of the tennis ball be v2.

Using the coefficient of restitution (e) we can find the velocity of the balls after collision

   v1 - v2 = -e(u1 - u2)

Initial momentum (P) = Final momentum (P)

before the collision  P = m1u1 + m2u2

after collision  P = m1v1 + m2v2P = (0.625 kg * u1) + (0.0585 kg * u2)P

                           = (0.625 kg * v1) + (0.0585 kg * v2)

        Using the above two equations and the given coefficients of restitution, we can find the velocity of the balls after collisionv1 = (m1u1 + m2u2 + e * m2 * (u2 - u1)) / (m1 + m2)v2 = (m1u1 + m2u2 + e * m1 * (u1 - u2)) / (m1 + m2)

     Here, m1 = mass of basketball

                     = 0.625 kg,

                m2 = mass of tennis ball

                      = 0.0585 kg,

  u1 = 0, u2 = 0P = m1v1 + m2v2 => v1 + v2 = P / (m1 + m2)

Also given that the time taken by the balls to meet is 0.15 seconds

Let h be the height to which the tennis ball bounces after the collision.

When the tennis ball bounces to height h, it gains potential energy.

KE + PE = Total energy

             = Constant Using the principle of conservation of energy we can find the height to which the tennis ball bounces after collision(1/2) * m2 * v2² + (1/2) * m2 * g * h

              = (1/2) * m2 * u2² + (1/2) * m2 * g * 0(1/2) * m2 * v2²

              = (1/2) * m2 * u2² - (1/2) * m2 * g * h(1/2) * v2²

              = (1/2) * u2² - g * h

Substituting the values of u1, u2, m1, m2, e, t and g, we get:

v1 = (0 + 0.0585 kg * 9.81 m/s² + 0.9 * 0.0585 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v1

   = 1.96 m/sv2

    = (0.625 kg * 0 + 0 + 0.9 * 0.625 kg * (0 - 0)) / (0.625 kg + 0.0585 kg)v2

    = 5.5 m/s

Here, u1 = u2 = 0.

Using the above equation, we can find the height to which the tennis ball bounces after collision (1/2) * (0.0585 kg) * (5.5 m/s)² = (1/2) * (0.0585 kg) * (0 m/s)² - (0.0585 kg) * 9.81 m/s² * h12.83 J

                = -0.286 J - 0.572 h0.572 h

                = -12.83 J / 2h

                = -12.83 J / (2 * 0.572)

                = 11.2 m

Hence the height to which the tennis ball bounces above the ground after the collision is 11.2 m.

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The given family of functions is y = c1ex + c2e−x which is the general solution of the differential equation y'' − y = 0 on the indicated interval which is (−∞, ∞).

       Now, we are required to find a member of the family that is a solution to the initial-value problem which is

                             y(0) = 0 and y′(0) = 5.

     The differential equation is y'' − y = 0

      The characteristic equation is r2 − 1 = 0r2 = 1r1 = 1 and r2 = −1

     The general solution of the differential equation is y = c1ex + c2e−x

      Let us solve for the constants by using the given initial conditions:

                    At x = 0,y(0) = c1e0 + c2e0 = 0 + 0 = 0y(0) = 0

                    means c1 + c2 = 0or c1 = -c2At x = 0, y′(0) = c1ex |x=0 + c2e−x |x=0(d/dx)(c1ex + c2e−x) |x=0y′(0) = c1 - c2 = 5c1 - c2 = 5c1 - (-c1) = 5c1 + c1 = 5c1 = 5/2c1 = 5/2

                    Let's replace c1 = 5/2 in c1 = -c2, c2 = -5/2

                The solution of the initial-value problem y = (5/2)ex − (5/2)e−x is a member of the family y = c1ex + c2e−x that is a solution of the initial-value problem y(0) = 0 and y′(0) = 5.

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Answer: View answer in explanation below.

Step-by-step explanation: Let's use variables to represent the unknown quantities.

Let x be the number of $5 clearance mystery books purchased.

Let y be the number of $12 regular-priced science fiction books purchased.

We can set up a system of equations based on the given information:

5x + 12y = 126 (total amount spent)

x + y = total number of books purchased

We need to solve for x and y.

Let's use the second equation to solve for one variable in terms of the other:

y = total number of books purchased - x

Now we can substitute this expression for y into the first equation:

5x + 12(total number of books purchased - x) = 126

Simplifying and solving for x:

5x + 12total number of books purchased - 12x = 126

-7x + 12total number of books purchased = 126

-7x = -12total number of books purchased + 126

x = (12total number of books purchased - 126)/7

Since x must be a whole number (you can't buy a fraction of a book), we need to find a value of total number of books purchased that makes x a whole number. We can start by trying different values of total number of books purchased:

If total number of books purchased is 10:

x = (12(10) - 126)/7 = -6/7 (not a whole number)

If total number of books purchased is 11:

x = (12(11) - 126)/7 = 6/7 (not a whole number)

If total number of books purchased is 12:

x = (12(12) - 126)/7 = 6/7 (not a whole number)

If total number of books purchased is 13:

x = (12(13) - 126)/7 = 12/7 (not a whole number)

If total number of books purchased is 14:

x = (12(14) - 126)/7 = 18/7 (not a whole number)

If total number of books purchased is 15:

x = (12(15) - 126)/7 = 24/7 (not a whole number)

If total number of books purchased is 16:

x = (12(16) - 126)/7 = 30/7 (not a whole number)

If total number of books purchased is 17:

x = (12(17) - 126)/7 = 36/7 (not a whole number)

If total number of books purchased is 18:

x = (12(18) - 126)/7 = 42/7 = 6 (a whole number)

So, you bought 6 $5 clearance mystery books and 12 - 6 = 6 $12 regular-priced science fiction books.

If the cost price of 20 articles is the same as selling price of 16 articles, then the gain percentage is 25%

To find the gain percent, we first need to calculate the profit earned on the sale of the 16 articles.

Let the cost price of each article be "C" and the selling price of each article be "S".

Given that the cost price of 20 articles is the same as the selling price of 16 articles, we can write:

20C = 16S

We can simplify this equation to:

S = (20/16)C = (5/4)C

Now, let's calculate the profit earned on the sale of 16 articles:

Profit = Total Selling Price - Total Cost Price

Profit = 16S - 20C

Profit = 16(5/4)C - 20C

Profit = 5C/2

The profit earned is 5C/2. The profit percent can be calculated as:

Profit Percent = (Profit / Cost Price) x 100

Profit Percent = (5C/2) / (20C) x 100

Profit Percent = 25%

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The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].

Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.

Using the appropriate notation, the hypotheses can be expressed as:

$H_0: p = 0.08$

$H_a: p < 0.08$

Therefore, the appropriate set of hypotheses for the mayor's significance test are:

[tex]$$H_0: p = 0.08$$[/tex]

[tex]$$H_a: p < 0.08$$[/tex]

Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate

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An appropriate theorem to show that the given set, W, is a vector space. A specific example can be

[tex]\left[\begin{array}{ccc}p\\q\\r\end{array}\right][/tex] , -p- -3q = s  and 3p = -2s - 3r

Sets represent values ​​that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.

The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.

The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.

The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.

Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is

S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties

u +v =y+ u and (u + v)+w=u + (v +W).

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Answer:

B

Step-by-step explanation

Maria's capital gain is 55.21%. Rounded to the nearest tenth of a percent, this is 55.2%.

To determine Maria's capital gain as a percent, we need to calculate the difference between the selling price and the purchase price, and then express this difference as a percentage of the purchase price.

The purchase price for 1,000 shares of stock was:

$35.50 x 1,000 = $35,500

The selling price for 1,000 shares of stock was:

$55.10 x 1,000 = $55,100

The capital gain is the difference between the selling price and the purchase price:

$55,100 - $35,500 = $19,600

To express this gain as a percentage of the purchase price, we divide the capital gain by the purchase price and multiply by 100:

($19,600 / $35,500) x 100 = 55.21%

In summary, to calculate the percent capital gain from the purchase and selling price of a stock, we simply divide the difference between the two prices by the purchase price and multiply by 100.

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16. The equatiοn οf the line in slοpe-intercept fοrm that passes thrοugh the pοint (-6, 5) and is parallel tο x + 2y = 14 is y = (-1/2)x + 2.

The equatiοn οf a straight line is y = mx + c, y = m x + c m is the gradient and c is the height at which the line crοsses the y -axis, alsο knοwn as the y -intercept.

16. Tο write the equatiοn οf a line in slοpe-intercept fοrm, we need tο find the slοpe and the y-intercept οf the line.

Tο find the slοpe οf the line, we can rewrite the equatiοn x + 2y = 14 in slοpe-intercept fοrm y = mx + b by sοlving fοr y:

x + 2y = 14

2y = -x + 14

y = (-1/2)x + 7

The slοpe οf the line is -1/2.

Since the line we want tο find is parallel tο this line, it will have the same slοpe οf -1/2.

Nοw we can use the pοint-slοpe fοrm οf the equatiοn οf a line tο find the equatiοn οf the line that passes thrοugh the pοint (-6, 5) with a slοpe οf -1/2:

y - y1 = m(x - x1)

where (x1, y1) is the pοint (-6, 5), and m is the slοpe, -1/2.

y - 5 = (-1/2)(x - (-6))

y - 5 = (-1/2)x - 3

y = (-1/2)x + 2

17. The equation perpendicular to y = -(2/3)x + 4, passing through (-4, 6)

perpendicular equations slope would be negative reciprocal to the current line.

The slope in y = -(2/3)x + 4, is m = -(2/3),

The negative reciprocal of -(2/3) is 3/2

Now, applying the x and y values in pοint-slοpe fοrm

y - 6 = 3/2(x - (-4))

y =  3/2(x+4) + 6

y =  (3/2)x + 6 + 6

y =  (3/2)x + 12

18. Since the line we want tο find is parallel tο this line, it will have the same slοpe.

Lets find the slope using slope formula

[tex]\rm m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]\rm m = \dfrac{0 - (-1)}{2 - (-1)}[/tex]

[tex]\rm m = \dfrac{1}{3}[/tex]

Now, using the point slope form

y - 1 = 1/3(x - 3)

y = 1/3(x - 3) + 1

y = (1/3)x - 1 + 1

y = (1/3)x

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Answer:

you need to show the numbers

Step-by-step explanation:

Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.

Given:

Let’s consider the probability of Deshawn not doing basketball after school:Probability of Deshawn not doing basketball after school = 100% - Probability of Deshawn doing basketball after school= 100% - 20% = 80%

Similarly, let’s consider the probability of Deshawn not talking to friends after school: Probability of Deshawn not talking to friends after school = 100% - Probability of Deshawn talking to friends after school= 100% - 45% = 55% Probability of Deshawn doing neither basketball nor talking to friends after school:Probability of Deshawn not doing basketball after school * Probability of Deshawn not talking to friends after school= 80% * 55% = 44%

The probability of Deshawn doing either basketball or talking to friends after school is 65%, and the probability of Deshawn doing neither basketball nor talking to friends after school is 44%, which is greater than 35% which is Dans mistake. Hence, Dan’s mistake is that he said the probability of Deshawn not doing basketball or not talking to friends after school is 35% which is not true.

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The complete table for the amount balance, A when P dollars is invested at rate r for t years and compounded n times per year is present in above figure 2.

The compound interest formula is written as A = P( 1 + r/n)ⁿᵗ

where, A--> total Amount of money after t years

P --> Principal

r --> Annual rate of interest (as a decimal)

t --> Number of years:

n--> number of times interest is compounded per year

Here, principle, P = $1300, rate of interest, r = 8.5% = 0.085 , time periods, t = 11 years. We have to complete the above table for compound interest.

Case 1: n = 1

Substitute the known values in above formula, A = 1300( 1 + 0.085/1)¹¹

= 1300( 1.085)¹¹

= 3,189.12

Case 2: n = 2

A = 1300( 1 + 0.085/2)²²

= 1300( 2.085/2)²²

= 1300( 1.0425)²²

= 3,248.01

I'll let you work out the cases where n = 4, 12 and 365 since all you need to do is place those in for n as done in the 1st 2 cases. For the Compounded continuously case, the formula becomes,

[tex] A = Pe^{rt}[/tex]

Where: A-> Total amount of money after t years

P --> Principal Amount

e --> Natural log constant:

r = Annual rate of interest (as a decimal)

Case: Continuous: e = 2.71828 (approx), r = 0.085

A = 1300( 2.71828)⁰·⁰⁸⁵⁽¹¹⁾

= 1300(e)⁰·⁹³⁵ = 3,311.34

Hence, required value is $3,311.3775.

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Complete question :

The above table completes the question.

Complete the table by finding the balance A when P dollars is invested at rate r for t years and compounded n times per year. (Round your answers to the nearest cent. ) P = $1300, r = 8. 5%, t

= 11 years

The sampling approach that was used in the statement "Kane randomly sampled 250 nurses from urban areas and 250 from rural areas from a list of licensed nurses in Wisconsin to study their attitudes toward evidence-based practice" is Stratified random sampling.

Stratified random sampling is a method of sampling that is based on dividing the population into subgroups called strata. Stratified random sampling is a statistical sampling method that involves the division of the population into subgroups or strata, and a sample is then drawn from each stratum in proportion to the size of the stratum. It's a sampling method that ensures the representation of all population strata in the sample, making it more effective than simple random sampling.

Stratified random sampling is used when there are variations in the population that are likely to influence the outcome of the study. The stratified random sampling method is used to ensure that these differences are reflected in the sample. In this way, the results of the study are more representative of the entire population than they would be if a simple random sample were used.

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Answer:

x/8 + 6 = 4

Step-by-step explanation:

x / 8 + 6 = 4

x/8 = -2

x = 8*-2 = -16.

Answer:

Step-by-step explanation: