lincoln high wants to estimate the number of seniors who plan to go to a 4-year college. answer the following.

When these conditions are met, you can use the dependent samples t-test to compare the mean of the difference between the two populations.

Paired samples

Random sampling.

Normal distribution

Independence of pairs.

To use the dependent samples t-test for the mean of the difference of two populations, the following conditions are necessary:
Paired samples:

The data must consist of pairs of observations (e.g., pre- and post-test scores) that are related or dependent on each other.
Random sampling:

The paired samples must be randomly selected from the populations.
Normal distribution:

The distribution of the differences between the paired samples should be approximately normally distributed.

This condition can be evaluated using a normality test, such as the Shapiro-Wilk test, or by visually inspecting a histogram or Q-Q plot of the differences.
Interval or ratio data:

The data should be measured on an interval or ratio scale (e.g., weight, height, test scores), rather than on an ordinal or nominal scale.
Independence of pairs:

The differences within each pair of observations should be independent of the differences in other pairs.

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If these conditions are met, then the dependent samples t-test can be used to test the null hypothesis that the mean difference between the two populations is zero.

The dependent samples t-test is used to compare the means of two related or dependent populations, where the samples are paired or matched. In order to use the dependent samples t-test for the mean of the difference of two populations, the following conditions should be met:

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The prove of given limit lim θ → 0 ( sin θ / θ ) = 1 is shown in below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

⇒ lim θ → 0 ( sin θ / θ ) = 1

Here, The form of given limit is 0/0, so we can apply the L - Hospital Rule.

⇒ lim θ → 0 ( sin θ / θ ) = 1

Take LHS;

⇒ lim θ → 0 ( d/dθ (sin θ)/ dθ/dθ )

⇒ lim θ → 0 ( cos θ / 1 )

⇒ ( cos 0 )

⇒ 1

⇒ RHS

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Answer:

Srry but no loser

Step-by-step explanation:

Answer:

18 x 3 √ 7

Step-by-step explanation:

I think is D

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The Rational Roots Theorem identifies possible rational roots of a polynomial equation in terms of factors of its coefficients.

The Rational Roots Hypothesis, otherwise called the Judicious Zeros Hypothesis, is a numerical hypothesis that assists with recognizing conceivable objective foundations of a polynomial condition. In particular, that's what it expresses on the off chance that a polynomial condition with number coefficients has a sane root, that root should be of the structure p/q, where p is a variable of the consistent term and q is an element of the main coefficient.

For instance, in the event that a polynomial condition has the structure ax^3 + bx^2 + cx + d = 0, and the main coefficient an and the consistent term d are numbers, then, at that point, the conceivable sane foundations of the situation are the quantities of the structure p/q, where p is a component of d and q is a variable of a.

The Normal Roots Hypothesis is valuable in tackling polynomial conditions and deciding if they have reasonable roots.

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The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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To get the decimal expansion of

We need to divide both numbers:

This is a periodic number. As we can see, the period is 12 after the decimal point, and it will repeat to the infinity:

We can represent it as:

or

The decimal expression for 4/33 is 0.121

The method for converting a fraction into a decimal expression can be done by dividing 4 by 33

First step would be dividing the 4 into 33 parts

As we know that 4 cannot be divided into 33 parts , hence we have to take an extra zero while dividing them, and while putting an extra zero in front of 4 we have to put a decimal sign.

4/33 = 4÷33

4÷33 = 0.121

now we have to put an extra zero in front of 4 in order to make it divisible by 33

Hence after calculation, we will get the answer nearest to 3 decimal places as 0.121

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The required equation of the line is represented by x + 2y = 10 in standard form.

A linear equation is written in the standard form as Ax + By = C, where A, B, and C are integers and x and y are variables.

The equation is given in the question

⇒ y = 5 - 1/2 x

We have to determine the standard form of the given linear equation

⇒ y = 5 - 1/2 x

⇒ 1/2 x + y = 5

Multiply by 2 into both sides of the above equation,

⇒ 2(1/2 x + y) = 2(5)

⇒ x + 2y = 10

Therefore, the required equation of the line is represented by x + 2y = 10 in standard form.

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the odds must be for outcomes less than or equal to 11

the possible combinations of rolling two dice are 36

the chances of getting more than 11 are only two 6 with one die 6 with another and vice versa

then we only have to remove two possibilities

there are 34 chances of getting no more than 11

and the probability is

and the percentage is

The required slopes are:

(a) slope = 4

(b) slope = 6/7

(c) slope =  -3

(d) slope = 4

(e) slope = -5/2

We know that,

When a line passing through (x₁, y₁) and (x₂, y₂)

Then  the slope of the line be,

slope (m) = (y₂ - y₁) / (x₂ - x₁)

Using this formula, calculate the slope for each given points

a. (9, 10) and (7, 2)

⇒ slope (m) = (2 - 10) / (7 - 9)

                    = -8/-2 = 4

So, the slope is 4.

b. (-8, -11) and (-1, -5)

⇒ slope (m) = (-5 - (-11)) / (-1 - (-8))

                    = 6/7

So, the slope is 6/7.

c. (5, -6) and (2, 3)

⇒ slope (m) = (3 - (-6)) / (2 - 5)

                    = 9/-3

                    = -3

So, the slope is -3.

d. (6, 3) and (5, -1)

⇒ slope (m) = (-1 - 3) / (5 - 6)

                    = -4/-1

                    = 4

So, the slope is 4.

e. (4, 7) and (6, 2)

⇒ slope (m) = (2 - 7) / (6 - 4)

                    = -5/2

So, the slope is -5/2.

Therefore, the slope of the line that joins (-8, -11) and (-1, -5) is 6/7.

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A histogram is a univariate display of quantitative data that organizes data into bins and shows the frequency of observations within each bin.


A histogram is a graphical representation that displays the distribution of quantitative data. It consists of a series of contiguous bars, where each bar represents a specific range or bin of values, and the height of the bar corresponds to the frequency or count of observations falling within that range.

Histograms are commonly used to visualize the shape, central tendency, and spread of a dataset. By examining the heights of the bars, one can determine the frequency of values within each bin and identify patterns such as peaks or clusters. This makes histograms an effective tool for exploring the distribution and characteristics of a single variable in a dataset.

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Answer:

I think u old number is 7 it is my luck number

The homogeneous solution is: y_h = c1e^(2x) + c2e^(3x), the particular solution is: y_p = (-1/10)e^(-2x) + (1/8)sin(2x) - (3/40)cos(2x) and The characteristic equation is: r^2 + 2r + 4 = 0

To find the general solutions of the given differential equations using the D-operator method, we can first find the homogeneous solution and then the particular solution.
The general solution is the sum of the homogeneous and particular solutions.

(D^2 - 5D + 6)y = e^(-2x) + sin(2x)

First, let's find the homogeneous solution by solving the associated homogeneous equation:

(D^2 - 5D + 6)y = 0

The characteristic equation is:

r^2 - 5r + 6 = 0

Factoring the characteristic equation, we get:

(r - 2)(r - 3) = 0

This gives us two distinct roots:

r = 2 and

r = 3.

Therefore, the homogeneous solution is:

y_h = c1e^(2x) + c2e^(3x)

Next, let's find the particular solution. We assume a particular solution of the form:

y_p = Ae^(-2x) + Bsin(2x) + Ccos(2x)

Taking the derivatives of y_p, we have:

y'_p = -2Ae^(-2x) + 2Bcos(2x) - 2Csin(2x)

y''_p = 4Ae^(-2x) - 4Bsin(2x) - 4Ccos(2x)

Plugging these derivatives into the differential equation, we get:

(4A - 4Bsin(2x) - 4Ccos(2x)) - 5(-2Ae^(-2x) + 2Bcos(2x) - 2Csin(2x)) + 6(Ae^(-2x) + Bsin(2x) + Ccos(2x)) = e^(-2x) + sin(2x)

Simplifying and matching like terms, we get:

(-2A + 2B - 2C)e^(-2x) + (8A + 4B - 4C)cos(2x) + (8C + 2B + 4A)sin(2x) = e^(-2x) + sin(2x)

To solve this system of equations, we equate the coefficients of each term:

-2A + 2B - 2C = 1

8A + 4B - 4C = 0

8C + 2B + 4A = 1

Solving this system of equations, we find:

A = -1/10

B = 1/8

C = -3/40

Therefore, the particular solution is:

y_p = (-1/10)e^(-2x) + (1/8)sin(2x) - (3/40)cos(2x)

Finally, the general solution is the sum of the homogeneous and particular solutions:

y = y_h + y_p

y = c1e^(2x) + c2e^(3x) - (1/10)e^(-2x) + (1/8)sin(2x) - (3/40)cos(2x)

(D^2 + 2D + 4)y = e^(2x)sin(2x)

Similarly, let's find the homogeneous solution first:

(D^2 + 2D + 4)y = 0

The characteristic equation is:

r^2 + 2r + 4 = 0

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The graph of the parametric equations x = -2cos(t) and y = -sin(t) within the range 0 ≤ t < 2π is an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis.

To sketch the graph of the parametric equations x = -2cos(t) and y = -sin(t), where 0 ≤ t < 2π, we need to plot the coordinates (x, y) for each value of t within the given range.

1. Start by choosing values of t within the given range, such as t = 0, π/4, π/2, π, 3π/4, and 2π.

2. Substitute each value of t into the equations to find the corresponding values of x and y. For example, when t = 0, x = -2cos(0) = -2 and y = -sin(0) = 0.

3. Plot the obtained coordinates (x, y) on a graph, using a coordinate system with the x-axis and y-axis. Repeat this step for each value of t.

4. Connect the plotted points with a smooth curve to obtain the graph of the parametric equations.

The graph will be an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis. It will have a vertical compression and a horizontal stretch due to the coefficients -2 and -1 in the equations.

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Answer: 4,280

Step-by-step explanation:

Hi

Answer:

After the first translation, the coordinates of the vertices of the triangle will be X (3,-13), Y (0,-8), Z (-7, 1). After the second translation, the coordinates of the vertices will be X (5,-7), Y (2,-2), Z (-5, 7).

The final translation rule that maps the pre-image to the final image is a translation of 2 units right and 6 units up. This can be written as a translation rule of the form (x, y) -> (x + 2, y + 6).

Step-by-step explanation:

After the first translation the coordinates are:

After the second translation the coordinates are:

The final translation rule is:

or

Step-by-step explanation:

Since it's a right triangle, you can use Pythagoras

a^2 + b^2 = c^2

We have b and c, we just need a, so let's plug it in

\( {x}^{2} + {24}^{2} = {25}^{2} \)

\( {x}^{2} + 576 = 625\)

\( {x}^{2} = 49\)

\(x = 7\)

Answer: 7ft

Step-by-step explanation:

hypotenuse (h) = 25

perpendicular (p) = 24

base (b) = ?

We know by using Pythagoras theorem

b = √h² - p²

= √ 25² - 24²

= √ 49

= 7 ft

Therefore , the solution to this problem is confidence interval 95% is given by Z =1.96.

In frequentist statistics, a confidence interval is the range of estimates for an unknown quantity. 95% is the most frequent confidence level used when calculating confidence intervals, however 90% and 99% are also occasionally used.

a)85 out of 100 paid at the pump using credit card

Thus,

p = proportion of customers who paid at the pump using credit card

  = 85/100

  = 0.850

Estimated Value of the population proportion = 0.850

b)

Given:

p' = 0.85           ....... Sample Proportion

n = 100           ....... Sample Size

For 95% Confidence interval

α = 0.05,      α/2 = 0.025

From z tables of Excel function

Z = \(\frac{p'-p}{\sqrt{p(1-p)/n} }\)

we find the z value

z = (0.025) = 1.96

We take the positive value of z

Therefore , the solution to this problem is confidence interval 95% is given by Z =1.96.

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Answer:

21a-14b

15b-20a

Step-by-step explanation:

Answer: a + 3b

Step-by-step explanation:

Okay, so...

7(3a - 2b) = 7(3a) - 7(2b) ... distributive property

21a - 14b

5(3b - 4a) = 5(3b) - 5(4a) ... distributive property

15b - 20a

(21a - 14b) + (15b - 20a) = 21a -12b + 15b - 20a =

a + 3b

Answer:

x int is where the line crosses the x axis. direct variation is proportional, straight line that goes through the origin. slope is the rate of change. y int is where the line crosses the y axis

For the 32" TV: height = 16", width = 28".

• For the second TV: height = 15", width = 61".

• For the 60" TV: height = 30", width = 52".

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Now let's determine the missing measurements for each TV:

1. For the 32" TV, we have the height as 16". To find the width, we need to use the Pythagorean theorem. Let's denote the width as 'w'. The theorem gives us the equation: 16^2 + w^2 = 32^2. Solving this equation, we find that the width is 28".

2. For the second TV with unknown height and a width of 61", we can use the Pythagorean theorem again. Denoting the height as 'h', we have the equation: h^2 + 61^2 = 34^2. Solving for 'h', we find that the height is 15".

3. For the 60" TV with a height of 30" and an unknown width, we can apply the Pythagorean theorem. Denoting the width as 'w', we have the equation: 30^2 + w^2 = 60^2. Solving for 'w', we find that the width is 52".

In summary:

• For the 32" TV: height = 16", width = 28".

• For the second TV: height = 15", width = 61".

• For the 60" TV: height = 30", width = 52".

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Farmer Ed has 3,000 meters of fencing and wants to enclose a rectangular plot that borders on a river.The largest area that can be enclosed is 750,000 square meters.

To get the largest area that can be enclosed, we have to find the dimensions of the rectangular plot. Let's assume that the width of the rectangle is x meters.The length of the rectangle can be found by subtracting the width from the total length of fencing available:L = 3000 - x. The area of the rectangle can be found by multiplying the length and width:Area = L × W = (3000 - x) × x = 3000x - x²To find the maximum value of the area, we can differentiate the area equation with respect to x and set it equal to zero.

Then we can solve for x: dA/dx = 3000 - 2x = 0x = 1500. This means that the width of the rectangle is 1500 meters and the length is 3000 - 1500 = 1500 meters.The area of the rectangle is therefore: Area = L × W = (3000 - 1500) × 1500 = 750,000 square meters. So the largest area that can be enclosed is 750,000 square meters.

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A pie chart is commonly used to compare relative parts of a whole. It is a circular chart that is divided into sectors, where each sector represents a proportionate part of the whole.

The size of each sector is proportional to the value it represents, and the whole circle represents the total value. Pie charts are frequently used in business, finance, and statistics to show the relative sizes of different categories or data points. They are easy to understand and can quickly convey complex information in a simple visual format. However, it's important to note that pie charts are not always the most effective way to display data and should be used appropriately depending on the type of data being presented.

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The image is located 6.7 cm behind the lens, and is 3.7 cm tall (1.34 times the height of the object).

Using the thin lens equation, we can find the position of the image formed by the lens:

1/f = 1/d0 + 1/di

where f is the focal length of the lens, d0 is the object distance (the distance between the object and the lens), and di is the image distance (the distance between the lens and the image).

Substituting the given values, we get:

1/20 = 1/5 + 1/di

Solving for di, we get:

di = 6.7 cm

This tells us that the image is formed 6.7 cm behind the lens.

To find the height of the image, we can use the magnification equation:

m = -di/d0

where m is the magnification (negative for an inverted image).

Substituting the given values, we get:

m = -(6.7 cm)/(5.0 cm) = -1.34

This tells us that the image is 1.34 times the size of the object, and is inverted.

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The negative sign indicates an inverted image. Thus, the image formed is located 8.0 cm from the lens and has a height of 1.6 times that of the object, making it 4.48 cm in height.

In this scenario, an object with a height of 2.8 cm is positioned 5.0 cm in front of a converging lens with a focal length of 20 cm. To determine the location and size of the image formed by the lens, we can use the lens formula and magnification formula.

The lens formula states that 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. Substituting the given values into the lens formula, we find:

1/20 = 1/v - 1/(-5.0)

Simplifying this equation yields:

1/v = 1/20 + 1/5.0

Solving for v, we obtain:

v = 8.0 cm

The positive value indicates that the image is formed on the opposite side of the lens. The magnification formula, M = -v/u, allows us to calculate the magnification of the image:

M = -8.0/-5.0 = 1.6

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Answer:

The area of Marlien's living room is 420 square ft

Step-by-step explanation:

Before calculating the real dimensions of Marlien's living room, we must find the value of x.

Given the total shape of the house is a rectangle, then both widths must be equal and both lengths must be equal.

The widths are already written width identical expressions x-2+x, but the lengths are given as different functions of x. Equating both expressions, we have:

\(2x-10+x-2+\frac{1}{2}x-4+x-2=2x+2+\frac{1}{2}x-4+x-2\)

Simplifying:

-10 + x - 2 = 2

x = 10 + 2 + 2

x = 14

Since x=14 feet, the dimensions of Marlien's living room are

width=x=14 feet

length=2x+2=30 feet

Thus the area is:

A = 14*30 = 420 square ft

The area of Marlien's living room is 420 square ft

The unit that is most appropriate for the time at which the number of weeks is 120 is given as follows:

Week.

The general format for an exponential function is given as follows:

\(y = a(b)^{\frac{x}{n}}\)

The parameters for the exponential function are defined as follows:

The number of weeds in my yard doubles every 3 weeks, and the initial number of weeks is of 80, hence the values of the parameters are given as follows:

a = 80, b = 2, n = 3.

As n = 3, we have that the unit of the output variable is of weeks, hence weeks is the appropriate measure in this problem.

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Answer:

Step-by-step explanation:

Calculator Use

A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Answer:

A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

A) The derivative of function k(x), i.e.,  k'(x) is equals to \(\frac{(-60x^{2} + 114x + 16)}{(-3x^{2} -4x + 3)^{2} }\)

B) The values of x where the tangent line of the function f(x)=15x−16x is parallel to the line y= 19x−2 are x= 2, -2.

C) The derivative of function h(x), i.e., h'(x) is equals to the\(\frac{ [(sin(x)(4x^{2} +2x-3) - (8x + 2)(-cos(x))]}{(4x^{2} +2x-3)^{2} .}\)

D) The value of \(\frac{d^{64} }{dx^{64} } (-7sinx)\) is -7sin(x) .

We have, k(x) = f(x)g(x)/h(x) and if f(x)

= −3x + 4,g(x) = -x + 4, and h(x)= −3x² −4x + 3, so, rewrite the function, k(x) =\(\frac{ (-3x + 4)(-x+ 4)}{(-3x^{2} -4x + 3)}\)

A) derivative of function, k(x)  : using the division rule of differentiation derivative of the k(x) with respect to x

k'(x) = \(\frac{[f'(x)h(x)g'(x) - h'(x)g(x)f(x)]}{(h(x)^{2} }\) --(1)

Now, differentiating each function w.r.t x   f'(x) = -3 , g'(x) = -1 , h'(x) = -6x -4

so, k'(x) \(=\)\(\frac{ [-3(-3x^{2} −4x + 3)(-1) - (-6x- 4 )(-3x + 4)(-x + 4)]}{(-3x^{2} -4x + 3)^{2} }\)

= \(\frac{(-60x^{2} + 114x + 16)}{(-3x^{2} -4x + 3)^{2} }\)

Hence, we get the required value.

B) Now, we have to determine value of x for f(x)= \(15x-\)\(\frac{16}{x}\) , tangent line is parallel to the line y = 19x−2. Slope of line y = 19x - 2 is   \(\frac{dy}{dx}\) = \(m\) = 19

Tangent line of f(x) is parallel  to line y = 19x - 2.  So, both have same slope,f'(x) = 19

f'(x) =\(\frac{ 15x^{2} - 16}{x^{2} }\) \(=19\)

=> 15x² - 16 = 19x²

=> 19x² - 15x² = 16

=> 4x² = 16

=> x² = 4

=> x = ± 2

So, required value of x are 2 and -2.

C) h(x) = \(\frac{f(x)}{g(x)}\). Also, we have f(x)

= −cos(x) and g(x) = 4x²+2x−3,

Similarly to part(a), h'(x) =\(\frac{ [f'(x)g(x) - g'(x)f(x)]}{(g(x))^2 }\)

f'(x) = derivative of (-cos(x) ) = -(- sin(x))

= sin(x)

g'(x) = 8x + 2

h'(x) = \(\frac{ [(sin(x)(4x^{2} +2x-3) - (8x + 2)(-cos(x))]}{(4x^{2} +2x-3)^{2} .}\)

D) Here, calculate \(\frac{d^{64} }{dx^{64} } (-7sinx)\)

As we know, \(\frac{d( sin(x))}{dx}\)= cos(x)

and \(\frac{d^{2} (sin(x))}{dx^{2} }\) = - sinx

\(\frac{d^{64} (-7sin(x))}{dx^{64} }\) =\(\frac{-7d^{64}(sin(x)) }{dx^{64} }\)

= - 7(sinx)  = -7 sin(x)

Hence, required value is -7sin(x).

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