Please help me and show all your own work, thank you!Differentiate the following function with respect to x. y = (2x + 4 - *)(4x4 – 5)

To obtain the sample group using cluster sampling, where each cluster is an individual year and you want to randomly select 3 of these clusters for your sample, you would first need to identify all the individual years that you want to include in your sample frame.

Next, you would randomly select 3 of these years as your clusters. To do this, you could use a random number generator or write each year on a piece of paper, put them in a hat, and draw out 3 years. Once you have your 3 clusters, you would then select all the individuals within those clusters to be included in your sample.
For example, let's say you want to use cluster sampling to select a sample of high school students in the United States. You decide to use individual states as your clusters, and you want to randomly select 3 states for your sample. You first identify all 50 states in the US and write them down on a list.

Next, you use a random number generator to select 3 states from the list. Let's say the random numbers generated were 7, 23, and 49, which correspond to the states of Connecticut, Mississippi, and Wyoming, respectively. You would then select all the high school students within those 3 states to be included in your sample.

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The probability of getting 14 successes out of 20 trials is approximately 0.0265 or 2.65% (rounded to 4 decimal places).

Given:
n (number of trials) = 20
k (number of successes) = 14
q (probability of failure) = 0.25

Since q is the probability of failure, the probability of success p can be calculated as:
p = 1 - q = 1 - 0.25 = 0.75

Now we can find the probability P(X = k) using the binomial distribution formula:

P(X = k) = [tex]C(n, k) * p^k * q^(n-k)[/tex]

First, calculate the binomial coefficient C(n, k):
C(20, 14) = 20! / (14! * (20-14)!) = 38760

Next, calculate p^k and q^(n-k):
[tex]p^k = 0.75^(14)[/tex] ≈ 0.00282
[tex]q^(n-k) = 0.25^6[/tex]≈ 0.000244

Finally, combine these values to find P(X = k):

P(X = k) = 38760 * 0.00282 * 0.000244 ≈ 0.0265

So, the probability of getting 14 successes out of 20 trials is approximately 0.0265 or 2.65% (rounded to 4 decimal places).

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We would expect about 2 of the 40 research projects to falsely reject a true null hypothesis.

Given a government agency funds 40 separate research projects testing the same drug for reducing brain tumors with an alpha level of 0.05, we can determine the expected number of projects that would falsely reject a true null hypothesis.

Step 1: Understand the alpha level (0.05), which is the probability of falsely rejecting a true null hypothesis (Type I error).

Step 2: Multiply the number of research projects (40) by the alpha level (0.05) to calculate the expected number of projects that would falsely reject a true null hypothesis.

Expected number of false rejections = Number of projects × Alpha level
Expected number of false rejections = 40 × 0.05
Expected number of false rejections = 2

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The volume of the portion of the solid sphere ρ≤a that lies between the cones ϕ=π/3 and ϕ=2π/3 is (2π/3) a³.

To find the volume of the portion of the solid sphere ρ≤a that lies between the cones ϕ=π/3 and ϕ=2π/3, we can use spherical coordinates. Since the solid sphere has a radius a, we have ρ≤a. The cones ϕ=π/3 and ϕ=2π/3 intersect the sphere at two latitudes, namely θ=0 and θ=π.

The volume of the portion of the sphere between the two cones can be obtained by integrating over the region of the sphere that lies between these two latitudes. Therefore, we need to integrate the volume element in spherical coordinates over the region of integration.

The volume element in spherical coordinates is given by:

dV = ρ² sin(ϕ) dρ dϕ dθ

where ρ is the radial distance, ϕ is the polar angle, and θ is the azimuthal angle.

The limits of integration for ρ, ϕ, and θ are:

0 ≤ ρ ≤ a

π/3 ≤ ϕ ≤ 2π/3

0 ≤ θ ≤ 2π

Substituting these limits into the volume element and integrating, we get:

V = ∫∫∫ dV

= [tex]\int\limits^a_0[/tex] ∫ [tex]\int\limits^{2\pi}_0[/tex] ρ² sin(ϕ) dθ dϕ dρ

= 2π ∫ [tex]\int\limits^a_0[/tex] ρ² sin(ϕ) dρ dϕ

= 2π ∫[(a³)/3 - 0] cos(π/3) dϕ

= 2π (a³)/3 cos(π/3) ∫ dϕ

= (2π/3) a³ (cos(π/3) - cos(2π/3))

Simplifying this expression, we get:

V = (2π/3) a³ (1/2 + 1/2)

= (2π/3) a³

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The equation of the tangent to the circle at P is y = (1/3)x – 6

What is equation of the circle?

The standard equation of a circle is:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

To work out the equation of the tangent to the circle at P, we need to use the fact that the tangent to a circle is perpendicular to the radius at the point of tangency.

Since P has x-coordinate 3 and is below the x-axis, its y-coordinate is given by:

y = -√(90 - x²) (taking the negative square root because P is below the x-axis)

So the coordinates of P are (3, -√(90 - 3²)) = (3, -9).

To find the equation of the radius OP, we can use the fact that O is the center of the circle and OP is a radius, so its equation is:

y - y₁ = m(x - x₁), where m is the gradient of OP.

The center of the circle is at the origin (0, 0), so the coordinates of O are (0, 0).

The coordinates of P are (3, -9), so the gradient of OP is:

m = (y - y₁)/(x - x₁) = (-9 - 0)/(3 - 0) = -3

Therefore, the equation of OP is:

y - 0 = -3(x - 0)

y = -3x

Since the tangent is perpendicular to the radius at P, its gradient is the negative reciprocal of the gradient of OP at P.

The gradient of OP at P is the same as the gradient of the tangent at P, which is:

m = -1/(-3) = 1/3

Therefore, the equation of the tangent to the circle at P is:

y - (-9) = (1/3)(x - 3)

y = (1/3)x – 6

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Step-by-step explanation:

19 mm = 1.9 cm

4.1 cm = 41 mm

1.) mm²

19 × 41 = 779 mm²

2.) cm²

1.9 × 4.1 = 7.79 cm²

The area of rectangle in centimeters is 7.79 cm² and Area of rectangle in mm² is 779 mm²

The area of Rectangle is length times of width.

In the given rectangle length is 4.1 cm

Width is 19 mm

Let us convert 4.1 cm to millimeters

We know that 1 cm = 10 millimeters

4.1 cm =4.1×10 mm

=41 millimeters

Now convert 19 mm to centimeter

19 mm = 1.9 cm

Now let us find area of rectangle in cm²

Area of rectangle =4.1 cm×1.9 cm

=7.79 cm²

Area of rectangle in mm²

Area of rectangle =41 mm×19 mm

=779 mm²

Hence, the area of rectangle in centimeters is 7.79 cm² and area of Area of rectangle in mm² is 779 mm²

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The distribution of the amount of coffee people drink per day is N(14, 7^2). The probability that one person drinks between 13.8 and 14.4 oz is 0.0248. For 32 people, the probability of the average coffee consumption being between 13.8 and 14.4 oz is 0.8913. The IQR for the average of 32 coffee drinkers is approximately 1.4442 oz.

The amount of coffee that people drink per day is normally distributed with a mean of 14 ounces and a standard deviation of 7 ounces.

X ~ N(14, 7²)

¯xx¯ ~ N(14, 7/√(32)²) = N(14, 1.237²)

Using the standard normal distribution, we can calculate the z-scores for these values

z1 = (13.8 - 14)/7 = -0.0571

z2 = (14.4 - 14)/7 = 0.0571

Then, we can use the z-table or calculator to find the probability

P(13.8 < X < 14.4) = P(-0.0571 < Z < 0.0571) = 0.0248 (rounded to 4 decimal places)

For the 32 people, find the probability that the average coffee consumption is between 13.8 and 14.4 ounces of coffee per day.

Using the central limit theorem, the distribution of sample means follows a normal distribution with mean = population mean = 14 and standard deviation = population standard deviation / sqrt(sample size) = 7 / sqrt(32) ≈ 1.237.

So, we can calculate the z-scores for the sample mean

z1 = (13.8 - 14) / (7 / √(32)) = -1.6325

z2 = (14.4 - 14) / (7 / √(32)) = 1.6325

Then, we can use the z-table or calculator to find the probability

P(13.8 < ¯xx¯ < 14.4) = P(-1.6325 < Z < 1.6325) = 0.8913 (rounded to 4 decimal places)

The IQR (interquartile range) can be calculated as Q3 - Q1, where Q1 and Q3 are the 25th and 75th percentiles of the distribution, respectively.

Since we know that the distribution of sample means follows a normal distribution with mean 14 and standard deviation 7 / √(32), we can use the z-score formula to find the values of Q1 and Q3 in terms of z-scores

z_Q1 = invNorm(0.25) ≈ -0.6745

z_Q3 = invNorm(0.75) ≈ 0.6745

Then, we can solve for the values of Q1 and Q3:

Q1 = 14 + z_Q1 * (7 / √(32)) ≈ 13.2779

Q3 = 14 + z_Q3 * (7 / √(32)) ≈ 14.7221

So, the IQR is Q3 - Q1 ≈ 1.4442 (rounded to 4 decimal places).

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The probability of selecting 3 or fewer individuals with excellent health from a sample of 11 individuals living close to a nuclear power plant is approximately 0.304, which is the option C.

In this question, we are interested in the probability of selecting 3 or fewer individuals with excellent health from a sample of 11 individuals living close to a nuclear power plant. Since the probability of success (selecting an adult with excellent health) is 0.35, and the probability of failure (selecting an adult without excellent health) is 0.65, we can calculate this probability as:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

P(X ≤ 3) = C(11, 0) x 0.35⁰ x 0.65¹¹ + C(11, 1) x 0.35¹ x 0.65¹⁰ + C(11, 2) x 0.35² x 0.65⁹ + C(11, 3) x 0.35³ x 0.65⁸

P(X ≤ 3) ≈ 0.304

So, the correct option is (c).

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The gradient of the curve when t = 3 is dy/dx = 6/3700.

First, let's find the expressions for dy/dt and dx/dt using the given parametric equations:
Differentiate x with respect to t:
[tex]x = t(t^2 + 1)^3[/tex]
[tex]dx/dt = (t^2 + 1)^3 + 3t^2(t^2 + 1)^2[/tex]
Differentiate y with respect to t:
[tex]y = t^2 + 1[/tex]
dy/dt = 2t
Now that we have dy/dt and dx/dt, we can find dy/dx:
Divide dy/dt by dx/dt to get dy/dx:
[tex]dy/dx = (2t) / [(t^2 + 1)^3 + 3t^2(t^2 + 1)^2][/tex]
Find the gradient of the curve when t = 3 by substituting t = 3 into the dy/dx expression:
[tex]dy/dx = (2 * 3) / [(3^2 + 1)^3 + 3 * 3^2 * (3^2 + 1)^2][/tex]
[tex]dy/dx = 6 / [(9 + 1)^3 + 3 * 9 * (9 + 1)^2][/tex]
[tex]dy/dx = 6 / [10^3 + 27 * 10^2][/tex]
dy/dx = 6 / [1000 + 2700]
dy/dx = 6 / 3700.

Note: Parametric equations are a way of expressing a set of equations for a function in terms of one or more parameters, rather than a single variable.

These parameters represent independent variables that vary independently of one another.

In other words, parametric equations are a way of describing a curve or surface in terms of a set of equations that define the position of points along that curve or surface as functions of one or more parameters.

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The derivative of function f(x) is f'(x) = x cosh(x) - 8 sinh(x) for f(x) = x sinh(x) - 9 cosh(x).

To find the derivative of f(x) = x sinh(x) - 9 cosh(x), we need to use the product rule of differentiation.

First, we differentiate the first term, which is x times the hyperbolic sine of x. Using the product rule, we get:

f'(x) = [x × cosh(x) + sinh(x)] - 9sinh(x)

Next, we simplify the expression by combining like terms:

f'(x) = x cosh(x) + sinh(x) - 9 sinh(x)

f'(x) = x cosh(x) - 8 sinh(x)

Therefore, the derivative of f(x) is f'(x) = x cosh(x) - 8 sinh(x).

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The exact value of cos(ecos⁻¹(-0.2) + sin(-2)) is calculated to be (cos(1))(cos(2)).

The expression cos⁻¹(-) means the inverse cosine of a negative value, but since the range of the inverse cosine function is restricted to [0,π], there is no real number whose cosine is -1. Therefore, this expression is undefined.

Assuming that the expression was intended to be cos⁻¹(-0.2) instead of cos⁻¹(-), we can proceed as follows:

cos(ecos⁻¹(-0.2) + sin(-2))

We know that cos(ecos⁻¹(x)) = x/|x| when x is not equal to zero, so we can apply this formula to simplify the expression:

cos(ecos⁻¹(-0.2)) = -0.2/|-0.2| = -1

Now we have:

cos(-1 + sin(-2))

The sine of any angle is between -1 and 1, so sin(-2) is between -1 and 1. Therefore, cos(-1 + sin(-2)) is a valid expression and we can evaluate it using the sum formula for cosine:

cos(-1 + sin(-2)) = cos(-1)cos(sin(-2)) - sin(-1)sin(sin(-2))

= cos(1)cos(-2) - 0sin(-2)

= cos(1)cos(2)

= (cos(1))(cos(2))

Therefore, the exact value of cos(ecos⁻¹(-0.2) + sin(-2)) is (cos(1))(cos(2)).

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The correct expressions that are equivalent to [tex]= 3^8[/tex] are:

(b) [tex]\frac{3^{10}}{3^2} = 3^8[/tex]

(d) [tex](3^4)^2 = 3^8[/tex]

(e) [tex](3*3)^4 = 3^8[/tex]

What is power?

The power of exponents is a mathematical operation that involves raising a number, variable, or expression to a certain power or exponent.

In general, if we have a base number or expression "a" raised to an exponent "n", we can represent this as:

[tex]a^n[/tex]

The correct expressions that are equivalent to [tex]= 3^8[/tex] are:

(b) [tex]\frac{3^{10}}{3^2} = 3^8[/tex]

(d) [tex](3^4)^2 = 3^8[/tex]

(e) [tex](3*3)^4 = 3^8[/tex]

Therefore, the correct answer is:

(b) [tex]\frac{3^{10}}{3^2}[/tex], (d) [tex](3^4)^2[/tex] and (e) [tex](3*3)^4[/tex]

Explanation:

(a) [tex]8^3[/tex] = 512, which is not equivalent to 3^8

(b) [tex]\frac{3^{10}}{3^2} = 3^{10-2}[/tex] = [tex]3^8[/tex]

(c) 3*8 = 24, which is not equivalent to 3^8

(f) [tex]\frac{1}{3^8} = 3^{-8}[/tex], which is not equivalent to 3^8

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Complete question : Select all expressions are equivalent to 3^8.

[tex](a) 8^3[/tex]

[tex](b) \frac{3^{10}}{3^2}[/tex]

[tex](c) 3*8[/tex]

[tex](d) (3^4)^2[/tex]

[tex](e) (3*3)^4[/tex]

[tex](f) \frac{1}{3^8}[/tex]

The point (-3, 2, 2) does not lie on the line with parametric equations x = 1 - 2t, y = 4 - t, z = 2 + 3t.

To determine if the point (-3, 2, 2) lies on the line with parametric equations x = 1 - 2t, y = 4 - t, z = 2 + 3t, we need to substitute x = -3, y = 2, and z = 2 into the parametric equations and see if there exists a value of t that satisfies all three equations simultaneously.

Substituting x = -3, y = 2, and z = 2 into the parametric equations, we get:

-3 = 1 - 2t -> 2t = 4 -> t = 2

2 = 4 - t

2 = 2 + 3t -> 3t = 0 -> t = 0

We obtained two different values of t, which means the point (-3, 2, 2) does not lie on the line with parametric equations x = 1 - 2t, y = 4 - t, z = 2 + 3t. Therefore, the answer is no.

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The 90% confidence interval for the population mean is approximately (2.51, 3.21).

To construct a confidence interval for the population mean at a 10% significance level, we'll use the given information: sample size (n=15), sample mean (x=2.86), and standard deviation (s=0.78). Since the population has a normal distribution, we can apply the t-distribution.

1. Find the degrees of freedom (df): df = n - 1 = 15 - 1 = 14
2. Determine the t-value for a 10% significance level (5% in each tail) and 14 degrees of freedom using a t-table or calculator. The t-value is approximately 1.761.

3. Calculate the margin of error (ME):
ME = t-value × (s / √n) = 1.761 × (0.78 / √15) ≈ 0.35

4. Construct the confidence interval by adding and subtracting the margin of error from the sample mean:
Lower limit = x - ME = 2.86 - 0.35 ≈ 2.51
Upper limit = x + ME = 2.86 + 0.35 ≈ 3.21

So, the 90% confidence interval for the population mean is approximately (2.51, 3.21).

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The value of x in the tangent and secant intersection is 9.

If a tangent segment and a secant segment are drawn to the exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.

Therefore, let's apply the theorem as follows:

20² = 16 × (16 + x)

400 = 16(16 + x)

400 = 256 + 16x

400 - 256 = 16x

144 = 16x

divide both sides of the equation by 16

x = 144 / 16

x = 9

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The outward flux of the given vector field F across the boundary surface of the solid region E is found to be 80π/3.

To apply the divergence theorem, we first need to find the divergence of the vector field F

div F = ∂/∂x (sin(9y) + 7xz) + ∂/∂y (zy + cos(x)) + ∂/∂z (z² + y²)

= 7x + z + 2z

= 7x + 3z

Next, we need to find the surface area and normal vector of the boundary surface dE. The boundary surface consists of the flat disk x² + y² ≤ 4 with z = 0. The surface area of the disk is A = πr² = 4π, where r = 2 is the radius of the disk. The normal vector points in the positive z direction, so we can take n = (0, 0, 1).

Now we can apply the divergence theorem

∫∫F · dS = ∭div F dV

where the triple integral is taken over the solid region E. Since E is symmetric about the xy-plane, we can write the triple integral as:

∭E (7x + 3z) dV = 2π ∫₀² [tex]\int\limits^0_{(\sqrt{(4-x^2)}[/tex]  [tex]\int\limits^0_{(\sqrt{(4-x^2-y^2)}[/tex] (7x + 3z) dz dy dx

Evaluating this integral using standard techniques (such as cylindrical coordinates) gives

∫∫F · dS = 80π/3

Therefore, the flux of the vector field F across the boundary surface dE is 80π/3.

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The statement, "When using binomial distribution, maximum possible number of "success" is number of trials." is, True because number of success is equal to number of trials.

When using the binomial distribution, the maximum possible number of successes is equal to the number of trials.

In each trial, there are two possible outcomes: success or failure.

The probability of success in each trial is denoted by "p" and the probability of failure is denoted by "q" (where q = 1 - p).

The binomial distribution calculates the probability of obtaining a specific number of successes in a fixed number of trials.

Since the number of possible successes is limited to the number of trials, the statement is true.

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The width of the 90% confidence interval for the average income of consumers in the particular region is $430.58.

To find the width of the 90% confidence interval, we first need to calculate the margin of error. The margin of error is given by:

Margin of error = Z × (population standard deviation / square root of sample size)

Where Z is the critical value for the desired level of confidence. For a 90% confidence level, Z is 1.645 (obtained from a standard normal distribution table).

Plugging in the values, we get:

Margin of error = 1.645 × (1000 / square root of 59) = 215.29

The width of the confidence interval is twice the margin of error, so:

Width = 2 × Margin of error = 2 × 215.29 = $430.58

Therefore, the width of the 90% confidence interval for the average income of consumers in the particular region is $430.58.

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Answer: No

Step-by-step explanation:

I MEAN- IT'S PRETTY CLEAR THAT'S NOT A RIGHT TRIANGLE--. I'm aware you can't assume in geometry but there's no box.....

----------------------------------------------------

3x - 4x - 5x makes a right triangle.

6x - 8x - 9x. No. It is not a right triangle,

Since the second derivative is always positive, we have a minimum at x = 12, which corresponds to the dimensions of the field we found.

To minimize the cost of the fence, we need to find the dimensions of the rectangular field that will give us the smallest perimeter.

Let's denote the width of the field as x and the length as y. Then, we have the area of the field as xy = 180.

The cost of the fencing for the width is $10/ft, which means the cost for the two width sides is $20x. The cost of the fencing for the remaining sides is $2/ft and $7/ft, which means the cost for the two length sides is $2y and the two remaining width sides is $7(x-2y).

So, the total cost of the fencing is C(x,y) = 20x + 2y + 7(x-2y) = 27x - 12y.

To find the dimensions that minimize the cost of the fence, we need to find the critical points of the cost function. Taking the partial derivatives of C(x,y) with respect to x and y, we get:

∂C/∂x = 27
∂C/∂y = -12

Setting both partial derivatives equal to zero, we find that there are no critical points since 27 and -12 are never equal to zero.

However, we can use the fact that the area of the field is xy = 180 to eliminate y from the cost function. Solving for y, we get:

y = 180/x

Substituting this into the cost function, we get:

C(x) = 27x - 12(180/x) = 27x - 2160/x

To find the minimum cost, we need to find the critical points of C(x). Taking the derivative of C(x) and setting it equal to zero, we get:

C'(x) = 27 + 2160/x^2 = 0

Solving for x, we get:

x = √(2160/27) = 12

Substituting this back into y = 180/x, we get:

y = 180/12 = 15

Therefore, the dimensions of the field that will minimize the cost of the fence are 12 ft by 15 ft. To justify that this is a minimum, we can use the second derivative test. Taking the second derivative of C(x), we get:

[tex]C''(x) = 4320/x^3 > 0 for all x ≠ 0[/tex]

Since the second derivative is always positive, we have a minimum at x = 12, which corresponds to the dimensions of the field we found.

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Therefore, the monthly mortgage payment is $555.63.

A function is a mathematical relationship between two sets of numbers, where each element in the first set (called the domain) is paired with a unique element in the second set (called the range). In other words, it is a rule or mapping that assigns each input value in the domain to exactly one output value in the range. Functions are often written in the form f(x) = y, where f is the name of the function, x is the input value, and y is the output value.

Here,

1. Monthly Mortgage Payment Calculation:

Using the given values, we can calculate the monthly mortgage payment using the formula:

[tex]M = P * r * (1 + r)^{n} / ((1 + r)^{n-1} )[/tex]

Where,

P = Loan amount = $150,000 - $30,000 (down payment)

= $120,000

r = Annual interest rate / 12

= 0.042 / 12

= 0.0035

n = Total number of payments

= 30 years * 12 months per year

= 360

Substituting the values in the formula, we get:

M = $120,000 * 0.0035 * (1 + 0.0035)³⁶⁰ / ((1 + 0.0035)³⁶⁰⁻¹)

M = $555.63 (rounded to the nearest cent)

2. Total Costs Calculation:

For the purchased home, the additional costs of home ownership include property taxes and home insurance. Let's assume the property taxes are $3,000 per year and home insurance is $1,500 per year.

a. After 1 year:

Rental home: $900 * 12

= $10,800

Purchased home: $30,000 (down payment) + $555.63 * 12 (mortgage payments) + $3,000 (property taxes) + $1,500 (home insurance)

= $41,966.56

b. After 5 years:

Rental home: $10,800 + ($75 * 5 / 4) * 5 = $12,562.50

Purchased home: $30,000 (down payment) + $555.63 * 60 (mortgage payments) + $15,000 (property taxes) + $7,500 (home insurance)

= $72,398.80

c. After 10 years:

Rental home: $10,800 + ($75 * 5) * 5 + ($75 * 5 / 4) * 10 = $20,287.50

Purchased home: $30,000 (down payment) + $555.63 * 120 (mortgage payments) + $30,000 (property taxes) + $15,000 (home insurance)

= $95,775.60

d. After 15 years:

Rental home: $10,800 + ($75 * 5) * 10 + ($75 * 5 / 4) * 15 = $29,012.50

Purchased home: $30,000 (down payment) + $555.63 * 180 (mortgage payments) + $45,000 (property taxes) + $22,500 (home insurance)

= $155,299.40

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The result of the subtraction is 4.234 x 10⁻³.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

When we subtract two numbers written in scientific notation, we first make sure they have the same exponent. In this case, we need to rewrite 1.6 x 10⁻² as 0.016 x 10⁻³ so that we can subtract it from 4.25 x 10⁻³:

4.25 x 10⁻³ - 0.016 x 10⁻³ = (4.25 - 0.016) x 10⁻³

Simplifying the expression inside the parentheses gives:

4.234 x 10⁻³

So the result of the subtraction is 4.234 x 10⁻³.

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The conjugate of 2x² + √3 is as follows:

(2x² - √3).

A pair of entities connected together is referred to as being conjugate. For instance, the two smileys—smiley and sad—are identical save from one set of characteristics that is essentially the complete opposite of the other. These smileys are identical, but you'll see if you look closely that they have the opposite facial expressions: one has a smile, and the other has a frown. Similar to this, the term "conjugate" in mathematics designates either the conjugate of a complex number or the conjugate of a surd when the number only undergoes a sign change with respect to a few constraints.

Here in the question,

The binomial is given as:

2x² + √3

The negative of this or when the operation sign is changed in the binomial, we get the conjugate as:

2x² - √3

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The probability that X is less than or equal to 48 is approximately 0.023.

To use the normal approximation, we first need to check if the conditions are met:

1. The sample size is large enough: n*p = 93*0.48 = 44.64 and n*(1-p) = 93*0.52 = 48.36, both greater than 10.

2. The observations are independent: we assume that the sample is random and that the sample size is less than 10% of the population size.

Given these conditions, we can use the normal distribution to approximate the binomial distribution.

We standardize X using the formula:

z = [tex](X - n*p) / \sqrt{(n*p*(1-p)) }[/tex]

Substituting the values, we get:

z = (48 - 93*0.48) / sqrt(93*0.48*0.52) = -1.99

Using a standard normal distribution table or calculator, we can find the probability:

P(X ≤ 48) ≈ P(z ≤ -1.99) = 0.023

Therefore, the probability that X is less than or equal to 48 is approximately 0.023.

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The answer to part a is: p-value = 0.0918. We do not reject the null hypothesis.

To calculate the p-value for a one-tail (lower) test with a z-score of -1.34 and a significance level of α=0.05, we need to find the probability of getting a z-score less than or equal to -1.34 under the null hypothesis.
Using a standard normal distribution table or calculator, we can find that the area to the left of -1.34 is 0.0918. This is the probability of obtaining a z-score less than or equal to -1.34.
To find the p-value, we compare this probability to the significance level. Since the p-value (0.0918) is greater than the significance level (0.05), we do not reject the null hypothesis.

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The statement false is:

Expanding the sample size can decrease the power of a hypothesis test.

The correct option is (d)

The significance level is the probability of rejecting the null hypothesis when it is true. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.

The level of statistical significance is often expressed as a p -value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. A p -value less than 0.05 (typically ≤ 0.05) is statistically significant.

The probability of making a type I error is α, which is the level of significance you set for your hypothesis test. An α of 0.05 indicates that you are willing to accept a 5% chance that you are wrong when you reject the null hypothesis.

The correct option is (d).

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The numbers  are common multiples of option A. 2 and 5 10, 20, 30, 40.

Numbers are equal to,

10, 20, 30, 40

Common multiples of all the numbers 10, 20, 30, 40 is equal to 10.

As all the numbers 10, 20, 30, 40  are ending with zero.

Lowest number present in the given numbers 10, 20, 30, 40  is 10.

Prime factors of 10 are equal to,

10 = 2 × 5

20 is divisible by 2 and 5 both.

30 is divisible by 2 and 5 both.

40 is divisible by 2 and 5 both.

Common multiples of 10, 20, 30, 40  are 2 and 5.

Therefore, the given numbers are common multiple of option A. 2 and 5.

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Answer: 40%

Step-by-step explanation:

The wording 9 out of 15 can be written into a fraction.

As a fraction, this would be 9/15.

Once you simplify that, you get 3/5.

You know that there is 100% in a whole.

3 * 20 / 5 * 20 so the denominator is 100.

60/100 people got the homework correct, 60/100 can be written into 60%.

Subtract this from the total 100% and you get 40% of students who got the homework assignment wrong.

Answer:

LP and PN are the radii of this circle.

Answer:

need a photo of it 6/5 x 6/5

Step-by-step explanation: