Independent rardom sampling from two normally distributed populations gives the reasts below. Find a 95% confidence interval ottimate of the difference between the means of the two population
nx = 63 x= 392 nx=16
ny = 40 y= 333 ny= 27
The confidence interval is <μx –μy<
(Round to four decimal places as needed)

Answer:

36

Step-by-step explanation:

The vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.

To find the vertex, focus, and directrix of the parabola with the equation 5x^2 + 16y, we can use the standard form of the equation for a parabola:

y = (1/4p)(x - h)^2 + k

where (h, k) is the vertex and p is the distance between the vertex and the focus or the vertex and the directrix.

Comparing the given equation to the standard form, we have:

5x^2 + 16y = 0
=> 16y = -5x^2
=> y = -(5/16)x^2

From this, we can determine that the vertex is at the origin (0, 0).

To find p, we can use the formula p = 1/(4a), where a is the coefficient of x^2. In this case, a = -5/16, so p = 1/(4*(-5/16)) = -4/5.

Therefore, the vertex is (0, 0), the focus is (-4/5, 0), and the directrix is x = 4/5.

In conclusion, the vertex, focus, and directrix of the parabola 5x^2 + 16y = 0 are (0, 0), (-4/5, 0), and x = 4/5, respectively.

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Answer:

17.2ft

Step-by-step explanation:

just add

11.4+5.8=17.2

Answer:

true

Step-by-step explanation:

M(x,y):-

\(\\ \rm\Rrightarrow \left(\dfrac{2+4}{2},\dfrac{5+9}{2}\right)\)

\(\\ \rm\Rrightarrow \left(\dfrac{6}{2},\dfrac{14}{2}\right)\)

\(\\ \rm\Rrightarrow (3,7)\)

Equation of L

Slope of the perpendicular line=-1/2

Equation of the perpendicular line

\(\\ \rm\Rrightarrow y-y_1=m(x-x_1)\)

\(\\ \rm\Rrightarrow y-7=-1/2(x-3)\)

\(\\ \rm\Rrightarrow 7-y=1/2(x-3)\)

\(\\ \rm\Rrightarrow 14-2y=x-3\)

\(\\ \rm\Rrightarrow x+2y-17=0\)

To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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Answer:

b is you answer hope it helps you

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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The area of land the charity planted was 17000 m². The charity met its target

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

1 km = 1000 m

1 km² = 1000000 m²

An environmental charity set a target to plant trees on 9000 m² of land in September.

In September, it planted trees on 0.017 km² of land. Hence:

Area of land planted = 0.017 km² * 1000000 m² per km² = 17000 m²

17000 m² is greater than 9000m². The charity met its target

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Unfortunately, I do not go to Harvard Business School so I am unable to solve this complex equation.

Answer: -9

Step-by-step explanation: you want to take away 12 from 3, which will leave you in the negatives

The value of angle S is 53°

Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.

With this theorem we can say that

7x+2 = 4x+13+19

collecting like terms

7x -4x = 13+19-2

3x = 30

divide both sides by 3

x = 30/3

x = 10

Since x = 10

angle S = 4x+13

angle S = 4(10) +13

= 40+13

= 53°

Therefore the measure of angle S is 53°

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If a group consists of 10 kids and 2 adults, the number of ways are there to form the line are 2 * 10!. So, correct option is C.

To form a line with an adult at the front and an adult at the back, we need to consider the positions of the 10 kids within the line. The two adults are fixed at the front and back, so we have 10 positions available for the kids.

To calculate the number of ways to arrange the kids in these positions, we can use the concept of permutations. Since each position can be occupied by a different kid, we have 10 options for the first position, 9 options for the second position, 8 options for the third position, and so on, until the last position, where only 1 kid remains.

Therefore, the number of ways to form the line is:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 10!

However, the problem also mentions that there are 2 adults, so we need to consider the arrangements of the adults as well. Since there are only two adults, there are 2 ways to arrange them in the line (adult at the front and adult at the back or vice versa).

Therefore, the total number of ways to form the line is:

2 x 10! = 2 * 10!

Hence, the correct option is b. 2 * 10!, which accounts for both the arrangements of the kids and the adults.

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Answer:

2% Sales tax

Step-by-step explanation:

Basically if you divide 7.40 by the 370 you get .02, and if you move the decimal 2 spots to the right then you get the sales tax percentage.

The solution is x=3/4

How can we solve given equation?

First, we will solve like terms. Then shift constant to other side and keep x on the same side to get the value of x.

We can solve given equation as shown below:

5/2-3x-5+4x=-7/4

(5-10)/2+x=-7/4

-5/2+x=-7/4

x=5/2-7/4

x= (10-7)/4

x=3/4

Hence, the solution is x=3/4.

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Answer:

Hello yes indeed I am here now vote me brainliest.

Step-by-step explanation:

Why you ask? well first I want it even though I did not do anything to help him/her even though, it is funny. :)

A function is a function that represents the area under a curve. In this case, f is the curve being considered. The function a(x) represents the area under the curve of f from x=0 up to x.

So, if we want to find the area under the curve of f from x=0 up to x=3, we would evaluate a(3) - a(0). This would give us the total area under the curve of f from x=0 to x=3. Similarly, if we have another area function, say b(x), that represents the area under the curve of f from some other starting point (e.g. from x=1), we would use b(x) to find the area under the curve of f from x=1 up to some other x value.
The graph of f, displayed in the figure to the right, represents a function that can be analyzed using various mathematical concepts. In this case, we can consider two area functions for f, denoted as A(x) and B(x), which would allow us to evaluate the areas under the curve of the graph with respect to the x-axis. These area functions can be used to understand properties and behaviors of the function f in different regions of the graph.

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The flux of the vector-field F = 1i + 1j + 2k across the surface S is 2. We find out the flux of the vector-field using Green's Theorem.

Flux form of Green's Theorem for the given vector-field

φ = ∫ F.n ds

= ∫∫ F. divG.dA

Here G is equivalent to the part of the plane = 2x+4y+z = 2.

and given F = 1i + 1j + 2k

divG = div(2x+4y+z = 2) = 2i + 4j + k

Flux = ∫(1i + 1j + 2k) (2i + 4j + k) dA

φ = ∫ (2 + 4 + 2)dA

= 8∫dA

A = 1/2 XY (on the given x-y plane)

2x+4y =2

at x = 0, y = 1/2

y = 0, x = 1

1/2 (1*1/2) = 1/4

Therefore flux = 8*1/4 = 2

φ = 2.

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The measurement  that  is accurate to 25 grams is 0.025Kg.

Measurement can be described as the  quantification of attributes  involving an object or event,  and it can be used in making comparism with other objects or events.

Hence  measurement serves as as way of  determining how large or small a physical quantity with respect to  basic reference quantity of the same kind.

1kg = 1000g

then X Kg = 25gram

Then cross multiply,  X = (25/ 1000)= 0.025kg

Therefore, The measurement  that  is accurate to 25 grams is 0.025Kg.

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The value of the given integral using the trigonometric substitution is:

∫x^2/√16-x^2 dx = 4arcsin(x/4) - (1/4)(16-x^2)^(3/2) + C

To integrate ∫x^2/√16-x^2 using trigonometric substitution, we can make the substitution x = 4sinθ, which gives √16-x^2 = 4cosθ.

We can then substitute these expressions for x and √16-x^2 in the integral, and use the identity sin^2θ + cos^2θ = 1 to simplify the integrand:

∫x^2/√16-x^2 dx = ∫(16sin^2θ)/(4cosθ) (4cosθ dθ)

= 16∫sin^2θ dθ

= 16∫(1-cos2θ)/2 dθ (using the identity sin^2θ = 1-cos^2θ)

= 8∫(1-cos2θ) dθ

= 8(θ - (1/2)sin2θ) + C

where C is the constant of integration.

Substituting back for θ, we get:

θ = arcsin(x/4)

sin2θ = 2sinθcosθ = 2(x/4)(√16-x^2)/4 = x√(16-x^2)/8

Therefore, the final answer is:

∫x^2/√16-x^2 dx = 8(arcsin(x/4) - (1/2)(x√(16-x^2)/8)) + C

or, simplifying:

∫x^2/√16-x^2 dx = 4arcsin(x/4) - (1/4)(16-x^2)^(3/2) + C

where C is the constant of integration.

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https://youtu.be/GZcm4mswivc

espero que te ayude

Answer:

π radians

Step-by-step explanation:

*view photo*

Tom's increased monthly rent after the 8.5% increase will be R1356.25.

From the question, we have the following parameters that can be used in our computation:

Monthly rent = R1250

Yearly rate = 8.5%

If Tom pays R1250 every month, then his annual rent is:

Annual rent = 1250 * 12 = R15000.

If his annual rent increased by 8.5%, his new annual rent will be

New = 15000 * (1 + 0.085) = 16275.

Divide by 12 to get the increased monthly rent

Increased monthly rent = 16275 / 12 = R1356.25.

Hence, the rent is R1356.25.

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Answer:

Height is 5.3 inches.

Step-by-step explanation:

2* base + 2*height = 35.8

2*12.6 + 2h = 35.8

h = (35.8 - 2(12.6) / 2

= (35.8 - 25.2) /2

=  10.6 / 2

= 5.3 inches.

Answer:

Step-by-step explanation:

The formula of a perimeter of a rectangle:

\(P=2(l+w)\)

l - length

w - width

We have

\(P=35.8in\\l=12.6in\)

Substitute:

\(35.8=2(12.6+w)\)       divide both sides by 2

\(\dfrac{35.8}{2}=\dfrac{2(12.6+w)}{2}\)

\(17.9=12.6+w\)       subtract 12.6 from both sides

\(17.9-12.6=12.6-12.6+w\\\\5.3=w\to w=5.3\ (in)\)

The given double integral can be interpreted as the volume of a solid region in three-dimensional space. By identifying the region R as a rectangle in the xy-plane with dimensions 2 units in the x-direction and 6 units in the y-direction.

The concept of volume in three-dimensional space and how it can be calculated using a double integral. The region R={(x,y)∣0≤x≤2,0≤y≤6} is a rectangle in the xy-plane with sides of length 2 units and 6 units. This rectangle can be thought of as the base of a solid prism.

To calculate the volume of this solid, we integrate the constant function f(x,y) = 1 over the region R. The double integral ∬ _R3dA represents the volume element dV in three dimensions, where dA is the differential area element in the xy-plane.

By integrating the constant function f(x,y) = 1 over the region R, we are essentially summing up the infinitesimal volumes of each small rectangular region within R. This integration process yields the total volume of the solid prism defined by the region R.

Evaluating the double integral over the rectangular region R={(x,y)∣0≤x≤2,0≤y≤6} gives us the volume of the solid.

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Answer:

130 degrees is your answer

Step-by-step explanation:

The measurement of angle C is given by the expression 180° – 25° – 25°. So, angle C measures 130°.- answer from edmentum

Answer:

Step-by-step explanation:

Dhddhhfjvjvmx,sfkiritifkflf,gjgi*jfckblhog

The probability of success is a measure of the likelihood that a specific event or outcome will occur successfully, typically expressed as a value between 0 and 1.

In a clinical trial with two treatment groups, group A and group B, the probability of success in group A is 0.5, while the probability of success in group B is 0.6. Each group consists of five patients.

To calculate the probability of a specific outcome, such as all patients in group A being successful, we can use the binomial distribution formula.

The binomial distribution formula is:
\(P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}\)

Where:
- P(X=k) represents the probability of getting exactly k successes
- nCk represents the number of ways to choose k successes from n trials
- p represents the probability of success in a single trial
- n represents the total number of trials

In this case, we want to find the probability of all five patients in group A being successful. Therefore, we need to calculate P(X=5) for group A.

Using the binomial distribution formula, we can calculate this as follows:
\($P(X&=5) \\\\&= \binom{5}{5} (0.5^5) (1-0.5)^{5-5} \\\\&= \boxed{\dfrac{1}{32}}\)

Simplifying the equation, we get:
\($P(X&=5) \\&= 1 (0.5^5) (1-0.5)^0 \\&= \boxed{\dfrac{1}{32}}\)

Simplifying further, we have:
\($P(X&=5) \\&= (0.5^5) (1) \\&= \boxed{\dfrac{1}{32}}\)

Calculating this, we get:
P(X=5) = 0.03125

Therefore, the probability of all five patients in group A being successful is 0.03125, or 3.125%.

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Based on the given values, we can compute the expected returns and expected standard deviations for different weightings of the stocks in the portfolio. The results are as follows:

a. When w1 = 1.00, the expected return of the two-stock portfolio is 0.13, and the expected standard deviation is 0.03.

b. When w1 = 0.65, the expected return of the two-stock portfolio is 0.1095, and the expected standard deviation is 0.0214.

c. When w1 = 0.60, the expected return of the two-stock portfolio is 0.104, and the expected standard deviation is 0.0222.

d. When w1 = 0.30, the expected return of the two-stock portfolio is 0.074, and the expected standard deviation is 0.0262.

e. When w1 = 0.10, the expected return of the two-stock portfolio is 0.038, and the expected standard deviation is 0.0324.

To calculate the expected return of the two-stock portfolio, we use the weighted average of the individual expected returns based on the given weights. For example, in part (a), where w1 = 1.00, the expected return is simply equal to E(R1) = 0.13.

To calculate the expected standard deviation of the two-stock portfolio, we use the formula:

σ = √(w1^2 * E(a1)^2 + w2^2 * E(q2)^2 + 2 * w1 * w2 * E(a1) * E(q2) * ρ)

where E(a1) is the expected standard deviation of stock 1, E(q2) is the expected standard deviation of stock 2, and ρ is the correlation coefficient.

Regarding the risk-return graph, without the specific details of the graph options provided, it is not possible to determine which graph is correct for the given weightings and correlation coefficient. The graph would typically depict the risk-return tradeoff for different weightings and correlation coefficients, showing the relationship between expected return and expected standard deviation of the portfolio.

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