Let X1, X2, ..., Xm be a random sample from a population with mean mu1 and variance of sigma1^2=, and let Y1, Y2, ... , Yn be a random sample from a population with mean mu2 and variance sigma2^2, and that X and Y samples are independent of one another. Which of the following statements are true? Xbar is normally distributed with expected value mu1 and variance sigma1^2/m Ybar is normally distributed with expected value mu2 and variance sigma2^2/m Xbar-Ybar is normally distributed with expected value mul-mu2 and variance (sigma1^2/m+sigma2^2/n). Xbar-Ybar is an unbiased estimator of mul-mu2. All of the above statements are true.

A=200in² is the area of the shaded polygon so 200in² ➗ 30in

The equation of the tangent line to the curve are  \(y=x-1 , y=\frac{xe-e^{2}+8 }{e}\).

It is required to find the solution.

A tangent is a line that touches the edge of a curve or circle at one point, but does not cross it. The tangent line to a curve at a point is that straight line that best approximates (or “clings to”) the curve near that point.

Given:

\(y=8\frac{lnx}{x} \\\\y'=8(\frac{1/x*x-lnx*1}{x^{2} } \\\\y'=\frac{1-lnx}{x^{2} }\)

Now, we find the slope of the tangent by inserting the point (1,0) into the derivative.

\(m_{tangent}=\frac{1-ln1}{1^{2} }\\\\m_{tangent}=1-0/1\\\\m_{tangent} =1\)

We can now find the equation, because we know the slope and a point (1, 0).

\(y-y_{1} =m(x-x_{1} )\\\)

y-0=1(x-1)

y=x-1

We can now find the equation, because we know the slope and a point (e, 8/e).

\(y-y_{1} =m(x-x_{1} )\\\\y-8/e=1(x-e)\\\\y=\frac{xe-e^{2}+8 }{e}\)

Therefore, the equation of the tangent line to the curve are  \(y=x-1 , y=\frac{xe-e^{2}+8 }{e}\).

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Answer:

Step-by-step explanation:

Remark

First of all, all the units must be the same. Inches is probably the best unit to use.

Second the base line at the bottom must be completed. How long is it

Givens

Left side = 48 inches

Top = 3 yards

Right side = 5 feet.

Bottom = 1 yard + top

Bottom = 1 yard + 3 yards

Bottom = 4 yards

Perimeter = 144 + 60 + 108 + 48

Perimeter = 360 Inches.

Answer

Perimeter = 360 inches

Perimeter = 360 / 12 = 30 feet     There are 12 inches in a foot

Perimeter = 360 / 36 = 10 yards.  There are 36 inches in a yard

The question does not specify the units. Probably inches would work, but if a computer is marking your answer and you get it wrong, you are going to have to try the other two answers in turn.

Answer:

Parallel

Step-by-step explanation:

Line A can be simplified to 1/5x = y.

Line B can be simplified to y = 1/5x + 16.

They both have the same slope, 1/5, so they will be parallel.

Answer:

Parallel

Step-by-step explanation:

Same thing as the last one. Put it in \(y=mx+b\)

A: \(y=1/5x\)

and

B: \(y=1/5x+16\)

These lines are parallel because they have the same slopes, but different y-intercepts.

The distance from the epicenter of the march 1964 earthquake to crescent city is 2600 kilometers and It took 400 seconds for the first p-wave to reach crescent city

In a seismic event like an earthquake, seismic waves propagate through the Earth at different speeds. The first type of seismic wave to reach a particular location is the primary wave, or P-wave. P-waves are compressional waves that travel faster than other seismic waves, such as S-waves or surface waves.

To calculate the time it took for the P-wave to reach Crescent City, we need to know the speed at which P-waves travel. On average, P-waves travel at a speed of about 6-7 kilometers per second in the Earth's crust. However, this speed can vary depending on the specific properties of the Earth's layers.

Using an average speed of 6.5 kilometers per second, we can calculate the time it took for the P-wave to travel a distance of 2600 kilometers:

Time = Distance / Speed = 2600 km / 6.5 km/s ≈ 400 seconds.

Therefore, it took approximately 400 seconds, or 6 minutes and 40 seconds, for the P-wave to reach Crescent City from the epicenter of the March 1964 earthquake.

It is important to note that the calculated time is an estimation based on average values, and the actual time may vary depending on the specific geological conditions along the propagation path of the P-wave.

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Answer:

length = 12.5 in, width = 12.5 in, Area = 156.25 in²

Step-by-step explanation:

To get the maximum area, the wire can be shaped into a square. We can say that the length and width of the rectangle must be equal to each other, and call this value "x".

Therefore, we can write an equation for the perimeter:

The area of the rectangle is calculated using the formula:

Or in our case, the area of the rectangle is the area of a square:

Substitute x = 12.5 into this equation.

The maximum area that can be formed from the wire is 156.25 in², and the dimensions of the rectangle are 12.5 x 12.5 in.

In a nonprobability sampling, not all members of a population have an equal probability of being included.

In a probability sampling, all members of the population have an equal probability of being included.

The strength of the association is described by the effect size.

Curvilinear association is one in which the correlation coefficient is zero (or close to zero) and the relationship between two variables isn't a straight line. False.

In nonprobability sampling, the selection of individuals from the population is not based on random sampling principles. This means that not all members of the population have an equal probability of being included in the sample.

In probability sampling, every member of the population has an equal and known chance of being selected for the sample. Random sampling methods, such as simple random sampling, stratified random sampling, and cluster sampling, are commonly used to achieve this. In probability sampling, the sample is representative of the population, and statistical inferences can be made.

The strength of the association between two variables is typically measured by the effect size. Effect size quantifies the magnitude or magnitude of the relationship between variables and provides an indication of the practical or substantive significance of the association.

Curvilinear association refers to a relationship between two variables that cannot be adequately described by a straight line. In such cases, the correlation coefficient between the variables may be zero or close to zero, indicating no linear relationship.

Nonprobability sampling involves selecting individuals without an equal probability of inclusion, while probability sampling ensures that all members of the population have an equal chance of being included. The strength of the association between variables is described by the effect size, and a curvilinear association indicates a non-straight line relationship between variables.

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Answer:

answer: 300

Step-by-step explanation:

the area of the parellologram is found just by doing base × height! So our base is 20 and our height is 15 so now that we know our base and height. all we have to do is multiply them so

20 x 15 = 300 so 300 is our answer! Hope that helps you!

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

\( \textbf{Let's see if the sequence is Arithmetic or Geometric :} \)

\( \textsf{If the difference between successive terms is } \) \( \textsf{equal then, the terms are in AP} \)

\( \textsf{Since the common difference is same, } \) \( \textsf{we can infer that it's an Arithmetic progression} \) \( \textsf{with common difference of } \sf \dfrac{1}{3} \)

Answer:

Arithmetic with common difference of \(\sf \frac{1}{3}\)

Step-by-step explanation:

\(\textsf{Given sequence}=4, \dfrac{13}{3}, \dfrac{14}{3}, 5, \dfrac{16}{3},...\)

If a sequence is arithmetic, the difference between consecutive terms is the same (this is called the common difference).

If a sequence is geometric, the ratio between consecutive terms is the same (this is called the common ratio).

\(\sf 4\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad\dfrac{13}{3}\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad \dfrac{14}{3}\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad 5\quad \overset{+\frac{1}{3}}{\longrightarrow}\quad \dfrac{16}{3}\)

As the difference between consecutive terms is \(\sf \frac{1}{3}\) then the sequence is arithmetic with common difference of \(\sf \frac{1}{3}\)

General form of an arithmetic sequence: \(\sf a_n=a+(n-1)d\)

where:

Given:

So the formula for the nth term of this sequence is:

\(\implies \sf a_n=4+(n-1)\dfrac{1}{3}\)

\(\implies \sf a_n=\dfrac{1}{3}n+\dfrac{11}{3}\)

Answer:

5s + 0.65 = 14.4

      - 0.65  - 0.65

______________

5s = 13.75

___.   ___

5          5

s = 2.75 meters of string for each pennant

Explanation:

s represents the length of string required for each pennant.

We know that Ingrid is using a total of 14.4 meters of string to hang a banner and 5 pennants.

We also know that out of that 14.4 meters, 0.65 meters is used to hang the banner. The rest of the string left is equally distributed among the 5 pennants.

So, therefore, we have a constant of 0.65 and a coefficient of 5 with variable, s.

Next, we solve this by first isolating the constant by subtracting 0.65 on both sides.

Then. we isolate the variable by dividing 5 into both sides.

So, s = 2.75 meters of string for each pennant

Answer:

a. 14 + x

b. There are several ways to write this, 6y, 6(y)

Step-by-step explanation:

Look for key words when you do these types of questions!

For addition, add, sum, greater than, etc.

For multiplication, product, times, etc.

For subtraction, difference, less than, minus, etc.

And for division, look for quotient, divide, etc.

Hope this helps : )

Step-by-step explanation:

5×3+4 =19

2-6+3=5

19+5

=24

Answer:

q= 1/2 or 0.5 depending

Step-by-step explanation:

The second derivative of v with respect to t, denoted as d²v/dt², is equal to 4

The second derivative of v with respect to t, we will differentiate v twice.

v = 2t² + 7t + 11

First, let's find the first derivative of v with respect to t (dv/dt):

dv/dt = d/dt (2t² + 7t + 11)

Using the power rule of differentiation, we differentiate each term separately:

dv/dt = 2(2t) + 7(1) + 0

dv/dt = 4t + 7

Now, let's find the second derivative of v with respect to t (d²v/dt²):

d²v/dt² = d/dt (4t + 7)

Again, using the power rule of differentiation, we differentiate each term separately:

d²v/dt² = 4(1) + 0

d²v/dt² = 4

Therefore, the second derivative of v with respect to t, denoted as d²v/dt², is equal to 4.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The inverse function of f(x) = \(b^x\) is g(x) = log_b(x), where log_b denotes the logarithm with base b. Therefore, g(x) is the inverse function of f(x) = \(b^x.\)

The inverse function of an exponential function f(x) =\(b^x\) is a logarithmic function g(x) = log_b(x), where the base of the logarithm matches the base of the original exponential function.

To find the inverse function, we switch the roles of x and y in the original function and solve for y. So, for f(x) = \(b^x\), we rewrite it as x = \(b^y\) and solve for y. Taking the logarithm of both sides with base b, we get log_b(x) = y, which can be written as g(x) = log_b(x).

The inverse function undoes the effect of the original function. In this case, the exponential function f(x) = \(b^x\) raises the base b to the power of x, while the inverse function g(x) = log_b(x) "undoes" the exponentiation by taking the logarithm base b of x, resulting in the original input value x. Therefore, g(x) is the inverse function of f(x) = \(b^x.\)

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Find the inverse function of f(x) = \(b^x\)

Answer:

Step-by-step explanation:

The measure of the length of arc with a cental angle of 50 degree and radius 7cm is approximately 35π/18 cm.

An arc length is simply the distance between two points along a section of a curve in a circle.

It can be expressed as:

Length of arc = θ/360 × 2πr

Where θ is the central angle in degree and r is the radius.

From the diagram:

Central angle θ = 50 degree

Radius r = 7 cm

Arc length = ?

Plug the given values into the above formula and solve for the arc length:

Length of arc = θ/360 × 2πr

Length of arc = 50/360 × 2 × π × 7cm

Length of arc = 35π/18 cm

Therefore, the arc length measures 35π/18 cm.

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Answer:

Tower is 9 ft tall when it is finished.

Step-by-step explanation:

Given that:

Height of the tower when Dominic takes a break = \(4\frac{1}{2}\) feet

The height of the tower as built by Dominic = \(\frac{3}8\) of the total height

Let the total height of the tower to be built = \(x\) feet

Let us have a look at the method to convert mixed fraction to a fractional number.

\(a\dfrac{b}{c} = \dfrac{a\times c +b}c\\\Rightarrow 4\dfrac{1}{2} = \dfrac{4\times 2 +1}{2}=\dfrac{9}2\)

As per question statement, \(\frac{3}8\) of the total height is equal to \(4\frac{1}{2}\) feet.

We can write the equation as:

\(\dfrac{3}{8}x = \dfrac{9}{2}\\\Rightarrow x = \dfrac{9}{2}\times \dfrac{8}{3}\\\Rightarrow x = \dfrac{72}{6}\\\Rightarrow x = \bold{9\ ft}\)

Therefore, tower is 9 ft tall when it is finished.

Eukaryotic cells have a true membrane-bound nucleus and prokaryotes do not.

Eukaryotic cells are larger than prokaryotic cells and have a “true” nucleus, membrane-bound organelles, and rod-shaped chromosomes. The nucleus houses the cell's DNA and directs the synthesis of proteins and ribosomes.

All cells have a plasma membrane, ribosomes, cytoplasm, and DNA. Prokaryotic cells lack a nucleus and membrane-bound structures. Eukaryotic cells have a nucleus and membrane-bound structures called organelles.

So..the answer should be Eukaryotic cells have a true membrane-bound nucleus and prokaryotes do not.

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Answer:

Prokaryotes

✔ do not have

a nucleus surrounding their chromosome of DNA.

Prokaryotes are

✔ more

simple cells than eukaryotes.

Prokaryotes have a

✔ cell wall

outside their cell membrane that gives protection and support.

Prokaryotes will often move by a tail-like

✔ flagellum

.

Step-by-step explanation:

Answer:

Imagie 1 and 2

monomial function graph look like this

<3 ily

Red

Answer:

The first image

Explanation:

Hope you have a great day!

Answer: 28282

Step-by-step explanation:

I think

If Archer can paint a room in 4 hours, while Ollie can do it in 3 hours. If they work together then it will take 206 minutes to paint two rooms.

What is the relation between work and time?

Work Problems are word problems that involve different people or entities doing work but at different rates.

Work = Efficiency x Time

According to the given question:

Archer paints a room in = 4 hours

Work done by him in an hour =1/4

Ollie paints a room in = 3 hours

Work done by him in an hour = 1/3

So, work done by them in an hour W = (1/4 +1/3)= 7/12.

They both will complete the work in = 1/W

= 1/7/12

= 12/7 hours

≈ 103 minutes

Therefore it take 103 minutes to paint one room together.

To paint two rooms it will take 103 x 2 = 206 minutes together.

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Answer: £2.4

Step-by-step explanation:

From the question, Erin buys 3 packs of potatoes costing £2 each, 4 packs of carrots for £2 per pack, and 4 turnips costing 90p each.

Total cost of potatoes = 3 × £2 = £6

Total cost of carrots = 4 × £2 = £8

Total cost of turnips = 4 × 90p = £360p = £3.6

The total cost of things bought by Erin will now be:

= £6 + £8 + £3.6

= £17.6

If she pays with a £20 note, she will collect a change of:

= £20 - £17.6

= £2.4

= 2 pounds, 40 pennies.

Answer:

C Hope this helps This may be wrong though

Step-by-step explanation:

Answer:

the length of the square is (2x+3)

Step-by-step explanation:

hope it helps<333

Answer:

225

Step-by-step explanation:

first the square

9*9 = 81

then the triangle

a is 8

triangles are l*w/2 so 8*4.5/2

8*4.5 = 36/2 = 18

There are 8 of these triangles

18*8 is 144

144+81 = 225

The surface area of the square pyramid is approximately `196` square cm.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

We can use the Pythagorean theorem to find the slant height of the pyramid:

\($$l = \sqrt{a^2 + \left(\frac{b}{2}\right)^2} \\= \sqrt{8^2 + \left(\frac{9}{2}\right)^2} \\= \sqrt{64+\frac{81}{4}} \\= \frac{\sqrt{433}}{2}$$\)

So, the lateral area of the pyramid is the area of the four triangles with base `b` and height `l`, which is:

\($$A_{lat} = 4\cdot\frac{1}{2}b\cdot l \\= 4\cdot\frac{1}{2}\cdot 9 \cdot \frac{\sqrt{433}}{2} \\= 27\sqrt{433}$$\)

So, The area of the base of the pyramid is a² then

\($$A = A_{lat} + a^2$$\)

=  = 27√433 + 8²

= 27√{433} + 64

= 196.4 cm²

Therefore, the surface area of the square pyramid is approximately `196` square cm.

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It would take roughly 13.86 times for the import values to coincide if the drop or growth in avocado exports to Spain and the United States.

To answer this question, we'd need to have specific data about the drop or growth rates of avocado exports to Spain and the United States in 2012, as well as the current import values for both countries. Without this information, it isn't possible to directly prognosticate how long it would take for the import values to coincide.

Assuming we have the necessary data, we can use the following formula to calculate the time it would take for the import values to coincide

t = ln( P2/ P1)/ ln( 1 r)

where t is the time it would take for the import values to coincide, P1 is the original import value, P2 is the final import value, and r is the growth rate.

For illustration, if we know that the original import value for avocado exports to Spain was$ 100 million in 2012, and it dropped at a rate of 5 per time, and the original import value for avocado exports to the United States was$ 200 million in 2012, and it increased at a rate of 10 per time, we can calculate how long it would take for their import values to coincide

For Spain P1 = $ 100 million, r = -0.05

For the US P1 = $ 200 million, r = 0.1

Assuming the final import values for both countries would be the same, we can set P2 equal to each other

ln( P2/$ 100 million)/ ln(0.95) = ln($ 200 million/ P2)/ ln(1.1)

working for P2, we get

P2 = $141.42 million

Substituting this value into the formula, we get

t = ln($141.42 million/$ 100 million)/ ln(0.95) = 13.86 times

thus, it would take roughly 13.86 times for the import values to coincide if the drop or growth in avocado exports to Spain and the United States, independently, continued as in 2012. still, this is just an academic illustration grounded on certain hypotheticals, and the factual time it would take for the import values to coincide would depend on the specific data for each country.

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The complete question in English is-

If the decrease or growth in avocado exports to Spain and the United States, respectively, continued as in 2012, how long would the export values coincide in both countries?

We take the value 2 for which y(2)=4 and \(y^{2}\)=2 and see that y(x)=\(x^{2}\) is a function and \(y^{2}\)=x is a relation.

Domain is the set of values that a variable can take in an algebraic expression.For the equation y(x)=\(x^{2}\), x can take any value from negative infinity to positive infinity so we can say that the domain for x is (-∞,∞). For the equation \(y^{2}\)=x, x can take any value greater than or equal to zero. Since x=\(y^{2}\) we can't take a negative value for x because squared numbers are always positive, so the domain of x will be [0,∞). The common domain for both the equations is [0,∞). Let us choose a value from this common domain,let's say 2. Then for

y(x)=\(x^{2}\)⇒y(2)=4 ...(i)

\(y^{2} =x\)=2 then y=±\(\sqrt{2}\)...(ii)

A function always has an output variable and one or more input variables.For first equation, y is the output variable and x is the input variable. A relation states that two expressions are equal and one is not dependant on another. For equation (i) y is dependant on x but in equation (ii) both the variables are independant.

Thus we can conclude that y(x)=\(x^{2}\) is a function and \(y^{2}\)=x is a realtion.

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Thus, the three terms of an arithmetic progression are (8, 13, and 18) or, (9, 13, and 17).

Let three terms of an arithmetic progression = (a - d), a, ( a + d)

According to the question:

The sum of three terms of an arithmetic progression = 39

∴  (a - d) + a + ( a + d) = 39

⇒ 3a = 39

⇒ a = 13

Also, The product of three terms of an arithmetic progression = 2145

∴  (a - d)a( a + d) = 2145

⇒ a(a^2 - d^2) =  2145

Put a = 13, and we get

d=4

Three terms of an arithmetic progression = (13 - 4), 13 and ( 13 + 4)

= 9,13,17

Put a = 13 and d = 4

Thus, the three terms of an arithmetic progression are (8, 13, and 18) or, (9, 13, and 17).

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