Find the dimensions of the rectangle of maximum area with perimeter 1000 feet. 2. You are to make a box with square base and no top. Find the dimensions that minimize the surface area of the box if the volume of the box is to be 32,000 cm3 3. The combined perimeter of a circle and a square is 16. Find the dimensions of the circle and square that produce a minimum total area. 4. Suppose you had to use exactly 200 m of fencing to make either one square enclosure or two separate square enclosures of any size you wished. What plan would give you the least area? What plan would give you the greatest area? 5. An architect is designing a composite window by attaching a semicircular window on top of a rectangular window, so the diameter of the top window is equal to and aligned with the width of the bottom window. If the architect wants the perimeter of the composite window to be 18 ft, what dimensions should the bottom window be in order to create the composite window with the largest area? 6. A geometry student wants to draw a rectangle inscribed in a semicircle of radius 8. If one side must be on the semicircle's diameter, what is the area of the largest rectangle that the student can draw?

The given statistic is said to be an "unbiased estimator". In this statistic, the mean is equal to the true value of the estimated parameter.

In a statistic, if the mean is equal to the estimated parameter, then that statistic is said to be an unbiased estimator. It is used to estimate a population parameter.

Consider a statistic.

"A statistic describes a portion of the target population".

"A parameter describes the whole population".

In a statistic, the mean of the sampling distribution is equal to the true value of the estimated parameter.

I.e., μ = E(x)

So, that statistic is said to be an unbiased estimator.

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The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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Answer:

I believe it's 2n+14

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

AB=6 therefore Pto Q should be 6

6^2=36

8^2=64

add them together

=100

square root 100=10

divide by 2=5

1 milligram = 0.001 gram

x milligrams = 6 grams

By crossmultiplying, it becomes

0.001 * x = 6 * 1

0.001x = 6

x = 6/0.001

x = 6000

The mass in milligrams is 6000 milligrams

The given statement "In the 1st law of thermodynamics for a CV, the W cv term includes all forms of power (rate of work) done on or by the CV EXCEPT flow work" is True because the first law of thermodynamics for a control volume (CV) states that the net change in energy within the CV is equal to the net energy transfer into or out of the CV, plus the net rate of work done on or by the CV.

The term W cv in this equation represents the net rate of work done on or by the CV, but it excludes flow work, which is the work done by or against the pressure forces as a fluid flows into or out of the CV.

However, it does not include flow work. Flow work represents the energy required to push the fluid into or out of the control volume. This energy is already accounted for separately in the enthalpy term within the 1st law of thermodynamics for a CV. Thus, the Wcv term does not include flow work. Therefore, W cv includes all forms of power (rate of work) done on or by the CV except flow work.

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Answer:

\(25+1*2=\)\(27\)

I think

Answer:

1570.796~

Step-by-step explanation:

v= πr² h/3

r is radius

h is height

v is volume

v=π*10² 15/3

v=π*10² *5

v=π*100 *5

v=π*500

v=1570.796~

Answer:

x = 9

Step-by-step explanation:

9x - 1 and 10 + 10x are same- side interior angles and sum to 180° , so

9x - 1 + 10 + 10x = 180

19x  + 9 = 180 ( subtract 9 from both sides )

19x = 171 ( divide both sides by 19 )

x = 9

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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Answer:

 z=  0.0000 - 2.0000 i

 z=  0.0000 + 2.0000 i

Step-by-step explanation: i used an algebraic calculator to find the two answers

Answer:

4/z + 4/3z - z/3= 0

12+4-z²/3z=0

12+4-z²=0

Z²=16

SO Z could be -4 or 4

I hope it helps❤

please give me brainliest

Answer:The answer is in the attached file below

Step-by-step explanation:

Answer:

angle 7=100 ,angle 8=80

Step-by-step explanation:

For angle 7:

By using definition of alternate interior angles:

angle 4=angle 6

Subtitute values of angles:

x+2y=3y+20

x+2y-3y=20

x-y=20.......(1)

Now by using definition of alternate opposite angles:

angle 4= angle 2

angle 2=x+2y

Angle 1 and angle 2 are the angles of straight line ,there sum will be 180.

2x+y+x+2y=180

3x+3y=180

x+y=60......(2)

Add (1) and (2):

x-y=20

x+y=60

_______

2x=80

x=40

subtitute x=40 in (2):

40+y=60

y=60-40

y=20

For angle 7:

By using definition of alternate exterior angle:

angle 1=angle 7

angle 7=2x+y

subtitute x and y:

angle 7=2(40)+20

=100

For angle 8:

By using definition of alternate opposite angle:

angle 8=angle 6

angle 8= 3y+20

angle 8=3(20)+20

=80

The solution of the given initial-value problem would be  y(x) = 3 cos(3x) + 2 sin(3x).

We are required to solve the given initial-value problem.

The initial value problem isy″ + 9y = 0, y(0) = 3, y′(0) = −6

To solve the initial-value problem, we follow these steps:

Step 1: We find the characteristic equation to be r² + 9 = 0.The roots of this equation are r = ±3i.Therefore, the general solution is

y(x) = c1 cos 3x + c2 sin 3x.

Step 2: We will use the initial conditions to find the values of c1 and c2.We know that y(0) = 3. Therefore,

3 = c1 cos 0 + c2 sin 0 ⇒ 3 = c1.

Using the second initial condition,y′(x) = -3c1 sin 3x + 3c2 cos 3x.

We know that y′(0) = −6.

Therefore,−6 = -3c1 sin 0 + 3c2 cos 0 ⇒ −6 = 3c2.

Therefore, c2 = −2.

Substituting the values of c1 and c2 in the general solution, we get

y(x) = 3 cos 3x − 2 sin 3x = 3 cos(3x) + 2 sin(3x).

Therefore, the solution of the given initial-value problem is

y(x) = 3 cos(3x) + 2 sin(3x).

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The empirical probability of drawing the cards will be 6 / 55.

The ratio of the number of outcomes in which a defined event occurs to the total number of trials, not in a theoretical sample space but in a real experiment, is the empirical probability, relative frequency, or experimental probability of an event.

Given that a card is drawn one at a time from a well-shuffled deck of 52 cards. In 13 repetitions of this experiment, 1 king is drawn.

The number of kings in a well-shuffled deck consists of 52 cards which is 4.

The number of ways of drawing consists of 4 kings in 13 repetitions which is ¹³C₄.

In 13 repetitions, 2 kings are drawn by ¹³C₂ ways,

The empirical probability will be calculated as,

P(E) = ¹³C₂ / ¹³C₄

P(E) = [ (13!) / (13-2)! ] ÷ [ (13!) / ( 13-4)!(4!) ]

P(E) = ( 4 x 3 ) / ( 11 x 10)

P(E) = 6 / 55

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Answer:

Scientific notation: 4 ⋅ 10 -4

expanded form: 0.0004

Answer:

A.

Step-by-step explanation:

the solution to a relation (like an equation, but also inequalities and so on) is the set of values that make the whole thing true (or consistent).

every other value is not a solution.

Answer:

A. n = 1/63

B. k = 13/3

C. g = 5

D. w = 21/17

Step-by-step explanation:

A. 9n = 15/7 - 2

9n = 15-14/7

9n = 1/7

n = 1/7 ÷ 9

= 1/7 × 1/9

n = 1/63

B. 1/3 = k - 4

1/3 + 4 = k

1+12/3 = k

13 /3 = k

k = 13/3

C. g - 2/5g = 3

5g-2g/5 = 3

3/5g = 3

g = 3 ÷ 3/5

= 3 × 5/3

= 15/3

g = 5

D. 3/7w + 2w = 3

3w+14w/7 = 3

17/7w = 3

w = 3 ÷ 17/7

= 3 × 7/17

= 21/17

w = 21/17

The simple interest rate of the loan is 8.8%. We can use the formula for simple interest to find the interest rate:

I = P * r * t

where I is the interest charged, P is the principal amount (the amount loaned), r is the interest rate, and t is the time period.

In this case, we know that P = $5,000, t = 2 years, and I = $880. Plugging these values into the formula, we get:

$880 = $5,000 * r * 2

Simplifying this expression, we get:

r = $880 / ($5,000 * 2)

r = 0.088 or 8.8%

Therefore, the simple interest rate of the loan is 8.8%.

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There will be 0.84% chances that resulting sequence in cat to occur.

Total number of nucleotides floating around = 10

Let the event of picking cat be "A"

Number of cat in group = 3

Probability of picking cat is picked at first position = P(A1) = 3 / 10

= 0.3

Probability of picking cat is picked at second position = P(A2) =  2 / 9

= 0.223

Probability of picking cat is picked at third position = P(A3) = 1 / 8

= 0.125

so , probability of picking cat in first position and again in second position and again in third position will be = P(A1) . P(A2) . P(A3)

= 0.3 × 0.223 × 0.125

= 0.0084 required probability

There will be 0.84% chances that resulting sequence in cat

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Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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Answer:

The “1” in the quotient represents the number of tens in each of the 5 groups.

Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.

Step-by-step explanation:

Given:

92÷5

Hailey's workings:

92 divided by 5.

5 goes into 9 1 time.

9 minus 5 = 4.

5 goes into 42 8 times.

42 minus 40 = 2.

The answer is 18 R 2.

The true statements about Hailey's work are:

The “1” in the quotient represents the number of tens in each of the 5 groups.

Since only 5 tens could be divided evenly among the groups, Hailey subtracted 5 from 9 to find out how many tens were left over.

Answer:

AB

I hope this helps you

:)

Answer:

Third option.

Step-by-step explanation:

\(5-2\left(3x-9\right)=-1\)

Use the distributive law: \(a(b-c)=ab-ac\)

\(5-2\times3x-\left(-2\right)\times9=-1\)

Double negative = Positive

\(5-6x+18=-1\)

According to fraction and ratio, second dog is 3/2 feet long.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

First dog is 5 feet long.

then,

5 feet is equal to 4/5 of the second dog's length.

multiply both sides by 5/4.

5/4 x 5 feet is the second dog's length.

The second dog is 25/4 feet long.

The second dog is 6(1/4) feet long.

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The equation for g(x) will be -x² + 16 + 8x

In the given graph of f(x) and g(x), we can clearly see following transformations happened in f(x) to become g(x):

Reflection over x-axis is given by a changing the sign of the function f(x), i.e.

g(x) = -f(x)

Horizontal left shift by c-units. Horizontal left shift is given by replacing x by x+c in the function f(x), i.e.

g(x) = f(x+c)

Thus on combining both the points we will get the equation of the g(x):

g(x) = f(x + 4)

g(x) = -(x + 4)².

g(x) = -(x² + 16 + 8x)

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The variance of the scores in a sample tends to be less than or equal to the variability of the scores in the population from which the sample was obtained.

When we take a sample from a population, it is expected that the variability within the sample will be somewhat representative of the variability in the population. However, due to the random nature of sampling, there is a chance that extreme scores or outliers in the population may not be fully captured in the sample, resulting in slightly reduced variability. Therefore, the sample variance typically provides an estimate that is close to the population variance but is generally smaller due to the potential sampling variability.

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The scale factor is 2 and center dilation is reduced.

The scale factor is a ratio that describes how much a figure has been enlarged or reduced. It is calculated by dividing the length of the corresponding sides of the original and dilated figures. If the scale factor is greater than 1, then the figure is enlarged, and if it is less than 1, then the figure is reduced.

To find the scale factor in an IXL dilations problem, you need to compare the corresponding sides of the original and dilated figures.

If the original figure has a side length of 4 units, and the dilated figure has a corresponding side length of 8 units, then the scale factor is 8/4=2. This means that the dilated figure is twice as large as the original figure.

The center of dilation is the point about which the figure is enlarged or reduced. It is the fixed point that remains unchanged during the dilation process.

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The radian measure of the central angle of a circle of radius r=90 inches that intercepts an arc of length s=130 inches is:

1.4444 radians.

To determine the radian measure of the central angle of a circle of radius r = 90 inches that intercepts an arc of length s = 130 inches, you can use the following formula:

θ = s/r

Where, θ = radian measure of the central angle of the circle of radius r.

s = length of the arc.

r = radius of the circle.

Substituting the given values,

θ = s/r

θ = 130/90

θ = 1.4444 radians (rounded to four decimal places).

Therefore, the radian measure of the central angle is approximately 1.4444 radians.

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