Romeo used a mirror to determine the height of Juliet’s window. He stood 0.5m from the mirror and the mirror is
5.0m away from Juliet’s window. If Romeo is 1.6m tall, how high is the window?

Step-by-step explanation:

1/2 as an exponential expression with a base of 2 can be written as:

\( \huge \purple{ {2}}^{ \red{\frac{1}{2} }} \)

Answer:

not simplified:12/14

reduced/simplified:6/7

Step-by-step explanation:

1/2 ÷ 7/12 =1/2×12/7=

1×12

-- -- = 12/14

2×7

and if simplified then you just do

12÷2=6

----

14÷2=7

In a Cartesian join, also known as a cross join, each row from the first table is combined with each row from the second table.

If the first table has 5 rows and the second table has 3 rows, the result of the Cartesian join will consist of 5 * 3 = 15 rows.

Answer:

1920

Step-by-step explanation:

Volume of larger rectangular prism: 10 * 8 * 14 = 1120

Volume of smaller rectangular prism: 10 * 10 * 8 = 800

Volume of whole prism: 1120 + 800 = 1920

Hence, your answer is 1920

Answer:

Step-by-step explanation:

So abc = 789.0

It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.

A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.

Now, consider an example;

When you wish to build a perpendicular line on a line segment, like line AB, you do the following;

A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.

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1) The first iteration, n, turns out to be (x1, y1) = ( , ).

2) If the second iteration, n, is (x2, y2) = ( , ).

To find the values of (x1, y1) and (x2, y2), we need additional information or the specific steps of the gradient method applied in MATLAB. The gradient method is an optimization algorithm that iteratively updates the variables based on the gradient of the function. Each iteration involves calculating the gradient, multiplying it by the learning rate (λ), and updating the variables by subtracting the result.

3) After s many iterations (and perhaps changing the value of λ to achieve convergence), it is obtained that the minimum is found at the point (xopt, yopt) = ( , ).

To determine the values of (xopt, yopt), the number of iterations (s) and the specific algorithm steps or convergence criteria need to be provided. The gradient method aims to reach the minimum of the function by iteratively updating the variables until convergence is achieved.

4) The value of the minimum, once the convergence is reached, will be determined by evaluating the function at the point (xopt, yopt). The specific value of the minimum is missing and needs to be provided.

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the complete question is:

Matlab The Gradient Method Was Used To Find The Minimum Value Of The Function North F(X,Y)=(X^2+Y^2−12x−10y+71)^2 Iterations Start At The Point (X0,Y0)=(2,2.6) And Λ=0.002 Is Used. (The Number Λ Is Also Known As The Size Or Step Or Learning Rate.) 1)The First Iteration N Turns Out To Be (X1,Y1)=( , ) 2)If The Second Iteration N Is (X2,Y2)=( ,

Matlab

The gradient method was used to find the minimum value of the function north

f(x,y)=(x^2+y^2−12x−10y+71)^2 Iterations start at the point (x0,y0)=(2,2.6) and λ=0.002 is used. (The number λ is also known as the size or step or learning rate.)

1)The first iteration n turns out to be (x1,y1)=( , )

2)If the second iteration n is (x2,y2)=( , )

3)After s of many iterations (and perhaps change the value of λ to achieve convergence), it is obtained that the minimum is found at the point (xopt,yopt)=( , );

4)Being this minimum=

Answer:

20

Step-by-step explanation:

just got it right on plato

Answer:

im pretty sure we need the previous value

The observed allele frequencies for the T102C locus are as follows: T allele frequency = 0.388 and C allele frequency = 0.612.


To calculate the observed allele frequencies, we divide the number of occurrences of each allele by the total number of alleles observed.

In this case, the T allele is observed in 108 TT genotypes and 194 TC genotypes, giving a total of 108 + 194 = 302 T alleles. Similarly, the C allele is observed in 194 TC genotypes and 48 CC genotypes, giving a total of 194 + 48 = 242 C alleles.

To calculate the T allele frequency, we divide the number of T alleles by the total number of alleles: 302 T alleles / (302 T alleles + 242 C alleles) = 0.388 (or approximately 0.39).

Similarly, the C allele frequency is calculated as: 242 C alleles / (302 T alleles + 242 C alleles) = 0.612 (or approximately 0.61).

Therefore, the observed allele frequencies for the T102C locus are T allele frequency = 0.388 and C allele frequency = 0.612.

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The nth term of the sequence can be expressed as: \(1 / (n^2)\)

The given sequence is: 1, 2, 1/3, 1/7, 1/25, 1/121, ...

To find an expression for the nth term of this sequence, we can observe that each term is the reciprocal of a specific pattern of numbers: 1, 2, 3, 4, 5, 6, ...

Notice that the numerator of each term follows a pattern of increasing consecutive positive integers: 1, 2, 3, 4, 5, 6, ...

The denominator of each term follows a pattern of perfect squares: \(1^2, 2^2, 3^2, 4^2, 5^2, 6^2, ...\)

Therefore, the nth term of the sequence can be expressed as:

\(1 / (n^2)\)

So, the expression for the nth term of the sequence is \(1 / (n^2)\). This formula will work for n = 1, 2, 3, and so on.

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For the system of linear equations 2- y = kx - y = k,

(a) The row-echelon form of the augmented matrix: [[1, -1, | 2], [0, k + 1, | -k]].

(b) k = -1 gives infinitely many solutions; for any other k, there is exactly one solution.

(a) To reduce the augmented matrix for the given system to row-echelon form, let's write the system of equations in matrix form. We have:

[[1, -1], [k, -1]] × \([x, y]^T\) = [2, k].

To perform row operations, we'll apply the following steps:

Step 1: Swap rows if necessary to make the first element of the first row non-zero.

Step 2: Multiply the first row by a constant to make the first element equal to 1.

Step 3: Add or subtract multiples of the first row from the subsequent rows to eliminate the first element in each row.

Let's apply these steps to the augmented matrix:

[[1, -1, | 2], [k, -1, | k]].

Step 1: No need to swap rows since the first element of the first row is already non-zero.

Step 2: Multiply the first row by 1/1 = 1:

[[1, -1, | 2], [k, -1, | k]].

Step 3: Subtract k times the first row from the second row:

[[1, -1, | 2], [k - k, -1 + k, | k - 2k]] = [[1, -1, | 2], [0, k + 1, | -k]].

The augmented matrix is now in row-echelon form.

(b) Let's analyze the row-echelon form to determine the values of k and the corresponding number of solutions.

From the row-echelon form, we can see that if k = -1, the second row becomes [0, 0, | 0]. This means the system has infinitely many solutions.

For any other value of k ≠ -1, the second row has a non-zero element, indicating that the system has a unique solution.

Therefore, the values of k are any real number except k = -1.

If k = -1, the system has infinitely many solutions.

If k ≠ -1, the system has exactly one solution.

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Answer:

$8170.10

Step-by-step explanation:

Given data

P=$3230

R= 5.8%

T= 16 years

The given expression for the account is

V = P*e^(rt)

substotute

V = 3230*e^0.058*16

V= 3230 e^ 0.928

V=3230*2.5294452249

V=$8170.10

Hence the balance is $8170.10

Answer:

8170.11

Step-by-step explanation:

3230e^0.058(16)

according to question the linearization of f(x) = x^(2/3) at a = 64 is:

l(x) = 16 + (1/6) * (x - 64)

To find the linearization of a function f(x) at a point a, we need to use the formula:

l(x) = f(a) + f'(a) * (x - a)

where f(a) is the value of the function at the point a, f'(a) is the derivative of the function evaluated at a, and (x - a) is the difference between x and a.

First, we need to find the value of f(a):

f(a) = a^(2/3) = 64^(2/3) = 16

Next, we need to find the derivative of f(x):

f'(x) = (2/3) * x^(-1/3)

Now, we evaluate f'(a):

f'(a) = (2/3) * 64^(-1/3) = (2/3) * (1/4) = 1/6

Finally, we can plug in these values into the formula for the linearization:

l(x) = 16 + (1/6) * (x - 64)

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Answer:

7+x

Step-by-step explanation:

You need to break down the question so starting with the word sum you know that it means addition. You then see the number 7 and addition so then you know thaat it is 7 plus something and then you can choose a variable and plug it in to be 7+x

Answer:

1: 5/6

2: 3 1/6

3: 12/25

hope this helps!!

p.s

    comment if wrong

Answer:

B

Step-by-step explanation:

I cant explain it but its B

Answer:

5

Step-by-step explanation:

subtract 192 from 379 and you get 187 so that is for adults then subtract 187 from 192 to get the answer which is 5

Answer:

i feel like kevin gates i dont get tired

Step-by-step explanation:

Answer:

11 peices left

Step-by-step explanation:

16-(2+3)

16-(5)

16-5=11

Answer:

Step-by-step explanation:

x + 300 =369

x = 69

subtract 300 on both sides

Hey there!

\(Answer:\boxed{x=69}\)

\(Explanation:\)

\(x+300=369\)

To solve, you can do 369 - 300.

\(369-300=69\)

Let's make x to 69 to see it it's true.

\(69+300=369\)

x = 69 is true.

\(\boxed{x=69}\text{ is your answer.}\)

Hope this helps!

\(\text{-TestedHyperr}\)

The difference between these two places is 14,776

What is difference?

The aim of finding the difference in math is to tell how many numbers lie between the two given numbers. The difference in math symbol is minus (-). Minuend is the first number in the subtraction sentence.

Given, the highest elevation = 14,494

lowest elevation = -282

Therefore, the difference is given as

highest elevation - lowest elevation = 14494 - (-282)

= 14776

Therefore, the difference is 14476.

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It may be necessary to use statistical methods to adjust for the missing data or to conduct additional analyses to assess the potential impact on the study findings.

Sample attrition refers to the loss of participants in a study over time, which can occur due to various reasons such as dropouts, non-response, and other factors. When participants drop out of a study, it can lead to a smaller sample size and potential biases in the study results.

Option D ("number of patients who drop out of a study") is the correct answer. Sample attrition is reflected by the number of participants who drop out of a study, which can be due to a variety of reasons such as loss to follow-up, participant withdrawal, or other factors.

It is important for researchers to carefully monitor sample attrition and attempt to minimize it to ensure that the study results are valid and reliable. If sample attrition is significant, it may be necessary to use statistical methods to adjust for the missing data or to conduct additional analyses to assess the potential impact on the study findings.

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AB and AC are equal in length and are represented by x, while BC (the hypotenuse) is √2 times the length of either leg.

We have,

The given triangle is an isosceles triangle.

So,

The angles opposite to the equal sides are equal.

The other angle = 90

Now,

The sum of the triangle = 180

So,

90 + 2x = 180

2x = 180 - 90

2x = 90

x = 45

Now,

In a right triangle with ∠A = 90 degrees, ∠B = 45 degrees, and ∠C = 45 degrees, we have a special case known as a 45-45-90 triangle.

In a 45-45-90 triangle, the sides are in a specific ratio: 1 : 1 : √2.

Let's use this ratio to find the lengths of the sides:

Since AB = AC, let's denote both lengths as x.

AB = AC = x

BC is the hypotenuse, which is √2 times the length of either leg:

BC = √2x

So, the lengths of the sides are:

AB = AC = x

BC = √2 * x

Therefore,

AB and AC are equal in length and are represented by x, while BC (the hypotenuse) is √2 times the length of either leg.

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Answer: 17

Step-by-step explanation: You take 47, multiply it by 2 and you should get 94. Subtract 128 and 94 which =34. Since the perimeter = 2 times the original width you divide that by 2 and get 17.

Step-by-step explanation:

\(P = 2w + 2l \\ P = 2(w + l) \\ 128 = 2(w + 47) \\ w + 47 = 64 \\ w = 17 \: cm\)

To use the ratio test, we need to take the limit of the absolute value of the ratio of consecutive terms:

| (n+1)th term / nth term | = | (n+1)!2(4n+3)x^n+1 / n!2(4n-1)x^n | = | (n+1)(n+2) / (4n+3)(4n+2) | * | x |

As n approaches infinity, the ratio simplifies to: | x | * 1/16

So, the ratio test tells us that the series converges when | x | < 16. The radius of convergence, R, is the distance from the center of the power series (which is 0) to the point where the series converges. So, R = 16.

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Answer:

1) slope is -1/3

2) slope is 3 or 3/1

3)slope is -3/2

4)slope is3/2

5)slope is 5/3

6)slope is 7/3

Step-by-step explanation:

The probability for the particle to exist between x=0 and x=L/3, when the quantum number n=3, is 1/9.

In quantum mechanics, a particle in a one-dimensional box of length L can only occupy certain discrete energy levels determined by the quantum number n. The energy levels are given by the equation En = (\(n^2\) * \(h^2\))/(8m\(L^2\)), where h is Planck's constant and m is the mass of the particle.

Given that the quantum number n = 3, we can determine the energy associated with this level as E3 = (\(3^2\) * \(h^2\))/(8m\(L^2\)).

The probability of finding the particle between x=0 and x=L/3 corresponds to the portion of the total probability density function (PDF) within that range. The PDF for a particle in a box is given by P(x) = |ψ\((x)|^2\), where ψ(x) is the wave function.

For the ground state (n = 1), the wave function is a sin(xπ/L) and the corresponding PDF is proportional to \(sin^2\)(xπ/L). For n = 3, the wave function becomes sin(3xπ/L), and the corresponding PDF is proportional to\(sin^2\)(3xπ/L).

To find the probability, we integrate the PDF from x=0 to x=L/3, which is equivalent to calculating the area under the PDF curve within that range. In this case, the integral is ∫[0 to L/3] \(sin^2\)(3xπ/L) dx.

Evaluating this integral gives us a result of 1/9, indicating that there is a 1/9 probability of finding the particle between x=0 and x=L/3 when the quantum number n=3.

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The missing lengths  in the triangles are h = 3/2√2 and b = 4√3

Triangle a and b

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

A special right triangle

For a right triangle with an angle of 45 degrees

The measure of the leg is

h = Hypotenuse/√2

So, we have

h = 3/√2

Evaluate

h = 3/2√2

For the other triangle, we have

sin(60) = b/6

So, we have

b = 6/sin(60)

Evaluate

b = 4√3

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The quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres. The total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.

To determine the quantity of fuel utilized by the water tanker in March 2022, we need to first calculate the total distance that the water tanker has covered in March 2022.

The total distance covered can be calculated using the formula:

distance = rate × time

From Annexure A, we can see that the water tanker was supplied to the construction site on the following dates in March 2022:

March 1, 2, 3, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29, 30, and 31

Counting the number of days, we get a total of 23 days. Since the water tanker was supplied every day, we can assume that it covered the same distance every day.

The rate of fuel consumption of the Mercedes water tanker averages 5 km/l, which means that it can travel 5 km for every litre of fuel it consumes. Therefore, the distance covered by the water tanker on a full tank of fuel is:

distance = rate × fuel capacity

= 5 km/l × 460 litres

= 2300 km

So, the total distance covered by the water tanker in March 2022 is:

distance = 23 days × 2300 km/day

= 52,900 km

Next, we can determine the quantity of fuel utilized by the water tanker in March 2022 using the formula:

quantity of fuel = distance ÷ rate

Using the values we have calculated, we get:

quantity of fuel = 52,900 km ÷ 5 km/l

= 10,580 litres

Therefore, the quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres.

To determine the total amount of money that was utilized on fuel for the water tanker in March 2022, we can multiply the quantity of fuel utilized by the fuel price in March 2022:

total cost = quantity of fuel × fuel price

From the problem statement, the fuel price in March 2022 was R19.55 per litre. Substituting the values we have calculated, we get:

total cost = 10,580 litres × R19.55/litre

= R206,929.00

Therefore, the total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.

Complete question:

Records of the number of water tankers that were supplied to the construction site appear in the calendar on ANNEXURE A. The water tanker has a fuel capacity of 460 litres. The rate of fuel consumption of the Mercedes water tanker averages 5 km/l. The prices of fuel per litre in March and June 2022 appear below. MARCH 2022 FUEL PRICES DIESEL 50 ppm (a 4. 1) (b ) COST R19,55 JUNE 2022 FUEL PRICES DIESEL 50 ppm Source: COST R24,14 Calculate the total distance that the water tanker has covered in March 2022. Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022. Determine the total amount of money that was utilized on fuel for the water tanker in March 2022​. Quantity of fuel utilized by water tanker March 2022

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Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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