A school is arranging a field trip to the zoo. The school spends 634.24 dollars on passes for 30 students and 2 teachers. The school also spends 256.20 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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We have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

To prove that the Newton-Raphson method for solving the equation \(x^k e^x = 0\), where k is a constant, is given by the formula

\(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,\)

we can start by considering the iterative process of the Newton-Raphson method.

Given an initial guess \(x_n\), we want to find a better approximation \(x_{n+1}\)that is closer to the root of the equation \(x^k e^x = 0.\)

The Newton-Raphson method involves the following steps:

Calculate the function value \(f(x_n) = x_n^k e^x_n\) and its derivative \(f'(x_n) = k x_n^(k-1) e^x_n.\)

Find the next approximation x_{n+1} by using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Let's apply these steps to our equation \(x^k e^x = 0\):

Calculate the function value and its derivative:

\(f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n\)

Find the next approximation x_{n+1} using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Substituting the function value and its derivative:

\(x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)\)

Simplifying the expression by combining like terms:

\(x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n\)

Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

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Answer:

Step-by-step explanation:

Tungsten is a very hard and strong metal that is commonly used in the production of various types of high-strength materials, such as steel alloys, filaments for incandescent light bulbs, and electrical contacts. Tungsten has the highest tensile strength of any metal, which means it can withstand the highest amount of stress without breaking or deforming. However, tungsten is not very resistant to corrosion, especially in the presence of oxygen. At high temperatures, tungsten can react with oxygen to form tungsten oxide, which can cause corrosion of the metal.

Tantalum, on the other hand, is a highly corrosion-resistant metal that is often used in applications where exposure to oxygen and other corrosive materials is a concern. Tantalum has a natural oxide layer on its surface that helps protect the metal from corrosion. This oxide layer is very stable and adheres strongly to the underlying metal, providing an effective barrier against oxygen and other corrosive substances. Tantalum also has a relatively high tensile strength, making it a good choice for applications where both strength and corrosion resistance are important considerations.

In summary, while tungsten has the highest tensile strength of any metal, it is not as resistant to corrosion as some other metals, such as tantalum. Tantalum is highly resistant to corrosion by oxygen and other corrosive substances, making it a good choice for applications where exposure to these materials is a concern. Tantalum also has a relatively high tensile strength, making it a good choice for applications where strength is important.

Answer:

stainless steel

Step-by-step explanation:

because it is made from uranium

The average rate of change of the function over the interval is 4

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

y = 4x + 1

The interval is given as

[-1, 1)

The function is a linear function

This means that it has a constant average rate of change

From y = 4x + 1, we have

Rate = 4

Hence, the rate is 4

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The measure of the new angle x on the ramp is 40 degrees

The figure represents the given parameter such that the toy car is on a ramp

As a general rule, we have

The sum of angles on a straight line equals 180

substitute the known values in the above equation, so, we have the following representation

x = 160 = 180

So, we have

x = 20

Increasing x by 20, we have

x + 20 = 40

Hence, the angle is 40 degrees

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The equation can you use to find the rental cost, d, of each day they used the RV is 895=8d+55

What does $895 comprises of?

The $895 paid  for the duration of the trip consists of the payments for the RV for 8 days and additional amount of $55 which is for the outdoors upgrade.

The equation that can be used to determine rental cost per , d , per day considers that the total rental cost is number of days, 8 days  multiply by the rental  cost per day, which is d, and also that the final $55 is specifically for outdoors upgrade

Total cost=d*8+$55

Remember total cost of the trip is $895

$895=8d+$55

Which we can rewrite the expression by ignoring the dollar sign as below:

895=8d+55

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Answer:

a) 99% of the sample means will fall between 0.933 and 0.941.

b) By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

(a) If the true mean is 0.9370 with a standard deviation of 0.0090 within what interval will 99% of the sample means fail?

Samples of 34 means that \(n = 34\)

We have that \(\mu = 0.937, \sigma = 0.009\)

By the Central Limit Theorem, \(s = \frac{0.009}{\sqrt{34}} = 0.0015\)

Within what interval will 99% of the sample means fail?

Between the (100-99)/2 = 0.5th percentile and the (100+99)/2 = 99.5th percentile.

0.5th percentile:

X when Z has a pvalue of 0.005. So X when Z = -2.575.

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(-2.575 = \frac{X - 0.937}{0.0015}\)

\(X - 0.937 = -2.575*0.0015\)

\(X = 0.933\)

99.5th percentile:

X when Z has a pvalue of 0.995. So X when Z = 2.575.

\(Z = \frac{X - \mu}{s}\)

\(2.575 = \frac{X - 0.937}{0.0015}\)

\(X - 0.937 = 2.575*0.0015\)

\(X = 0.941\)

99% of the sample means will fall between 0.933 and 0.941.

(b) If the true mean 0.9370 with a standard deviation of 0.0090, what is the sampling distribution of ¯X?

By the Central Limit Theorem, approximately normal, with mean 0.937 and standard deviation 0.0015.

The graph of a proportional relationship can be described as a graph that always starts at point zero and is always a straight line graph.

A straight line graph is defined as the type of graph that is also called a linear graph which shows a relationship between two or more quantities that uses a graphical form of representation.

There are some characteristics that shows that a graph is of proportional relationship which include the following:

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the HCF of the numbers 81 and 154 must be 1.

HCF means the highest common factor that the two numbers have between them. When the numbers are divided by HCF, they become composite numbers. It is the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

We are given two numbers:

81 and 154

We know that 81 is:

81 = 3 × 3 × 3 × 3

And 154 is:

154 = 2 × 7 × 11

We can see that both the numbers do not have any factor in common.

So, the highest common factor that is the HCF can be 1 only.

Therefore, the HCF of the numbers 81 and 154 must be 1.

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Answer:

y = 7

Step-by-step explanation:

3y + (y+1) + (4y-3) = 54

3y + y + 4y + 1 - 3 = 54

8y - 2 = 54

8y = 54 + 2

8y = 56

y = 56/8

y = 7

Check:

3*7 + (7+1) + ((4*7)-3) = 54

21 + 8 + 28-3 = 54

29 + 25 = 54

Answer:

other person is right he deserves a brain thing

Step-by-step explanation:

The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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Answer:  Vertex is (0,8)        

Answer:

wz is the corresponding part

Step-by-step explanation:

The corresponding parts between PQRS and WXYZ are, PQ corresponds to WX, QR corresponds to XY, RS corresponds to YZ, SP correspond, ds to ZW.

If PQRS is congruent (≅) to WXYZ, it means that the two figures are identical in shape and size. Each letter represents a corresponding part between the two congruent figures.

To find the corresponding parts, we can match the corresponding vertices of the polygons. Let's match the vertices of the polygons:

P corresponds to W.

Q corresponds to X.

R corresponds to Y.

S corresponds to Z.

Therefore, the corresponding parts between PQRS and WXYZ are:

PQ corresponds to WX.

QR corresponds to XY.

RS corresponds to YZ.

SP corresponds to ZW.

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Answer:

Step-by-step explanation:

f(x) = x^2

reflect along the x-axis

g(x) = -x^2

expand vertilcally by a factor of 1/3

g(x) = (-1/3) x^2

move horizontally 4 units to the left

g(x) = (-1/3) (x+4)^2

hope this helps

Answer:

B. The graph of G(x) is the graph of F(x) stretched vertically, flipped over the x-axis, and shifted 4 units to the left.

Step-by-step explanation:

The \(\frac{-1}{3}\) is less than one, making it stretch wider, and the (-) made it flip over the x-axis. The +4 in \((x+4)^2\) made the function on the graph shift 4 units to the left.

This makes the correct answer be "B."

If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

\(v^T A^T = \lambda v^T\)

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)

Now, for transpose of A:

\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)

The eigen vectors are:

\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

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Answer:

Did u mean triangle? There are no angles on a line.

Or do you mean two angles of 90 degrees?

Step-by-step explanation:

Answer:

Step-by-step explanation:10 quarters is $2.50

11 nickels is $0.55

14 dimes is $1.40

159 pennies is $1.59

Add the sum of all of those ($6.04) to the money that was originally in the bank acc.

6.04+46.76=52.80

Answer:52.80

At confidence, how large a sample should be taken to obtain a margin of error for the estimation of a population proportion? We now assume that past data are not available for developing a planning value for

Preliminary estimate for proportion (Not Known) is equal to 0.5

Margin of error = E = 0.03

Level of significance = 1-0.99 = 0.01

Z critical value is considered as (by using Z table) = 2.576

So, the sample size formula is taken as

n = [p(1 – p)]\(\left[Z/E]^{2}\)

=[0.5*(1-0.5)] [2.576/0.03]\(^{2}\)

=1,843.03                    

Hence, the sample size is approximately will be 1,844

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Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Answer:

It's C

Step-by-step explanation:

Because the angle measurements are the same on rectangles and they have the same side lengths but the one on the right is a smaller rectangle which its only half the side of the bigger one.  

Dy/dx = (dy/dt)/(dx/dt) denotes the slope of the tangent line of a parametric curve whose parametric equations are x = /(t) and y = g(t). Wherever dy/dt is zero and dx/dt is zero, a parametric curve has a horizontal tangent.

The x and y coordinates are defined as functions of t when parametric form is used to represent angles: Plot the entire circle by using the equations x = r cos t and y = r sin t. Polar equations are the name given to these parametric equations.

The given x=1+12+ dx=dt 0+12(1) =12

Parametric y Curve is as follows: ts-t dy 5t-1 dt z = ts+t dz dt 5t +1 (dz, dy, dz) = (12, 5t-1, St+1) dt 7 dt dt x = 13 =) When, 1+12 t = 13 12

(x(t), y(t), and z(t)) = (13,0,2) + + (12, 4, 6) x(t), y(t), and 2(t)) = (13+12t, ut, 2+ 6+) x(t) = 13+12t, y(t) = ut, 2(t).

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Full Question = Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

x = 1 + 12 t , y = t5 − t, z = t5 + t; (13, 0, 2)

x(t), y(t), z(t) =

Answer:

2)  Minimum = 15
     Lower Quartile = 19
     Median = 30.5
     Upper Quartile = 45
     Maximum = 62

3)  Minimum = 82
     Lower Quartile = 89
     Median = 99.5
     Upper Quartile = 112.5
     Maximum = 120

Step-by-step explanation:

A box and whisker plot (also known as a "box plot"), is a graph displaying the distribution of a set of data based on a five number summary.

\(\hrulefill\)

Given data set:

To calculate the values of the five-number summary, order the given data values from smallest to largest:

There are 10 data values in the data set, so this is an even data set.

As there are an even number of data values, the median is the mean of the middle two values, 30 and 31:

\(\sf Median=\dfrac{30+31}{2}=30.5\)

The lower quartile is the median of the data points to the left of the median. Therefore:

The upper quartile is the median of the data points to the right of the median. Therefore:

Therefore, the five-number summary of the given data set is:

To draw the box-and-whisker plot (see attachment 1):

\(\hrulefill\)

Given data set:

To calculate the values of the five-number summary, order the given data values from smallest to largest:

There are 12 data values in the data set, so this is an even data set.

As there are an even number of data values, the median is the mean of the middle two values, 99 and 100:

\(\sf Median=\dfrac{99+100}{2}=99.5\)

The lower quartile is the median of the data points to the left of the median. As there is an even number of data points to the left of the median, the lower quartile is the mean of the middle two values, 88 and 90:

\(\sf Lower\;Quartile=\dfrac{88+90}{2}=89\)

The upper quartile is the median of the data points to the right of the median. As there is an even number of data points to the right of the median, the upper quartile is the mean of the middle two values, 110 and 115:

\(\sf Upper\;Quartile=\dfrac{110+115}{2}=112.5\)

Therefore, the five-number summary of the given data set is:

To draw the box-and-whisker plot (see attachment 2):

Let's find this length first

6√2 is the hypotenuse, then

Then we can find x because

The length of x is

Answer:

Step-by-step explanation:

vdvfdvfdvfvfb fd

Option D. The mountainous geography of Athens influence the economy as The people of Athens relied on sea trade.

Greece's rugged terrain caused some areas, particularly Athens, to become dependent on trade. Many Greeks went on to become seafaring tradesmen and merchants. Greeks engaged in trade with other Mediterranean people for pottery, wine, and olive oil. They communicated with the outside world by sailing to neighboring islands.

The geography of the area influenced the ancient Greeks' political system and way of life. Mountains, seas, and islands formed natural barriers between the Greek city-states, forcing the Greeks to relocate to coastal areas.

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Answer:

here you go !!

hope his helps

For the given equation, the binomial factor is (5x² + 3).

In mathematics, the largest positive integer that divides each of the integers is known as the greatest common divisor of two or more integers that are not all equal to zero. The greatest common divisor of two numbers x and y

Factors in polynomial equations with exactly two terms are called binomial factors. Because binomials are simple to solve and their roots are the same as the polynomial's roots, binomial factors are fascinating. Finding a polynomial's roots begins with factoring it.

5x³ - 25x² + 3x - 15

Taking 5x² and 3 as common factors -

⇒ 5x² (x - 5) + 3 (x - 5)

GCF of 1 step is 5x²

⇒ (5x² + 3) (x - 5)

GCF of 2 step is 5x² + 3

Common binomial factor is (5x² + 3)

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