If a pen and a pencil cost £1.10 for both and the pen costs £1 more than the pencil, what is the cost of the pen?

Answer:

The answer is 17%

Step-by-step explanation:

The vertex of the parabola is of the form,

The vertex given is,

The general equation of parabola is

Here, p is the distance between vertex and focus.

Susbtitute the values,

The correct option is C.

Evaluating p(4) using Horner's algorithm:

1. To use Horner's algorithm, we write the polynomial in nested form as follows:

p(z) = ((3z - 7)z - 5)z^2 + (z - 8)z + 2

Now, we can evaluate p(4) by starting from the inside and working our way out:

p(4) = ((3(4) - 7)4 - 5)4^2 + (4 - 8)4 + 2

= (5)4^2 - 4 + 2

= 78

Therefore, p(4) = 78.

2. Finding the Taylor series expansion of p(z) about z0 = 4:

To find the Taylor series expansion of p(z) about z0 = 4, we need to compute the derivatives of p(z) at z0 = 4. First, we compute p'(z) = 6z^2 - 28z^3 - 10z^2 + 2z - 8, then p''(z) = 12z - 84z^2 - 20z + 2, p'''(z) = 12 - 168z - 20, and so on.

Using these derivatives, we can write the Taylor series expansion of p(z) about z0 = 4 as follows:

p(z) = p(4) + p'(4)(z - 4) + p''(4)(z - 4)^2/2! + p'''(4)(z - 4)^3/3! + ...

Substituting in the values we computed, we get:

p(z) = 78 + 10(z - 4) - 41(z - 4)^2/2! - 14(z - 4)^3/3! + ...

Therefore, the Taylor series expansion of p(z) about z0 = 4 is:

p(z) = 78 + 10(z - 4) - 20.5(z - 4)^2 - 2.333(z - 4)^3 + ...

3. Using Newton's method to find a root of p(z):

To use Newton's method to find a root of p(z), we start with an initial guess z0 = 4 and iterate the formula z1 = z0 - p(z0)/p'(z0) until we reach a desired level of accuracy.

4. We already computed p'(z) in part 2, so we can use the formula to compute z1 as follows:

z1 = z0 - p(z0)/p'(z0)

= 4 - (78 + 10(4) - 20.5(4 - 4)^2 - 2.333(4 - 4)^3)/[6(4)^2 - 28(4)^3 - 10(4)^2 + 2(4) - 8]

= 3.9167

We can continue to iterate using this formula to get better approximations for the root of p(z).

Horner's algorithm is a fast and efficient way to evaluate a polynomial at a particular point. It involves using the distributive property of multiplication to rewrite a polynomial in a nested form, then evaluating the polynomial from the inside out.

In this problem, we will use Horner's algorithm to evaluate p(4) for a given polynomial, find its Taylor series expansion about the point z0 = 4, and then use Newton's method to find an approximation for a root of the polynomial.

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Answer:

Hi how are you

Step-by-step explanation:

i thhink the answer is B if im wrong im srry

Answer:

i think it would be the first answer which is, 173 units

Answer:

Step-by-step explanation:

45° Corresponds to (π÷4) which is a remarkable measure

We are all supposed to learn by heart the values of it’s ‘sin’ , ‘cos’ , ‘tan’ and ‘cot’ .

the same apply to 30° (corresponds to (π÷6))

……………………………………………………………

So without a calculator:

tan 45° = 1

cot 45° = 1

sin 30°​ = 1/2

therefore ,

tan 45°.sin 30° - cot45°​ = 1 × (1÷2) − 1 = (1÷2) − 1 = −(1÷2) = −0.5

Answer:

p = 44cm

perimeter of a square = 4l

44/4 = 11

area = l²

area = 11²

area = 121cm²

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

20% is the same as 1/5, so we can multiply 11 by 5:

11*5=55

The required quadratic equation of h(x) is given as h(x) = (x + 1)² + 2. Option C is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The required function that shows the relationship shown in the table can be evaluated just by putting values in the function,
So by putting value in each function this values only satisfied in function,
h(x) = {x + 1}² + 2
As,
h(0) = 3
h(-1) = 2

Thus, the required quadratic equation of h(x) is given as h(x) = (x + 1)² + 2. Option C is correct.

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Answer:

The answer is A: x + 0

Step-by-step explanation:

I got it correct on Edge. Please give 5 stars and have a great day! :)

The translation of the x-coordinate is written as x⇒0 for the triangle ABC.

A translation in mathematics moves a shape left, right, up, or down but does not turn it. The translated (or image) shapes appear to be the same size as the original shape, indicating that they are congruent. They've just moved in one or more directions.

A coordinate system is a two-dimensional number line, such as two perpendicular axes. This is an example of a typical coordinate system: The horizontal axis is referred to as the x-axis, and the vertical axis is referred to as the y-axis.

Given that on a coordinate plane, triangle A B C has shifted 6 units up. The x translation for the triangle is zero.

The x-coordinate translation is written as,

x ⇒ 0

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The probability of rolling a sum of 5 on a standard pair of six sided dice is 1/9.

According to the given question.

A standard pair of dice is rolled.

So, the sample sapce for rolling a pair of dice = {(1,1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4),(5, 5),(5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

⇒ Total number of outcomes = 36

And, the outcomes for getting a sum of five on a sandard pair of six sided dice = {(2, 3), (3, 2), (4, 1), (1, 4)}

⇒ Total number of favorable outcomes = 4

As we know that " probability is the ratio of total number of favorable outcomes to the total number of outcomes".

Therefore,

The probability of rolling a sum of 5 on a standard pair of six-sided dice

= 4/36

= 1/9

Hence, the probability of rolling a sum of 5 on a standard pair of six sided dice is 1/9.

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Answer:

12

Step-by-step explanation:

2+2+2+2+2+2=12

6×2=12

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

$125

Step-by-step explanation:

11,000 - 9,500 = 1,500

1,500 / 12 = 125 (we use 12 because 12 months = 1 year)

Answer:

125

Step-by-step explanation:

took the test

Answer:

<     (less than)

Step-by-step explanation:

4.7*0.001 ___ 4

0.0047___4

0.0047 < 4

Answer:

Watermelon A weighs 2 kg, watermelon B weighs 4 kg and watermelon C weighs 10 kg.

Step-by-step explanation:

Watermelon A is 2 kg lighter than watermelon B and 5 times lighter than watermelon C. This means that:

A = B - 2

and

A = C / 5 => C = 5A

Watermelons A and C together are 3 times heavier than watermelon B. This means that:

A + C = 3*B = 3B

Put C = 5A:

A + 5A = 3B

6A = 3B

=> B = 6/3 A = 2A

=> A = 2A - 2

=> 2A - A = 2

=> A = 2 kg

B = 2 * 2 = 4 kg

C = 5 * 2 = 10 kg

Therefore, watermelon A weighs 2 kg, watermelon B weighs 4 kg and watermelon C weighs 10 kg.

Based on the information presented, the ratio represents 8th-grade baseball players to total athletes.

A ratio is a mathematical expression that shows the proportion or the number of a specific element in a category compared to the number of another element in the same category. For example, if you count the animals on a farm the ratio of cows to chickens can be 5:7, which means that for every 5 cows there are 7 chickens.

here, we have,

What does the ratio 5:73 mean?

5 : This is the number of baseball players who are in 8th-grade

73: This is the total of players. You get this number if you add all the numbers given.

Based on this, this ratio is comparing the number of baseball players and total players, which means the meaning of this ratio is " the ratio of 8th grade baseball players to total athletes".

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Answer: I just did

Step-by-step explanation:

(a) The vector u = 〈3, 4〉 can be expressed as the sum of the parallel component p = 〈7/2, 7/2〉 (parallel to v = 〈1, 1〉) and the orthogonal component n = 〈-1/2, 1/2〉 (orthogonal to v). (b) The vector u = 〈2, 2, 7〉 can be expressed as the sum of the parallel component p = 〈3, 3, 6〉 (parallel to v = 〈1, 1, 2〉) and the orthogonal component n = 〈-1, -1, 1〉 (orthogonal to v).

(a) To express vector u = 〈3, 4〉 as the sum u = p + n, where p is parallel to v = 〈1, 1〉 and n is orthogonal to v, we can use vector projection.

The parallel component p of u with respect to v can be found using the formula:

p = (u · v / ||v||²) * v

where · represents the dot product and ||v|| represents the magnitude of vector v.

Calculating p:

p = (u · v / ||v||²) * v

\(= ((3 * 1) + (4 * 1)) / (1^2 + 1^2)\) * 〈1, 1〉

= (3 + 4) / 2 * 〈1, 1〉

= 7/2 * 〈1, 1〉

= 〈7/2, 7/2〉

The orthogonal component n of u with respect to v can be found by subtracting the parallel component p from u:

n = u - p

= 〈3, 4〉 - 〈7/2, 7/2〉

= 〈6/2 - 7/2, 8/2 - 7/2〉

= 〈-1/2, 1/2〉

(b) To express vector u = 〈2, 2, 7〉 as the sum u = p + n, where p is parallel to v = 〈1, 1, 2〉 and n is orthogonal to v, we will use the same approach.

First, calculate the parallel component p:

p = (u · v / ||v||²) * v

\(= ((2 * 1) + (2 * 1) + (7 * 2)) / (1^2 + 1^2 + 2^2)\) * 〈1, 1, 2〉

= (2 + 2 + 14) / 6 * 〈1, 1, 2〉

= 18/6 * 〈1, 1, 2〉

= 〈3, 3, 6〉

Next, calculate the orthogonal component n:

n = u - p

= 〈2, 2, 7〉 - 〈3, 3, 6〉

= 〈2 - 3, 2 - 3, 7 - 6〉

= 〈-1, -1, 1〉

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Answer:

20 horses

Step-by-step explanation:

35 / 7 = 5

4 * 5 = 20

Best of Luck!

Answer:

6

Step-by-step explanation:

The estimated cost of producing the 15th unit is $10.30.

Given the following information about a process that makes high-end boards that get mounted on skateboards:Process starts with a unit cost of $13 for the first unit. Learning rate of LR = 0.90.

Solution :Let's use the learning curve formula to calculate the estimated cost of producing the 15th unit.C = a * N^b .Where:

C = cost per unit ,N = cumulative production volume, a = the unit cost of the first unit, b = log(LR) / log(2) = log(0.90) / log(2) = -0.152N = 15a = 13 (given)

Now, b = -0.152

Therefore ,C = 13 * (15)^(-0.152)C = 13 * 0.789C = 10.3 dollars.

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Answer:

56m^2

Step-by-step explanation:

The formula on getting the area of a rectangle is width x height. Therefore you just have to multiply 8 (height) to 7 (width). the answer is ^^^

Answer:

7×8 56

so it,s area should be 56

Answer:

B.

Step-by-step explanation:

To use the vertical line test, take a ruler or other straight edge and draw a line parallel to the y-axis for any chosen value of x. If the vertical line you drew intersects the graph more than once for any value of x then the graph is not the graph of a function.

Answer:

i believe the perimeter is 36 im sorry if its not correct

Step-by-step explanation:

simple adding

Answer:

add a pic

Step-by-step explanation:

The statement that Study 2, with a sample size of 100 bottles, is more likely to provide a more precise estimate of the mean caffeine content of the energy drink compared to Study 1 is true.

Based on the given information, the statement that is true is that Study 2, which uses a larger sample size of 100 bottles, is more likely to provide a more precise estimate of the mean caffeine content of the energy drink compared to Study 1, which uses a smaller sample size of 25 bottles.

When estimating a population parameter, such as the mean, using a sample, a larger sample size generally leads to a more accurate and precise estimate.

In this case, Study 2 has a larger sample size, which means it provides more information about the variability of the caffeine content in the energy drink.

With a larger sample, the estimate of the mean caffeine content is likely to have a smaller margin of error and be more representative of the true population mean.

On the other hand, Study 1 with a smaller sample size is more susceptible to sampling variability and may have a larger margin of error. This means that the estimate obtained from Study 1 may have more uncertainty and be less reliable compared to Study 2.

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There are an infinite number of planes that are orthogonal to a given plane in space, and this is due to the fact that a plane can be thought of as a flat surface that extends indefinitely in all directions.

Orthogonal Planes in Space: In three-dimensional space, a plane is said to be orthogonal to another plane if the two planes are perpendicular to each other, i.e., their normal vectors are perpendicular. Since the normal vectors of two orthogonal planes are perpendicular to each other, this means that the angle between them is equal to 90 degrees.

Given a plane in space, there are an infinite number of planes that are orthogonal to it. This is because a plane can be thought of as a flat surface that extends indefinitely in all directions.

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