This part has 3 problems of equal weight. Show all the work to get full credit

1. Consider the fixed-point iteration P_k= g(P_k), where g is continuously differentiable on [a, b].

(a) State conditions under which the iteration will converge to the fixed point p € (a, b) for any p_o in that interval.
(b) x= g(x) for g(x)=1/3x²-2/3x+4/3 has two fixed points: 1 and 4. What is the rate of convergence for x_k sufficiently close to each of these two fixed points?

Answer:

Yes

Step-by-step explanation:

Well to figure out if 210879 is divisible by 3 we do,

210879 / 3

= 70 293.

Thus,

210879 is divisible by 3.

Hope this helps :)

Answer: Yes

Explanation: To determine whether 210,879 is divisible by 3, first we need to find the sum of the digits.

Image is provided below.

The divisibility rules tell us that if the sum of the digits is divisible by 3,

then the number is also divisible by 3.

So since 27 is divisible by 3, 210,879 must also divisible by 3.

So our answer is yes, 210,879 is divisible by 3.

To calculate the equation of the tangent plane to the surface \(z = x^2 + y^2 + 1\) at the point (1, 1, 3), we can use the concept of partial derivatives. The equation of the tangent plane is in the form \(ax + by + cz = d\) with \(a \geq 0\), and any common factors should be reduced.

The equation of a plane can be determined using the gradient vector of the surface function evaluated at the given point. In this case, the gradient vector of \(z = x^2 + y^2 + 1\) is \(\nabla f(x, y) = \langle 2x, 2y, -1 \rangle\). Evaluating it at (1, 1, 3) gives \(\nabla f(1, 1) = \langle 2, 2, -1 \rangle\).

Using the point-normal form of a plane equation, we can write the equation of the tangent plane as \((x - 1)2 + (y - 1)2 - (z - 3) = 0\). Expanding this equation gives \(2x + 2y - z = -2\), which can be rearranged as \(2x + 2y + (-1)z = -2\).

Therefore, the equation of the tangent plane to the surface \(z = x^2 + y^2 + 1\) at the point (1, 1, 3) is \(2x + 2y - z = -2\), with \(a = 2\), \(b = 2\), \(c = -1\), and \(d = -2\).

To know more about tangent plane here: brainly.com/question/33052311

#SPJ11

Answer:

no it is not literal

Step-by-step explanation:

because no matter what you do you will just get whats in the picture sorry it wouldnt let me type it

The equation z = 4x + 9y is a literal equation because the literal equation is an equation that contains more than one variable.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The equation is:

z = 4x + 9y

As we know, the literal equation is an equation that contains more than one variable.

In the equation z = 4x + 9y there are three variables then it is literal.

Thus, the equation z = 4x + 9y is a literal equation because the literal equation is an equation that contains more than one variable.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ2

The measures of angles C and D are 70° and 100°, respectively.

Understanding angles is a fundamental concept in geometry. A quadrilateral is a polygon with four sides, and its angles are essential to determining its properties.

Let's start by labeling the angles in the quadrilateral. We know that two angles measure 100° and 90°, so let's label them as A and B, respectively. The other two angles, which we are trying to find, can be labeled as C and D.

Now, we are given that the ratio of angles C and D is 7:10. This means that we can write the following equation:

C/D = 7/10

We can use this equation to solve for one of the angles. Let's choose angle C. We can rewrite the equation as:

C = (7/10)D

We also know that the sum of the angles in a quadrilateral is 360°. Therefore, we can write another equation:

A + B + C + D = 360°

We can substitute the values we know into this equation and solve for angle D:

100° + 90° + (7/10)D + D = 360°

Simplifying the equation:

(17/10)D = 170°

D = 100°

Now that we know the value of angle D, we can use the equation we derived earlier to find the value of angle C:

C = (7/10)D = (7/10) x 100° = 70°

To know more about angles here.

https://brainly.com/question/4316040

#SPJ4

Answer:

x = 11/8

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

2×(4 +3) =(2 ×4) +3

2 ×7 =8 +3

14 =11

False

Step-by-step explanation:

.5miles = 2640 ft

tan a = 2640/1390

a - angle of descent

a = 62.22

The formula for the general term an of the sequence is an = 2n + 3.

Given that the pattern of the first few terms continues.

To find a1, we can substitute n=1 in the formula and use the first term of the sequence, which is 5:

a1 = 5

Therefore, the general term of the sequence is:

an = 5 + 7(n-1) = 7n - 2

The given sequence has a common difference of 7 that is each term in the sequence is obtained by adding 7 to the previous term.

Therefore, the formula for the general term an can be obtained as:

an = a1 + (n - 1)d

where a1 is the first term of the sequence and d is the common difference.

Here, a1 = 5 and d = 7. Substituting these values in the formula, we get:

an = 5 + (n - 1)7

Simplifying this expression, we get:

an = 2n + 3

Therefore, the formula for the general term an of the sequence is          an = 2n + 3

Know more about sequence here:

https://brainly.com/question/7882626

#SPJ11

Combinations exist ways to select elements from a collection in mathematics where the order of the selection exists irrelevant. He can choose the question in 28 ways.

Combinations exist mathematical operations that count the number of potential configurations for a set of elements when the order of the selection exists is irrelevant. You can select the components of combos in any order.

The combination formula is used to determine how many options there are for choosing things from a collection so that the order in which they are chosen is irrelevant. Combination, to put it simply, is the choosing of items or things from a bigger group when the order doesn't important.

Given: Number of questions in part A = 10

Number of questions in part B = 10

A student chooses 7 from part A and 4 from part B

Required number of ways = ( 10C7 × 10C4) × ( 10C3 × 10C6)

= 5040 × 24/ 6 × 720

= 28

He can choose the question in 28 ways.

To learn more about factorial, refer to:

https://brainly.com/question/25997932

#SPJ4

The median number of employees in Seattle's industries, as indicated by the dot plot, is around 800 thousand.

According to the dot plot, the median number of employees in Seattle's industries is approximately 800 thousand. The dot plot displays the recorded data rounded to the nearest 10,000, so we can determine the median by finding the middle value in the dataset. As there are an equal number of dots on either side of the median, we locate the central dot, which represents the median value. In this case, it falls on or near the 80th position on the dot plot, which corresponds to the value of 800 thousand employees.

The median number of employees in Seattle's industries, as indicated by the dot plot, is around 800 thousand. The median represents the middle value in a dataset and is a robust measure of central tendency that is less influenced by extreme values or outliers. By examining the dot plot and identifying the position of the central dot, we can approximate the median as 800 thousand employees.

Learn more about median here:

https://brainly.com/question/300591

#SPJ11

Answer:

Loan Amount= $4500

Monthly Payment= $600

9 months= $600*9= $5400

Interest = $5400-$4500= $900

The probability that the system will work is approximately 0.7267, or 72.67%.

To calculate the probability that the system will work, we need to consider the probabilities of each component working and combine them using the principles of probability theory.

Let's break down the problem step by step:

Probability of the key working: The given probability of the key working is 0.826. This means there is an 82.6% chance that the key will function properly.

Probability of the battery working: The given probability of the battery working is 0.971. This means there is a 97.1% chance that the battery will function properly.

Probability of the wire working: The given probability of the wire working is 0.890. This means there is an 89% chance that the wire will function properly.

Probability of the plug working: The given probability of the plug working is 0.954. This means there is a 95.4% chance that the plug will function properly.

To calculate the probability that all components work together, we multiply these individual probabilities:

Probability of the system working = Probability of key working× Probability of battery working× Probability of wire working× Probability of plug working

Probability of the system working = 0.826× 0.971× 0.890 ×0.954

Calculating this expression, we find:

Probability of the system working ≈ 0.726656356

Therefore, the probability that the system will work is approximately 0.7267, or 72.67%.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Answer:

5/12

Step-by-step explanation: I used a calculator

The number of bacteria in the petri dish after 24 hours will be y = 125 + 24x

Given is Gina was working in the laboratory on an experiment involving the population of bacteria. Her initial starting amount in a petri dish was 125 bacteria.

Assume that each hour the bacteria rises by [x] bacteria per hour. Then,

the number of bacteria in the petri dish after 24 hours will be -

y = 125 + 24x

Therefore, the number of bacteria in the petri dish after 24 hours will be y = 125 + 24x.

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ1

The length of the chord RT, PQ, and RS will be 5, 14, and 13. Then the correct option is C.

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

The graph is given below.

The ratio will remain constant. Then we have

y/10 = 4/8

    y = 5

Then the length of PQ will be

PQ = 4 + 10

PQ = 14

Then the length of RS will be

RS = 5 + 8

RS = 13

More about the circle link is given below.

https://brainly.com/question/11833983

#SPJ1

We can see here that the factor pairs of 16 are:

(1, 16), (2, 8), (4, 4).

The different ways Kevin and his friends could divide into groups are:

(1, 15), (2, 8), (4, 4).

Factors are numbers that can be divided into a larger number without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12 because each of these numbers can be divided into 12 with no remainder. Factors are used in mathematics to simplify or evaluate expressions and to find common denominators in fractions.

16 is an odd number of factors because it is a square number.

A square number is a number that can be written as the product of an integer multiplied by itself.

For example, 16 can be written as 4 x 4. Every square number has an odd number of factors because it has one more factor than its square root, which is an integer (e.g 4 in this case). So, 4 x 4 = 16 has 5 factors (1, 4, 2, 8, 16) which is an odd number.

Yes, you can stop checking for factor pairs when you find a pair that repeats. This is because when you find a pair that repeats, you have reached the square root of the number, so you have already found all the factors.

For example, in the case of 16, the square root is 4, so when you find the pair (4, 4), you can stop looking because you have already found all of the factors.

Learn more about factors on https://brainly.com/question/219464

#SPJ1

Part A:

The new deck will be a 4:5 scaled version of the original deck. This means that every dimension of the new deck will be 4/5 times the corresponding dimension of the original deck.

The original deck has a base of 15 feet and a height of 9 feet.

The new deck will have a base of (4/5) * 15 = 12 feet and a height of (4/5) * 9 = 7.2 feet.

Therefore, the dimensions of the new deck are 12 feet for the base and 7.2 feet for the height.

Part B:

To find the area of the original deck, we use the formula for the area of a triangle:

Area = (1/2) * base * height = (1/2) * 15 * 9 = 67.5 square feet.

To find the area of the new deck, we use the same formula with the new dimensions:

Area = (1/2) * 12 * 7.2 = 43.2 square feet.

Therefore, the area of the original deck is 67.5 square feet, and the area of the new deck is 43.2 square feet.

Part C:

The ratio of the areas is:

Area of new deck / Area of original deck = 43.2 / 67.5

Simplifying this fraction, we get:

Area of new deck / Area of original deck = 8 / 15

The scale factor is 4/5, which simplifies to 8/10 or 4/5.

Comparing the ratio of the areas to the scale factor, we see that:

Area ratio / Scale factor = (8/15) / (4/5) = (8/15) * (5/4) = 1

Therefore, the ratio of the areas is equal to the scale factor. This makes sense since the area of a triangle is proportional to the square of its dimensions. In this case, the scale factor is applied to both the base and the height, so the area ratio is equal to the scale factor squared, which is 16/25.

Answer:

Step-by-step explanation:

Part A: To find the dimensions of the new deck, we need to scale the base and height of the original deck by a factor of 4:5.

Scaling factor = 4/5

New base = 15 * (4/5) = 12 feet

New height = 9 * (4/5) = 7.2 feet

Therefore, the dimensions of the new deck are 12 feet for the base and 7.2 feet for the height.

Part B: The area of the original deck can be found by using the formula for the area of a triangle:

Area = (1/2) * base * height = (1/2) * 15 * 9 = 67.5 square feet.

The area of the new deck can also be found using the same formula:

Area = (1/2) * base * height = (1/2) * 12 * 7.2 = 43.2 square feet.

Part C: The ratio of the areas of the two decks can be found by dividing the area of the new deck by the area of the original deck:

Ratio of areas = (43.2 / 67.5) ≈ 0.64

The scale factor is 4:5 or 0.8.

Comparing the ratio of areas to the scale factor:

Ratio of areas / scale factor = (0.64 / 0.8) = 0.8

The ratio of the areas divided by the scale factor is equal to 0.8, which makes sense since the scale factor is the factor by which the dimensions were scaled up, and the ratio of areas tells us how much the area was scaled up.

Using z - score the minimum score required for the scholarship is 31.8

Since ACT Reading scores are normally distributed with a mean of 21.3 and a standard deviation of 6. Since a university plans to award scholarships to students whose scores are in the top 4%. To find the minimum score required, we use the z-score.

Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. It is given by

z = (x - μ)/σ where

Since we require x, making x subject of th formula, we have

x = σz + μ

Since  ACT Reading scores are normally distributed with a mean of 21.3 and a standard deviation of 6. Since a university plans to award scholarships to students whose scores are in the top 4%, we have that

For the minimum score p value = 4% which is in the 100 - 4 = 96 percentile.

So, the p value , p = 0.96. Thus the z-score z = 1.75

So, substituting these into the equation for x , we have

x = σz + μ

x = 6 × 1.75 + 21.3

x = 10.5 + 21.3

x = 31.8

So, the minimum score is 31.8

Learn more about minimum score here:

https://brainly.com/question/12992229

#SPJ1

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To know more about probability visit :

https://brainly.com/question/13604758

#SPJ11

Answer:

list in the explanation

Step-by-step explanation:

BOOT x2

SKINNY x2

RELAXED x2

BOOT, SKINNY

BOOT, RELAXED

SKINNY, BOOT

SKINNY, RELAXED

RELAXED, BOOT

RELAXED, SKINNY

The solution set is given by Set A = { BB , SS , RR , BS , BR , SR } , where B , S and R are boot cut (B), skinny (S), and relaxed fit (R) respectively

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the set be represented as A

Now , the equation will be

Marcus is shopping for pants and the available pants are boot cut (B), skinny (S), and relaxed fit (R)

He wants to buy 2 pair of pants , and the possible ways of 2 pants are

Set A = { BB , SS , RR , BS , BR , SR }

So , the total number of elements in set A = 6 pairs

Therefore , the value of A is 6 pairs

Hence , the set A is { BB , SS , RR , BS , BR , SR }

To learn more about sets click :

https://brainly.com/question/28278437

#SPJ2

We find that the approximation converges to 9.74679419, accurate to eight decimal places. So, the square root of 95, approximated using Newton's method, is 9.74679419.

Newton's method is a way to approximate the roots of a function. In this case, we want to approximate the square root of 95 correct to eight decimal places. To use Newton's method, we start with an initial guess and then apply the following formula repeatedly:
x1 = x0 - f(x0) / f'(x0)
where x0 is our initial guess, f(x) is the function we are trying to find the root of (in this case, f(x) = x^2 - 95), and f'(x) is the derivative of f(x) (which is 2x).
Let's start with an initial guess of 10:
x1 = 10 - (10^2 - 95) / (2 * 10) = 5.75
We can continue this process, plugging in our new guess into the formula each time, until we reach a value that is accurate to eight decimal places. After a few iterations, we get:
x8 = 9.74679434
This is our final answer, correct to eight decimal places.
Using Newton's method, we can approximate the square root of a number, such as 95, to eight decimal places. Newton's method is an iterative process that starts with an initial guess and refines the guess using the formula:
x1 = x0 - f(x0)/f'(x0)
For square root approximation, f(x) = x^2 - a, where a is the number we want to find the square root of (95 in this case), and f'(x) = 2x.
Let's start with an initial guess x0 = 9 (since 9^2 = 81 is close to 95). We can then perform the following iterations:
1. x1 = 9 - (9^2 - 95)/(2*9) ≈ 9.72222222
2. x2 = 9.72222222 - (9.72222222^2 - 95)/(2*9.72222222) ≈ 9.74679424
3. x3 = 9.74679424 - (9.74679424^2 - 95)/(2*9.74679424) ≈ 9.74679419
Continuing this process, we find that the approximation converges to 9.74679419, accurate to eight decimal places. So, the square root of 95, approximated using Newton's method, is 9.74679419.

To know more about Decimal visit:

https://brainly.com/question/680614

#SPJ11

SOLUTIION

The given equations are

This further gives

Therefore the solutions are:

From the option considering the value q=8, it follows

And

Therefore the solution is

Under division, the set of polynomials is not closed. In that, they are closed under addition, subtraction, and multiplication, polynomials constitute a system like the system of integers.

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

The word polynomial is pronounced as "many terms" since it comes from the Greek words "poly," which means "many," and "nominal," which means "terms." A polynomial is not infinite, although it can have any number of terms.

To learn more about polynomials, visit the link below:

brainly.com/question/27800603

#SPJ4

Answer:

6*10^-4 has a greater value.

Step-by-step explanation:

7*10^-9=   0.000000007

6*10^-4=   0.0006

Answer:

The complete factored form of the given \(f(x)\) is \((x+5)(x^2+16)\).

Step-by-step explanation:

Answer:

f(x)=x*3+5x+2+16x+80 y=x*3+5x*2+16x+80 x=y*3+5y*2+16y+80=8 3y+10y+16y+80=x29y+80=x29y=x-80y=1/29x-80/29 f(x)-1=1/29x-80/29

The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

Using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).

So, candidate A has a projection of winning 53% votes.

A sample of 2436 voters is pulled, then:

Can candidate A be guaranteed 95% votes which are:

Difference: 2,314 - 1,291 = 1,023

Therefore, using percentages we can conclude that 95% of votes that is 2,314 votes (B) cannot be guaranteed which is 1,023 votes more than the projected 53% winning votes (1,291 votes).

Know more about percentages here:

https://brainly.com/question/9553743

#SPJ13

Answer:

Correct option: First one -> 16 mm

Step-by-step explanation:

The equilateral triangle has its three sides with the same length.

So if the perimeter is 96 mm, we have:

\(Perimeter = 3*side\)

\(3*side = 96\)

\(side = 32 mm\)

The segment MA is the height of the equilateral triangle, and its length can be calculated with the equation:

\(height = \frac{side * \sqrt{3}}{2}\)

\(height = 16\sqrt{3}\)

Using the Pythagoras' theorem in the triangle ACM, we have:

\(side^2 = MC^2 + height^2\)

\(1024 = MC^2 + 768\)

\(MC^2 = 256\)

\(MC = 16\ mm\)

Correct option: First one

Answer:

(A) 16mm

Step-by-step explanation: