Use Newton's method to approximate the zero(s) of the given function to five decimal places. Restrict the domain to the given interval where indicated.

f(x)=x^3-x+2
f(x)=2x^3 + x^2 −5x+1
f(x)=x^4 - 6.1x^3 +4.7x^2 -12.2x+5.4
f(x)=0.25x^4-2x^2+x+0.69
f(x)= x^5 +x+1

The distance from home plate to second base is 180 feet, which is double the distance from home plate to first base.

A baseball diamond is a square with four bases, with home plate in the middle. 90 feet separate first base from home plate, and 90 more feet separate first base from second base. Therefore, the total distance from home plate to second base is twice that distance, or 180 feet. The same applies to all of the bases; the distance between them is always 90 feet, so the total distance from home plate to any base is twice that of the distance from home plate to first base. This means that the distance from home plate to second base, third base, and home plate is all 180 feet.

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Eliza is 212 feet above the ground as the given sector area of the half of the wheel is 5618 pi ft^2 and ride is stuck at 180 degrees.

Ferris wheel has a shape of a circle

So, we can use this formula

Area = πr²

Sector area of half the circle = πr²/2

From Eliza to the ground is the diameter of the wheel

5618 π ft² = πr²/2

r² = √2×5618ft²

r = 106 feet

The diameter of the wheel is twice the radius

= 2 × 106 feet = 212 feet

Therefore, Eliza is 212 feet above the ground.

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The required life is any living thing that has the property to be born, grow and end of the life cycle is life.

Any object that has characteristics of life is called living a being.

Here,

Life can be defined as the ability for growth, response to encouragements, metabolism, energy vitality and reproduction are characteristics that set life apart from matter that lacks biological activities, such as signaling and self-sustaining processes.

Thus, the required life is any living thing that has the property to be born, grow and end the life cycle is life.

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The amount of water in the pond per hour is 300 liters per hour

From the graph, we have the following points:

(x,y) = (0,100) and (1,400)

This means that:

The amount of water per hour is the calculated using:

Rate = (y2 - y1)/(x2 - x1)

Substitute known values

Rate = (400 - 100)/(1 - 0)

Evaluate the quotient

Rate = 300

Hence, the amount of water in the pond per hour is 300 liters per hour

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Answer: y= 4x -7

Step-by-step explanation:  

The maximum number of possible effects that could be tested in a 2x2x2 factorial design with 3 main effects, 3 two-way interactions, and 1 three-way interaction is 7.

In a 2 x 2 x 2 factorial design, we can test the following maximum number of possible effects:
Main effects:

There are 3 main effects in this design, one for each factor (A, B, and C). You would analyze the effect of each factor independently on the outcome variable.

Two-way interactions:

There are 3 possible two-way interactions that can be tested in this design: AxB, AxC, and BxC.

These interactions examine the combined effects of two factors on the outcome variable.
Three-way interactions:

There is 1 possible three-way interaction that can be tested in this design: AxBxC.

This interaction examines the combined effect of all three factors (A, B, and C) on the outcome variable.

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A higher margin of error indicates that the estimate is less accurate. The confidence interval gives us a range of values for the true population proportion.

a. Sample proportion (p)The sample proportion (p) refers to the number of individuals in a population who possess a particular trait divided by the entire population size. It is calculated by dividing the number of people who prefer balancing the United States government's budget by raising taxes by the total number of people surveyed, thus:

p = 702/1200 = 0.585. b.

Normality conditions Yes, the normality conditions are met since np and n (1 - p) are greater than

10:np = 1200(0.585) = 702n (1 - p) = 1200(1 - 0.585) = 498.

Therefore, the sample size is large enough, and both conditions are met.C. Critical z-score (Z)The significance level is 5%, which corresponds to the standard normal distribution Z value of 1.96. This is because 95% of the normal distribution falls within 1.96 standard deviations from the mean (0).D. Margin of error (E)Using the sample proportion (p) and the significance level Z, the margin of error can be determined as follows:

E = Z*square root[p(1 - p) / n] = 1.96*square root (0.585)(1 - 0.585) / 1200] = 0.036. E = 0.036 (or 3.6%)

means that the estimate of the percentage of individuals who would prefer balancing the budget by raising taxes has an error of plus or minus 3.6%. Therefore, the actual percentage of individuals who prefer raising taxes could be between

58.5% ± 3.6% (54.9%, 62.1%).

E. Confidence interval (write as an interval)The 95% confidence interval can be expressed as

0.585 ± 0.036 (54.9%, 62.1%).

The interpretation of this interval is that if we were to randomly draw a sample of 1,200 individuals from the population many times and calculate the proportion of individuals who prefer balancing the budget by raising taxes each time, 95% of these intervals would contain the true proportion. Therefore, we can be 95% confident that the true proportion of individuals who would prefer raising taxes falls between 54.9% and 62.1%.f. The margin of error is a crucial concept that is used to measure the precision of an estimate. A higher margin of error indicates that the estimate is less accurate. The confidence interval gives us a range of values for the true population proportion.

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The number of hours Natalie worked babysitting last week is 6hrs and the number of hours she worked landscaping last week is 2 hrs.

Let x be the number of hours Natalie worked babysitting and y be the number of hours she worked landscaping. Then, the total earnings were 11x + 10y = $86.

Also, x = 3y, because she worked 3 times as many hours babysitting as she did landscaping.

Substitute x = 3y into the first equation:

11(3y) + 10y = $86

Expanding the first term we get,

33y + 10y = $86

Combining terms,

43y = $86

Dividing both sides by 43 we get,

y = $2

So, Natalie worked y = 2 hours of landscaping.

To find the number of hours she worked babysitting, substitute y = 2 into x = 3y as follows -

x = 3(2) = 6

So Natalie worked x = 6 hours babysitting.

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b < 45 represents the inequality of how many books can be put on the shelves.

An inequality is a mathematical statement that shows the relative size or ordering of two values. It is represented using symbols such as "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), and "≠" (not equal to).

The inequality that represents how many books can be put on the shelves is:

b < 45

This inequality states that the number of books to be shelved, represented by b, must be less than 45 in order to fit on the bookshelf.

The inequality "b > 45" would represent a scenario in which the number of books to be shelved is greater than 45, which is not possible given the constraint that the bookshelf can hold a maximum of 45 books.

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Answer: A solution to an equation is a number that can be plugged in for the variable to make a true number statement. Example 1: Substituting 2 for x in.

Step-by-step explanation:

,11

Step-by-step explanation:

let's face it.

100-45=55. 55/5=11

therefore,The maxium number is 11

Equation of the line passing through  (1, -9) and (1, 12) is y = -9

The equation to the line in  slope intercept form

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

calculation of slope, m for (1, -9) and (1, 12)

(y - y₁) /  (x - x₁)   = m

m = (-9 - 12) /  (1 - 1)

m = 1 / 0

m = undefined slope (this is the slope of vertical line)

equation of the line  (1, -9)

(y - -9) = 0

y + 9 = 0

y = -9

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The value of the liquid assets of the person is given by:

$1,131,677.

Liquid assets are assets that can easily be converted into cash, such as retirement funds and investments.

Assets like houses and cars are not considered liquid assets, as even if you put them for sale, there is no guarantee that you will sell them quickly, that is, access the money quickly.

Hence the liquid assets of the person, along with their values, are listed as follows:

The total value of the person's liquid assets is given by the sum of the values of each of these two assets, hence:

$781,056 + $350,621 = $1,131,677.

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Answer:

x=63

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

Given

3 - 4x = - 60 + 3x ( subtract 3x from both sides )

3 - 7x = - 60 ( subtract 3 from both sides )

- 7x = - 63 ( divide both sides by - 7 )

x = 9

Answer:

C. 12/15 is not equivalent to the rest

Step-by-step explanation:

12/15 simplifies to 4/5, whereas all the others simplify to 2/3

Answer:Rounding To Nearest Billion (1000000000) = 0

Step-by-step explanation:

Answer:

5,000,000,000

Step-by-step explanation:

when rounding any number below 5 stays the same.

x<3

Step-by-step explanation:

–2(5 – 4x) < 6x – 4

(–10 + 8x) < 6x – 4

8x –6x < –4 + 10

2x < 6

x < 3

The scale used but Brenda is 1 inch = 5 feet

A scale is used to give context to the user about the size of the area that map covers. It is made by converting real-life measurements into physical measurements for quick calculations.

Brenda measured the middle school and made a scale drawing.

The actual length of the gym = 90 ft.

The length she used in her drawing = 18 inches.

So we will now find the scale used for this drawing,

18 inches = 90 ft.

therefore, 1 inch = 90/18 ft.

             i.e. 1 inch = 5 ft.

Hence, The scale used but Brenda is 1 inch = 5 feet.

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Answer:

200

Step-by-step explanation:

\(p=2\cdot \:79+2\cdot \:21\\2\cdot \:79=158\\p=158+2\cdot \:21\\2\cdot \:21=42\\p=158+42\\p=200\)

Answer:C I hope this helps

Step-by-step explanation:

The probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

b) To find the probability that exactly 4 children would draw the nickel too small, we can use the binomial probability formula. The formula is: P(X = k) = (nCk) * (p^k) * (q^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and q is the probability of failure.

In this case, n = 8 (as 8 children are chosen), k = 4 (as exactly 4 children drawing the nickel too small), p = 0.15 (as the probability of a child drawing the nickel too small), and q = 1 - p = 1 - 0.15 = 0.85.

So, the probability that exactly 4 children would draw the nickel too small is: P(X = 4) = (8C4) * (0.15^4) * (0.85^(8-4)).

c) To find the probability that at least one child would draw the nickel too small, we can use the complement rule. The probability of at least one success is equal to 1 minus the probability of no success.

The probability of no success (all children drawing the nickel of the right size) is given by: P(X = 0) = (8C0) * (0.15^0) * (0.85^8).

Therefore, the probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

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9514 1404 393

Answer:

  A, B, D

Step-by-step explanation:

For appropriate values of 'a', the log function has the following characteristics:

Any log function will tend toward negative infinity as x tends to zero (for |a|>1).

The first five terms of the sequence using the recursion formula are:

(2, -1, -1/2, 1/2, 1/2).

The given sequence starts with a₁ = 2.

To find the next term a₂, we use the recursion formula aₙ₊₁ = (-1)ⁿ⁺¹ .aₙ/2. Plugging in the values, we have a₂ = (-1)⁽²⁺¹⁾ .1/2. Here, (n+1) becomes 2+1 = 3, and aₙ becomes a₁, which is 2.

Now, let's evaluate the expression. (-1)⁽²⁺¹⁾ is (-1)³, which equals -1. Multiplying -1 by 1/2, which is 2/2, gives us -1. 1= -1.

Therefore, the second term, a₂, is -1.

To find the next term, a₃, we once again use the recursion formula. Substituting the values, we have a₃ = (-1)⁽³⁺¹⁾ .a₂/2. Here, (n+1) becomes 3+1 = 4, and aₙ becomes a₂, which is -1.

Evaluating the expression, (-1)⁽³⁺¹⁾becomes (-1)⁴, which equals 1. Multiplying 1 by a₂/2, which is -1/2, gives us 1. -1/2 = -1/2.

Hence, the third term, a₃, is -1/2.

We can continue this process to find the remaining terms:

a₄ = (-1)⁽⁴⁺¹⁾ .3/2 = (-1)⁵ . -1/2 = 1 . -1/2 = 1/2

a₅= (-1)⁽⁵⁺¹⁾. 4/2 = (-1)⁶. 1/2 = 1 .1/2 = 1/2

Therefore, the first five terms of the sequence are:

(2, -1, -1/2, 1/2, 1/2).

The sequence alternates between positive and negative values while being halved in magnitude at each step.

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To solve:

We multiply the denominator by 5:

To write it as a simplified fraction, we can note that 4 * 6 = 24

Then:

Answer:

about 45%

Step-by-step explanation:

it should be right

The area of the triangle is 31.54 square units

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

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

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

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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Answer:

Simple interest after 2 year = $36

Step-by-step explanation:

Given:

Amount invested = $300

Number of year amount invested = 2 year

Rate of interest per year = 6% = 6/100 = 0.06

Find:

Simple interest after 2 year

Computation:

Simple interest formula;

Simple interest = [Amount invested][Rate of interest][Number of year]

Simple interest after 2 year = [300][0.06][2]

Simple interest after 2 year = [18][2]

Simple interest after 2 year = $36

Answer:

The total number of vehicles in a traffic jam would depend on the average length of the vehicles. If there are a large number of SUVs and trucks, which are typically larger than other vehicles like sedans and compact cars, the total number of vehicles would likely be less because each vehicle takes up more space.

Here's how you could estimate this:

Let's assume the average length of a car is about 15 feet, and for an SUV or truck it's about 20 feet. This is a rough estimate and the actual lengths can vary significantly depending on the model of the car, SUV, or truck.

If the entire 13-mile stretch of the interstate was filled with cars that are each 15 feet long, the number of cars would be:

13 miles * 5280 feet/mile / 15 feet/car = about 46,080 cars.

If the same stretch was filled with SUVs or trucks that are each 20 feet long, the number of vehicles would be:

13 miles * 5280 feet/mile / 20 feet/vehicle = about 34,560 vehicles.

So if there were a large number of SUVs and trucks, you would expect fewer total vehicles in the traffic jam because each vehicle takes up more space.

Keep in mind this is a simplified calculation and doesn't take into account the space between vehicles or the different lanes on the interstate, among other factors.

The number of cubic centimeters in the space which is inside the cylinder but outside the cone for given volume is equal to 72 cubic centimeters.

As right circular cone inscribed in a right circular cylinder.

Let A be the apex of the cone and B be the center of the base of the cone.

Let r be the radius of the base of the cone,

and let h be the height of the cone.

Let R be the radius of the base of the cylinder,

and let H be the height of the cylinder.

Volume of the cylinder =  72π cubic centimeters.

⇒ πR^2H = 72π

⇒ R^2H = 72

Base of the cone is a circle with radius r.

⇒ area of the base of the cone is πr^2.

Height of the cone is h.

Volume of the cone = 1/3 × πr^2h

Volume of the space inside the cylinder but outside the cone.

= volume of the cylinder -  volume of the cone.

= πR^2H - 1/3 × πr^2h

Substituting R^2H = 72, we get,

⇒ Required Volume = 72π - 1/3 × πr^2h

Find r and h in terms of R and H.

Using the concept of similar triangles .

For similar triangle sides are in proportion.

⇒r/R = h/H

Solving for r, we get,

r = R × ( h/H )

Substituting this into the equation for the volume,

Volume = 72π - 1/3 × π(R × ( h/H ))^2h

Simplifying, we get,

⇒ Volume = 72π - 1/3 × πh^3R^2/H^2

Value of h that maximizes the volume.

Take the derivative of the volume with respect to h and set it equal to zero,

dV/dh = -2/3 × πh^2R^2/H^2

⇒ -2/3 × πh^2R^2/H^2= 0

Solving for h, we get,

⇒h = 0

Substituting this value of h back into the equation for the volume, we get,

⇒ Required Volume = 72π - 0

⇒ Required Volume = 72π cubic centimeters.

Therefore, the number of cubic centimeters in the space inside the cylinder but outside the cone is 72π cubic centimeters.

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Answer:

\(G=-\frac{5}{4}t+15\)

Slope = \(-\frac{5}{4}\)

Step-by-step explanation:

Let the equation representing the number of gallons left in the gas tank is,

G = mt + b

Where m = slope of the line

b = y-intercept of the line

Slope of the line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is,

'm' = \(\frac{y_2-y_1}{x_2-x_1}\)

Slope of the line passing through (8, 5) and (4, 10),

m = \(\frac{10-5}{4-8}\)

m = -\(\frac{5}{4}\)

Equation of line will be,

G = \(-\frac{5}{4}t+b\)

Since, point (8, 5) lies on this line,

5 = \(-\frac{5}{4}(8)+b\)

5 = -10 + b

b = 15

Therefore equation of the function will be,

G = \(-\frac{5}{4}t+15\)

Here slope of the function represents the \(\frac{5}{4}\) gallons of gas is consumed to drive the car for one hour.