suppose that g is 3-regular and that each of the regions in g is bounded by a pentagon or a hexagon. let p and h represent, respectively, the number of regions bounded by pentagons and by hexagons. find a formula for p that uses as few of the other variables as possible.

The polynomial h(x)=x^4+2x^3-13x^2-14x+24 in the factored form is (x−1)(x+2)(x−3)(x+4). The real roots of the polynomial is x= 1, x = 3, x = -2, x  = -4.

What is a polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

The polynomial function is -

h(x)=x^4+2x^3-13x^2-14x+24

Divide the polynomial h(x) by (x-1) -

(x^4+2x^3−13x^2−14^x+24)=(x−1)(x3+3x2−10x−24)

Divide (x^3+3x^2−10x−24) by (x+2) -

(x−1)(x^3+3x^2−10x−24)=(x−1)(x+2)(x^2+x−12)

Solve the quadratic equation x^2+x−12=0.

x^2+x−12=0

x^2+4x-3x-12=0

x(x+4)-3(x+4)=0

(x+4)(x-3)=0

So, (x−1)(x+2)(x^2+x−12)=(x−1)(x+2)(x−3)(x+4)

Therefore, x^4+2x^3−13x^2−14x+24=(x−3)(x−1)(x+2)(x+4) .

The Rational Root Theorem tells us that if the polynomial has a rational zero then it must be a fraction q/p, where p is a factor of the constant term and q is a factor of the leading coefficient.

We can see that p(1)=0 so x=1 is a root of a polynomial h(x).

Divide the polynomial by (x-1) -

(x^4+2x^3−13x^2−14x+24)/(x-1)=(x^3+3x^2−10x−24)

Divide (x^3+3x^2−10x−24) by (x-3) -

(x^3+3x^2−10x−24)/(x-3) = (x^2+6x+8)

To find the last zero, solve equation x+4=0

x=-4

Therefore, the real roots are - x = 1, 3, -2, -4.

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The probability that no two adjacent people will stand is 47/256. This is a problem that represents a combination.

A combination is a grouping of items where order does not matter. The formula of combination is

\(_{n}C_{r} = \frac{n!} {r! (n-r)!}\)

Where

Given the case eight people sit around a circular table, flip coins, and those who flip heads will stand while those who flip tails will remain seated.

What is the probability that no two adjacent people will stand?

First, we count the total standing arrangements. They will be 2⁸ = 256 arrangements. n(S) = 256.

The number of arrangements according to the number of people standing.

Case 1: 0 people standing = 1 arrangement.

Case 2: 1 people standing = \(_{8}C_{1}\) = \(\frac{8!} {1! 7!}\) = 8 arrangements.

Case3: 2 people standing = \(_{8}C_{2}\) = \(\frac{8!} {2! 6!}\) = \(\frac{7 \times 8} {2}\) = 28 arrangements, but no two people are next to each other. There are 8 arrangements that two people in this case are standing next to each other. So, it will be 28 - 8 = 20 arrangements.

Case 4: 3 people standing = \(_{8}C_{3}\) = \(\frac{8!} {3! 5!}\) = \(\frac{6 \times 7 \times 8} {6}\) = 56 arrangements. In this case, three people standing are next to each other = \(_{8}C_{1}\) = 8 arrangements. Two people standing are next to each other and the third person is not = \(_{8}C_{1} \times _{4}C_{1}\) = 8 × 4 = 32. So, it will be 56 - 8 - 32 = 16 arrangements.

Case 5: 4 people standing but no two adjacent people = 2 arrangements.

The number of arrangements that no two adjacent people will stand.

n(A) = 1 + 8 + 20 + 16 + 2 = 47

The probability that no two adjacent people will stand is

P(A) = n(A)/n(S)

P(A) = 47/256

Hence, the probability that no two adjacent people will stand is 47/256.

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Answer:

p = 36 in

Step-by-step explanation:

9 in + 15 in + 12 in = 36 in

The two lines intersect. The point of intersection of the two given lines is (-2, -20, 10). The distance between the planes π1 and π2 is 29 / √322.

Equation of line ℓ2**, which is parallel to v = 2i - 3j + 4k and passing through A(2, -4, 1), will be of the form:

\(x - 2/2 = y + 4/-3 = z - 1/4.\)

As ℓ1 and ℓ2 are parallel, we will use the distance formula between skew lines. Let Q(x, y, z) be a point on ℓ1 and P(x1, y1, z1) be a point on ℓ2.

Let m be the direction ratios of ℓ1. Then,

\(PQ = (x - x1)/3 = (y + 8)/1 = (z - 2)/(-1) ... (i).\)

Let the direction ratios of ℓ2 be a, b, and c. Then, (a, b, c) = (2, -3, 4).

Now, \(AQ = (x - 2)/2 = (y + 4)/(-3) = (z - 1)/4 ... (ii)\).

Solving equations (i) and (ii), we get:

(x, y, z) = (-2 - 6t, -20 - 3t, 10 + 4t).

Coordinates of the point of intersection are: (-2, -20, 10).

Therefore, the lines intersect. The point of intersection of the two given lines is (-2, -20, 10).

Now, we are given three points A(2, -1, 5), B(3, 3, 1), and C(5, 2, -2). The equation of the plane that passes through these points is given by the scalar triple product and is given by:

\((x - 2)(3 - 2)(-2 - 1) + (y + 1)(1 - 5)(5 - 2) + (z - 5)(2 - 3)(3 - 2) = 0\).

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Answer:

Step-by-step explanation:

so first

Answer:

your invers of operations are right and X = 7.5

Step-by-step explanation:

Answer:

B

Using gradient of two points and equation of a straight line graph.

The simplified expression for the given algebraic expression \(a^{2} c^{2} -b^{2} c^{2} -4a^{2} d^{2} +4b^{2} d^{2}\) is \((a+b)(a-b)(c+2d)(c-2d)\)

As per the question statement, we are given an algebraic expression

\(a^{2} c^{2} -b^{2} c^{2} -4a^{2} d^{2} +4b^{2} d^{2}\) and we are supposed to solve and simplify it.

Solution:

\(a^{2} c^{2} -b^{2} c^{2} -4a^{2} d^{2} +4b^{2} d^{2}\\c^{2} (a^{2} -b^{2})-4d^{2}(a^{2} -b^{2})\\(a^{2} -b^{2})(c^{2}-4d^{2})\\(a^{2} -b^{2})(c^{2}-(2d)^{2})\\\)

Have used Distributive property for solving and simplifying the above algebraic expression.

Now using the property, \(a^{2} -b^{2} =(a+b)(a-b)\)

We get,

\((a+b)(a-b)(c+2d)(c-2d)\)

Therefore \((a+b)(a-b)(c+2d)(c-2d)\) is our required answer.

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The value of z for a 95% confidence interval is approximately 1.960, rounded to three decimal places.

To find the value of z for a 95% confidence level, we can use the standard normal distribution table or a calculator.
Therefore,

The value of z that should be used to calculate a confidence interval for the percentage of married couples in which at least one partner has a doctorate with a 95% confidence level is:
z ≈ 1.96
To find the value of z for a 95% confidence interval, you will use the standard normal distribution table or a calculator with a built-in function.
For a 95% confidence interval, you want to find the z-score that corresponds to the middle 95% of the distribution, which leaves 2.5% in each tail.

Look for the z-score that corresponds to the 0.975 percentile (1 - 0.025) in the table or calculator.
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Answer:

30 min

Step-by-step explanation:

The tank can be filled in 15 min, this means that in one min, 1/15 of the tank can be filled.

The tank can be emptied in 10 min, this means that in one min, 1/10 of the tank can be emptied.

the outflow rate - the inflow rate = rate of emptying the tank

1/10 - 1/15 = 1/x

where x is the time it will take to empty the tank

solving, we'll have

1/30 = 1/x

the reciprocal of the equation gives

x = 30 min

20 seconds is equal to 0.00555555555555556 hours.

Speed is a measure of how quickly an object is moving. It is typically measured in units of distance per unit of time, such as meters per second or miles per hour. Speed can also be thought of as the rate at which an object is changing its position. Speed is a scalar quantity, meaning that it has magnitude but not direction.

20 seconds is equal to 0.00555555555555556 hours. So, when we use the distance = rate x time formula with the given values, it looks like this:

distance = rate x time

200 yards = rate x 0.00555555555555556 hours

By solving for rate, we can determine Phil's speed:

rate = 200 yards / 0.00555555555555556 hours

rate = 36,036.3636363636 yards per hour

Therefore, 20 seconds is equal to 0.00555555555555556 hours.

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Answer: Goofy ahhh question

Step-by-step explanation:

Answer:

I believe it's D

Step-by-step explanation:

You plug in 0 and you get 5 as your Y value

The function of the graph is y = (5 + 3x)/(1 + x), so the correct option is d.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

The graph is first shifted to the right by 4 units and another one to the left by 1/2.

So, we have:

y = (5 + 3x)/(1 + x)

Hence, the function of the graph is y = (5 + 3x)/(1 + x)

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Step-by-step explanation:

calculating backwards :

12:39 pm minus 1 hour 13 minutes = 11:26 am

the cake needs to get into the oven latest at that time.

caucuses further backwards :

11:26 am minus 26 minutes = 11:00 am

Evan has to start latest at 11:00 am to have the cake ready at 12:39 pm.

yes, it's a scaled version of a triangle with side lengths 3, 4 and 5.

by a factor of 20

a triangle with side lengths 3, 4 and 5 is a right triangle and it holds true for a²+b²=c², because 9+16=25

the 3,4,5-triangle is the simplest right triangle to calculate it's numbers seem somehow elegant.

the triangle in your problem is just a bigger version of it (wich means all angles stay the same).

My reasoning is lacking, but I'm sure

The value of the standard error of the mean in each of the following cases:

a. The population size is infinite = 1.4142

b. The population size is N = 50,000 = 1.4135

c. The population size is N = 5000 = 1.4073

d. The population size is N = 500 = 1.343

The standard error is a statistical technique used to measure variability. SE is the abbreviation. A statistic's or parameter estimate's standard error is the standard deviation of its sample distribution. It can be defined as an approximation of that standard deviation.

Standard error calculation:

σ = 10

n = 50

A) when size is infinite, the standard deviation of the sample mean is given by the formula;

σ_x' = σ/√n

Thus,

σ_x' = 10/√50

σ_x' = 1.4142

B) size is given, thus, the standard deviation of the sample mean is given by the formula;

σ_x' = (σ/√n)√((N - n)/(N - 1))

Thus, with size of N = 50,000, we have;

σ_x' = 1.4142 x √((50000 - 50)/(50000 - 1))

σ_x' = 1.4142 x 0.9995

σ_x' = 1.4135

C) at N = 5000;

σ_x' = 1.4142 x √((5000 - 50)/(5000 - 1))

σ_x' = 1.4073

D) at N = 500;

σ_x' = 1.4142 x √((500 - 50)/(500 - 1))

σ_x' = 1.343

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The height of the Empire State Building is approximately 1,454 feet. In order to determine how many pennies would equal this height, we need to know the height of one penny. The thickness of a penny is 1.55 millimeters or 0.061 inches. Therefore, 1 foot is equivalent to 12 inches, which means that there are 196.85 pennies in one foot (12 inches / 0.061 inches).

Now, we need to convert the height of the Empire State Building into millimeters to match the unit of the penny's thickness.

3. Convert Empire State Building's height to millimeters: 443.2 meters * 1,000 mm/m = 443,200 mm

Next, we can calculate how many pennies, when stacked on top of each other, would equal the height of the Empire State Building:

4. Divide the height of the Empire State Building (in millimeters) by the thickness of a penny: 443,200 mm / 1.52 mm/penny ≈ 291,447 pennies

So, it would take approximately 291,447 pennies, if stacked on top of each other, to equal the height of the Empire State Building.

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Answer:

35 ok

Step-by-step explanation:

35 Men ok byeee3eeeeeeeeeeeeewwww

Answer:

10,000>3,200 (inequality).......3,200+6,800=10,000

Step-by-step explanation:

The answer is , the dimension of the range of f is equal to the number of vectors in this basis, which is 3.

Given the linear map f: R³, given by f(x, y, z) = (x+2y+52, x+y+3z, y + 2z, x+2).

To find the basis for the range of f, we will find the column space of the matrix associated with the map f.

Writing the map f in terms of matrices, we have:
f(x,y,z) = [ 1 2 0 1 ] [ x ]
            [ 1 1 3 0 ] [ y ]
            [ 0 1 2 0 ] [ z ]
            [ 1 0 0 2 ] [ 1 ]
Now, we can easily find the row echelon form of this matrix, as shown below:
[ 1 2 0 1 | 0 ]
[ 0 -1 3 -1 | 0 ]
[ 0 0 0 1 | 0 ]
[ 0 0 0 0 | 0 ]
The pivot columns in the above matrix correspond to the columns of the original matrix that span the range of the map f.

Therefore, the basis for the range of f is given by the columns of the matrix that contain the pivots.
In this case, the first, second, and fourth columns contain pivots, so the basis for the range of f is given by the set:
{ (1, 1, 0, 1), (2, 1, 1, 0), (1, 3, 0, 2) }
This set of vectors spans the range of f, and any linear combination of these vectors can be written as a vector in the range of f.

The dimension of the range of f is equal to the number of vectors in this basis, which is 3.

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1) Let's find the standard deviation for this data set:

2) So, let's apply the formula for standard deviation:

3) Let's find the mean and compute the variance:

The sum of all entries is divided by the number of data points.

Now, for the variance:

Finally, we can take the square root of that variance to get the standard deviation:

In a multiple regression problem involving two independent variables X1 and X2, if b1 is computed to be +2.0, it means that. the relationship between X1 and Y is significant .

Multiple regression is a statistical method that may be used to assess a single dependent variable and several independent variables. Multiple regression analysis use known independent variables to anticipate the value of a single dependent variable. Each predictor value is assigned a weight, which indicates how much each predictor contributed to the overall forecast.

In a multiple regression problem involving two independent variables X1 and X2, if b1 is computed to be +2.0, it means that. the relationship between X1 and Y is significant .

The estimated value of Y increases by an average 2 units for each increase of 1 unit of X1, holding X2 constant.

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The transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units

Transformation is the technique used to change the position of a figure on an xy-plane.

Given the parent function f(x) = x², the transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units

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Answer:

1:1 and 1:87

Step-by-step explanation:

Answer:

To solve the equation |x+3|=9, we need to split it into two separate equations, one for the positive value and one for the negative value of the absolute value:

For the positive value:

x+3=9

Solving for x, we get x=6

For the negative value:

-(x+3)=9

Multiplying both sides by -1, we get:

x+3=-9

Solving for x, we get x=-12

Therefore, the solutions to the equation |x+3|=9 are x=6 and x=-12.

Hope This Helps!

The mean for the random variable X is 0.8 and The variance for the random variable X is 0.672.

In this case, we have a binomial distribution with n=5 trials and a success probability of p=0.16 for each trial (the probability of corrosion).

The following formula gives the mean or expected value of the binomial distribution:

μ = np

Putting the given values, we get:

μ = 5 × 0.16 = 0.8

Therefore, the mean for the random variable X is 0.8.

The variance of the binomial distribution is given by the formula:

\(\sigma^2\) = np(1-p)

Putting the given values, we get:

\(\sigma^2\) = 5 × 0.16 × (1-0.16) = 0.672

Hence, the variance for the random variable X is 0.672.

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Answer:

the remNING MAS IS 345

Step-by-step explanation:

I DID THIS BEFORE

Answer:

I can't see the file

Step-by-step explanation: