what is the highest common factor of 168 and 140
what is the highest common factor of 268 and 168

If the mean of the data set is 32.6. Then the number of pages he read in 5 days is 163.

Mean is simply defined as the average of the given set of numbers. The mean is considered as one of the measures of central tendencies in statistics. The mean is said to be an arithmetic mean. It is the ratio of the sum of the observation to the total number of observations.

Han recorded the number of pages that he read each day for five days.

If the mean of the data set is 32.6 pages. Then the total number of the pages he read till now, will be

Let the total number of the pages be x. Then we have

\(\rm \dfrac{x}{5} = 32.6\\\\x \ = 5 \times 32.6 \\\\x \ = 163\)

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The net force exerted on the dipole is 2.12 x 10⁻³ N, directed towards the line of charge.

This force is a result of the electric field produced by the line of charge and the dipole moment of the dipole. The electric field at the position of the dipole can be calculated using the formula E = k*l*y/(y² + x²), where k is the Coulomb constant, l is the charge density, and y is the distance from the y axis.

The dipole moment can be calculated as p = q*d, where q is the charge and d is the separation between the charges. Using the angle between the dipole moment and x axis, the components of the dipole moment along and perpendicular to the electric field can be found.

Finally, the net force on the dipole can be found using the formula F = p*E*sin(theta), where theta is the angle between the dipole moment and the electric field.

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We have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Let A and B be two sets in a generalized rectangle R, i.e., R = A x B. The boundary of R, denoted by bd(R), is defined as the closure of the set of points that are not in the interior of R. In other words, bd(R) = cl(R) \ int(R), where cl(R) is the closure of R and int(R) is the interior of R.

To show that bd(R) is the union of finitely many closed generalized rectangles with volume zero, we first note that the closure of R can be expressed as the union of R and its boundary, i.e., cl(R) = R ∪ bd(R). Therefore, it suffices to show that R can be expressed as the union of finitely many closed generalized rectangles with volume zero and that bd(R) can also be expressed as the union of finitely many closed generalized rectangles with volume zero.

Let (a,b) be a point in R. Then there exists an open ball B((a,b), r) around (a,b) that is contained in R, where r > 0. Without loss of generality, we can assume that r is small enough so that B((a,b), r) is a generalized rectangle. Since B((a,b), r) is open, it follows that int(R) is the union of all such generalized rectangles. Therefore, R can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such generalized rectangles.

Next, we show that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero. Let (a,b) be a point in bd(R). Then every open ball B((a,b), r) around (a,b) contains points both in R and in the complement of R. By definition of bd(R), the closure of B((a,b), r) intersects both R and the complement of R. Therefore, B((a,b), r) can be expressed as the union of two closed generalized rectangles, one contained in R and one contained in the complement of R. It follows that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such balls B((a,b), r) and their decompositions into closed generalized rectangles.

Therefore, we have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

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One car travel South at 64 mi/h and the other travels west at 48 mi/h. The distance between the cars increases with rate at 80 mi/h.

To find the rate of change, we need to find the derivative of the variables with respect to time.

Let:

p = distance between 2 cars

q = distance between car 1 and the start point

r = distance between car 2 and the start point

Using the Pythagorean Theorem:

p² = q² + r²

Take the derivative with respect to time:

2p dp/dt = 2q dq/dt + 2r dr/dt

dq/dt = speed of car 1 = 64 mi/h

dr/dt = speed of car 2 = 48 mi/h

The distance of car 1 and car 2 from the start point after 4 hours:

q = 64 x 4 = 256 miles

r = 48 x 4 = 192 miles

Using the Pythagorean theorem:

p² =256² + 192²

p = 320 miles

Hence,

2p dp/dt = 2q dq/dt + 2r dr/dt

p dp/dt = q dq/dt + r dr/dt

320  x dp/dt = 256 x 64 + 192  x 48

dp/dt = 80

Hence, the distance between the cars increases with rate at 80 mi/h

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The home's price is worth today's compared to the original price, which increased by 9% per year, equal to $803,310.

Purchase price of the house bought by Sunita in 1992 = $289,000

Percent increase in the average home price from 1992 to today per year

= 9% per year.

Let us consider 'y' be the home price worth today.

Total number of years = 2023 - 1992

                                     = 31 years

Todays price = 289,000 × 9 % × 31

                      = ( 289,000 × 9 × 31 )/100

                      = $803,310

Therefore, for the increased in home price by 9% per year the worth todays home price is equal to $803,310.

The given question is incomplete, I answer the question in general according to my knowledge:

From 1992 to today the average home price increased by 9% per year. In 1992 Sunita Bath bought a house for $289,000. What was it worth today?

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To find the inverse function of F(x) = 2x - 3, we replace F(x) with y, swap the positions of x and y, and solve for y. The inverse function is f⁻¹(x) = (x+3)/2.

To find the inverse function of F(x) = 2x - 3, follow these steps

Replace F(x) with y. The equation now becomes y = 2x - 3.

Switch the positions of x and y, so the equation becomes x = 2y - 3.

Solve for y in terms of x. Add 3 to both sides: x + 3 = 2y.

Divide both sides by 2 (x + 3)/2 = y.

Replace y with the notation for the inverse function, f⁻¹(x): f⁻¹(x) = (x + 3)/2.

So, the inverse function of F(x) = 2x - 3 is f⁻¹(x) = (x + 3)/2.

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--The given question is incomplete, the complete question is given

" How do I find the inverse function of F(x) = 2x - 3"--

To conduct a phone survey about a new movie, a surveyor plans to take a simple random sample. By using a simple random sample, the surveyor can generate reliable and unbiased data that can be used to draw conclusions about the entire population's opinions on the new movie.

A simple random sample is a subset of a statistical population, where each member of the population has an equal chance of being selected. A surveyor may use this method to generate an unbiased representation of the entire population's opinions on the new movie in question. This method ensures that all individuals have an equal chance of being selected for the survey, thereby reducing the risk of potential bias.

To create a simple random sample, the surveyor must first define the population from which they intend to draw their sample. For example, the population could be moviegoers, movie critics, or people of a certain age group or location. The surveyor can then assign each member of the population a number and use a random number generator to select the sample members. This process guarantees that each member of the population has the same probability of being chosen for the survey.

The surveyor must also ensure that the sample size is sufficient to represent the entire population accurately. The larger the sample size, the greater the likelihood that the sample's results will reflect the population as a whole. By using a simple random sample, the surveyor can generate reliable and unbiased data that can be used to draw conclusions about the entire population's opinions on the new movie.

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Q.21:

We are asked what f(3) = 32 means?

In Q.20, we are given the following function

Where f(x) is the height (in feet) of the apple and x is the time in seconds.

If we substittute x = 3 seconds into the function, we get the corresponding height of the apple.

As you can see, the height of the apple is 32 feet at 3 seconds.

Therefore, the correct answer is the option (B)

The height of the apple at 3 seconds is 32 feet.

Answer:

 2 • (x2 + 5x + 73)

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant

Step-2 : Find two factors of  73  whose sum equals the coefficient of the middle term, which is   5

Pulling out like terms/factors

Trying to factor by splitting the middle term

Answer: 2 • (x2 + 5x + 73)

Hope this helps.

Answer:

2x^2 + 10x + 146

Step-by-step explanation:

x^2 + 121 + (x+5)^2

x^2 +121 + (x+5)(x+5)

x^2 + 121 + x^2 + 5x + 5x + 25

2x^2 + 10x + 146

The translation from preimage P(9. 1.5) to image P'(12, 1)) in ordered pair is (3, -0.5)

Translation refers to a type of transformation that involve a straight line movement.

The type of movements related to translation includes

The up and down movements are on the vertical direction controlled by the y coordinate. In the question, the preimage moved form 1.5 to 1

hence we say

The left right movement is controlled by the x coordinate. The preimage moved from 9 to 12 ⇒ 9 + 3. Hence we say that

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Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.

When the spring is stretched and the distance from point a to point b is 5.3 feet, the value of θ is 53.13  degrees

The distance between point a to point b = 5.3 feet

The length of the top side = 3 feet

Therefore, it will form a right triangle

Here we have to use trigonometric function

Here adjacent side and the hypotenuse of the triangle is given

The trigonometric function that suitable for the given conditions is

cos θ = Adjacent side / Hypotenuse

Substitute the values in the equation

cos θ = 3 / 5

θ = cos^-1(3 / 5)

θ = cos^-1(0.6)

θ = 53.13 degrees

Therefore, the value of θ is 53.13  degrees

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Answer:

Step-by-step explanation:

\(eq. ~of~line~through~(x_{1},y_{1}) ~with~slope~m~is\\y-y_{1}=m(x-x_{1})\\x_{1}=-2\\y_{1}=9\\point~ is ~ (-2,9)\)

To isolate cc in the equation (1/c - 1), we need to rearrange the equation to solve for cc. By applying algebraic manipulation, we can transform the equation into a form where cc is isolated on one side.

Let's start with the equation:

(1/c - 1)

To isolate cc, we can follow these steps:

Step 1: Combine the fractions by finding a common denominator. The common denominator is cc, so we rewrite 1 as cc/cc:

(cc/cc)/c - 1

Simplifying further, we have:

cc/ccc - 1

Step 2: Combine the terms:

(cc - ccc)/ccc

Step 3: Factor out cc:

cc(1 - cc)/ccc

Now we have cc isolated on one side of the equation.

In summary, by rewriting the equation (1/c - 1) as cc(1 - cc)/ccc, we have successfully isolated cc.

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Answer:

C is correct

Step-by-step explanation:

Answer:

the value of x is 8

x=8

HOPE IT'S HELP

Answer:

2 real roots

Step-by-step explanation:

y = ax^2 + bx + c

Thus, we can plug in 4 for a, 0 for b, and -16 for c to determine how many real roots y = 4x^2 - 16 has:

0^2 - 4(4)(-16)

(-16)(-16)

256

256 > 0

Since 256 is greater than 0, there are 2 real roots for y = 4x^2 - 16.

Answer:

$0.05

Step-by-step explanation:  first, divided $4.80 and 16= $0.30. Then, divided $4.20 by 12= $0.35. And subtract your two answers

Moo Valley's cost per ounce is $0.05 per ounce more than the  Cheetah Chedda cost of per ounce.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

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,
Cheetah Chedda cost per ounce = 4.80 / 16 = $0.3 per ounces
Moo Valley cost per ounce = 4.20 / 12 = $0.35 per ounces

Thus, Moo Valley's cost per ounce is $0.05 per ounce more than the  Cheetah Chedda cost of per ounce.

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The correct statements about these pairs is The GCF of Pair C is 12. (option c).

Pair A:

The given pair A is (52, 72). To find the GCF of these numbers, we can factor them into their prime factors. The prime factorization of 52 is 2 x 2 x 13, and the prime factorization of 72 is 2 x 2 x 2 x 3 x 3. To find the GCF, we take the common factors with the highest exponent, which in this case is 2 x 2 = 4. Therefore, the GCF of Pair A is 4.

Pair C:

The given pair C is (48, 84). Again, we can factor these numbers into their prime factors. The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, and the prime factorization of 84 is 2 x 2 x 3 x 7. To find the GCF, we take the common factors with the highest exponent, which in this case is 2 x 2 x 3 = 12. Therefore, the GCF of Pair C is 12.

Pair B:

The given pair B is (96, 64). We can factor these numbers into their prime factors. The prime factorization of 96 is 2 x 2 x 2 x 2 x 2 x 3, and the prime factorization of 64 is 2 x 2 x 2 x 2 x 2 x 2. To find the GCF, we take the common factors with the highest exponent, which in this case is 2 x 2 x 2 x 2 x 2 = 32. Therefore, the GCF of Pair B is 32.

This statement is incorrect because the GCF of Pair A is 4, and the GCF of Pair C is 12. They are not the same.

This statement is correct. We found earlier that the GCF of Pair C is indeed 12.

Hence the correct option is (c).

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Answer:

2/3

Step-by-step explanation:

First,  find the slope of Line P

1. Slope = rise over run (\(\frac{y_{2} - y_{1}}{x_{2} - x_{1}}\))

\(\frac{2- (-4)}{-1-(-3)}\) -> \(\frac{6}{-4}\)

So the slope of Line P is  \(\frac{6}{-4}\) or \(\frac{-3}{2}\)

2. Find the negative reciprocal of Line P

*the product of two lines that are perpendicular to each other is -1

negative: \(\frac{3}{2}\)

negative reciprocal: \(\frac{2}{3}\)

So the slope of the line perpendicular to Line P is 2/3.

Check:

\(\frac{-3}{2}\)* \(\frac{2}{3}\)= -1

The slope of the line perpendicular to the line p passing through the point (−1, 2) and (−3,−4) will be -1/3

The formula for calculating the slope of a line is expressed as:

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

If the slope of a line is "m", the slope of the line perpendicular will be -1/m

Given the coordinate points (−1, 2) and (−3,−4), we need to first get the slope of the line as shown:

\(m=\frac{-4-2}{-3+1}\\m=\frac{-6}{-2}\\m = 3\)

The slope of the line perpendicular to the line will be -1/3

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The standard error of the sample mean is 1.21.

Given;

Suppose a diet regimen for men results in an average weight loss of between 13. 4 and 18. 3 pounds, according to a 95% confidence interval. These findings were based on a group of 42 men who were classified as overweight at the beginning of the four-month trial.

A 95% confidence interval for a population mean is (13.4, 18.3)

Upper limit = 18.3

Lower limit = 13.4

Since population SD is unknown, this interval is constructed using the t distribution.

n = 42

c = 0.95

∴ α = 1 - c = 1 - 0.95 = 0.05

α/2 = 0.025

Also, d.f = n - 1 = 42 - 1 = 41

∴ ta/2.d.f =  ta/2.n-1  =  t0.025,41  =  2.02 . . . . use t table

Now,

The margin of error = (Upper limit - Lower limit)/2

                                 = (18.3 - 13.4)/2

                                 = 2.45

But,

Margin of error = ta/2.d.f-  * (s / \sqrt{} n)

Margin of error = ta/2.d.f-  * Standard error

2.45 = 2.02 * Standard error

Standard error = 1.2129

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Answer:

one gallon is $3.80

Step-by-step explanation:

divide 28.12 by 7.4 then bam

The answer choice which correctly models the range of pH values of bleach is; 11< x < 14.

According to the task content; Bleach is said to have a pH of less than 14 and greater than 11.

Hence; pH < 14. and pH > 11.

Therefore, when written as a compound inequality; we have;

11< pH < 14.

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To find the weight of the bowl, we need to first find the volume of the bowl. We can do this by using the formula for the volume of a solid of revolution: The weight of the bowl made out of steel is approximately 0.066 kg.

To find the weight of the bowl, we need to first find the volume of the bowl. We can do this by using the formula for the volume of a solid of revolution:

\(V = \pi \int\limits^b_a { y^2} \, dx\)

In this case, a = 0 and b = 1, since we are revolving the region bounded by y = 20x and y = 20x^2 in the first quadrant about the y-axis. So we have:

\(V = \pi \int\limits^1_o{(20x^2)^2 - (20x)^2 } \, dx\)

\(V = \pi\int\limits^1_0 { 400x^4 - 400x^2 } \, dx\)

\(V = \pi (80/15)\)

\(V = 16\pi /3 m^3\)

Next, we need to find the mass of the bowl, which we can do by multiplying the volume by the density of steel:

m = ρV

m = 8050 * (16π/3)

m ≈ 134,388.09 g

Finally, we convert the mass to kilograms to find the weight of the bowl:

w = m/1000

w ≈ 0.066 kg

Therefore, the weight of the bowl made out of steel is approximately 0.066 kg.

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Answer:

12x3+6x2+34x+17

Step-by-step explanation:

(2x+1)(6x2+8+9)

=(2x+1)(6x2+8+9)

=(2x)(6x2)+(2x)(8)+(2x)(9)+(1)(6x2)+(1)(8)+(1)(9)

=12x3+16x+18x+6x2+8+9

=12x3+6x2+34x+17

Answer:

3x×5x=15x² so what's the second way

very far, but it can come to beaches as well

i. The Fourier transform of (t - 2) - 38(t - 3) is [(jw)^2 + 38jw]e^(-2jw). ii. The Fourier transform of e^(-2t)u(t) is 1/(jw + 2). iii. The Fourier transform of e^(-3t+12)u(t-4) can be obtained using the result of ii. as e^(-2t)u(t-4)e^(12jw). iv. The Fourier transform of e^(-2|t|)cos(t) is [(2jw)/(w^2+4)].

i. To find the Fourier transform of (t - 2) - 38(t - 3), we can use the linearity property of the Fourier transform. The Fourier transform of (t - 2) can be found using the time-shifting property, and the Fourier transform of -38(t - 3) can be found by scaling and using the frequency-shifting property. Adding the two transforms together gives [(jw)^2 + 38jw]e^(-2jw).

ii. The function e^(-2t)u(t) is the product of the exponential function e^(-2t) and the unit step function u(t). The Fourier transform of e^(-2t) can be found using the time-shifting property as 1/(jw + 2). The Fourier transform of u(t) is 1/(jw), resulting in the Fourier transform of e^(-2t)u(t) as 1/(jw + 2).

iii. The function e^(-3t+12)u(t-4) can be rewritten as e^(-2t)u(t-4)e^(12jw) using the time-shifting property. From the result of ii., we know the Fourier transform of e^(-2t)u(t-4) is 1/(jw + 2). Multiplying this by e^(12jw) gives the Fourier transform of e^(-3t+12)u(t-4) as e^(-2t)u(t-4)e^(12jw).

iv. To find the Fourier transform of e^(-2|t|)cos(t), we can use the definition of the Fourier transform and apply the properties of the Fourier transform. By splitting the function into even and odd parts, we find that the Fourier transform is [(2jw)/(w^2+4)].

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