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Estimate an equation for the line of best fit for the following scatter plot.

The centroid of the region bounded by the curves y = 2 sin(3x), y = 2 cos(3x), x = 0, and x = 12 is approximately (x, y) = (6, 0).

To find the centroid of the region bounded by the given curves, we need to determine the x-coordinate (x-bar) and y-coordinate (y-bar) of the centroid. The x-coordinate of the centroid is given by the formula:

x-bar = (1/A) * ∫[a,b] x * f(x) dx,

where A represents the area of the region and f(x) is the difference between the upper and lower curves.

Similarly, the y-coordinate of the centroid is given by:

y-bar = (1/A) * ∫[a,b] 0.5 * [f(x)]^2 dx,

where 0.5 * [f(x)]^2 represents the squared difference between the upper and lower curves.

Integrating these formulas over the given interval [0, 12] and calculating the areas, we find that the x-coordinate (x-bar) of the centroid is equal to 6, while the y-coordinate (y-bar) evaluates to 0.

Therefore, the centroid of the region is approximately located at (x, y) = (6, 0).

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You write something wrong

An inconsistent, independent system of equations is a system with not intersecting lines that have the same slope but different y intercepts.

(a) This can be seen by multiplying u1 by -5 and comparing it to u2: -5u1 = (5, -10, -20), which is equal to u2. (b) This can be seen by adding u1 and u2 together and comparing it to u3: u1 + u2 = (7, 4) and u3 = (-4, 7), which are equal. (c) This can be seen by multiplying p1 by 2 and comparing it to p2: 2p1 = 6 - 4x + 2x², which is equal to p2. (d) A and B are not scalar multiples of each other and are linearly independent.

(a) The two vectors u1 and u2 are linearly dependent because u2 is equal to -5 times u1. This can be seen by multiplying u1 by -5 and comparing it to u2: -5u1 = (5, -10, -20), which is equal to u2.
(b) The three vectors u1, u2, and u3 are linearly dependent because u3 is equal to the sum of u1 and u2. This can be seen by adding u1 and u2 together and comparing it to u3: u1 + u2 = (7, 4) and u3 = (-4, 7), which are equal.
(c) The two polynomials p1 and p2 are linearly dependent because p2 is equal to twice p1. This can be seen by multiplying p1 by 2 and comparing it to p2: 2p1 = 6 - 4x + 2x², which is equal to p2.
(d) The two matrices A and B are linearly independent because they have different determinants. The determinant of A is -15 and the determinant of B is 16, which are not equal. Therefore, A and B are not scalar multiples of each other and are linearly independent.

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Answer:

70

Step-by-step explanation:

Answer:

-0.5

Step-by-step explanation:

Given

The triangle ABC at points A = (2, 2) B = (4, 5) C = (6, 3).

To find:

EXPLANATION

Applying the appropriate conjunction:

p q p ^ q

T T T

T F F

F T F

F F F

Answer:

x=3

Step-by-step explanation:

Answer:x=3

Step-by-step explanation:

2x+4=10

Step 1: Subtract 4 from both sides.

2x+4-4=10-4

2x=6

Step 2: Divide both sides by 2.

2x/2=6/2

X=3

Hope that helps have a great day :D

Answer:

n + 30

Step-by-step explanation:

\(4(n+9)-3(2+n)\\\\\mathrm{Expand}\:4\left(n+9\right):\quad 4n+36\\=4n+36-3\left(2+n\right)\\\\\mathrm{Expand}\:-3\left(2+n\right):\quad -6-3n\\=4n+36-6-3n\\\\\mathrm{Simplify}\:4n+36-6-3n:\\\quad n+30\)

Answer:

4n + 36 - 6 -3n

n + 30

Step-by-step explanation:

Answer:

85 degrees Fahrenheit

Step-by-step explanation:

Answer:

504

Step-by-step explanation:

The probability of rolling a 1 with the first die and a 5 with the second die is P(A ∩ B) = (1/6) x (1/6) = 1/36.

The probability of rolling a 1 with the first die and a 5 with the second die can be calculated using the joint probability formula. The joint probability formula is P(A ∩ B) = P(A) x P(B|A). In this case, A is rolling a 1 with the first die and B is rolling a 5 with the second die. P(A) is the probability of rolling a 1 with the first die, which is 1/6. P(B|A) is the probability of rolling a 5 with the second die given that a 1 was rolled with the first die, which is also 1/6. Therefore, the probability of rolling a 1 with the first die and a 5 with the second die is P(A ∩ B) = (1/6) x (1/6) = 1/36.

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The answer is

Step-by-step explanation:

Since there is 3 even numbers and 3 odd numbers it makes a 50/50 chance when spun once. If you spin it 60 times you will have spun it 30 times theoretically.

An equation is $52.47x - $26.72 = $253.63 and Jeff worked last week 5 days.

In the given question, Jeff made $52.47 each day that he worked last week.

He spent $26.72.

He still had $235. 63 of his earnings left.

We have to write an equation to find out how many days Jeff worked last week.

Let Jeff worked total x days in last week.

So Jeff earned last week = $52.47x

He spent $26.72.

So he have left money = $52.47x - $26.72

But from the he have left money = $253.63

So now the equation is

$52.47x - $26.72 = $253.63

Now solving the equation to find the working days.

Add $26.72 on both side, we get

$52.47x = $280.35

Divide by $52.47 on both side, we get

x = 5.34

So, he worked total 5 days.

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Answer:

420 is the answer

Step-by-step explanation:

15/2 * 56L =

l = 15/2 = 7.5

7.5 * 56 = 420

Answer:

420

Step-by-step explanation:

Attached below

The area of the circle with a circumference of 30m is OA= 706.50 mm², the correct option is C.

Let us suppose that the circle has radius of 'r' units, than, its area will be given as;

\(A = \pi \times r^2\)sq. units

Since radius of the circle is 1/2 of its diameter, so if diameter is of 'd' length, then r= d/2, So, area can be rewritten as:

\(\pi \times (\dfrac{d}{2})^2\)sq. units

We are given that;

Circumference=30m

The formula for the circumference of a circle is given by:

C = 2πr

where C is the circumference and r is the radius.

We are given that the circumference is 30m, so we can use this to solve for the radius:

30 = 2πr

r = 30 / (2π)

r ≈ 4.77 m

Now that we have the radius, we can use the formula for the area of a circle:

A = πr²

A = π(4.77)²

A ≈ 71.53 m²

Rounding this to the nearest hundredth gives us an area of 71.54 m².

Therefore, the area will be OA= 706.50 mm².

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Answer:

9/14

Step-by-step explanation:

2/7÷4/9=9/14

Solution with Steps

2/7÷4/9=?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

2/7×9/4=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

2×9/7×4=1/8 2/8

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 18 and 28 using

GCF(18,28) = 2

1/8÷2 2/8÷2=9/14

Therefore:

2/7÷4/9=9/14

The result of 2/7 divided by 4/9 in simplest form is 9/14 .

Hence option D is correct.

Division: It is one of the four basic mathematical operation, the other three being addition, subtraction, multiplication.

Given, that 2/7 divided by 4/9 .

Division of fractional terms :

= \(\dfrac{\frac{a}{b}}{\frac{c}{d}}\)

= \(a \times d/b\times c\)

Apply division process on fractional terms,

= \(\dfrac{\frac{2}{7}}{\frac{4}{9}}\)

= \(2 \times 9/ 7 \times4\)

= \(\frac{18}{28}\)

= \(\frac{9}{14}\)

Thus option D is correct.

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the probability that a top-selling red and voss tire wears out before 80,000 miles is about 2.56%.

The student question asks about the probability that a top-selling red and voss tire, rated for 80,000 miles, wears out before reaching 80,000 miles. The tire's lifespan follows a normal distribution with a mean of 94,000 miles and a standard deviation of 7200 miles.
To find the probability, we need to calculate the z-score first. The z-score is a measure of how many standard deviations away from the mean a particular value is. We can use the following formula to calculate the z-score:
z = (X - μ) / σ
where X is the value (in this case, 80,000 miles), μ is the mean (94,000 miles), and σ is the standard deviation (7200 miles).

Calculate the z-score:
z = (80,000 - 94,000) / 7200
z = -14,000 / 7200
z ≈ -1.944
The z-score is approximately -1.944, which means the tire wearing out at 80,000 miles is about 1.944 standard deviations below the mean.
Find the probability:
Now, we can use the z-score to find the probability. We can look up the z-score in a standard normal distribution table or use a calculator with a built-in function for this purpose.
Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of -1.944 is approximately 0.0256 or 2.56%.

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Answer:

Step-by-step explanation:

As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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(d) The ordered pair solution of this equation 3x/4  + 2y = 15 is (4, 6).

(e) The ordered pair solution of this equation xy ≥ 6 is (-2, -4).

The ordered pair solution of the equations is calculated by simplifying the equations as follows;

The given equations;

(d) 3x/4  + 2y = 15

(e) xy ≥ 6

(d) The solution of this equation 3x/4  + 2y = 15 is calculated as follows;

let the value of x = 4 and the value of y = 6

so we will substitute this value into the equation and check if it will be equal to 15.

(4, 6) = (3 x 4 )/4  +  2(6)

(4, 6) = 3  +  12

(4, 6) = 15

(e) The solution of this equation xy ≥ 6 is calculated as follows;

let x = -2, and let y = - 4

(-2, -4) = (-2)(-4) = 8

8 ≥ 6 (this solution is true)

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Answer:    0.185

Step-by-step explanation:

Divide 120.99 and 654:

120.99÷654=0.185

So the final answer is 0.185 units.

Answer:

1. -2, 1, 4, 7, 10

2. -12, -8, -4, 0, 4

3. -7, -5, -3, -1, 1

4. -13, -3, 2, 7, 17

5. 2, 4, 7, 10, 12

6. -2, 0, 2, 4, 6

Step-by-step explanation:

sorry it took so long

Erika has 6.53 kilograms of apples, which is more than the 6 kilograms she needed for the recipe. Therefore, she has enough apples to make the recipe.

To determine if Erika has at least 6 kilograms of apples, we need to add the weight of all three bags of apples. The total weight of the apples is:

2.56 kg + 1.18 kg + 2.79 kg = 6.53 kg

Erika needs a certain amount of apples for a recipe, specifically 6 kilograms. She goes to the store and picks three different bags of apples - a 2.56-kilogram bag of red apples, a 1.18-kilogram bag of green apples, and a 2.79-kilogram bag of yellow apples. To determine if she has enough apples, she needs to add the weight of all three bags. The total weight of the apples comes out to be 6.53 kilograms. This means that Erika has more than the required 6 kilograms of apples and is sufficient to make the recipe. It's important to note that Erika has an excess of apples, which can be helpful in case she needs extra for the recipe or for future use. The combination of different types of apples can also add variety and flavor to the recipe.

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When researching, here is where each aspect of an index card should be placed: Match the letter that corresponds to one of the items below to the correct location (1,2,3,4,5) on an index card.A.

Title of card (aspect of subject) - (2) This should be the center or topmost part of the index card. It should be clear and concise enough to reflect what is contained in the index card.B.

Source Number - (4) This is the number allocated to each source in your reference list.C. Page Number - (3) This refers to the page number(s) where the information was sourced from. It is usually written on the top right or left corner of the index card.D.

Quotation - (1) This refers to the exact words that were used in the source materials and is written verbatim. This is usually written in quotation marks.E.

Paraphrase - (5) This refers to rewording a particular section of information in your own words without changing its meaning. The paraphrase should be accurate, concise, and written in a sentence format.

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Let the price of ticket be "p"

and attendance be "A"

First, given,

When p = 16, A = 950

Then, given,

When p = 5, A = 1550

We can model these two pairs of points as coordinates,

We have to come up with the equation in the form A = mp + b, where

m is the slope and b is the y-intecept of the line.

We can use the following formula to find the equation of the line:

Let's substitute the points and find the linear equation in the form A = mp + b.

Answer:0.0285 hope this helps :)

Step-by-step explanation:

The expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.

Given a taxi charges $2.50 for the first mile and $0.40 for each mile

We are required to make an expression showing total cost and total cost of a 20 mile ride.

let the miles ride by tax be x.

Total cost of the product or service=Number of units*price of one units.

We have been given that $2.50 is fixed so we will not multiply our variable charge with $2.50 and multiply 0.40 with x.

So,the expression showing looks like 2.50+0.40x.

Now to find the cost when taxi travels 20 miles, we have to put x=20,

Cost=2.50+0.40*20

=2.50+(40*20)/100

=2.50+800/100

=2.50+8

=$10.50

Hence the expression which shows the total cost is 2.50+0.4x and the cost of riding 20 miles is $10.50.

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The statement is True.

In an analysis of variance (ANOVA), the larger the differences between the sample means are, the larger the F-ratio will be. The F-ratio compares the between-group variability to the within-group variability, and a larger F-ratio indicates more significant differences between the groups.

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