Simplify: (9x^3+2x^2-5x+4)-(5x^3-7x+4)
Show all steps used to solve this problem and write your final answer in factored form in the space provided.

If A central angle has a measure of 2. 3 radians and the subtended arc length is 12 cm, then the radius of the circle is approximately 5.2 cm.

The formula relating the central angle, radius, and arc length of a circle is:

arc length = radius × central angle

We can use this formula to find the radius of the circle, given the central angle and arc length.

Substituting the given values, we get:

12 cm = r × 2.3 rad

Solving for r, we divide both sides by 2.3 rad:

r = 12 cm / 2.3 rad

Using a calculator, we get:

r ≈ 5.2174 cm

Rounding to the nearest tenth, we get:

r ≈ 5.2 cm

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The distance that the ball was hit, considering that it was hit at an angle of 25° and a velocity of 80 mph, is given as follows:

d = 99.7 meters.

First we must obtain the time that the ball was in the air, and the equation is given as follows:

t = 2vy/g.

In which:

The y-component of the velocity is given as follows:

vy = vsin(y)

vy = 35.71 x sine of 25 degrees. (35.71 m/s = 80 mph)

vy = 15.1 m/s.

As the gravity is of 9.81 m/s², the time is given as follows:

t = 2 x 15.1/9.81

t = 3.08 s.

The distance is then given as follows:

d = Vxt.

d = 35.71 x cosine of 25 degrees x 3.08

d = 99.7 meters

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Step-by-step explanation:

as I just explained in your other posting of the same question :

y = cos(30) × 8 = sqrt(3)/2 × 8 = 4×sqrt(3).

so, the number in the green box is 4.

Answer:

  99.6 cm²

Step-by-step explanation:

You want to know the area of a sector that has radius 6 cm, and subtends an arc of 317°.

The formula for the area of a sector is ...

  A = 1/2r²θ . . . . . . where θ is the central angle in radians

  A = 1/2(6 cm)²(317·π/180) ≈ 99.6 cm²

The area of the sector is about 99.6 square centimeters.

The rate of change of the function f(x) = -2x² + 6x + 1 at x = 1 is approximately 0.302.

What is the definition of a function?

In mathematics, a function is a rule that assigns to each element in a set (called the domain) exactly one element in another set (called the range). In other words, a function takes an input value and produces a unique output value. The input value is usually represented by the variable x, while the output value is represented by the variable y or f(x).

Now,

The rate of change of a function is the slope of the line that connects any two points on the graph of the function. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

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

So to find the rate of change of the function f(x) = -2x² + 6x + 1, we need to choose two values of x and find the corresponding values of f(x), and then calculate the slope of the line passing through these two points.

Let's choose two values of x that are close to each other, say x1 = 1 and x2 = 1.01. Then, we have:

f(x1) = -2(1)² + 6(1) + 1 = 5

f(x2) = -2(1.01)² + 6(1.01) + 1 = 5.0302

Now, we can calculate the slope of the line passing through these two points:

slope = (f(x2) - f(x1))/(x2 - x1) = (5.0302 - 5)/(1.01 - 1) = 0.302

So,

     the rate of change of the function f(x) = -2x² + 6x + 1 at x = 1 is approximately 0.302. Note that the rate of change of a function is not constant, but varies with the value of x.

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Length times width = area of a rectangle.

16ft×24ft= 384

Area of the patio since all sides are equal to

4

width×width×width×width= 384

Answer=4.4267276788

Based on the given criterion, the variables that are sufficiently reliable for middle adolescents are creativity, critical thinking, and cognitive ability

Traditionally, authors of textbooks on tests and measurements have suggested that, at a minimum, a test should have a test-retest reliability of .70 to be considered sufficiently reliable to use for the assessment of individuals. Using this criterion when evaluating the test-retest reliability coefficients for middle adolescents, the variables measured by the test that are sufficiently reliable are as follows:In this scenario, the variables measured by the test, which are sufficiently reliable for middle adolescents, can be determined by identifying the variables whose test-retest reliability coefficients are greater than or equal to 0.70. It can be observed that variables such as creativity, critical thinking, and cognitive ability are all variables that are considered reliable for middle adolescents. Therefore, based on the given criterion, the variables that are sufficiently reliable for middle adolescents are creativity, critical thinking, and cognitive ability.A reliability coefficient is a statistical method used to assess the reliability of a measurement by determining the consistency of scores obtained by the measurement instrument. A test-retest reliability is a statistical method used to determine the reliability of a test's measurements by comparing the scores obtained from taking the same test multiple times over a period of time. The coefficient of test-retest reliability measures the consistency of test scores over time, indicating whether a test is stable and reliable enough to be used as an assessment tool.

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Answer: 48 old houses

Step-by-step explanation:

Ratio 5:8

Ratio 30:?

30/5=6

8 x 6= ...

48!!!

30:48

did this make sense??

The answer of the question based on the representing the value in two different methods are given below;

Distance refers to amount of space between the two objects or points in the space. It is measure of  length of  path traveled by object or person from one point to the another.

Distance can be measured in various units like  meters, kilometers, feet, miles, etc. It is fundamental concept in a  geometry and is used in a various areas of science, engineering, and everyday life.

1:50000 can be represented in two different ways as follows:

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The answer will be as follows after answering the supplied question After  equation reaching the break-even threshold, the firm will begin to profit.

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

Rental rate per day x number of rental days Equals total revenue

Total revenue = $59.99 multiplied by

Total cost = vehicle cost + daily maintenance cost * number of rental days

Total expenditure = $18,000 + $35x

We can now put these two equations equal to determine the break-even point:

$59.99x = $18,000 + $35x

When we solve for x, we get:

$24.99x = $18,000

x = 720.29

We round up to 721 days since we can't rent a vehicle for a fractional amount of days.

As a result, in order to break even, the corporation needs rent a vehicle for at least 721 days.

After reaching the break-even threshold, the firm will begin to profit.

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The integers and radius for different circles as instructed are; (1.) Circle A (1, 3) with r= 3   (2.) Circle B (5, 3) with r= 5.

1. On a y and x graph, create a dot and get the integers for the dot which are the numbers you find when you trace the dot to the x and y axis.

Integers are a set of numbers that include positive numbers, negative numbers, and zero. Integers are whole numbers (not fractions or decimals) that can be represented on the number line. Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on.

For the diagram below, diagram A and B share a similar point at the y axis and a different point at the x axis. There integers are

A ( 1, 3) and

B (5, 3)

The radius of choice for A is r= 3

The radius of choice for B is r= 5

Therefore the diagram should look like the one in the attached file.

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Answer:

x=7 & y=-7

Step-by-step explanation:

from the 2nd equation 7x+7y=0 we can get that

x=-y

substitute that into the first equation to get

3y-5y=14

-2y=14

y=-7

then

x=7

The value of x in the regular octagon is 14°. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

All real numbers are claimed to be able to be described by the four basic operations, sometimes known as "arithmetic operations". Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.

We are given that the measure of each angle is (8x + 23)°.

We know that the sum of angles of an octagon is 1080°.

So, using the arithmetic operation, we get

⇒ 8 * (8x + 23)° = 1080°

⇒ 64x + 184 = 1080°

⇒ 64x = 896°

⇒ x = 14°

Hence, the value of x in the regular octagon is 14°.

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Hence the amount of savings of Rick and Halens is = 9x+24.

When we write any linguistic statement in mathematics form called mathematical expression.

Rick has 3x to start with

Let w = the number of weeks he will save.

Savings = 3x + 3*w  

Let w = 4

Savings = 3x+3*4

Savings = 3x + 12

Halen has twice Rick's amount,

Let w = the number of weeks she will save.

Savings=6x+3w

let w=4

savings=6x+12

Now we come to the question. It seems to want the total combining both of them.

Rick + Halen =  3x+12+6x+12 = 9x+24

Hence the amount of savings of rick and Halens is = 9x+24.

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it will take about 9.90 years to double the initial investment of $4000 at 7% continuous compound interest.

We can use the formula for continuous compound interest:

[tex]A = Pe^(rt)[/tex]

where A is the amount of money after time t, P is the principal (initial investment), r is the interest rate, and e is the mathematical constant approximately equal to 2.71828.

To find the time it takes to double the initial investment, we want to solve for t when A = 2P (twice the initial investment). Substituting the given values, we have:

[tex]2P = Pe^(rt)[/tex]

Dividing both sides by P, we get:

[tex]2 = e^(rt)[/tex]

Taking the natural logarithm (ln) of both sides, we have:

[tex]ln(2) = ln(e^(rt))[/tex]

ln(2) = rt * ln(e)

Since ln(e) = 1, we can simplify further to:

ln(2) = rt

Solving for t, we get:

t = ln(2) / r

Substituting the given values, we have:

t = ln(2) / 0.07

t ≈ 9.90 years

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in vector D [-2,1,3,0], we can multiply [-6,-4,7,1] by -2 and [-4,-3,2,-1] by 1 and add the two results together to obtain [-2,1,3,0]. This means that vector D can be written as a linear combination of vector [-6,-4,7,1] and [-4,-3,2,-1], making it the correct answer.

We can use the concept of linear combinations to answer this question. A linear combination of two vectors is a vector that can be written as the sum of two or more vectors. To solve this problem, we need to express the four given vectors as a linear combination of vector [-6,-4,7,1] and [-4,-3,2,-1]. We can do this by multiplying each vector element by a scalar and then adding them together. For example, in vector D [-2,1,3,0], we can multiply [-6,-4,7,1] by -2 and [-4,-3,2,-1] by 1 and add the two results together to obtain [-2,1,3,0]. This means that vector D can be written as a linear combination of vector [-6,-4,7,1] and [-4,-3,2,-1], making it the correct answer.

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The perimeter of a rectangle is given by the formula P = 2(l+w), where l is the length and w is the width of the rectangle. The correct answer is that the perimeter is increased by a factor of 10.

In this case, the width is 3 cm and the length is 10 cm, so the initial perimeter is:

P = 2(10+3) = 26 cm

Now, if we multiply the dimensions by 10, the new length would be 10 x 10 = 100 cm and the new width would be 3 x 10 = 30 cm. The new perimeter would then be:

P' = 2(100+30) = 260 cm

Comparing the initial perimeter to the new perimeter, we can see that the new perimeter is 260/26 = 10 times larger than the initial perimeter. Therefore, the correct answer is that the perimeter is increased by a factor of 10

It's important to note that the word "factor" is often used to describe the degree to which something changes. In this case, a factor of 10 means that the new perimeter is 10 times larger than the initial perimeter. If we were to use the word "increase" instead, we would say that the perimeter is increased by 250% (or 2.5 times).

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Answer:

B

Step-by-step explanation:

The only way for two numbers to = zero when they're added together is if one is negative. There are no two positive numbers that when added together will equal 0, therefore if p and t are positive, their sum cannot be 0

Answer: Yes the soultuion is corrrect

Step-by-step explanation:

The difference in commission for selling goods worth Rs. 20 lakhs and Rs. 30 lakhs is Rs. 7,500.

The commission on sales worth Rs. 20 lakhs would be:

1% of (20 lakhs) = 0.01 x 20,00,000 = Rs. 20,000

The commission on sales worth Rs. 30 lakhs would be:

1% of (25 lakhs) + 1.5% of (5 lakhs) = (0.01 x 25,00,000) + (0.015 x 5,00,000) = Rs. 27,500

The difference in commission between the two sales would be:

Rs. 27,500 - Rs. 20,000 = Rs. 7,500

Therefore, the difference in commission for selling goods worth Rs. 20 lakhs and Rs. 30 lakhs is Rs. 7,500.

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The two points that a line of fit would go through to best fit the data are (3, 5) and (10, 1).

We need to find which pair of points have a line passing through them that best fits the data. One way to do this is to calculate the slope of the line passing through each pair of points and choose the pair of points with the slope closest to the average slope.

The slope of a line passing through two points [tex](x_1, y_1)[/tex]  [tex](x_2, y_2)[/tex] is given by the formula:

slope = [tex]\frac{(y_2 - y_1)}{ (x_2 - x_1)}[/tex]

Using this formula, we can calculate the slopes of the lines passing through each pair of points:

Pair 1: slope = [tex]\frac{(1 - 4)}{(9-6)}[/tex]  = -1

Pair 2: slope = [tex]\frac{(1 - 5)}{(10-3)}[/tex] = -0.67

Pair 3: slope = [tex]\frac{(1 - 8) }{(10-1)}[/tex] = -0.88

Pair 4: slope =[tex]\frac{ (3 - 5)}{(7-1)}[/tex] = -0.33

The average slope is:

average slope = [tex]\frac{(-1 + (-0.67) + (-0.88) + (-0.33))}{4}[/tex] = -0.72

The pair of points with the slope closest to the average slope is pair 2, with a slope of -0.67. Therefore, the two points that a line of fit would go through to best fit the data are (3, 5) and (10, 1).

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Answer:

M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]

where M is the monthly payment, P is the principal (the cost of the house minus the down payment), i is the monthly interest rate (6.00% divided by 12), and n is the total number of payments (30 years times 12 months per year).

Plugging in the values, we get:

P = $450,000 - 0 (assuming no down payment)

i = 0.06 / 12 = 0.005

n = 30 x 12 = 360

M = $450,000 [ 0.005(1 + 0.005)^360 ] / [ (1 + 0.005)^360 - 1] = $2,695.55

So the monthly mortgage payment is $2,695.55.

To find the monthly payment with taxes and insurance, we need to add the yearly taxes and insurance and divide by 12 to get the monthly amounts. So:

Monthly Taxes = $2,000 / 12 = $166.67

Monthly Insurance = $1,500 / 12 = $125.00

Total Monthly Payment with Taxes and Insurance = $2,695.55 + $166.67 + $125.00 = $2,987.22

Therefore, the monthly payments with taxes and insurance for the $450,000 house loan are $2,987.22.

a .The probability that x of the top 25 pairs play east-west is: P(X = x) = (25 choose x) / (50 choose 25) , b. The probability that the top 5 pairs all play in the same direction is: P(all 5 play the same direction) = (1/2) * (24/49) * (23/48) * (22/47) * (21/46), c. The pmf of X is given by P(X = x) = [(n choose x) * (n choose n - x)] / [(2n choose n)], and the expected value and variance of X are E(X) = n/2 and V(X) = (n² - 1)/12.

P(X = x) = [(n choose x) * (n choose n - x)] / [(2n choose n)] yields the pmf of X. , and X's expected value and variance are, respectively, E(X) = n/2 and V(X) = (n² - 1)/12.

(a) Let X be the number of top 25 pairs that play east-west. Since there are 25 east-west pairs and 25 north-south pairs, the total number of ways to choose 25 pairs to play east-west is (50 choose 25) = 50! / (25! * 25!). Similarly, the total number of ways to choose x top pairs to play east-west is (25 choose x) * (25 choose 25 - x) = (25 choose x), since the remaining 25 pairs automatically play east-west. Therefore, the probability that x of the top 25 pairs play east-west is:

P(X = x) = (25 choose x) / (50 choose 25)

(b) The probability that the top pair plays east-west is 25/50 = 1/2. Once the top pair has been assigned a direction, the probability that the second pair plays in the same direction is 24/49, the probability that the third pair plays in the same direction is 23/48, and so on. Therefore, the probability that the top 5 pairs all play in the same direction is:

P(all 5 play the same direction) = (1/2) * (24/49) * (23/48) * (22/47) * (21/46)

(c) Let X be the number of top n pairs that play east-west, where there are 2n pairs total. Then X can take on values from 0 to n. To find the pmf of X, we can use the same method as in part (a):

P(X = x) = [(2n - n) choose x] / [(2n) choose n]

= [(n choose x) * (n choose n - x)] / [(2n choose n)]

The expected value of X is:

E(X) = sum[x * P(X = x), {x, 0, n}]

= sum[x * (n choose x) * (n choose n - x) / (2n choose n), {x, 0, n}]

Using the identity sum[x * (n choose x) * (n choose k - x), {x, 0, k}] = k * (n choose k), we can simplify this to:

E(X) = n/2

The variance of X is:

V(X) = E(X²) - E(X)²

= sum[x² * P(X = x), {x, 0, n}] - (n/2)²

= sum[x * (n choose x) * (n choose n - x) / (2n choose n), {x, 0, n}] - (n/2)²

= (n² - 1)/12

Therefore, the pmf of X is given by P(X = x) = [(n choose x) * (n choose n - x)] / [(2n choose n)], and the expected value and variance of X are E(X) = n/2 and V(X) = (n² - 1)/12, respectively.

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The estimated length of the zip line is 62.8 feet.

The length of a zip line can be estimated using the formula for the length of a side of a right triangle, which is the square root of the sum of the squares of the two shorter sides. In the case of the obstacle course, the two shorter sides are the height of the tower and the horizontal distance from the base of the tower to the point on the ground.

To calculate the length of the zip line, we first need to calculate the height of the tower. The angle of elevation of the zip line is 33°, so we can use trigonometry and the Law of Sines to calculate the height of the tower. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is the same for all sides of the triangle. Since we know the angle of elevation (33°) and the horizontal distance (48.2 feet), we can calculate the height of the tower using the formula:

h = (48.2 * sin(33°)) / sin(90°)

h = 42.7 feet

Now we can calculate the length of the zip line using the formula for the length of a side of a right triangle:

[tex]L = sqrt(h^2 + d^2)L = sqrt(42.7^2 + 48.2^2)L = 62.8 feet[/tex]

Rounding to the nearest tenth of a foot, the length of the zip line is 62.8 feet.

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The surface area of the three-dimensional figure represented by this net is 54 square inches, which is calculated by multiplying the area of the base (9 square inches) by the height of the four congruent triangles (8 inches).

The surface area of the three-dimensional figure represented by this net is 54 square inches. To calculate this, first we need to find the area of the base. The base is a square, with side lengths of 3 inches each. Therefore, the area of the base is 3 x 3 = 9 square inches. Next, we need to find the height of the four congruent triangles. The height is 8 inches. Finally, we can calculate the surface area by multiplying the area of the base (9 square inches) by the height of the four congruent triangles (8 inches). This gives us a total surface area of 54 square inches.

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Statement (3) follows from statements (1) and (2) by the Law of Syllogism. So, the correct option c) which is Yes; Law of Syllogism

Here's the reasoning:

(1) If you use a pencil you can erase mistakes.

(2) If you can erase mistakes your paper will be neater.

Therefore, by the Law of Syllogism,

(3) If you use a pencil your paper will be neater.

The Law of Syllogism states that if we have two conditional statements (if A then B) and (if B then C), we can logically conclude a third conditional statement (if A then C). That's exactly what we've done here since statement (1) is the first conditional statement, statement (2) is the second conditional statement, and statement (3) is the conclusion that follows from applying the Law of Syllogism to the first two statements.

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From the given data provided, the probability that number of adults selected in process are 3, less than 5, between 5 and 9, more than 5 but less than 10, 6 or more is 0.096, 0.41, 0.336, 0.232, 0.168 and mean of number of people tested for HIV is 3.6.

(a) The probability that an adult has not been tested for HIV is 1-0.20=0.80. Therefore, the probability that the first adult selected has not been tested for HIV is 0.80. The probability that the first and second adults selected have not been tested for HIV is 0.80 x 0.80=0.64. Continuing in this way, we see that the probability that X adults must be selected until one who has been tested for HIV is found is given by:

P(X≤x) = 1 - 0.80ˣ

(b) Using the formula from (a), we can find the probabilities as follows:

(i) P(X=3) = P(X≤3) - P(X≤2) = (1-0.80³) - (1-0.80²) = 0.096

(ii) P(X<5) = P(X≤4) = 1-0.80⁴ = 0.41

(iii) P(5≤X≤9) = P(X≤9) - P(X≤4) = (1-0.80⁹) - (1-0.80⁴) = 0.336

(iv) P(6≤X<10) = P(X≤9) - P(X≤5) = (1-0.80⁹) - (1-0.80⁵) = 0.232

(v) P(X≥6) = 1 - P(X≤5) = 1 - (1-0.80⁵) = 0.168

(c) To find the mean and variance of X, we first note that X follows a geometric distribution with parameter p=0.20. Therefore, the mean and variance of X are:

Mean of X = E(X) = 1/p = 1/0.20 = 5

Variance of X = Var(X) = (1-p)/p² = 0.8/0.04 = 20

(d) To find the probabilities for a random sample of 18 adults, we use the binomial distribution with parameters n=18 and p=0.20. The probabilities are:

(i) P(X=3) = (18 choose 3) x 0.20³ x 0.80¹⁵ = 0.236

(ii) P(X<5) = P(X≤4) = Σ(18 choose x) x 0.20ˣ x 0.80⁽¹⁸⁻ˣ⁾ for x=0 to 4 = 0.678

(iii) P(5≤X≤9) = Σ(18 choose x) x 0.20ˣ x 0.80⁽¹⁸⁻ˣ⁾ for x=5 to 9 = 0.286

(iv) P(6≤X<10) = Σ(18 choose x) x 0.20ˣ x 0.80⁽¹⁸⁻ˣ⁾ for x=6 to 9 = 0.207

(v) P(X≥6) = 1 - P(X≤5) = 1 - Σ(18 choose x) x 0.20ˣ x 0.80⁽¹⁸⁻ˣ⁾ for x=0 to 5 = 0.322

(e) The mean and variance of X for a sample of 18 adults are:

Mean of X = E(X) = n x p = 18 x 0.20 = 3.6

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Answer:

Let's start by translating the sentence into an equation using algebra.

Let's say the number is represented by "x".

According to the problem:

"Twice a number" can be written as "2x".

"If twice a number is decreased by 13" can be written as "2x - 13".

"The result is 9" can be written as "= 9".

Putting it all together, we get the equation:

2x - 13 = 9

Now we can solve for x:

2x = 22

x = 11

Therefore, the number is 11.