a circle has an arc of length 48π that is intercepted by a central angle of 120°. what is the radius of the circle? enter your answer in the box. 72 units

The given recurrence relation is an = 400 - 5an-2 + 200-3, with initial values a0 = 1 and a1 = 2. We need to find an explicit formula for a(n).

To find an explicit formula for a(n), we will first solve the recurrence relation and then generalize the pattern. Let's expand the relation for a few terms to observe the pattern:

a2 = 400 - 5a0 + 200-3 = 400 - 5(1) + 200-3 = 397

a3 = 400 - 5a1 + 200-3 = 400 - 5(2) + 200-3 = 388

a4 = 400 - 5a2 + 200-3 = 400 - 5(397) + 200-3 = -9603

a5 = 400 - 5a3 + 200-3 = 400 - 5(388) + 200-3 = -1260

From the given examples, we can observe that the recurrence relation alternates between positive and negative values. This suggests that the relation might have a periodic pattern. Since the given recurrence is a second-order relation (in terms of n), it is reasonable to assume that the pattern repeats every two terms.

Based on this observation, we can establish the following explicit formula for a(n):

a(n) = (-1)^(n mod 2) * (200n - 5^(n/2) + 200-3)

In this formula, the term (-1)^(n mod 2) alternates between -1 and 1 depending on the parity of n, ensuring the alternating pattern. The other terms account for the linear and exponential components of the recurrence relation.

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c = 1/2 ,the mean is μ = 1/2,  the CDF of f(x) is 2x^2   and the variance is σ² = 1/6.

The given pdf is f(x) = 4xc for 0 ≤ x ≤ 1.

To find the constant c such that f(x) is a pdf: We know that, For f(x) to be a pdf, it must satisfy the following two conditions:

The integral of f(x) over its support should be equal to 1. f(x) must be greater than or equal to 0 for all values of x. So,

Let us find the value of c first integral of f(x) from 0 to 1 should be equal to 1, therefore∫f(x)dx = ∫(4xc)dx for 0 ≤ x ≤ 1∫f(x)dx = 4∫xc dx for 0 ≤ x ≤ 1∫f(x)dx = 4[c(x^2/2)]_0^1∫f(x)dx = 2c

Therefore,∫f(x)dx = 1 implies 2c = 1 or c = 1/2.

Now we know the value of c. Let us find the CDF of f(x): CDF of f(x) = P(x ≤ X) = ∫f(t)dt from -∞ to x= ∫f(t)dt from 0 to x= ∫(4xt)dt from 0 to x= 2x^2 from 0 to x= 2x^2Therefore, the CDF of f(x) is 2x^2.

Graph of the PDF of f(x)For graphing the PDF of f(x), we need to know the values of x for which f(x) is defined as well as its shape and maximum value.f(x) = 4xc for 0 ≤ x ≤ 1The given function is a straight line with a slope of 4c and intersects the x-axis at 0 and the y-axis at 0.

We know that c = 1/2, thus (x) = 2x for 0 ≤ x ≤ 1The graph of f(x) will look as follows: Graph of the CDF of f(x)The graph of the CDF of f(x) will look as follows:

We can find the mean and variance of the PDF of f(x) using the following formulae: Mean, μ = ∫xf(x)dx from -∞ to ∞.Variance, σ² = ∫(x - μ)²f(x)dx from -∞ to ∞.

Substituting f(x) and its limits in the above formulae, we get: Mean, μ = ∫xf(x)dx from 0 to 1= ∫(2x^2)x dx from 0 to 12(1^4 - 0^4)/4= 1/2.

Variance, σ² = ∫(x - μ)²f(x)dx from 0 to 1= ∫(x - 1/2)²(2x)dx from 0 to 1= 1/6.

Therefore, the mean is μ = 1/2, and the variance is σ² = 1/6.

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Answer:

x= -1 and 5

hope that helps

The solutions to the quadratic equation [tex]4(x+2)^2=36[/tex] are x = -5 and x = 1.

Given the following data:

In this exercise, you're required to determine the value of x by solving for the factors (roots) of the given quadratic equation.

In Mathematics, the standard form of a quadratic equation is given by;

[tex]ax^2 + bx + c =0[/tex]

Where:

Dividing both sides by 4, we have:

[tex]4(x+2)^2=36\\\\(x+2)^2=9[/tex]

Taking the square root of both sides, we have:

[tex]x+2=\pm3\\\\x=\pm 3-2[/tex]

x = -5 or 1.

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Answer:

139 cm

Step-by-step explanation:

The p-value for testing the hypothesis that the average runtime of HP laptops is not equal to 120 minutes, based on a sample mean of 130 minutes from a sample of 50 laptops, is approximately 0.0006 (rounded to four decimal places).

To calculate the p-value, we use the t-test. Given the null hypothesis that the average runtime is 120 minutes, the alternative hypothesis is that it is not equal to 120 minutes. We compare the sample mean to the hypothesized population mean using the t-distribution.

Using the formula for the t-statistic:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (130 - 120) / (25 / sqrt(50))

t = 10 / (25 / 7.0711)

t = 2.8284

The degrees of freedom for the t-distribution are (sample size - 1) = (50 - 1) = 49.

Using the t-distribution table or statistical software, we find that the two-tailed p-value for a t-value of 2.8284 with 49 degrees of freedom is approximately 0.0006.

Therefore, the p-value for this hypothesis test is approximately 0.0006.

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If an equation indicates addition in its presentation, in order to solve for the unknown, you must perform the inverse operation, which is subtraction.

Equations typically involve an equality between two expressions, with one or more unknown variables.

To isolate the unknown variable and determine its value, you need to perform operations on both sides of the equation to simplify and solve for the variable.

When an equation shows addition, you can undo that operation by subtracting the same value from both sides of the equation. This ensures that the equation remains balanced and maintains equality.

For example, consider the equation:

x + 5 = 10

To solve for x, you need to eliminate the 5 added to x. To do so, you subtract 5 from both sides of the equation:

x + 5 - 5 = 10 - 5

x = 5

By subtracting 5 from both sides, you isolate the variable x and find that its value is 5.

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The product of 3x³-5x² + 3 and 2x² + 5x – 4 in Z7[x] / < x² +1 > is 2x + 1.

The product of the polynomials 3x³-5x² + 3 and 2x² + 5x – 4 in Z7[x] / < x² +1 > can be determined using polynomial long division.

To perform the division, we divide 3x³-5x² + 3 by x² + 1. The result of this division gives us the quotient and the remainder. In this case, the quotient is 2x and the remainder is 2x + 1.

The quotient represents the coefficient of x in the resulting product, while the remainder represents the constant term. Therefore, the resulting product is d. 2x + 1.

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Answer:

its c  because its not a b or d  and its alround 13 feet

Step-by-step explanation:

Answer:

(5,6)

Step-by-step explanation:

I'm guessing you mean the coordinates for the point where the lines intersect

Answer:

I believe it is b: (5,6)

Explanation:

The point (5,6) is the only point on the graph that both lines go through.

Answer:

i cat see it

Step-by-step explanation:

Answer:

The exact same

Step-by-step explanation:

^ just means put it up like 3^2=3²

Answer:

2x+10=-8

x=9

3x=9

x=3

2x=8

x=4

4x=20

x=5

Step-by-step explanation:

Answer:

1. 11

2. -13

3. -6

Step-by-step explanation:

Hope this helps. Have a great day! (I got this correct on edge :})

Answer:

21.952 [tex]yards^{3}[/tex]

Step-by-step explanation:

The volume of a cube is side length cubed.

So [tex]2.8^{3}[/tex] = 21.952

To approximate the value of f(1.5) using the tangent line to the graph of f at x = 1, we first find the derivative of f(x) to determine the slope of the tangent line at x = 1. The derivative is f'(x) = -2 sin x. Evaluating f'(x) at x = 1, we find the slope to be approximately -1.6829.

Next, we use the point-slope form of a line to find the equation of the tangent line. We have the point (1, f(1)) ≈ (1, 1.5839) and the slope -1.6829. Plugging these values into the point-slope form, we obtain the equation of the tangent line as y ≈ -1.6829x + 3.2668.

Finally, we substitute x = 1.5 into the equation of the tangent line to approximate f(1.5). After calculation, we find that f(1.5) is approximately 0.0009.

Therefore, the approximation for f(1.5) using the tangent line to the graph at x = 1 is approximately 0.0009.

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Answer:

without numbers= 10x + 15y = 120

Step-by-step explanation:

grocery store= 10x (x=8 in this case)

music lessons= 15y

Answer:

2) 4/5

3) 3

Step-by-step explanation:

2) 4/8-3=4/5

3)5x-4=3x+2

2x=6

x=3

Answer:

2) 4/5

3)x=3

Step-by-step explanation:

1) 4/8-3= 4/5

2) 5x-4=3x+2

bring 3x to left side and bring -4 to right side (remember signs will be reversed that is 3x becomes -3x and -4 will be 4

5x-3x=4+2

2x=6

x=6/2

x=3

put 3 in place of x

5*3-4=3*3+2

15-4=9+2

11=11

The gallons of paint that Beth used is 6 gallons.

The first step is to convert pint to gallon:

1 pint = 0.125 gallon

The second step is to multiply 0.125 by 48 : 0.125 x 48 = 6 gallons

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Answer:

5 is c 6 is b

Step-by-step explanation:

Answer:

5) C 6) B

Step-by-step explanation:

Yw

Answer:

The answer is C. 8 mm

Step-by-step explanation:

For me, i was able to divide the 80 by 12 and get 6.667 thus i was able to round up and conclude the answer in the answer choices

Answer:

c

Step-by-step explanation:

Answer:

2x^2+8x - 16

Step-by-step explanation:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

Given

R(x) = 6x ^ 2 + 5x - 8

C(x) = 4x ^ 2 - 3x + 7

P(x) = 6x ^ 2 + 5x - 8-(4x ^ 2 - 3x + 7)

P(x) = 6x ^ 2 + 5x - 8 - 4x ^ 2 + 3x - 8

Collect the like terms;

P(x) = 6x^2-4x^2+5x+3x-8-8

P(x) = 2x^2+8x - 16

Hence the company's profit for the fiscal year is 2x^2+8x - 16

Answer: 6

Step-by-step explanation:

The total amount needed by Kallen for the gift and the wrapping paper will be:

= $43.87 + $2.94

= $46.81

Since he earns $8.25 for each lawn he mows, the number of lawns they he will need to complete to buy the gift and wrapping will be:

= $46.81 / $8.25

= 5.67

= 6 lawns approximately

He'll need to mow 6 lawns

Answer: f

=  x = − 3 x + 1 = x = 1 4 g = x 2 + 2 x − 5f( x ) = f ( x )

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

5a2-7-b3

[tex]5*a*2-7-b*3[/tex]

[tex]5\cdot \left(-2\right)\cdot \left(2\right)-7-\left(-3\right)\cdot 3[/tex]

Therefore, -18 is your answer.

Hope this helped! :)

Answer:

first is no second is yes third is no fourth is yes

Step-by-step explanation:

I'm not sure btw

Answer:

[tex]M(7 ; 4)[/tex]

Step-by-step explanation:

midpoint -M

[tex]M(\frac{x_{1}+x_{2}}{2} ; \frac{y_{1}+y_{2}}{2} )[/tex]

[tex]M(\frac{9+5}{2} ; \frac{6+2}{2} )[/tex]

[tex]M(7 ; 4)[/tex]

Answer:

(7, 4 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Here (x₁, y₁ ) = (9, 6) and (x₂, y₂ ) = (5, 2) , then

midpoint = ( [tex]\frac{9+5}{2}[/tex] , [tex]\frac{6+2}{2}[/tex] ) = ([tex]\frac{14}{2}[/tex] , [tex]\frac{8}{2}[/tex] ) = (7, 4 )

Answer:

2

Step-by-step explanation:

60 divided by 28.3 which gives u 2.120141342756184

so round it which gives u 2

The given expression -13n^{2}+5n+23[/tex] is odd using modulo.

We are given to show that -13n2 + 5n + 23 is odd by using modulo.

Let's try to understand what modulo means:Modulo is a mathematical operation that finds the remainder when one number is divided by another. It is represented by the percentage symbol (%).

Now we can use the concept of modulo to show that -13n2 + 5n + 23 is odd.Note:An integer is odd if it is not even. In other words, odd numbers can't be divided evenly by 2. They leave a remainder of 1 when divided by 2.To show that -13n2 + 5n + 23 is odd, we need to take the given expression modulo 2.$$-13n^2 + 5n + 23 \; \mathrm{mod} \; 2$$We know that every odd integer can be written in the form of 2n + 1 where n is an integer. Now we just have to show that the expression -13n2 + 5n + 23 can be written in the form 2n + 1.$$-13n^2 + 5n + 23 \equiv 1 \; \mathrm{mod} \; 2$$Let's assume k is an integer such that $$-13n^2 + 5n + 23 = 2k + 1$$Rearranging the above expression, we get$$-13n^2 + 5n + 22 = 2k$$Now, we can use the concept of odd and even numbers. We know that an even number can be represented in the form 2n, where n is an integer. Now we just have to show that the expression -13n2 + 5n + 22 can be represented in the form 2n.$$-13n^2 + 5n + 22 = -13n^2 + 13n - 8n + 22$$$$= 13(n-1)(n-2) - 8$$We know that the product of two odd numbers is odd, and the subtraction of an even number from an odd number is odd. Here, (n-1) and (n-2) are consecutive integers, which means one of them is even and the other is odd. Therefore, the product (n-1)(n-2) is even. Hence, the above expression is odd.Since -13n2 + 5n + 23 is equivalent to 1 modulo 2, which means it can be represented in the form of 2n+1. Therefore, -13n2 + 5n + 23 is odd.

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Answer:

A. a + b = 180 is the correct option.