Solve (4-2) x 32
plz help

The limit of the function lim(θ→0) sin(2θ)/θ can be estimated by using a graph.

To estimate this limit graphically, you would first plot the function y = sin(2θ)/θ on a graph with the x-axis representing θ and the y-axis representing the function value. Since θ is measured in radians, make sure your graph is set to radians as well. As θ approaches 0, observe the behavior of the function.

Based on the graph, you will notice that the function approaches a value of 2 as θ approaches 0. Therefore, lim(θ→0) sin(2θ)/θ ≈ 2.

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Answer:

2 hours and 24 minutes.

We are supposed to determine whether the given statement is true or false, "f(x) = x^3 - x^2 has inflection at

x = 1/3. In other words, the second derivative of f(x) changes its sign from positive to negative or from negative to positive at the point x = a.

"Recall that the function f(x) has an inflection point at the point x = a

if its concavity changes at the point x = a.

In other words, the second derivative of f(x) changes its sign from positive to negative or from negative to positive at the point x = a.

Let us find the first and second derivatives of the function f(x).f(x) = x^3 - x^2

f'(x) = 3x^2 - 2x

f''(x) = 6x - 2

From the above second derivative, we can observe that f''(1/3) ≠ 0

since f''(1/3) = 6(1/3) - 2

= 0.

Therefore, the concavity of the function f(x) does not change at the point x = 1/3. Hence, the given statement is False.

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Answer: 70

Step-by-step explanation:

it will take 8 days to completely drain the pool. Ms. Cristaudo purchases a coffee and 6 donuts from Dunkin Donuts for a total of $1.
We don't have information about the price of individual donuts, so we can't determine the cost of the donuts separately from the coffee.

Mr. Wilson pays $5 to enter the spring festival and $0.75 per ride. We don't know how many rides he takes, so we can't calculate his total cost without more information.

Mr. Wilson has $50 in his lunch account and spends $2.50 on school lunch every day. To calculate how many days he can purchase lunch, we can divide his total balance by the daily cost:

$50 / $2.50 per day = 20 days

So Mr. Wilson can purchase school lunch for 20 days before running out of funds.

Mrs. Nelson is draining her pool, which has 4 feet of water. It drains 1/2 of a foot each day. To calculate how many days it will take to completely drain the pool, we can divide the initial depth of the water by the daily drain rate:

4 feet / (1/2 foot per day) = 8 days

So it will take 8 days to completely drain the pool.
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In summary, the radius of convergence is √2 and the interval of convergence is [-√2, √2].

To find the radius of convergence and interval of convergence of the power series, we can use the ratio test.

The given power series is:

∑ ((-1)^n (x^2)^n) / (n*2^n)

Let's apply the ratio test:

lim(n->∞) |((-1)^(n+1) (x^2)^(n+1)) / ((n+1)2^(n+1))| / |((-1)^n (x^2)^n) / (n2^n)|

Simplifying and canceling terms:

lim(n->∞) |(-1) (x^2) / (n+1)*2|

Taking the absolute value and applying the limit:

|(-1) (x^2) / 2| = |x^2/2|

For the series to converge, the ratio should be less than 1:

|x^2/2| < 1

Solving for x:

-1 < x^2/2 < 1

Multiplying both sides by 2:

-2 < x^2 < 2

Taking the square root:

√(-2) < x < √2

Since the radius of convergence is the distance from the center (x = 0) to the nearest endpoint of the interval of convergence, we can take the maximum value from the absolute values of the endpoints:

r = max(|√(-2)|, |√2|) = √2

Therefore, the radius of convergence is √2.

For the interval of convergence, we consider the endpoints:

When x = √2, the series becomes:

∑ ((-1)^n (2)^n) / (n*2^n)

This is the alternating harmonic series, which converges.

When x = -√2, the series becomes:

∑ ((-1)^n (2)^n) / (n*2^n)

This is again the alternating harmonic series, which converges.

Therefore, the interval of convergence is [-√2, √2].

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The best buy is from dealership B because dealership B has a lesser base price

For the purpose of this exercise, the add-on options to select are:

The total amount of the add-on options is:

Total = $500 + $1500

Total = $2000

The inequality

This is represented using:

Base price * (1 + Tax) + Fees + Add-on total ≤ 20000

So, we have:

(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000

Solve for x

We have:

(1 + 6.75%) * x + 751.56 + 2000 ≤ 20000

Evaluate the like terms

(1 + 6.75%) * x  ≤ 17248.44

Divide both sides by (1 + 6.75%)

x  ≤ 16157.79

The solution means that the base price of the car cannot exceed $16157.78 for dealership A

The graph of the possible base price

See attachment

The total amount of the add-on options is:

Total = $750 + $1000

Total = $1750

The inequality

This is represented using:

Base price * (1 + Tax) + Fees + Add-on total ≤ 20000

So, we have:

(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000

Solve for x

We have:

(1 + 6.75%) * x + 1524.72 + 1750 ≤ 20000

Evaluate the like terms

(1 + 6.75%) * x  ≤ 16725.28

Divide both sides by (1 + 6.75%)

x  ≤ 15667.71

The solution means that the base price of the car cannot exceed $15667.71 for dealership B

The graph of the possible base price

See attachment

Buy from dealership B because dealership B has a lesser base price

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The first part of the function is a constant function, so its Fourier Transform is zero. The second part of the function is a linear function, so its Fourier Transform is a constant times

the Fourier Transform of the given function:

F(w) = where and is the Heaviside step function.

To find the Fourier Transform of the given function, we can use the following steps:

Start with the definition of the Fourier Transform:

F(w) = ∫ f(x) e^(-iwx) dx

Substitute the given function into the formula:

F(w) = ∫ 1 - x/2 0 -1 otherwise e^(-iwx) dx

Split the integral into two parts:

F(w) = ∫ 1 e^(-iwx) dx + ∫ -x/2 e^(-iwx) dx

Evaluate the first integral:

∫ 1 e^(-iwx) dx = -i/w

Evaluate the second integral:

∫ -x/2 e^(-iwx) dx = i/(2w) (e^(-iwx) - e^(iwx))

Add the two integrals to get the final answer:

F(w) =

The given function is a piecewise function, so we need to use the Heaviside step function to evaluate the Fourier Transform. The Heaviside step function is defined as follows:

H(x) = where is a real number.

In this case, the Heaviside step function is used to represent the two parts of the given function. The first part of the function is zero for

and one for. The second part of the function is zero for and

The Fourier Transform of a piecewise function can be found using the following steps:

For each part of the function, find the Fourier Transform of the function.

Add the Fourier Transforms of each part to get the final answer.

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Answer:

1 unit

......................................

Answer:

10x+12 is the answer in my calculation.

Answer:

x = 4, y = 5.

Step-by-step explanation:

4x-2=3y-1

y+3=3x-4

Rearranging:

4x - 3y =  1       (A)

-3x + y = -7      (B)

Multiply  B by 3:

-9x + 3y = -21   (C)
Adding A and C:

-5x = -20

x = 4

Substitute for x in equation A:

4(4) - 3y = 1

3y = 15

y = 5.

Answer:

D

Step-by-step explanation:

Because I know

Answer:

1. The bar interval is correct, the height does not need to be changed.

2. The bar interval is not correct, the height has to change higher by 1.

3. The bar interval is not correct, the height has to change lower by 1.

4. The bar interval is correct, the height does not need to be changed.

I hope this helped

Answer:

Could you Write the question more clearly?

Step-by-step explanation:

The Beta distribution is a continuous probability distribution with support on the interval [0,1], and is often used to model random variables that have limited range, such as probabilities or proportions.

The Beta [a, b] density has the form f(x) = {[(a+b)/([(a) r()) } Xa-1 (1 - X)B-1 +, where a and b are constants and 0 <= x <= 1. This density function describes the probability of observing a value x from a Beta [a, b] distribution.

The parameters a and b are often referred to as shape parameters, and they control the shape of the distribution. Specifically, the larger the values of a and b, the more peaked the distribution will be, while smaller values of a and b will lead to flatter distributions.

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Answer:

Aisha ran farther

Step-by-step explanation:

Aisha - 1 9/12

Paula - 1 5/12

Make the denominator the same

The z-score of the value 62 in the distribution is -4.25

From the question, the given parameters about the distribution are

Mean value of the set of data = 79

Standard deviation value of the set of data = 4

The actual data value = 62

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the known values in the above equation, so, we have the following representation

z = (62 - 79)/4

Evaluate the difference

z = -17/4

Evaluate the quotient

z = -4.25

Hence, the z-score is -4.25

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The required equation of the line is y = -18x + 1673.  

One of the most common ways to represent a line's equation is in the slope-intercept form of a line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line.

Slope-intercept form of a line is y = mx + c

where m = slope and c - y-intercept of the line.

Here we have

Given points (86, 125) and

Slope of the line m = -18  

As we know

Slope intercept form of a line is y = mx + c  

Given m = - 18

=> y = (-18)x + c

=> y = -18x + c

Given points (86, 125) substitute in the above line

=> 125 = -18(86) + c

=> 125 = -1548 + c

=> c = 1673  

Therefore,

The required equation of the line is y = -18x + 1673.  

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The general solution form for the recurrence tn = 120,-2 - 166n-3 + 2.

Given a recurrence relation tn = 120,-2 - 166n-3 + 2 we have to derive the general solution form for the recurrence sequence.

We have the recurrence relation tn = 120,-2 - 166n-3 + 2

We need to find the solution for the recurrence relation.

Associated Homogeneous Equation: First, we need to find the associated homogeneous equation.

                                     tn = -166n-3 …..(i)

The characteristic equation is given by the following:tn = arn. Where ‘a’ is a constant.

We have tn = -166n-3..... (from equation i)ar^n = -166n-3

                                Let's assume r³ = t.

Then equation i becomes ar^3 = -166(r³) - 3ar^3 + 166 = 0ar³ = 166

Hence r = ±31.10.3587Complex roots: α + iβ, α - iβ

Characteristics Polynomial:

                   So, the characteristic polynomial becomes(r - 31)(r + 31)(r - 10.3587 - 1.7503i)(r - 10.3587 + 1.7503i) = 0

The general solution of the Homogeneous equation:

Now we have to find the general solution of the homogeneous equation.

                  tn = C1(-31)n + C2(31)n + C3 (10.3587 + 1.7503i)n + C4(10.3587 - 1.7503i)

                        nWhere C1, C2, C3, C4 are constants.

Computing a Particular Solution:

                Now we have to compute the particular solution.

                                  tn = 120-2 - 166n-3 + 2

Here the constant term is (120-2) + 2 = 122.

The solution of the recurrence relation is:tn = A122Where A is the constant.

The General Solution of Non-Homogeneous Equation:

        The general solution of the non-homogeneous equation is given bytn = C1(-31)n + C2(31)n + C3 (10.3587 + 1.7503i)n + C4(10.3587 - 1.7503i)n + A122

Hence, we have derived the general solution form for the recurrence tn = 120,-2 - 166n-3 + 2.

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Answer:

πd = circumference of a circle

π53 = 166.504410

166.5 X 18 = 2997cm = 29.97m

If the parallelogram is rotated 270° about the origin. Then the coordinate of the image will be (1,-2), (1,-7), (-3, -6), and (-3, -1).

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

Parallelogram JKLM has vertices J(2, 1), K(7, 1), L(6, −3), and M(1, −3).

If the parallelogram is rotated 270° about the origin. Then the coordinate of the image will be

J(2, 1) → (1, -2)

K(7, 1) → (1, -7)

L(6, −3) → (-3, -6)

M(1, −3) → (-3, -1).

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Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Answer:

x = 10, y = 5

Step-by-step explanation:

The sine of 60 is given by the division of the opposite side of 60º by the hypothenuse.

We have that:

sine of 60 is sqrt(3)/2

The oopposite side is 5sqrt(3)

The hypothenuse is x.

So

Then we apply cross multiplication.

The cosine of 60 is the adjacent side divided by the hypothenuse.

The cosine of 60 is 1/2.

The adjacent side is y.

The hypothenuse is x = 10. So

Applying cross multiplication

2y = 10

y = 5

The sentences are 4 = false, 5 = true and 6 = false.

4 = False: Measures of central tendency, such as the mean, median, and mode, actually show the center or average of a set of data.

They do not provide information about how the data tends to move away from the center.

Measures of dispersion, such as the standard deviation or range, are used to assess the spread or variability of the data.

5 = True: Measures of central tendency are used to determine the center or typical value of a dataset.

The mean, for example, calculates the average of all the data points, while the median represents the middle value when the data is arranged in ascending or descending order.

The mode identifies the most frequently occurring value.

6 = False: "Inferential" statistics involves making inferences or drawing conclusions about a population based on information obtained from a sample.

It uses probability theory and sampling techniques to generalize findings from a smaller group (sample) to a larger group (population).

In essence, inferential statistics allows researchers to make educated guesses or predictions about a larger population based on the information gathered from a representative sample.

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Answer:

3rd choice

Step-by-step explanation:

y = mx + b

Look at where the line crosses the y-axis. That is the y-intercept. It is 2, so b = 2, and you have

y = mx + 2

Now we need the slope, m.

Start at (0, 2). Go up 1 and right 2.

slope = m = rise/run = 1/2

Now you have

y = 1/2 x + 2

Answer: 3rd choice

Answer:

\(c)y=\frac{1}{2}x+2\)

Step-by-step explanation:

\(We\ know\ that,\\The\ equation\ of\ a\ graph\ is\ given\ by\ the\ formula:\\y=mx+b,\ where\ m\ is\ the\ slope\ of\ the\ graph,\ and\ b\ is\ the\ y-intercept;\\Here,\\First,\\Lets\ calculate\ the\ slope\ of\ the\ graph:\\We\ also\ know\ that,\\Slope(m)=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}\\Lets\ consider\ any\ two\ points\ which\ lie\ on\ the\ line:\\(2,3),(-2,1)\\Hence,\\The\ slope\ of\ the\ given\ line=\frac{1-3}{-2-2}=\frac{-2}{-4}=\frac{1}{2}\\Hence,\\m=\frac{1}{2}\\\)

\(Now,\\The\ y-intercept\ is\ the\ point\ at\ which\ the\ graph\ intersects\ the\ whole\ y-axis.\\Hence,\\Here,\\The\ line\ of\ the\ graph\ cuts\ the\ y-axis\ at\ (0,2).\\The\ y-intercept\ of\ the\ line=2\\Hence,\\The\ equation\ of\ the\ line:\\y=(\frac{1}{2})x+(+2)\\y=\frac{1}{2}x+2\)

Now

\(\\ \rm\longmapsto Speed=\dfrac{Distance}{Time}\)

\(\\ \rm\longmapsto Time=\dfrac{Distance}{Speed}\)

\(\\ \rm\longmapsto Time=\dfrac{150\times 10^6}{3\times 10^5}\)

\(\\ \rm\longmapsto Time=50\times 10^1\)

\(\\ \rm\longmapsto Time=500s\)

\(\\ \rm\longmapsto Time=8.33min\)

Given the expression

Use the facts that

So, the expression can be simplified as:

Answer:

x - 2 and x - 1 can be possible length and width of the rectangle.

Step-by-step explanation:

Area = x² - 3x + 2

◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇

To find possible length and width we can factorize the above expression.

◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇

x² - 3x + 2 ( 2 = -1 × -2 )

x² - x - 2x + 2 ( 3 = -1 + -2 )

x(x - 1) + -2(x - 1)

(x - 2) (x - 1)

◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇◇

x - 2 and x - 1 can be possible length and width of the rectangle.

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Answer:

C) 65 degrees

Step-by-step explanation:

Both of the angles given are supplementary angles meaning the equal 180 degrees. So you format it as (28x + 3) + (17x - 3) = 180. Simplify the equation to get 45x = 180. Divide 180 by 45 to recieve 4. We now know x is equal to 4. Plug 4 into x for 17x - 3 to get 17(4) - 3. Which equals 65.

Probabilities are used to determine the chances of events

The probability that an applicant with a college degree or an applicant who hasn't attended  college is hired is 0.80

Using the following representations

\(\mathbf{Attending\ college\ without\ experience \to A}\)

\(\mathbf{Completed\ college\ without\ experience \to B}\)

\(\mathbf{Have\ experience\ no\ college\to C}\)

So, we have:

\(\mathbf{A = 9}\)

\(\mathbf{B = 24}\)

\(\mathbf{C = 12}\)

The probability that an applicant with a college degree or an applicant who hasn't attended  college is hiredis: P(B or C)

So, we have:

\(\mathbf{P(B\ or\ C) = P(B) + P(C)}\)

This gives

\(\mathbf{P(B\ or\ C) = \frac{B + C}{Total}}\)

So, we have:

\(\mathbf{P(B\ or\ C) = \frac{24+12}{9+24+12}}\)

\(\mathbf{P(B\ or\ C) = \frac{36}{45}}\)

\(\mathbf{P(B\ or\ C) = 0.80}\)

Hence, the probability that an applicant with a college degree or an applicant who hasn't attended  college is hired is 0.80

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