(1/2) (10)- (-12) -25

We can conclude that the sequences (a) and (d) are geometric sequences, while the sequences (b) and (c) are not geometric sequences.

Let's determine whether or not each of the given sequences are geometric sequences:

a) 1, 2.5, 6.25, 15.625

This is a geometric sequence with a common ratio of:

r = 2.5/1 = 6.25/2.5 = 15.625/6.25 = 2.5

b) 2, 8, 24, 48

This is not a geometric sequence because the difference between terms is not the same. (6, 16, 24)

c) 15, 22, 29, 36

This is not a geometric sequence because the difference between terms is not the same. (7, 7, 7)

d) 180, -90, 45, -22.5

This is a geometric sequence with a common ratio of:

r = -90/180 = 45/-90 = -22.5/45 = -1/2

So, we can conclude that the sequences (a) and (d) are geometric sequences, while the sequences (b) and (c) are not geometric sequences.

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The area A of the region S that lies under the graph of the continuous function f is \(\frac{1}{4}\).

(a)

\(A =\)  \(\int\limits^A_b {f(x)} \, dx\)  

   = \(\lim_{n \to \infty}\)∑ f(xi) Δ x

a = 0, b = 1 → Δ x = \(\frac{1-0}{n}\) = \(\frac{1}{n}\)

x₀ = 0, x₁ = \(\frac{1}{n}\) , x₂ = \(\frac{2}{n}\), x₃ = \(\frac{3}{n}\), ..., xi = \(\frac{i}{n}\)

f(x) = \(x^{3}\)

f(xi) = \([\frac{i}{n} ]^{3}\) = \(\frac{i^{3} }{n^{3} }\)

Then,

A = \(\lim_{n \to \infty}\) ∑(\(\frac{i^{3} }{n^{3} }\)) * \(\frac{1}{n}\)

(b)

A = \(\lim_{n \to \infty}\) [\(\frac{1}{n}\) * ∑ \(\frac{i^{3} }{n^{3} }\) ]

  = \(\lim_{n \to \infty}\) [\(\frac{1}{n}\) * \(\frac{1}{n^{3} }\) ∑ \(i^{3}\)]

  = \(\lim_{n \to \infty}\) [\(\frac{1}{n^{4} }\) * [\(\frac{n(n+1)}{2}\)]^2]

  = \(\lim_{n \to \infty}\) [\(\frac{1}{n^{4} }\) * \(\frac{n^{2}(n+1)^{2} }{4}\)]  

  = \(\lim_{n \to \infty}\) \(\frac{(n+1)^{2} }{4n^{2} }\)

  = \(\frac{1}{4}\) * \(\lim_{n \to \infty}\) \((\frac{n+1}{n} )^{2}\)

  = \(\frac{1}{4}\) * \(1^{2}\)

A = \(\frac{1}{4}\)

Therefore the area A of the region is \(\frac{1}{4}\).

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Answer:

x = 26

Step-by-step explanation:

68=x +(16+x) and if you plug in 26 it is 68

The age of the sample equation is t = (ln|0.3N₀| - C) / (-k).

The age of an organic artifact can be determined by solving the differential equation that describes the decay of carbon-14. In this case, if 30% of the original carbon-14 amount remains in the artifact, we can calculate its age.

The differential equation that describes the decay of carbon-14 is given by:

dN/dt = -kN,

where dN/dt represents the rate of change of carbon-14 amount with respect to time, N is the amount of carbon-14 in grams, t is time in years, and k is the decay constant.

To solve this differential equation, we can separate variables and integrate both sides:

∫ 1/N dN = -∫ k dt.

Integrating, we get:

ln|N| = -kt + C

where C is the constant of integration.

Now, let's consider the given information that 30% of the original carbon-14 amount remains. This implies that the current amount of carbon-14 (N) is equal to 0.3 times the original amount (N₀):

N = 0.3N₀.

Substituting this into the equation, we have:

ln|0.3N₀| = -kt + C.

Solving for t, we find:

t = (ln|0.3N₀| - C) / (-k).

The age of the sample can be calculated using this equation by substituting the known values of ln|0.3N₀|, C, and the decay constant k.

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The value of x is 18.4.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given that,

sin (2x + 7)° = cos (3x - 9)°  [Equation 1]

We have the trigonometric rule that,

cos (θ) = sin(90 - θ)

So, cos (3x - 9)° = sin (90 - (3x - 9))

So from equation 1,

sin (2x + 7)° = sin (90 - (3x - 9))

Equating,

2x + 7 = 90 - (3x - 9)

2x + 7 = 90 - 3x + 9

2x + 7 = 99 - 3x

5x = 92

x = 18.4

Hence the value of x is 18.4.

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Answer:

15-20%

Step-by-step explanation:

can u make me brainiest thanks

Using combination formula, there are 125,970 ways to select players who will travel.

To determine the number of ways to select 12 players to travel from a team of 20 members, we can use the concept of combinations.

The number of ways to select a group of players from a larger set without considering the order is given by the combination formula:

C(n, r) = n! / (r! * (n - r)!)

Where:

C(n, r) represents the number of combinations or ways to choose r items from a set of n items.

n! represents the factorial of n, which is the product of all positive integers from 1 to n.

In this case, we want to select 12 players to travel from a team of 20 members, so we can calculate:

C(20, 12) = 20! / (12! * (20 - 12)!)

Calculating the factorials:

20! = 20 * 19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

(20 - 12)! = 8!

Now, we can substitute these values into the combination formula:

C(20, 12) = 20! / (12! * 8!)

By calculating this expression, we can find the number of ways to select 12 players to travel:

C(20, 12) = 20! / (12! * 8!) ≈ 125,970

Therefore, there are approximately 125,970 ways to select the players who will travel from the basketball team.

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Answer:

1. x = 40; measure of angle is 110 deg

2. x = 37.2; the angles measure 100.6 deg and 79.4 deg

Step-by-step explanation:

1.

The two angles with measures are vertical angles. Vertical angles are congruent, so their measures are equal.

3x - 10 = 2x + 30

x = 40

3x - 10 = 3(40) - 10 = 120 - 10 = 110

The measure of the angles with measures is 110 deg.

2.

The two angles form a linear pair. Angles in a linear pair are supplementary. That means that their measures add to 180 deg.

3x - 11 + 2x + 5 = 180

5x - 6 = 180

5x = 186

x = 37.2

3x - 11 = 3(37.2) - 11 = 111.6 - 11 = 100.6

2x + 5 = 2(37.2) + 5 = 79.4

The angles measure 100.6 deg and 79.4 deg

The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

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A. The arc length of y=13x^(3/2) on the interval [4,6] is given by the integral ∫[4,6]√(1+(39x)^(2/3))dx. The arc length of y=√(4x) on the interval [0,4] can be expressed as an integral, but it is unclear whether it converges or diverges.

A. The arc length of a function y=f(x) on the interval [a,b] is given by the formula ∫[a,b]√(1+(f'(x))^2)dx. For the function y=13x^(3/2) on the interval [4,6], the derivative is f'(x) = (39/2)x^(1/2). Substituting this into the arc length formula gives ∫[4,6]√(1+(39x)^(2/3))dx.

B. The arc length of y=√(4x) on the interval [0,4] can also be expressed as an integral using the arc length formula, which becomes ∫[0,4]√(1+(2/x)^2)dx. However, it is uncertain whether this integral converges or diverges without evaluating it. Further analysis is needed to determine its convergence.

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Answer:

P = 44 feet

Step-by-step explanation:

P = 2(10) + 2(12)

P = 20+24

The p-value of the test statistic is p-value = 0.006. The null hypothesis will be rejected at 5% level of significance.

A two-tailed test in statistics determines if a sample is more than or less than a specific range of values by using a two-sided critical area of a distribution. It is employed in testing the null hypothesis and determining statistical significance. The alternative hypothesis is accepted in place of the null hypothesis if either of the critical areas apply to the sample under test.

A two-tailed test in statistics determines if a sample is greater or less than a range of values by using a two-sided critical area of a distribution.

It is employed in testing the null hypothesis and determining statistical significance.

The alternative hypothesis is accepted in place of the null hypothesis if either of the crucial areas apply to the sample under test.

Conventionally, two-tailed tests with a 2.5% cutoff on each side of the distribution are employed to evaluate significance at the 5% level.

How to calculate the p-value?

Determine the level of relevance, sometimes referred to as the level, in step one. Assume 0.05 if it isn't specified. Step 2: Evaluate the level of significance in relation to the p-value. Make the conclusion that supports the possible change and reject the null hypothesis if the p-value is lower.

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Answer:

42.1 for me

Step-by-step explanation:

goodluck ..

Answer:

i think its 49.6

If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.

When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.

This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.

The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.

In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.

It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.

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(-35-42-63)/7= (-140)/7=-20

Solving the given equation, the value of v that makes the statement true is:

A. v = 8.

The equation is:

\(12 = 12 + \frac{v - 8}{2}\)

Hence:

\(\frac{v - 8}{2} = 0\)

Applying cross multiplication:

v - 8 = 0

v = 8.

Hence option A is correct.

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1) Let's make use of Trigonometry to find out the sine of the sum of the angles:

So plugging into that the given values for x and y we have:

So now we can calculate the sin of 229.5º and multiply by the cosine of 117.6 and the cosine of 117.6º times the sine of 229.5º

Answer:

Min: (-3,2)

Hope this helps!!

(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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Answer:

y = 5x

Step-by-step explanation:

1. The slope-intercept form of any linear equation is \(y = mx + b\), where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept.

2. To find the slope, let's take the two points (0,0) and (100,500) to then plug their values in this formula: \(\frac{y_2-y_1}{x_2-x_1}\)

3. Okay, great! Now that we have our slope, the equation, so far, looks like this: y = 5x + b.

4. Because b is the y-intercept, b will equal 0 because the line intersects with the y-axis at the coordinate (0,0).

Therefore, our equation is y = 5x.

Answer:

A is incorrect

Step-by-step explanation:

when you see -(- it makes the thing plus sign/positive

The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer:

13

Step-by-step explanation:

|3(5)-2|

|15-2|

|13|

13

The value of the phrase to one significant figure is estimated to be 17.

To find an estimate for the value of the expression (2.8 × 82.6)/(27.8-13.9),

we can first perform the calculations using the given values to obtain a more precise answer, and then round the final result to one significant figure.

Using a calculator, we have:

(2.8 × 82.6)/(27.8-13.9) ≈ 16.63

Rounding this to one significant figure, we get:

(2.8 × 82.6)/(27.8-13.9) ≈ 17

Therefore, an estimate for the value of the expression to one significant figure is 17.

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The terms β3, β4, and β5 allow different intercepts, the terms β6 to β8 allow different slope coefficients for X, and the terms β9 to β11 allow different slope coefficients for X^2.

To incorporate three separate quadratic models, one per medium, into the regression model, we can use indicator variables (z1, z2, z3) to represent the mediums. These indicator variables will allow us to have different intercepts, slope coefficients for X, and slope coefficients for X^2 for each medium.

The regression model incorporating the quadratic models for each medium can be represented as follows:

μY = β0 + β1X + β2X^2 + β3z1 + β4z2 + β5z3 + β6(X * z1) + β7(X * z2) + β8(X * z3) + β9(X^2 * z1) + β10(X^2 * z2) + β11(X^2 * z3)

In this model:

- β0 represents the overall intercept of the regression equation.

- β1 and β6 to β8 represent the slope coefficients for X (temperature) and allow different slopes for each medium.

- β2 and β9 to β11 represent the slope coefficients for X^2 (temperature squared) and allow different slopes for each medium.

- β3, β4, and β5 represent the intercept differences for each medium (z1, z2, z3), allowing different intercepts for each medium.

Therefore, the terms β3, β4, and β5 allow different intercepts, the terms β6 to β8 allow different slope coefficients for X, and the terms β9 to β11 allow different slope coefficients for X^2.

Note: The specific values of the coefficients β0 to β11 will depend on the data and the results of the regression analysis.

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Answer:

Look below!

Step-by-step explanation:

Angle A = 180-47 = 133

Angle B = 180-32-Angle A = 180-32-47 = 101

Angle D = 90-32 = 58

Angle C = 180-47-58 = 75

Hope I helped!

Answer:

A=133 ,B=15, C=75  D= 58

Step-by-step explanation:

Angle 32, d, and right angle add up to 180. So 180=32+90+x. Then x = 58 (D). The all 3 angles in the triangle add up too 180 so 180=47+58+x. x=75 (C). The 47 and a equal to 180 degrees. 180-47=133. The 133+32+x=180. x=15 (B).

Answer:

x = 10

Step-by-step explanation:

Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x?

The sum of the exterior angles of a decagon = 360°

Decagon = 10 sides

Each angle in a decagon = 360/10

= 36°

We are told that:

Each exterior angle of a regular decagon has a measure of (3x + 6)°.

Hence,

(3x + 6)° = 36°

Collect like terms

3x = 36 - 6

3x = 30

x = 30/3

x = 10

Answer: The person above me is correct! It is B. X=10 I got a 100% on the test! Edge2021

Step-by-step explanation:

In summary, the limits of the function f(x) are as follows: lim(x→2-) f(x) = 2, lim(x→2+) f(x) = 1, lim(x→∞) f(x) = ∞, lim(x→-∞) f(x) = -∞

To determine the limits of the function f(x) as x approaches certain values, we can plot the graph of the function and observe the behavior. Let's analyze the limits of f(x) as x approaches different values.

First, let's plot the graph of the function f(x):

For x ≤ 2, the graph of f(x) is a downward-opening parabola that passes through the points (2, 0) and (0, 10). The vertex of the parabola is located at x = 1, and the curve decreases as x moves further away from 1.

For x > 2, the graph of f(x) is a linear function with a positive slope of 2. The line intersects the y-axis at (0, -3) and increases as x moves further to the right.

Now, let's analyze the limits:

Limit as x approaches 2 from the left: lim(x→2-) f(x)

Approaching 2 from the left side, the function approaches the value of 10 - 2 - 2^2 = 2. So, lim(x→2-) f(x) = 2.

Limit as x approaches 2 from the right: lim(x→2+) f(x)

Approaching 2 from the right side, the function follows the linear segment 2x - 3. So, lim(x→2+) f(x) = 2(2) - 3 = 1.

Limit as x approaches positive infinity: lim(x→∞) f(x)

As x approaches positive infinity, the linear segment 2x - 3 dominates the function. Therefore, lim(x→∞) f(x) = ∞.

Limit as x approaches negative infinity: lim(x→-∞) f(x)

As x approaches negative infinity, the parabolic segment 10 - x - x^2 dominates the function. Therefore, lim(x→-∞) f(x) = -∞.

These limits are determined by observing the behavior of the function as x approaches different values and analyzing the graph of the function.

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