Algebra 1
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The 50th percentile is a commonly used statistic in data analysis. It represents the value below which 50% of the data falls.

In other words, it divides the data into two equal parts. There are two other statistics that have the same value as the 50th percentile, namely the second quartile and the median. The second quartile is the middle value of the data when it is arranged in ascending or descending order.

It is also known as the 50th percentile or the median. The first quartile is the value below which 25% of the data falls, and the third quartile is the value below which 75% of the data falls.

The mean is another commonly used statistic in data analysis. It is the sum of all the values in the data divided by the total number of values. Unlike the median, the mean is affected by extreme values or outliers in the data. This means that if there are outliers in the data, the mean may not be a good measure of central tendency.

The mode is the value that occurs most frequently in the data. It is another measure of central tendency that can be used in addition to the median and mean.

In summary, the 50th percentile is equivalent to the second quartile and the median. These statistics are all measures of central tendency that help to describe the distribution of data. The choice that best answers the question is option A: Second quartile; median.

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The box plot would show the distribution of Tori's training runs and provide insights into the Central tendency and variability of the data.

A box plot, also known as a box-and-whisker plot, is a visual representation of the distribution of a dataset. It shows the median, quartiles, and range of the data. The median is the middle value of the dataset, the first quartile is the value that separates the lowest 25% of the data from the rest, and the third quartile is the value that separates the lowest 75% of the data from the rest. The range is the distance between the minimum and maximum values of the data.

To create a box plot for Tori's training runs, you would first order the data from smallest to largest: 6, 7, 8, 8, 11, 12, 13, 15, 16, 16, 20. Then, you would find the median (the middle value), which is 12.5. Next, you would find the first quartile (the value that separates the lowest 25% of the data from the rest), which is 8, and the third quartile (the value that separates the lowest 75% of the data from the rest), which is 16. Finally, you would calculate the range (the distance between the minimum and maximum values), which is 14 (20 - 6).

To draw the box plot, you would draw a rectangle with the bottom edge at the first quartile and the top edge at the third quartile. Inside the rectangle, draw a line at the median. Then, draw whiskers (lines) from the edges of the rectangle to the minimum and maximum values of the data (6 and 20). Any outliers (values that are more than 1.5 times the interquartile range away from the nearest quartile) can be plotted as individual points outside of the whiskers.

Without a visual representation of the data, it is difficult to say which box plot represents the data. However, the box plot would show the distribution of Tori's training runs and provide insights into the central tendency and variability of the data.

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Answer: To find the distance between Jannick's house and Milos' house, we can use the Pythagorean theorem. We first need to find the total distance travelled by Jannick:

Distance north + Distance east + Distance south =
√(2^2 + 5^2) + 4.5 = √29 + 4.5 ≈ 8.74 miles

Therefore, the distance between Jannick's house and Milos' house is approximately 8.74 miles.

The opposite side is 12x. Since angle β terminates in Quadrant I, both the adjacent and opposite sides are positive. cosβ = 5/13, sinβ = 12/13, and tanβ = sinβ/cosβ = 12/5

The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this information, we can find the lengths of the sides of two right triangles that have angles α and β.

For angle α, since sinα = 3/5 and the sine of an angle is the opposite side divided by the hypotenuse, we can let the opposite side be 3x and the hypotenuse be 5x for some positive value of x. Then, using the Pythagorean theorem, we can find the length of the adjacent side:

cosα = √(1 - sin^2α) = √(1 - 9/25) = 4/5

Therefore, the adjacent side is 4x. Since angle α terminates in Quadrant II, the adjacent side is negative. So, we have:

cosα = -4/5, sinα = 3/5, and tanα = sinα/cosα = -(3/4)

For angle β, since cosβ = 5/13 and the cosine of an angle is the adjacent side divided by the hypotenuse, we can let the adjacent side be 5x and the hypotenuse be 13x for some positive value of x. Then, using the Pythagorean theorem, we can find the length of the opposite side:

sinβ = √(1 - cos^2β) = √(1 - 25/169) = 12/13

Therefore, the opposite side is 12x. Since angle β terminates in Quadrant I, both the adjacent and opposite sides are positive. So, we have:

cosβ = 5/13, sinβ = 12/13, and tanβ = sinβ/cosβ = 12/5

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The probability of two sixes when the dice is rolled twice is 9/25

Given that;

probability of getting 6,

P(6) = 3/5

Since both dice can be rolled independently

Therefore,

So to find probability of getting two 6 when two dices are rolled twice

We directly multiply it

= (3/5) x (3/5)

=  9/25

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Para escolher o pote de miçangas que permitirá fazer uma quantidade exata de pulseiras sem sobrar nenhuma miçanga no pote, precisamos encontrar um número que seja divisível por 16 em cada um dos valores apresentados nos potes.

Analisando as opções apresentadas no quadro, podemos ver que apenas a quantidade de miçangas no pote B é divisível por 16, já que 16 x 9 = 144. Portanto, Ana deve escolher o pote B com 144 miçangas para confeccionar as pulseiras de seus amigos. Dessa forma, ela poderá fazer 9 pulseiras utilizando todas as miçangas disponíveis no pote. As outras opções apresentam quantidades de miçangas que não são divisíveis por 16, o que resultaria em sobras de miçangas no processo de confecção das pulseiras.

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Answer:

38

Step-by-step explanation:

Answer: The volume of the solid obtained by rotating the region between the curve y = 3x − x^2 and the x-axis, about the y-axis, is 27π/5.

Step-by-step explanation:

To obtain the volume of the solid obtained by rotating the region between the curve y = 3x − x^2 and the x-axis, about the y-axis, we use the formula:

V = ∫a^b π y^2 dx

where a and b are the x-coordinates of the points of intersection of the curve with the x-axis.

To obtain these points, we set y = 0:

3x − x^2 = 0x(3 − x) = 0x = 0, x = 3

Thus, the limits of integration are a = 0 and b = 3. Now we express y in terms of x:

y = 3x − x^2

We substitute this expression for y in the formula for V:

V = ∫0^3 π (3x − x^2)^2 dx

Expanding the square, we get:

V = ∫0^3 π (9x^2 − 6x^3 + x^4) dx

Integrating, we obtain:

V = π [3x^3 − 3/2 x^4 + 1/5 x^5]0^3V = π [27/5]

Therefore, the volume of the solid obtained by rotating the region between the curve y = 3x − x^2 and the x-axis, about the y-axis, is 27π/5

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If the marginal cost differs across the two groups, then a monopoly can price discriminate among groups of buyers. This is because the monopoly can charge a higher price to the group with a relatively lower elasticity of demand, which will generate more revenue and profits for the monopoly.

A monopoly can price discriminate among groups of buyers. A monopoly can price discriminate among groups of buyers if demand elasticity differs across the two groups. This means that the monopoly can charge different prices based on the varying price sensitivities of different consumer groups.

                                     However, if the average total cost differs across the two groups, then price discrimination may not be possible because the monopoly cannot charge a higher price without incurring higher costs. Therefore, the correct answer is C) marginal.

The options A (average total cost differs), B (marginal cost differs), and C (marginal) do not complete the sentence accurately.

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Answer:

C. -18

Step-by-step explanation:

3(-3)+4(-6)+15=

-9+-24+15

-33+15=-18

Answer:

Step-by-step explanation:

x=-3 and y=-6  ⇒

so if we add these numbers together, we will have :

-9 + (-24) + 15 = -18

and it is C .

Part A:

The population declined the fastest over the time interval [20,30], which has the greatest negative average rate of change (-138.11).

Part B:

The population declined the slowest over the time interval [60,70], which has the smallest negative average rate of change (-35.14).

We have,

To calculate the average rate of change of the population, we need to find the change in population over the given time interval and divide it by the length of the time interval.

The formula for an average rate of change over an interval [a, b].

average rate of change = (f(b) - f(a)) / (b - a)

where f(x) is the population function.

Using this formula, we can calculate the average rate of change over the given intervals as follows:

[0,10]:

f(10) = -1.2^(0.710) + 10,000 = 7,686.53

f(0) = -1.2^(0.70) + 10,000 = 8,800

average rate of change = (7,686.53 - 8,800) / (10 - 0) = -111.45

[20,30]:

f(30) = -1.2^(0.730) + 10,000 = 2,376.47

f(20) = -1.2^(0.720) + 10,000 = 3,759.54

average rate of change = (2,376.47 - 3,759.54) / (30 - 20) = -138.11

[40,50]:

f(50) = -1.2^(0.750) + 10,000 = 742.39

f(40) = -1.2^(0.740) + 10,000 = 1,690.88

average rate of change = (742.39 - 1,690.88) / (50 - 40) = -94.55

[60,70]:

f(70) = -1.2^(0.770) + 10,000 = 231.51

f(60) = -1.2^(0.760) + 10,000 = 581.92

average rate of change = (231.51 - 581.92) / (70 - 60) = -35.14

Thus,

Part A:

The population declined the fastest over the time interval [20,30], which has the greatest negative average rate of change (-138.11).

Part B:

The population declined the slowest over the time interval [60,70], which has the smallest negative average rate of change (-35.14).

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Answer:

Set your calculator to degree mode.

Using the Law of Cosines:

c = √(27^2 + 13^2 - 2(27)(13)(cos 106°))

= 33.0378

Now use the Law of Sines:

sin A/13 = sin 106°/33.0378

sin A = 13 sin 106°/33.0378

A = 22.2°

The measure of angle ∠A will be 22.1°. Then the correct option is B.

Given that:

a = 13 in

b = 27 in

∠C = 106°

Let the triangle ΔABC, then the cosine law is given as,

c² = a² + b² - 2 a·b cos C

The length AB of the triangle is calculated as,

c² = 13² + 27² - 2 · 13 · 27 · cos 106°

c² = 169 + 729 - (-196.5)

c² = 1094.5

c = 33.08 inches

The measure of ∠A is calculated as,

a² = b² + c² - 2 b·c cos A

13² = 27² + 33.08² - 2 x 27 x 33.08 x cos A

cos A = 0.9262

A = 22.1°

The measure of angle ∠A will be 22.1°. Then the correct option is B.

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A triangle is a shape with 3 sides and angles. The measure of angle ∠ABC is 57.6 degrees

Here, we have,

Application of trigonometry identity

A triangle is a shape with 3 sides and angles. Given the following parameters

∠CAB = 90°.

AB = 5.9 m and;

BC = 11.1m.

Determine the measure of ∠ABC

cos∠ABC = AB/BC

cos∠ABC = 5.9/11

cos∠ABC = 0.5363

∠ABC = arccos0.5363

∠ABC = 57.6 degrees

Hence the measure of angle ∠ABC is 57.6 degrees

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To conduct a hypothesis test to compare the gestation periods of the two frog species, we can use a two-sample t-test assuming equal variances.

State the hypotheses:

The null hypothesis (H0) is that there is no difference in the mean gestation periods between species A and B.

H0: μA = μB

The alternative hypothesis (Ha) is that there is a difference in the mean gestation periods between species A and B.

Ha: μA ≠ μB

Set the significance level:

The significance level, denoted as α represents the probability of making a Type I error (rejecting the null hypothesis when it is actually true). In this case, the significance level is given as 0.05.

Calculate the test statistic:

We can use the two-sample t-test formula to calculate the t-statistic.

Where A and B are the sample means of gestation periods for species A and B, respectively, s is the pooled standard deviation and nA and nB are the sample sizes for species A and B, respectively.

The pooled standard deviation can be calculated as:

t = -6.28

Determine the critical value:

The critical value of t can be found using a t-distribution table with degrees of freedom (df) equal to nA + nB - 2.

At a significance level of 0.05 with df = 16 + 23 - 2 = 37 the critical values are -2.02 and 2.02 (two-tailed test).

Make a decision and interpret the results:

The absolute value of the calculated t-statistic (6.28) is greater than the critical value (2.02).

Indicating that we can reject the null hypothesis.

Thus, we can conclude that there is a statistically significant difference in the mean gestation periods between species A and B.

Calculate the p-value:

The p-value is the probability of obtaining a t-statistic as extreme as the one calculated or more extreme, assuming the null hypothesis is true.

We can use a t-distribution table or a statistical software package to find the p-value.

For this example,

The p-value is very small (p < 0.0001), indicating strong evidence against the null hypothesis.

Therefore, we can conclude that the average lengths of the gestational periods differ significantly between the two newly discovered frog species, with species B having a longer gestation period than species A.

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Answer:  B. Acting as a lender of last resort.

A bank run occurs when a large number of depositors withdraw their funds from a bank, which can lead to a bank's insolvency.

A central bank like the Federal Reserve can help banks survive a bank run by acting as a lender of last resort.

This means that the central bank will provide funds to the bank in the form of loans or other financial assistance to ensure that it has enough cash on hand to meet the demands of depositors who are withdrawing their funds.

By doing so, the central bank can prevent the bank from going bankrupt and restore confidence in the banking system.

Other measures such as increasing the required reserve ratio or raising the discount rate may also be used to control the money supply and stabilize the economy, but they may not directly address the issue of a bank run.

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Answer:

203

Step-by-step explanation:

We have to solve this according to BODMAS THEOREM to solve this.

That is,

B ⇒ Brackets

O ⇒ Orders.

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Let us solve it now.

2 + 1000 - 789 + 12 - 2 x 10 - 2

2 + 1000 - 789 + 12 - 20 - 2

1002 - 789 + 12 -20 - 2

213 + 12 - 20 - 2

225 - 20 - 2

205 - 2

203

The solution of 2+1000-789+12-2x10-2 using BODMAS is 203.

We know about BODMAS which shows the correct order to solve mathematical expression as

B ⇒ Brackets

O ⇒ Of

D ⇒ Division

M ⇒ Multiplication

A ⇒ Addition

S ⇒ Subtraction

Now, we have to solve 2+1000-789+12-2x10-2 using BODMAS

= 2 + 1000 - 789 + 12 - 2 x 10 - 2

= 2 + 1000 - 789 + 12 - 20 - 2

= 1002 - 789 + 12 -20 - 2

= 213 + 12 - 20 - 2

= 225 - 20 - 2

= 205 - 2

= 203

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The statement that best describes how to determine whether

f(x) = x² - x + 8 is an even function is "Determine whether (-x)² - (-x) + 8 is equivalent to x² - x + 8."

Option

We have,

To determine whether f(x) = x² - x + 8 is an even function, we need to check whether the function satisfies the property of even functions, which is f(-x) = f(x) for all values of x in the domain of the function.

We can test this property by plugging in -x for x in the given function and simplifying it to see if we get the same function back.

Testing each option:

Option 1:

-x² - (-x) + 8 = x² - x + 8

This option does not satisfy the property of even functions, so it cannot be the correct answer.

Option 2:

(-x)² - (-x) + 8 = x² + x + 8

This option also does not satisfy the property of even functions, so it cannot be the correct answer.

Option 3:

-x² - (-x) + 8 = -(x² - x + 8)

This option satisfies the property of even functions since both sides are equal after multiplying the right-hand side by -1.

However, this option describes whether the function is odd, not even.

Option 4:

(-x)² - (-x) + 8 = x² - x + 8

This option satisfies the property of even functions since both sides are equal. This is the correct answer.

Therefore,

The statement that best describes how to determine whether

f(x) = x² - x + 8 is an even function is "Determine whether (-x)² - (-x) + 8 is equivalent to x² - x + 8."

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a multiple regression model, the error term `e’ is assumed to be a random variable with a mean of is A) zero. This means that in a multiple regression model, the errors are assumed to have a mean of zero. This assumption is necessary to ensure that the model is unbiased and accurate in predicting the outcome variable.

this assumption is that the error term represents the unexplained variation in the outcome variable that is not accounted for by the predictor variables. If the error term had a mean value other than zero, this would indicate that there is a systematic bias or error in the model, which would affect the accuracy of the predictions.

the assumption of a zero mean error term is a critical aspect of multiple regression modeling and helps to ensure that the model is reliable and valid for predicting the outcome variable.

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The answer to this question is  the test statistic is a. option a. 100.75.

To arrive at this answer, we need to use the chi-square distribution to test the null hypothesis that the population variance (σ2) is equal to 20. The test statistic for this hypothesis test is given by:

χ2 = (n - 1) * s²  / σ2

where n is the sample size, s is the sample standard deviation, and σ is the population standard deviation (which is assumed to be equal to the hypothesized value of 20).

Substituting the given values, we get:

χ2 = (41 - 1) * 5² / 20
χ2 = 40 * 25 / 20
χ2 = 50

Therefore, the test statistic is 50.

However, to determine the p-value (i.e. the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true), we need to consult a chi-square distribution table with (n - 1) degrees of freedom. For this problem, the degrees of freedom is 40 (i.e. 41 - 1).

Using the chi-square distribution table, we find that the p-value for a test statistic of 50 with 40 degrees of freedom is less than 0.001. This means that the probability of obtaining a sample with a variance as extreme or more extreme than 20 (assuming the null hypothesis is true) is less than 0.001.

Therefore, we can reject the null hypothesis at a significance level of 0.001 or lower. This leads us to the conclusion that the population variance is unlikely to be 20, based on the given sample of 41 observations with a sample standard deviation of 5.

finding the p-value using a chi-square distribution table, and making a conclusion based on the significance level. The main answer is option a. 100.75, which corresponds to the test statistic calculated using the formula χ2 = (n - 1) * s²  / σ2.

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Answer:

He would have 20,00

Step-by-step explanation:

You first have to calculate the profit them add it to your original price and since he put 2,500 in for five years you multiply 2,500 by five to get your original price before you add your interest to it

The probability of getting a head on the first coin flip is 1/2. Assuming that the coins are fair and independent, the probability of getting another head on the second coin flip is also 1/2. By the multiplication rule of probability, we can find the probability of both events occurring by multiplying their individual probabilities:

P(head, then another head) = P(head on first flip) * P(head on second flip)

= (1/2) * (1/2)

= 1/4

Therefore, the probability of getting a head on the first coin flip and another head on the second coin flip is 1/4.

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To perform a statistical test on the sample and determine if the average age is consistent with your hypothesis that it is less than 50, we can use a one-sample t-test. The null hypothesis (H0) is that the population average age is equal to or greater than 50, and the alternative hypothesis (Ha) is that the population average age is less than 50.

Using the sample data, we calculate the t-test statistic by subtracting the assumed population mean (50) from the sample mean, dividing it by the standard error of the mean, and considering the sample size.

Next, we compare the t-test statistic with the critical t-value at a significance level of 5%. If the t-test statistic is smaller than the critical t-value, we reject the null hypothesis and conclude that the average age is consistent with being less than 50.

The p-value from the test represents the probability of obtaining a t-test statistic as extreme as the observed value, assuming the null hypothesis is true. We compare the p-value with the significance level to make our decision.

Unfortunately, the p-value was not provided in the answer choices. The p-value obtained from the test would need to be calculated separately to determine the correct answer option.

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The correct statements that describe the graph of the function

f(x) = x^4 - 2x² + 1 are:

c. When x = -2, f(x) = 0.

f. When x = -1, f(x) = 0.

e. As x approaches positive infinity, f(x) approaches positive infinity.

b. As x approaches negative infinity, f(x) approaches negative infinity.

We have,

Statement (a) is incorrect because as x approaches positive infinity, f(x) approaches positive infinity, not negative infinity.

Statement (d) is incorrect because as x approaches negative infinity, f(x) approaches negative infinity, not positive infinity.

The graph of the function f(x) = x^4 - 2x² + 1 is a parabola that opens upwards, which means that as x approaches positive infinity, the value of f(x) also approaches positive infinity.

This makes statement (e) true.

Similarly, as x approaches negative infinity, the value of f(x) also approaches negative infinity because the polynomial function contains even powers of x. This makes statement (b) true.

The function f(x) has two real roots, which occur when f(x) = 0. These roots are x = -2 and x = -1.

At these values, the function crosses the x-axis and changes sign from positive to negative.

This makes statements (c) and (f) true.

Thus,

The correct statements that describe the graph of the function

f(x) = x^4 - 2x² + 1 are:

c. When x = -2, f(x) = 0.

f. When x = -1, f(x) = 0.

e. As x approaches positive infinity, f(x) approaches positive infinity.

b. As x approaches negative infinity, f(x) approaches negative infinity.

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Answer: The correct statements are: As x approaches negative infinity, f(x) approaches positive infinity; When x = -1, f(x) = 0; and As x approaches positive infinity, f(x) approaches positive infinity.

Step-by-step explanation:

Step 1: Analyze the function

The given function is f(x) = x^4 - 2x^2 + 1.

Step 2: Determine the behavior as x approaches infinity

Since the highest degree term is x^4, as x approaches positive or negative infinity, the x^4 term will dominate the function. Since x^4 is always positive for any real value of x, f(x) will approach positive infinity as x approaches both positive and negative infinity.

Step 3: Check for zeros of the function

To find the zeros of the function, we need to solve the equation f(x) = 0.

x^4 - 2x^2 + 1 = 0

This is a quadratic equation in terms of x^2. Let y = x^2, then the equation becomes:

y^2 - 2y + 1 = 0

(y - 1)^2 = 0

y = 1

Now, substitute back x^2 for y:

x^2 = 1

x = ±1

Step 4: Check the given statements

1. As x approaches negative infinity, f(x) approaches positive infinity. (True)

2. As x approaches negative infinity, f(x) approaches negative infinity. (False)

3. As x approaches positive infinity, f(x) approaches negative infinity. (False)

4. When x = -1, f(x) = 0. (True)

5. As x approaches positive infinity, f(x) approaches positive infinity. (True)

6. When x = -2, f(x) = 0. (False)

The graph 1 represents the subtraction of given vectors.

Hence option (a) is correct.

The given vectors are

vector c = < 5, 2 , -4>

vector d = < 6, -3, -2>

To show the graphical representation of subtraction of vectors

We add the vectors after changing the direction vector which would be subtracted.

Now ,

vector c - vector d = < 5, 2 , -4> - < 6, -3, -2>

                               = < 5-6, 2+3, -4+2 >  

                               = < -1, 5, -2 >

Thus,

vector c - vector d = < -1, 5, -2 >

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The sum of the given finite geometric series is approximately 0.6640625.

[tex]S_n= \frac{ a(1 - r^n)}{(1 - r)}[/tex]

Substituting the values, we get:

[tex]S_n =\frac{ 1(1 - (-1/2)^n) }{1 - (-1/2)}[/tex]

=  [tex]\frac{1(1 - (-1/2)^n)}{(3/2)}[/tex]

= [tex]2/3(1 - (-1/2)^n)[/tex]

To find the sum of the given series, we need to evaluate S_8, since there are 8 terms in the series:

[tex]S_8 = 2/3(1 - (-1/2)^8)[/tex]

=  2/3(1 - 0.00390625)

=  2/3(0.99609375)

=  0.6640625

Therefore, the sum of the given finite geometric series is approximately 0.6640625.

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Answer:

[tex]a_n=1.04\cdot a_{n-1}\ \ ,\ \ a_1=35,000[/tex]

Step-by-step explanation:

The salary is dependent upon the number of years you have worked.

Your salary increases by 1.04 times every year.

So, your salary over the years can be expressed as a Geometric Progression

35000, 35000*(1.04)², 35000*(1.04)³, ...

=> Common Ratio (r) = 1.04

∴ [tex]a_n=1.04\cdot a_{n-1}\ \ ,\ \ a_1=35,000[/tex]

Answer: The interval of convergence is: x ∈ (2, 4) and the series is convergent from x=2, left end included, to x=4, right end included.

Step-by-step explanation:

To get the power series for 1/x with center 3, we can use the fact that:

1/x = (1/(x-3)) / (1/3)

Then, we can use the formula for the geometric series:

1/(1-r) = ∑n=0^∞ r^n, for |r| < 1

to obtain:

1/(x-3) = -1/(3(1-(x-3)/3)) = -1/3 ∑n=0^∞ ((x-3)/3)^n, for |(x-3)/3| < 1

Multiplying both sides by 1/3, we get:

1/x = -1/9 ∑n=0^∞ ((x-3)/3)^n, for |(x-3)/3| < 1

So, the power series for 1/x with center 3 is:[infinity]∑n=0 (-1/9) ((x-3)/3)^n

To obtain its interval of convergence, we note that the series converges if:|(x-3)/3| < 1 which is equivalent to:

-1 < (x-3)/3 < 1

Solving for x, we get:

2 < x < 4

Therefore, the interval of convergence is: x ∈ (2, 4)

And the series is convergent from x=2, left end included, to x=4, right end included.

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The marble took 4 seconds to roll from one end of the room to the other end.

To find the time it took for the marble to roll from one end of the room to the other, we can use the formula:

Time = Distance / Speed

Given that the distance between the two ends of the room is 1.92 m and the speed of the marble is 48 cm/s, we need to convert the distance to centimeters to match the unit of speed.

1.92 m = 192 cm

Now we can calculate the time:

Time = 192 cm / 48 cm/s

Time = 4 seconds

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10 is the number that belongs to the green box in the triangle.

Let us find the third interior angle in the triangle

By angle sum property the sum of three angles is 180 degrees

78+56+x=180

134 + x =180

Subtract 134 from both sides

x=180-134

x=46

So sin 56 /12 = sin 46/x

0.829/12=0.7193/x

0.069=0.7193/x

x=0.7193/0.069

The number in green box x=10.42

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The student used 0.545 liters of the solution in the experiment.

We have,

To convert the unit milliliters to liters, you need to divide by 1000 since there are 1000 milliliters in 1 liter.

So, to find how many liters were used, you can divide 545 milliliters by 1000.

= 545 mL ÷ 1000

= 0.545 L

Therefore,

The student used 0.545 liters of the solution in the experiment.

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