the convergence or divergence of the series at various values of x is shown in the table above. what is the interval of convergence for the power series?

The scale factor used to produce Figure 2 from Figure 1 is: 7/3. The correct option is 1.

A scale factor is a number in mathematics that scales or multiplies some quantity.

The scale factor in geometry refers to the ratio of the lengths of two corresponding sides of two similar geometric figures.

The scale factor is the ratio of two similar figures' corresponding sides. The two triangles in this case are similar because they have the same shape but different sizes.

Figure 2's legs are 7 units long, which is 7/3 the length of Figure 1's legs, which are 3 units long.

Thus, the scale factor used to generate Figure 2 from Figure 1 is 7/3.

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Answer:

percentage of change=75%

Step-by-step explanation:

percent of change =(final-initial)/initial×100

now

percent of change=(7-4)/4×100

                             =3/4×100

                             =75%

The given system of equations can be written as a vector equation (7x1 + x2 - 3x3) = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].

An equation is a mathematical statement that expresses the equality of two expressions. It usually consists of two expressions separated by an equals sign (=). The expressions may contain numbers, variables, and operations, such as addition, subtraction, multiplication, and division. The solution of an equation is the value of the variable that makes the equation true.

Vector equation:

(7x1 + x2 - 3x3) = 7

Part 2
Write the system as a matrix equation. Select the correct choice below and fill in any answer boxes to complete your choice.

Matrix equation:

=

A =

[7 1 -3
3 2 2]

B =

[7
0]

Conclusion:

The given system of equations can be written as a vector equation (7x1 + x2 - 3x3) = 7 and as a matrix equation = , where A = [7 1 -3 3 2 2] and B = [7 0].

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The value of the expression  [tex]\frac{27^{\frac{1}{3}b} }{9^{ \frac{1}{2} a} }[/tex]  is 1/9.

Exponent rules are a set of mathematical properties that help simplify expressions with exponents and make it easier to manipulate them in algebraic operations.

The fractional exponent or power rule:

The rule states that for any real numbers a and b, and any positive integer n, the expression [tex]a^{\frac{1}{n} }[/tex] is equal to the nth root of the fraction a/b. That is:   [tex]a^{\frac{1}{n} }[/tex]  = [tex]\sqrt[n]{a}[/tex]

Here we have

=>  [tex]\frac{27^{\frac{1}{3}b} }{9^{ \frac{1}{2} a} }[/tex]  

Using the fomrula, [tex]a^{\frac{1}{n} }[/tex]  = [tex]\sqrt[n]{a}[/tex]

=> [tex]27^{ \frac{1}{3} b} = (\sqrt[3]{27})^{b}[/tex]  

As we know 27 = 3³  

=> [tex](\sqrt[3]{27})^{b} = (\sqrt[3]{3^{3} })^{b} = 3^{b}[/tex]  

=> [tex]9^{ \frac{1}{2} a} = (\sqrt {9})^{a}[/tex]    

As we know 9 = 3²

=> [tex](\sqrt {9})^{a} = [\sqrt{3^{2} } ]^{a} = 3^{a}[/tex]    

Hence the expression will be

=>  [tex]\frac{27^{\frac{1}{3}b} }{9^{ \frac{1}{2} a} } = \frac{3^{b} }{3^{a} }[/tex]

=>  [tex]\frac{3^{b} }{3^{a} } = \frac{1}{3^{a-b} }[/tex]

=>  [tex]\frac{1}{3^{a-b} } = \frac{1}{3^{2} }[/tex]

=>  [tex]\frac{1}{3^{2} } = \frac{1}{9}[/tex]

Therefore,

The value of the expression  [tex]\frac{27^{\frac{1}{3}b} }{9^{ \frac{1}{2} a} }[/tex]  is 1/9.

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The area of the circular mirror hanging on Julie's wall is approximately 379.94 square centimeters.

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

Where r is radius and π is constant pi ( π = 3.14 )

Given that, the diameter of the mirror is given as 22 cm, the radius is half of that:

r = diameter/2

r = 22/2

r = 11 cm

Substituting this into the formula, we get:

A = π × r²

A = 3.14 × ( 11 cm )²

A = 3.14 × 121 cm²

A = 379.94 cm²

Therefore, the area of the mirror is 379.94 cm².

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The equation of the hyperbola is y²/49 - x²/25 = 1

Given that the vertex of a hyperbola is (0, 7), (0, -7) and the asymptotes are at y = ±7x/5,

We need to find the equation of the hyperbola,

For the vertical transverse axis consider an equation of the hyperbola :

(y-k)²/a² - (x-h)²/b² = 1

Comparing the points,

h = 0,

k + a = 7

k - a = -7

So,

k = 0

So,

a = 7

The formula for the equation of the asymptotes of a hyperbola =

y-k = ±a/b (x-h)

Therefore,

y-0 = ±7/b(x-0)

y = ±7/b

The given equation of asymptotes is y = ±7/5,

Comparing both,

7/b = 7/5

b = 5

Put the values in the standard equation of the hyperbola,

(y-0)²/7² - (x-0)²/5² = 1

y²/49 - x²/25 = 1

Hence the equation of the hyperbola is y²/49 - x²/25 = 1

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Answer:

c

Step-by-step explanation:

The statement is True, When using dummy variables to represent categorical variables in regression analysis, it's important to include all of the dummy variables as a package deal or none of them.

A statistical technique used to simulate the connection between two or more variables is regression analysis.  It involves identifying and quantifying the relationships between a dependent variable and one or more independent variables. The dependent variable is the outcome variable, while the independent variables are the predictors or explanatory variables.

Regression analysis can be used to understand and predict the relationship between variables. It can help researchers to examine the effects of one variable on another and to make predictions about future outcomes. For example, regression analysis can be used to predict the sales of a product based on its price, advertising expenditure, and other factors. There are different types of regression analysis, including linear regression, logistic regression, and polynomial regression.

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he theater sold 356 adult tickets and 144 child tickets for a certain showtime to make a total of $3157 in ticket sales.

We have,

Let's assume that the number of adult tickets sold is x, and the number of child tickets sold is y.

We know that the total number of tickets sold cannot exceed the maximum capacity of the theater, so we have the inequality:

x + y ≤ 500

We also know that the total revenue from ticket sales is $3157, so we can write another equation based on the ticket prices:

7.25x + 4y = 3157

We have two equations with two variables, so we can solve for x and y using any method of our choice.

Here, we will use substitution.

We can write,

y ≤ 500 - x.

We can substitute this into the second equation.

7.25x + 4(500 - x) = 3157

Simplifying and solving for x.

7.25x + 2000 - 4x = 3157

3.25x = 1157

x = 355.69

We can't sell a fractional number of tickets, so we must round x to the nearest whole number.

Let's assume that x = 356.

Then, from the first inequality.

356 + y ≤ 500

y ≤ 144

Therefore, we can sell at most 144 child tickets.

To check if this solution satisfies the equation 7.25x + 4y = 3157, we substitute x = 356 and y = 144 into the equation:

7.25(356) + 4(144) = 3157

This is true, so our solution is valid.

Therefore,

The theater sold 356 adult tickets and 144 child tickets for a certain showtime to make a total of $3157 in ticket sales.

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Answer:

Answer:

x > - 3 or x < -1

I cannot see this answer choice; perhaps you typed it wrong and it is option C. Please check again

Step-by-step explanation:

The absolute value rule says for a given variableu,
if |u| < a where a is a constant,

then -a < u < a

Here we can represent x + 2 as u giving

|u| < 1

=> - 1 < u < 1

Substituting for u = x + 2 gives

-1 < x + 2 < 1

Subtract 2 from all sides
-1 - 2 < x + 2 - 2 < 1 - 2

-3 < x < -1

This can be represented as
x > -3 or x < -1

I do not see this choice anywhere but that is the correct answer. Check your answer choices

Answer:

-----------------

The 90° angle is:

It is also called a right angle.

Therefore the matching choice is B.

The points that represent this data are shown in the scatter plot attached below.

In this scenario, the age (in years) would be plotted on the x-axis (x-coordinate) of the scatter plot while the hair length (in inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the age (in years) and the hair length (in inches), a linear equation for the line of best fit is given by:

y = 0.0502x + 7.73

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The value of the side is 6. 2

To determine the value of the missing side, we need to know the Pythagorean theorem.

The Pythagorean theorem of triangles states that the square of the longest side of a triangle which is called the hypotenuse side is equal to the sum of the squares of the other two sides of the triangle.

This is represented as;

c² = b² + a²

Such that the parameters are;

Substitute the values

8² = 5² + b²

find the square value, we have;

64 = 25 +b²

subtract the values

b² = 64 - 25

b² = 39

Find the square root of both sides

b = 6. 2

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The number of standard deviations from the mean for the 64 inches of snow last year is 2.5 standard deviations.


First, we need to find the difference between the actual snowfall (64 inches) and the mean snowfall (39 inches). To do this, subtract the mean from the actual snowfall:

64 - 39 = 25 inches.
Next, we need to divide this difference by the standard deviation (10 inches) to find how many standard deviations away from the mean the actual snowfall is:

25 / 10 = 2.5.

Hence, Last year's snowfall of 64 inches is 2.5 standard deviations away from the mean annual snowfall of 39 inches.

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Answer:

  x = 52°

Step-by-step explanation:

Given various inscribed angles in a circle, you want the measure of central angle x.

The inscribed angle theorem tells you an arc is double the measure of the inscribed angle it subtends:

  arc JKM = 2·80° = 160°

  arc JNL = 2·126° = 252°

The sum of arcs around a circle is 360°. This tells you ...

  arc JKL = 360° -252° = 108°

An arc has a measure equal to the sum of its parts, so ...

  arc JKM = arc LM +arc JKL

  160° = x + 108°

  x = 52° . . . . . . . . . . subtract 108°

The radius and the circumeference of the first semicircle is 6 inches and 18.85 inches².

Given that the diameter of the semi-circle is 12 inches.
The radius is always half the diameter. Therefore, the radius of the given semi-circle is:

Radius of the semicircle = Diameter / 2

= 12 inches / 2

= 6 inches

The circumference of the semicircle is:

Circumference = π × r

= π × 6 in.

= 18.85 in

The area of the purple semicircle:

Area = (π/8) × d²

        = (π/8) × 5²

        = 9.817 inches²

The area of the blue semicircle:

Area = (π/8) × d²

        = (π/8) × 5²

        = 16.085 inches²

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Answer:

c and d are worth 24 if c4.285 and d 3.75 multiply c and d and divide 24

After considering all the given data  we conclude that the upper estimate regarding t= 5 is 74.65 ft/sec, the lower estimate regarding t = 5 is 45.28 ft/sec, the upper estimate regarding t = 3 is 63.18 ft.

It is known that acceleration of the object is measured in ft/sec² and measured every second after the drop for 5 seconds. The acceleration decreases over time because of air resistance.

The upper estimate for the speed when t=5 is 32+19.41+11.77+7.14+4.33= 74.65 ft/sec.

The lower estimate for the speed when t=5 is 19.41+11.77+7.14+4.33+2.63=45.28 ft/sec.

The upper estimate for the distance fallen when t=3 is 32+19.41+11.77=63.18 ft.

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Answer:

Letting x be an element of the universal set, this set will be {x | -1 < x < 4}.

The probability that the trainee class will consist entirely of men is option (c) 0.133

To calculate the probability that the trainee class will consist entirely of men, we need to determine the total number of ways to select two people from the pool of ten applicants, as well as the number of ways to select two men from the pool of four men

The total number of ways to select two people from the pool of ten applicants is given by the combination formula

C(10, 2) = 10! / (2! × (10 - 2)!) = 45

This means that there are 45 different ways to select two people from the pool of ten applicants.

The number of ways to select two men from the pool of four men is given by the combination formula

C(4, 2) = 4! / (2! × (4 - 2)!) = 6

This means that there are 6 different ways to select two men from the pool of four men.

Therefore, the probability that the trainee class will consist entirely of men is given by the ratio of the number of ways to select two men from the pool of four men to the total number of ways to select two people from the pool of ten applicants

P(2 men) = C(4, 2) / C(10, 2) = 6/45 = 2/15

=0.133

Therefore, the correct option is (c) 0.133

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Answer:

(x−h)2+(y−k)2=r2

(x−0)^2+(y+5)^2=25

Step-by-step explanation:

The firm's expected rate of return is approximately 9.90%.

To calculate the expected rate of return of the given firm, we have to very simply do a multiplication of the probability of the each possible return by the return itself and then sum the results.

Hence, the expected rate of return can be calculated with simple formulations as follows:

The Expected rate of return = (0.4 x 0.25) + (0.4 x 0.15) + (0.2 x -0.22) = 0.10 or 10%

Therefore, the expected rate of return for Taggart Inc. S stock is 9.90%.

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Answer:

3

Step-by-step explana

sorry if its wrong

The theoretical probability of the spinner not landing on yellow is 0.625 Option B

You should know that theoretical Probability is defined as the ratio of the number of favorable outcomes to the number of possible outcomes

The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

This is to say that

The number of possibility=8

the number of sample case=5

Probability that spinner is spun once and color is not blue,

=5/8

=0.625

The probability that spinner is spun once and color is not blue is0.625 when spinner divided evenly into eight sections with three colored blue, one colored orange, two colored purple, and two colored yellow.

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Answer:

x-5y=-11

Step-by-step explanation:

Step-by-step explanation:

she finishes by 3:45 at 30minutes

The length of the shadow cast by a person 1.82 m tall will be 4.09m

A ray of sunlight forms a angle of Elevation to the sub is 24°.

The angle from horizontal to the point where we stopped our head is called angle of elevation.

On this note, the shadow cast on the floor shows the adjacent of the angle of Elevation.

Hence, the length of the shadow cast can be calculated from Tangent identify as;

Tan 24° = 1.82/l

l = 1.82/Tan 24

l = 1.82/0.445

Thus, Length of shadow = 4.09m

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These hypotheses can be tested using the data collected from the random sample of 25 typists.

The appropriate set of hypotheses in this scenario would be:

Null hypothesis (H0): There is no significant difference in typing speed between word processor a and word processor b.

Alternative hypothesis (Ha): There is a significant difference in typing speed between word processor a and word processor b.

In this case, the publishing company wants to test if there is a difference in typing speeds between word processor A and word processor B. The appropriate set of hypotheses can be defined as follows:

Null hypothesis (H0): The mean typing speed difference between word processor A and word processor B is equal to 0. In other words, there is no significant difference in typing speeds between the two processors.
H0: μA - μB = 0

Alternative hypothesis (H1): The mean typing speed difference between word processor A and word processor B is not equal to 0. In other words, there is a significant difference in typing speeds between the two processors.
H1: μA - μB ≠ 0

These hypotheses can be tested using the data collected from the random sample of 25 typists.

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The bacterial culture loses half it's size every 0.167 seconds.

An exponential function has the definition presented as follows:

y = ab^x.

In which the parameters are given as follows:

The function in the context of this problem is defined as follows:

B(t) = 9300(1/64)^t.

The time needed for the population to lose half it's size is obtained as follows:

(1/64)^t = (1/2)

Considering the powers of two, in the denominator causing the negative signal, we have that:

2^(-6t) = 2^(-1)

6t = 1

t = 1/6

t = 0.167 seconds.

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If the manufacturer's claim is correct, the probability that the average deviation from perfect accuracy would be 34 seconds or more in the sample obtained by the consumer review website is 0.033

We can use a one-sample t-test to test the manufacturer's claim. The null hypothesis is that the true mean deviation from perfect time is equal to 30 seconds per month, and the alternative hypothesis is that the true mean deviation from perfect time is greater than 30 seconds per month.

The test statistic for this one-sample t-test is calculated as follows

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values given in the problem, we have

x = 34 seconds

μ = 30 seconds

s = 15 seconds

n = 40 clocks

t = (34 - 30) / (15 / √40) = 1.89

Using a t-distribution table with degrees of freedom (df) = n-1 = 39 and a significance level of α = 0.05 (one-tailed test), the critical value is 1.686.

Since our calculated t-value (1.89) is greater than the critical value (1.686), we reject the null hypothesis and conclude that the true mean deviation from perfect time is greater than 30 seconds per month.

To calculate the probability that the average deviation from perfect accuracy would be 34 seconds or more in the sample obtained by the consumer review website, we need to find the area under the t-distribution curve to the right of t = 1.89. Using a t-distribution calculator, we find this probability to be approximately 0.033

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