Use the ratio test to find the radius of convergence of the power series
2x + 2² · (2x)² + 3² · (2x)³ + 4² · (2x) + 5² · 2x)⁵ + ...
R = ...

Answer:

choice one and choice two

Step-by-step explanation:

Here is a rule: If the bisector of an angle in a triangle is perpendicular to the opposite side, the triangle is isosceles.

Since the question states that QST is isosceles, and that RT is an angle bisector, we can safely assume that RT is perpendicular to SQ.

All perpendicular line segments form right angles, so ∠QRT and ∠SRT are right angles

All right angles are equal to 90°

So, ∠QRT is 90°

All right are congruent, so ∠QRT ≅ ∠SRT

So the answer to this question is choice one and choice two

Answer:

c) 2700 m

Step-by-step explanation:

El atleta corre una carrera de 10 km.

Ya ha cubierto 7300 m. La distancia que queda por recorrer se puede encontrar restando 7300 m de 10 km.

10 km en metros son 10000 m (1 km = 1000 m)

Por lo tanto, la distancia que queda por recorrer es:

10000-7300 = 2700 m

The equation of the least-squares regression line based on these data is, y= 106.92 +2.044x where y =predicted height of child and x = child’s foot length.

To determine the equation of the least-squares regression line, we need to fit a linear model to the data using the method of least squares. The equation of the line can be written as:

height = intercept + slope * foot length

where the intercept and slope are the parameters we need to estimate from the data. The intercept represents the predicted height when foot length is 0, and the slope represents the change in height for each unit increase in foot length.

Substituting the values form the graph,

y= 106.92 +2.044x where y =predicted height of child and x = child’s foot length.

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--The complete question is, Can we predict the heights of school-aged children from foot length? below is computer output from a regression analysis of this relationship for 15 randomly-selected canadian children from 8 to 15 years old, along with a residual plot. the explanatory variable is each child's foot length (in centimeters), and the response variable is the child's height (in centimeters).

What is the equation of the least-squares regression line based on these data?  Define any parameters used.--

When we conclude that the results we have gathered from our sample are probably also found in the population from which the sample was drawn, we say that the results are statistically significant.

In statistical analysis, we use hypothesis testing to determine whether the results of a sample are likely to be representative of the population as a whole. If the results are statistically significant, we can infer that there is a low probability that the observed differences between the sample and the population occurred by chance alone.

This allows us to generalize the findings from the sample to the larger population with a reasonable degree of confidence.

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Answer:B

Step-by-step explanation:

Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

The steady-state solution of the heat conduction equation refers to the temperature distribution that remains constant over time. This occurs when the heat flow into a system is balanced by the heat flow out of the system.

To find the steady-state solution of the heat conduction equation, follow these steps:

1. Set up the heat conduction equation: The heat conduction equation describes how heat flows through a medium and is typically given by the formula:

  q = -k * A * dT/dx,

  where q represents the heat flow, k is the thermal conductivity of the material, A is the cross-sectional area through which heat flows, and dT/dx is the temperature gradient in the direction of heat flow.

2. Assume steady-state conditions: In the steady-state, the temperature does not change with time, which means dT/dt = 0.

3. Simplify the heat conduction equation: Since dT/dt = 0, the equation becomes:

  q = -k * A * dT/dx = 0.

4. Apply boundary conditions: Boundary conditions specify the temperature at certain points or surfaces. These conditions are essential to solve the equation. For example, you might be given the temperature at two ends of a rod or the temperature at the surface of an object.

5. Solve for the steady-state temperature distribution: Depending on the specific problem, you may need to solve the heat conduction equation analytically or numerically. Analytical solutions involve techniques like separation of variables or Fourier series expansion. Numerical methods, such as finite difference or finite element methods, can be used to approximate the solution.

It's important to note that the exact method for solving the heat conduction equation depends on the specific problem and the boundary conditions given. However, the general approach is to set up the heat conduction equation, assume steady-state conditions, simplify the equation, apply the boundary conditions, and solve for the steady-state temperature distribution.

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Given equation of the line is

Dividing both sides of the above equation by -18, we get

The line cuts the x axis at (-9,0) and the y axis at (0,-3).

Therefore, the x intercept is -9 and the y intercept is -3.

The graph of the line is shown below.

The possible sets of intensities that fit the given pattern are options (d) 63%, 65%, 67%.

We can use the given pattern to determine the possible intensities for the fourth, fifth, and sixth visits:

Constant intensity for 3 visits: This means that the intensity will be the same for the first three visits. Let's call this intensity level "I".

Increasing intensity over 3 visits: This means that the intensity will increase for the next three visits. Let's call the new intensity levels "I + x", "I + 2x", and "I + 3x".

Decreasing intensity over 3 visits: This means that the intensity will decrease for the final three visits. Let's call the new intensity levels "I + 2x", "I + x", and "I".

Note that the intensity increases by the same amount "x" during the increasing intensity visits, and decreases by the same amount during the decreasing intensity visits.

Now, let's look at each answer choice:

a. 63%, 63%, 63%: This corresponds to a constant intensity throughout all 3 visits, which does not fit the pattern given in the question.

b. 66%, 69%, 72%: This corresponds to an increasing intensity, but the amount of increase is not specified. Therefore, we cannot determine if this fits the given pattern.

c. 66%, 62%, 58%: This corresponds to a decreasing intensity, but the amount of decrease is not specified. Therefore, we cannot determine if this fits the given pattern.

d. 63%, 65%, 67%: This corresponds to an increasing intensity, with a constant increase of 2% per visit. This fits the given pattern of increasing intensity over 3 visits.

e. 67%, 72%, 77%: This corresponds to an increasing intensity, with a constant increase of 5% per visit. This does not fit the given pattern of increasing intensity over 3 visits, as the increase is too large.

Therefore, the possible sets of intensities that fit the given pattern are options (d) 63%, 65%, 67%.

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The exponential function that would give the population after t years is given by:

\(P(t) = 100 \times 2^{\frac{t}{9}}\)

An exponential function is modeled by:

\(y = ab^{\frac{x}{n}}\)

In which:

Considering that the population starts with 100 individuals and doubles every 9 years, the parameters are given as follows:

a = 100, b = 2, n = 9.

Hence the function is given by:

\(P(t) = 100 \times 2^{\frac{t}{9}}\)

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Answer:100 x 2 t/9

Step-by-step explanation:

Answer:

False. 2/3 is positive so therefore, it would be increasing, not decreasing.

Step-by-step explanation:

Answer:

98 units.

Step-by-step explanation:

Circumference = 2 * pi * radius

615.44 = 2 * 3.14 * r

r = 615.44 / (2 * 3.14)

 =2 * 3.14

 = 98 units.

Figure E is a rotated and reflected version of Figure D that has been shifted to the right and up as a result of this transformation sequence.

The sequence transformation (which may be dependent on n). This is known as a linear sequence transformation. Nonlinear sequence transformations are nonlinear sequence transformations.

We can use the following transformations to map Figure D onto Figure E:

Figure D should be translated 4 units to the right and 1 unit up.

Figure D should be rotated 90 degrees clockwise around the origin.

Cross the y-axis with the resulting figure.

This transformation sequence results in Figure E, which is a rotated and reflected version of Figure D that has been shifted to the right and up.

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Answer:36cm

Step-by-step explanation:

Answer:

41 1/4 and 15

Step-by-step explanation:

So for the first question, we know that a single inch of thread has 16 1/2 bolts. We know that there are 2 1/2 inches of thread.

To find the total anount of bolts in the thread, we can multiply 2 1/2 by 16 1/2:

2 1/1*16 1/2 = 41 1/4

That is our first answer.

For our next answer, we know that a book is 1 7/8 inches big.

The bookshelf is 28 1/8 inches big.

To find how many of the 1 7/8 inch big books can fit in the 28 1/8 inch big bookshelf, we can divide 28 1/8 by 1 7/8:

28 1/8/1 7/8

=

15

So our 2nd answer is 15.

Hope this helps!

Check the picture below.

Answer:

D; 85 leaves

Step-by-step explanation:

From what we can see, each 4 days there is a growth of an additional 9 leaves

So for the 20th day, we can see 58

The difference between the 20th and 32nd day is 12

The number of 4s we can see here is 12/4 = 3

For each 4, we can count extra 9 leaves

So for the 12, the number of leaves we can count is 3 * 9 = 27

we proceed to add this to 58

That will yield 58 + 27 = 85

It's c Bye bye have a amazing day

Answer:

We can conclude that someone used more tiles then the other because both equations are not equal.

Step-by-step explanation:

If you try to solve it both equations will not be shown as equal.

Answer:

Option C

Step-by-step explanation:

Consider each of these graphs. Let us formulate an inequality for each of them, and match the one with an inequality of \(x > - 14.5\);

\(Graph 1, x > 13.5\\Graph 2, x \geq 14\\Graph 3, x > 14.5\\Graph 4, x \geq 15\)

Graph 3 is the only one that matches with the inequality provided to us.

* Note that shaded circles are represented by a greater / less than or equal to, and non - shaded circles are represented by a greater / less than sign.

Solution ⇒ Graph 3

Answer:c

Step-by-step explanation:first of all,you have to understand the expression.it means -14.5 is less than x. Pin point where -14.5 is located on the number line.Then,u focus on the symbol '<' which says less than and we know that -13 and -12 downwards are lesser than 14 so our arrow would be drawn the way it is in c since x is greater than -14.5.

The abbreviation of the postulate or theorem that supports the conclusion that the triangles are congruent is not provided in the given information.

The given information states that ∠c and ∠f are right angles (rt. ∠'s), and ∠b is not explicitly mentioned. In order to determine the abbreviation of the postulate or theorem that supports the conclusion of triangle congruence, we would need additional information regarding the sides or angles of the triangles.

Triangle congruence can be established using various postulates and theorems, such as the Side-Angle-Side (SAS) postulate, Angle-Side-Angle (ASA) theorem, Side-Side-Side (SSS) postulate, and others. These criteria establish specific conditions that need to be met in order to prove that two triangles are congruent.

Without knowing the specific side or angle relationships between the triangles in the given information, it is not possible to determine the appropriate postulate or theorem that supports the conclusion of triangle congruence.

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The surface area after larger by scale factor is  11700 \(in^2\).

The surface area οf an οbject refers tο the οverall space filled by its surfaces. Many 3D shapes in geοmetry have variοus surface areas, which may be quickly estimated using the fοrmulas we shall learn in this lessοn. Twο categοries are used tο classify the surface area:

Here the given rectangular prism ,

Surface area = 1300 square inches

Here the given prism is larger by scale factor of 3 then,

=> surface area = 1300\(\times3^2\) =  1300\(\times9\) = 11700 \(in^2\).

Hence the surface area after larger by scale factor is  11700 \(in^2\).

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Answer:

37   9/20

Step-by-step explanation:

Answer:

\({ \bf{answer \: is \: { \underline{37 \frac{9}{20} }}}}\)

Step-by-step explanation:

When converting to fraction, you must get to know about the place values.

3 » tens

7 » ones

.4 » tenth

5 » hundredth

since last place value is hundredth, fraction denominator must be 100

therefore:

\(37.45 = \frac{3745}{100} \)

then you can reduce by 5:

\( = \frac{3745 \div 5}{100 \div 5} \\ \\ = \frac{749}{20} \)

In mixed fraction:

\( = 37 \frac{9}{20} \)

The answer to the question is given in parts:

a. The mean of this distribution is 2.55.

The mean of a uniform distribution is the average of its minimum and maximum values, which is given by the following formula:

Mean = (Maximum value + Minimum value)/2

Therefore, Mean = (3.4 + 1.7)/2 = 2.55.

b. The standard deviation is 0.4243.

The formula for the standard deviation of a uniform distribution is given by the following formula:

Standard deviation = (Maximum value - Minimum value)/√12

Therefore, Standard deviation = (3.4 - 1.7)/√12 = 0.4243 (rounded to four decimal places).

c. The probability that fawn will weigh exactly 2.9 kg is 0.

The probability of a continuous random variable taking a specific value is always zero.

Therefore, the probability that the fawn will weigh exactly 2.9 kg is 0.

d. The probability that a newborn fawn will weigh between 2.2 and 2.8 is P(2.2 < x < 2.8) = 0.25.

The probability of a continuous uniform distribution is given by the following formula:

Probability = (Maximum value - Minimum value)/(Total range)

Therefore, Probability = (2.8 - 2.2)/(3.4 - 1.7) = 0.25.

e. The probability that a newborn fawn will weigh more than 2.84 is P(x > 2.84) = 0.27.

The probability of a continuous uniform distribution is given by the following formula:

Probability = (Maximum value - Minimum value)/(Total range)

Therefore, Probability = (3.4 - 2.84)/(3.4 - 1.7) = 0.27.f. P(x > 2.3 | x < 2.6) = 0.5.

This conditional probability can be found using the following formula:

P(x > 2.3 | x < 2.6) = P(2.3 < x < 2.6)/P(x < 2.6)

The probability that x is between 2.3 and 2.6 is given by the following formula:

Probability = (2.6 - 2.3)/(3.4 - 1.7) = 0.147

The probability that x is less than 2.6 is given by the following formula:

Probability = (2.6 - 1.7)/(3.4 - 1.7) = 0.441

Therefore,

P(x > 2.3 | x < 2.6) = 0.147/0.441 = 0.5g.

Find the 60th percentile. The 60th percentile is the value below which 60% of the observations fall. The percentile can be found using the following formula:

Percentile = Minimum value + (Percentile rank/100) × Total range

Therefore, Percentile = 1.7 + (60/100) × (3.4 - 1.7) = 2.38 (rounded to two decimal places).

Therefore, the 60th percentile is 2.38.

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Answer:

Marco is 21

Step-by-step explanation:

Let the sister's age = x

Marco's age = 2*x - 5

x + 2x - 5 + 14 = 48            Combine the left side of the equation.

3x + 9 = 48                         Subtract 9 from both sides

3x = 48 - 9

3x = 39                               Divide by 3

x = 39/3

x = 13

So the sister is 13

Marco = 2x - 5 = 2*13 - 5

Marco = 21

Answer:

A.

Step-by-step explanation:

Wren is at the grocery store buying fruit. She buys x pounds of apples for $1.68 per pound. She buys 2 fewer pounds of grapes for $2.48 per pound. The cost of the fruit, before tax, is $13.76. How many pounds of each fruit is she buying?

A.

2.8 pounds of apples and 4.8 pounds of grapes

B.

3.3 pounds of apples and 1.3 pounds of grapes

C.

3.8 pounds of apples and 1.8 pounds of grapes

D.

4.5 pounds of apples and 2.5 pounds of grapes

Answer:

1) 3

2) 1

3) -5

Step-by-step explanation:

The coefficients are the numbers that come before each variable.

The 3 in the first term is in front of the x^2; so the coefficient is 3.

There is no visible number in front of the y in the second term, but there is a y, so we can assume there's at least 1; so the coefficient is 1.

The term in front of x for the third term is -5, so the coefficient is -5.

Answer:

3 2/3 and -5 are the coffecients

The number π/9 is not between √9/3 and 2π because the value of the number π/9 in the decimal form is 0.349

Option C is correct.

number line is described as a  representation of the numbers on a straight line that goes infinitely on both sides.

We check the number line as:

From the number line:

√9/3 = 3/3 = 1

2π = 2(22/7) = 6.28

The numbers are:

A) π = 3.141

B) √9 = 3

C) π/9 = 0.349

D) π²/9 = 1.096

In conclusion, the number π/9 is not between √9/3 and 2π because the value of the number π/9 in the decimal form is 0.349

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#complete question: