(1 point) Consider the power series (-1)"x" Vn +5 Find the radius of convergence R. If it is infinite, type "infinity" or "inf". Answer: R= What is the interval of convergence? Answer (in interval not

Using the chain rule, we have: f'(x) = 2ln(x^4 + 5) * 2(x^4 + 5)^1 * 4x^3
f'(x) = 16x^3 * ln(x^4 + 5) * (x^4 + 5)

To find f'(-2), we plug in -2 for x:

f'(-2) = 16(-2)^3 * ln((-2)^4 + 5) * ((-2)^4 + 5)
f'(-2) = -128 * ln(21) * 21
f'(-2) ≈ -599.92 (rounded to 2 decimal places)

Therefore, f'(-2) is approximately -599.92.
To find f'(-2) for the function f(x) = ln((x^4 + 5)^2), we will first find the derivative of the function, and then evaluate it at x = -2.

1. Differentiate the function using the chain rule:
f'(x) = (d/dx) ln((x^4 + 5)^2) = (1/((x^4 + 5)^2)) * (d/dx) ((x^4 + 5)^2)

2. Differentiate the inner function:
(d/dx) ((x^4 + 5)^2) = 2(x^4 + 5) * (d/dx) (x^4 + 5) = 2(x^4 + 5) * (4x^3)

3. Combine the derivatives:
f'(x) = (1/((x^4 + 5)^2)) * (2(x^4 + 5) * (4x^3)) = (8x^3(x^4 + 5))/((x^4 + 5)^2)

4. Evaluate the derivative at x = -2:
f'(-2) = (8(-2)^3((-2)^4 + 5))/((-2)^4 + 5)^2 = (-128(21))/(21^2) = -128/21

So, f'(-2) is -128/21 as an exact fraction.

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The resultant component of the vector addition, 1/3a - 2b is (-9, 0).

The resultant component of the vector is calculated as follows;

a = (-9, 6)

b = (3, 1)

The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)

The result of 2b = 2(3, 1) = (6, 2)

The result of the vector addition is calculated as follows;

1/3a - 2b

= (-3, 2) - (6, 2)

= (-3 -6, 2 -2)

= (-9, 0)

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The equations that will find the distance between the lions and giraffes include the following:

B. 11² + 16² = c².

D. 11(2) + 16(2) = 2.

In Mathematics and Science, distance can be defined as the amount of ground that is travelled by a physical object or body over a particular period of time and speed, irrespective of its direction, starting point or ending point.

Mathematically, the distance traveled by both the lions and giraffes when they are positioned one (1) unit apart can be calculated by using this equation:

11² + 16² = c²

Additionally, the distance traveled by both the lions and giraffes when they are positioned two (2) unit apart can be calculated by using this equation:

11(2) + 16(2) = c

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Answer:

Answer:17

Explanation: 5-0.75=4.25 4.25÷0.25=17

Hope this helps

The number of students who drive to school can be calculated as one-sixth of the total number of students.

Let's assume the total number of students in the Mupuvr CLC MLMMS4 group is represented by the variable 'x'. According to the given information, half of the students walk to school, which is equal to (1/2) * x. One-third of the students take a taxi, which is equal to (1/3) * x. The remaining students, who claim to drive, can be calculated as x - [(1/2) * x + (1/3) * x].

Simplifying this expression, we have x - (5/6) * x, which is equal to (1/6) * x. Therefore, the number of students who claim to drive to school is one-sixth of the total number of students.

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The ratio of a : b : c : d is 3 : 7 : 2 : 7.

The ratios are determined as follows from the data given.

The given data is:

7a = 2b

b = (7/2)a.

a and b have no common factors, thus a must be even and b must be odd.

c : d is 2 : 7

For an integer x, c = 2x and d = 7x

a : d is 3 : 1

So for an integer y, a = 3y and d = y

Substituting into 7a = 2b:

7(3y) = 2(7/2)y a

21y = 7y * b

b = 3a

Substituting these expressions for a and b into c : d = 2:7, we get:

2x : 7x = 3 : 1

2x = 3y and 7x = y

y = 14x/3

a : b : c : d = 3y : 7y : 2x : 7x

a : b : c : d = 3(3y) : 3(7y) : 3(2x) : 3(7x)

a : b : c : d = 9y : 21y : 6x : 21x

a : b : c : d = 3 : 7 : 2 : 7

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To find -F+2G+H-R using the Graphical Tail-to-Tip method, measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

To find the vector sum F+2G+H-R using the graphical tail-to-tip method, follow these steps:

Now, place the vectors tail-to-tip in the following order: F, 2G, H, and R (in opposite directions).

The sum of these vectors can be found by connecting the starting point (tail of F) to the endpoint (tip of R in the opposite direction).

Measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.

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The doctor would prescribe 8 milliliters of acetaminophen for Jocelyn, who weighs 40 pounds.

According to the given information, pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child's weight. So, if a child weighs 50 pounds, the doctor would prescribe 10 ml of acetaminophen.

Now, let's apply this formula to Jocelyn's weight. As Jocelyn weighs 40 pounds, we need to calculate how many 25-pound increments her weight contains. To do this, we can divide her weight by 25:

40 pounds ÷ 25 pounds = 1.6 increments

This means that Jocelyn's weight is equivalent to 1.6 times the 25-pound increment used in the prescription. To determine the amount of acetaminophen she needs, we can multiply 5 ml (the prescribed dose for 25 pounds) by 1.6:

5 ml × 1.6 = 8 ml

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The surface area of the pyramid is 72 + 486√3 metres.

The pyramid above is an hexagonal pyramid. The surface area of the hexagonal pyramid can be found as follows:

surface area of a hexagonal pyramid = ph / 2 + B

where

Therefore,

Base area = 1 / 2pa

where

Base area = 1 / 2 × (18 × 6) × 9√3

Base area = 1 / 2 × 108 × 9√3

Base area = 54 × 9√3

Base area = 486√3 metres

surface area of a hexagonal pyramid = 108 × 18 / 2 + 486√3

Therefore,

surface area of a hexagonal pyramid = 972 + 486√3 metres

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The best interpretation of one of the values of the function is  The number of microorganisms increases by 16% each week.

The given function of the number of the microorganisms present in the water sample at the end of x weeks is

h(x) = 146(1.16)ˣ

To find the number of microorganisms present in the water sample after one week, we substitute x = 1 in the above equation

h(1) = 146(1.16)¹

h(1) = 169.36

Therefore, after one week, there will be approximately 169 microorganisms in the water sample.

Thus, the correct interpretation of one of the values of the function is F.

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A. Approximately 9.85% of New York City commutes are less than 30 minutes

B. Approximately 16.91% of New York City commutes are between 30 and 35 minutes.

A. To find the percent of New York City commutes that are less than 30 minutes, we need to calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value we are interested in (30 minutes), μ is the mean commute time (39.7 minutes), and σ is the standard deviation (7.5 minutes).

z = (30 - 39.7) / 7.5 = -1.29

We can use a standard normal distribution table or calculator to find the area to the left of z = -1.29, which gives us:

P(z < -1.29) = 0.0985

Therefore, approximately 9.85% of New York City commutes are less than 30 minutes.

B. To find the percent of New York City commutes that are between 30 and 35 minutes, we need to calculate the z-scores for both values using the same formula:

z1 = (30 - 39.7) / 7.5 = -1.29

z2 = (35 - 39.7) / 7.5 = -0.62

We can then find the area between these two z-scores using a standard normal distribution table or calculator, which gives us:

P(-1.29 < z < -0.62) = P(z < -0.62) - P(z < -1.29) = 0.2676 - 0.0985 = 0.1691

Therefore, approximately 16.91% of New York City commutes are between 30 and 35 minutes.

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The height of the cone that the volume of a cylinder is twice the volume of a cone is 7.5 meters.

Let's first define some variables to represent the dimensions of the cone and cylinder. Let's use r for the radius of both shapes, h for the height of the cone, and 5 for the height of the cylinder.

The volume of a cone is given by V_cone = (1/3)πr^2h, and the volume of a cylinder is given by V_cylinder = πr^2h.

We are told that the volume of the cylinder is twice the volume of the cone:

V_cylinder = 2V_cone

Substituting the formulas for the volumes of the cone and cylinder, we get:

πr^2(5) = 2[(1/3)πr^2h]

Simplifying, we can cancel the π and the r^2 terms on both sides:

5 = (2/3)h

Multiplying both sides by 3/2, we get:

h = 7.5

Therefore, the height of the cone is 7.5 meters.

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The solutions of the equation algebraically are x = 5 and x = -7

From the information given, we have the quadratic equation;

|x| = x2 + x − 35

The sign , '| |' represents the modulus sign and says that the value must be a positive value.

Then, we have;

x² + x + x - 35

add the like terms

x² + 2x - 35

Find the pair factors of -35 that add up to 2, we have;

x² + 7x - 5x - 35

Group the expression in pairs

(x² + 7x) - (5x - 35)

factorize the expression

x(x + 7) - 5(x + 7)

Then, we have that;

x - 5 = 0

x = 5

x + 7 = 0

x = -7

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I'm sorry, but I cannot determine the values of the line segment lengths

and angle measures without further information or context about the

geometry problem. Please provide me with more details or the specific

problem in question.

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Answer:

I think the answer might be -4 = 3x.

Step-by-step explanation:

-2 times x + 2 = -4 and 5 - 2x = 3x so i think the answer is -4 = 3x. Also, you're welcome if this helps.

Answer:

SSA

Step-by-step explanation:

It would be SSA (Side-Side-Angle).  They are congruent where they intersect at B (opposite angles).  Since CF is congruent to GH, and CB is congruent to HB, you have an angle and two sides congruent, in the order SSA.

The value of x is 2.8 The scale factor of left polygon to the right polygon, GKNM to RPTV is 1.4.

Since the two polygons GKNM and RPTV are similar, their corresponding sides are proportional. Thus, we can set up the following proportion

(GK + KN + NM)/GK = (RP + PT + TV + VR)/RP

Plugging in the given values and simplifying, we get

(8.4 + 3x - 2 + 4)/8.4 = (x + 5 + 3 + 3 + 6.3)/(x + 5)

15.4/(3x + 2.4) = (x + 17.3)/(x + 5)

Cross-multiplying and solving for x, we get

x = 2.8

To find the scale factor of GKNM to RPTV, we can divide the corresponding side lengths

(GK + KN + NM)/(RP + PT + TV + VR) = (8.4 + 3(2.8) - 2 + 4)/(2.8 + 5 + 3 + 3 + 6.3) = 1.4

Therefore, the scale factor of GKNM to RPTV is 1.4.

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There were approximately 586,800 elephants in Africa, rounded up to the nearest elephant.

In 1980, there were 1.2 million elephants in Africa. With a decrease of 6.8% per year, we need to calculate the population in 1987, which is 7 years later.

To find the population in 1987, we use the formula:

Final population = Initial population * (1 - decrease rate) ^ number of years

Final population = 1,200,000 * (1 - 0.068) ^ 7

Final population ≈ 1,200,000 * 0.489

Final population ≈ 586,800

In 1987, there were approximately 586,800 elephants in Africa, rounded up to the nearest elephant.

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Answer: B

Step-by-step explanation: I did the quiz :p

Hope this helps

The correct answer is B. 12. There are 12 numbers in the table, which represents the number of observations Beckett recorded.

The table shows the number of days each of Beckett's classmates floss their teeth in a typical week. The number of observations recorded is simply the number of classmates, or the number of entries in the table. In this case, there are 12 entries, so the answer is 12.

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Answer:

x=50

Step-by-step explanation:

1. multiply the numbers

48x25=24x

1200=24x

2. Divide both sides by the same factor

1200/24 = 24/24x

simplify the expression

x=50

The power rule for derivatives is  -26/5.

The derivative is a fundamental concept that measures how much a function changes as its input changes. It is a mathematical tool used to find the instantaneous rate of change of a function at a specific point. The derivative of a function f(x) at a point x=a, denoted by f'(a), is the slope of the tangent line to the graph of f(x) at the point (a, f(a)).

a. f(x) = 2x³

Using the power rule for derivatives, we have:

f'(x) = 6x²

So, f'(2) = 6(2)² = 24.

b. g(x) = 13x^(1/2)

Using the power rule for derivatives, we have:

g'(x) = (1/2) * 13x^(-1/2) = (13/2√x)

So, g'(3) = (13/2√3).

c. h(x) = hx

Using the power rule for derivatives, we have:

h'(x) = h

So, h'(4) = h.

d. j(x) = 130x^(-1)

Using the power rule for derivatives, we have:

j'(x) = -130x^(-2)

So, j'(5) = -130(5)^(-2) = -130/25 = -26/5.

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The average change in temperature per hour during the temperature drop from 48°F to -16°F in Sioux Falls, South Dakota on February 6, 1995, was 8°F per hour.

On February 6, 1995, the temperature in Sioux Falls, South Dakota dropped dramatically from 48°F to -16°F in just eight hours. To calculate the average change in temperature per hour, we can use the formula:

Average Change in Temperature per Hour = (Change in Temperature) ÷ (Time)

Using this formula, we can calculate the average change in temperature per hour in Sioux Falls as follows:

Average Change in Temperature per Hour = (48°F - (-16°F)) ÷ 8 hours

Average Change in Temperature per Hour = 64°F ÷ 8 hours

Average Change in Temperature per Hour = 8°F per hour

Therefore, the average change in temperature per hour during that eight-hour period in Sioux Falls, South Dakota was 8°F. This rapid and significant change in temperature was likely due to a strong cold front moving through the area.

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Cubic inches of popcorn does the jumbo size hold compared to the regular size round to the nearest tenth

To determine how many more cubic inches of popcorn the jumbo size holds compared to the regular size, you would need to:

1. Find the volume (in cubic inches) of both the jumbo and regular size popcorn containers.
2. Subtract the volume of the regular size container from the volume of the jumbo size container.

Unfortunately, without specific dimensions for the jumbo and regular size popcorn containers, I cannot provide a numerical answer. Please provide the dimensions, and I would be happy to help you with the calculations.

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Part a. The magnitude of the angular acceleration of the salad spinner as it slows down is 4.00 radians/s².

Part b. It takes 1.00 seconds for the salad spinner to come to rest.

Part A:

The initial angular velocity of the spinner is given by:

ω1 = 20.0 rotations / 5.00 s = 4.00 rotations/s

The final angular velocity of the spinner is zero.

The number of rotations between the initial and final angular velocities is:

Δθ = 6.00 rotations

Using the equation of motion for rotational kinematics with constant angular acceleration:

Δθ = 1/2 α t^2 + ω1 t

where α is the angular acceleration, and t is the time it takes to stop spinning.

At the final angular velocity, ω2 = 0, so we can rearrange the equation to solve for t:

t = ω1 / α

Substituting the given values:

Δθ = 6.00 rotations

ω1 = 4.00 rotations/s

t = (4.00 rotations/s) / α

Solving for α:

Δθ = 1/2 α t^2 + ω1 t

6.00 rotations = 1/2 α (t^2) + (4.00 rotations/s) t

Substituting t = (4.00 rotations/s) / α:

6.00 rotations = 1/2 α [(4.00 rotations/s) / α]^2 + (4.00 rotations/s) [(4.00 rotations/s) / α]

6.00 rotations = 8.00 rotations + 16.00 rotations/s^2 / α

α = 16.00 rotations/s^2 / (6.00 rotations - 8.00 rotations)

α = 8.00 rotations/s^2 / 2.00 rotations

α = 4.00 radians/s^2

Therefore, the magnitude of the angular acceleration of the salad spinner as it slows down is 4.00 radians/s^2.

Part B:

Using the equation of motion for rotational kinematics with constant angular acceleration:

ω2 = ω1 + α t

At the final angular velocity, ω2 = 0, so we can rearrange the equation to solve for t:

t = -ω1 / α

Substituting the given values:

ω1 = 4.00 rotations/s

α = 4.00 radians/s^2

t = -(4.00 rotations/s) / (4.00 radians/s^2)

t = -1.00 s

Since the time cannot be negative, we take the absolute value of t:

t = 1.00 s

Therefore, it takes 1.00 seconds for the salad spinner to come to rest.

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The equation in slope-intercept form for the line passing through each pair of points, (-4, 4) and (-5, -3) is expressed as: y = 7x + 32

Given the points, (-4, 4) and (-5, -3), first find the slope of the line.

Slope (m) = change in y / change in x = -3 - 4 / -5 -(-4)

m = -7/-1

m = 7

Substitute m = 7, a = -4, and b = 4 into y - b = m(x - a):

y - 4 = 7(x + 4)

Rewrite im slope-intercept form:

y - 4 = 7x + 28

y - 4 + 4 = 7x + 28 + 4

y = 7x + 32

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Answer:

V = 1,728 mi³

SA = 864 mi²

Step-by-step explanation:

We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.

First, we can solve for the area of one of the triangle sides:

A(triangle) = (1/2) · b · h

A(triangle) = (1/2) · 24 · 18

A(triangle) = 12 · 18

A(triangle) = 216 mi²

Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.

V = A(triangle) · depth

V = 216 · 8

V = 1,728 mi³

__

We can find the surface area by finding the area of each side, then adding all of those areas together.

We already know that the area of each of the triangle sides is 216 mi².

Now, we can solve for the area of the base.

A(base) = length · width

A(base) = 24 · 8

A(base) = 192 cm²

Then, we can find the area of the top side.

A(top) = length · width

A(top) = 30 · 8

A(top) = 240 mi²

Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.

SA = (2 · A(triangle)) + A(base) + A(top)

SA = 2(216) + 192 + 240

SA = 432 + 192 + 240

SA = 624 + 240

SA = 864 mi²

Answer:

B) <FBG

Step-by-step explanation:

An adjacent angle is an angle that is right next to the given angle.

In this case, the given angle is <EBF.

We can see that the only 2 options here for an adjacent set of angles is either <FBG or <EBD.

Looking at the options, we can only see that <FBG is an option, making B the correct option.

Hope this helps :)

The height of the replica souvenir is approximately 7.55 inches.

To find the height of the replica souvenir of the Statue of Liberty, we'll use the given scale factor of 1 inch = 20 feet. The original height of the statue is 151 feet. Divide the original height by the scale factor:

151 ft / 20 ft/in = 7.55 inches

The height of the replica souvenir is approximately 7.55 inches.

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(a) The 92% CI for overall proportion of pudding packs containing less than 3.25oz of pudding at α = 0.08 is (0.5806, 0.6994);

(b) The 99% CI for overall proportion of pudding packs containing more than 3.25oz of pudding at α = 0.01 is (0.2726, 0.4474).

Part (a) : To construct a confidence-interval for the overall proportion of pudding packs containing less than 3.25oz of pudding, we use the following formula : CI = p' ± [tex]z_{\frac{\alpha}{2} }[/tex] × √(p'(1-p')/n);

where p' is = sample proportion, [tex]z_{\frac{\alpha}{2} }[/tex]  is = critical z-value for the desired confidence level, and n is = sample size.

In this case, p' = (200-72)/200 = 128/200 = 0.64, the sample size is n = 200, and

We know that the critical z-value for a 92% confidence interval(α = 0.08) is approximately 1.75;

Substituting the values,

We get,

CI = 0.64 ± 1.75 × √(0.64(1 - 0.64)/200)

CI = 0.64 ± 0.059421;

CI = (0.5806, 0.6994);

Therefore, the required confidence interval is (0.5806, 0.6994).

Part (b) : In this case, p' = 72/200 = 0.36, the sample-size is n = 200, and

We know that the critical z-value for a 99% confidence interval (α = 0.01) is approximately 2.57;

Substituting the values,

We get,

CI = 0.36 ± 2..57 × √(0.36(1 - 0.36)/200)

CI = 0.36 ± 0.087426;

CI = (0.2726, 0.4474);

Therefore, the required confidence interval is (0.2726, 0.4474).

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