What type of number?

The series ∑((-1)ⁿ⁺¹/(2n⁴) from n=0 to infinity is converges.

To test the convergence or divergence of the series ∑((-1)ⁿ⁺¹/(2n⁴) from n=0 to infinity, we can use the alternating series test.

The alternating series test states that if a series has the form ∑((-1)ⁿ)bₙ or ∑((-1)ⁿ⁺¹)bₙ.

where bₙ is a positive sequence that converges to zero as n approaches infinity, then the series converges.

We have ∑(-1)ⁿ⁺¹/2n⁴.

Let's analyze the sequence bₙ=1/2n⁴

The sequence bₙ = 1/(2n⁴) is always positive.

As n approaches infinity, 1/(2n⁴) approaches zero.

Therefore, we can apply the alternating series test to our series. T

The alternating series ∑((-1)ⁿ⁺¹/(2n⁴) converges because the sequence bₙ=1/2n⁴ satisfies the conditions of the alternating series test.

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Answer:

More than 40 students

Step-by-step explanation:

Let x be the number of students .

Given : Mrs. Williams is deciding between two field trips for her class. The Science Center charges $80 plus $5 per student.

i.e. Total cost : 80+5x       (1)

The Dino Discovery Museum simply charges $7 per student.

i.e. Total cost : 7x              (2)

The inequality that shows Science Center charge less than the Dino Discovery Museum charges will be :-

80+5x<7

Subtract 5x on both sides , we get

80<2x

Divide both sides by 2 , we get

40<x

Hence, for more than 40 students the Science Center charge will less than the Dino Discovery Museum charges.

Answer by: JeanaShupp

The possible values of k are k = 2 and k = -2. These are the values of the constant k for which f(x) is continuous at x = 2.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To determine the values of the constant k for which f(x) is continuous at x = 2, we need to ensure that the left-hand limit, the right-hand limit, and the value of f(x) at x = 2 are all equal.

First, let's find the left-hand limit as x approaches 2. We evaluate the function for x < 2:

f(x) = x² + 5kx    (for x < 2)

Taking the limit as x approaches 2 from the left side (x < 2), we have:

lim(x→2-) f(x) = lim(x→2-) (x² + 5kx) = 2² + 5k(2) = 4 + 10k

Next, let's find the right-hand limit as x approaches 2. We evaluate the function for x > 2:

f(x) = k²x + 4x + 4    (for x > 2)

Taking the limit as x approaches 2 from the right side (x > 2), we have:

lim(x→2+) f(x) = lim(x→2+) (k²x + 4x + 4) = k²(2) + 4(2) + 4 = 2k² + 8 + 4 = 2k² + 12

Now, let's evaluate the value of f(x) at x = 2:

f(x) = 3k² - 4    (for x = 2)

f(2) = 3k² - 4

For f(x) to be continuous at x = 2, the left-hand limit, the right-hand limit, and the value of f(x) at x = 2 should all be equal. Therefore, we set up the following equation:

4 + 10k = 2k² + 12 = 3k² - 4

Simplifying, we have:

2k² + 8 = 3k² - 4

Rearranging the terms, we get:

k² - 12 = 0

Factoring, we have:

(k - 2)(k + 2) = 0

So, the possible values of k are k = 2 and k = -2. These are the values of the constant k for which f(x) is continuous at x = 2.

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Answer:

0 = 4x

Step-by-step explanation:

-2(2 - 2x) = 4 - 8(1 - x)

-4 + 4x = 4 - 8 + 8x

-4 + 4x = -4 + 8x

-4 + 4 = 8x - 4x

0 = 4x

Answer:

0=4x

Step-by-step explanation:

You can read this problem as simplify -2(2-2x)=4-8(1-x), because being equivalent to something can be started with simplification.

So now, on to the simplification now:

-2(2-2x)=4-8(1-x)

Step 1: Open Parantheses -4+4x=4-8+8x

(Remember, two negatives equal a postitive. That's why you get 4x and 8x, not -4x nor -8x.)

Step two: Tidy (Put x's on one side, others on the other.) 4x-8x=4-8+4

(Remember, when you move a number/variable to one side, the negative/positive sign becomes the opposite.)

Step three: Solve -4x=0

Now, be get -4x=0. But then again, if -4x=0, then 4x=0, considering x will be zero.

I hope you liked this explanation! If you have more problems, I'm always free to help.

The width of the rectangle is 60 meters

The area A, in square meters, of a rectangle is given by the equation

A = 70w - w²

where w is the width of the rectangle in meters.

70w - w² = 600

70w - w²- 600 = 0

w²-70w+600 = 0

w²-60w-10w+600 = 0

(w-60)(w-10) = 0

w =60

w =10

the width of the rectangle is 60 meters

Subtraction:

The act of removing elements from a collection is represented by subtraction. Subtraction is symbolized by the negative symbol. The stack will now include five oranges rather than nine if, for instance, four of the nine oranges that are stacked together (as in the figure above) are then moved to a basket. As a result, 5 is the difference between 9 and 4, which is the same as 9 less 4. Subtraction can be applied to other types of numbers in addition to natural numbers. Subtraction is represented by the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference.

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Step-by-step explanation:

\(f(x) = {2}^{(x - 5)} \)

\(f(8) = {2}^{(8 - 5)} \)

\(f(8) = {2}^{3} \)

\(f(8) = 8\)

Answer:

Answer: Third objective

Step-by-step explanation:

\({ \tt{f(x) = {2}^{(x - 5)} }}\)

when x is 8, f(x) is f(8):

\(\dashrightarrow \: { \tt{f(8) = {2}^{(8 - 5)} }} \\ \\ { \tt{f(8) = {2}^{3} }} \\ \\ { \tt{f(8) = 2 \times 2 \times 2}} \\ \\ \dashrightarrow \: { \boxed{ \tt{f(8) = 8}}}\)

1. The area of the scale drawing of the park is 146,880 square inches (Option J).

2. The perimeter of the park is 126 feet (Option D).

3. The length of the south side of the park is 40% of the length of the north side (Option F).

1. To find the area of the scale drawing of the park, we need to calculate the area of the trapezium. The formula for the area of a trapezium is (base1 + base2) * height / 2.

Using the scale, the lengths of the bases (parallel sides) in feet would be:

Base1 = 28 inches * 1.5 feet/inch = 42 feet

Base2 = 40 inches * 1.5 feet/inch = 60 feet

Plugging in the values into the formula, we have:

Area = (42 + 60) * 16 / 2 = 1020 square feet

Since the answer options are in square inches, we need to convert the area back to square inches:

Area = 1020 square feet * 144 square inches/square foot = 146880 square inches

Therefore, the area of the scale drawing of the park is 146880 square inches.

2. The perimeter of the park can be calculated by summing up the lengths of all sides.

The lengths of the sides in feet would be:

Side1 = 28 inches * 1.5 feet/inch = 42 feet

Side2 = 40 inches * 1.5 feet/inch = 60 feet

Side3 = 16 inches * 1.5 feet/inch = 24 feet

Adding up all sides, we have:

Perimeter = Side1 + Side2 + Side3 = 42 feet + 60 feet + 24 feet = 126 feet

Therefore, the perimeter of the park is 126 feet.

3. To find the percentage length of the south side compared to the north side, we can calculate:

Percentage = (South Side Length / North Side Length) * 100

Using the scale, the length of the south side in feet would be:

South Side Length = 16 inches * 1.5 feet/inch = 24 feet

The length of the north side is already given as 40 inches * 1.5 feet/inch = 60 feet.

Plugging in the values, we have:

Percentage = (24 feet / 60 feet) * 100 = 40%

Therefore, the length of the south side of the park is 40% of the length of the north side.

Complete Question:

Mikea, an intern with the Parks and Recreation Department, is developing a proposal for the new trapezoidal Springdale Park. The figure below shows her scale drawing of the proposed park with 3 side lengths and the radius of the merry-go-round given in inches. In Mikea's scale drawing, 1 inch represents 1.5 feet.

1. What is the area, in square inches, of the scale drawing of the park? 448 544 H. 640 672 K. 1.088

2. Mikea's proposal includes installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park? A. 84 B. 88 C. 104 D. 126 E 156

3. The length of the south side of the park is what percent of the length of the north side? F. 112% G. 1245 H. 142 J. 1754 K. 250%

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We utilize a two factors, independent measurements ANOVA, where, factor has 2 level and a factor likewise has 2 levels.

A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.

Factors and multiples are a part of our daily life. For example, they are employed in arranging objects in a box, handling money, recognizing patterns in numbers, solving ratios, and working with expanding

A number totally divides the provided number without leaving any residual is said to be the factor of that number.

The components of a number might be positive or negative. For example, let us find the factors of 8. Since 8 is divisible by 1, 2, 4, and 8, we may list the positive factors of 8 as, 1, 2, 4, and 8. Apart from this, 8 has negative elements as well, which might be stated as, -1, -2, -4,

According to our question-

Degrees of freedom for the F-test of the two way ANOVA

In this case, we utilize an ANOVA with two independent variables and two factors, each with two levels.

So, here,

= 2 for the number of layers of A

= B's level count is 2,

Moreover, n = sample size in each treatment condition is equal to 10.

So we have,

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of interaction effect (A x B) = ( - 1)( - 1) ( - 1)

= (2-1)(2-1) (2-1)

= 1

And = df of within variation (i.e. error variation) =

= 2 x 2 x (10 - 1) (10 - 1)

= 36

Consequently, the df value for the F-ratio measuring factors-primary A's impact is

= () ()

= (1, 36) (1, 36)

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Answer:

11.8

Step-by-step explanation:

x+(-13.4)=-1.6

aka -1.6+13.4

which =11.8

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

it has 14 sides

360/14= 25.714

rounding to the nearest tenth we get:

25.7

Answer:

813.33 N/m²

Step-by-step explanation:

Before finding the answer to this, let us convert 750cm² to m².

1 m ⇒ 100cm

1 m × 1 m ⇒ 100 cm × 100 cm

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

1 m² ⇒ 10000 cm²

 x    ⇒ 750 cm²

Let us use cross multiplication to find the value of x.

10000x = 750 × 1

10000x = 750

x = 750/10000

x = 0.075

∴ 750 cm² = 0.075 m²

And now let us find the pressure.

Pressure = Force ÷ Area

Pressure = 61 N ÷ 0.075 m²

Pressure = 813.33 N/ m²

y'' - y' + (1/4)y = 0 .

This the correct / main answer .

Explanation:

To solve the differential equation by undetermined coefficients, we first find the general solution to the homogeneous equation:

y'' - y' + 1/4 y = 0

The characteristic equation is r^2 - r + 1/4 = 0, which has roots r = 1/2 ± i/2. Therefore, the general solution to the homogeneous equation is:

y_h = c_1 e^(x/2) cos(x/2) + c_2 e^(x/2) sin(x/2)

To find a particular solution to the non-homogeneous equation, we guess a form for y_p based on the right-hand side of the equation. In this case, since the right-hand side includes the term ex/2, we guess that y_p takes the form:

y_p = A x e^(x/2)

where A is a constant to be determined.

We now substitute this guess into the differential equation to find A:

y_p'' - y_p' + 1/4 y_p = 8 + ex/2

Differentiating y_p twice, we get:

y_p'' = (1/4 + 1/2x + 1/4x^2) A e^(x/2)

y_p' = (1/2 + 1/2x) A e^(x/2)

Substituting these expressions into the differential equation and simplifying, we get:

(1/4 + 1/2x + 1/4x^2) A e^(x/2) - (1/2 + 1/2x) A e^(x/2) + 1/4 (A x e^(x/2)) = 8 + ex/2

Simplifying further, we get:

(1/4)x^2 A e^(x/2) = 8

Solving for A, we get:

A = 32 / (x^2 e^(x/2))

Therefore, the particular solution is:

y_p = 32x / (x^2 + 4) e^(x/2)

The general solution to the non-homogeneous equation is the sum of the homogeneous and particular solutions:

y = y_h + y_p

 = c_1 e^(x/2) cos(x/2) + c_2 e^(x/2) sin(x/2) + 32x / (x^2 + 4) e^(x/2)

Hence, the correct  answer is:

y(x) = yp(x) + yc(x) = 28 + yc(x)

where yc(x) is the complementary solution obtained by solving the homogeneous equation:

y'' - y' + (1/4)y = 0.

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Answer:

74 inches

Step-by-step explanation:

82 inches - 8 inches = 74 inches

y = 1.5x + 0.5 is the equation of the line passing through the coordinate points

The formula for finding the equation of a line in slope-intercept form is expressed as:

y =mx + b

where:

m is the slope

b is the intercept

Determine the slope

slope = 5-2/3-1

slope = 3/2

slope = 1.5

Determine the y-intercept

y = mx + b

5 = 1.5(3) + b

5 = 4.5 + b

b = 0.5

Hence the required equation of the line passing through ( 1,2) and (3,5) is

y = 1.5x + 0.5

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Complete question

What's the equation of a line that passes through (1,2) (3,5)?

Answer:

  42, 38, 34, 30

Step-by-step explanation:

You want the first 4 terms of the sequence described by ...

  an = 42 -4(n -1), n ∈ ℕ

You can write the first 4 terms of the sequence by evaluating the 'an' expression for n = 1, 2, 3, 4.

Or, you can recognize the expression describes a sequence with a first term of 42 and a common difference of -4. That is, each term is 4 less than the one before.

The terms you want are ...

  42, 38, 34, 30

__

Additional comment

The equation for the n-th term of an arithmetic sequence is ...

  an = a1 +d(n -1)

where a1 is the first term, and d is the common difference. Comparing this to the given equation, we see a1 = 42, d = -4.

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Answer: I think it is ten but can I have brainlest

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(3\left(x+1\right)=5\left(x-2\right)+7\\Expand\\3x+3 =5x -10+7\\Collect \:like\: terms\\3x-5x = -10+7-3\\-2x = -6\\Divide \:both\:sides\:of\:the\:equation\:by\:-2\\\frac{-2x}{-2} = \frac{-6}{-2}\\ \\x = 3\)

Answer:

 x = 3

Step-by-step explanation:

3(x+1)=5(x−2)+7

Use the distributive property to multiply 3 by x+1.

3x+3=5(x−2)+7

Use the distributive property to multiply 5 by x−2.

3x+3=5x−10+7

Add −10 and 7 to get −3.

3x+3=5x−3

Subtract 5x from both sides.

3x+3−5x=−3

Combine 3x and −5x to get −2x

−2x+3=−3

Subtract 3 from both sides.

−2x=−3−3

Subtract 3 from −3 to get −6.

−2x=−6

Divide both sides by −2.

x = -6/2

Divide −6 by −2

x = 3

Answer:

The coordinates of Y' will be:  A'(4, -3)

Step-by-step explanation:

Triangle XYZ with vertices

We have to determine the answer for the image Y' of the point Y(-3, 4) with respect to the line mirror y=x.

We know that when P(x, y) is reflected in y = x, we get P'(y, x)

i.e.

The rule of y=x:

As we are given that Y(-3, 4), so the coordinates of Y' will be:

A(-3, 4) → A'(4, -3)

Therefore, the coordinates of Y' will be:  A'(4, -3)

Answer:

Sample Response: To find the image after a reflection over the x-axis, I would negate the y-coordinate. To find the image after a reflection over the y-axis, I would negate the x-coordinate. So, reflecting the point (5, 2) over the x- and y-axis, I would get (–5, –2).

Step-by-step explanation:

Answer:

A

\(2y {}^{4} \div x {}^{4} \)

Step-by-step explanation:

Divide 14 by 7 it will be 2.

Now divide the variables.

X variable will give you X{}^{-4} and y{}^{4}.

So bring X variable in the denominator to make it positive.

So your answer will be option A.

Answer:

A

Step-by-step explanation:

It was right for me

Answer:

6 months

Step-by-step explanation:

Gym1

12 + 20m

Gym2

22m

Set them equal

12 +20m = 22m

Subtract 20 m from each side

12 +20m-20m = 22m-20m

12 = 2m

Divide by 2

12/2 = 2m/2

6 =m

The numbers that cannot be probabilities are: square root of 2, -53, 5/3, and 1.31.

Probability is a measure of the likelihood of a particular event occurring in a random experiment. It is a value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that an event is certain to occur.

In statistics, probability is used to make predictions or draw inferences about a population based on a sample of data. For example, if we were to flip a coin, the probability of getting heads is 0.5, or 50%. In general probability can be defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, which is the mathematical framework behind the random experiments.

From the set of numbers, 0, 0.08, and 3/5 are all possible values of probability.

Therefore, square root of 2, -53, 5/3, and 1.31 cannot be probabilities.

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Answer:

40, leg

Step-by-step explanation:

The triangle has side lengths of 9, 40, and 41.

41 is the hypotenuse, so 40 is a leg.

Answer:

I think this is the distributive property.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

The average rate of change of h(x) in the closed interval [ a, b ] is

\(\frac{h(b)-h(a)}{b-a}\)

Here [ a, b ] = [ 1, 2 ], then from the table

h(b) = h(2) = 0

h(a) = h(1) = - 3 , then

average rate of change = \(\frac{0-(-3)}{2-1}\) = \(\frac{3}{1}\) = 3

Answer:

x=10

Step-by-step explanation:

3(4x-12) = 84

Divide each side by 3

3/3(4x-12) = 84/3

4x-12 =28

Add 12 to each side

4x-12+12 = 28+12

4x= 40

Divide each side by 4

4x/4 = 40/4

x = 10

If her pay is $8002.14. then 20% of this amount is:

After five-month this amount will be:

Therefore, after 5 month she will have $8002