Lily has $2. 75 in her pocket, consisting of dimes and quarters. If there are 17 coins in all, how many of each does she have?.

The root test is inconclusive for the series Σ 1/n8n.

To determine the convergence or divergence of the series Σ 1/n8n using the root test, we need to calculate the limit as n approaches infinity of the nth root of the absolute value of the nth term. In this case, the nth term is 1/n8n.

Calculating the limit, we have lim n→∞ (n√|1/n8n|).

Simplifying the expression inside the absolute value, we get 1/n^8n = 1/n^(8n) = 1/n^(8n) = 1/(nⁿ⁸) = 1/(n⁸ⁿ).

Taking the nth root of the absolute value, we have

n√|1/n⁸ⁿ| = n√(1/(n⁸ⁿ)).

As n approaches infinity, the expression (1/(n^8n)) approaches zero because the denominator, n⁸ⁿ, grows much faster than the numerator, 1. Therefore, the nth root of the absolute value approaches 1.

Since the limit is equal to 1, the root test is inconclusive. The root test does not provide sufficient information to determine whether the series

Σ 1/n8n is convergent or divergent.

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Answer:

F=40

Step-by-step explanation:

you have to get rid of the five. What's the oposite of division? Mutiplaction, so you mutiply 5 times 8. The five cancels, and you are left with 40.

Answer:

I think thé answer is C 0 contadict me if it is dring please

Option D is correct, 6 is the value of the range in the given graph.

A relation is a function if it has only One y-value for each x-value.

We have to find the  values are in the range of the function graphed below

The domain of the given graph is -2≤x≤4

What can go into a function is called the Domain.

What may possibly come out of a function is called the Codomain.

What actually comes out of a function is called the Range.

The range of the given graph is y values.

The y value is 6

Hence, 6 is the value of the range in the given graph.

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1/4π is area of a circle when the radius is 6 cm.

What is the circumference of a circle?

 A = πr²

differentiate both sides with respect to 't'

dA/dt = πr² dr/dt

dA/dt = 2πr dr/dt

dA/dt = 3  ,     r = 6

3 = 2π * 6dr/dt

dr/dt = 1/4π

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A. The maximum rate of change of f at (-4, -2, 4) is approximately 1.031.

B. The direction in which the maximum rate of change of f occurs at (-4, -2, 4) is approximately the unit vector u = <0.970, 0.242, 0.048>.

To find the maximum rate of change of the function f(x,y,z) = x + y/z at the point (-4, -2, 4), we need to find the gradient vector of f and then evaluate it at the given point. The gradient vector of f is given by:

∇f(x,y,z) = <∂f/∂x, ∂f/∂y, ∂f/∂z>

= <1, 1/z, -y/z²>

So, at the point (-4, -2, 4), we have:

∇f(-4,-2,4) = <1, 1/4, -(-2)/16>

= <1, 1/4, 1/8>

The magnitude of the gradient vector gives us the maximum rate of change of f at the given point:

|∇f(-4,-2,4)| = √(1² + (1/4)² + (1/8)²) ≈ 1.031

Therefore, the maximum rate of change of f at (-4, -2, 4) is approximately 1.031. To find the direction in which this maximum rate of change occurs, we need to normalize the gradient vector:

u = ∇f(-4,-2,4)/|∇f(-4,-2,4)|

= <1, 1/4, 1/8>/√(1² + (1/4)² + (1/8)²)

≈ <0.970, 0.242, 0.048>

So, the direction in which the maximum rate of change of f occurs at (-4, -2, 4) is approximately the unit vector u = <0.970, 0.242, 0.048>.

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Answer:

d because it makes the most sense

Step-by-step explanation:

Answer:

D- 50

Step-by-step explanation:

.6 (60%) times 50 = 30

Answer:

94

Step-by-step explanation:

a1+ 23d =2+23*4= 94

94 is the 24 th term

Simplifying the equation gives us the length of the great circle between cities A and B. You can follow the same process to calculate the distances between other pairs of cities.

To find the length of a great circle on Earth, we need to calculate the distance between the two points given by their latitude and longitude.

Using the formula for calculating the distance between two points on a sphere, we can find the length of the great circle.

Let's calculate the distance between cities A and B:

- The latitude of the city A is 37°59'N, which is approximately 37.9833°.

- The longitude of city A is 84°28'W, which is approximately -84.4667°.

- The latitude of city B is 34°55'N, which is approximately 34.9167°.

- The longitude of city B is 138°36'E, which is approximately 138.6°.

Using the Haversine formula, we can calculate the distance:
\(distance = 2 * radius * arcsin(sqrt(sin((latB - latA) / 2)^2 + cos(latA) * cos(latB) * sin((lonB - lonA) / 2)^2))\)

Substituting the values:
\(distance = 2 * 3960 * arcsin(sqrt(sin((34.9167 - 37.9833) / 2)^2 + cos(37.9833) * cos(34.9167) * sin((138.6 - -84.4667) / 2)^2))\)

Simplifying the equation gives us the length of the great circle between cities A and B. You can follow the same process to calculate the distances between other pairs of cities.

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The length of a great circle on Earth is approximately 24,892.8 miles.

To find the length of a great circle on Earth, we need to calculate the distance along the circumference of a circle with a radius of 3960 miles.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.

Substituting the given radius, we get C = 2π(3960) = 7920π miles.

To find the length of a great circle, we need to find the circumference.

Since the circumference of a great circle is equal to the length of the equator or any meridian, the length of a great circle on Earth is approximately 7920π miles.

To calculate this value, we can use the approximation π ≈ 3.14.

Therefore, the length of a great circle on Earth is approximately 7920(3.14) = 24,892.8 miles.

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The x-component of vector A is approximately 1.4, and the y-component of vector A is approximately -0.6.

To determine the x-component and y-component of vector A, we need to use the given magnitude and angle information.

Given that vector A has a magnitude of 1.5 and is at an angle of 25 degrees below the positive x-axis, we can use trigonometric functions to find the x-component and y-component.

The x-component can be found using the formula: A_x = A * cos(theta), where A is the magnitude of the vector and theta is the angle with respect to the positive x-axis. Substituting the values, we have: A_x = 1.5 * cos(25°) ≈ 1.4.

The y-component can be found using the formula: A_y = A * sin(theta), where A is the magnitude of the vector and theta is the angle with respect to the positive x-axis. Substituting the values, we have: A_y = 1.5 * sin(25°) ≈ -0.6.

Therefore, the x-component of vector A is approximately 1.4, and the y-component of vector A is approximately -0.6.

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9514 1404 393

Answer:

  C.  The zeros are -1 and 5/2, because f(x) = (x + 1)(2x-5).

Step-by-step explanation:

The zeros of the function are the values that make the factors zero. The factors need to multiply out to give the original standard-form equation.

The sign of the constant (-5) tells you the product of the constants in the factors must be -5. That is only true for choices B and C.

Additionally, the x-term needs to match the result of multiplying out the factors.

  B.  (x -1)(2x +5) = 2x^2 +3x -5 . . . . . . . . . wrong x-term (not -3x)

  C.  (x +1)(2x -5) = 2x^2 -3x -5 . . . . . . . . . matches the given f(x)

The factors of C are zero when x=-1, x=5/2.

Answer:

Cells create usable energy through Cellular Respiration.

Step-by-step explanation:

If you think about it, cellular respiration is the way cells make their food, or usable energy. Therefore, the answer would be up above-------------------------^^

The probability that both of his kids are boys are 1/3.

If a man has 2 kids, the possible combinations of kids are:

There are 4 possible combinations of the sexes of the two kids.

The fourth possibility is impossible, because one of the kids is a boy. So it can't be both girls. Then the possible combinations are:

The number of combinations of the both kids are boys = 1

The number of combinations that minimum one kid is boy = 3

Then the probability that both of kids are boys are:

\(P_{both boy}=\frac{both boy}{minimal one boy} \\P_{both boy}=\frac{1}{3} \\\)

So the probability both of kids are boy is 1/3.

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Joshua will need 7 additional customers.

The parameters that will help us to determine the number of customers is give as follows:

Joshua's goal is to sell more than 20 items at a farmers' market. So far, he has sold 6 items. Each customer buys 2 items.

Since Joshua's goal is to sell more than 20 items at a farmers' market and he has sold 6 items. and If each of his customers buys 2 items, the number of additional customers needed will be:

= (20 - 6) / 2

This is given as  14 / 2

The the number of customers needed = 7

In conclusion He will  need 7 additional customers.

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Answer:60

Step-by-step explanation:

The Greatest Common Factor of 32 and 48 is 16.

The longest necklace she can make is of 16 inches length.

Answer: ($2100+96d) + ($2755+116d)

               = $4855+212d

The options that can be used as indices for the array are option A (i) and option E ((int)(Math.random() * 100)).

To determine which expressions can be used as an index for the array double[] t = new double[100], let's evaluate each option :

A. i: Since i is an integer variable with a value of 5, it can be used as an index because it falls within the valid index range of the array (0 to 99).

B. I + 6.5: This expression adds 6.5 to the variable i. Since array indices must be integers, this expression would result in a double value and cannot be used as an index.

C. 1 + 10: This expression evaluates to 11, which is an integer value and can be used as an index.

D. Math.random() * 100: The Math.random() function returns a double value between 0.0 (inclusive) and 1.0 (exclusive). Multiplying this value by 100 would still result in a double value, which cannot be used as an index.

E. (int)(Math.random() * 100): By multiplying Math.random() by 100 and casting the result to an integer, we obtain a random integer between 0 and 99, which falls within the valid index range and can be used as an index.

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Answer:

AE:\(\sqrt{15300}\)

DE:150

PABCDE: 720

Step-by-step explanation:

We can find AE by the pythagorean theorem, \(a^{2}+b^{2}=c^{2}\)

AE is the hypotenuse so AE=c, and the leg of the triangle would be 150-30=120

\(50^{2}+120^{2}=c^{2}\)

c^2=2500+14400

AE=130

We can use the pythagorean theorem again to find DE.

The base would equal 140-50=90 and the height would equal 120

\(90^{2} +120^{2} =DE^{2}\)

DE^2=22500

DE=150

The perimeter would be 150+140+150+130+150=720

Let me know if somethings wrong

I'll do problems 2 through 6 to get you started.

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Problem 1

You have the correct answer. You add the take home pay of his first job (504.64) to the amount he earns on his second job (40) to get 541.64 as his net monthly income.

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Problem 2

Add up any dollar amount that's leaving his pocket. Only focus on expenses that occur monthly. So we will ignore the one time payment of getting that theme park ticket, and we'll also ignore any gifts he buys.

In the second paragraph of the info you're given, all of the expenses we need are here. He has car insurance (110), gas and maintenance (65), and a cell plan (30). In total, his monthly expenses are 110+65+30 = 205 dollars per month.

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Problem 3

Subtract the net monthly income (problem 1) and the expenses (problem 2) to get the amount of discretionary spending he has

541.64 - 205 = 336.64

This value is a positive number, so that means he has money to do whatever he wants with it such as buying that park ticket or buying those gifts.

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Problem 4

His short-term goals are to buy the Six Flags ticket, and buy gifts for his friends and family. He also wants to buy an e-reader for himself.

These are all short-term goals as they are in a relatively short time window of less than a year.

Add up those values to get

135+200+80 = 415

So his short-term goals will cost a total of $415

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Problem 5

His long-term goals are saving up for college to pay for tuition and books. As the instructions say, long-term goals are ones that you need more than a year in advance to plan for. This is because the expense is much greater compared to those various short-term goal items.

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Problem 6

Subtract 135 from the net monthly income you calculated in problem 1

541.64 - 135 = 406.64

Answer:

x > -2/3

Step-by-step explanation:

\(\frac{x}{2} +\frac{1}{3} > 0\) , subtract 1/3 from both sides

\(\frac{x}{2} > \frac{-1}{3}\) , multiply both sides by 2

\(x > \frac{-2}{3}\)

\(_9C_4=\dfrac{9!}{4!5!}=\dfrac{6\cdot7\cdot8\cdot9}{2\cdot3\cdot4}=126\)

Answer:

25 minutes

Step-by-step explanation:

usan started her homework at 1:59 pm. And finished her homework 96 minutes later. Susan had volleyball practice at 4:00 p.M. How much time did Susan have between finisng her homework and the beginning of volleyball practice?

1 hour = 60 minutes

If her assignment took her 96 minutes, converted to hours, then it took her 1 hour 36 minutes

Time she finished her assignment = 1:59 + 1:36 = 3:35 pm

time between when she finished and started practice = 4 : 00 - 3:35 = 25 minutes

Answer:B

Step-by-step explanation:

Answer:

that's is the correct answer

Step-by-step explanation:

hope it helps

Answer: 2584

Step-by-step explanation: Length × height × width

The function that is likely the best fit is given as follows:

Logarithmic regression.

The function of a best fit is a logarithmic regression, as the function starts with a fast increasing rate until it approaches the vertical asymptote.

As for the other options, we have that:

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Answer:

42 meters

Step-by-step explanation:

The length of the factory floor will be 42 meters. This is found by multiplying the length of 0.3 meters by the scale factor of 140, which yields 42 meters.

Answer:

42 meters

Step-by-step explanation:

its correct :)