if a sequence c 1 , c 2 , c 3 , ... has limit k then the sequence e c 1 , e c 2 , e c 3 , ... has limit e k . use this fact together with l'hopital's rule to compute the limit of the sequence given by
bn=(n)^(5.6/n).

Answer:

angle 2 and angle 6 i think lol

Step-by-step explanation:

Answer:

1) 0.9 = 9/10

2) 2 x (4² - 5) = 2 x (16-5) = 2 x 11= 22

3)  t/4=16 16*4=t 64=t t=64

4) 2.4p=7.56  p=7.56/2.4  p=3.15

5) 8*5=40m² 40*4=160m³ v=160m³

6) 3x=27  x=27/3  x=9

Based on the t-test assuming equal variances a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal."

It is vital to establish whether or not the variances of the two groups being compared are indeed identical before performing a t-test under the assumption of equal variances. This is significant since the t-calculation statistic depends on the assumption that variances are equal.

One can look at the ratio of the variances between the two groups to evaluate the assumption of equal variances. Typically, it is acceptable to infer that the variances are not equal if the ratio of the variances is more than two or lower than half. One can presume that the variances are equal in the absence of such proof. Since the variances are not equal, it is not logical to infer that they are.

Complete and correct Question:

Based on the t-test assuming equal variances on the T-Test Equal worksheet, is it reasonable to assume that the variances are equal?
a. Examining the ratio of the variances, it is reasonable to conclude that the variances are unequal.
b. Whether the variances are equal or not is not relevant for this situation.
c. Examining the ratio of the variances, it is reasonable to conclude that the variances are equal.
d. It is impossible to determine if the variances are equal given the data we have.

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The values that represent the square root of 9 are given as follows:

-3 and 3.

The square root of 9 is composed by the two numbers that when they are multiplied by themselves, result in 9.

The most well known solution of this problem is the number three, as:

3² = 9.

However, the number -3 is also a solution to the expression, as:

(-3)² = (-3) x (-3) = 9.

(when two negative numbers are multiplied, the result is positive).

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Answer:

No, No, Yes, No, Yes, Yes

Step-by-step explanation:

A graph is a function if it passes the vertical line test (in other words, every vertical line that can be drawn intersects the graph at no more than one point).

This is because for a function, each input must map onto no more than one output.

The general solution to the given Cauchy-Euler equation for t > 0 is:

y(t) = C1 * t⁻⁵ + C2 * t⁴

Let's consider the given Cauchy-Euler equation for t > 0:

t²(d²y/dt²) + 2t(dy/dt) - 20y = 0

To solve this equation, we can assume a solution of the form y(t) = tⁿ, where r is a constant to be determined.

Now, let's find the derivatives of y(t) with respect to t:

dy/dt = rtⁿ⁻¹ d²y/dt² = r(r-1)tⁿ⁻²

Substituting these derivatives back into the Cauchy-Euler equation, we get:

t²(r(r-1)tⁿ⁻²) + 2t(rtⁿ⁻¹) - 20tⁿ = 0

Simplifying this equation, we have:

r(r-1)tⁿ + 2rtⁿ - 20tⁿ = 0

Factoring out tⁿ, we get:

tⁿ [r(r-1) + 2r - 20] = 0

Since t > 0 for the given equation, we can divide both sides of the equation by tⁿ to obtain:

r(r-1) + 2r - 20 = 0

Expanding and rearranging this equation, we get:

r² + r - 20 = 0

Now, we can solve this quadratic equation for r. Factoring it, we have:

(r + 5)(r - 4) = 0

Setting each factor equal to zero, we find two possible values for r:

r + 5 = 0, which gives r = -5 r - 4 = 0, which gives r = 4

These values of r represent the roots of the characteristic equation associated with the Cauchy-Euler equation. Since we have two distinct roots, the general solution to the Cauchy-Euler equation can be written as a linear combination of the corresponding solutions:

y(t) = C1 * t⁻⁵ + C2 * t⁴

Where C1 and C2 are arbitrary constants that can be determined using initial conditions or boundary conditions if provided.

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Answer:

Well all you have to do is answer questions, i have 2 hundred more points until I'm an expert but i have 20 brainliests!

Step-by-step explanation:

Answer:

I can help you, In a few minutes I may post some questions so I'll let you answer em- the thing is, two people need to answer for me to give brainliest so itll take a bit.

Step-by-step explanation:

Mind answering some stuff I have in the meantime?

The area of the region enclosed by the curves: Y = 3X and Y = 6X² is

1/8 sq. unit.

Linear equation are those in which power is 1 or maximum degree is 1. For example: x + y = 3 here the maximum degree is 1.

Quadratics equation are those in which power is 2 or maximum degree is 2. For example: X² + 6X + 3 = 0. here the maximum degree is 2.

Here, we have given two equation:

Y = 3X

Y = 6X²

To find the limit we will equate the both equation:

3X = 6X²

6X² - 3X = 0

3X ( 2X - 1 ) = 0

here we get two values of X, X = 0 and X = 1/2

so, Lower limit = 0 and Upper limit = 1/2.

Area = \(\int\limits^ \frac{1}{2} _0 {(3x - 6x^{2} ) } \, dx\)

Area = ( 3/2 ( x ⁸ )  - 2 ( x³ ) )          --- Limit from: 0 to 1/2

Area = (3/2 ( 1/2 ² ) - 2 ( 1/2 ³) ) - ( 3/2 ( 0² ) - 2 ( 0³) )

Area = 3/8 - 1/4 - 0 + 0

Area = 1/8 sq. unit

Hence,

The area of the region enclosed by the curves: Y = 3X and Y = 6X² is

1/8 sq. unit. For graph See the attached image.

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Answer:

x²+15x+26

Step-by-step explanation:

zeros are x=-13, x=-2

x=-13 then x+13=0

x=-2 then x+2=0

(x+13) (x+2)

x²+15x+26

y=ax²+bx+c

In order to determine the optimal number of bedrooms and bathrooms for Doreen to rent, we need to consider her utility function and the budget constraint. Doreen's utility function is U(x,y) = min(x, 2y), where x represents the number of bedrooms and y represents the number of bathrooms. The rental price per bedroom is £400 and per bathroom is £200.

Let's assume Doreen rents x bedrooms and y bathrooms. The total cost of renting can be calculated as follows:

Rent = (x * £400) + (y * £200)

Doreen's budget constraint is £1000 per month, so we have:

(x * £400) + (y * £200) ≤ £1000

To optimize Doreen's utility within her budget, we can substitute the utility function into the budget constraint:

min(x, 2y) ≤ £1000 - (y * £200)

min(x, 2y) ≤ £1000 - £200y

min(x, 2y) ≤ £1000 - £200y

Now we need to analyze the possible combinations of x and y that satisfy the budget constraint. Since the utility function U(x,y) = min(x, 2y), Doreen will choose the combination of x and y that maximizes the minimum value between x and 2y while still satisfying the budget constraint.

To find the optimal solution, we can substitute different values of y into the inequality and determine the corresponding x that satisfies the budget constraint. We start with y = 0 and gradually increase y until the budget constraint is reached. The optimal solution occurs when the maximum utility is achieved within the budget constraint.

b. In this case, Doreen has a budget of £500 to spend on both furniture and clothing. The cost of furniture per unit is £50, and the cost of clothing per unit is £20. Her utility function is U(f,c) = 10.3c^0.7, where f represents furniture and c represents clothing.

To determine how much Doreen spends on furniture and clothing, we need to maximize her utility within the budget constraint. Let's assume Doreen spends £x on furniture and £y on clothing.

We have the following budget constraint:

£50x + £20y ≤ £500

To optimize Doreen's utility, we substitute the utility function into the budget constraint:

10.3c^0.7 ≤ £500 - (£50x + £20y)

Similarly to part a, we need to analyze different combinations of x and y that satisfy the budget constraint. By substituting different values of x and y, we can determine the optimal solution that maximizes Doreen's utility within her budget.

c. If the local furniture shop offers a 50% discount on all prices, the cost of furniture per unit is reduced by half (£50/2 = £25 per unit). However, the price of clothing remains the same at £20 per unit.

To calculate how much Doreen spends on furniture and clothing after the discount, we use the same budget constraint as in part b:

£50x + £20y ≤ £500

Since the price of furniture per unit is now £25, we replace £50x in the budget constraint with £25x:

£25x + £20y ≤ £500

By substituting different values of x and y into the modified budget constraint, we can determine the new optimal solution that maximizes Doreen's utility within her budget.

d. The utility function for Doreen's preferences over pizza and vegan burgers is given as U(p, v) = 2p + v.

To calculate the marginal utility from pizza

, we differentiate the utility function with respect to p:

∂U(p, v)/∂p = 2

The marginal utility from pizza is a constant value of 2.

To calculate the marginal utility from vegan burgers, we differentiate the utility function with respect to v:

∂U(p, v)/∂v = 1

The marginal utility from vegan burgers is a constant value of 1.

Diminishing marginal utility occurs when the marginal utility of consuming an additional unit of a good decreases as the quantity of that good increases. In this utility function, the marginal utility of pizza remains constant at 2, while the marginal utility of vegan burgers also remains constant at 1. Therefore, this utility function does not exhibit diminishing marginal utility for either pizza or vegan burgers.

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Since 3n² + 6n is both O(n² log n) and Ω(n² log n), we can conclude that it is indeed Θ(n² log n).

To prove that 3n² + 6n is in Θ(n² log n), we need to show both the upper and lower bounds.

First, we will prove the upper bound by showing that 3n² + 6n is O(n² log n). This means we need to find constants c and n₀ such that 3n²+ 6n ≤ c(n² log n) for all n ≥ n₀.

Let's simplify the expression 3n² + 6n:

3n² + 6n ≤ 3n² + 6n² (for n ≥ 1, since n is always positive)

            = 9n²

Now, we can set c = 9 and n₀ = 1. For all n ≥ 1:

3n² + 6n ≤ 9n² (which is the same as c(n²))

           ≤ 9n² log n

Therefore, we have shown that 3n² + 6n is O(n² log n), satisfying the upper bound.

Next, we will prove the lower bound by showing that 3n² + 6n is Ω(n² log n). This means we need to find constants c and n₀ such that 3n²+ 6n ≥ c(n² log n) for all n ≥ n₀.

Let's simplify the expression 3n² + 6n:

3n² + 6n ≥ 3n² (for n ≥ 1, since n is always positive)

            = 3n² log n

Now, we can set c = 3 and n₀ = 1. For all n ≥ 1:

3n² + 6n ≥ 3n² log n (which is the same as c(n² log n))

Therefore, we have shown that 3n² + 6n is Ω(n² log n), satisfying the lower bound.

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Answer: I thinks it’s B

Step-by-step explanation:

The floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be A. 2.3e^7.

It should be noted that scientific notation simply means. way that's used to express numbers that are either too large or too small to be written in decimal form.

Therefore, it should be noted that the floating-point literal that correctly represents the scientific notation value: 2.3 x 10^7 will be:

= 2.3 × 20^7

= 2.3 × e^7

= 2.3e7

The correct option is A.

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Which floating-point literal correctly represents the scientific notation value: 2.3 x 10^7?

a. 2.3e^7

b. 2.3 × 10e^7

c. 2.3e × 10^7

d. 2.3 × e^7

Answer:

-14

Step-by-step explanation:

=> - 3 - (+ 11)

=> - 3 - 11

=> - 14...ans

HOPE IT HELPS U!!!!

A nurse provides a back massage as a palliative care measure to a client who is unconscious, grimacing, and restless.

The therapeutic response that the nurse should identify in the client after a back massage includes relaxing of facial muscles and the pulse remaining within the expected range.
Massage is a fundamental nursing measure that is often utilized as part of palliative care for patients. The purpose of back massage is to promote relaxation, improve blood circulation, reduce muscle tension, and alleviate pain, stress, and anxiety. The nursing assessment of the patient before and after the massage is essential to determine its effectiveness as a therapeutic intervention for the patient.
When providing back massage as a palliative care measure to an unconscious, grimacing, and restless client, the nurse should identify several therapeutic responses as follows;
The shoulders droop: The nurse should expect the shoulders of the client to relax during massage therapy. If this occurs, it is a sign that the patient is experiencing relaxation and tension relief.
The facial muscles relax: Relaxation of the facial muscles is a common therapeutic response during back massage. The nurse should observe the patient's face for any signs of relaxation, which may include softening of facial lines, eyelids drooping, or a general expression of peacefulness.
The respiratory rate (RR) decreases: The nurse should expect the client's respiratory rate to decrease during a back massage. This is because relaxation stimulates the parasympathetic nervous system, resulting in decreased respiratory rate, heart rate, and blood pressure.
The pulse is within the expected range: The nurse should expect the client's pulse to remain within the expected range during a back massage. A normal pulse rate is between 60-100 beats per minute for adults. If the pulse remains within this range, it is a sign that the patient is responding positively to the massage therapy.

In conclusion, providing back massage as a palliative care measure to an unconscious, grimacing, and restless client can help to promote relaxation, improve blood circulation, reduce muscle tension, and alleviate pain, stress, and anxiety. The nurse should identify therapeutic responses in the patient during the massage therapy, which may include relaxation of the shoulders, facial muscles, decreased respiratory rate, and pulse remaining within the expected range.

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Answer:

2

Step-by-step explanation:

if it is parelel, changing the eqation into slope intercept will give you the slope-

2x-y=3

-y = -2x+3

y=2x-3

y=mx+b

m is slope so

slope = 2

One of k , k + 2 , k + 4 is divisible by 3 .

Given,

Positive integer(K) .

Here,

To prove this statement by cases, we can consider the three different cases: k is divisible by 3, k+2 is divisible by 3, and k+4 is divisible by 3.

Case 1: k is divisible by 3

If k is divisible by 3, then k is already a positive integer that is divisible by 3. Therefore, this case satisfies the statement that "at least one of k, k+2, or k+4 is divisible by 3."

Case 2: k+2 is divisible by 3

If k+2 is divisible by 3, then we can write k+2 = 3n for some positive integer n. Then, k = 3n-2 is a positive integer that is divisible by 3. Therefore, this case also satisfies the statement.

Case 3: k+4 is divisible by 3

If k+4 is divisible by 3, then we can write k+4 = 3n for some positive integer n. Then, k = 3n-4 is a positive integer that is divisible by 3. Therefore, this case also satisfies the statement.

Hence from cases we can justify our statement .

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20 m longer it is to walk from A to B along the diagonal of the walk than to walk along the edges of the park.

Given:

Assume ABCD is a rectangular park of right triangles ABC of length = 40m, width = 30m, ∠C = 90

In the right-angled triangle ABC,

By Pythagoras' theorem,

AB² = AC² + BC²

AB² = 30² + 40²

AB² = 900 + 1600

AB² = 2500

AB² = \(\sqrt{2500}\)

AB = 50m

The distance from A to B along the diagonal of the park = 50m

The distance from A through to C = 30m.

The distance from A through C to B = 30 + 40 = 70m.

Therefore, 20 m longer it is to walk from the diagonal of the park to walk along the edges of the park.

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Answer: Non proportional

Step-by-step explanation:

To know if the values given are proportional or not, we will use the formula:

y = kx

where

y = number of organisms

x = number of minutes

k = constant of proportionality

After 5 minutes, a bacteria colony has 1.3 million organisms. Using the formula, y = kx

1,300,000 = 5k

k = 1,300,000 / 5

k = 260,000

After 12 minutes, the same colony has 41.5 million organisms. Using y= kx

41,500,000 = 12x

x = 41500000 / 12

x = 3458333.8

After 15 minutes, the colony has grown to 101.3 million organisms.

y = kx

101,300,000 = 15k

k = 101,300,000 / 15

k = 6753333.8

It is a non-proportional relationship as the constant of proportionality is different for each.

When you multiply two integers with the same signs, the result is always positive. Just multiply the absolute values and make the answer positive. When you multiply two integers with different signs, the result is always negative.

Answer:

21°

Step-by-step explanation:

<CBE=<ABD=69°

in triangle ABD, <ABD+<ADB+<DAB=180°

69°+90°+x=180°

So, x= 21°

Answer:

y=3x—1

Step-by-step explanation:

The line contains point (2,5)

so if we put x=2 in the equation, that'll give us y=5

only option that contains point (2,5) is:

\(y = 3x - 1 \\ (5) = 3(2) - 1 \\ 5 = 5 \: true\)

Answer:

y = 3x - 1

Step-by-step explanation:

From this equation we can get that the point at which the line touches the y osis is - 1 by replacing x with 0:

y = 3(0) - 1

we can expect there to be approximately 696 rats (rounded to the nearest whole) in the bay area of the city after 18 months of growth at a rate of 6% per month.

To solve this problem, we can use the formula for exponential growth:
\(P(t) = P(0)e^{rt}\)

where P(0) is the initial population, r is the growth rate (in decimal form), t is the time period, and e is the mathematical constant approximately equal to 2.718.

In this case, P(0) = 310, r = 0.06 (since the population grows at a rate of 6% per month), and t = 18 months. So we have:

\(P(18) = 310 e^{(0.06 * 18)}\)
P(18) =696

Therefore, we can expect there to be approximately 696 rats (rounded to the nearest whole) in the bay area of the city after 18 months of growth at a rate of 6% per month.

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The circumference of the smaller circle is C =  2*pi*x/3.

We have given that radius ob measures x units

circumference of the circle is given by,

\(C = 2\times \pi \times R\)

where pi = 3.14

R= radius

we have two circles, A and B, where B is the larger circle and A is the smaller circle.

We know that,The circumference of B is 3 times the circumference of A.

The radius of circle B is OB = x

The radius of circle A is OA

We want to find an expression of OA.

The circumference of circle B is given by

\(C(B) = 2\times \piOB = 2\times pi\times x\)

The circumference of circle A  is given by

\(C(A) = 2\times\pi\times OA\)

we know that the circumference of circle B is 3 times the circumference of circle A,

\(C(B) = 3\times C(A)\)

replacing the equations for the circumferences

\(2\times\pi\times x = 3\times (2\times pi\times OA)\)

We have divide both sides by \(2\pi\)we get:

\(x = 3\times OA\)

Now we want to solve this for OA, then we need to isolate it,

\(x/3 = OA\)

We can conclude that the radius of the smaller circle is equal to x/3.

Then the circumference of circle A is

\(C(A) = 2\times pi\times x/3\)

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Answer:

c

Step-by-step explanation:

Answer: 50g steel, 30g gold and 70g brass

Step-by-step explanation:

     This means for every 5g of steel there is 3g of gold and 7g of brass. We will find how many g there are total for every 5g of steel.

           5 + 3 + 7 = 15

     Next, we will divide 150g by 15g to see how many times the ratio will "repeat" to create the 150g of alloy.

           150g / 15g = 10g

     Next, we will multiply each amount of metal in one ratio by 10.

5g * 10 = 50g steel

3g * 10 = 30g gold

7g * 10 = 70g brass

Answer:

Step-by-step explanation

                                          to get 50g of steel.

\

The value of the function g o f (x) will be;

⇒  (2x + 3) / 4

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The value of the function are;

f (x) = 2x + 3

And, g (x) = x / 4

Now,

The value of composite function is,

g o f (x) = g ( f(x) )

           = g (2x + 3)

           = (2x + 3) / 4

So, g o f (x) = (2x + 3) / 4

Thus, The value of the function g o f (x) will be;

⇒  (2x + 3) / 4

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Answer:

a) 16, b) 16

Step-by-step explanation:

1. Find f. Plug in 2 for x.

\(2^{2} +6(2)=16.\)

2. Find g by performing the same action.

2-1=1.

3. Now that we have f and g, we can multiply them.

\((fg)(2)=16(1)=16.\)

a) is 16.

4. b) is (gf)(2)=1(16), which is still 16.

b) is 16.