find this using the box method

The sequence diverges and the limit does not exist therefore we can write (DNE).

We need to find the limit as n approaches infinity: lim (n→∞) (7n!) / (2^n)

To determine convergence or divergence, let's use the ratio test. We will find the limit of the absolute value of the ratio between consecutive terms as n approaches infinity:

lim (n→∞) |(a_(n+1)) / (a_n)|

lim (n→∞) |((7(n+1)!) / (2^(n+1))) / ((7n!) / (2^n))|

Simplify the expression:

lim (n→∞) |(7(n+1)!) / (2^(n+1)) * (2^n) / (7n!)|

Now cancel out the common terms:

lim (n→∞) |(n+1) / 2|

As n approaches infinity, the limit does not approach 0; it increases without bound. Therefore, according to the ratio test, the sequence diverges.

So, the limit does not exist, and we can write it as DNE.

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Answer:

-5

Step-by-step explanation:

-7 - (-2)

-7 + 2

Example: If you owe someone $7, and you give them $2, how much do you still owe? You are owing him $7 so it's a negative and you give him $2 which is a negative as well since you are giving it to him. So, to answer how much do you still owe, you would add $2  to the $7 you owed, so now, you owe him $5, which is a negative since you OWE him.

Hope this helps:)

Answer:

35 degrees

Step-by-step explanation:

for all positive angles less than 360°, if csc (2x+30°)= cos (3y-15°), the sum of x and y is?​

Let the given expression be equal to 1, hence;

csc (2x+30°)= cos (3y-15°) = 1

csc (2x+30°) = 1

1/sin(2x+30) = 1

1 = sin(2x+30)

sin(2x+30) = 1

2x+30 = arcsin(1)

2x+30 = 90

2x = 90-30

2x = 60

x = 60/2

x = 30 degrees

Get the value of y;

cos (3y-15°) = 1

3y - 15 = arccos (1)

3y - 15= 0

3y = 0+15

3y = 15

y = 15/3

y = 5

Sum of x and y;

x+y = 30 + 5

x+y = 35degrees

Hence the sum of x and y is 35 degrees

Answer:

The solution of the system of equations be:

\(x=8,\:y=4\)

Hence, option C is true.

Step-by-step explanation:

Given the system of equations

\(\begin{bmatrix}4x+7y=60\\ -4x+7y=-4\end{bmatrix}\)

adding both the equations

\(-4x+7y=-4\)

\(+\)

\(\underline{4x+7y=60}\)

\(14y=56\)

so the system of equations becomes

\(\begin{bmatrix}4x+7y=60\\ 14y=56\end{bmatrix}\)

solve 14y for y

\(14y=56\)

Divide both sides by 14

\(\frac{14y}{14}=\frac{56}{14}\)

Simplify

\(y=4\)

\(\mathrm{For\:}4x+7y=60\mathrm{\:plug\:in\:}y=4\)

\(4x+7\cdot \:4=60\)

\(4x+28=60\)

Subtract 28 from both sides

\(4x+28-28=60-28\)

Simplify

\(4x=32\)

Divide both sides by 4

\(\frac{4x}{4}=\frac{32}{4}\)

\(x=8\)

Therefore, the solution of the system of equations be:

\(x=8,\:y=4\)

Hence, option C is true.

The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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If Jane and Sarah share an amount of £63 and Jane receives "5/9" of  money, then the amount of money Sarah receives is £28..

The total amount that needs to be shared between Jane and Sarah is = £63,

We know that , Jane receives "5/9" of the total amount,

Which means , Jane receives = (5/9)×63 = £35,

The total-sum of money is = £63,

So, We can write,⇒ Total money = Jane + Sarah,

Substituting the values ,

We get,

⇒ 63 = 35 + Sarah,

⇒ Sarah = 63 - 35 = £28.

Therefore, Sarah's share of money is = £28.

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Answer: (9x + 11i) (9x - 11i)

Step-by-step explanation:

When i is squared, you are given a negative value, but by multiplying a positive by a negative, we reverse that and are left with positive 121. The 9x will be cancelled out by the 11's and squaring the 9x will give 81x^2.

It's hard to fully explain this, but if I do find something, I will update this or comment more explanation. You could try to solve using the quadratic formula.

Hope this helps.

The expression be 1/4(c³+ d²) then the value exists 9.

The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication and division (left to right), addition and subtraction (from left to right).

The rules that specify the order in which we should perform several operations to solve an expression are known as the order of operations.

Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are in the following order: PEMDAS (from left to right).

Let the given expression be 1/4(c³+ d²)

The value of c = -4 and d = 10

substitute the values in the above equation, we get

Follow the PEMDAS order of operations

Calculate within parentheses  ((-4)³ + (10)²) = 36

1/4((-4)³ + (10)²)

simplifying the above equation, we get

= 1/4 × 36

= 9

Therefore, the correct answer is option B. 9.

The complete question is:

What is the value of this expression when c = -4 and d = 10?

1/4(c³+ d²)

A. 2

B. 9

C. 21

D. 41

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Because b > 1, the correct response in this situation would be: "1.022 is the growth factor for the GDP since 1950, and the GDP increases by a factor of 1.022 every year."

In this instance, we're assuming that we can use the following function to simulate the US GDP, or gross domestic product, in dollars:

\(GDP = 11(1.0220)^{t}\)

We can also see that the exponential model formula given by: governs this formula.

\(GDP = 11(1.0220)^{t\)

Where a denotes the starting sum, b the model's growth/decay rate, and t is the number of years since 1950.

The value of b in this instance is provided by:

b = 1.022

And when we calculated r as the growth rate, we obtained:

1.022 = 1 + r

r = 1.022 - 1

r = 0.022

Because b > 1, the correct response in this situation would be: "1.022 is the growth factor for the GDP since 1950, and the GDP increases by a factor of 1.022 every year."

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The closed formula of h(t) and f(t) for

h(0)=f(0)=100b => h(t) = 100(2t+1), f(t) = 100(2t-1) ,

h(0)=200, f(0)=100 => h(t) = 200(2t+1), f(t) = 100(2t-1)

h(0)=600, f(0)=500 =>h(t) = 300 + 200(2t+\((-1)^{t}\)), f(t) = 200 - 100\((-1)^{t}\)

The recursive equations for the given two interacting population of hares and foxes are

h(t+1)=4h(t)-2f(t)

f(h+1)=h(t)+f(t)

for the given initial population in parts from a to c we need to create a close formula for h(t) and f(t)

h(t) = 100(2t+1)

f(t) = 100(2t-1)

h(t) = 200(2t+1)

f(t) = 100(2t-1)

h(t) = 300 + 200(2t+\((-1)^{t}\))

f(t) = 200 - 100\((-1)^{t}\)

The closed formula of h(t) and f(t) for

h(0)=f(0)=100b => h(t) = 100(2t+1), f(t) = 100(2t-1) ,

h(0)=200, f(0)=100 => h(t) = 200(2t+1), f(t) = 100(2t-1)

h(0)=600, f(0)=500 =>h(t) = 300 + 200(2t+\((-1)^{t}\)), f(t) = 200 - 100\((-1)^{t}\)

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The ratio of p:q:r is 1 : 6 : 5 / 6

Ratio compares values. Ratios compares relationship between two numbers of same units. Ratios can be express in fraction too.

Therefore,

p:q = 1/3 : 2  = 1 / 3 × 1 / 2 = 1 / 6

p : r = 3/4:1/2  = 3 / 4 × 2 / 1 = 6 / 5

p:q  = 1 /  6

p / q = 1 / 6

p = 1 / 6 q

q = 6p

Therefore,

p : r = 6 / 5

p / r = 6 / 5

6r = 5p

r = 5 / 6 p

Therefore,

P : q: r = p : 6p : 5 /6 p

Therefore,

P : q: r = 1 : 6 : 5 / 6

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Answer:

$8000

Step-by-step explanation:

For every $1000 Katrina sells, she earns $75. This is becuase when we multiply what she sold by her commision price, we get what she made

If we want to find how much she needs to make to earn $600, we can divide 600 by 75. This gives us 8. So, she will need to sell $8000 in order to earn $600

The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.

Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:

= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3

= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]

= (1/3) × [(9/2 + 6) - 0]

= (1/3) × (21/2)

= 7/2

Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.

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The relation ⊂ (subset) can be considered as a binary relation between sets, and it is a partial order on the power set P(S) of an arbitrary nonempty set S. However, it is not a total order.

A partial order is a binary relation that satisfies three properties: reflexivity, antisymmetry, and transitivity. Let's analyze whether ⊂ satisfies these properties for the power set P(S).

Reflexivity: For any set A, A is a subset of itself (A⊂A) holds true. Therefore, ⊂ is reflexive.

Antisymmetry: If A⊂B and B⊂A, then A and B must be equal sets. In other words, if two sets are subsets of each other, they must be the same set. This property is satisfied, and ⊂ is antisymmetric.

Transitivity: If A⊂B and B⊂C, then A⊂C. If one set is a subset of another set, and the other set is a subset of a third set, then the first set is also a subset of the third set. This property is satisfied, and ⊂ is transitive.

Therefore, ⊂ satisfies the properties of reflexivity, antisymmetry, and transitivity, making it a partial order on P(S).However, ⊂ is not a total order because it does not satisfy the total ordering property. In a total order, for any two distinct elements, one must be greater than or equal to the other. In the case of ⊂, there are sets A and B that are not subsets of each other (neither A⊂B nor B⊂A). Therefore, it is not a total order.

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so basically we just us do this

tan(26)=33/FE

Multiply to get rid of fraction

tan(26)FE=33

divide to get FE alone

FE = tan(26) * 33

FE=16.0951m

so it should be 16.0951m

Answer:

∆ stands for \vartriangle a example of this is A ∆ B (or A ⊖ B) means the set of elements in exactly one of A or B. or {1,5,6,8} ∆ {2,5,8} = {1,2,6} thats all I have for you sorry if this doesn't help

Step-by-step explanation:

Answer:

2 3/20

Step-by-step explanation:

Answer:

you have to tell us the question honey

Answer:

please mark me

length of the diagonal is 14 feet good luck

Step-by-step explanation:

Answer:

y-5=2/3(x-2)

y=2/3x+11/3

Answer:

Step-by-step explanation:

Nope!  the multiples of three are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36...and so on.

Answer:

no

Step-by-step explanation:

Answer:

5,4 and 4,4

Step-by-step explanation:

The mean abosolute deviation of the given data set is: 42.9422.

The mean absolute deviation is the avergae of the distance of each data point from the mean of the data set.

Given:

23, 75, 79, 99, 105, 110, 110, 142, 149, 168, 168, 170, 183, 195, 202

Mean: (23 + 75 + 79 + 99 + 105 + 110 + 110 + 142 + 149 + 168 + 168 + 170 + 183 + 195 + 202)/15

Mean = 1978/15 = 131.8667

Mean aboslute deviation = [(23 - 131.8667) + ( 75 - 131.8667) + ( 79 - 131.8667) + ( 99 - 131.8667) + ( 105 - 131.8667) + ( 110 - 131.8667) + ( 110 - 131.8667) + ( 142 - 131.8667) + ( 149 - 131.8667) + ( 168 - 131.8667) + ( 168 - 131.8667) + ( 170 - 131.8667) + ( 183 - 131.8667) + ( 195 - 131.8667) + ( 202 - 131.8667)] / 15

Mean aboslute deviation = 644.1333/15 = 42.9422

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Answer:

Neither, they are both equal.

Step-by-step explanation:

FYI, that three in front of the radical in the first expression is actually cube root. The cube root of 64 is 4, and the square root of 16 is 4.

\(\sqrt[3]{64} =4\\\sqrt{16}=4\\4=4\)

\(\huge\text{Hey there!}\)

\(\huge\textsf{Option A }\huge\boxed {\downarrow}\)

\(\huge\boxed{\rm{\sqrt[3]{64}}}}\\\huge\boxed{= \rm{\sqrt[3]{4^3}}}}\\\huge\boxed{= \rm{\sqrt[3]{4\times4 \times4}}}\\\huge\boxed{\rm{\rightarrow \sqrt{64}= 8, \ because \ 8\times8 = \bf 64}}\\\huge\boxed{\rm{{= \dfrac{8}{2}\rightarrow 8\div 2 \rightarrow \bf 4}}}\)

\(\huge\boxed{\textsf{Option A.) answer: \bf 4}}\)

\(\huge\textsf{Possible Option A. part II }\huge\boxed\downarrow\)

\(\huge\boxed{\rm{\sqrt{64} = \sqrt{8\times8}= \bf 8}}\\\huge\boxed{\text{Possible answer for Option A. part II: \bf 8}}\)

\(\huge\textsf{Option B }\huge\boxed\downarrow\)

\(\huge\boxed{\rm{\sqrt{16}}}\\\huge\boxed{\rm{= \sqrt{4\times4}}}\\\huge\boxed{\rm{= \sqrt{16} \rightarrow \bold{4}\rightarrow 4\times4 \rightarrow \bf 16}}\)

\(\huge\boxed{\textsf{Option B.) answer: \bf 4}}\)

\(\huge\boxed{{\textsf{Based on the given information \boxed{\textsf{\bf NEITHER}} is}}}\\\huge\boxed{\textsf{the answer because it seems reasonable \& both}}\\\huge\boxed{\textsf{choices are very much equivalent to each other}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:5x^2

Step-by-step explanation:

combine like terms
it can be rewritten as 12x^2 - 7x^2
which is 12-7
which is 5
add x^2
it becomes 5x^2

It is not possible to determine the level of water in the tank using only the given information. To determine the level of water in the tank, we need to know either the height of the water column or the total pressure at the bottom of the tank, which includes the pressure due to the water column and the pressure due to the atmosphere.

Therefore, we can't fill the blank with any value since the problem does not provide any information regarding it. In order to find the level of water in the tank, we need to know either the height of the water column or the total pressure at the bottom of the tank, which includes the pressure due to the water column and the pressure due to the atmosphere.

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Answer:

The standard deviation is the best measurement of spread for games and movies.