Can someone help me with this question? A Ferris wheel has: a diameter of 80ft, an axel height of 60ft, and completes 3 turns in 1 minute. What would the graph look like?

Answer:

The ratio test formula is a infinite series which is based on calculating the ratio an+1/an a n + 1

how to solve a ratio: first add all the parts of a ratio together to find the total number. For example, if you have to split 20 sweets into a ratio of 3:1, you add the ratio figures up to find the total. In this case, that's 3 + 1 = 4

For series ∑a_n, the ratio test with limits is - \($$L=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_n}\right|$$\) .

What is limit?

A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity. It is employed in the analysis process and constantly considers how the function will behave at a specific point.

The usual form of the ratio test makes use of the limit -

\(L=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_n}\right|\)

According to the ratio test -

If L = 1 or the limit does not exist, the test is inconclusive because both convergent and divergent series exist that fulfil this condition.

If L 1, the series converges absolutely.

If L > 1, the series diverges.

If limit superior and limit inferior are utilised, it is feasible to make the ratio test usable in some situations when the limit L does not exist.

If the test requirements are adjusted, the test may occasionally be conclusive even when L = 1.

In more detail, let -

\(\begin{aligned}& R=\lim \sup \left|\frac{a_{n+1}}{a_n}\right| \\& r=\liminf \left|\frac{a_{n+1}}{a_n}\right|\end{aligned}\)

The ratio test therefore shows that -

The test is otherwise ambiguous.

If R < 1, the series converges absolutely.

If r > 1, the series diverges.

If \(\begin{aligned}& \left|\frac{a_{n+1}}{a_n}\right| \\\end{aligned}\) > 1 for all large n (independent of the value of r), the series likewise diverges since |a_n| is nonzero and rising and therefore a_n does not approach zero.

Therefore, the ratio test formula is \($$L=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_n}\right|$$\).

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Answer:

Earnings (E), Time (T) Rate (R) E = 9t

On Friday he worked 9 hours

Step-by-step explanation:

divide 36 by 4 to get 9 (Fo that for all the earnings to make sure you got the correct answer) Then just divide 81 by 9 to get 9 hours.

Answer: 10.2

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

The length is 52 meters and the width is 23 meters.

Step-by-step explanation:

Let l stand for length, and w stand for width.

l = 2w + 6

The length is 6 more than twice the width.

2l + 2w = 150

Twice the length plus twice the width is the perimeter of a rectangle.

2(2w + 6) + 2w = 150

4w + 12 + 2w = 150

6w + 12 = 150

6w = 138

w = 23

l = 2(23) + 6

l = 46 + 6

l = 52

The correct unscrambling of whyrot is worthy.

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Answer: $51.48

Step-by-step explanation:

If a $52 item is marked up by 10%, its new price will be:

$52 + 10% of $52 = $52 + $5.20 = $57.20

Then, if this new price is marked down by 10%, the final price will be:

$57.20 - 10% of $57.20 = $57.20 - $5.72 = $51.48

Therefore, the final price of the item after the markup and markdown is $51.48.

Its molecules' monatomic fraction is 0.444.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

The fact that

The formula gamma monatomic

Determines the specific heat ratio of monoatomic gas.

5/3=1.67

Calculates the specific heat ratio of a diatomic gas.

Gamma monatomic =7/5=1.4

We have a monoatomic and diatomic gas mixer with a gamma mixer specific heat ratio of 1.52.

Calculating the monoatomic gas fraction is as follows:

Let's assume that "x" is the percentage of monoatomic

1.67* x+1.4* (1-x)=1.52

1.67* x+1.4-1.4* x=1.52

0.27* x=0.12

x = 0.12/0.27

x= 0.444

Its molecules' monatomic fraction is 0.444.

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The area of the region bounded by the curve r = θ² in the sector 0 ≤ θ ≤ π/4 is π/32 square units.

To explain how we find the area of the region bounded by the curve r = θ² in the sector 0 ≤ θ ≤ π/4, we need to use polar coordinates and integrate.

The equation r = θ² represents a curve in polar coordinates. In this case, the curve is a parabola. The given sector 0 ≤ θ ≤ π/4 specifies the range of θ values over which we need to find the area.

To find the area of the region, we integrate the function r(θ) with respect to θ over the given range. The formula for finding the area in polar coordinates is:

A = ∫[θ₁,θ₂] (1/2) r(θ)² dθ

In this case, we have:

r(θ) = θ²

θ₁ = 0

θ₂ = π/4

Substituting these values into the formula, we have:

A = ∫[0,π/4] (1/2) (θ²)² dθ

Simplifying the expression:

A = (1/2) ∫[0,π/4] θ⁴ dθ

Integrating θ⁴ with respect to θ gives:

A = (1/2) [(θ⁵)/5] [0,π/4]

Plugging in the limits of integration:

A = (1/2) [(π/4)⁵/5 - (0)⁵/5]

Simplifying further:

A = (1/2) [(π⁵/4⁵)/5]

A = (1/2) (π⁵/4⁵)/5

A = π/32

Therefore, the area of the region bounded by the curve r = θ² in the sector 0 ≤ θ ≤ π/4 is π/32 square units.

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Answer:

see explanation

Step-by-step explanation:

Given

\(\frac{6c-2}{2}\) + 2c + 11

= \(\frac{6c}{2}\) - \(\frac{2}{2}\) + 2c + 11

= 3c - 1 + 2c + 11

= 5c + 10

(b)

We have the expression

5c + 10 ← factor out 5 from each term

= 5(c + 2)

Leonora made 12 number of 2-point baskets, solved using the system of equations

In the question, we are given that Leonora made 14 total baskets during her basketball game, in which she made x baskets worth 2 points each and y baskets worth 3 points each.

We are asked that if she scored 30 points total throughout the game, how many 2-points basket did she make.

Number of 2-points basket scored = x.

Number of 3-points basket scored = y.

Thus, total number of baskets scored = x + y.

But, the total number of baskets scored is given to be 14.

Thus, we get an equation x + y = 14 ... (i).

The total worth of 2-points basket scored = 2x.

The total worth of 3-points basket scored = 3y.

Thus, the total points scored = 2x + 3y.

But, the total points scored is given to be 30.

Thus, we get an equation 2x + 3y = 30 ... (ii).

(i) and (ii) together gives us a system of equation.

To solve the system of equations, we multiply (i) by 3, and then subtract (ii) from it.

3x + 3y = 42

2x + 3y = 30.

(-) (-)     (-)

__________

x = 12.

Thus, Leonora made 12 number of 2-point baskets, solved using the system of equations.

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In order to get the value of n, which is what we are trying to find, it is important to know how to isolate the variable.

When something is added to n, you subtract to isolate n. Going with this logic, you would multiply by a number if you wanted to isolate n with a fraction.

\(\frac{n}{5}+4=-4\)

The first step would be to get rid of the 4 on the left side so we can work on the variable. We can do this by subtracting both sides by 4, so the left side cancels out to 0.

\(\frac{n}{5}+4-4=-4-4\)

\(\frac{n}{5} =-8\)

Next, we can multiply both sides by 5, so we can isolate the variable, because it is being divided by 5.

\(\frac{n}{5} *5=-8*5\)

n=-40

The inverse Laplace transform of the given function is:

\(L^{-1}\) {2\(s^{2}\) / (s - 8) + (s + 12) / (s - 8)} = 2\(t^{2}\) + 16t + 64 + δ(t) + 20\(e^{8t}\)

To determine the inverse Laplace transform of the given function, we'll use partial fraction decomposition and refer to the table of Laplace transforms.

The function can be written as:

2\(s^{2}\)  / (s - 8) + (s + 12) / (s - 8)

Let's perform the partial fraction decomposition:

2\(s^{2}\)  / (s - 8) + (s + 12) / (s - 8)

= 2\(s^{2}\)  / (s - 8) + (s - 8 + 20) / (s - 8)

= 2\(s^{2}\)  / (s - 8) + (s - 8) / (s - 8) + 20 / (s - 8)

= 2\(s^{2}\)  / (s - 8) + 1 + 20 / (s - 8)

Now, let's find the inverse Laplace transform of each term separately using the table of Laplace transforms:

\(L^{-1}\) {2\(s^{2}\)  / (s - 8)} = 2\(t^{2}\)  + 16t + 64 (Using the table of Laplace transforms)

\(L^{-1}\) {1} = δ(t) (Using the table of Laplace transforms, where δ(t) represents the Dirac delta function)

\(L^{-1}\) {20 / (s - 8)} = 20\(e^{8t}\) (Using the table of Laplace transforms)

Therefore, the inverse Laplace transform of the given function is:

\(L^{-1}\) {2\(s^{2}\) / (s - 8) + (s + 12) / (s - 8)} = 2\(t^{2}\)  + 16t + 64 + δ(t) + 20\(e^{8t}\)

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Answer:

Distributive property

Subtraction property

Division property

Step-by-step explanation:

took test

Step-by-step explanation:

1 ×68/4×1

=68/4

hope it helps

Answer:

CD = \(\sqrt{164}\)

Step-by-step explanation:

Calculate the distance d using the distance formula

d = \(\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }\)

with (x₁, y₁ ) = C(5, - 2) and (x₂, y₂ ) = (D(- 3, 8)

d = \(\sqrt{(-3-5)^2+(8+2)^2}\)

   = \(\sqrt{(-8)^2+10^2}\)

    = \(\sqrt{64+100}\)

    = \(\sqrt{164}\)

     = 2\(\sqrt{41}\) ← in simplest form

As, we have C (5, - 2) and D (- 3, 8), to find CD let's use distance formula :

\( \underline{\boxed{\tt{Distance \: between \: two \: points = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}}}}\)

Here,

So, by filling values :

\( \sf : \implies CD = \sqrt{(-3 - 5)^{2} + (8 - (-2))^{2}}\)

\( \sf : \implies CD = \sqrt{(-8)^{2} + (8 +2))^{2}}\)

\( \sf : \implies CD = \sqrt{64 + (10)^{2}}\)

\( \sf : \implies CD = \sqrt{64 + 100}\)

\( \sf : \implies CD = \sqrt{164}\)

Hence, distance of CD is \( \bold{\sf \sqrt{164}.}\)

Answer:

9300$

Step-by-step explanation:

The appropriate statistical tool for predicting the value of a random variable based on the values of other random variables is regression.

A statistical measure that identifies the link or co-relationship between two variables. explains the relationship between an independent variable and a dependent variable. The two methods most frequently employed for examining the relationship between quantitative variables are correlation and regression. Regression is used here to allude to linear regression. While linear regression employs an equation to represent this relationship, correlation is employed to show the link between the variables. When two quantitative variables are supposed to have a linear relationship, correlation and regression are employed to identify some kind of association.

Given

The appropriate statistical tool for predicting the value of a random variable based on the values of other random variables is

a) Regression

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The number of verbs memorized after two hours (t = 120) is:y = 50 - 15(30/2)^(-1/30)(120)= 45.92. Therefore, the student will memorize about 45 verbs in two hours.

(a) A student studying a foreign language has 50 verbs to memorize. Suppose the rate at which the student can memorize these verbs is proportional to the number of verbs remaining to be memorized, 50 – y, where the student has memorized y verbs. Initially, no verbs have been memorized.

Suppose 20 verbs are memorized in the first 30 minutes.

For part a) we have to find how many verbs will the student memorize in two hours.

It can be seen that y (the number of verbs memorized) and t (the time elapsed) satisfy the differential equation:

dy/dt

= k(50 – y)where k is a constant of proportionality.

Since the time taken to memorize all the verbs is limited to two hours, we set t = 120 in minutes.

At t

= 30, y = 20 (verbs).

Then, 120 – 30

= 90 (minutes) and 50 – 20

= 30 (verbs).

We use separation of variables to solve the equation and integrate both sides:(1/(50 - y))dy

= k dt

Integrating both sides, we get;ln|50 - y|

= kt + C

Using the initial condition, t = 30 and y = 20, we get:

C = ln(50 - 20) - 30k

Solving for k, we get:

k = (1/30)ln(30/2)Using k, we integrate to find y as a function of t:

ln|50 - y|

= (1/30)ln(30/2)t + ln(15)50 - y

= e^(ln(15))e^((1/30)ln(30/2))t50 - y

= 15(30/2)^(-1/30)t

Therefore,

y = 50 - 15(30/2)^(-1/30)t

Hence, the number of verbs memorized after two hours (t = 120) is:y = 50 - 15(30/2)^(-1/30)(120)

= 45.92

Therefore, the student will memorize about 45 verbs in two hours.

(b) Now, we are supposed to determine after how many hours will the student have only one verb left to memorize.

For this part, we want y

= 1, so we solve the differential equation:

dy/dt

= k(50 – y)with y(0)

= 0 and y(t)

= 1

when t = T.

This gives: k

= (1/50)ln(50/49), so that dy/dt

= (1/50)ln(50/49)(50 – y)

Separating variables and integrating both sides, we get:

ln|50 – y|

= (1/50)ln(50/49)t + C

Using the initial condition

y(0) = 0, we get:

C = ln 50ln|50 – y|

= (1/50)ln(50/49)t + ln 50

Taking the exponential of both sides, we get:50 – y

= 50(49/50)^(t/50)y

= 50[1 – (49/50)^(t/50)]

When y = 1, we get:

1 = 50[1 – (49/50)^(t/50)](49/50)^(t/50)

= 49/50^(T/50)

Taking natural logarithms of both sides, we get:

t/50 = ln(49/50^(T/50))ln(49/50)T/50 '

= ln[ln(49/50)/ln(49/50^(T/50))]T

≈ 272.42

Thus, the student will have only one verb left to memorize after about 272.42 minutes, or 4 hours and 32.42 minutes (approximately).

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By applying the Schroder-Bernstein theorem, we can conclude that (0,1) and R have the same cardinality.

To show that (0,1) and R have the same cardinality, we can apply the Schroder-Bernstein theorem, which states that if there exist injective functions from set A to set B and from set B to set A, then A and B have the same cardinality.

First, we can define a function from (0,1) to R by using a bijection. For example, we can use the function f(x) = tan[(πx - π/2)].

This function maps each value in the interval (0,1) to a unique real number in R. Since the tangent function is injective in the interval (-π/2, π/2), the function f(x) is also injective.

Next, we can define a function from R to (0,1) by using the inverse of the tangent function. For example, we can use the function g(x) = (π/2 + arctan[x])/π.

This function maps each real number to a unique value in the interval (0,1). The function g(x) is also injective since the inverse of the tangent function is injective.

By applying the Schroder-Bernstein theorem, we can conclude that (0,1) and R have the same cardinality.

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Answer:

In order to find the fraction of the 20 dollars that has been spent, we have to divide the amount spent by the total amount. So 0.65 is the fraction of 20 that is spent.

Step-by-step explanation:

Answer:

\(x = \sqrt{ {16}^{2} + {21}^{2} } = \sqrt{256 + 441} = \sqrt{697} = 26.4\)

The percentage of each is 0.66% , 1.65% , 2.97% , 37.21% , 37.48%, 20.1% respectively

The percentage of the total for each layer is calculated by dividing the depth of the layer in kilometers by the total depth

Percentage = (layer depth in km / total depth) × 100%

Crust= (40 / 6046) × 100 = 0.66%

Lithosphere = (100 / 6046) × 100 = 1.65%

Asthenosphere = (180/6046) × 100 = 2.98%

Mantle = (2250/6046) × 100 = 37.21%

Outer core = (2266/6046) × 100 = 37.48%

Inner core = (1210/6046) × 100  = 20.01%

The Depth in centimeters for each layer multiply the depth of the jar, 16.5 cm, by the percent you calculated for the crust

Crust = 0.66 × 16.5 cm =0.11 cm

Lithosphere = 1.65 × 16.5 = 0.27 cm

Asthenosphere = 2.98 × 16.5 = 0.49 cm

Mantle = 37.21 × 16.5 = 6.14 cm

Outer Core = 37.48 × 16.5 = 6.18 cm

Inner Core = 20.01 × 16.5 = 3.30 cm

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The question is incomplete the complete question is :

i. Divide the depth of the layer by the total depth. For example, to calculate the percentage of the total depth that the crust represents, divide 40 by 6,046.

ii. Write your answer in the Percent column.

iii. Repeat for the rest of the layers.

Use the calculator to determine the depth in centimeters for each layer. This is the depth of sand

you will put in your jar.

i. Multiply the depth of the jar, 16.5 cm, by the percent you calculated for the crust.

ii. Write your answer in the Centimeters column.

iii. Repeat for the rest of the layers.

Answer:

Step-by-step explanation:

Testing if 6 is the solution:

6 is not a solution

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

Solving for x:

Answer:

x = 7

Step-by-step explanation:

- Events A, B, C, and D are exhaustive.
- Events A and B, B and D are not mutually exclusive.
- Events A and C, C and D, A and D are mutually exclusive.

To determine whether the events are exhaustive or mutually exclusive, we need to understand the definitions of these terms:
1. Exhaustive events: Events are considered exhaustive if the union of all the events covers the entire sample space S. In other words, there are no outcomes in the sample space that are not included in any of the events.
2. Mutually exclusive events: Events are considered mutually exclusive if they have no outcomes in common. In other words, the events cannot occur simultaneously.
Now let's analyze the given events:
A = {1, 2, 4}
B = {1, 2, 4, 5, 6}
C = {5, 6}
D = {2, 3, 6}
To determine if the events are exhaustive, we need to check if their union covers the entire sample space S.
The union of A, B, C, and D is {1, 2, 3, 4, 5, 6}, which covers the entire sample space S. Therefore, the events A, B, C, and D are exhaustive.

To determine if the events are mutually exclusive, we need to check if any outcomes are shared between the events.
The outcomes 1, 2, and 4 are shared between events A and B. Therefore, events A and B are not mutually exclusive.
The outcomes 2 and 6 are shared between events B and D. Therefore, events B and D are not mutually exclusive.
No outcomes are shared between events A and C, C and D, or A and D. Therefore, events A and C, C and D, and A and D are mutually exclusive.

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The response variable in this experiment is the scores on the midterm exam. The response variable is the one that is measured or observed to determine whether it has been affected by the explanatory variable.

The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.

The explanatory variable in this experiment is the type of music played in the background during the exam. The explanatory variable is the one that is deliberately manipulated or changed by the researcher in order to observe its effect on the response variable. In this case, the researcher wanted to investigate whether the type of music played during the exam would have an effect on the students' performance, so they manipulated the type of music and observed its effect on the exam scores.

The response variable in this experiment is the scores on the midterm exam. The response variable is the one that is measured or observed to determine whether it has been affected by the explanatory variable. In this case, the researcher measured the exam scores of the two groups to see if there was a difference between the group that listened to Dave Matthews Band and the group that listened to Death Cab for Cutie.

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Here we must calculate the power from 3 to 4.

Solving:

The answer would be 81

The missing value of "a" is 2.5.

To find the value of "a", we can use the fact that "m" is the midpoint of segment "fg".

Given that "fm" = 8a + 1 and "fg" = 42, we can set up the equation:

fm = fg / 2

Substituting the given values, we get:

8a + 1 = 42 / 2

Simplifying the right side of the equation, we have:

8a + 1 = 21

To isolate "a", we can subtract 1 from both sides:

8a = 21 - 1
8a = 20

Now, we can solve for "a" by dividing both sides by 8:

a = 20 / 8
a = 2.5

Therefore, the missing value of "a" is 2.5.

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