3 Consider the series nẻ tr n=1 a. The general formula for the sum of the first n terms is S₂ = Your answer should be in terms of n. b. The sum of a series is defined as the limit of the sequence

Answer:

24 km/h and 17 km/h

Step-by-step explanation:

We know that when two cyclists are traveling together, they will meet in the same time as if one cyclist with the combined speed of the two cyclists travelled the whole length. We don't know the speeds of the cyclists, so let's assign the one with the slower speed "x", and the one with the faster speed "x+7" the combined speeds is "2x+7"

Since the speed = distance / time, we can plug in the values

2x+7=205/5
2x+7=41
2x=34
x=17
We substitute x into the equation for the speed of the cyclists

Cyclist 1's speed: x, so their speed is 17 km/h
Cyclist 2's speed: x+7, so their speed is 17 + 7, or 24 km/h

Check the picture below.

Answer:

x=-2, -4

Step-by-step explanation:

1(x+3)^2-1=0

Add 1 to each side

1(x+3)^2-1+1=0+1

(x+3)^2=1

Take the square root of each side

sqrt((x+3)^2)=sqrt(1)

x+3 = ±1

x+3 = 1    x+3 = -1

Subtract 3 from each side

x+3-3 = 1-3    x+3-3 = -1-3

x = -2     x=-4

Answer:

X = -2 X = -4

Step-by-step explanation:

A $100 bill and a dime differ by a magnitude of 3.

Orders of magnitude can be used in order to define large quantities efficiently and more easily. A dime is a currency used in the US that is equivalent to 0.10 dollars.

So we can represent a dime as 10-¹ of a dollar

and we can write 100 dollars as 10² of a dollar.

Therefore the difference in the order of magnitude of 100 dollars and a dime would be the difference between the powers or exponents of those two quantities,

That is,

2-(-1) = 3

So, the dollar differs by a magnitude of 3 from a dime.

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The coefficient of determination is 0.233, then 23.3% of the variation in the data about the regression line is explained.

The coefficient of determination, represented by R2, is a measure of how much of the variation in the data is explained by the regression line. It is calculated by squaring the correlation coefficient, R.

If the coefficient of determination is 0.233, then the percentage of the variation in the data about the regression line that is explained is 23.3%. This is calculated by multiplying the coefficient of determination by 100 to convert it to a percentage.

In other words, 23.3% of the variation in the data is explained by the regression line, and the remaining 76.7% of the variation is unexplained.

It is important to note that the coefficient of determination does not indicate causation, but rather the strength of the relationship between the independent and dependent variables.

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Answer:

B

Step-by-step explanation:

B. a + (-7 + 7) = a +0

When you remove a from both sides, you're left with -7+7=0 which shows that the opposites of the numbers add up to 0.

Answer:

Step-by-step explanation:

B

Answer:

Step-by-step explanation:

Answer:

\(2 + 2 = 4\)

\(4 + 6 = 10\)

\(10 - 1 = 9\)

Step-by-step explanation:

Answer =9

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer: If n>1, then any positive number raised to the power of n will always be greater than 1. Therefore, any number greater than 1 raised to the power of n, such as 2^n, 3^n, etc., will also always be greater than 1.

Step-by-step explanation:

The condition for a portfolio to be self-financing in the Black-Scholes model is that the portfolio's value does not change due to trading (buying or selling) costs or external cash flows. In other words, the portfolio's value remains constant over time, excluding the effects of the underlying assets' price changes.

For the given portfolio, a = -t (units of the stock) and b = S_t (units of the savings account). To determine if this portfolio is self-financing, we need to check if its value remains constant over time. Using Ito's lemma, we can express the value of the portfolio as:

d(Vt) = a_t * d(St) + b_t * d(Ct)

Substituting the values of a and b, we have:

d(Vt) = -t * (2St * dt + 4St * dBt) + S_t * d(t)

Simplifying this expression, we get:

d(Vt) = -2tSt * dt - 4tSt * dBt + S_t * dt

The portfolio is self-financing if d(Vt) = 0. However, in this case, we can see that the terms involving dBt do not cancel out, indicating that the portfolio is not self-financing.

Girsanov's theorem states that under certain conditions, it is possible to transform a Brownian motion under the real-world measure into a Brownian motion under an equivalent martingale measure (EMM). The EMM is a probability measure under which the discounted asset prices are martingales. By applying Girsanov's theorem or alternative techniques, we can derive the expression for St, the stock price, under the EMM. Unfortunately, without further information or specifications, it is not possible to provide the specific expression in this case.

To determine the price Ct of the call option on the stock at time t ≤ 2, with an exercise price K = 1 and expiration date T = 2, additional information or an appropriate result is required. Without specific details, such as the volatility of the stock or the risk-free interest rate, it is not possible to provide an expression for Ct.

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A random variable X is distributed as Poisson distribution with λ = 3.5. a. P(X < 5) = 0.0302 + 0.1057 + 0.1841 + 0.2139 + 0.1705 = 0.7044. b. P(2 ≤ X ≤ 6) = 0.1841 + 0.2139 + 0.1705 + 0.1008 + 0.0462 = 0.7155. c. P(X > 7) = 1 - P(X ≤ 7) = 1 - 0.8676 = 0.1324. d. P(X ≥ 5) = 1 - P(X < 5) = 1 - 0.7044 = 0.2956.

(a) P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

Using Table A.3 with λ = 3.5, we have:

P(X = 0) = 0.0302

P(X = 1) = 0.1057

P(X = 2) = 0.1841

P(X = 3) = 0.2139

P(X = 4) = 0.1705

Therefore, P(X < 5) = 0.0302 + 0.1057 + 0.1841 + 0.2139 + 0.1705 = 0.7044.

(b) P(2 ≤ X ≤ 6) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

Using Table A.3 with λ = 3.5, we have:

P(X = 2) = 0.1841

P(X = 3) = 0.2139

P(X = 4) = 0.1705

P(X = 5) = 0.1008

P(X = 6) = 0.0462

Therefore, P(2 ≤ X ≤ 6) = 0.1841 + 0.2139 + 0.1705 + 0.1008 + 0.0462 = 0.7155.

(c) P(X > 7) = 1 - P(X ≤ 7)

Using Table A.3 with λ = 3.5, we have:

P(X ≤ 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)

P(X ≤ 7) = 0.0302 + 0.1057 + 0.1841 + 0.2139 + 0.1705 + 0.1008 + 0.0462 + 0.0162

P(X ≤ 7) = 0.8676

Therefore, P(X > 7) = 1 - P(X ≤ 7) = 1 - 0.8676 = 0.1324.

(d) P(X ≥ 5) = 1 - P(X < 5)

Using Table A.3 with λ = 3.5, we have already calculated P(X < 5) in part (a) to be 0.7044.

Therefore, P(X ≥ 5) = 1 - P(X < 5) = 1 - 0.7044 = 0.2956.

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To find the amounts of each canned juice drink needed to obtain 15L of a 21% orange juice mixture, we can use a mixture equation.

Let's assume we need x liters of the 25% orange juice drink and y liters of the 10% orange juice drink.

To set up the equation, we need to consider the amount of orange juice in each drink. The 25% orange juice drink contains 25% of x liters of orange juice, while the 10% orange juice drink contains 10% of y liters of orange juice.

To find the total amount of orange juice in the mixture, we add the amounts of orange juice from each drink:

0.25x + 0.10y = 0.21 * 15

Simplifying this equation, we have:

0.25x + 0.10y = 3.15

To solve for x and y, we can use substitution or elimination.

Let's use the substitution method. Solve the first equation for x:

x = (3.15 - 0.10y) / 0.25

Substitute this value of x into the second equation:

0.25 * [(3.15 - 0.10y) / 0.25] + 0.10y = 3.15

Simplifying, we get:

3.15 - 0.10y + 0.10y = 3.15

The variable y cancels out, leaving us with:

3.15 = 3.15

This equation is always true, which means that y can take any value.

Therefore, there are infinite combinations of the two juice drinks that can be mixed to obtain 15L of a 21% orange juice mixture. The specific values of x and y will depend on the chosen combination.

For example, if we let y = 0, meaning we use only the 25% orange juice drink, then x would be 15L. On the other hand, if we let x = 0, meaning we use only the 10% orange juice drink, then y would be 15L.

In summary, to obtain 15L of a 21% orange juice mixture, you can mix any amount of the 25% and 10% orange juice drinks as long as the total amounts of orange juice from each drink add up to 3.15L (which is 21% of 15L).

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Answer in decimal form = -26.25

Answer as an improper fraction = -105/4

========================================================

Work Shown:

1/2 = 0.5

Replace every copy of x with 0.5 in the f(x) function.

f(x) = x-8

f(0.5) = 0.5-8

f(0.5) = -7.5

Repeat the same idea for the g(x) function

g(x) = x+3

g(0.5) = 0.5+3

g(0.5) = 3.5

Then multiply the results

f(0.5)*g(0.5) = (-7.5)*(3.5) = -26.25

Then optionally convert to an improper fraction following the steps shown below.

-26.25 = -(26.25)

-26.25 = -(26+0.25)

-26.25 = -(26+1/4)

-26.25 = -(26*(4/4)+1/4)

-26.25 = -(104/4+1/4)

-26.25 = -105/4

Answer:

The resultant velocity is 12.21 m/s.

Step-by-step explanation:

We are given that the water from a fire hose follows a path described by y equals 2.0 plus 0.9 x minus 0.10 x squared ​(units are in​ meters).

Also, v Subscript x is constant at 10.0 ​m/s.

The water from a fire hose follows a path described by the following equation below;

\(y=2.0 + 0.9x-0.10x^{2}\)

The velocity of the \(x\) component is constant at =  \(v_x=10.0 \text{ m/s}\)

and the point at which resultant velocity has to be calculated is (9.0,2.0).

Let the velocity of x and y component be represented as;

\(v_x=\frac{dx}{dt} \text{ and } v_y=\frac{dy}{dt}\)

Now, differentiating the above equation with respect to t, we get;

\(y=2.0 + 0.9x-0.10x^{2}\)

\(\frac{dy}{dt} =0 + 0.9\frac{dx}{dt} -(0.10\times 2)\frac{dx}{dt}\)

\(\frac{dy}{dt} = 0.9\frac{dx}{dt} -0.2\frac{dx}{dt}\)

\(v_y = 0.9v_x -0.2v_x\)

\(v_y = 0.7v_x\)

Now, putting \(v_x=10.0 \text{ m/s}\) in the above equation;

\(v_y = 0.7 \times 10.0\) = 7 m/s

Now, the resultant velocity is given by = \(v=\sqrt{v_x^{2}+v_y^{2} }\)

                            \(v=\sqrt{10^{2}+7^{2} }\)

                               = \(\sqrt{149}\) = 12.21 m/s

Answer:

All are true

Step-by-step explanation:

You’re welcome

the measure of  ∠B = 19° in right angle tringle .

What is a triangle's right angle?

In Δ ABC

Sin∠B = 7/21

Sin∠B = 1/3

   ∠B = Sin⁻¹(1/3)

   ∠B = 19°

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Answer:

About 4.5 units

Step-by-step explanation:

Please let me know if you want me to add an explanation

The Poisson distribution with a parameter λ = 1 accurately models the production stoppages, where on average, the company experiences one stoppage per month with a relatively small amount of variability.

The  scenario describes a company's production stoppages, which can be modeled using a Poisson distribution with a parameter (mean) of λ = 1. In a Poisson distribution, the mean, variance, and standard deviation are all equal.

The mean (μ) represents the average number of stoppages per month, which in this case is 1. This means that, on average, the company experiences one production stoppage per month.

The variance (σ^2) also has a value of 1 in a Poisson distribution. It measures the spread or variability of the data around the mean. In this case, the variance of 1 indicates that there is some fluctuation in the number of stoppages, but it is relatively small.

The standard deviation (σ) is equal to the square root of the variance, which is also 1 in this scenario. It represents the average amount of deviation from the mean. A standard deviation of 1 suggests that most of the observations will be within one unit of the mean.

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Answer:

I'm not sure what X is but I am pretty sure the PAW angle is the same as -1x+43. Dont count me on it though...

Step-by-step explanation:

The equation in slope-intercept form that represents the given graph of the cost y (in dollars) to open an online gaming account and buy x games is y = 15x + 60.

To write an equation in slope-intercept form that represents the given graph, we need to find the slope and y-intercept of the line.

From the graph, we can see that the line passes through the point (0, 60), which is the y-intercept. We can also see that the line goes through the point (4, 120), which is another point on the line.

The slope of the line is the change in y divided by the change in x, which is:

slope = (120 - 60) / (4 - 0) = 60 / 4 = 15

Therefore, the equation of the line in slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

Plugging in the values of m and b, we get:

y = 15x + 60

So the equation in slope-intercept form that represents the given graph is y = 15x + 60.

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Answer:

4. rise

match the following definition with the correct term:

the vertical distance between two points on a line

1. run

2. rate of run

3. slope

4. rise

ANSWER

EXPLANATION

We want to find the value of the expression:

for:

To do this, substitute the values of x and y into the expression.

That is:

The answer is option b.

Answer:

$34.05

Step-by-step explanation:

The ultimate purpose of constructing a standard curve is to use it to calculate the concentration of a substance in solution.

What is a standard curve?

A standard curve is a graphical representation of a mathematical function that relates the concentration of a solution to the amount of light that passes through it. The majority of standard curves have a linear relationship between the dependent and independent variables. These curves are particularly useful for chemical tests that require the use of an instrument, such as a spectrophotometer.

A standard curve is created by generating a series of known concentrations of a specific compound in a solution. The absorption values are measured, and the data are then plotted on a graph. The resulting data points can then be utilized to create a standard curve, which can be used to identify the concentration of unknown samples.

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(a) The probability that both score more than 175 is 0.12 and (b) the probability that Thomas scores more than 175 and Sarah scores higher than Thomas is 0.04

If the occurrence of one event say A does not affect the occurrence of event B, then the two events are said to be independent such that;

P (A ∩ B) = P (A) × P (B)

a:

consider; event A represents Sarah scoring more than 175 and event B represents Thomas scoring more than 175

Thus, P(A) = Probability that Sarah scores more than 175 = 0.6

P(B) = The probability that Thomas scores more than 175 = 0.2

Since the scores are independent, therefore the probability that both Sarah and Thomas score more than 175 is,

P (A ∩ B) = (0.6) × (0.2)

P (A ∩ B) = 0.12

b:

If the occurrence of one event say A affects the occurrence of another event say B, then the two events are said to be dependent on each other such that;

P (A ∩ B) = P (B) × P (A|B)

As; P(B) = The Probability that Thomas scores more than 175 = 0.2

and P(A|B) = Sarah scores more than Thomas given that Thomas scores more than 175 = 0.2

Therefore;

P (A ∩ B) = (0.2) × (0.2) = 0.04

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The line which contains the points (4,0) and (0,-2), value of y when x =3 is,  -1/2

The equation of a straight line is a relationship between x and y coordinates, The two point form of a straight line is y-y₁ =  y₂-y₁/x₂-x₁(x-x₁).

Given that,

The points, (4,0) and (0,-2)

Equation of line for given two points,

y-y₁ =  y₂-y₁/x₂-x₁(x-x₁)

y-0 =  -2 - 0/0-4(x-4)

y = 1/2(x - 4)

2y = x - 4

when x = 3,

y =  1/2(3 - 4)

y = - 1/2

Hence, the value of y is -1/2

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Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them. So the monthly charge for Danielle's cable bill is $5.

Danielle pays a monthly charge of $69 for her cable bill.

She also pays a fee every time she watches a movie on demand.

Last month Danielle watched 7 movies on demand, and her total monthly bill was $104.

We have to find the monthly charge for Danielle's cable bill to choose.

Remove the monthly fee of 69 dollars for cable service from the total of 104 dollars, then check the statement to see that there is still a mystifying 35 dollars on it.

Danielle viewed 7 movies on demand, thus you must divide her 35 dollars among them, giving you the result of $5 per on-demand movie.

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