List the first five terms of the sequence.
a_1 = 5, a_n+1 = 2a_n+4
a_1 = ______
a_2 = ______
a_3 = ______
a_4 = ______
a_5 = ______

The intersection points of the equations represents; C: The time when the height of the ball and the bird are the same.

We are given;

The height of the baseball over time:

h = -16t² + 65t

The height of the bird over time:

h = 8t + 20

The intersection point will be the value of t when; 8t + 20 = -16t² + 65

Rearranging gives;

16t² + 8t - 45 = 0

Using online quadratic equation calculator gives us;

t = -1.94 s or t = 1.44 s

Now, since both equations measure height vs time, it means that the points of intersection tell us the time when the height of the ball and the bird are the same.

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Answer:

C: the time when the height of the ball and the bird are the same

Step-by-step explanation:

because i just took it on edge 2022.

The probability that first card is a two and the second card is a ten is 0.006.

Probability is an area of mathematics that deals with the occurrence of a random event. There are four varieties of probability: classical, empirical, subjective, and axiomatic.

Probability is equivalent with possibility, therefore you might say it's the likelihood that a specific occurrence will occur.

Now, according to the question;

Let n(2) be the number of cards marked 2 ( = 4 cards).

Let n(10) be the number of cards marked 10 ( = 4 cards).

The total number of card in a pack is; n = 52.

Each card is chosen without replacement.

So the likelihood of the first being 2 and the second being 10 is:

\(\operato{Pr}=\frac{n(2)}{n} \times \frac{n(10)}{n-1}\)

Substitute the values;

\(P r=\frac{4}{52} \times \frac{4}{52-1}\)

Simplifying the equation;

\(P r=\frac{16}{2652}\)

\(P r=0.006\)

Therefore, the probability that first card is a two and the second card is a ten is 0.006.

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Answer:

n has to be negative

Step-by-step explanation:

To solve this equation, 15 has to be subtracted from 2 which is negative

Since n is positive then the overall result will be negative

Answer:

95

Step-by-step explanation:

if you see that line in between 90, 100 that is a five and it is past 90 making it 95

The measure of the angle from the given figure is 85°.

In the given figure, the measure of angle is given.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

In the given figure, the ray is between 90° and 80°

So, the measure of the angle is 85°

Hence, the measure of the angle from the given figure is 85°.

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Answer:

We can use the formula for conditional probability to solve this problem:

P(Scholarship | Accepted) = P(Scholarship and Accepted) / P(Accepted)

We know that P(Accepted) = 18/25 and P(Scholarship and Accepted) = 13/25 (from the given information). Therefore:

P(Scholarship | Accepted) = (13/25) / (18/25) = 13/18 or approximately 0.722

So the probability that you receive a scholarship, given that you are accepted to your preferred college, is about 0.722 or 72.2%.

Step-by-step explanation:

The use of match data will display team standings during and at the end of the tournament.

The given data, "Time Remaining 29 minutes 7 seconds 00:29:07" is not relevant to the question.

The 2019 FIFA Women's World Cup held in France comprised 52 matches with 24 teams competing.

The matches were played in 9 venues located across France.

Every team played a total of three matches against other teams in their respective groups.

16 teams (the top two teams from each group and the four best third-place teams) advanced to the knockout stage to compete in a single-elimination competition, which will eventually decide the winner of the tournament.

The use of match data will display team standings during and at the end of the tournament.

The points earned from every match determine the ranking of teams.

The team with the highest number of points in a group will be ranked first, and the team with the lowest number of points will be ranked last.

Every group consists of four teams.

A win earns a team three points, a draw one point, and a loss earns zero points.

The group stage also uses tie-breakers to rank teams in case of equal points.

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Answer:

372 miles

Step-by-step explanation:

You need to multiply 62 and 6

Answer:

372

Step-by-step explanation:

just mulitple

i hope thi shelps

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Hey there!

Answer: \( \Rightarrow \sf{\frac{x+3}{x -2}}\)

\( \rightarrow \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } }\)

\( \rightarrow{ \rm{factorise} \sf{ \frac{ {x}^{2} + 5x + 6 }{ {x}^{2} - 4 } } = \frac{(x + 2)(x + 3)}{ {x}^{2} - 4} = \frac{(x + 2)(x + 3)}{(x + 2)(x - 2)} = \Rightarrow \sf{\frac{x+3}{x -2}}}\)

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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\(\dfrac{7x^2+14}{(x^2+3)^2}=\dfrac{7x^2+21-7}{(x^2+3)^2}=\dfrac{7x^2+21}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\dfrac{7(x^2+3)}{(x^2+3)^2}-\dfrac{7}{(x^2+3)^2}=\\=\dfrac{7}{x^2+3}-\dfrac{7}{(x^2+3)^2}\)

Using probabilities P(A₁) = 0.40 , P(A₂) = 0.60, P(B|A₁) = 0.20, P(B|A₂) = 0.05,

a) No, A₁ , A₂ are not mutually exclusive because , their intersection probability is not a zero.

b) P(A₁∩ B) is 0.08 , P(A₂ ∩ B) is 0.03

c) P(B) = 0.09

d) Using Bayes' theorem P(A₁|B) is 0.89 , P(A₂|B) is 0.33 .

a. A₁ and A₂ are not mutually exclusive, as their intersection probability is non-zero (given as 0 in the problem statement).

b. We can compute P(A₁∩ B) and P(A₂∩ B) using the formula for conditional probability:

P(A₁∩ B) = P(B|A₁) * P(A₁) = 0.20 * 0.40 = 0.08

P(A₂ ∩ B) = P(B|A₂) * P(A₂) = 0.05 * 0.60 = 0.03

c. To compute P(B), we can use the law of total probability, which states that the probability of an event B can be calculated as the sum of the probabilities of B given each possible event in the sample space:

P(B) = P(B|A₁) * P(A₁) + P(B|A₂) * P(A₂) = 0.20 * 0.40 + 0.05 * 0.60 = 0.09

d. To compute P(A₁|B) and P(A₂|B), we can use Bayes' theorem:

P(A₁|B) = P(B|A₁) * P(A₁) / P(B) = 0.20 * 0.40 / 0.09 ≈ 0.89

P(A₂|B) = P(B|A₂) * P(A₂) / P(B) = 0.05 * 0.60 / 0.09 ≈ 0.33

Therefore, the probability that event A₁ occurred given that event B occurred is approximately 0.89, and the probability that event A₂ occurred given that event B occurred is approximately 0.33.

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Answer:

If you are refering to the 4th in a sequence being 3/5 the first.

3/5, 6/10, 12/20, 24/40

24/40 would be your answer.

If you are looking for 3/5 in 4ths

2.4/4

The p-value is less than the significance level (typically 0.05), we reject the null hypothesis and conclude that the majority of teens in this age range do not respond better to the new drug therapy for autism.

The correct answer is not provided in the question. The chi-square test statistic cannot be used for testing hypotheses about a single proportion. Instead, we use a z-test for proportions. To find the test statistic, we first calculate the sample proportion:

p-hat = 411/900 = 0.4578

Then, we calculate the standard error:

SE = \(\sqrt{[p-hat(1-p-hat)/n] } = \sqrt{[(0.4578)(1-0.4578)/900]}\) = 0.0241

Next, we calculate the z-score:

z = (p-hat - p) / SE = (0.4578 - 0.50) / 0.0241 = -1.77

Finally, we find the p-value using a normal distribution table or calculator. The p-value is the probability of getting a z-score as extreme or more extreme than -1.77, assuming the null hypothesis is true. The p-value is approximately 0.0392.

Since the p-value is less than the significance level (typically 0.05), we reject the null hypothesis and conclude that the majority of teens in this age range do not respond better to the new drug therapy for autism.

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Answer:

A

Step-by-step explanation:

The equation representing a proportional relationship is

y = kx ← k is the constant of proportion

The only equation in this form is

y = 24x ( k = 24 ) → A

Step-by-step explanation:

x=120⁰

hdbdbdddfhcydhgdjvds

Answer:

\(x\geq 3\)

Step-by-step explanation:

Answer:

103.6ft

Step-by-step explanation:

21ft + 18ft + 17.6ft + 29ft + 18

The random variable x is uniformly distributed between 5 and 19. To compute the standard deviation of x, we can use the formula for the standard deviation of a uniformly distributed continuous random variable:

SD = √[(b - a)^2 / 12]
Here, 'a' represents the lower bound (5) and 'b' represents the upper bound (19). Plugging these values into the formula, we get:
SD = √[(19 - 5)^2 / 12]
SD = √[(14)^2 / 12]
SD = √[196 / 12]
SD = √[16.333]
Therefore, the standard deviation of x is approximately 4.041. The correct answer is option (a) 4.041.

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Answer:

Step-by-step explanation:

Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

The equation of the line tangent to the graph of the equation y = −2 - 5x^2 at the point (5, -127) is y = -214.5x - 509. This can be determined by finding the derivative of the equation, which is y' = -10x, and then using the point-slope formula.

The point-slope formula states that the equation of a line passing through the point (x1, y1) with slope m is y - y1 = m(x - x1).
Therefore, the equation of the line tangent to y = -2 - 5x^2 at (5, -127) is:
y - (-127) = -10(x - 5)
y = -10x + (-127 + 50)
y = -10x - 77
This equation represents the line tangent to y = -2 - 5x^2 at (5, -127). The slope of this line is -10, which is the same as the slope of the graph of y = -2 - 5x^2 at (5, -127). This means that the line is tangent to the graph at this point.
This equation can also be used to determine the y-intercept of the line, which is (-77). The y-intercept is the point at which the line crosses the y-axis. This means that the line crosses the y-axis at the point (0, -77).
Overall, the equation of the line tangent to y = -2 - 5x^2 at (5, -127) is y = -214.5x - 509.

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In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

Given,

You want to run a regression to predict the probability of a flight delay, but there are flights with delays of up to 12 hours that are really messing up your model.

I immediately think of grouping delays into ranges such as those under 40 minutes, those between 40 minutes and 2 hours, those between 2 hours and 10 hours, and those above 10 hours. But doing so requires the use of a classification model, such as logistic regression. We frequently consider whether there will be a delay rather than how long it might last when thinking about delays. In the event that linear regression is required, we have two options: (1) change the delay column 2) ignore them.

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Answer:

y=12

Step-by-step explanation:

y=2x ,so 2x=8x-x^2

x^2=8x-2x

x^2=6x

x^2/x=6x/x

x=6

y=2x ,2(6)

y=12

Wrong answer sorry. Hope you find it!

Answer:

Its either 4 or 4.6

Step-by-step explanation:

I used multiplication.

The probability of obtaining a sample mean as large or larger is 0.0228.

option B.

The probability of obtaining a sample mean as large or larger is calculated as follows;

The given parameters;

The standard error (SE) of the sampling distribution is calculated as;

SE = σ / √n

SE = 0.8 / √64

SE = 0.8 / 8

SE = 0.1

The z-score of the sample mean is calculated as follows;

z = (x - μ) / SE

z = (3.4 - 3.2) / 0.1

z = 0.2 / 0.1

z = 2

Using a z-score calculator;

P (X > Z) = 0.0228

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The probability of obtaining a sample mean as large or larger than 3.4 pounds is 0.0228.

The correct answer is: b. 0.0228

Given data:

Population mean (μ) = 3.2 pounds

Population standard deviation (σ) = 0.8 pound

Sample size (n) = 64

Sample mean (x) = 3.4 pounds

We have to standardize the sample mean using the z-score formula and then find the corresponding area under the standard normal distribution curve.

The formula for calculating the z-score is:

z = (x - μ) / (σ / √n)

substituting the values:

z = (3.4 - 3.2) / (0.8 / √64)

z = 0.2 / (0.8 / 8)

z = 0.2 / 0.1

z = 2

Using a calculator, the area to the right of z = 2 is the probability 0.0228.

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The angle is decreasing at a rate of 0.0133 radians per second.

The height of the kite from the ground is y = 75 feet.

The kite moves horizontally at a speed of dx/dt = 4 ft/s

The length of the string L = 150 feet

The formula for the sine angle is:

sin ( θ ) = 75/150

sin ( θ ) = 1/2

The horizontal displacement (x) is calculated using the following tangent ratio:

tan θ = 75/x

1 / tanθ = x/75

cot θ = x/75

Differentiating the above equation with respect to t.

- csc² ( θ ) × dθ/dt  = 1/75 × dx/dt

Substituting the values in the equation,

- csc² ( θ ) × dθ/dt  = 1/75 × 4

- csc² ( θ ) × dθ/dt = 4/75

Now,

csc θ = 1/sin θ = 2

So,

- 2² × dθ/dt = 4/75

dθ/dt = - 1/75

dθ/dt = 0.0133

Hence, the angle is decreasing at a rate of 0.0133 radians per second.

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