Find a formula for the nth term in
this arithmetic sequence:
a1 = 28, 22 = 21, a3 = 14, 24 = 7, ...
an = -7n + [?]

The normal approximation is used to estimate probabilities in a medication study for weight gain as a side effect, providing insights into specific outcomes.

To approximate the probabilities using the normal approximation to the binomial, we need to know the success probability (percent of patients gaining weight) and the number of patients involved in the study. Let's denote the success probability as p and the number of patients as n.

(a) To calculate the probability that exactly k patients will gain weight, we can use the formula for the binomial distribution:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

However, since we are using the normal approximation, we can approximate it as:

P(X = k) ≈ P(k - 0.5 < X < k + 0.5)

(b) To calculate the probability that no more than k patients will gain weight, we can sum the probabilities from 0 to k:

P(X ≤ k) ≈ P(0.5 < X < k + 0.5)

(c) To calculate the probability that at least k patients will gain weight, we can subtract the probability of the complement event (less than k patients) from 1:

P(X ≥ k) ≈ 1 - P(X < k + 0.5)

These approximations rely on the assumption that n is sufficiently large and that p is not too close to 0 or 1. The result suggests that we can estimate the probabilities of specific outcomes in the medication study using the normal distribution, providing an approximate understanding of the likelihood of different scenarios.

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9514 1404 393

Answer:

  (a) 6² +3² +1² +1² = 47

  (b) 5² +4² +2² +1² +1² = 47

  (c) 3³ +4² +2² = 47

Step-by-step explanation:

It can work reasonably well to start with the largest square less than the target number, repeating that approach for the remaining differences. When more squares than necessary are asked for, then the first square chosen may need to be the square of a number 1 less than the largest possible.

The approach where a cube is required can work the same way.

(a) floor(√47) = 6; floor(√(47 -6^2)) = 3; floor(√(47 -45)) = 1; floor(√(47-46)) = 1

__

(b) floor(√47 -1) = 5; floor(√(47-25)) = 4; ...

__

(c) floor(∛47) = 3; floor(√(47 -27)) = 4; floor(√(47 -43)) = 2

Answer:

Right rectangular prism

Solve for surface area

A=94

l Length  3

w Width  5

h Height  4

Step-by-step explanation:

''.''

Answer:

where can i buy that pan with lasanga

Answer:

1. y=3x-2 -> x= (y+2)/3

Step-by-step explanation:

You simply sub-in the m and b, then "reverse" the problem by doing the steps to get from the 2nd, to the first.

Answer:

Step-by-step explanation:

1.y=3x-2

2.y=2/5x+2

3.y=-1/2x+4

4.y=-4x+3

5.y=5x+18

8.y=-3/2+1

you didn't include 6 & 7 that's why i skipped them

hope this helped :)

Answer: y= 3/2x - 6

Step-by-step explanation:

The equation is y=mx + b

The y-intercept is when x = 0, so on the table y-intercept = -6

The slope is rise/run, we see that y increase by three and x increase by 2, so the slope is 3/2

to get the slope of any straight line, we simply need two points off of it, let's use those ones in the picture below.

\((\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}} \implies \cfrac{3 +3}{4} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 } \end{array}}\)

now, the y-intercept occurs when x = 0, recheck the picture below.

Once we have categorized an object, our memory of the object increasingly resembles the category is B) prototype. This means that when we categorize an object, our memory of it begins to resemble the prototype or typical example of that category. For example, if we categorize a bird as a robin, our memory of the bird will increasingly resemble the characteristics of a typical robin.

This happens because our brain uses prototypes as a shortcut to process information and make sense of the world around us. We use prototypes to quickly identify objects and make assumptions about their characteristics based on their category.

our memory of an object after categorization is influenced by the prototype of the category. This helps us to quickly process and make sense of information, but it can also lead to errors and biases in our thinking.


A prototype is a mental image or best example of a category. When we categorize an object, our memory of the object increasingly resembles the prototype because we tend to recall the most representative or typical example of the category.

Once we categorize an object, our memory of the object becomes more like the prototype, which is the best example of the category. This is because we tend to remember the most representative or typical examples of a category.

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The single biggest factor accounting for how people decide to vote is difficult to pinpoint with certainty as it can vary depending on the individual and the specific election.

The single biggest factor accounting for how people decide to vote is often considered to be their "party identification." Party identification refers to the political party that an individual feels a strong affiliation with, and it plays a significant role in shaping their voting choices.

People typically vote for candidates from the party they identify with, as they believe that party best represents their values and interests.

However, research suggests that factors such as political party affiliation, candidate's perceived competence and charisma, their stance on important issues, and their past track record can all play a significant role in how people decide to vote.

                              Additionally, external factors such as media coverage and political advertisements can also influence voter decisions. Ultimately, the decision to vote is complex and multifaceted, and can be influenced by a variety of factors.

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Answer:

d = 13

Step-by-step explanation:

First, the distance formula is needed:

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

Next we assign the points

(2,-4) is point 1, (7,8) is point 2

\(d = \sqrt{(7 - 2 )^{2} +(8 - (-4))^{2} } \\d = \sqrt{5^{2} +12^{2} } \\d = \sqrt{25 + 144}\\ d = \sqrt{169} \\d = 13\)

Given two points (2,-4) and (7,8)

To find - The distance between given points.

We know the formula that is used to find the distance is given as

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

We let P = (2,-4)

and Q = (7,8)

\(x_1=2, y_1=-4\\x_2=7,y_2=8\)

on substituting we get

\(d=\sqrt{(7-2)^2+(8+4)^2}\\ d=\sqrt{(5)^2+(12)^2} \\d=\sqrt{25+144} \\d=\sqrt{169}\\ d=13\)

Hence we get the distance between (2,-4) and (7,8) is 13.

Final answer - The distance is 13.

Answer:  A. 0 to 100 per hour

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

Explanation:

The phrasing "Depends on its speed" tells us that the speed is the independent variable, and therefore it's the x variable.

The domain is the set of allowed x values of a function, or allowed inputs. In this case, it appears the car's max speed is 100 mph.

Answer:

0 to 100 miles per hour

Answer:

Options A and C and F are correct.

Step-by-step explanation:

5(2+4)

5*2+5*4

5*6

Have a great day! :)

and can I please have brainliest?

Thanks!

Answer: Your answers would be 5(2+4), 5x2+5x4, and 5x6

Hope this helps you!

Imagine that a survey of randomly selected people finds that people who used sunscreen were more likely to have been sunburned in the past year.

There are several possible explanations for the finding that people who used sunscreen were more likely to have been sunburned in the past year.

However, without additional context or data, it is difficult to determine the most likely explanation definitively. Here are a few possible explanations to consider:

1. Ineffective or improper use of sunscreen: It is possible that the individuals who reported using sunscreen did not apply it correctly or did not reapply it as recommended.

Inadequate application or failure to follow proper sunscreen usage guidelines could result in insufficient protection from the sun's harmful rays, leading to sunburn.

2. Self-selection bias: It is possible that individuals who have previously experienced sunburns may be more likely to use sunscreen. They may be more aware of the potential risks and take precautions, including using sunscreen.

This could create an association between sunscreen use and sunburn, even though sunscreen itself is intended to prevent sunburn.

3. Recall bias: The survey responses may be subject to recall bias, where individuals may inaccurately remember or report their sunscreen use and sunburn experiences.

Memory limitations or subjective perceptions of sunburn severity could influence the reported data and the observed association between sunscreen use and sunburn.

4. Confounding factors: There may be other factors or variables at play that are related to both sunscreen use and sunburn. For example, individuals who engage in activities that increase sun exposure or who have certain skin types may be more likely to both use sunscreen and experience sunburn.

It is important to note that further investigation, including more detailed surveys, data collection and statistical analysis, would be necessary to determine the most likely explanation for the observed association between sunscreen use and sunburn.

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By using the inverse matrices we get the matrix as

(AB)⁻¹ =\(\left[\begin{array}{ccc}-1&-4\\3&11\end{array}\right]\)

A⁻¹= \(\left[\begin{array}{ccc}1&1\\2&3\end{array}\right]\)

2A⁻¹ = \(\left[\begin{array}{ccc}1/2&1\\1/2&3/2\end{array}\right]\)

Given that,

We have to use inverse matrices to find (ab)⁻¹, (a)⁻¹ and (2a)⁻¹.

The matrix A⁻¹=\(\left[\begin{array}{ccc}1&2\\1&3\end{array}\right]\) and B⁻¹ =\(\left[\begin{array}{ccc}1&-2\\-2&5\end{array}\right]\)

We know that,

The arrangement of numbers, variables, symbols, or phrases in a rectangular table with different numbers of rows and columns is called a matrix, which is also known as a matrix plural. They are rectangular arrays that are defined to do several operations, including addition, multiplication, and transposition.

(AB)⁻¹ = B⁻¹A⁻¹

=\(\left[\begin{array}{ccc}1&-2\\-2&5\end{array}\right]\\\) \(\left[\begin{array}{ccc}1&2\\1&3\end{array}\right]\)

=\(\left[\begin{array}{ccc}-1&-4\\3&11\end{array}\right]\)

A⁻¹= \(\left[\begin{array}{ccc}1&1\\2&3\end{array}\right]\)

2A⁻¹ = 1/2\(\left[\begin{array}{ccc}1&2\\1&3\end{array}\right]\) = \(\left[\begin{array}{ccc}1/2&1\\1/2&3/2\end{array}\right]\)

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Answer:  C

Step-by-step explanation:

400 multiply by 2 equals 800

and then 800 subtracted by 400 will be 400

and 400 subtracted by 1 will be 399.

Therefore, answer is C

The relationship between the distance S and time t is:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2.

Let the velocity and acceleration of the first car be v1 and a1 respectively.The velocity of the second car be v2 and acceleration be a2.Let the distance between the two cars at any time after t=0 be given by S.If the initial distance between them is 50 feet, then S=S0+50ft where S0 is the distance between them at time t=0.

From the given conditions, we can set up the following relationships for the two cars.1) For the first car:S=ut+(1/2)at^2 where u is the initial velocity.

2) For the second car:S=vt+(1/2)at^2 where v is the initial velocity.In the first equation, we can substitute u=0 (since it started from rest) and a=a1.

In the second equation, we can substitute v=50ft (since it is 50ft behind) and a=a2.

Substituting the above values in the above two equations, we get:S= (1/2)a1t^2 and

S= 50ft + v2t + (1/2)a2t^2

From the problem statement, we are also given that the lead car is accelerating in such a way that the distance S in feet between the two cars at any time t after t=0 seconds is 50 more than twice the square of t.

Therefore,S = 2t^2 + 50ft

We can now equate the above two expressions for S, and solve for t, to get the relationship between the distance S and time t:

S = 2t^2 + 50ft = (1/2)a1t^2 + 50ft + v2t + (1/2)a2t^2

Simplifying the above expression, we get:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2

Therefore, the relationship between the distance S and time t is:2t^2 = (1/2)a1t^2 + v2t + (1/2)a2t^2.

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The magnitude of the impulse needed to bring the brick to rest is given by the initial momentum of the brick.

The correct responses are;

Reasons:

The velocity of the brick as it reaches the ground is given by the formula;

v² = 2·g·h

v = √(2·g·h)

Where;

h = The height of the brick, h = 1.6 m

g = The acceleration due to gravity ≈ 9.81 m/s²

Therefore;

v ≈ √(2 × 9.81 m/s² × 1.6 m) ≈ 5.6 m/s

(a) Momentum = Mass × Velocity

The momentum of the brick = 5.6 m/s × 8 kg = 44.8 kg·m/s

(b) Impulse = Force × Δt = Mass × Δv

Mass × Δv = 8 kg × (5.6 m/s - 0) = 44.8 kg·m/s = 44.8 N·s

Therefore, the impulse = 44.8 N·s

(c) The distance over which the carpet stops the brick = 2.0 cm = 0.02 m

Initial energy in the brick, E = m·g·h

Which gives;

E = 8 kg × 9.81 m/s² × 1.6 m = 125.568 J

Energy = Force × Distance

\(\displaystyle Force \ carpet \ exerts \ on \ brick, \ F = \frac{125.568 \, J}{0.02 \, m} = \mathbf{ 6,278.4 \, N}\)

The average force the carpet exerts, F = 6,278.4 N

(d) If the brick falls on a foam which is 6.0 cm (thickness), we have;

Distance = 6.0 cm = 0.06 m

Therefore;

\(\displaystyle Force, \, F = \frac{125.568 \, J}{0.06 \, m} = \mathbf{2,092.8 \, N}\)

The constant force needed to bring the brick to rest is, F ≈ 2,092.8 N

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The total amount that a customer will pay for the jeans is $33.696.

From the information given, pair of jeans at a local retail store has a cost of $32.00. If the sales tax is 5.3%,

The value of the sales tax will be:

= Sales percentage × Amount

= 5.3% × $32

= $1.696

The total amount paid will be:

= Cost + Tax

= $32 + $1.696

= $33.696

The amount is $33.696.

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The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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Answer:

y = 2x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (2, 2)

m = \(\frac{2+2}{2-0}\) = \(\frac{4}{2}\) = 2

The line crosses the y- axis at (0, - 2) ⇒ c = - 2

y = 2x - 2 ← equation of line

The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.

The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.

It is calculated simply by dividing the standard deviation by the square root of the sample size. That is \(SE = \frac{σ }{\sqrt{n}}\)

where , n --> sample size

σ --> population standard deviations

Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.

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Complete question:

standard error of an estimator is not affected by the multiple choice question.

a) population standard deviation

b) sample size

c) population size

Answer:

Option A

Step-by-step explanation:

Expression: y = 12h

If h = 15, then:

y = 12(15)

y =  $180

Option A

the solution of the given differential equation is:y = [16 ln |x| + 8x2 + C1]1/16

The given differential equation is y15 x dy/dx = 1 + x. Now, we will solve the given differential equation.

The given differential equation is y15 x dy/dx = 1 + x. Let's bring all y terms to the left and all x terms to the right. We will then have:

y15 dy = (1 + x) dx/x

Integrating both sides, we get:(1/16)y16 = ln |x| + (x/2)2 + C

where C is the arbitrary constant. Multiplying both sides by 16, we get:y16 = 16 ln |x| + 8x2 + C1where C1 = 16C.

Hence, the solution of the given differential equation is:y = [16 ln |x| + 8x2 + C1]1/16

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Each side of cube is 100 cm.

In Maths or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedron.

Given that,

Volume of cube = 1 cubic meter

We know that,

1 m = 100 cm

Also  volume of cube = \(a^{3}\)

Then,

Volume of cube = 1000000 cm

                   \(a^{3}\)  = \(100^{3}\)

                   a = 100 cm

Hence, Each side of cube is 100 cm.

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The value of the function f(x)=6/-2+2\(e^{-0.3x}\) at x=4 after rounded to the nearest tenth is -2.4.

Given Function of x : f(x)=6/-2+2\(e^{-0.3x}\)

The given function showing the relationship between x and f(x) is f(x)=6/-2+2\(e^{-0.3x}\) where e is exponential and we have to find the value of f(4) by just putting the value of x=4 in the given function and round to the nearest tenth means replacing a number with an approximate value.

f(4)=6/-2+2\(e^{-0.3*4}\)   ( The value of e is 2.7812)

f(4)=-3+2\(e^{-1.2}\)                    

f(4)=-3+2*0.30119   (The value of \(e^{-1.2}\) is 0.30119)          

f(4)=-3+0.60238

f(4)=-2.3972

Round -2.3972 to tenth is -2.4.

Hence the value of function of at x=4 is -2.4.

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The value of f(4) is -4.3.

The function is a relation between two different sets X and set Y which are in one-one or many-one relation. Here set X is called as the domain and set Y is called as the codomain.

For example: f(x)=3x+9

To get the value of the function at any point of x, we have to put the number in the function to get its function value.

For example the value of f(x) in above function at x=a will be f(a)=3a+9

Similarly given function in the question

\(f(x)=\frac{6}{-2+2e^{-0.3x}}\)

to get the value of f(x) at x=4 put the value of x in the function,

\(f(x)=\frac{6}{-2+2e^{-0.3*4}}\)

⇒\(f(x)=\frac{6}{-2+2e^{-1.2}}\)

⇒f(x)=-4.3

Therefore the value of f(4) is -4.3.

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a) Consider the experiment of picking 3 tax returns at random as 3 related experiments (due to the fact that it is without replacement); then, as for the first time one selects a tax return,

As for the second time we grab a tax return, there are 69 tax returns in total and 9 of them contain errors; thus,

Similarly, as for the third picking round,

Finally, the probability of experiment a) is

Rounded to one decimal place, the probability of event a) is 65.7%

b) Similarly, in the event of all three tax returns containing errors,

Thus,

The probability of event b) is 0.2%. It is quite unusual.

c) The condition 'at least one of those containing errors' includes the cases when 1, 2, or 3 tax returns of the ones selected have errors. Notice that

Therefore,

And we found the probability of picking 3 tax returns without any errors in part a); thus,

The probability of event c) is 34.3%.

d) Analogously to part c), the probability of selecting at least one without errors is

The probability of event d) is 99.8%, and it is not improbable at all.

Answer:

3:7

Step-by-step explanation:

3 parts of lemonade to 7 parts punch

Answer:

$13,724

Step-by-step explanation:

From the above question, we are given the following values:

Principal = P = $12,000

Interest = r = 2.25% = 0.0225

Compounded semi annually = n = 2

Time (t) = 6 years

From the question, we understand that we are to find the total (full) Amount Karen withdrew.

The formula to use to calculate the Total Amount of money given that this is a compound interest question is:

Total(full) Amount = P( 1 + r/n) ^n/t

= $12,000( 1 + 0.0225/2) ^2×6

= $12,000(1.01125)^12

= $13724.093289

Approximately to the nearest cent

≈ $13,724

Therefore, Karen withdrew $13,724 from the account.

Karen Gaines invested $14000 in a money market account with an interest rate of 2.75% compounded semiannually. Six years later, Karen withdrew the full amount to put toward the down payment

Round to the nearest cent as needed.)

Answer:

28

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

BD is the perpendicular bisector of AC (AB = BC, and ∠CBD = 90°).

Therefore, by side-angle-side congruence (SAS), ΔABD and ΔCBD are congruent.

So AD = CD = 32.

For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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