(7) What is the value of the series 3 F? Justify your (n + 1)2+1 answer. n=0

Answer:

round 3.62to the nearest kilogram

Step-by-step explanation:

Answer: The number is 38

Step-by-step explanation:

Answer:

To simplify this expression, you can divide the numbers and subtract the exponents:

9 x 10^11 / 1.5 x 10^7 = 6 x 10^(11-7) = 6 x 10^4

In scientific notation: 6 x 10^4

In standard notation: 60,000

Answer:

a

Step-by-step explanation:

A) The probability that the sample mean is within $500 of the population mean for a sample of size 60 is 0.6611

B) The probability that the sample mean is within $500 of the population mean for a sample of size 120 is 0.7362

The EAI (Error of the Estimate) sampling problem is a specific case of the Central Limit Theorem, which states that the distribution of sample means from a population with a finite variance will be approximately normally distributed as the sample size increases.

The formula for calculating the standard error of the mean is

SE = σ/√n

where SE is the standard error, σ is the population standard deviation, and n is the sample size.

For n = 30, SE = 4,000/√30 = 729.16

A. For a sample size of n = 60, SE = 4,000/√60 = 516.40

To find the probability that the sample mean is within $500 of the population mean, we need to calculate the z-score for a range of +/- $500

z = (x - μ) / SE

where x is the sample mean, μ is the population mean, and SE is the standard error.

For a range of +/- $500, the z-scores are

z = ($51,300 - $51,800) / 516.40 = -0.969

z = ($52,300 - $51,800) / 516.40 = 0.969

Using a standard normal distribution table, the area between z = -0.969 and z = 0.969 is 0.6611.

B. For a sample size of n = 120, SE = 4,000/√120 = 368.93

Following the same steps as above, the z-scores for a range of +/- $500 are

z = ($51,300 - $51,800) / 368.93 = -1.364

z = ($52,300 - $51,800) / 368.93 = 1.364

Using the standard normal distribution table, the area between z = -1.364 and z = 1.364 is 0.7362.

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Answer:

y-intercept = 20

y = 5x + 20

Step-by-step explanation:

Slope: 5

Point: (2,30)

y-intercept: 30 - (5)(2) = 30 - 10 = 20

Answer:

second table

Step-by-step explanation:

Out of the 8 options on the spinner, 2 of them are 0's, 1 of them is a 1, 2 of them are 2's and 3 of them are 3's so the probability of spinning a 0, 1, 2 or 3 is 2/8, 1/8, 2/8 or 3/8 which becomes 0.25, 0.125, 0.25 or 0.375 respectively. Therefore, the answer is the second table.

the probability that the sample mean would differ from the population mean by less than 2 gallons is approximately 0.9793, rounded to four decimal places.

The Central Limit Theorem,

The sample mean of a sufficiently large sample (n > 30) will be normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Here, we have a population with a mean of \(\mu = 103\) gallons and a variance of\(\sigma^2 = 36 gallons^2.\)

Therefore, the standard deviation of the population is \(\sigma = \sqrt(36) = 6\)gallons.

The probability that the sample mean would differ from the population mean by less than 2 gallons.

In other words, we want to find the probability that the difference between the sample mean and the population mean is less than 2 gallons.

We can use the formula for the standard error of the mean to find the standard deviation of the sampling distribution of the sample mean:

\(SE = \sigma / sqrt(n)\)

where n is the sample size. In this case, n = 38, so we have:

\(SE = 6 / \sqrt(38) = 0.979\)

The difference between the sample mean and the population mean is given by:

\(\bar X - \mu\)

The probability that this difference is less than 2 gallons. We can standardize this difference by dividing by the standard error of the mean:

\(Z = (\bar X - \mu) / SE\)

A standard normal distribution table or calculator to find the probability that Z is less than \(2 / 0.979 = 2.04.\)This probability is approximately 0.9793.

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The probability that the sample mean would differ from the population mean by less than 2 gallons is approximately 0.9544 or 95.44% (rounded to four decimal places).

To solve this problem, we can use the Central Limit Theorem which states that the sample mean of a large enough sample will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Given that the mean of gas consumption per race is 103 gallons and the variance is 36, we can calculate the standard deviation as follows:

Standard deviation = \(\sqrt{36}\) = 6 gallons

Now, we need to find the probability that the sample mean would differ from the population mean by less than 2 gallons. We can calculate the standard error of the mean as follows:

Standard error of the mean = standard deviation / sqrt(sample size) = 6 / \(\sqrt{38}\)= 0.974

To find the probability, we can use the z-score formula:

z = (sample mean - population mean) / standard error of the mean

z = (sample mean - 103) / 0.974

Since we want to find the probability that the sample mean would differ from the population mean by less than 2 gallons, we need to find the probability that the z-score is between -2 and 2.

Using a standard normal distribution table or calculator, we can find that the probability of a z-score being between -2 and 2 is approximately 0.9544.

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Answer:

5.y=5x-10+5x+1

y=10x-9

6.y=2x+12+2x+6

  y=4x+18

7.y=-2x-8-2x+10

 y=-4x+2

8.y=-4x-8-4x-12

  y=-8x-20

ANSWER

7x + y = -19 Option A

EXPLANATION

Step 1:

y = mx + c where,

m = slope = -7,

y = -5,

x = -2 and

c = intercept = ?

-5 = -7(-2) +c

-5 = 14 + c

-5 - 14 = c

c = -19

Step 2: Insert the value of c

y = -7x - 19

add -7x to both sides

y + 7x = -7x - 19 + 7x

7x + y = - 19

The Solomon four-group design includes two control groups: one that is not pretested and does not receive treatment, and another that is not pretested but receives treatment.

In the Solomon four-group design, there are two treatment groups and two control groups. The purpose of this design is to examine the interaction effect between pretesting and treatment.

The first control group does not receive any treatment, while the second control group also does not receive treatment but is pretested. These two control groups help to measure the impact of pretesting on the dependent variable.

The two treatment groups receive the treatment being studied, with one group being pretested and the other group not being pretested. By comparing the pretested and non-pretested treatment groups, researchers can determine if there is an interaction effect between pretesting and the treatment.

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Answer:

plot the point (0,10), and then from that point, plot the point that it 7 points up and 1 point to the right, plot that, and repeat

Step-by-step explanation:

Answer:

I graphed the line for you

Step-by-step explanation:

Step-by-step explanation:

In Fraction

= 3 2/8 + 2 3/4

= (3 + 2) + (1/4 + 3/4)

= 5 + 4/4

= 5 + 1

= 6

In Decimals

= 3 2/8 + 2 3/4

= 3,25 + 2,75

= (3 + 2) + (0,25 + 0,75)

= 5 + 1,00

= 5 + 1

= 6

a) the odds against the team winning its next match are 8/19.

b) the probability of winning a new TV is 3/16.

(a) To find the odds against the rugby team winning its next match, we can use the probability of the team winning. The odds against an event are calculated by subtracting the probability of the event from 1 and expressing it as a ratio.

Probability of the team winning = 11/19

Odds against the team winning = 1 - (11/19) = 8/19

Therefore, the odds against the team winning its next match are 8/19.

(b) To find the probability of winning a new TV, we can use the given odds in favor of winning. The odds in favor of an event can be expressed as a ratio of favorable outcomes to total outcomes.

Odds in favor of winning a new TV = 3/13

Probability of winning a new TV = favorable outcomes / total outcomes

Probability of winning a new TV = 3 / (3 + 13) = 3/16

Therefore, the probability of winning a new TV is 3/16.

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The equation of line passes through the points (- 9, 6) and (- 7, -8) will be;

⇒ y = - 7x - 57

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (- 9, 6) and (- 7, -8)

Now,

Since, The equation of line passes through the points (- 9, 6) and (- 7, -8)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 8 - 6) / (- 7 - (-9))

m = - 14 / 2

m = - 7

Thus, The equation of line with slope - 7 is,

⇒ y - 6 = - 7 (x - (-9))

⇒ y - 6 = - 7 (x + 9)

⇒ y - 6 = - 7x - 63

⇒ y = - 7x - 63 + 6

⇒ y = - 7x - 57

Therefore, The equation of line passes through the points ((- 9, 6) and

(- 7, -8)  will be;

⇒ y = - 7x - 57

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A philosophy professor assigns letter grades on a test according to the following scheme is A score that falls within the top 12% of all scores on the test would receive an A grade. A.

The grading scheme for the philosophy professor is:

A: Top 12% of scores

B: Scores below the top 12% and above the bottom 58%

C: Scores below the top 42% and above the bottom 25%

D: Scores below the top 75% and above the bottom 8%

F: Bottom 8% of scores

To clarify, the percentages given in the scheme are used to determine the cutoffs for each letter grade.

A score that falls within the top 12% of all scores on the test would receive an A grade.

It is important to note that the percentages given in the grading scheme are not fixed values, but rather are dependent on the distribution of scores on the test.

For instance, if the scores on the test were very tightly clustered together, it is possible that the cutoff for an A grade might be higher than the top 12%.

This grading scheme rewards students who perform well on the test while still allowing for some degree of variation in scores.

Students perform poorly relative to their peers may receive a lower letter grade but are still given the opportunity to learn and improve in future assignments.

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Answer: B. It was a completely new and different plan.

Step-by-step explanation:

The angular area of the HST's field of view is 25 square degrees.

The field of view is the extent of the sky that the Hubble Space Telescope (HST) can observe at a given time. It is usually measured in degrees.

To calculate the angular area, we can use the formula for the area of a circle:

Area = π * (angular size/2)^2

Where π is a mathematical constant approximately equal to 3.14, and the angular size is in degrees.

Let's say the angular size of the HST's field of view is 10 degrees.

First, we divide the angular size by 2:

10 degrees / 2 = 5 degrees

Next, we square the result:

5 degrees * 5 degrees = 25 square degrees

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I believe it is the bookshelf one

Answer:

2nd option

Step-by-step explanation:

If AB  is a tangent to the circle then ∠ B is right angle

Using the converse of Pythagoras' identity.

If the square of the longest side is equal to the sum of the squares on the other 2 sides, then the triangle is right

longest side = 52 and 52² = 2704

48² + (10 + 10)² = 48² + 20² = 2304 + 400 = 2704

Then AB  is a tangent to the circle since ∠ B is a right angle

The length of the line is approximately 5 people.

To find the length of the line given the arrival rate, service rate, and average waiting time, you can use the following formula:

Length of the line = (Arrival rate × Average waiting time) + (Arrival rate / Service rate)

First, convert the average waiting time from minutes to hours:

24 minutes = 24/60 = 0.4 hours

Now, plug in the given values into the formula:

Length of the line = (9 arrivals/hour × 0.4 hours) + (9 arrivals/hour / 14 services/hour)

Length of the line = (3.6 arrivals) + (0.6429 arrivals)

Length of the line ≈ 4.24 arrivals

Since you can't have a fraction of a person in the line, round up to the nearest whole number:

Length of the line ≈ 5 arrivals

So, the length of the line is approximately 5 people.

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149 because

3(-7)^2+2 =149

Answer:

33 miles

Step-by-step explanation: I think it is correct

Monday: 3 miles

Tuesday: 10 miles

Wednesday: 20 miles because 10 x 2 = 20

3 miles + 10 miles + 20 miles = 33 miles

Hope this helps!

Answer:

Value of f is $ 12.44

Step-by-step explanation:

Steps :

    f - $ 3.83 = $ 8.61

         f = $ 8.61 + $3.83

         f = $ 12.44

We can use the initial condition y(0) = -3 to solve for the constant C. Plugging in t = 0 and y = -3 into the above equation.

To solve the given differential equation, we can use the method of integrating factor.

The given differential equation is: dy/dt - 2ty = \(12t^2\times e^(t^2)\)

First, we identify the integrating factor (IF), which is given by the exponential of the integral of the coefficient of y. In this case, the coefficient of y is -2t, so we integrate -2t with respect to t:

IF = e^∫(-2t)dt

IF = e^(-t^2)

Next, we multiply the entire differential equation by the integrating factor:

\(e^(-t^2)\times (dy/dt - 2ty) = e^(-t^2) \times 12t^2\times e^(t^2)\)

This simplifies to:

\(e^(-t^2) \times dy/dt - 2ty \times e^(-t^2) = 12t^2\)

Now, we can integrate both sides of the equation with respect to t. Integrating the left-hand side (LHS) requires integration by parts, while the right-hand side (RHS) can be integrated directly:

∫(e^(-\(t^2\)) \(\times\) dy/dt) dt - ∫(2ty \(\times\) e^(-\(t^2\))) dt = ∫(12\(t^2\)) dt

Using integration by parts on the LHS with u = e^(-\(t^2\)) and dv = dy/dt dt, we get:

e^(-\(t^2\)) \(\times\)y - ∫(e^(-\(t^2\)) \(\times\) y') dt - ∫(2ty \(\times\) e^(-\(t^2\))) dt = 12\(t^3\) / 3 + C

where C is the constant of integration.

Rearranging the equation and simplifying, we get:

e^(-\(t^2\)) \(\times\) y - ∫(e^(-\(t^2\)) \(\times\) y') dt - 2∫(ty \(\times\) e^(-\(t^2\))) dt = 4\(t^3\) + C

Now, we can integrate the remaining integrals. For the second term on the left-hand side, we use u = t and dv = y \(\times\) e^(-\(t^2\)) dt, and for the third term on the left-hand side, we use u = y and dv = t \(\times\) e^(-\(t^2\)) dt. This gives us:

e^(-\(t^2\)) \(\times\) y - (y \(\times\) e^(-\(t^2\))) - (e^(-\(t^2\))\(\times\) t \(\times\) y) = 4\(t^3\) + C

Combining like terms and multiplying both sides by e^(t^2) to eliminate the exponential factor, we get:

y - y \(\times\) e^(-\(t^2\)) - t \(\times\) y = 4\(t^3\) \(\times\) e^(\(t^2\)) + C \(\times\) e^(\(t^2\))

Factoring out y on the left-hand side and simplifying, we get:

y \(\times\) (1 - e^(-\(t^2\)) - t) = 4t^3 \(\times\)e^(\(t^2\)) + C \(\times\)e^(\(t^2\))

Finally, dividing both sides by (1 - e^(-\(t^2\)) - t) to isolate y, we get:

y(t) = (4\(t^3\) \(\times\) e^(\(t^2\)) + C \(\times\) e^(\(t^2\))) / (1 - e^(-\(t^2\)) - t)

Now, we can use the initial condition y(0) = -3 to solve for the constant C. Plugging in t = 0 and y = -3 into the above equation.

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A conservative worst-case scenario sample size for a poll measuring the proportion of citizens holding a political belief with a margin of error of 2.3%, a confidence level of 95% would be approximately 1049.

The sample size required for a poll depends on several factors, such as the population size, the level of confidence desired, and the margin of error tolerated.

In the case of a simple poll measuring the proportion of citizens holding a particular political belief, the worst-case scenario sample size would be the largest possible sample size required to achieve the desired margin of error.

To determine the worst-case scenario sample size, we need to use a formula for calculating the sample size, which takes into account the population size, the level of confidence desired, and the margin of error tolerated.

One such formula is:

Sample size = [(Z-score)^2 * p * (1 - p)] / (margin of error)^2

Where:

Z-score represents the level of confidence desired, which is typically 1.96 for a 95% confidence level.

p represents the proportion of citizens holding the particular political belief we are measuring.

(1 - p) represents the proportion of citizens not holding the particular political belief we are measuring.

Assuming a worst-case scenario where p = 0.5, meaning that we have no prior knowledge about the proportion of citizens holding the political belief, and using a margin of error of 2.3% and a confidence level of 95%, the sample size required would be:

Sample size = [(1.96)^2 * 0.5 * (1 - 0.5)] / (0.023)^2 ≈ 1049

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The equivalent expressions to 5x + 30x - 15x are given as follows:

A) 5x(1 + 6 - 3).

B) 5(x + 6x - 3x).

C) (5 + 30 - 15)x.

Equivalent expressions are expressions that have the same result when they are simplified as much as possible.

The expression for this problem is given as follows:

5x + 30x - 15x

Combining the like terms, the result is given as follows:

35x - 15x = 20x.

Hence the equivalent expressions are given as follows:

A) 5x(1 + 6 - 3) = 5x + 30x - 15x = 20x.

B) 5(x + 6x - 3x) = 5x + 30x - 15x = 20x.

C) (5 + 30 - 15)x = 5x + 30x - 15x = 20x.

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The main function is given by:

f (x) = sine (x)

We then have the following transformations:

Reflections:

Reflection or turning is the mirror image of a figure. It can also be said that it is the turning of points and graphs around the axes.

To graph y = -f (x), reflect the graph of y = f (x) on the x-axis. (Vertical reflection)

f (x) = - sine (x)

Expansions and vertical compressions:

To graph y = a*f (x)

If a> 1, the graph of y = f (x) is expanded vertically by a factor a.

f (x) = - 2 * sine (x)

Vertical translations

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

f (x) = - 2 * sine (x) + 3

Answer:

C. reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up

The set of transformations which is needed to graph f(x) = –2sin(x) + 3 is reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up, the correct option is C.

A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).

We are given that;

The function= f(x) = –2sin(x) + 3

Now,

To graph f(x) = –2sin(x) + 3 from the parent sine function y = sin(x), we need to apply the following transformations:

A reflection across the x-axis, because of the negative sign in front of the 2.

A vertical stretching by a factor of 2, because of the absolute value of the coefficient of sin(x), which is 2.

A vertical translation 3 units up, because of the constant term 3.

Therefore, by transformations answer will be Reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up.

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Jessica has three dice with 10 sides, 13 sides and 5 sides respectively and she rolls all dice once and if Z is number of ones occur then

The expectation value i.e, E(Z) is 0.376 and variance V[Z] = 0.321..

Indicator method :

This is a powerful way to find expected counts. This follows from the observation that the number of "good" outcomes in a trial can be counted by first coding each "good" outcome as one, coding each other outcome as zero, and then adding 1 and 0.

let X₁ be the outcome of a 10 sided die

X₂ be the outcome of 13 sided die

X₃ be the outcome of 5 sided die

let l₁ ,I₂ ,I₃ be three indicator functions such that

I₁ =1 if X₁ = 1

=0 otherwise

I₂ = 1 if X₂ = 1

=0 otherwise

I₃ = 1 if X₃ = 1

=0 otherwise

so Z denotes the number of ones showing when the three dice are rolled once.

so Z=I₁ +I₂ +I₃

so E[Z]=E[I₁]+E[I₂]+E[I₃]

so E[I₁]=1×P[X₁=1] = 1/10

E[I₂]=1×P[X₂=1] = 1/13

E[I₃]=1×P[X₃=1] = 1/5

so, E[Z]=1/10+1/13+1/5=49/130 = 0.3769

the variance = V[Z] = V[I₁]+V[I₂]+V[I₃] since the outcomes of the 3 different die are independent to each other hence no covariance term.

V[I₁]= 1²P[X₁=1]- E²[I₁]=1/10 -(1/10)²= 0.09

V[I₂]= 1²P[X₂=1]- E²[I₂]=1/13-(1/13)²= 12/169 = 0.071

V[I₃]= 1²P[X₃=1]- E²[I₃]=1/5 -(1/5)²= 4/25 = 0.16

so V[Z]= 0.09 + 0.071 + 0.16 = 0.321

Hence, the expectation value i.e, E(Z) is 0.3769..

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