is 2.281 a rational number

Answers

Answer 1

Answer:

no i dont think it is

Step-by-step explanation:

Answer 2
Yes it is a rational number because it can be written in the form p/q which is 2281/1000.

Related Questions

Solve. x+y+z=6 3x−2y+2z=2−2x−y+3z=−4

Answers

Answer:

-4?

hope dis helps ^-^

pls help me asap !!!

Answers

Answer:

11

Step-by-step explanation:

Hopefully you can see that this is an isosceles triangle and remembering the inequality theorem of a triangle (4,4,11 triangle cannot exist).  Iso triangle has two side the same length - as well as two angles the same.

can some0ne help me?

Answers

Answer:

(x - 2)/3

(x - 4)/-5 or (-x + 4)/5

Step-by-step explanation:

this is an inverse function, and to solve an inverse function you would :

swap x and g(x) without bringing the x coefficient with it, just simply swap the variables. Then, solve for g(x), and that's it

the first question's answer is :

g(x) = 3x + 2

x = 3(g(x)) + 2

x - 2 = 3(g(x))

(x - 2)/3 = g(x)

the second one is:

g(x) = 4 - 5x

x = 4 - 5(g(x))

x - 4 = -5(g(x))

(x-4)/-5 = g(x)

g(x) = 3x + 2

y = 3x + 2

x = 3y + 2

3y = x - 2

y = x/3 - 2/3

inverse g(x) = (x - 2) / 3

g(x) = 4 - 5x

y = 4 - 5x

x = 4 - 5y

5y = 4 - x

y = 4/5 - x/5

inverse g(x) = (4 - x) / 5

Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print​ lengths, foot​ lengths, and heights of males. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Based on these​ results, does it appear that police can use a shoe print length to estimate the height of a​ male? Use a significance level of α=0.01

Answers

It does not appear that police can use a shoe print length to estimate the height of a​ male.

The given parameters are:

[tex]\begin{array}{cccccc}{Shoe\ Print} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ Height (cm) & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]

Rewrite as:

[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]

See attachment for scatter plot

To determine the correlation coefficient, we extend the table as follows:

[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} & y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} & x^2 & {817.96} & {864.36} & {1036.84} & {1049.76} & {745.29} & y^2 & {29756.25} & {31222.89} & {35494.56} & {28934.01} & {32112.64} & x \times y & {4933.5} & {5194.98} & {6066.48} & {5511.24} & {4892.16} \ \end{array}[/tex]

The correlation coefficient (r) is:

[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]

We have:

[tex]n =5[/tex]

[tex]\sum xy =4933.5+5194.98+6066.48+5511.24+4892.16 =26598.36[/tex]

[tex]\sum x =28.6+29.4+32.2+32.4+27.3=149.9[/tex]

[tex]\sum y =172.5+176.7+188.4+170.1+179.2=886.9[/tex]

[tex]\sum x^2 =817.96+864.36+1036.84+1049.76+745.29=4514.21[/tex]

[tex]\sum y^2 =29756.25+31222.89+35494.56+28934.01+32112.64=157520.35[/tex]

Calculate mean of x and y

[tex]\bar x = \frac{\sum x}{n} = \frac{149.9}{5} = 29.98[/tex]

[tex]\bar y = \frac{\sum y}{n} = \frac{886.9}{5} = 177.38[/tex]

Calculate SSx and SSy

[tex]SS_x = \sum (x - \bar x)^2 =(28.6-29.98)^2 + (29.4-29.98)^2 + (32.2-29.98)^2 + (32.4-29.98)^2 + (27.3-29.98)^2 =20.208[/tex]

[tex]SS_y = \sum (y - \bar x)^2 =(172.5-177.38)^2 + (176.7-177.38)^2 + (188.4-177.38)^2 + (170.1-177.38)^2 + (179.2-177.38)^2 =202.028[/tex]

Calculate [tex]\sum(x - \bar x)(y - \bar y)[/tex]

[tex]\sum(x - \bar x)(y - \bar y) = (28.6-29.98)*(172.5-177.38) + (29.4-29.98)*(176.7-177.38) + (32.2-29.98)*(188.4-177.38) + (32.4-29.98)*(170.1-177.38) + (27.3-29.98) *(179.2-177.38) =9.098[/tex]

So:

[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]

[tex]r = \frac{9.098}{\sqrt{20.208 * 202.028}}[/tex]

[tex]r = \frac{9.098}{\sqrt{4082.581824}}[/tex]

[tex]r = \frac{9.098}{63.90}[/tex]

[tex]r = 0.142[/tex]

Calculate test statistic:

[tex]t = \frac{r}{\sqrt{\frac{1 - r^2}{n-2}}}[/tex]

[tex]t = \frac{0.142}{\sqrt{\frac{1 - 0.142^2}{5-2}}}[/tex]

[tex]t = \frac{0.142}{\sqrt{\frac{0.979836}{3}}}[/tex]

[tex]t = \frac{0.142}{\sqrt{0.326612}}[/tex]

[tex]t = \frac{0.142}{0.5715}[/tex]

[tex]t = 0.248[/tex]

Calculate the degrees of freedom

[tex]df = n - 2 = 5 - 2 = 3[/tex]

The [tex]t_{\alpha/2}[/tex] value at:

[tex]df =3[/tex]

[tex]t = 0.248[/tex]

[tex]\alpha = 0.01[/tex]

The value is:

[tex]t_{0.01/2} = \±5.841[/tex]

This means that we reject the null hypothesis if the t value is not between -5.841 and 5.841

We calculate the t value as:

[tex]t = 0.248[/tex]

[tex]-5.841 < 0.248 < 5.841[/tex]

Hence, we do not reject the null hypothesis because they do not appear to have any correlation.

Read more about regression at:

https://brainly.com/question/18405415

You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten.

Answers

Answer:

[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]

Step-by-step explanation:

There are 52 cards in a standard deck, and there are 4 suits for each card. Therefore there are 4 twos and 4 tens.

At first we have 52 cards to choose from, and we need to get 1 of the 4 twos, therefore the probability is just

[tex]\frac{4}{52}[/tex]

After we've chosen a two, we need to choose one of the 4 tens. But remember that we're now choosing out of a deck of just 51 cards, since one card was removed. Therefore the probability is

[tex]\frac{4}{51}[/tex]

Now to get the total probability we need to multiply the two probabilities together

[tex]\frac{4}{52} \times \frac{4}{51} = \frac{16}{2652} = 0.00603 = 0.603\%[/tex]

a farmer needs 5 men to clear his farm in 10 days. How many men will he need if he must finish clearing the farm in two days if they work at the same rate?

Answers

Answer:

25 workers

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

,

the number of multiples of a given number is infinite ( )​

Answers

Answer:

make an 8 horizontal

oooookkkk

Answer:

TRUE

The number of multiples of a given number is finite is a false statement. The number of multiples of a given number is infinite.

Examples:

Multiples of 2 = 2,4,6,8,10,…..

Multiples of 3 = 3,6,9,12,15,18,…

Multiples of 4 = 4, 8, 12, 16, 120, 24….

∴ The number of multiples of a given number is infinite .

Answer From Gauth Math

hlo anyone free .... im bo r ed

d​

Answers

Step-by-step explanation:

Excuse me! Who r u? where r u frm? tell me tht frst.

Answer:

Oop

Step-by-step explanation:

I’m bored

The PTA sells 100 tickets for a raffle and puts them in a bowl. They will randomly pull out a ticket for the first prize and then another ticket for the second prize. You have 10 tickets and your friend has 10 tickets. What is the probability that your friend wins the first prize and you win the second prize?

Answers

Jÿïôò śfrtÿ hjkÿï èrï

190 of 7
6 7 8 9 10
-3
4
5
6
The slope of the line shown in the graph is
and the intercept of the line is

Answers

Answer:slope 2/3

Y-int 6

Step-by-step explanation:

If a normally distributed population has a mean (mu) that equals 100 with a standard deviation (sigma) of 18, what will be the computed z-score with a sample mean (x-bar) of 106 from a sample size of 9?

Answers

Answer:

Z = 1

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean (mu) that equals 100 with a standard deviation (sigma) of 18

[tex]\mu = 100, \sigma = 18[/tex]

Sample of 9:

This means that [tex]n = 9, s = \frac{18}{\sqrt{9}} = 6[/tex]

What will be the computed z-score with a sample mean (x-bar) of 106?

This is Z when X = 106. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{106 - 100}{6}[/tex]

[tex]Z = 1[/tex]

So Z = 1 is the answer.

Solve this equation for x. Round your answer to the nearest hundredth.
1 = In(x + 7) ​

Answers

Answer:

[tex]\displaystyle x \approx -4.28[/tex]

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra II

Natural logarithms ln and Euler's number e

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle 1 = ln(x + 7)[/tex]

Step 2: Solve for x

[Equality Property] e both sides:                                                                     [tex]\displaystyle e^1 = e^{ln(x + 7)}[/tex]Simplify:                                                                                                             [tex]\displaystyle x + 7 = e[/tex][Equality Property] Isolate x:                                                                            [tex]\displaystyle x = e - 7[/tex]Evaluate:                                                                                                            [tex]\displaystyle x = -4.28172[/tex]

e^1 = x+7

e - 7 = x

x = -4.28


In the figure above, AD and BE intersect at point C, and
the measures of angles B, D, and E are 98°, 81°, and 55°,
respectively. What is the measure, in degrees, of
angle A ? (Disregard the degree sign when gridding your
answer.)

Answers

answer in screenshot

A shop sells a particular of video recorder. Assuming that the weekly demand for the video recorder is a Poisson variable with the mean 3, find the probability that the shop sells. . (a) At least 3 in a week. (b) At most 7 in a week. (c) More than 20 in a month (4 weeks).

Answers

Answer:

a) 0.5768 = 57.68% probability that the shop sells at least 3 in a week.

b) 0.988 = 98.8% probability that the shop sells at most 7 in a week.

c) 0.0104 = 1.04% probability that the shop sells more than 20 in a month.

Step-by-step explanation:

For questions a and b, the Poisson distribution is used, while for question c, the normal approximation is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

In which

x is the number of successes

e = 2.71828 is the Euler number

[tex]\lambda[/tex] is the mean in the given interval.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Poisson distribution can be approximated to the normal with [tex]\mu = \lambda, \sigma = \sqrt{\lambda}[/tex], if [tex]\lambda>10[/tex].

Poisson variable with the mean 3

This means that [tex]\lambda= 3[/tex].

(a) At least 3 in a week.

This is [tex]P(X \geq 3)[/tex]. So

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

Then

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

So

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0498 + 0.1494 + 0.2240 = 0.4232[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 1 - 0.4232 = 0.5768[/tex]

0.5768 = 57.68% probability that the shop sells at least 3 in a week.

(b) At most 7 in a week.

This is:

[tex]P(X \leq 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)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]

[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]

[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]

[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]

[tex]P(X = 4) = \frac{e^{-3}*3^{4}}{(4)!} = 0.1680[/tex]

[tex]P(X = 5) = \frac{e^{-3}*3^{5}}{(5)!} = 0.1008[/tex]

[tex]P(X = 6) = \frac{e^{-3}*3^{6}}{(6)!} = 0.0504[/tex]

[tex]P(X = 7) = \frac{e^{-3}*3^{7}}{(7)!} = 0.0216[/tex]

Then

[tex]P(X \leq 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) = 0.0498 + 0.1494 + 0.2240 + 0.2240 + 0.1680 + 0.1008 + 0.0504 + 0.0216 = 0.988[/tex]

0.988 = 98.8% probability that the shop sells at most 7 in a week.

(c) More than 20 in a month (4 weeks).

4 weeks, so:

[tex]\mu = \lambda = 4(3) = 12[/tex]

[tex]\sigma = \sqrt{\lambda} = \sqrt{12}[/tex]

The probability, using continuity correction, is P(X > 20 + 0.5) = P(X > 20.5), which is 1 subtracted by the p-value of Z when X = 20.5.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{20 - 12}{\sqrt{12}}[/tex]

[tex]Z = 2.31[/tex]

[tex]Z = 2.31[/tex] has a p-value of 0.9896.

1 - 0.9896 = 0.0104

0.0104 = 1.04% probability that the shop sells more than 20 in a month.

The probability of the selling the video recorders for considered cases are:

P(At least 3 in a week) = 0.5768 approximately.P(At most 7 in a week) = 0.9881 approximately.P( more than 20 in a month) = 0.0839 approximately.

What are some of the properties of Poisson distribution?

Let X ~ Pois(λ)

Then we have:

E(X) = λ = Var(X)

Since standard deviation is square root (positive) of variance,

Thus,

Standard deviation of X = [tex]\sqrt{\lambda}[/tex]

Its probability function is given by

f(k; λ) = Pr(X = k) = [tex]\dfrac{\lambda^{k}e^{-\lambda}}{k!}[/tex]

For this case, let we have:

X = the number of weekly demand of video recorder for the considered shop.

Then, by the given data, we have:

X ~ Pois(λ=3)


Evaluating each event's probability:

Case 1: At least 3 in a week.

[tex]P(X > 3) = 1- P(X \leq 2) = \sum_{i=0}^{2}P(X=i) = \sum_{i=0}^{2} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 3) = 1 - e^{-3} \times \left( 1 + 3 + 9/2\right) \approx 1 - 0.4232 = 0.5768[/tex]

Case 2: At most 7 in a week.

[tex]P(X \leq 7) = \sum_{i=0}^{7}P(X=i) = \sum_{i=0}^{7} \dfrac{3^ie^{-3}}{i!}\\\\P(X \leq 7) = e^{-3} \times \left( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120 + 729/720 + 2187/5040\right)\\\\P(X \leq 7) \approx 0.9881[/tex]

Case 3: More than 20 in a month(4 weeks)

That means more than 5 in a week on average.

[tex]P(X > 5) = 1- P(X \leq 5) =\sum_{i=0}^{5}P(X=i) = \sum_{i=0}^{5} \dfrac{3^ie^{-3}}{i!}\\\\P(X > 5) = 1- e^{-3}( 1 + 3 + 9/2 + 27/6 + 81/24 + 243/120)\\\\P(X > 5) \approx 1 - 0.9161 \\ P(X > 5) \approx 0.0839[/tex]


Thus, the probability of the selling the video recorders for considered cases are:

P(At least 3 in a week) = 0.5768 approximately.P(At most 7 in a week) = 0.9881 approximately.P( more than 20 in a month) = 0.0839 approximately.

Learn more about poisson distribution here:

https://brainly.com/question/7879375

Solve x∕3 < 5 Question 5 options: A) x ≥ 15 B) x > 15 C) x < 15 D) x ≤ 15

Answers

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{x}{3}[/tex] < 5 ( multiply both sides by 3 to clear the fraction )

x < 15 → C

The distance between Ali's house and 1 point
college is exactly 135 miles. If she
drove 2/3 of the distance in 135
minutes. What was her average speed
in miles per hour?

Answers

First we have to figure out how long it would take for the full voyage and that would be 135 + (135 x 1/3) and the answer to that would be 135 + 45 = 180 and that means that 180 is the total minutes it would take to travel the whole trip, now we have to calculate average speed which would be 135(distance)/180(time) which would end up being 135 miles/ 3 hours, now we divide the entire equation by 3 which would be 45/1
CONCLUSION ——————————
Ali would be driving 45 miles per hour

Ali's average speed was 40 miles per hour.

What is an average speed?

The total distance traveled is to be divided by the total time consumed brings us the average speed.

How to calculate the average speed of Ali?

The total distance between the college from Ali's house is 135 miles.

She drove 2/3rd of the total distance in 135 minutes.

She drove =135*2/3miles

=90miles.

Ali can drive 90miles in 135 mins.

Therefore, her average speed is: 90*60/135 miles per hour.

=40 miles per hour.

Learn about average speed here :

https://brainly.in/question/14787217

#SPJ2

please help me on this

Answers

Answer:

Median

Step-by-step explanation:

Using the median to measure central tendency, rather than the mean, is better for a skewed data set.

Since a skewed data set will have either very high or low extreme data points, the mean will be less representative and accurate when measuring central tendency.

Using the median will measure this better because it is not as vulnerable as the mean when there are extreme data points.

So, the answer is the median.

The answer is median his is because the mean value is depend on the correct media

Một công ty sản xuất ván trượt có thể bán một cái ván trượt với giá $60.

Tổng chi phí cho sản xuất bao gồm chi phí cố định là $1200 và chi phí để sản xuất một cái ván trượt là $35.

Nếu công ty đó bán được 80 cái ván trượt thì công ty đó

Answers

can you translate so I can help you out

The measure of angle tis 60 degrees.
What is the x-coordinate of the point where the
terminal side intersects the unit circle?
1
2
O
O
Isla Isla
2
DONE

Answers

Answer:

Step-by-step explanation:

Not a clear list of options and/or reference frame

Probably     0.5      if angle t is measured from the positive x axis.

Please help!!

Find BD​

Answers

Answer:  [tex]8\sqrt{2}[/tex]

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

Work Shown:

Focus entirely on triangle ABD (or on triangle BCD; both are identical)

The two legs of this triangle are AB = 8 and AD = 8. The hypotenuse is unknown, so we'll say BD = x.

Apply the pythagorean theorem.

[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\x = \sqrt{8^2 + 8^2}\\\\x = \sqrt{2*8^2}\\\\x = \sqrt{8^2*2}\\\\x = \sqrt{8^2}*\sqrt{2}\\\\x = 8\sqrt{2}\\\\[/tex]

So that's why the diagonal BD is exactly [tex]8\sqrt{2}\\\\[/tex] units long

Side note: [tex]8\sqrt{2} \approx 11.3137[/tex]

what is sqrt 2x-3 = sqrt 3x-9

Answers

Answer:

x=6

Step-by-step explanation:

sqrt (2x-3) = sqrt (3x-9)

Square each side

(sqrt (2x-3))^2 = (sqrt (3x-9))^2

2x-3 = 3x-9

Subtract 2x from each side

2x-3-2x = 3x-2x-9

-3 = x-9

Add 9 to each side

-3+9 = x-9+9

6 =x

Check solution

sqrt (2*6-3) = sqrt (3*6-9)

sqrt (9) = sqrt (9)

3=3

Solution is valid

sqrt (2x-3) = sqrt (3x-9)

Square each side

(sqrt (2x-3))^2 = (sqrt (3x-9))^2

2x-3 = 3x-9

Subtract 2x from each side

2x-3-2x = 3x-2x-9

-3 = x-9

Add 9 to each side

-3+9 = x-9+9

6 =x

sqrt (2*6-3) = sqrt (3*6-9)

sqrt (9) = sqrt (9)

3=3

Therefore ans x = 6

Answered by Gauthmath must click thanks and mark brainliest

how many distinct permutations can be formed using the letters of the word robberies

Answers

Answer:

45360 arrangements

Step-by-step explanation:

Given the word 'robberies'

Number of letters = 9 letters in total

Repeated letters ; r = 2 ; b = 2 ; e = 2

Therefore, the number of distinct arrangement of letters is :

(total letters)! / repeated letters!

The number of distinct arrangement of letters is :

9! / (2! * 2! * 2!) = (9*8*7*6*5*4*3*2*1) / (2*2*2)

362880 / 8 = 45360 arrangements

In a random sample of 7 residents of the state of Maine, the mean waste recycled per person per day was 1.4 pounds with a standard deviation of 0.23 pounds.
a. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Maine. Assume the population is approximately normal.
b. Find the critical value that should be used in constructing the confidence interval.

Answers

Answer:

a) The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.

b) [tex]T_c = 2.4469[/tex]

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 7 - 1 = 6

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 6 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.4469, and the answer to question b is [tex]T_c = 2.4469[/tex]

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.4469\frac{0.23}{\sqrt{7}} = 0.21[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 1.4 - 0.21 = 1.19 pounds.

The upper end of the interval is the sample mean added to M. So it is 1.4 + 0.21 = 1.61 pounds.

The 95% confidence interval for the mean waste recycled per person per day for the population of Maine is between 1.19 and 1.61 pounds.

A rectangle has a length of 7 in. and a width of 2 in. if the rectangle is enlarged using a scale factor of 1.5, what will be the perimeter of the new rectangle

Answers

Answer:

27 inch

Step-by-step explanation:

Current perimeter=18

New perimeter=18*1.5=27 in

Use the commutative law of multiplication to rewrite 67 x 13.

A. 3 X 671
B. 13 x 67
C.6 X 7 X1 X3
D.80

Answers

Answer:

A. 671*3

B. 67*13

C. 3*1*7*6

D. 1*80

Calculus II Question

Identify the function represented by the following power series.

[tex]\sum_{k = 0}^\infty (-1)^k \frac{x^{k + 2}}{4^k}[/tex]

Answers

With some rewriting, you get

[tex]\displaystyle \sum_{k=0}^\infty (-1)^k\frac{x^{k+2}}{4^k} = x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k[/tex]

Recall that for |x| < 1, you have

[tex]\displaystyle \frac1{1-x} = \sum_{k=0}^\infty x^k[/tex]

So as long as |-x/4| = |x/4| < 1, or |x| < 4, your series converges to

[tex]\displaystyle x^2 \sum_{k=0}^\infty \left(-\frac x4\right)^k = \frac{x^2}{1-\left(-\frac x4\right)} = \frac{x^2}{1+\frac x4} = \boxed{\frac{4x^2}{4+x}}[/tex]

Based on known expressions from Taylor series, the power series [tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex]Taylor series-derived formula of the rational function [tex]\frac{4\cdot x^{2}}{4+x}[/tex].

How to derive a function behind the approximated formula by Taylor series

Taylor series are polynomic approximations used to estimate values both from trascendental and non-trascendental functions. It is commonly used in trigonometric, potential, logarithmic and even rational functions.

In this question we must use series properties and common Taylor series-derived formulas to infer the expression behind the given series. Now we proceed to find the expression:

[tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex]

[tex]x^{2}\cdot \sum\limits_{k = 0}^{\infty} \left(-\frac{x}{4} \right)^{k}[/tex]

[tex]x^{2}\cdot \left(\frac{1}{1+\frac{x}{4} } \right)[/tex]

[tex]\frac{4\cdot x^{2}}{4+x}[/tex]

Based on power and series properties and most common Taylor series- derived formulas, the power series [tex]\sum \limits_{k = 0}^{\infty} (-1)^{k}\cdot \frac{x^{k+2}}{4^{k}}[/tex] represents a Taylor series-derived formula of the rational function [tex]\frac{4\cdot x^{2}}{4+x}[/tex]. [tex]\blacksquare[/tex]

To learn more on Taylor series, we kindly invite to check this verified question: https://brainly.com/question/12800011

could someone please answer this? :) thank you

Answers

Answer:

The last one

Step-by-step explanation:

What we know:

We have a total of 16 coins

The 16 coins consist of dimes and quarters

The value of the coins is 3.10

The value of a dime is .10

The value of a quarter is .25

Using this information we can create a system of linear equations

First off we know that we have a total of 16 coins which consist of dimes and quarters

The number of Quarters can be represented by q and then number of dimes can be represented by d.

If we have a total of 16 coins then q + d must equal 16

So equation 1 is q + d = 16

Now we need to create a second equation

We know that the total value of the coins is 3.10 and we know that the coins consist of dimes and quarters

As you may know a quarter has a value of .25 cents and a dime has a value of 10 cents

If the total value of the coins is 3.10 the the number of dimes (d) times .10 + the number of Quarters times .25 must equal 3.10

This can also be written as

.25q + .10d = 3.10

So the two equations are

q + d = 16 and .25q + .10d = 3.10

These equations are shown in the last answer choice

Note: b is very similar to d

However the the value of the coins are incorrect in B

In B the value of the dime is represented by 10 which is not correct because the value of a dime is .10 not 10

[tex]\sqrt{25}[/tex]

Answers

Answer:

5

Step-by-step explanation:

Calculate the square root of 25 and get 5.

5 I just thought of what # gets me to 25

Doyle Company issued $500,000 of 10-year, 7 percent bonds on January 1, 2018. The bonds were issued at face value. Interest is payable in cash on December 31 of each year. Doyle immediately invested the proceeds from the bond issue in land. The land was leased for an annual $125,000 of cash revenue, which was collected on December 31 of each year, beginning December 31, 2018

Answers

Answer:

f

Step-by-step explanation:

5x-22 3x +105 x minus 22 3 X + 10 ​

Answers

-291x+10

:)))))) Have fun

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