Noaya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read. Let y represent the number of pages left to read after x hours.

Answers

Answer 1

Answer: –55x + 570

Step-by-step explanation:

The person above me completely missed the question so this is the right one


Related Questions

If you vertically stretch the exponential function f(x)=2x by a factor of 3, what is the equation of the new function

Answers

Answer:

g(X)=3(2^x)

Step-by-step explanation:

You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.3. A random sample of 735 men over the age of 50 found that 203 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim

Answers

Answer:

[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]  

Now we can claculate the p value with this formula:

[tex]p_v =P(z<-1.42)=0.0778[/tex]  

If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.

Step-by-step explanation:

Information to given

n=735 represent the random sample taken

X=203 represent the number of people who have their prostate regularly examined

[tex]\hat p=\frac{203}{735}=0.276[/tex] estimated proportion of people who have their prostate regularly examined  

[tex]p_o=0.3[/tex] is the value to verify

z would represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true proportion is less than 0.3, the ystem of hypothesis are.:  

Null hypothesis:[tex]p \geq 0.3[/tex]  

Alternative hypothesis:[tex]p < 0.3[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{0.276 -0.3}{\sqrt{\frac{0.3(1-0.3)}{735}}}=-1.42[/tex]  

Now we can claculate the p value with this formula:

[tex]p_v =P(z<-1.42)=0.0778[/tex]  

If we use a signifiacn level of 5% we see that the p value is higher than 0.05 so then we have enough evidence to fail to reject the null hypothesis and we can't conclude that the true proportion is significantly higher than 0.3 at 5% of significance.

A=(-2,-7) B=(-6,4) C=(-2,7) D=(2,4) What is the perimeter?

Answers

 

[tex]\displaystyle\bf\\AB=\sqrt{\Big(-6-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AB=\sqrt{\Big(-6+2\Big)^2+\Big(4+7\Big)^2}\\\\AB=\sqrt{\Big(-4\Big)^2+\Big(11\Big)^2}\\\\AB=\sqrt{16+121}\\\\\boxed{\bf AB=\sqrt{137}}[/tex]

.

[tex]\displaystyle\bf\\BC=\sqrt{\Big(-2-(-6)\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(-2+6\Big)^2+\Big(7-4\Big)^2}\\\\BC=\sqrt{\Big(4\Big)^2+\Big(3\Big)^2}\\\\BC=\sqrt{16+9}\\\\BC=\sqrt{25}\\\\\boxed{\bf BC=5}[/tex]

.

[tex]\displaystyle\bf\\CD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(2+2\Big)^2+\Big(4-7\Big)^2}\\\\CD=\sqrt{\Big(4\Big)^2+\Big(-3\Big)^2}\\\\CD=\sqrt{16+9}\\\\CD=\sqrt{25}\\\\\boxed{\bf CD=5}[/tex]

.

[tex]\displaystyle\bf\\AD=\sqrt{\Big(2-(-2)\Big)^2+\Big(4-(-7)\Big)^2}\\\\AD=\sqrt{\Big(2+2\Big)^2+\Big(4+7\Big)^2}\\\\AD=\sqrt{\Big(4\Big)^2+\Big(11\Big)^2}\\\\AD=\sqrt{16+121}\\\\\boxed{\bf AD=\sqrt{137}}[/tex]

.

[tex]\displaystyle\bf\\P=AB+BC+CD+AD=\sqrt{137}+5+5+\sqrt{137}\\\\\boxed{\bf P=10+2\sqrt{137}}[/tex]

 

In 2 + In 8 - In 4
In 4
In 6
In 64
DONE

Answers

Answer:

ln 4

Step-by-step explanation:

plus(+) will become times and minus(-)will become divide. Combine all together as all are in terms of ln

ln (2x8)/4

=ln 4

Answer: In 4

Step-by-step explanation: edge 2021

A group of professors investigated​ first-year college​ students' knowledge of astronomy. One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 149149 freshmen​ students, 3232 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this​ information, is it correct at the alphaαequals=0.100.10 level of significance to state that more than​ 20% of all freshmen college students believe the Big Bang theory describes the creation of planetary​ systems? State the null and alternative hypotheses. Choos

Answers

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

A group of professors investigated first-year college students' knowledge of astronomy. One concept of interest was the Big Bang theory of the creation of the universe. In a sample of 149 freshmen students, 32 believed that the Big Bang theory accurately described the creation of planetary systems. Based on this information, is it correct at the alpha = 0.01 level of significance to state that more than 20% of all freshmen college students believe the Big Bang theory describes the creation of planetary systems? State the null and alternative hypotheses. Choose the correct answer below. H_0: p = 0.20 H_a: p not equal to 0.20 H_0: p not equal to 0.20 H_a: p = 0.20 H_0: p = 0.20 H_a: p 0.20 If alpha = 0.05, find the rejection region for the test. Choose the correct answer below. z > 1.645 z > 1.96 z

Solution:

We would set up the null and alternative hypothesis. The correct options are

For null hypothesis,

p ≥ 0.2

For alternative hypothesis,

p < 0.2

This is a left tailed test.

Considering the population proportion, probability of success, p = 0.2

q = probability of failure = 1 - p

q = 1 - 0.2 = 0.8

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 32

n = number of samples = 149

P = 32/149 = 0.21

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.21 - 0.2)/√(0.2 × 0.8)/149 = 0.31

The calculated test statistic is 0.31 for the right tail and - 0.31 for the left tail

Since α = 0.05, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.05/2 = 0.025

The z score for an area to the left of 0.025 is - 1.96

For the right, α/2 = 1 - 0.025 = 0.975

The z score for an area to the right of 0.975 is 1.96

In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96

Therefore, the rejection region is z > 1.96

A bicycle ramp used for competitions is a triangle prism. The volume of the ramp is 313.2 cubic feet. Write and solve an equation to find the the width of the ramp.

Answers

Answer:

8.7 ft

Step-by-step explanation:

The diagram of the ramp is attached below.

Volume of a Triangular Prism = Base Area X Width

From the diagram:

Base of the triangle = 6 ft

Height of the Triangle = 12 ft

Therefore:

Base Area of the Prism [tex]=\frac{1}{2}X 12X6=36$ ft^2[/tex]

From the diagram, Width of the ramp =x

Given that the volume of the ramp is 313.2 cubic feet.

Therefore, substituting into the formula for Volume of a Triangular Prism

[tex]313.2=36 X x\\x= 313.2 \div 36\\$Width of the ramp, x=8.7 ft[/tex]

Answer:

8.7

Step-by-step explanation:

The tallest church tower in the Netherlands is the Dom Tower in Utrecht. If the angle of elevation to the top of the tower is 77° when 25.9 m from the base, what is the height of the Dom Tower to the nearest metre.

Answers

Answer:

Height of the Dom is 112.18 m.

Step-by-step explanation:

The tallest church tower in the Netherlands is the Dom Tower in Utrecht. The angle of elevation to the top of the tower is 77° when 25.9 m from the base. It is required to find the height of the Dom Tower. Let its height is h. So, using trigonometric formula to find it as :

[tex]\tan\theta=\dfrac{h}{b}\\\\\tan(77)=\dfrac{h}{25.9}\\\\h=\tan(77)\times 25.9\\\\h=112.18\ m[/tex]

So, the height of the Dom is 112.18 m.

sorry it’s hard to see. please help!!!

Answers

I wish i could help

During the worst periods of inflation in America, the price of food increased at a rate of 12 % per month. If your food bill was $300 one month during this period, what was it two months later?
Exponential; $337.08
Linear; $672.00
Exponential; $376.32
Linear; $372.00

Answers

Answer:

  Exponential; $376.32

Step-by-step explanation:

Generally, an increase of 12% in a month means the prices are 12% more than they were in the previous month. That is, the value has been multiplied by 1.12.

The same would be true for the second month, so the overall multiplier for the two months is ...

  (1.12)(1.12) = 1.12^2 = 1.2544

This makes the food bill for the second month amount to ...

  1.2544 × $300 = $376.32

_____

As with all percentages, you need to be clear about what base is being used. Here, we have assumed the base for a monthly increase is the value at the beginning of the month.

If, instead, it is the value at the beginning of the year, then the increase is linear, not exponential. 12% of the value at the beginning of the year is the same throughout the year.

The given line segment passes through the points (0, -3) and (-5, -4).
What is the equation of the line that is parallel to the given line and passes through the point (-2, 2)?​

Answers

Answer:

y= 1/5x + 12/5

Step-by-step explanation:

Points: (0, -3) and (-5, -4)Line: y= mx+bSlope: m=(y2-y1)/(x2-x1)= (-4+3)/(-5-0)= -1/-5= 1/5Y-intercept: -3= 0*1/5+b ⇒ b= -3So the line is: y= 1/5x - 3

Parallel line to this has same slope and passes through the point (-2, 2)

Its y- intercept is: 2= 1/5(-2)+b ⇒ b= 2+2/5= 12/5

The required equation in slope- intercept form is:

y= 1/5x + 12/5

The amount of coffee that people drink per day is normally distributed with a mean of 17 ounces and a standard deviation of 4 ounces. 15 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.
a) What is the distribution of XX? XX ~ N(,)
b) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
c) What is the probability that one randomly selected person drinks between 15.5 and 18 ounces of coffee per day?
d) For the 15 people, find the probability that the average coffee consumption is between 15.5 and 18 ounces of coffee per day.
e) For part d), is the assumption that the distribution is normal necessary? YesNo
f) Find the IQR for the average of 15 coffee drinkers.
Q1 = ounces
Q3 = ounces
IQR: ounces

Answers

Answer:

Step-by-step explanation:

(a)

The distribution of X is Normal Distribution with mean [tex]= \mu =17[/tex] and Variance [tex]= \sigma^{2} = 16 \ i.e., X \sim N (17, 16),[/tex]

(b)

The distribution of [tex]\bar{x}[/tex] is Normal Distribution with mean [tex]= \mu =17[/tex] and Variance = [tex]\sigma^{2}/n = 16/15= 1.0667[/tex].i.e., [tex]\bar{x}\sim N(17,1.0667)[/tex]

c)

To find P(15.5 < X < 18):

Case 1: For X from 15.5 to mid value:

Z = (15.5 - 17)/4 = - 0.375

Table of Area Under Standard Normal Curve gives area = 0.1480

Case 2: For X from mid value to 18:

Z = (18 - 17)/4 = 0.25

Table of Area Under Standard Normal Curve gives area = 0.0987

So,

P(15.5 < X< 18) = 0.1480 +0.0987 = 0.2467

So,

Answer is:

0.2467

(d)

[tex]SE = \sigma/\sqrt{n}\\\\= 4/\sqrt{15}[/tex]

= 1.0328

To find [tex]P(15.5 < \bar{x}< 18):[/tex]

Case 1: For [tex]\bar{x}[/tex] from 15.5 to mid value:

Z = (15.5 - 17)/1.0328 = - 1.4524

Table of Area Under Standard Normal Curve gives area = 0.4265

Case 2: For X from mid value to 18:

Z = (18 - 17)/1.0328 = 0.9682

Table of Area Under Standard Normal Curve gives area = 0.3340

So,

[tex]P(15.5 < \bar{x}< 18) = 0.4265 + 0.3340 = 0.7605[/tex]

So,

Answer is:

0.7605

(e)

Correct option:

No

because Population SD is provided.

(f)

(i)

Q1 is given by:

[tex]- 0.6745 = (\bar{x} - 17)/1.0328[/tex]

So,

X = 17 - (0.6745 * 1.0328) = 17 - 0.6966 = 16.3034

So,

Q1 = 16.3034

(ii)

Q3 is given by:

[tex]0.6745 = (\bar{x} - 17)/1.0328[/tex]

So,

X = 17 + (0.6745 * 1.0328) = 17 + 0.6966 = 17.6966

So,

Q3= 17.6966

(iii)

IQR = Q3 - Q1 = 17.6966 - 16.3034 = 1.3932

So

Answers are:

Q1 = 16.3034 ounces

Q3 = 17.6966 Ounces

IQR = 1.3932 Ounces

Solve 3(a + 3) – 6 = 21.

Answers

Answer:

a=6

Step-by-step explanation:

to find the value of a you need to simplify the equation first. so...

3(a+3)-6=21 (you remove the bracket first)

3a+9-6=21

3a+3=21 (you collect the like terms then)

3a=21-3

3a=18 (then you both divide both sides by 3 to find the value of a)

a=18/3

a=6

to check your answer substitute 3 instead of a

3(a+3)-6=21

3(6+3)-6=21

3(9)-6=21 (according to BODMAS since multiplication comes first you multiply 3 with 9 before subtracting it from 6.)

29-6=21

21=21

Answer:6

Step-by-step explanation:

3(a + 3) - 6 = 21

3(a + 3) = 21 + 6

3(a + 3) =27

a + 3. = 27 ÷ 3

a + 3. = 9

a. = 9 - 3

a. = 6

he dot plot shows how many swimmers are in each line at a waterpark: Is the median or the mean a better measure of center for these data and why? Median, because the data are skewed and there is an outlier Median, because the data are symmetric and there are no outliers Mean, because the data are skewed and there is an outlier Mean, because the data are symmetric and there are no outliers

Answers

Answer:

Step-by-step explanation:

There's no plot, but I can give you this: Median is better with a large outlier, while mean is better for symmetry. Therefore, the correct answer would be either the first or fourth. Ofc, we can't see the plot so that's all I can give you.

Hope that helped,

-sirswagger21

On a recent trip, Lamar's distance varied directly with the number of hours he drove. He traveled 288 miles in 6 hours. Which equation shows Lamar's distance, d, based on the number of hours, h, he drove?

(A) d = 6h
(B) d = 50h
(C) d = 48h
(D) d = 288h


Answers

Answer:

d = 48 h

Step-by-step explanation:

Lamar's distance traveled is directly proportional to the number of hours be drove.

So distance (d) ∝ hours (h)

Lamar traveled 288 miles in 6 hours

Since d ∝ h

then d = kh    [ where k is the proportionality constant ]

if     288 = k × 6

k =  =288/48

Therefore, equation will be d = 48 h will be the equation

If triangles DEF and NPQ are similar, what is the length of side d? As fraction or whole number.

Answers

The length of the side d would be 77/18.

What is the ratio of two quantities?

Suppose that we've got two quantities with measurements as 'a' and 'b'

Then, their ratio(ratio of a to b) a:b

or

[tex]\dfrac{a}{b}[/tex]

If triangles DEF and NPQ are similar, then

7/9 = d/ (11/2)

By cross multiply

9d = 7 x 11/2

d = 77/2 ÷ 9

d = 77/18

Thus, The length of the side d would be 77/18.

Learn more about ratios here:

brainly.com/question/186659

#SPJ2

In monitoring lead in the air after the explosion at the battery factory, it is found that the amounts of lead over a 6 day period had a standard error of 1.93. Find the margin of error that corresponds to a 95% confidence interval. (Round to 2 decimal places) 4.56

Answers

Answer:

1.54

Margin of error M.E = 1.54

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

x+/-M.E

Where M.E = margin of error

M.E = zr/√n

Given that

Standard deviation r = 1.93

Number of samples n = 6

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

M.E = (1.96×1.93/√6) = 1.544321633166

M.E = 1.54 (to 2 decimal place)

Margin of error M.E = 1.54

A student takes a multiple-choice test that has 11 questions. Each question has five choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. (a) Find P (6). (b) Find P (More than 3). Round the answers to at least four decimal places.

Answers

Answer:

a) P(6) = 0.0097

b) P(More than 3) = 0.1611

Step-by-step explanation:

For each question, there are only two possible outcomes. Either it is guessed correctly, or it is not. Questions are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A student takes a multiple-choice test that has 11 questions.

This means that [tex]n = 11[/tex]

Each question has five choices.

This means that [tex]p = \frac{1}{5} = 0.2[/tex]

(a) Find P (6)

This is P(X = 6).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{11,6}.(0.2)^{6}.(0.8)^{5} = 0.0097[/tex]

P(6) = 0.0097

(b) Find P (More than 3).

Either P is 3 or less, or it is more than three. The sum of the probabilities of these outcomes is 1. So

[tex]P(X \leq 3) + P(X > 3) = 1[/tex]

We want P(X > 3). So

[tex]P(X > 3) = 1 - P(X \leq 3)[/tex]

In which

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

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{11,0}.(0.2)^{0}.(0.8)^{11} = 0.0859[/tex]

[tex]P(X = 1) = C_{11,1}.(0.2)^{1}.(0.8)^{10} = 0.2362[/tex]

[tex]P(X = 2) = C_{11,2}.(0.2)^{2}.(0.8)^{9} = 0.2953[/tex]

[tex]P(X = 3) = C_{11,3}.(0.2)^{3}.(0.8)^{8} = 0.2215[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0859 + 0.2362 + 0.2953 + 0.2215 = 0.8389[/tex]

Then

[tex]P(X > 3) = 1 - P(X \leq 3) = 1 - 0.8389 = 0.1611[/tex]

P(More than 3) = 0.1611

1. Use limit comparison test to determine whether the series converges or diverges:

Σ[infinity]_n=1 n^2 + 1 / 2n^3 - 1

2. Use limit comparison test to determine whether the series converges or diverges:

Σ[infinity]_n = 1 n / √n^5 + 5

3. Use direct comparison test to determine whether the series converges or diverges:

Σ[infinity]_n = 1 4 + 3^n / 2^n

Answers

Answer:

1. Diverges

2. Converges

3. Diverges

Step-by-step explanation:

Solution:-

Limit comparison test:

- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ). Then the following three conditions are applicable for the limit:

                          Lim ( n-> ∞ )   [tex][ \frac{a_n}{b_n} ][/tex]  = c

Where,

1) If c is finite: 0 < c < 1, then both series ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] either converges or diverges.

2) If c = 0, then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges.

3) If c = ∞ or undefined, then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges.

a) The given series ∑[tex]a_n[/tex] is:

                   (n = 1) ∑^∞  [tex][ \frac{n^2+1}{2n^3-1} ][/tex]

- We will make an educated guess on the comparative series  ∑[tex]b_n[/tex] by the following procedure.

                  (n = 1) ∑^∞   [tex][ \frac{n^2( 1 + \frac{1}{n^2} )}{n^3 ( 2 - \frac{1}{n^2} ) } ] = [ \frac{( 1 + \frac{1}{n^2} )}{n( 2 - \frac{1}{n^2} ) } ][/tex]

- Apply the limit ( n - > ∞ ):

                 (n = 1) ∑^∞  [tex][ \frac{1}{2n}][/tex]    .... The comparative series ( ∑[tex]b_n[/tex] )

- Both series  ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.

- Compute the limit:

                 Lim ( n-> ∞ )  [tex][ \frac{n^2 + 1}{2n^3 - 1} * 2n ] = [ \frac{2n^3 + 2n}{2n^3 - 1} ][/tex]

                 Lim ( n-> ∞ )    [tex][ \frac{2n^3 ( 1 + \frac{1}{n^2} ) }{2n^3 ( 1 - \frac{1}{2n^3} ) } ] = [ \frac{ 1 + \frac{1}{n^2} }{ 1 - \frac{1}{2n^3} } ][/tex]

- Apply the limit ( n - > ∞ ):

                Lim ( n-> ∞ )  [tex][ \frac{a_n}{b_n} ][/tex]  = [tex][ \frac{1 + 0}{1 + 0} ][/tex] = 1   ... Finite

- So from first condition both series either converge or diverge.

- We check for ∑[tex]b_n[/tex] convergence or divergence.

- The ∑[tex]b_n[/tex] = ( 1 / 2n ) resembles harmonic series ∑ ( 1 / n ) which diverges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 1 ≤ 1. Hence, ∑

- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also diverges.

Answer: Diverges    

b)          

The given series ∑[tex]a_n[/tex] is:

                   (n = 1) ∑^∞  [tex][ \frac{n}{n^\frac{5}{2} +5} ][/tex]

- We will make an educated guess on the comparative series  ∑[tex]b_n[/tex] by the following procedure.

                  (n = 1) ∑^∞   [tex][ \frac{n( 1 )}{n ( n^\frac{3}{2} + \frac{5}{n} ) } ] = [\frac{1}{( n^\frac{3}{2} + \frac{5}{n} )} ][/tex]

- Apply the limit ( n - > ∞ ) in the denominator for  ( 5 / n ), only the dominant term n^(3/2) is left:

                  (n = 1) ∑^∞    [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] .... The comparative series ( ∑[tex]b_n[/tex] )

- Both series  ∑[tex]a_n[/tex] and ∑[tex]b_n[/tex] are positive series. You can check by plugging various real number for ( n ) in both series.

- Compute the limit:

                 Lim ( n-> ∞ )   [tex][ \frac{n}{n^\frac{5}{2} +5} * n^\frac{3}{2} ] = [ \frac{n^\frac{5}{2}}{n^\frac{5}{2} +5} ][/tex]

                 Lim ( n-> ∞ )    [tex][ \frac{n^\frac{5}{2}}{n^\frac{5}{2} ( 1 + \frac{5}{n^\frac{5}{2}}) } ] = [ \frac{1}{1 + \frac{5}{n^\frac{5}{2}} } ][/tex]

- Apply the limit ( n - > ∞ ):

                Lim ( n-> ∞ )  [tex][ \frac{a_n}{b_n} ][/tex]  = [tex][\frac{1}{1 + 0}][/tex] = 1   ... Finite

- So from first condition both series either converge or diverge.

- We check for ∑[tex]b_n[/tex] convergence or divergence.

- The ∑[tex]b_n[/tex] = ( [tex][ \frac{1}{n^\frac{3}{2} } ][/tex] ) converges by p-series test ∑ ( [tex]\frac{1}{n^p}[/tex] ) where p = 3/2 > 1. Hence, ∑

- In combination of limit test and the divergence of ∑[tex]b_n[/tex], the series ∑[tex]a_n[/tex] given also converges.

Answer: converges

Comparison Test:-  

- Given, ∑[tex]a_n[/tex] and suppose ∑[tex]b_n[/tex] such that both series are positive for all values of ( n ).

-Then the following conditions are applied:

1 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) < 0 , then ∑[tex]a_n[/tex] diverges only if ∑[tex]b_n[/tex] diverges

2 ) If ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≤ 0 , then ∑[tex]a_n[/tex] converges only if ∑[tex]b_n[/tex] converges

c) The given series ∑[tex]a_n[/tex] is:

                   (n = 1) ∑^∞ [tex][ \frac{4 + 3^2}{2^n} ][/tex]

- We will make an educated guess on the comparative series  ∑[tex]b_n[/tex] by the following procedure.

                  (n = 1) ∑^∞ [tex][ \frac{3^n ( \frac{4}{3^n} + 1 )}{2^n} ][/tex]

- Apply the limit ( n - > ∞ ) in the numerator for  ( 4 / 3^n ), only the dominant terms ( 3^n ) and ( 2^n ) are left:  

                 (n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex]   ... The comparative series ( ∑[tex]b_n[/tex] )

- Compute the difference between sequences ( [tex]a_n[/tex] - [tex]b_n[/tex] ):

                 [tex]a_n - b_n = \frac{4 + 3^n}{2^n} - [ \frac{3^n}{2^n} ] \\\\a_n - b_n = \frac{4 }{2^n} \geq 0[/tex], for all values of ( n )

- Check for divergence of the comparative series ( ∑[tex]b_n[/tex] ), using divergence test:

               ∑[tex]b_n[/tex] = (n = 1) ∑^∞ [tex][ \frac{3^n}{2^n} ][/tex]  diverges

- The first condition is applied when  ( [tex]a_n[/tex] - [tex]b_n[/tex] ) ≥ 0, then ∑diverges only if ∑[tex]b_n[/tex] diverges.

Answer: Diverges

                 

Two airplanes leave an airport at the same time, flying in the same direction. One plane is flying at twice the speed of the other. If after 4 hours they are 1800 km apart, find the speed of each plane.

Answers

Answer:

One plane has a speed of 450 km/h and the other has a speed of 900 km/h.

Step-by-step explanation:

I am going to say that:

The speed of the first plane is x.

The speed of the second plane is y.

One plane is flying at twice the speed of the other.

I will say that y = 2x. We could also say that x = 2y.

Two airplanes leave an airport at the same time, flying in the same direction

They fly in the same direction, so their relative speed(difference) at the end of each hour is y - x = 2x - x = x.

If after 4 hours they are 1800 km apart, find the speed of each plane

After 1 hour, they will be x km apart. After 4, 1800. So

1 hour - x km apart

4 hours - 1800 km apart

4x = 1800

x = 1800/4

x = 450

2x = 2*450 = 900

One plane has a speed of 450 km/h and the other has a speed of 900 km/h.

A spinner is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinner landing on 5? A. 1 over 13 B.1 over 8 C.5 over 13 D.5 over 8 PLEASE HURRY!!!!!!!!!!!!!!!!!

Answers

Answer:

B.   1 over 8

Step-by-step explanation:

To determine the probability of the spinner landing on 5, we need to first know what probability is,

probability = required outcome/all possible outcome

since the spinner is divided into 8 equal sections and each section contains number from 1-8, this implies there are total of 64 numbers on the spinner.  This implies that all possible outcome = 64

In each section there is 5, since there are 8 sections on the spinner, the number of 5's on the spinner are 8.

This implies that the required outcome = 8

but

probability = required outcome/all possible outcome

probability (of the spinner landing on 5) = 8/64    =1/8

Answer:

b

Step-by-step explanation:

Louis had 19 dogs. He feeds them with 38 pounds of biscuits. If there are 4 more
dogs, then how much more pounds of biscuit are needed?

Answers

Answer:

14

Step-by-step explanation:

Answer:

Which of these factors will affect the friction on a road

Step-by-step explanation:

What is the simplified value of the exponential expression 27 1/3?
1/3
1/9
3
9

Answers

Answer:3

Step-by-step explanation:

Answer:

C.3

Step-by-step explanation:

3/11 ÷ 3/11
and
9/10 ÷ 3/5

PLZ HELP ME

Answers

Answer:

3/11 divided by 3/11 is 1

9/10 divided by 3/5 is 1 1/2 (1.5)

Step-by-step explanation:

Answer:

1

1.5

Step-by-step explanation:

3/11 ÷ 3/11 = 1

9/10 ÷ 3/5 = 3/2 ≈ 1.5

a pail holds 3 1/2 gallons of water. How much is it in cups

Answers

Answer:

3 1/2 gallons of water is 56 cups

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

1 gallon=4cups

1/2 gallon=2cups

3*4=12

or 4cups+4cups+4cups=12

12+2=14

Find the​ (a) mean,​ (b) median,​ (c) mode, and​ (d) midrange for the data and then​ (e) answer the given question. Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. What do the results tell​ us? 24 72 41 76 15 29 64 93 74 38 99

Answers

Answer:

a) 56.82

b) 64

c) there is no mode

d) 57

e) the jersey numbers are nominal data and they do not measure or count anything, so the resulting statistic are meaningless

Step-by-step explanation:

The first thing is to organize the data from least to greatest:

15 24 29 38 41 64 72 74 76 93 99

a) the mean would be the average of the data, thus:

m = (15 + 24 + 29 + 38 + 41 + 64 + 72 + 74 + 76 + 93 + 99) / 11

m = 56.82

b) the median is the data of half, when the data is organized, in this case the value of half would be the sixth data that is 64.

c) the mode is the value that is most repeated, therefore as none is repeated there is no mode.

d) the midrange is the average between the minimum value and the maximum value:

mr = (15 + 99) / 2

mr = 57

e) the jersey numbers are nominal data and they do not measure or count anything, so the resulting statistic are meaningless

What is the quotient if 3/8 of 30 is divided by 15/16 of 5/10?

Answers

Answer:

24

Step-by-step explanation:

That would be:

(3/8)(30)

---------------

(15/16)(1/2)

This can be reduced in various ways.  First, divide that 30 by 15, obtaining:

   6/8

-----------

   1/32

Now invert the divisor (1/32) and multiply:

(6/8)(32/1)

This reduces to 6*4, or 24.

write any two numbers less than 15 , which has exactly four factors​

Answers

Answer:

4 can be divided by 1 and 2

6 can be divided by 1 and 2

12 is wrong because it can be divided by 1,2, and 4 so it has 6 factors instead of 4

Step-by-step explanation:

Use slope-intercept form to write the equation of a line
that has a slope of -3 and passes through the point
(1,-5).
Use the drop-down menus to select the proper value
for each variable that is substituted into the slope-
intercept equation
y =
X
DPM
m =

Answers

Answer:

y=-3x-2

Step-by-step explanation:

There is enough information to make a point-slope form equation that which we can convert into slope-intercept form.

Point-slope form is: [tex]y-y_1=m(x-x_1)[/tex]

We are given the slope of -3 and the point of (1,-5).

[tex]y-y_1=m(x-x_1)\rightarrow y+5=-3(x-1)[/tex]

Convert into Slope-Intercept Form:

[tex]y+5=-3(x-1)\\y+5-5=-3(x-1)-5\\\boxed{y=-3x-2}[/tex]

g A two-tailed test is one where: Select one: a. results in only one direction can lead to rejection of the null hypothesis b. negative sample means lead to rejection of the null hypothesis c. results in either of two directions can lead to rejection of the null hypothesis d. no results lead to the rejection of the null hypothesis

Answers

Answer:

c. results in either of two directions can lead to rejection of the null hypothesis.

Step-by-step explanation:

A two tailed test is performed when we want to test if there is statistically significant difference from the null state. That means that if the statistic value is significantly higher or significantly lower, we will reject the null hypothesis. Both tails have rejection areas.

What’s the correct answer for this question?

Answers

Answer:

A.

Step-by-step explanation:

In the attached file

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