According to a recent study, annual per capita consumption of milk in the United States is 23.8 gallons. Being from the Midwest, you believe milk consumption is higher there and wish to test your hypothesis. A sample of 14 individuals from the Midwestern town of Webster City was selected and then each person's milk consumption was entered below. Use the data to test your hypothesis.
a. Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City is higher than the national mean.
b. What is a point estimate of the difference between mean annual consumption in Webster City and the national mean? (2 decimals)
c. At α=0.01
test for a significant difference by completing the following.
Calculate the value of the test statistic (2 decimals).
The p-value is _____ (4 decimals).
Reject the null hypothesis?
27.8
23.84
25.25
21
17.52
19.61
19.83
26.18
34.97
30
28.59
20.57
26.94
27.24

Answers

Answer 1

Answer:

a. In the explanation.

b. The point estimate of the difference can be calculated as the difference between the sample mean and the population mean:

[tex]d=M-\mu=24.95-23.8=1.15[/tex]

c. Test statistic t = 0.90

P-value = 0.1932

The null hypothesis failed to be rejected.

Step-by-step explanation:

We have a sample, wich mean and standard deviation are calculated as:

[tex]M=\dfrac{1}{14}\sum_{i=1}^{14}(27.8+23.84+25.25+21+17.52+19.61+...+26.94+27.24)\\\\\\ M=\dfrac{349.34}{14}=24.95[/tex]

[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{14}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(27.8-(24.95))^2+(23.84-(24.95))^2+...+(27.24-(24.95))^2]}\\\\\\s=\sqrt{\dfrac{1}{13}\cdot [(8.106)+(1.238)+...+(5.23)]}\\\\\\ s=\sqrt{\dfrac{304.036}{13}}=\sqrt{23.39}\\\\\\s=4.8[/tex]

This is a hypothesis test for the population mean.

The claim is that the consumption of milk in the Midwest is significantly higher than the national average.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=23.8\\\\H_a:\mu> 23.8[/tex]

The significance level is 0.01.

The sample has a size n=14.

The sample mean is M=24.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=4.8.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{4.8}{\sqrt{14}}=1.28[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{24.95-23.8}{1.28}=\dfrac{1.15}{1.28}=0.9[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=14-1=13[/tex]

This test is a right-tailed test, with 13 degrees of freedom and t=0.9, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t>0.9)=0.1932[/tex]

As the P-value (0.1932) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the consumption of milk in the Midwest is significantly higher than the national average.


Related Questions

The temperature in a town is −2.7°C. The temperature decreases 3°C. What is the new temperature? Incorrect

Answers

Answer:

-5.7° C

Step-by-step explanation:

-2.7 °C (degrees Celsius) - 3 °C (degrees Celsius) = -5.7° C

Simplify (x2y)3. x 5y 3 x 2y 3 x 6y 3

Answers

Answer:

[tex]x^{6} y^{3}[/tex]

Step-by-step explanation:

[tex](x^2y)3[/tex]

[tex]x^{2 \times 3} \times y^3[/tex]

[tex]x^{6} \times y^3[/tex]

In the rectangular prism, express each of the following in terms of s, t, and u. Give an explanation for each of your answers.
(a) HK
(b) GL
(c)JH

Answers

Complete Question

The complete question is shown on the first  and second uploaded image

Answer:

a

  [tex]\= HK = \= t + \= u[/tex]

b

  [tex]\= GL = \= s - \= t[/tex]

c

[tex]\= JH = \= u + \= s[/tex]

Step-by-step explanation:

Now looking at the diagram

Following the direction of the unit vectors [tex]\= u , \= s, \= t[/tex]

     [tex]\= {HK} = \= {KI} + \= KL[/tex]

=>   [tex]\= HK = \= t + \= u[/tex]

And  

    [tex]\= GL = \= GH + \= GF[/tex]  jjj

=>   [tex]\= GL = \= s - \= t[/tex]

Also

    [tex]\= JH = \= JG + \= JI[/tex]

=>  [tex]\= JH = \= u + \= s[/tex]

15 POINTS & BRAINLIEST!!!

How do you find the axis of symmery in the form f(x) = 3(x - 4)^2 + 5?

Answers

Answer:

so the axis of symmetry is x=4

Answer: X = 4

Explanation: Hope it helps you♡

Felicia walks 3 blocks west, 4 blocks south, 3 more blocks west, then
2 blocks south again. How far is Felicia from her starting point?
Answer:
blocks

Answers

Answer: i did the question i told you the steps

Step-by-step explanation:

From the starting point move three to the left. Then move four down. Then move three times to the left. Lastly move two down.

Solve for x
A) 10
B) 20
C) 30
D) 60
Help me I’m so pretty and funny I need help, worms infesting my brain.

Answers

Answer:

Option (2). x = 20°

Step-by-step explanation:

In the figure attached,

ΔABC is an equilateral triangle.

By the property of equilateral triangle, all sides of the triangle are equal and measure of all angles of the triangle is 60°.

By this property,

m∠B = 60°

and y = 46 - 16 = 30

By applying Sine rule in ΔBCD,

[tex]\frac{\text{sin}60}{BD}=\frac{\text{sin}80}{46}=\frac{\text{sin}(\angle CBD)}{DC}[/tex]

[tex]\frac{\text{sin}80}{46}=\frac{\text{sin}(\angle CBD)}{y}[/tex]

sin(∠CBD) = [tex]\frac{30\times \text{sin}80}{46}[/tex]

                 = 0.6423

m∠CBD = 39.96

              ≈ 40°

m∠ABD = 60° - 40°

             = 20°

Therefore, Option (2). 20° will be the answer.

What is the value of X ? A-17 B-26 C-39 D-41

Answers

Answer:

D.

Step-by-step explanation:

It's a right triangle so

[tex]x^2=40^2+9^2[/tex]

x = 41

Which answer is equivalent to the equation shown below?
7c = 49
A.log7 c = 49
B.c = log49 7
C.logc49 = 7
D.c = log7 49

Answers

Answer:

D.

Step-by-step explanation:

The base of a log is also the base of an exponent. So 7 to the c power, our 7 would be the base. To find c, we simply just do log base 7 of 49, which comes out to be 2.

Answer: D
Hope this helped

Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication a at what time will you need to stop the infusion

Answers

Answer:

6 PM

Step-by-step explanation:

125 mg --- 300 mL

500 mg --- x mL

x = 500*300/125 = 1200 mL solution contains 500 mg

rate = 100 mL/h

1200 mL* 1h/100 mL = 12 h

6AM + 12 h = 6 PM

You need to stop infusion  at 6 PM

It is found that You need to stop infusion at 6 PM.

What is the unitary method?

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that Liquid suspension contains 125 MG of medication aide for every 300 ML solution this is Spenton is being infused into a patient at the rate of 100 ML per hour if the infusion started at 6 AM and the patient needs 500 MG of the medication.

125 mg = 300 mL

500 mg = x mL

x = 500*300/125

x = 1200 mL

Here solution contains 500 mg

The rate = 100 mL/h

1200 mL* 1h/100 mL = 12 h

6AM + 12 h = 6 PM

Therefore, You need to stop infusion at 6 PM.

Learn more about the unitary method;

https://brainly.com/question/23423168

#SPJ2

A solid lies between planes perpendicular to the​ x-axis at xequals=0 and xequals=1212. The​ cross-sections perpendicular to the axis on the interval 0less than or equals≤xless than or equals≤1212 are squares with diagonals that run from the parabola y equals negative 2 StartRoot x EndRooty=−2x to the parabola y equals 2 StartRoot x EndRooty=2x. Find the volume of the solid.

Answers

Question:

A solid lies between planes perpendicular to the​ x-axis at x=0 and x=12. The​ cross-sections perpendicular to the axis on the interval 0≤x≤12 are squares with diagonals that run from the parabola y=-2√x to the parabola y=2√x. Find the volume of the solid.

Answer:

576

Step-by-step explanation:

Given:

Length of diagonal square:

[tex] D = 2\sqrt{x} - (-2\sqrt{x}) [/tex]

[tex] D = 4\sqrt{x} [/tex]

Here, the diagonal is the hypotenus of a right angle triangle, with leg S, where the square has a side of length S.

Using Pythagoras theorem:

[tex] S^2 + S^2 = D^2 [/tex]

[tex] S^2 + S^2 = (4\sqrt{x})^2 [/tex]

[tex] 2S^2 = 16x [/tex]

Divide both sides by 2

[tex] S^2 = 8x [/tex]

Thus,

Area, A = S² = 8x

Take differential volume, dx =

dV = Axdx

dV = 8xdx

Where limit of solid= 0≤x≤12

Volume of solid, V:

V =∫₀¹² dV

V = 8 ∫₀¹² xdx

V = [4x²]₀¹²

V = 4 (12)²

V = 12 * 144

= 576

Volume of solid = 576

The sum is type answer as integer proper fraction or mixed number simplify answer

Answers

Answer:

[tex]9\dfrac{5}{6}[/tex]

Step-by-step explanation:

[tex]5\dfrac{1}{6}+4\dfrac{2}{3}=\\\\5\dfrac{1}{6}+4\dfrac{4}{6}=\\\\9\dfrac{5}{6}[/tex]

Hope this helps!

Suppose Carol Danvers invested $1,000 into an account paying 6% annual interest compounded
annually.

How much is in her account at the end of one year?

Answers

Answer:

$ 1,060.00

Step-by-step explanation:

A = $ 1,060.00

A = P + I where

P (principal) = $ 1,000.00

I (interest) = $ 60.00

Compound Interest Equation

A = P(1 + r/n)^nt

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

What is 1.036 that add up to 4

Answers

Answer:

2.964

Step-by-step explanation:

Answer 2.964

Explanation

Bonita said that the product of 5/6 x 1 2/3 is 7/3. How can you tell that her answer is wrong.

Answers

Answer:=

1 7/18

Step-by-step explanation:

Turn the improper fraction into a mixed fraction.

A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled "The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes, and depth D is in meters. The report then says, "The regression equation for this bird is: DD = 2.69 + 0.0138D.
1. What is the slope of the regression line?
2. Explain in specfic language what this slope says about this penguin's dives.
A. If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.
B. If the depth of the dive is decreased by one meter, it adds 0.0138 minutes to the time spent under water.
C. If the depth of the dive is increased by 0.0138 meter, it adds one minute to the time spent under water.
3. According to the regression line, how long does a typical dive to a depth of 200 meters last?
4. According to the regression line, how long does a typical dive to a depth of 210 meters last?
5. According to the regression line, how long does a typical dive to a depth of 220 meters last?
6. According to the regression line, how long does a typical dive to a depth of 230 meters last?
7. According to the regression line, how long does a typical dive to a depth of 240 meters last?
8. According to the regression line, how long does a typical dive to a depth of 150 meters last?
9. According to the regression line, how long does a typical dive to a depth of 160 meters last?
10. According to the regression line, how long does a typical dive to a depth of 170 meters last?
11. According to the regression line, how long does a typical dive to a depth of 180 meters last?
12. According to the regression line, how long does a typical dive to a depth of 190 meters last?

Answers

Answer:

(1)0.0138

(2)A. If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.

Nos 3-12: See Explanation

Step-by-step explanation:

Given the regression equation for the relation of dive duration (DD) to depth (D).

[tex]DD = 2.69 + 0.0138D\\$Where: Duration DD is measured in minutes\\epth D is in meters.[/tex]

(1)The slope of the regression lie =0.0138

(2)

When D=1, DD = 2.69 + 0.0138(1)=2.7038

When D=2, DD = 2.69 + 0.0138(2)=2.7176

2.7176-2.7038=0.0138

Therefore, If the depth of the dive is increased by one meter, it adds 0.0138 minutes to the time spent under water.

(3) When depth, D =200 meters

DD = 2.69 + 0.0138(200)=5.45 Minutes

(4) When depth, D =210 meters

DD = 2.69 + 0.0138(210)=5.588 Minutes

(5) When depth, D =220 meters

DD = 2.69 + 0.0138(220)=5.726 Minutes

(6) When depth, D =230 meters

DD = 2.69 + 0.0138(230)=5.864 Minutes

(7) When depth, D =240 meters

DD = 2.69 + 0.0138(240)=6.002 Minutes

(8) When depth, D =150 meters

DD = 2.69 + 0.0138(150)=4.76 Minutes

(9) When depth, D =160 meters

DD = 2.69 + 0.0138(160)=4.898 Minutes

(10) When depth, D =170 meters

DD = 2.69 + 0.0138(170)=5.036 Minutes

(11) When depth, D =180 meters

DD = 2.69 + 0.0138(180)=5.174 Minutes

(12) When depth, D =190 meters

DD = 2.69 + 0.0138(190)=5.312 Minutes

A regression line is only a single line that fits the data the best. It tells how steep it is, whereas the intercept reveals where it intersects an axis.

Regression line:

For question 1):

By calculating the slope of the regression line we get the slope value that is [tex]= 0.0138[/tex]

For question 2):

Describe whatever this slope means about this penguin's dives in precise terms.

The time spent under liquid increases by 0.0138 minutes whenever the diving depth is raised by one meter, which is equal to "Option A".

For question 3):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times200 = 2.69+2.76 = 5.45\ minutes[/tex]

For question 4):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times210 = 2.69 + 2.898 = 5.588\ minutes[/tex]

For question 5):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 220 = 2.69 + 3.036 = 5.726\ minutes[/tex]

For question 6):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times230 = 2.69 + 3.174 = 5.864 \ minutes[/tex]

For question 7):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times240 = 2.69 + 3.312 = 6.002\ minutes[/tex]

For question 8):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 150 = 2.69 + 2.07 = 4.76\ minutes[/tex]

For question 9):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 160 = 2.69 + 2.208 = 4.898\ minutes[/tex]

For question 10):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 170 = 2.69 + 2.346 = 5.036\ minutes[/tex]

For question 11):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 180 = 2.69 + 2.484 = 5.174 \ minutes[/tex]

For question 12):

Calculated equation:

[tex]\to DD = 2.69 + 0.0138\times 190 = 2.69 + 2.622 = 5.312\ minutes[/tex]

Find out more about the regression line here:

brainly.com/question/7656407

Name the x-axis of symmetry for the parabola sketched below

Answers

Answer:

x=-3

Step-by-step explanation:

The vertex is at x = -3

The axis of symmetry is along the vertex

x=-3

Answer:

x=-3

Step-by-step explanation:

To find the axis of symmetry, you just need to find the x-coordinate of the vertex using this formula: -b/2a=x  

*Only when provided a three variable quadratic equation.

For looking at a graph, you find the center of the parabola in which when you reflect it over itself, it will be symmetrical.

According to the graph, x=-3 is the line which you can draw to fold over to the other side and it can fit perfectly.

A thermometer shows a temperature of Negative 20 and three-fourths degrees. A chemist recorded this temperature in her notebook using a decimal. Which number did the chemist write in the notebook?

Answers

Answer:

20.75

Step-by-step explanation:

Answer:

C. -20.75

Step-by-step explanation:

A political analyst believes that a senator's recent decision to support a bill resulted in a drop of approval ratings. To test this claim, he selects random cities in the state that voted the senator in and compares the approval ratings before the decision to the approval ratings after the decision. Suppose that data were collected for a random sample of 8 cities, where each difference is calculated by subtracting the percent approval rating before the decision from the percent approval rating after the decision. Assume that the percentages are normally distributed. What type of test is this hypothesis test?

Answers

Answer:

A paired sample t-test

Step-by-step explanation:

A paired sample t-test is most of the time used when in determining the difference between two related dependent variables and in this context; we have

approval ratings before the senator's decision variables and

approval rating after the senator's decision variables for the same subject

These revolves around the senator's decision causing a decrease in approval ratings. Often the two variables are separated by time.

It is used to determine whether the mean of the dependent variable (approval ratings) is the same in the two related groups (the before and after decision groups).

The perimeter of the rectangle is 28 units.

A rectangle with perimeter 28 units is shown. The length of the sides is w, and the length of the top and bottom sides are 2 w minus 1.

What is the value of w?

5 units
7 units
14 units
15 units

Answers

Answer:

5 units

Step-by-step explanation:

P=2(w)+2(2w-1)

28=2w+4w-2

30=6w

w=5

Answer:

5

Step-by-step explanation:

Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation. Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths. What is OB'? 1.5 units 3 units 4.5 units 6 units

Answers

If the length of OB was ³/₄, then the length of OB' after dilation is; Option B: 3 units.

Dilation of an object simply means enlarging or shrinking of the object by a scale factor.

Now, we are told that Triangle ABC was dilated to Triangle A'B'C' using the rule D₀,₄.

What this means is that it was enlarged by a scale factor of 4 with point O as the center of dilation.

Now, if the length of OB is 3/4, it means that the new dilated length is gotten from;

Scale factor = new dilated length OB'/(³/₄)

new dilated length OB' = ³/₄ × 4

new dilated length OB' = 3 units

Read more on dilation at; https://brainly.com/question/8532602

Answer:

its 4 units trust just answered it

Step-by-step explanation:

A random sample of 1,000 StatCrunchU students contains 598 female and 402 males. We analyze responses to the question, "What is the total amount (in dollars) of your student loans to date?" Two sample T confidence interval: μ 1: Mean of Loans where Gender="Female" μ 2: Mean of Loans where Gender="Male" μ 1 − μ 2: Difference between two means (without pooled variances) 95% confidence interval results: Difference Sample Diff. Std. Err. DF L. Limit U. Limit μ 1 − μ 2 516.74334 368.41116 907.34739 -206.29374 1239.7804 What can we conclude from the 95% confidence interval? Check all that apply. Group of answer choices

Answers

Based on the information given, these are the conclusions we can draw from the 95% confidence interval.

Here, we have,

From the provided 95% confidence interval, we can make the following conclusions:

The point estimate of the difference between the mean student loans for females and males is 516.74334 dollars.

The standard error of the difference between the means is 368.41116 dollars.

The degrees of freedom (DF) associated with the confidence interval is 907.34739.

The lower limit of the confidence interval is -206.29374 dollars.

The upper limit of the confidence interval is 1239.7804 dollars.

The confidence interval does not contain zero.

Since zero is not within the interval, we can conclude that the difference between the mean student loans for females and males is statistically significant at the 95% confidence level.

Based on the information given, these are the conclusions we can draw from the 95% confidence interval.

Learn more about confidence interval here:

brainly.com/question/32546207

#SPJ12

The estimated difference in the mean student loans between females and males is 516.74334.

There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.

Based on the 95% confidence interval provided for the difference in means between the loans of female and male StatCrunchU students, we can draw the following conclusions:

The sample difference in means is 516.74334.

The standard error of the difference is 368.41116.

The degrees of freedom (DF) for the analysis is 907.34739.

The lower limit of the confidence interval is -206.29374.

The upper limit of the confidence interval is 1239.7804.

Therefore, we can conclude the following:

The estimated difference in the mean student loans between females and males is 516.74334.

There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.

Note: Since the confidence interval includes both positive and negative values, we cannot conclude with certainty whether there is a significant difference or not in the mean student loans between females and males. The confidence interval suggests that the difference could be positive, negative, or even zero.

For more such questions on difference in the mean

https://brainly.com/question/29160629

#SPJ8

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

                 

Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication. At this rate of decay, how many bacteria will there be in 8 hours?

Answers

Answer:

There will be 66 bacteria in 8 hours.

Step-by-step explanation:

The number of bacteria after t hours is given by the following formula.

[tex]P(t) = P(0)(1-r)^{t}[/tex]

In which P(0) is the initual number of bacteria and r is the decay rate.

Researchers recorded that a certain bacteria population declined from 750,000 to 250 in 48 hours after the administration of medication.

This means that [tex]P(0) = 750000, P(48) = 250[/tex]

We use this to find r. So

[tex]P(t) = P(0)(1-r)^{t}[/tex]

[tex]250 = 750000(1-r)^{48}[/tex]

[tex](1-r)^{48} = \frac{250}{750000}[/tex]

[tex]\sqrt[48]{(1-r)^{48}} = \sqrt[48]{\frac{250}{750000}}[/tex]

[tex]1-r = 0.84637[/tex]

So

[tex]P(t) = 750000(0.84637)^{t}[/tex]

How many bacteria will there be in 8 hours?

8 hours from now, in this context, is 8 + 48 = 56 hours. So this is P(56).

[tex]P(56) = 750000(0.84637)^{56} = 65.83[/tex]

Rounding to the nearest number

There will be 66 bacteria in 8 hours.

Answer:

197,488

Step-by-step explanation:

This problem requires two main steps. First, we must find the unknown rate, k. Then, we use that value of k to help us find the unknown number of bacteria.

Identify the variables in the formula.

AA0ktA=250=750,000=?=48hours=A0ekt

Substitute the values in the formula.

250=750,000ek⋅48

Solve for k. Divide each side by 750,000.

13,000=e48k

Take the natural log of each side.

ln13,000=lne48k

Use the power property.

ln13,000=48klne

Simplify.

ln13,000=48k

Divide each side by 48.

ln13,00048=k

Approximate the answer.

k≈−0.167

We use this rate of growth to predict the number of bacteria there will be in 8 hours.

AA0ktA=?=750,000=ln13,00048=8hours=A0ekt

Substitute in the values.

A=750,000eln13,00048⋅8

Evaluate.

A≈197,488.16

At this rate of decay, researchers can expect 197,488 bacteria.

Dan buys a car for £2300. It depreciates at a rate of 0.2% per year. How much will it be worth in 6 years? Give your answer to the nearest penny where appropriate.

Answers

9514 1404 393

Answer:

  £2272.54

Step-by-step explanation:

An equation for the value is ...

  v = £2300(0.998^t)

Then for t=6, the value is ...

  v = £2272.54

_____

Additional comment

The growth factor (0.998) is (1 - decay rate) = (1 -0.002).

Answer:

the answer is 2272.54

Step-by-step explanation:

:))

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: –55x + 570

Step-by-step explanation:

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

a consumer affairs company is interested in testing at the 5% level of significance that the average weight of a package of butter is less than 16 oz if the p value is 0.003 the conclusion is​

Answers

1.7789 should be the correct answer

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:

The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.

Step-by-step explanation:

Two planes:

The first one's speed is x

The second is y.

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

I will say that y = 2x.

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

Same direction, so their relative speed is the subtraction of their speeds. 2x - x = x.

Means that after 1 hour, they will be x miles apart.

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

After 1 hour, 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

The slower plane has a speed of 450 km/h and the faster one has a speed of 900 km/h.

Graph the line that represents this equation. 3x - 4y =8

Answers

Answer:

See attachment

Step-by-step explanation:

The solution is given in the image.

Which graph is the graph of the function?

The graph of a feature f is the set of all factors in the plane of the form (x, f(x)). We can also outline the graph of f to be the graph of the equation y = f(x). So, the graph of a feature is a special case of the graph of an equation.

What does the axis of a graph constitute?

An axis is a line to the aspect or backside of a graph; it's far labeled to give an explanation for the graph's meaning and the devices of measurement. The x-axis, the horizontal line at the lowest of a graph, may be labeled to present facts about what the graph represents.

Learn more about graphs here: brainly.com/question/4025726

#SPJ2

n a group of 40 people, 10 people are healthy. The 30 unhealthy people have either high blood pressure, high cholesterol, or both. Suppose 15 have high blood pressure and 25 have high cholesterol. If a person is randomly selected from this group, what is the probability that they have both high blood pressure and high cholesterol

Answers

Answer:

If a person is randomly selected from this group, the probability that they have both high blood pressure and high cholesterol is P=0.25.

Step-by-step explanation:

We can calculate the number of people from the sample that has both high blood pressure (HBP) and high cholesterol (HC) using this identity:

[tex]N(\text{HBP or HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP and HC})\\\\\\ N(\text{HBP and HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP or HC})\\\\\\ N(\text{HBP and HC})=15+25-30=10[/tex]

We can calculate the probability that a random person has both high blood pressure and high cholesterol as:

[tex]P(\text{HBP and HC})=\dfrac{10}{40}=0.25[/tex]

luke is 5 years younger than 3 times sydenys age, s in this situation what does 3s represent

Answers

3s represents three times Sydney's age. Sydney's age is symbolized with an S.

Other Questions
Hewlett-Packard introduced its HP Tablet a few years after Apple launched its original iPad, about the same time Apple introduced its next-generation iPad2. HP Tablet sales were very disappointing, and Hewlett-Packard eventually killed the product. According to the text, the primary reason for the HP Tablets failure was due in large part to:_____a. poor product qualityb. not satisfying customer needs on critical factors.c. an insignifanct point of differenced. bad timing There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 7/10There are 42 red marbles in the bag and each is equally likely to be chosen. How many marbles in total must there be? The sum of an infinite geometric sequence is seven times the value of its first term. a) Find the common ratio of the sequence.b) Find the least number of terms of the sequence that must be added in order for the sum to exceed half the value ofthe infinite sum. If 20 drops fall in 76 seconds, how long will 8 drops take? Find a linear second-order differential equation F(x, y, y', y'') = 0 for which y = c1x + c2x4 is a two-parameter family of solutions. Make sure that your equation is free of the arbitrary parameters c1 and c2. (Use yp for y' and ypp for y''.) Many colonist were angered by Proclamation of 1763 mainly to (1) took to much land from California (2) Gave Florida to the French (3) Limited their Freedom to move west (4) Encouraged raids by Native American Indians Subject complements follow action verbs and rename or describe thesubject. true or false? *I WILL MARK YOU BRAINLIEST!!!!!!* Problem 15-10 The term structure for zero-coupon bonds is currently: Maturity (Years) YTM (%) 1 4.1 % 2 5.1 3 6.1 Next year at this time, you expect it to be: Maturity (Years) YTM (%) 1 5.1 % 2 6.1 3 7.1 a. What do you expect the rate of return to be over the coming year on a 3-year zero-coupon bond? (Round your answer to 1 decimal place.) b-1. Under the expectations theory, what yields to maturity does the market expect to observe on 1- and 2-year zeros at the end of the year? (Round your answers to 2 decimal places.) b-2. Is the market's expectation of the return on the 3-year bond greater or less than yours? Greater Less rev: 09_14_2018_QC_CS-134332 What clue do you use when you dont know the meaning of a word in a sentence In his Revolutionary-era pamphlet Common Sense, Thomas Paine uses thephrases "Tis not the affair" and "Tis not the concern" to help illustrate theimportance of separating from Great Britain. This is an example of whichrhetorical technique?A. HyperboleB. DictationC. EthosD. Parallelism Question 19 / 50In a class of forty students, one fifth of the students also play on the school'sfootball team. If four more students from the class join the football team, whatpercentage of students in the class will be on the football team?25%30%0 33%O 35%40%Submit Answer Which of the following best describes The League of Nations in postwar Europe?O a successful peacekeeping forceO a forum for solving problemsO a weak and ineffective organizationOa group that provoked international distrust which of the speakers words provide clues to the tone ? Find the slope of a line that crosses through (-5,-2) and (9,3) Why do some quadratic graphs move left or right and others do not? Is there a correlation between this and them moving up and down? How would you demonstrate your reasoning is correct? Which of these triangle pairs can be mapped to each other using a reflection and a translation?OLARKKQAPR Simplify. x+5/x^2+6x+51/x+1; where x -11/x+1; where x -1,-51/x-5; where x 5X-5 describe what factors can make it difficult to reintroduce captive animals into their natural habitats. Las palabras estn desordenadas, alguien que las ordene por favor ;-; se les agradecera muchsimooo, este es el refrn desordenado : vaya - pero - amistad - La - prejuicio - sin - ninguno - venga