Test the claim that the proportion of people who own cats is significantly different than 80% at the 0.2 significance level. The null and alternative hypothesis would be:______.
A. H0 : μ = 0.8 H 1 : μ ≠ 0.8
B. H0 : p ≤ 0.8 H 1 : p > 0.8
C. H0 : p = 0.8 H 1 : p ≠ 0.8
D. H0 : μ ≤ 0.8 H 1 : μ > 0.8
E. H0 : p ≥ 0.8 H 1 : p < 0.8
F. H0 : μ ≥ 0.8 H 1 : μ < 0.8
The test is:_____.
a. left-tailed
b. right-tailed
c. two-tailed
Based on a sample of 200 people, 79% owned cats.
The test statistic is:______.
The p-value is:_____.
Based on this we:_____.
A. Fail to reject the null hypothesis.
B. Reject the null hypothesis.

Answers

Answer 1

Answer:

C. H0 : p = 0.8 H 1 : p ≠ 0.8

The test is:_____.

c. two-tailed

The test statistic is:______p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]

The p-value is:_____. 0.09887

Based on this we:_____.

B. Reject the null hypothesis.

Step-by-step explanation:

We formulate null and alternative hypotheses as  proportion of people who own cats is significantly different than 80%.

H0 : p = 0.8 H 1 : p ≠ 0.8

The alternative hypothesis H1 is that the 80% of the  proportion is different and null hypothesis is , it is same.

For a two tailed test for significance level = 0.2 we have critical value  ± 1.28.

We have alpha equal to 0.2  for a two tailed test . We divided alpha with 2 to get the answer for a two tailed test. When divided by two it gives 0.1 and the corresponding value is ± 1.28

The test statistic is

p ± z (base alpha by 2) [tex]\sqrt{\frac{pq}{n} }[/tex]

Where p = 0.8 , q = 1-p= 1-0.8= 0.2

n= 200

Putting the values

0.8 ± 1.28 [tex]\sqrt{\frac{0.8*0.2}{200} }[/tex]

0.8 ± 0.03620

0.8362, 0.7638

As the calculated value of z lies within the critical region  we reject the null hypothesis.


Related Questions

A number is chosen at random from 1 to 10. Find
the probability of selecting 4 or a factor of 6.
Step by step.

Answers

Answer:

1/2

Step-by-step explanation:

The possible outcomes are

1,2,3,4,5,6,7,8,9,10

Factors of 6 are 1,2,3,6

or a 4

1,2,3,4,6 are the outcomes we want

There are 5 "good" outcomes

P( 4 or a factor of 6) = "good" outcomes/ total

                                  = 5/10

                                   =1/2

Answer:

[tex]\boxed{\frac{1}{2} }[/tex]

Step-by-step explanation:

There are total 10 outcomes.

[tex]1,2,3,4,5,6,7,8,9,10[/tex]

The probability of selecting 4 is 1 outcome out of total 10 outcomes.

Factors of 6 are [tex]1,2,3,6[/tex].

These are 4 outcomes out of total 10 outcomes.

The probability of selecting 4 or a factor of 6 is:

[tex]\displaystyle \frac{1}{10} +\frac{4}{10} =\frac{5}{10} =\frac{1}{2}[/tex]

STUCK Basic geometry A for senior year school

Answers

Answer:

(C) A reflection across a horizontal line and a horizontal translation

Step-by-step explanation:

We can see that, near the x-axis, these shapes are 3 y values away from the x-axis, meaning that if we reflect one over the x-axis we will be at the same y values as the other shape.

Reflecting these points shows that we’ve got the same shape, just skewed the one side. We can then translate this shape horizontally to get it to where we want it.

Hope this helped!

Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute.
1. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = (x - mu )?
2. What are the units of the corresponding z scores?
A. The z scores are measured with units of "beats per minute".
B. The z scores are measured with units of "minutes per beat".
C. The z scores are measured with units of "beats."
D. The z scores are numbers without units of measurement.

Answers

Answer:

D. The z scores are numbers without units of measurement.

Step-by-step explanation:

Z-scores are without units, or are pure numbers.

Find a set of parametric equations for y= 5x + 11, given the parameter t= 2 – x

Answers

Answer:

[tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex]

Step-by-step explanation:

Given that [tex]y = 5\cdot x + 11[/tex] and [tex]t = 2-x[/tex], the parametric equations are obtained by algebraic means:

1) [tex]t = 2-x[/tex] Given

2) [tex]y = 5\cdot x +11[/tex] Given

3) [tex]y = 5\cdot (x\cdot 1)+11[/tex] Associative and modulative properties

4) [tex]y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11[/tex] Existence of multiplicative inverse/Commutative property

5) [tex]y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11[/tex] Associative property

6) [tex]y = -5\cdot (-x)+11[/tex]  [tex]\frac{a}{-b} = -\frac{a}{b}[/tex] / [tex](-1)\cdot a = -a[/tex]

7) [tex]y = -5\cdot (-x+0)+11[/tex] Modulative property

8) [tex]y = -5\cdot [-x + 2 + (-2)]+11[/tex] Existence of additive inverse

9) [tex]y = -5 \cdot [(2-x)+(-2)]+11[/tex] Associative and commutative properties

10) [tex]y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11[/tex] Distributive property

11) [tex]y = (-5)\cdot (2-x) +21[/tex] [tex](-a)\cdot (-b) = a\cdot b[/tex]

12) [tex]y = (-5)\cdot t +21[/tex] By 1)

13) [tex]y = -5\cdot t +21[/tex] [tex](-a)\cdot b = -a \cdot b[/tex]/Result

14) [tex]t+x = (2-x)+x[/tex] Compatibility with addition

15) [tex]t +(-t) +x = (2-x)+x +(-t)[/tex] Compatibility with addition

16) [tex][t+(-t)]+x= 2 + [x+(-x)]+(-t)[/tex] Associative property

17) [tex]0+x = (2 + 0) +(-t)[/tex] Associative property

18) [tex]x = 2-t[/tex] Associative and commutative properties/Definition of subtraction/Result

In consequence, the right answer is [tex]x = 2-t[/tex] and [tex]y = -5\cdot t +21[/tex].

Musah stands at the centre of a rectangular field. He first takes 50 steps north, then 25 steps

west and finally 50 steps on a bearing of 3150

.

i. Sketch Musah’s movement​

Answers

Answer:

Step-by-step explanation:

Following the cardinal points as regards location of points, the sketch of Musah's movement can be as what is attached to this answer.

What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)?

Answers

Answer:

90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

Here is the equation

[tex]20+3\times(7+4)+5+2\times(7+9)[/tex]

In the order of operations parentheses go first so we get

[tex]20+3\times11+5+2\times16[/tex]

Next we do the multiplication

[tex]20+33+5+32\\[/tex]

And finally we add them all up

[tex]20+33+5+32=90\\[/tex]

Thus, 90 is the answer of [tex]20+3\times(7+4)+5+2\times(7+9)[/tex] or [tex]20+3(7+4)+5+2(7+9)[/tex]

A company has 8 mechanics and 6 electricians. If an employee is selected at random, what is the probability that they are an electrician

Answers

Answer:

[tex]Probability = \frac{3}{7}[/tex]

Step-by-step explanation:

Given

Electrician = 6

Mechanic = 8

Required

Determine the probability of selecting an electrician

First, we need the total number of employees;

[tex]Total = n(Electrician) + n(Mechanic)[/tex]

[tex]Total = 6 + 8[/tex]

[tex]Total = 14[/tex]

Next, is to determine the required probability using the following formula;

[tex]Probability = \frac{n(Electrician)}{Total}[/tex]

[tex]Probability = \frac{6}{14}[/tex]

Divide numerator and denominator by 2

[tex]Probability = \frac{3}{7}[/tex]

Hence, the probability of selecting an electrician is 3/7

* The American Diabetes Association estimates that 8.3% of people in the
United States have diabetes. Suppose that a medical lab has developed
a simple diagnostic test for diabetes that is 98% accurate for people who
have the disease and 95% accurate for people who do not have it. The
medical lab gives the test to a randomly selected person. What is the
probability that the diagnosis is correct? Explain each step.​

Answers

Answer:

The probability that the diagnosis is correct is 0.95249.

Step-by-step explanation:

We are given that the American Diabetes Association estimates that 8.3% of people in the United States have diabetes.

Suppose that a medical lab has developed a simple diagnostic test for diabetes that is 98% accurate for people who have the disease and 95% accurate for people who do not have it.

Let the probability that people in the United States have diabetes = P(D) = 0.083.

So, the probability that people in the United States do not have diabetes = P(D') = 1 - P(D) = 1 - 0.083 = 0.917

Also, let A = event that the diagnostic test is accurate

So, the probability that a simple diagnostic test for diabetes is accurate for people who have the disease = P(A/D) = 0.98

And the probability that a simple diagnostic test for diabetes is accurate for people who do not have the disease = P(A/D') = 0.95

Now, the probability that the diagnosis is correct is given by;

    Probability = P(D) [tex]\times[/tex] P(A/D) + P(D') [tex]\times[/tex] P(A/D')

                      = (0.083 [tex]\times[/tex] 0.98) + (0.917 [tex]\times[/tex]0.95)

                      = 0.08134 + 0.87115

                      = 0.95249

Hence, the probability that the diagnosis is correct is 0.95249.

In a simple regression analysis with age as the only explanatory variable, the effects of other factors, such as faminc, are

Answers

Answer:

In the error term.

Step-by-step explanation:

A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).

Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.

An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind. What is the speed of the plane in still air and what is the wind speed?

Answers

Answer:

Speed of plane in still air is 270 mph

Wind speed is 30 mph

Step-by-step explanation:

Check the picture.

The speed of the plane in still air is 270 mph and the speed of the wind will be 30 mph.

What is the distance formula?

The distance traveled by an object is the product of the speed of an object and the time taken.

Distance = speed x time

An airplane travels 1200 miles in 4 hours with the wind. The same trip takes 5 hours against the wind.

Let the speed of the plane be x

The speed of wind be y

Distance covered with the wind = (x + y)t

                  1200   =  (x + y)4

                   (x + y) = 1200/4

                     (x + y)= 300       .....(a)

Distance covered against the wind = (x - y)t

                                              1200   =  (x - y)5

                                               (x - y) = 1200/5

                                                 (x - y) = 240         .......(b)

By solving both the equation

(x + y)= 300    

(x - y) = 240    

Therefore the values will be x= 270mph and  y = 30 mph

Learn more about the distance formula:

https://brainly.com/question/15172156

In a recent year, a sample of grade 8 Washington State public school students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34.4. Possible test scores could range from 0 to 500. Assume that the scores are normally distributed. Question 9 (2.5 points) If 2000 students are randomly selected, how many would you expect to have a score between 250 and 305?

Answers

Answer:

The  number is  [tex]N =1147[/tex] students

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 281[/tex]

     The standard deviation is  [tex]\sigma = 34.4[/tex]

    The sample size is  n = 2000

percentage of the would you expect to have a score between 250 and 305 is mathematically represented as

      [tex]P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )[/tex]

Generally  

             [tex]\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )[/tex]

So  

         [tex]P(250 < X < 305 ) = P(-0.9012< Z<0.698 )[/tex]

       [tex]P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)[/tex]

From the z table  the value of  [tex]P( z_2 < 0.698) = 0.75741[/tex]

                                         and  [tex]P(z_1 < -0.9012) = 0.18374[/tex]

     [tex]P(250 < X < 305 ) = 0.75741 - 0.18374[/tex]

      [tex]P(250 < X < 305 ) = 0.57[/tex]

The  percentage is  [tex]P(250 < X < 305 ) = 57\%[/tex]

The  number of students that will get this score is

           [tex]N = 2000 * 0.57[/tex]

           [tex]N =1147[/tex]

This solid shape is made from 5 cubes. Which of the diagrams show the plan of the solid? Please help!

Answers

Answer:

A Maybe

Step-by-step explanation:

Cogntive identification

Unable to answer mathematically or analytically

The Plan of the solid shape is shown by : (A)

What is the Meaning of solid shape?

A solid shape can be defined as a shape that possesses three dimensions. that is to say they are three dimensional shapes.

A solid shape has both length, width and height. They are more tangible and look physical than two dimensional shape.

solid shapes can take up space in the universe because they are more tangible and realistic.

In conclusion, the Plan of the solid shape is shown by : (A)

Learn more about solid shape: https://brainly.com/question/16717260

#SPJ2

Write 8:18 as a fraction in simplest form.

Ratio as a Fraction:

Fraction in Simplest Form:

Answers

Answer:

[tex]\text{Ratio as a fraction - \: \boxed{\frac{8}{18}}}[/tex]

[tex]\text{Fraction in simplest form - \boxed{\frac{4}{9}}}[/tex]

Step-by-step explanation:

Part 1: Writing a ratio as a fraction

A fraction and a ratio are the same thing - just a different name. Therefore, the colon in a ratio is the same as a divisor line in a fraction. Therefore, to write a ratio as a fraction,

Replace the colon with a divisor line or the divisor line with a colon (use the first portion to transform a ratio into a fraction and the second form to transform a fraction into a ratio).

Therefore, 8:18 as a fraction is 8/18.

Part 2: Fraction in simplest form

To put a fraction in simplest form, first divide the numerator by the denominator. If it contains a remainder, you cannot use this step to verify it.

8 only goes into 18 twice and leaves a 2 as a remainder, so this method does not work.

Instead, if both numbers are even, divide by 2.

8/2 = 4

18/2 = 9

Check to see if the new numerator and denominator can reduce any further.

4/9 = 4/9

The fraction in simplest form is 4/9.

Multiply the following complex numbers:
(7+2i)(2+3i)

Please don’t guess

Answers

Answer:

14 + 25l + 6l^2

Step-by-step explanation:

(7 + 2i) (2 + 3i)

=> 14 + 4l + 21l + 6l^2

=> 14 + 25l + 6l^2

This is the correct answer

14+ 25|+ 6|^2 is the correct answer

helppppppppppppppppppppppppppppppppppppppppppppppppp

Answers

Answer:

Brainliest!

Step-by-step explanation:

36x^-4y^2/5x^2y^-3z^-2

36y^5z^2/5x^6

make everything positive

Smoking by Race for Males Aged 18-24
Smoker Nonsmoker Row Total
(S) (N)
White(W) 290 560 850
Black(B) 30 120 150
Column Total 320 680 1,000
Calculate the probabilities given below (Round your answers to 4 decimal places.):
i. P(S) 0.3200
ii. P(W) 0.8500
iii. P(S | W) 0.2720
iv. P(S | B) 0.0300
v. P(S and W) 0.9062
vi. P(N and B) 0.1765

Answers

Answer:

(i) 0.32          (ii) 0.85

(iii) 0.3412    (iv) 0.20

(v) 0.29         (vi) 0.12

Step-by-step explanation:

The data provided is as follows:

   Race                    Smoker (S)         Nonsmoker (N)             Row Total

 White(W)                    290                       560                           850

  Black(B)                     30                        120                           150

Column Total                320                       680                        1,000

(i)

Compute the value of P (S) as follows:

[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]

P (S) = 0.32.

(ii)

Compute the value of P (W) as follows:

[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]

P (W) = 0.85.

(iii)

Compute the value of P (S|W) as follows:

[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]

P (S|W) = 0.3412.

(iv)

Compute the value of P (S|B) as follows:

[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]

P (S|W) = 0.20.

(v)

Compute the value of P (S∩W) as follows:

[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]

P (S∩W) = 0.29.

(vi)

Compute the value of P (N∩B) as follows:

[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]

P (S∩W) = 0.12.

Beer shelf life is a problem for brewers and distributors because when beer is stored at room temperature, its flavor deteriorates. When the average furfuryl ether content reaches 6 μg per liter, a typical consumer begins to taste an unpleasant chemical flavor. At α = .05, would the following sample of 12 randomly chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold? 8.92 6.99 5.54 5.73 6.38 5.51 6.45 7.50 8.48 5.56 6.90 6.46

Answers

Answer:

As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means  chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.

Step-by-step explanation:

We formulate our null and alternative hypotheses as

H0 u≤ 6 ug     Ha : u > 6 ug

The significance level ∝ = 0.05

The test statistic used is

t = X` - u / s/ √n

which if H0 is true, has the students' t test with n-1 = 11 degrees of freedom.

The critical region t > t (0.05,11) = 1.796

We compute the t value from the data

Xi               Xi²

8.92         79.5664

6.99          48.8601

5.54          30.6916

5.73           32.8329

6.38           40.7044

5.51            30.3601

6.45           41.6025

7.50           56.25

8.48           71.9104

5.56          30.9136

6.90          47.61

6.46          41.7316          

80.42         553.0336      

Now x` = ∑x/ n = 80.42/12 = 6.70

S²= 1/n-1 ( ∑(xi- x`)²= 1/11 ( 553.034 - (80.42)²/12)

= 1/11 (553.034-538.948) = 1.2805

s= 1.1316

Putting the values in the test statistics

t = X` - u / s/ √n = 6.70- 6 / 1.1316 / √12

= 2.1698

The critical region t > t (0.05,11) = 1.796

As the calculated value of t =2.1698 is greater than t (0.05,11) = 1.796 reject H0 . It means  chosen bottles stored for a month convince you that the mean furfuryl ether content exceeds the taste threshhold.

A video rental store keeps a list of their top 15 movie rentals each week. This week the list includes 6 action, 4 comedies, 3 dramas, and 2 mysteries. The store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store. What is the probability that she selected 2 comedies and 1 action movie?

Answers

Answer:

32/1125

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome of event/Total outcome.

If a video rental store keeps a list of their top 15 movie rentals each week, the total outcome is 15.

If the list for the week includes 6 action, 4 comedies, 3 dramas, and 2 mysteries and the store manager removes a copy of each of the 15 movies from the shelf, then randomly selects 3 of the 15 to show on the display monitors in the store, the probability that she selected 2 comedies and 1 action movie will be calculated as shown;

Probability of selecting 2 comedies  = 4/15*4/15 = 16/225 (Note that the expected outcome in this case is 4).

Probability of selecting 1 action movie = 6/15 = 2/5

Hence, the probability that she selected 2 comedies and 1 action movie will be equivalent to 16/225*2/5 = 32/1125

Note that the rented movies will have to be returned hence reason for the replacement.

which expression is equivalent to x^-5/3

Answers

Answer:

B

Step-by-step explanation:

Since the power is negative, you automatically know it has to be a or b, because the only way it would be negative is if it was brought from the denominator to the numerator.

The answer is B, because the numerator of the power, is what is inside the square root, while the denominator is what is outside the square root.

find the value of each variable and the measure of each angle​

Answers

Answer:

Left angle = 60°

Top angle = 120°

Right angle = 60°

Step-by-step explanation:

Use what you know about angle relationships to set up equations you can solve for each variable.

The top top angle, for example, added to one of the other angles must equal 180° because they are supplementary.

You have two variables, so you need at least two equations (I made three but only used two).

The work is in my attachment, comment of you have questions.

if 2500 amounted to 3500 in 4 years at simple interest. Find the rate at which interest was charged

Answers

Answer:

35%

Step-by-step explanation:

[tex]Principal = 2500\\\\Simple\:Interest = 3500\\\\Time = 4 \:years\\\\Rate = ?\\\\Rate = \frac{100 \times Simple \: Interest }{Principal \times Time}\\\\Rate = \frac{100 \times 3500}{2500 \times 4} \\\\Rate = \frac{350000}{10000}\\\\ Rate = 35 \%[/tex]

[tex]S.I = \frac{PRT}{100}\\\\ 100S.I = PRT\\\\\frac{100S.I}{PT} = \frac{PRT}{PT} \\\\\frac{100S.I}{PT} = R[/tex]

Answer:

35%

Step-by-step explanation:

I REALLY HOPE I HELPED

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

 ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                PEACE!

Suppose the radius of a circle is 5 units. What is its circumference?​

Answers

Answer:

C≈31.42

Step-by-step explanation:

C=2πr

C=2xπx5

C≈31.42

pls mark as brainliest

in a gp the sixth term is 8 times the third term, and the sum of the seventh and eighth term is 192. determine the common ratio​

Answers

Answer:

common ratio = 2

Step-by-step explanation:

T6 = ar^5

T3 = ar²

T6 = 8 x T³

ar^5 = 8 x ar²

ar^5/ar² = 8

r³ = 8

r = ³√8

r = 2

In Triangle A B C, what is the value of x? Triangle A B C. Angle A is (10 x minus 10) degrees, angle B is (8 x) degrees, angle C is (10 x + 8) degrees.

Answers

Answer:

6.5

Step-by-step explanation:

The sum of all angles in a triangle are 180 degrees.

=> 10x -10 + 8x + 10x + 8 = 180

=> 28x -2 = 180

=> 28x = 182

=> x = 6.5

So, Angle A = 10 x 6.5 -10 = 65 - 10 = 55 degrees

     Angle B = 8 x 6.5 = 52 degrees

     Angle C = 10 x 6.5 + 8 = 65 + 8 = 73 degrees.

55 + 52 + 73 = 55 + 125 = 180 degrees

How many adults must be randomly selected to estimate the mean FICO​ (credit rating) score of working adults in a​ country? We want ​% confidence that the sample mean is within points of the population​ mean, and the population standard deviation is .

Answers

Answer: hello below is the complete question

How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number

answer : 737 adults

Step-by-step explanation:

confidence interval = 90% = 0.9

( E ) = 4

standard deviation = 66

first we have to calculate the value of a

a = 1 - confidence interval

  = 1 - 0.9 = 0.10      hence  a / 2 = 0.05

next find the value of Z a/2 from table

Z[tex]_{0.05}[/tex]  = 1.645

The number of Adults selected can be determined using this relation

N = [tex](Z_{a/2} * (s/E))^2[/tex]

   = [tex](Z_{0.05} * ( 66/4))^2[/tex]

   = 737

Determine the equation of the exponantial function with a common ratio of 2, a horizontal asymptote at y=4 and passin through the point (2,10).

Answers

Answer:

Step-by-step explanation:

Bighorn sheep are beautiful wild animals found throughout the western United States. Data for this problem are based on information taken from The Desert Bighorn, edited by Monson and Sumner 9University of Arizona Press). Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information:
x 1 2 3 4 5
y 14 18.9 14.4 19.6 20.0
∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275
(a) Draw a scatter diagram.
(b) Find the equation of the least-squares line, and plot the line on the scatter diagram of part (a).
(c) Find the correlation coefficient r. Find the coefficient of determination . What percentage of variation in y is explained by the variation in x and the least squares model?

Answers

Answer:

The answer and explanation are below

Step-by-step explanation:

i followed the data that was given in the question.

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

a.)  please refer to the attachment for the scatter diagram. Y was plotted against X.

b. The equation is given as:

Y = b₁ + b₀X

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

b₁ = n∑xy - (∑x)(∑y)/n(∑x²) - (∑x)²

b₁ = 5 x 275 - 15 x 87.3/5 x 55 - (15²)

= 1375-1309.5/275-225

= 65.5/50

= 1.31

b₀ = 87.3/5 - 1.31(15/5)

= 87.3/5 - 1.31x3

= 13.53

the regression line is

Y = 13.53 + 1.31X

please refer to the attachment for the diagram for the regression line.

c. we are required to find r.

r = n∑XY - (∑X)(∑Y)/√n∑X²-(∑X)² × √n∑y²-(∑y)²

∑x=15 ; ∑y=87.3;∑x2=55; ∑y2=1569.77; ∑xy=275

inserting these values:

r = 5 x 275-(15)(87.3)/√275-225 x √7848.85 - 7621.29

= 65.5/106.69

= 0.6139

Coefficient of determination = r²

r = 0.6139

r² = 0.3769 = 37.69%

Therefore 37.69% variation in y is explained by variation in x and the least square model.

a function includes the points (4, -3) and (-9,4). what fraction in lowest terms represents the output value of this function for an input of zero

Answers

Answer:

  -11/13

Step-by-step explanation:

The equation of the line through these points can be written using the 2-point form of the equation of a line:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (4 -(-3))/(-9-4)/(x -4) -3

  y = (-7/13)x +28/13 -3

For x=0, the value of y is ...

  y = 28/13 -39/13 = -11/13

The output for an input of 0 is -11/13.

In a school, there are 25% fewer 11th graders than 10th graders, and 20% more 11th graders than 12th graders. The total number of students in 10th, 11th, and 12th grades in the school is 190. How many 10th graders are there at the school?

Answers

Answer:

There are 80 10th graders in the school

Step-by-step explanation:

Let the number of 10th graders be x

There are 25% fewer 11th graders

That mean x - 25% of x

x -0.25x = 0.75x

There are 20% more 11th graders than 12th graders

So if number of 12th graders = y, then

0.75x = y + 20/100 * y = y + 0.2y = 1.2y

Since ;

0.75x = 1.2y

then y = 0.75x/1.2 = 0.625x

So let’s add all to give 190

x + 0.75x + 0.625x = 190

2.375x = 190

x = 190/2.375

x = 80

what is 76.32 divided by 24.98 using compatible numbers to estimate each quotient?

Answers

Answer:

Approximately 3.05

Step-by-step explanation:

Using "compatible numbers" we can simply round these numbers to integer values.  Let's make 76.32 => 76 and 24.98 => 25

So from here let's do 76/25 to get 3 R 1/25

1/25 as a decimal is .04

So far, we have 3.04.  Going back to Look at our decimals, .32 and .98, there is a larger difference in our down rounding with the .32 than the up rounding from our .98.  So we should consider an extra value in our decimal.

Considering our whole number of 3.0, we can assume that our rounding will have an increase of about .01 or .015 in error.

Thus our number will be 3.04 + .01.

Making our quotient approximately 3.05.

Cheers.

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