In a study of the relationship of the shape of a tablet to its dissolution time, 6 disk-shaped ibuprofen tablets and 8 oval-shaped ibuprofen tablets were dissolved in water. The dissolve times, in seconds, were as follows:
Disk: 269.0, 249.3, 255.2, 252.7, 247.0, 261.6
Oval: 268.8, 260.0, 273.5, 253.9, 278.5, 289.4, 261.6, 280.2 Can you conclude that the mean dissolve times differ between the two shapes? Conduct a hypothesis test at the
α = 5% level.
a. State the appropriate null and alternative hypotheses.
b. Compute the test statistic.
c. Compute the P-value.
d. State the conclusion of the test in the context of this setting.

Answer:

(a) Probability distribution is prepared below.

(b) The probability that two or fewer heads are observed in three tosses is 0.875.

(c) The probability that at least one head is observed in three tosses is 0.875.

(d) The expected value of X is 1.5.

(e) The standard deviation of X is 2.121.

Step-by-step explanation:

The complete question is: A fair coin is tossed three times. Let X be the number of heads observed in three tosses of this fair coin.

(a) Find the probability distribution of X.

(b) Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.)

(c) Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.)

(d) Find the expected value of X. (Round your answer to one decimal place.)

(e) Find the standard deviation of X. (Round your answer to three decimal places.)

Now, firstly the sample space obtained in three tosses of a fair coin is given as;

Sample Space (S) = {HHH, HHT, HTH, THH, HTT, TTH, THT, TTT}

(a) The Probability distribution of X is given below;

   Number of Heads (X)         P(X)            [tex]X \times P(X)[/tex]               [tex]X^{2} \times P(X)[/tex]

              0                               [tex]\frac{1}{8}[/tex] = 0.125            0                           0

              1                                [tex]\frac{3}{8}[/tex] = 0.375         0.375                     0.375  

              2                               [tex]\frac{3}{8}[/tex] = 0.375         0.75                          3

              3                               [tex]\frac{1}{8}[/tex] = 0.125          0.375                    3.375

           Total                                                    1.5                        6.75          

(b) The probability that two or fewer heads are observed in three tosses is given by = P(X [tex]\leq[/tex] 2)

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

                     = 0.125 + 0.375 + 0.375

                     = 0.875

(c) The probability that at least one head is observed in three tosses is given by = P(X [tex]\geq[/tex] 1)

      P(X [tex]\geq[/tex] 1) =  1 - P(X = 0)

                    =  1 - 0.125

                    =  0.875

(d) The expected value of X = E(X) =  [tex]\sum (X \times P(X))[/tex]

                                                              =  1.5

(e) The Variance of X = V(X) = [tex]E(X^{2} ) - ( E(X))^{2}[/tex]

                                      =  [tex]\sum (X^{2} \times P(X))- (\sum (X \times P(X)))^{2}[/tex]

                                      =  [tex]6.75 - 1.5^{2}[/tex]  = 4.5

Now, Standard deviation of X = [tex]\sqrt{V(X)}[/tex]

                                                  = [tex]\sqrt{4.5}[/tex]  = 2.121.

Answer:

2.143

Step-by-step explanation:

An urn contains 8 black and;

6 pink balls.

5 balls are randomly drawn from the urn in succession, with replacement.

What is the probability that all the 5 balls drawn from the urn are pink?

The probability that all the 5 balls drawn is pink is 5 × 6/14 = 30/14 = 2.143 (rounded off to 3 decimal places)

The probability of drawing 5 pink balls is 0.271

Since the balls are replaced after each draw, the probability of drawing a pink ball each time is always  

6/14

=3/7

Since we are drawing 5 balls, the probability of drawing 5 pink balls with replacement is

[tex](3/7)^{5}[/tex]

≈0.2706

Rounding to 3 decimal places, the probability is  0.271

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​

Answer:

#1

Step-by-step explanation:

The associative property of addition states that we can "flip" two expressions that are being added. Therefore, our answer is the first one because it can be rewritten as 3x + (-7y) which then is equivalent to -7y + 3x.

Answer:

Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):

[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]

Step-by-step explanation:

The volume rate of the fire hidrant with a purple cap is equal to the product of the proportion factor and the volume rate of the fire hydrant with a concrete cap.

[tex]\dot Q_{i} = k \cdot \dot Q_{j}[/tex]

There are two different solutions:

Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):

[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]

Fire hydrant with a purple cap (with respect to a fire hydrant with a blue cap):

[tex]\dot Q_{purple} = \frac{1}{2} \times \frac{1000\,gpm}{1500\,gpm}\cdot \dot Q_{blue}[/tex]

[tex]\dot Q_{purple} = \frac{1}{3}\cdot \dot Q_{blue}[/tex]

Answer:

[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]

And we can find the probability using the complement rule and with the normal standard table like this:

[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]

The probability that the mean height for the sample is greater than 65 inches is 0.007

Step-by-step explanation:

Let X the random variable that represent the women heights of a population, and we know the following parameters

[tex]\mu=64.2[/tex] and [tex]\sigma=2.84[/tex]

We are interested on this probability

[tex]P(X>65)[/tex]

Since the sample size selected is 75>30 we can use the centrel limit theorem and the appropiate formula to use would be the z score given by:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

If we find the z score for 65 inches we got:

[tex] z=\frac{65-64.2}{\frac{2.84}{\sqrt{75}}} = 2.440[/tex]

And we can find the probability using the complement rule and with the normal standard table like this:

[tex] P(Z>2.440) =1-P(Z<2.440) = 1-0.993 =0.007[/tex]

The probability that the mean height for the sample is greater than 65 inches is 0.007

Answer:

1. Option c

2. Option d

Step-by-step explanation:

This type of survey is includes a sample made up of voluntary responses. People only choose to or do not choose to respond.

This type of sampling method is most of the time unbelievable because generally only people with strong opinions about this particular questions will respond and it is usually towards the same direction as the question and this might not reflect the opinion of the whole population making the survey biased.

Part A: The respondents are a voluntary response sample (Option C)

Part B: Responses may not reflect the opinions of the general population (Option D)

The total number of internet users = 1072

Percentage of the total number of people that chose to respond = 38%

Note that this survey does not compel all the population to respond to the survey. Responses are gotten from voluntary respondents.

Also note that a voluntary response sample is a sample that consists of participants who chose to participate in a sample group voluntarily.

In this type of survey, the people who decided to provide voluntary responses to the survey are called voluntary response samples

The percentage of those that chose to respond to this survey (38%) is less than half of the total population. This obviously shows that the responses may not reflect the opinions of the general population

Learn more on sampling methods here: https://brainly.com/question/16587013

Answer:

2, -1/2

Step-by-step explanation:

2m²-3m-2=0

2m² - 4m + 1m - 2=0

2m(m-2)+(m-2)=0

(2m+1)(m-2)=0

2m+1=0 ⇒ m= -1/2

m-2=0 ⇒ m=2

Answer:

g(x)= 1/4 |x-2| + 1

Step-by-step explanation:

line:

points on same line:

slope based on the points

And the line is moved to the right by 2 units:

So the function becomes:

Considering movement up by 1 unit as well:

This is the final of equation for the line.

Answer:

Step-by-step explanation:

For this kind of question you'd be better off if you'd write down and share your own answers to these conceptual questions and then ask for Brainly feedback on what you have written.  You'll need to understand the concept of "function" often in algebra and beyond.

What concepts (only the names) did you need to accommodate the concept of function in your mind?  input, output, rule, domain, range, mapping, variation (direct and inverse)

Simplest function:  y = c  (there's only one x-value and y equals that value)

In your day to day, is there any occurring fact that can be interpreted as a function?  An electronic parking meter:  the amount of time you can park at the meter without risking getting a ticket is dependent upon the number of quarters you insert into the meter, e. g, 15 minutes for 25 centers, 30 minutes for 50 cents, and so on.

Is it possible to view a function?  Sure.  Graph the function.

What strategy are you using to get the graph of a function?  Set up a coordinate plane.  Label the horizontal axis "x" and the vertical axis "y".  Choose x (input) values that are included in the domain of the function.  If the domain includes '0' you will be finding the 'y-intercept' of the function.  Write the input and output as a point:  (x, y).  Plot that point.  Choose other x values within the domain and calculate the corresponding y value for each.  Plot several more points and draw a line or a curve through them.  Of course there are more sophisticated strategies for graphing functions.  Remember:  If you're working with a function, there is never more than one output or y value for any particular input value.

Step-by-step explanation:

x and x+2 are the numbers

x(x+2)=143

x²+2x-143=0

x²+13x-11x-143=0

x(x+13)- 11(x+13)=0

(x+13). (x-11)=0

x+13=0. x=-13

x-11=0. x=11

Answer:

Slope is 4

slope of the line perpendicular to it: x=-1/4

Answer:

A)1/18

B)1/6

C)13/18

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW,

The chess clubs of two schools consist of, respectively, 8 and 9 players. Four members from each club are randomly chosen to participate in a contest between the two schools. The chosen players from one team are then randomly paired with those from the other team, and each pairing plays a game of chess. Suppose that Rebecca and her sister Elise are on the chess clubs at different schools. What is the probability that (a) Rebecca and Elise will be paired? (b) Rebecca and Elise will be chosen to represent their schools but will not play each other? (c) either Rebecca or Elise will be chosen to represent her school?

CHECK THE ATTACHMENT'S FOR STEP BY STEP EXPLANATION

Answer:

  ΔA'B'C' is congruent to ΔABC

Step-by-step explanation:

See attached for the construction of ΔA'B'C'. (The vertices are labeled ABC.)

We computed angle B to be ...

  ∠B = 180° -∠A -∠C

  ∠B = 180° -103° -57° = 20°

We constructed segment BC of length 6.5. Then we constructed angles of 20° and 57° from B and C, respectively. The location where the rays from those angles cross is point A', and the angle there is 103°, as required.

__

ΔA'B'C' is congruent to ΔABC by the ASA congruence postulate.

Answer:

(-4,-7)

Step-by-step explanation:

Adding 1 to the x and subtracting 3 from the y we get

-5+1= -4

And

-4-3= -7

Answer:

D (4,11)

Step-by-step explanation:

Answer: it’s d

x is just going up by 1 and y is going up by 2

Answer:

a) Level of significance α=0.05

Two-tailed test, with null and alternative hypothesis:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

b) Student's t distribution. We assume equal variances for both populations, independent sampled values and populations normally distributed.

Test statistic t=-2.4

c) P-value = 0.018

d) Rejection of the null hypothesis.

The data is statistically significant.

e) There is evidence to conclude there is significant difference in average off-schedule times between the bus lines. The difference we see in the samples seems not due to pure chance.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that there is a significant difference in average off-schedule times for this bus lines.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

The significance level is 0.05.

The sample 1 (bus line A), of size n1=51 has a mean of 53 and a standard deviation of 17.

The sample 2 (bus line B), of size n2=60 has a mean of 60 and a standard deviation of 13.

The difference between sample means is Md=-7.

[tex]M_d=M_1-M_2=53-60=-7[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{17^2}{51}+\dfrac{13^2}{60}}\\\\\\s_{M_d}=\sqrt{5.667+2.817}=\sqrt{8.483}=2.913[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-7-0}{2.913}=\dfrac{-7}{2.913}=-2.4[/tex]

The degrees of freedom for this test are:

[tex]df=n_1+n_2-1=51+60-2=109[/tex]

This test is a two-tailed test, with 109 degrees of freedom and t=-2.4, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t<-2.4)=0.018[/tex]

As the P-value (0.018) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that there is a significant difference in average off-schedule times for this bus lines.

Answer:

true

Step-by-step explanation:

just took test

If it is asking if that equation is the quadratic formula, then the answer is false. The reason why is that the first 'b' should be negative

The quadratic formula is

[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

We have a right triangle and we're given the leg lengths.  

tan X = |YZ| / |XZ| = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

tan X = YZ / XZ = 20/8 = 5/2

X = arctan(5/2) = 68.2°

Answer: 68.2°

Answer:

The minimum score that she must earn to get admitted is 523.

Step-by-step explanation:

As the scores are normally distributed, we can calculate the probability using the z-score.

The distribution has a mean of 420 and a standard deviation of 80.

We have to calculate the z-score z* that satisfies:

[tex]P(z>z^*)=0.1[/tex]

This happens for z*=1.28155.

Then, we can calculate the score as:

[tex]X=\mu+z\cdot\sigma=420+1.28155\cdot 80=420+102.524=522.524[/tex]

Answer: 360 cubic centimeters.

Step-by-step explanation:

Since it  has a base shaped like a square and we know that it has a side length of 6 cm then we could square it an multiply it by the height.

6^2 = 36  

36 * 10 = 360

Answer:

see explanation

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

(a)

Given a₁ = - 2 and a₄ = 16, then

a₁ + 3d = 16 , that is

- 2 + 3d = 16 ( add 2 to both sides )

3d = 18 ( divide both sides by 3 )

d = 6

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

(b)

Given

[tex]a_{n}[/tex] = 11998 , then

a₁ + (n - 1)d = 11998 , that is

- 2 + 6(n - 1) = 11998 ( add 2 to both sides )

6(n - 1) = 12000 ( divide both sides by 6 )

n - 1 = 2000 ( add 1 to both sides )

n = 2001

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

Answer:

(A) [tex]y=-0.762+0.119x[/tex]

(B) If a country increases its life expectancy, the happiness index will increase.

(C) If the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.

(D) If the life expectancy is 67 years in a certain country, the happiness index will be 7.21.

Step-by-step explanation:

A regression analysis was performed to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).

The output of the regression analysis are as follows:

a = -0.762

b = 0.119

r² = 0.8649

r = 0.93

(A)

The equation of the Least Squares Regression line of the form y = _ + _ x is:

[tex]y=-0.762+0.119x[/tex]

(B)

The correction between the variables happiness index (y) and life expectancy in years of a given country (x) is, 0.93.

The correlation coefficient is positive. This implies that there is a positive relation between the two variables, i.e. as the value of life expectancy in years increases the happiness index also increases.

Thus, if a country increases its life expectancy, the happiness index will increase.

(C)

Compute the value of y for x = x + 3.5 as follows:

[tex]y=-0.762+0.119x[/tex]

  [tex]=-0.762+0.119\times (x+3.5)\\\\=(-0.762+0.119x)+0.4165\\\\=y+0.4165[/tex]

Thus, if the life expectancy is increased by 3.5 years in a certain country, the happiness index will increase by 0.4165.

(D)

Compute the value of y for x = 67 as follows:

[tex]y=-0.762+0.119x[/tex]

  [tex]=-0.762+0.119\times 67\\\\=-0.762+7.973\\\\=7.211\\\\\approx 7.21[/tex]

Thus, if the life expectancy is 67 years in a certain country, the happiness index will be 7.21.

Answer:

21-25 = 4

26-30 = 3

Step-by-step explanation:

16-20 (4)= 17 17 17 18

21-25 (4)= 21 22 24 25

26-30 (3)= 26 27

30

31-35 (3)= 32 35 35

36-40 (5)= 36 37 37 38 39

41-45 (2)= 41 42

Answer:

Step-by-step explanation:

24/3 - 4

8 - 4 = 4

Answer:

2

Step-by-step explanation:

Given the system of equations:

[Tex]x^2+y^2=9\\9x+2y=16[/tex]

Comparing [Tex]x^2+y^2=9[/tex] with the general standard equation of a circle [Tex](x-h)^2+(y-k)^2=r^2[/tex].

The first equation is an equation of a circle centred at (0,0) with a Radius of 3.

The second equation 9x+2y=16 is a straight line equation.

A straight line can only intersect a circle at a maximum of 2 points.

Therefore the greatest possible number of solutions to the equations in the system is 2.

Answer:

2

Step-by-step explanation:

and jj is gay of outer banks

Answer:

A meter is not part of the metric system. It's part of the U.S. customary system.

Answer:

$2350

Step-by-step explanation:

If 94 is 4%, multiply it by 25 to get $2350, or 100%

the cost of the item is $ 2350.

To find the cost of the item, we can set up an equation using the information given.

Let's denote the cost of the item as $ x.

According to the given information, the sales tax on the item is 4 % and is equal to $ 94. We can express this as:

0.04 x = 94

To solve for x, we divide both sides of the equation by 0.04:

x = tax on item / sales tax

x = 94 / 0.04

x = 2350

Therefore, the cost of the item is $ 2350.

Learn more about Sales Tax here

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Answer:

A =12.56 m^2

Step-by-step explanation:

Find the area of a circle with radius 4

A = pi r^2

A = 3.14 * 4^2

A =50.24

Since this is 1/4 of the circle, multiply by 1/4

A = 1/4 * 50.24

A =12.56 m^2

Answer:

12.56

Step-by-step explanation:

the formula for the area of a circle is the following:

[tex]\pi r^{2}[/tex]

so divide that formula by 4 to get a quarter and plug in the radius for r.

[tex](\pi )(4^2)/4= 12.56[/tex]

Answer:

14, 32

Step-by-step explanation:

45,15,44,17,40,20,31,25

this is combination of 2 series:

In the first series we can see the pattern as:

In the second series we can see the pattern as:

The series will continue as: