solve for x in terms of y: 5y = 3x + 2

Step-by-step explanation:

Descending means from highest to lowest values, so look for the one that goes in order counting down.

Option A is going down all the way unlike any of the other answers, so A is the correct option.

Answer:

A. \(-2x^3+6x^2-9x+5\)

The population is approximately 17,957 in 2019, approximately 2.25 years in 1995 and reachs 9,000 in 1997

By estimating the population at the beginning of 2019, we can use the exponential growth formula. Assuming a continuous exponential growth rate, we can calculate the population as follows:

A) Estimating the population at the beginning of 2019:

Using the exponential growth formula P(t) = P₀ * e^(rt), where P(t) is the population at time t, P₀ is the initial population, e is the base of the natural logarithm, r is the growth rate, and t is the time elapsed, we can find the growth rate (r).

Given that the population in 2015 (t=0) is 5,459 and the initial population (P₀) is 3,721, we can solve for r:

5,459 = 3,721 * e^(r*0)

e^0 = 1

5,459/3,721 = e^r

r = ln(5,459/3,721)

Using the calculated growth rate, we can find the population at the beginning of 2019 (t=4):

P(4) = 3,721 * e^(ln(5,459/3,721) * 4)

P(4) ≈ 3,721 * e^(0.394 * 4)

P(4) ≈ 3,721 * e^1.576

P(4) ≈ 3,721 * 4.826

P(4) ≈ 17,957

Therefore, the estimated population at the beginning of 2019 is approximately 17,957.

B) Calculating the time it takes to reach a population of 9,000:

To determine the time it takes for the population to reach 9,000, we rearrange the exponential growth formula to solve for time (t):

9,000 = 3,721 * e^(ln(5,459/3,721) * t)

9,000/3,721 = e^(ln(5,459/3,721) * t)

ln(2.42) = ln(5,459/3,721) * t

Using the natural logarithm ln(2.42) = 0.889, we can solve for t:

t = 0.889 / ln(5,459/3,721)

t ≈ 0.889 / 0.394

t ≈ 2.25

Therefore, it will take approximately 2.25 years from the beginning of 1995 for the population to reach 9,000.

C) Determining the year when the population reaches 9,000:

Since the population reaches 9,000 approximately 2.25 years after the beginning of 1995, we can add this time to find the year:

1995 + 2.25 ≈ 1997.25

Therefore, the population is projected to reach 9,000 around the year 1997.

Learn more about population here:
https://brainly.com/question/24285232

#SPJ11

Answer:

Undefinable

Step-by-step explanation:

5 + 2x = 2x + 6

5 = 6                              Subtract 2x on both sides

There is no answer

Answer: 2.5, 5.3

Step-by-step explanation:

\(-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3\)

Answer:

i need help

Step-by-step explanation:

After 10 years, the voter percentages would be approximately 50.3% for LEFT and 49.7% for RIGHT.

The Markov assumption in this context is that the probability of a voter's next vote depends only on their current vote and not on their past voting history. In other words, the Markov assumption states that the future behavior of a voter is independent of their past behavior, given their current state.

Transition diagram:

        LEFT      RIGHT

    |--------->--------|

LEFT |   0.8        0.2   |

    |                   |

RIGHT|   0.1        0.9   |

    |--------->--------|

The diagram represents the two possible states: LEFT and RIGHT. The arrows indicate the transition probabilities between the states. For example, if a voter is currently in the LEFT state, there is a 0.8 probability of transitioning to the LEFT state again and a 0.2 probability of transitioning to the RIGHT state.

Transition matrix:

     |  LEFT   |  RIGHT  |

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

LEFT  |   0.8   |   0.2   |

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

RIGHT |   0.1   |   0.9   |

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

The transition matrix represents the transition probabilities between the states. Each element of the matrix represents the probability of transitioning from the row state to the column state.

If 55% of the electorate votes RIGHT one year, we can use the transition matrix to find the percentage of voters who vote RIGHT the next year.

Let's assume an initial distribution of [0.45, 0.55] for LEFT and RIGHT respectively (based on 55% voting RIGHT and 45% voting LEFT).

To find the percentage of voters who vote RIGHT the next year, we multiply the initial distribution by the transition matrix:

[0.45, 0.55] * [0.2, 0.9; 0.8, 0.1] = [0.62, 0.38]

Therefore, the percentage of voters who vote RIGHT the next year would be approximately 38%.

To find the voter percentages in 10 years' time, we can repeatedly multiply the transition matrix by itself:

[0.45, 0.55] * [0.2, 0.9; 0.8, 0.1]^10 ≈ [0.503, 0.497]

After 10 years, the voter percentages would be approximately 50.3% for LEFT and 49.7% for RIGHT.

Interpretation: The results suggest that over time, the voter percentages will tend to approach an equilibrium point where the percentages stabilize. In this case, the percentages stabilize around 50% for both LEFT and RIGHT parties.

No, there will not be a steady state where the party percentages don't waiver. This is because the transition probabilities in the transition matrix are not symmetric. The probabilities of transitioning between the parties are different depending on the current state. This indicates that there is an inherent bias or preference in the voting behavior that prevents a steady state from being reached.

Learn more about probability  at:

brainly.com/question/13604758

#SPJ4

Answer:

\(\boxed{\sf n= \dfrac{2}{5} ,\: n=1}\)

Step-by-step explanation:

\(\rightarrow 5n^2 = 7n -2\)

\(\rightarrow 5n^2 - 7n +2=0\)

\(\rightarrow 5n^2 - 5n -2n+2=0\)

\(\rightarrow 5n(n - 1) -2(n-1)=0\)

\(\rightarrow (5n-2)(n-1)=0\)

\(\rightarrow 5n-2= 0,\: n-1=0\)

\(\rightarrow 5n= 2,\: n=1\)

\(\rightarrow n= \dfrac{2}{5} ,\: n=1\)

Step-by-step explanation:

\(\hookrightarrow\sf{5n^2 = 7n -2}\\\\\hookrightarrow\sf{5n^2 - 7n +2=0}\\\\\hookrightarrow\sf{5n^2 - (5+2)n +2=0}\\\\\hookrightarrow\sf{5n^2 - 5n -2n+2=0}\\\\\hookrightarrow\sf{ 5n(n - 1) -2(n-1)=0}\\\\\hookrightarrow\sf{ (5n-2)(n-1)=0}\\\\\hookrightarrow\sf{ 5n-2= 0\:or~ n-1=0}\\\\\hookrightarrow\sf{ 5n= 2\:or~n=1}\\\\\hookrightarrow\bold{ n= \dfrac{2}{5} \:or~ n=1}\)

There is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

Given, the Pearson correlation coefficient of +0.91,

There appears to be a strong +ve correlation between the number of cats she owns and the number of times an old widow was married.

It suggests that the more times a widow was married,the more cats she tends to own.

Approximately 82% of the variance in the number of cats owned can be explained by the number of times a widow was married is indicated by the coefficient of determination (r²).

Hence, we can say that there is a significant relationship between the number of cats she owns and the number of times an old widow was married (r = +0.91, p < 0.05, r² = 0.82).

Learn more about Pearson correlation coefficient here,

https://brainly.com/question/31801929

#SPJ4

Answer:

Step-by-step explanation:

Evaluate the expression:

When a= −15 and b=−5

Substitute values:

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

In case the expression is b²/a + 5, the value is:

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

Answer:

a= one mile in 4 minutes

b =48 minutes

Step-by-step explanation:

A

t = 20 minutes

d = 5 miles

Average speed = distance ÷ time

5 miles÷ 20 minutes

= 1 mile in 4 minutes

= 0.25 miles in 1 minute

B

0.25 miles in 1 minute

12 miles in g minutes

12 miles in 48 minutes

we get this answer because 0.25 in one minute is 1 ÷4

12÷ 12 × 4

12÷ 48

= 12 miles In 48 minutes

In the given situation (D) randomized block design was used to experiment with incorporating randomization into this study.

An experimental design known as a randomized block design divides the experimental units into units known as blocks.

The experimental units inside each block are assigned the treatments at random.

We have a fully randomized block design when each block has at least one instance of each treatment.

By ensuring that a crucial predictor of the outcome is fairly distributed amongst research groups to require them to be balanced, something that a completely randomized design cannot guarantee, a randomized block design differs from a completely randomized design.

Therefore, in the given situation (D) randomized block design was used to experiment with incorporating randomization into this study.

Know more about a randomized block design here:

https://brainly.com/question/14727460

#SPJ4

Complete question:

R.A. Fisher, a famous statistician, describes a well-known design in his book, Design of Experiments. Five varieties of wheat were compared to determine which gave the highest yield in bushels per acre. Eight farms were available for planting. Each farm was divided into five plots. For each farm, the five varieties were randomly assigned to the five plots with one variety per plot. The varieties were planted on their assigned plots and their yields were measured and compared.

How was randomization incorporated into this study?

A. All five varieties were randomly assigned to the five plots at each farm.

B. The five varieties were randomly assigned to the eight farms - three varieties were planted twice and two varieties only once.

C. It was not incorporated. The wheat seeds were not randomly selected from the population of wheat seeds.

D. Experiment - randomized block design

In summary, the order of reaction for the given complex reaction is 2 with respect to A. The change in ionic strength, represented by the symbol I, can potentially affect the rate constant and the reaction rate as the reaction progresses, but the specific effect cannot be determined without additional information about the ions and their concentrations.

The effect of surfactants on the surface tension of a solvent can be explained by their ability to lower the intermolecular forces between the molecules at the surface of the liquid. Surfactants are molecules that have both hydrophilic (water-loving) and hydrophobic (water-hating) regions. When added to a solvent, they align at the surface with their hydrophilic regions facing the liquid and their hydrophobic regions facing the air. This arrangement disrupts the intermolecular forces between the solvent molecules, reducing the surface tension.

Experimentally, the Gibbs isotherm can be applied to determine the effect of surfactants on the surface tension. The Gibbs isotherm is a relationship that describes the change in surface tension with the concentration of the surfactant. By measuring the surface tension of a solvent at different surfactant concentrations, one can plot a graph of surface tension versus concentration. The slope of this graph provides information about the effectiveness of the surfactant in reducing the surface tension. A steeper slope indicates a greater reduction in surface tension with increasing surfactant concentration.

In the given data, the concentration of butadiene ([C4H8]) is provided at different times (t). To determine the order of reaction, we can use the four kinetic methods:

1. Initial Rates Method: This method involves comparing the initial rates of the reaction at different concentrations. By determining the order with respect to the concentration of butadiene, we can determine the overall order of the reaction. However, since only the concentration of butadiene is given and not the initial rates, this method cannot be applied.

2. Half-life Method: This method involves measuring the time it takes for the concentration of a reactant to decrease by half. By comparing the half-lives at different concentrations, we can determine the order of reaction. However, the given data does not provide information about the half-life of butadiene, so this method cannot be applied.

3. Method of Initial Rates: This method involves comparing the initial rates of the reaction with different initial concentrations of reactants. Since the given data does not provide information about the initial rates, this method cannot be applied.

4. Integrated Rate Equation Method: This method involves integrating the rate equation for the reaction and plotting the concentration of reactant versus time. By determining the slope of the resulting graph, we can determine the order of reaction. Since the given data provides the concentration of butadiene at different times, we can plot a graph of [C4H8] versus t and determine the slope. The slope of this graph will give us the order of reaction.

Moving on to the complex reaction 2 A + B → C + D, the given reaction mechanism indicates that the slow determining step is the conversion of 2 A to C. Based on this mechanism, we can determine the order of reaction as follows:

a) The order of reaction is determined by the sum of the exponents of the reactant concentrations in the rate equation. In this case, since the slow determining step involves only A, the order of reaction with respect to A is 2.

b) The ionic strength, represented by the symbol I, refers to the concentration of ions in a solution. In this reaction, only A and B are present at the beginning, and the rate constant is affected by the ionic strength. As the reaction progresses, the concentration of C and D increases, leading to an increase in the ionic strength. This increase in the ionic strength can affect the rate constant, potentially slowing down the reaction rate. The exact effect will depend on the specific reaction and the ions present. However, since the given information does not provide details about the specific ions or their concentrations, we cannot determine the exact effect of the change in ionic strength on the reaction rate.

In summary, the order of reaction for the given complex reaction is 2 with respect to A. The change in ionic strength, represented by the symbol I, can potentially affect the rate constant and the reaction rate as the reaction progresses, but the specific effect cannot be determined without additional information about the ions and their concentrations.

learn more about reaction on :

https://brainly.com/question/11231920

#SPJ11

An increase in ionic strength (I) would decrease the reaction rate. This is because an increase in ionic strength increases the concentration of ions in the solution, leading to stronger electrostatic interactions and hindering the reaction.

The effect of surfactants on the surface tension of a solvent can be determined experimentally using the Gibbs isotherm. Surfactants are compounds that lower the surface tension of a liquid by accumulating at the liquid-air interface. This reduces the attractive forces between liquid molecules and decreases the surface tension.

By applying the Gibbs isotherm, we can determine the surface excess concentration of the surfactant at the liquid-air interface, which is related to the change in surface tension. The Gibbs isotherm equation is:

Γ = (RT/γ) ln (c/c₀)

Where Γ is the surface excess concentration, R is the gas constant, T is the temperature, γ is the surface tension, c is the concentration of the surfactant in the bulk phase, and c₀ is the standard concentration.

By measuring the surface tension of a solvent with different concentrations of surfactants, we can plot a graph of surface tension versus surfactant concentration. From this graph, we can determine the critical micelle concentration (CMC), which is the concentration at which the surfactant forms micelles and the surface tension becomes constant.

Regarding the given data on the concentration of butadiene over time, we can determine the order of the reaction using the following kinetic methods:

1. Initial rate method: This method involves measuring the initial rate of the reaction at different initial concentrations of reactants. By comparing the rates, we can determine the order of the reaction.

2. Half-life method: This method involves measuring the time taken for the reactant concentration to decrease by half. By comparing the half-lives at different concentrations, we can determine the order of the reaction.

3. Integrated rate method: This method involves integrating the rate equation and plotting concentration versus time. By analyzing the slope of the resulting graph, we can determine the order of the reaction.

4. Method of initial rates: This method involves comparing the initial rates of the reaction at different concentrations of reactants. By analyzing the ratio of the initial rates, we can determine the order of the reaction.

For the given complex reaction, 2A + B → C + D, the order of the reaction can be determined by examining the slow determining step, which is 2A → C. The order of the reaction is determined by the stoichiometric coefficients of the reactants in the slow step. In this case, the order is 2.

Considering the effect of ionic strength on the rate constant and the fact that only A and B are present at the beginning of the reaction, an increase in ionic strength (I) would decrease the reaction rate. This is because an increase in ionic strength increases the concentration of ions in the solution, leading to stronger electrostatic interactions and hindering the reaction.

Learn more about ionic strength from this link

https://brainly.com/question/13630255

#SPJ11

The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

To know more about differential equation:

https://brainly.com/question/2273154

#SPJ4

Answer:

2x+10=20 so x=5

Step-by-step explanation:

The probability that a plane will arrive in less than 5 minutes is approximately 0.1813, not 0.3333.

The probability that a plane will arrive in less than 5 minutes is equal to 0.3333. This statement is false. In an exponentially distributed process, the probability of an event occurring in a given time interval is determined by the exponential distribution function. The exponential distribution is characterized by a parameter called the rate parameter, often denoted as λ (lambda).

In this case, the rate parameter λ = 1/15, as planes arrive approximately once every 15 minutes. To calculate the probability of a plane arriving in less than 5 minutes, we can use the cumulative distribution function (CDF) of the exponential distribution. Using the exponential CDF, we find: P(X < 5) = 1 - e^(-λt). Substituting λ = 1/15 and t = 5, we have: P(X < 5) = 1 - e^(-1/15 * 5) ≈ 0.1813. Therefore, the probability that a plane will arrive in less than 5 minutes is approximately 0.1813, not 0.3333.

To learn more about   probability click here: brainly.com/question/31828911

#SPJ11

Answer:

The slope is: 20/-8, or -20/8

Step-by-step explanation:

to find the rate of change, you do change in y over change in x

so you minus the y numbers and minus the x numbers

so,

20-0/0-8 = 20/-8

or you can do

0-20/8-0 = -20/8

both of them are the same

sorry I'm really bad at explaining myself

hope this helps! :D

Answer:

Step-by-step explanation:

(0 - 20)/(-8 - 0)= -20/-8= 20/8= 5/4

The probability that for a randomly chosen integer n between 1 and 10 inclusive there exist no real solutions to the equation x^2 + 5 = n is 3/10.

we can first find the values of n for which there are real solutions to the equation x^2 + 5 = n. We can do this by rearranging the equation to get x^2 = n - 5 and then seeing that there are real solutions only if n - 5 is non-negative, i.e. n >= 5.

Since we are choosing a random integer between 1 and 10 inclusive, there are 10 possible values for n. Out of these, only 5, 6, 7, 8, 9, and 10 are greater than or equal to 5, which means that there are real solutions to the equation for these values of n. Therefore, there are only 6 possible values of n for which there exist no real solutions to the equation.

Therefore, the probability of choosing one of these 6 values of n is 6/10, which simplifies to 3/5. However, we need to find the probability of choosing one of the values of n for which there exist no real solutions to the equation, which is the complement of the probability of choosing one of the values of n for which there are real solutions. This complement is 1 - 6/10, which simplifies to 2/5.

Therefore, the main answer to the question is that the probability that for a randomly chosen integer n between 1 and 10 inclusive there exist no real solutions to the equation x^2 + 5 = n is 2/5.

The probability that for a randomly chosen integer n between 1 and 10 inclusive there exist no real solutions to the equation x^2 + 5 = n is 2/5. This can be found by first determining the values of n for which there are real solutions to the equation, and then finding the complement of this probability.

To know more about equation test visit:

https://brainly.com/question/29657983

#SPJ11

Answer:

y= -x + 6

Step-by-step explanation:

It has a negative slope and the y-intercept is 6

The equation of the line in fully simplified slope-intercept form.

y= -x + 6

It has a negative slope and the y-intercept is 6

A slope is a numerical measurement of the slope of a line with respect to the horizontal. In analytic geometry, the slope of a line, ray, or line segment is the ratio of the vertical distance to the horizontal distance between any two points on it ("the slope is higher than the run").

In mathematics, the slope or slope of a line is a number that describes both the direction and the slope of the line. [1] The gradient is often denoted by the letter m. There is no clear answer as to why the letter m is used for gradients, but its first use in English is due to O'Brien (1844) who gave the equation of a straight line as 'y = MX + B Appears in I have written. It is also mentioned in Todhunter (1888) where ``y = MX + c''

Learn more about slopes here

https://brainly.com/question/3493733

#SPJ1

Answer:  each-121      leftover: 5

The income statement and Accounting Information System, along with the balance sheet and cash flow statement, help you understand your company's financial health.

MIS employs non-financial data, but AIS exclusively uses financial data.

MIS indirectly to other external users.

The income management account is most likely affected by Selling, General, and Administrative Expenses.

In accounting, an instrument that provides the data needed to effectively manage an organization and make decisions is a management information system (MIS).

It is used to locate, collect, process, and distribute economic data about a company to a variety of users (AIS).

MIS concentrates on the financial and accounting aspects of a business, diagnosing problems and proposing solutions. The former management system, that occasionally relied on intuition and unscientific approaches and was arbitrarily constructed, has been replaced with MIS.

Learn more about Accounting Information System (AIS ):

https://brainly.com/question/28259878

#SPJ12

Answer:

Step-by-step explanation:

1/3 - 1/6

2/6 -1/6= 1/6

find common denominator

For  \(\dfrac{1}{3}-\dfrac{1}{6}\)  the fraction will be \(\dfrac{1}{6}\) .

Given to us,

\(\dfrac{1}{3}-\dfrac{1}{6}\)

To solve this, firstly we need to make the denominators the same, thus taking the LCM of both 3 and 6.

As we know the LCM of 3 and 6 is 6 itself.

So, multiplying and dividing by 2.

\(\dfrac{1}{3}\rightarrow \dfrac{1\times 2}{3\times 2}\rightarrow \dfrac{2}{6}\)

Now,

\(\dfrac{2}{6}-\dfrac{1}{6} = \dfrac{1}{6}\)

Hence, for  \(\dfrac{1}{3}-\dfrac{1}{6}\)  the fraction will be \(\dfrac{1}{6}\) .

To know more visit:

https://brainly.com/question/1301963

\(\huge{ \mathrm{ \underline{ Answer }}}࿐\)

\(\large\boxed{x = 45° \: \: or \: \: 135°}\)

\(\#TeeNForeveR\)

The null hypothesis (H0) states that there is no significant difference between the batting averages of Ohio State and Michigan players.

The alternative hypothesis (H1) posits that there is a significant difference between the two. By conducting the hypothesis test at a significance level of .05, the goal is to determine if the observed difference in sample means (.400 - .390) is statistically significant enough to reject the null hypothesis and support the claim that there is indeed a difference in batting averages between Ohio State and Michigan players.

A rivalry between Ohio State and Michigan alumni has sparked a debate about the difference in batting averages between their baseball players. A sample of 60 Ohio State players showed an average of .400 with a standard deviation of .05, while a sample of 50 Michigan players had an average of .390 with a standard deviation of .04. A hypothesis test with a significance level of .05 will be conducted to determine if there is a significant difference between the two schools' batting averages.

For more information on null hypothesis visit: brainly.com/question/33194057

#SPJ11

Answer:

0.4

Step-by-step explanation:

slope =Change in y /change in x

pick two points (0,1) and (-2.5,0)

slope=(1-0/0--2.5 )=0.4

Answer:

75 onces 15 eggs and I dont know for the brown sugar

Step-by-step explanation:

The equation best represents the relationship between x, the age of the machine in years, and y, the value of the machine in dollars over this 10-year period is y = 500x + 8,000(option c).

Equations are mathematical representations that describe relationships between variables. In this case, we are looking for an equation that accurately represents how the value of the machine changes as it ages over a 10-year period.

Unlike the previous two equations, this equation indicates that as the age of the machine (x) increases, the value (y) actually increases. The positive coefficient of 500 suggests a linear increase in value over time. The initial value of the machine is $8,000. This equation predicts a realistic relationship where the machine's value increases as it ages.

Therefore, the equation C, y = 500x + 8,000, best represents the relationship between the age of the machine (x) and its value in dollars (y) over a 10-year period.

Hence the correct option (c).

To know more about equation here

https://brainly.com/question/21835898

#SPJ4

Complete Question:

Which equation best represents the relationship between x, the age of the machine in years, and y, the value of the machine in dollars over this 10-year period?

A)  y=-0.002x + 2,500

B) y=-500x + 8,000

C)  y = 500x + 8,000

D) y = 0.002x + 2,500

Answer:

(pound sign) 11.44

Step-by-step explanation:

Reject the claim by accepting H0.

What is null hypothesis and alternate hypothesis?

The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making decisions on the basis of data.

Explanation for the answer:

Mean of observations, x bar \(=\frac{(23+19+23+23)}{4}=22\)

Then for each number: subtract the Mean and square the result:

\(1+9+1+1=12\)

Sample Variance:

       \(\frac{12}{3} = 4\)

Sample Standard Deviation:

\(\sqrt{4} = 2\)\((\sqrt{4})^{0.5} = 1.1412\)

Standard error,

  \(se = (\frac{s}{n} )^{0.5}\)

\(se = (\frac{1.1412}{4} )^{0.5}\)

\(se = 0.5341\)

Hypothesis,

\(H_0: Xbar \geq 21, against\)

\(H_1: Xbar < 21\\\)  (Lower tailed test)        

t-statistic:  

\(t-statistic=\frac{xbar-Xbar}{se}=\frac{22-21}{0.5341}=1.8723\)

p value for 3 (=n-1) degrees of freedom = 0.039805 or 3.9805%

As p-value < 1% (level of significance), so, we reject the null hypothesis. Hence, the mean running time of runners is not significantly atleast 21 miles.    

Find out more about sample mean and t-statistic:

https://brainly.com/question/28195252

#SPJ4