Explain why the initial value ofany function of the form f(x)=a(b^x) is equal to a

The complete question is :

People tend to be more generous after receiving good news. Are they less generous after receiving bad news? The average tip left by adult Americans is 20%. Give 20 patrons of a restaurant a message on their bill warning them that tomorrow’s weather will be bad and record the tip percentage they leave. Table 1 contains the tips as a percentage of the total bill.

Table :  18.0 19.1 19.2 18.8 18.4 19.0 18.5 16.1 16.8 18.2 14.0 17.0 13.6 17.5 20.0 20.2 18.8 18.0 23.2 19.4

Suppose that tip percentage is Normal with ? = 2 and assume that the patrons in this study are a random sample of all patrons of this restaurant. Is there good evidence that the mean tip percentage for all patrons of this restaurant is less than 20 when they receive a message warning them of tomorrow’s bad weather? State \($H_0$\) and \($H_a$\) and carry out a significance test. Use significance level 0.05.

Solution:

The given data is :

18.0, 19.1, 19.2, 18.8, 18.4, 19.0, 18.5, 16.1, 16.8, 18.2, 14.0, 17.0, 13.6, 17.5, 20.0, 20.2, 18.8, 18.0, 23.2, 19.4

Therefore, sample mean,

\($\bar x= \frac{\Sigma x}{n}$\)

  \($=\frac{18+19.1+19.2+...+19.4}{20}$\)

 = 18.19

Now test : μ  < 20 with normal distance

Hypothesis test:

\($H_0=\mu \geq20$\)

\($H_a=\mu <20$\)      

This is the lower tailed test.

\($\bar x = 18.19$\)

\($\sigma =2$\)

n = 20

Significant level, α = 0.05

Test statistics, \($z^*=\frac{\bar x - \mu}{\sigma / \sqrt n }$\)

                           \($=\frac{18.19 - 20}{2 / \sqrt{20}}$\)

                          ≈ -4.05

P value is in direction of alternative hypothesis or \($H_a$\)

Since, \($H_a=\mu <20$\) , P value = P(Z<-4.05)

P value is the area to the left of the test statistics = -4.05 (from the figure)

P value = P(Z< -4.05) = 0.000 (from z table)

P value = 00000

Rejection rule : Reject  \($H_0$\)  if P value < α

Using excel functional normdist \($\left(\frac{18.19-20}{2 / \sqrt{20}}, 0, 1 , \text{TRUE} \right )$\) or TI's function normaldf \($\left( 1E-99, \frac{18.19-20}{2 / \sqrt{20}}\right)$\) answer is 0.0000259078

Decision : Since 0.0000 < 0.05, we reject the null hypothesis

Hence at 5% significance level, we have sufficient evidence to conduct that μ is less than 20.

At the 5% significance level, we have shown that μ is less than 20.

What are test statistics?

A test statistic is defined in such a way as to the quantity, within observed data that would distinguish the null from the alternative hypothesis

\({\displaystyle z={\frac {{\overline {x}}-\mu _{0}}{({\sigma }/{\sqrt {n}})}}}\)

The given data is

18.0, 19.1, 19.2, 18.8, 18.4, 19.0, 18.5, 16.1, 16.8, 18.2, 14.0, 17.0, 13.6, 17.5, 20.0, 20.2, 18.8, 18.0, 23.2, 19.4

Mean = Sum of the terms / number of terms

         = \(\frac{18.0 + 19.1 + 19.2, +........+23.2 1+ 9.4}{20}\)

         = 18.19

Now with a normal distance test, we get

\(\rm H_{0} = \mu \geq 20\\\rm H_{\alpha } = \mu < 20\)

lower tailed test

Mean  = 18.19

\(\sigma = 2\)

n = 20

Test statistics,   \({\displaystyle z={\frac {{\overline {x}}-\mu _{0}}{({\sigma }/{\sqrt {n}})}}}\)

                  z = \(\frac{18.19-20}{2/\sqrt{20} }\)

                   = -4.05

Significant level, α = 0.05

P-value is in direction of an alternative hypothesis or

Since, P-value = P(Z<-4.05)

= 0.000 (from z table)

P value = 00000

By Rejection rule, Reject \(\rm H_{0}\) if P value < α

Using excel functional normdist, the answer is 0.0000259078

Since 0.0000 < 0.05, we reject the null hypothesis

Therefore, at the 5% significance level, we have shown that μ is less than 20.

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Answer:

22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42

Step-by-step explanation:

Any number that ends with, 0,2,4,6,8 is even, hope it helped!

22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 43

Answer:

1/8

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

the cake was divided in 1/4ths so half of that is 1/8

Answer:

UW = EW+UE=2×EW because, EW=UE

7x-2=2×6= 12

7x=14

x=14/7

x=2

\((x+4)(x-1) = x^{2} -x+4x-4=x^{2} +3x-4\)

ok done. thank to me :>

False. In a chi-square goodness-of-fit test, the test statistic is calculated based on the discrepancies between the observed frequencies and the expected frequencies. The test statistic measures the degree of deviation between the observed and expected frequencies.

Therefore, the larger the value of the test statistic, the greater the discrepancy between the observed and expected frequencies, indicating poorer fit between the observed and expected data.

In other words, a larger test statistic suggests a greater departure from the expected frequencies and indicates poorer fit between the observed and expected data. On the other hand, a smaller test statistic suggests a closer match between the observed and expected frequencies, indicating a better fit.

Therefore, the statement should be reversed: The more closely the observed frequencies match the expected frequencies, the smaller the value of the test statistic.

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Answer:

(12ab)^1/2

Step-by-step explanation:

(⁶√12ab)³

= [(12ab)^1/6]³

= (12ab)^(1/6 * 3)

= (12ab)^1/2.

A data set has a mean of 177 and a standard deviation of 20. 11.3% is the coefficient of variance for this collection of data.

The ratio of a data set's standard deviation to its mean, stated as a percentage, is represented by a coefficient of variation (CV), a dimensional measure of variability. It is a practical tool for contrasting the relative variance of two or more data groups with various means or measurement units.

We divide the usual level deviation by the mean, multiply the result by 100, and that number is the coefficient of variation. The coefficient in variation can be computed as follows in this situation: Using the formula CV = (standard deviation / mean) x 100, (20 / 177) x 100, and 11.3%

A low coefficient for variation means that the mean is a good indicator of the data and that the set of data has low relative variability. On the other hand, a high coefficient for variation shows substantial relative variability, which could point to the need for additional research or alternate metrics of central tendency.

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Answer:

y= -1.5x+2

Step-by-step explanation:

Answer:

A one tailed test

Step-by-step explanation:

Chi-Square Distributions That Are Positively Skewed Have A Research Hypothesis That Is A One-Tailed Test.

Chi-Square distributions are positively skewed, with the degree of skew decreasing with increasing degrees of freedom.

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One-Tailed Test

Chi-Square distributions that are positively skewed have a research hypothesis that is a One-Tailed Test.

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Coordinates of point A are

(-3,-2)

Origin lies in the center of coordinate system. That means that you can picture this as right triangle with sides 3 and 2 and you need to find hypotenuse of it.

Using pythagoras theorem we calculate:

h^2 = 3^2 + 2^2 = 13

h = sqrt 13

Answer is b

Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

\(\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the Straight lines.

equation of the line perpendicular to the given line is

\(y = \frac{1}{4} x + 3\)

Answer:

1/3 x 3/4

Step-by-step explanation:

in this case, 3/4 is correct because it is 3 of 4 shaded.

hope this helps!

Hii! Its your friend Nat! :)

Known: 3/4 of the model is shaded, we are multiplying.

The model repersents 3/4

This is because only 3 out of 4 pieces are shaded in.

If all pieces were shaded it would be 4/4 or 1 whole.  

1/3 x 3/4  is 3/12

3/12 simplifed is 1/4

Hope dis helps!

Brainliest?

~Learning with  Natalia~

Answer:

A.  9.4 mi

Step-by-step explanation:

Sketch a right triangle with legs of 8 and 5.  Shortest distance back to the starting point is the hypotenuse (h) of the triangle:

h² = 8² + 5² = 89

h = √89 = 9.43 mi

Answer:

y = 16

Step-by-step explanation:

11y = 2(24 + 4y)

11y = 48 + 8y

3y = 48

   y = 16

Answer:

Step-by-step explanation:

(⅚ pound)/(3 people) = (⅚÷3 pound)/person = 5/18 pound per person.

Step-by-step explanation:

Here is a linear program that would decide how James should invest his money to maximize the total amount of money he would have at year 10:

Let x[i][j] represent the amount of money invested in bond type j in year i, where j = A, B, C. Let s[i] represent the amount of money in the savings account at the end of year i.

Maximize: s[10]

Subject to:

s[0] = M

s[i] = s[i-1]*1.025 + n + 1.045*x[i-2][A] + 1.07*x[i-3][B] + 1.4641*x[i-4][C] + 0.045*x[i-1][A] + 0.07*x[i-2][B] for 2 < i < 9

s[9] = s[8]*1.025 + n + 1.045*x[7][A] + 1.07*x[6][B] + 1.4641*x[5][C] + 0.045*x[8][A]

s[10] = s[9]*1.025 + 1.045*x[8][A] + 1.07*x[7][B] + 1.4641*x[6][C]

x[i][j] >= 0 for all i and j

The objective function maximizes the amount of money in the savings account at the end of year 10.

The first constraint sets the initial amount of money in the savings account to M.

The second constraint calculates the amount of money in the savings account at the end of each year for years 2 to 8, taking into account the interest earned on the savings account, additional investment n, and any matured bonds or interest payments.

The third constraint calculates the amount of money in the savings account at the end of year 9, taking into account the interest earned on the savings account, additional investment n, and any matured bonds or interest payments.

The fourth constraint calculates the amount of money in the savings account at the end of year 10, taking into account any matured bonds.

The last constraint ensures that all investments are non-negative.

This linear program can be solved using a linear programming solver to determine how James should invest his money to maximize his total amount at year 10.

To maximize the total amount of money James would have at year 10, we can formulate a linear program considering James's investments in bonds A, B, and C, as well as his savings account.

Let's define the decision variables as follows:

xA: The amount invested in Bond A in each year.

xB: The amount invested in Bond B in each year.

xC: The amount invested in Bond C in each year.

xS: The amount placed in the savings account in each year.

The objective function to maximize would be:

Maximize Z = 1.045^2 * xA + 1.07^3 * xB + 1.1^4 * xC + 1.025^10 * xS

Subject to the following constraints:

xA, xB, xC, xS ≥ 0 (non-negativity constraint)

xA + xB + xC + xS ≤ M + (n * 7) (total investment limit each year)

xA ≤ M (investing limit in Bond A)

xB ≤ M + n (investing limit in Bond B)

xC ≤ M + (n * 3) (investing limit in Bond C)

The sum of the investments in each year (xA + xB + xC + xS) should be less than or equal to the amount available in the previous year plus the additional amount (n) available for the current year.

These constraints ensure that James invests within the given limits and distributes his investments appropriately each year. By solving this linear program, we can determine the optimal investment strategy for James to maximize his total amount of money at year 10, considering the interest rates and maturity periods of the bonds as well as the savings account interest rate.

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In the class of Mr. Kendrick's, Jonah is in Group B and Janeka is in Group A using the concept of Logical Reasoning.

As per the question statement, we are given that in Mr. Kendrick's class, students are divided into two groups for an activity. Students in group A must always tell the truth and correct info. Students in group B must always lie. Jonah and Janeka are in Mr. Kendrick's class. When asked if Jonah and Janeka are in group A or B, Jonah says, "We are both in Group B. "

By their statement and using the concept of Logical Reasoning, we can conclude that Jonah is in Group B and Janeka is in Group A.

As Jonah said, "We are both in Group B. " and as both the students can't be in same group so Jonah lied and hence he is in group B and Janeka is in group A.

This is a classic example of  Logical Reasoning.

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The best approximation of the area of the circle is 113.04 square inches.

A circle is a shape with all points equidistant from a central point, known as the center. The distance from the center to any point on the edge of the circle is called the radius.

It can be calculated using the formula π \(r^2\), where r is the radius.

Since the diameter of the circle is 12 inches, the radius would be half of that which is 6 inches.

So, the area would be approximately 3.14 * \(6^2\) = 113.04 square inches.

Therefore, The best approximation of the area of the circle is 113.04 square inches.

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Quantitative easing refers to the process whereby the Federal Reserve buys securities to stimulate the economy.

A central bank, such as the U.S. Federal Reserve, uses quantitative easing (QE), a type of monetary policy, to buy assets on the open market in order to lower interest rates and expand the money supply.

New bank reserves are created as a result of quantitative easing, giving banks additional liquidity and promoting lending and investment. The Federal Reserve in the US carries out QE initiatives. The methods available to central banks to affect economic development are restricted, such as lowering interest rates. In order to strategically raise the money supply, central banks must be unable to further reduce interest rates. Quantitative easing is frequently used when interest rates are close to zero and the economy remains stagnant.

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quantitative easing refers to the process whereby the central bank, such as the Federal Reserve (Fed), purchases government securities to increase the money supply and lower interest rates. It is used to stimulate the economy by encouraging borrowing and spending, especially during economic downturns or when traditional monetary policy tools are ineffective.

quantitative easing is a monetary policy tool used by central banks, such as the Federal Reserve (Fed), to stimulate the economy. It involves the purchase of government securities, such as bonds, by the central bank in order to increase the money supply and lower interest rates.

The purpose of quantitative easing is to encourage borrowing and spending, which in turn stimulates economic growth and helps combat deflationary pressures. By injecting money into the economy, central banks aim to increase liquidity and promote lending by financial institutions.

This policy is typically implemented during times of economic downturn or when traditional monetary policy tools, such as lowering interest rates, have become ineffective.

Quantitative easing can have both positive and negative effects on the economy. On the positive side, it can help stimulate economic growth, lower borrowing costs, and prevent deflation. However, it can also lead to inflationary pressures and create risks in the financial markets.

The success of quantitative easing depends on various factors, including the overall health of the economy and the effectiveness of other fiscal and monetary policies.

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Answer:

5.3

Step-by-step explanation:

Since they are similar triangles, we assume the ratio between AM/AN is equal to the ratio between MB/NC.
AM/AN = 6/8 = 3/4
If MB is 4
3/4 = MB/NC = 4/NC
3/4 = 4/NC

3NC = 16
NC = 16/3
16/3 = 5.333333

Answer:

6

Step-by-step explanation:

divide by 3 on both sides

The domain of a function f(x) = 2√(-x² + 10x) in interval notation is given by (-∞, 0] ∪ [10, ∞).

Function f(x) = 2√(-x² + 10x).

Domain of a function is the set of all possible input values of x for which the function is defined.

Values of x for which the expression inside the square root is non-negative.

As the square root of a negative number is not a real number.

Take out the common factor -x we have,

-x² + 10x ≥ 0

⇒ -x(x - 10) ≥ 0

⇒ -x ≥ 0 or ( x - 10 ) ≥ 0

The inequality is satisfied when x ≤ 0 or x ≥ 10.

This implies,

The domain of the function f(x) = 2√(-x² + 10x) is the set of all real numbers such that x ≤ 0 or x ≥ 10.

In interval notation form,

The domain is represented as,

(-∞, 0] ∪ [10, ∞).

Therefore, the domain of the given function is equal to (-∞, 0] ∪ [10, ∞).

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The above question is incomplete , the complete question is:

What is the domain of a function f(x) = 2√-x²+ 10x

0.688 will be the probability of getting a nickel from the jar.

Given,

Probability;-

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.

Therefore,

P(nickel) = 19/69

P(penny) = 17/68

That is,

P = 19/69 × 17/68

P = 323/4692

P = 0.0688

That is,

The probability of getting nickel from the jar is 0.06888

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If each consumer demands one item of groceries and faces a travel cost of $12 per kilometer. BetaMarket chooses the price of $33.33 in equilibrium.

AlphaMart sells groceries at the west end of Main Street, a street that is one kilometer long. AlphaMart competes with BetaMarket, which is located at the east end of the street. AlphaMart and BetaMarket sell groceries that are identical in every respect, apart from the locations of the two stores. The marginal cost of an item of groceries is $3 for both retailers.

Main Street is home to 200 consumers; the consumers are evenly spaced along the street. Each consumer demands one item of groceries and faces a travel cost of $12 per kilometer. To calculate the equilibrium price of BetaMarket, we first need to find out the quantity demanded at each price point.

The quantity demanded for each price point can be found by subtracting the number of consumers who are closer to AlphaMart than to BetaMarket from the total number of consumers. Let the price charged by BetaMarket be P. If BetaMarket charges P, then the demand for BetaMarket's groceries is given by:

QB = 200/2 - 1/2 (P + 12) = 100 - 1/2 (P + 12)

QB = 100 - 1/2P - 6

We can now write down BetaMarket's profit function as:

πB = QB(P - 3) = (100 - 1/2P - 6)(P - 3)

πB = 100P - 3/2P² - 309

From this, we can find the first-order condition for profit maximization by differentiating the profit function with respect to P and setting it equal to zero:

∂πB/∂P = 100 - 3P = 0P = 100/3

Thus, BetaMarket chooses to set the price at $33.33 in equilibrium.

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Answer:

b; |-4|<|-5|

Step-by-step explanation:

Absolute value is the distance from zero, so the absolute value of -5 is greater than the the absolute value of -4.

Reyna will need 0.048 quart of orange juice.

In this question, we have been given a recipe for a punch call for 12 fluid ounces of orange juice.

Reyna needs to make 4 batches of punch for a party.

We need to find number of quarts of orange juice Reyna will need.

From given conditions, we formulate:

= 4 × 12 ÷ 1000

= 12 ÷ 250                  .................(Separate out the common factor)

= 6/125

= 0.048 quart

Therefore, Reyna will need 0.048 quart of orange juice.

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The two numbers that satisfy both conditions are from quadratic equation :x =

1) -10/3, y = ±(10√7)/3

2)x = 10/3, y = ±(10√7)/3.

Let's denote the two numbers as x and y. We are given the following information:

1. The sum of their squares is 100: x^2 + y^2 = 100.

2. The square of the larger number is equal to the sum of the product of the larger number and four times the smaller number and eight times the larger number: y^2 = x(4y + 8x).

To solve this problem, we can start by simplifying the second equation. By expanding the equation, we get:

y^2 = 4xy + 8x^2.

Now, we can substitute this equation into the first equation to eliminatey:

x^2 + (4xy + 8x^2) = 100.

Combining like terms, we have:

9x^2 + 4xy - 100 = 0.

To find the values of x and y that satisfy this equation, we can use various methods such as factoring, completing the square, or the quadratic formula. In this case, let's solve it by factoring.

Factoring the quadratic equation, we get:

(3x + 10)(3x - 10) = 0.

Setting each factor equal to zero, we have two possibilities:

1. 3x + 10 = 0, which gives x = -10/3.

2. 3x - 10 = 0, which gives x = 10/3.

Now that we have the values of x, we can substitute them back into one of the original equations to find the corresponding values of y. Let's use the first equation:

For x = -10/3, we have (-10/3)^2 + y^2 = 100. Solving this equation, we find y = ±(10√7)/3.

For x = 10/3, we have (10/3)^2 + y^2 = 100. Solving this equation, we find y = ±(10√7)/3.

Therefore, the two numbers that satisfy both conditions are:

1. x = -10/3, y = ±(10√7)/3.

2. x = 10/3, y = ±(10√7)/3.

These are the two sets of numbers that meet the given conditions.

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