Falls City has a current population of 3,300 and is increasing 4.1% every year. How large will the population be in 8 years? Round your answer to the nearest whole number.​

The standardized test statistic is -2.68  and the critical value is 1.44.

Given that, Claim: h = 30 Sample statistics: x = 28.9, n = 65 α = 0.08 σ = 3.31

We need to calculate the standardized test statistic and critical value.

Test statistic: The standardized test statistic can be calculated as follows:

Z = (x - μ) / (σ / √n)

Substitute the given values in the above formula to get

Z = (28.9 - 30) / (3.31 / √65) = -2.68

Critical value: Since the level of significance α is given, we can calculate the critical value using the z-score table for standard normal distribution.

Since α is given,  the right-tailed test is conducted.

The critical value is obtained by subtracting the α-level from 1 and then find the z-score value.

Let's find the z-score value corresponding to the area 0.92 in the z-score table.

We get the corresponding z-score as 1.44, which is the critical value.

Hence, the standardized test statistic is -2.68 (Round to two decimal places as needed.) and the critical value is 1.44.

To learn more about standard normal distribution

https://brainly.com/question/12892403

#SPJ11

Below are the corrected versions of the sentences with grammar, capitalization, usage, and spelling errors addressed.

Learn more about spelling errors here:

https://brainly.com/question/28275742

#SPJ11

The answer is arg 2 = tan^-1(3/2) where : = (a + ai)(b + b/3i) where a and b are positive real numbers.

To determine arg 2, we need to first find the value of :.

Expanding the given expression, we get:

: = (a + ai)(b + b/3i)

: = ab + ab/3i^2 + abi + ab/3i

: = ab - ab/3 + abi + ab/3i

: = (2ab/3) + (ab)i

Now, we can find the modulus of : as:

|:| = sqrt((2ab/3)^2 + (ab)^2)

|:| = sqrt(4a^2b^2/9 + a^2b^2)

|:| = sqrt(13a^2b^2/9)

And, we can find the argument of : as:

arg(:) = tan^-1((ab)/(2ab/3))

arg(:) = tan^-1(3/2)

To know more about positive real numbers refer here:

https://brainly.com/question/30882899#

#SPJ11

Answer:

x = 9

Step-by-step explanation:

5x + 7 = 52

5x = 52-7

5x = 45

x= 9

Answer:

1/30 ton of rock left

Step-by-step explanation:

1/3+ 1/2= 5/6

5/6 - 4/5= 1/30 ton of rock left at the construction site.

Answer:

y= -1/3x + 13/3

Step-by-step explanation:

we can find the equation of the line thanks to this formula

y-y1 = m(x-x1) where y1 and x1 indicate the coordinates of the point, while m indicates the slope

y-2 = -1/3(x-7)

y = -1/3x+7/3+2

y= -1/3x + (7+6)/3

y = -1/3x+13/3

The two alternative formulations of the OLS regressions have differences in their parameter estimates and interpretations. The first model can be represented as: inci = Be + B1edi + B2sexi + εi, where sexi equals 1 for males and 0 for females. The second model is given by: inci = a0 + a1edi + a2sexi + ei, where sexi equals 0 for males and 1 for females.

The first model, the intercept term B0 represents the average income earned by men (when sexi equals zero) who have no education. The coefficient B1 represents the increase in income for each additional year of education. B2 represents the average difference in income between men and women when education is the same. Thus, B2 is the coefficient of the dummy variable for sex.In the second model, a0 represents the average income earned by women (when sexi equals one) who have no education. a1 represents the increase in income for each additional year of education, and a2 represents the average difference in income between men and women when education is the same. Thus, a2 is the coefficient of the dummy variable for sex.The interpretation of the coefficients is different between the two models. In the first model, B2 represents the average difference in income between men and women. In the second model, a2 represents the average difference in income between women and men. Thus, the coefficients of the dummy variable for sex have opposite signs and different interpretations. Also, the intercept terms in the two models are different, which reflects the difference in the average income earned by men and women in the two models. The parameter estimates from the OLS regressions for these alternative formulations will differ as well.

Learn more about  OLS regressions here:

https://brainly.com/question/32230501

#SPJ11

Answer: 6

Step-by-step explanation:

Step 1: Set up equation:

90=40.62+8.23p

^ the 'p' represents pounds.

Step 2: Subtract 40.62 from both sides

49.38 = 8.23p

Step 3: Divide both sides by 8.23 (We do this to get the variable "p" by itself)

6=p

Trust Milky. Milky Smart

Answer:

I can't see the whole picture, but if it's half of the circle, it's the radius. if the line goes all the way through the circle, it's the diameter

Answer:

I think it’s the diameter

Step-by-step explanation:

Answer:

r= 9

Step-by-step explanation:

radius (r) = diameter (D)/2

= 18/2

= 9

Answer:

A.   52°

Step-by-step explanation:

The measure of an inscribed angle is 1/2 the measure of the intercepted arc.

m∠B = 1/2 (m of arc AC)

26 = 1/2 (m of arc AC)

52 = (m of arc AC)

Answer:

x = 6

Step-by-step explanation:

Using the rules of logarithms

logx - logy = log ([tex]\frac{x}{y}[/tex] )

logx = logy , then x = y

Given

log(x) - log(x + 6)

= log([tex]\frac{x}{x+6}[/tex] )

Then

log )[tex]\frac{x}{x+6}[/tex] ) = log([tex]\frac{1}{2}[/tex] ) , thus

[tex]\frac{x}{x+6}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = x + 6 ( subtract x from both sides )

x = 6

Answer:

[tex]15 x = 6.60[/tex]

[tex]x = 44\ hundredths[/tex]

Step-by-step explanation:

Given

[tex]\frac{6.60}{15}[/tex]

Required

Complete the model

[ ] x = 6.60

x = _ hundredths

[tex]\frac{6.60}{15}[/tex]

Equate to x

[tex]x = \frac{6.60}{15}[/tex]

Multiply both sides by 15

[tex]15 * x = \frac{6.60}{15} * 15[/tex]

[tex]15 * x = 6.60[/tex]

[tex]15 x = 6.60[/tex]

So, we have:

[ ] x = 6.60 =====> [tex]15 x = 6.60[/tex]

Recall that:

[tex]x = \frac{6.60}{15}[/tex]

[tex]x = 0.44[/tex]

This implies that:

[tex]x = 44\ hundredths[/tex]

Hence:

x = _ hundredths =====> [tex]x = 44\ hundredths[/tex]

Answer:

864

Step-by-step explanation:

To find the area of a shape, you have to multiply length times width.

Answer:

72 ft. sq.

Step-by-step explanation:

The way to look at it it to multiply length times width ( l x w )

there are 2 obvious  numbers to get the answer, which is 8 and 9 so 8 x 9 = 72

yes,Pi is 3.142 or 22/7

Step-by-step explanation:

22/7=3.14285714

Answer:

The number 1/3 is a rational number. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero.

1/3 is not a natural number, whole number, or integer. Natural numbers are the set of positive integers (1, 2, 3, …). Whole numbers are the set of non-negative integers (0, 1, 2, 3, …). Integers are the set of whole numbers and their additive inverses (-3, -2, -1, 0, 1, 2, 3, …).

Step-by-step explanation:

The y-values are changing at a rate of 24 units per second at the point Q(1, 8).

To find how fast the y-values are changing at the point Q(1, 8), we need to calculate the derivative of the given equation with respect to x. The derivative of y = x^3 + x^2 + 6 is dy/dx = 3x^2 + 2x.

At the point Q(1, 8), we substitute x = 1 into the derivative to find the rate of change.

dy/dx = 3(1)^2 + 2(1) = 3 + 2 = 5.

Therefore, the y-values are changing at a rate of 5 units per second at the point Q(1, 8). However, the rate at which the x-values are changing is given as 2 units per second.

Thus, to determine how fast the y-values are changing with respect to time, we multiply the rate of change in y by the rate of change in x: 5 units/second * 2 units/second = 10 units/second. Hence, the y-values are changing at a rate of 10 units per second at the point Q(1, 8).

LEARN MORE ABOUT  point here: brainly.com/question/32083389

#SPJ11

The Answer is:

−72 r + 755

Answer:

-72r + 755

Step-by-step explanation:

-8(9r – 1) – 9(-85 + 2)

-72r + 8 - 9(-83)

-72r + 8 + 747

-72r + 755

Answer:

yes your answer is correct

Step-by-step explanation:

Answer:

2000.2 cm³

Step-by-step explanation:

Finding the volume of a cylinder is quite simple if you under what pi (3.14) is. You can watch khan academy. It has some useful videos on solving for volume. It also explains very well. Hope this helps!

a) Language L = {u#v: u, v ∈ {0,1}* and u is a substring of v}

b) Language L = {0^2^k : for k ≥ 0}

Time Analysis: The time complexity of this program is O(n), where n is the length of the input. This is because we only need to scan through the input string once, counting the consecutive '0' symbols, and check if the count is a power of 2.

a) Language L = {u#v: u, v ∈ {0,1}* and u is a substring of v}

To sketch a 1-tape Turing machine program for this language, we can follow these steps:

1. Start at the leftmost symbol of the input.

2. Scan to the right until we encounter the '#' symbol, marking all the scanned symbols.

3. Once we encounter the '#' symbol, start scanning to the right again, comparing each scanned symbol with the marked symbols.

4. If a match is found, continue scanning until the end of the input, ensuring that the remaining symbols match the unmarked symbols.

5. If a mismatch is found at any point, reject the input.

6. If the end of the input is reached and all symbols match, accept the input.

Time Analysis: The time complexity of this program is O(n^2), where n is the length of the input. This is because, in the worst case, we need to compare each symbol in the input string with the marked symbols, and we may need to scan through the input string twice.

b) Language L = {0^2^k : for k ≥ 0}

To sketch a 1-tape Turing machine program for this language, we can follow these steps:

1. Start at the leftmost symbol of the input.

2. Scan to the right, counting the number of consecutive '0' symbols until a different symbol is encountered.

3. If the count of '0' symbols is not a power of 2, reject the input.

4. If a different symbol is encountered, check if it is the end of the input. If it is, accept the input.

5. If a different symbol is encountered and it is not the end of the input, reject the input.

Learn more about 1-tape TM:

https://brainly.com/question/15404091

#SPJ11

The required results are:

(i) E(S) = -m₁

(ii) [tex]Var(S) = k(1 − p)(m₂ - m₁²)/p + [k(1-p)/p]² (m₁² + m₂ - m₁²)[/tex]

(iii) Skew = 3(1 − 2p)/sqrt{k(1 − p)}.

The aggregate claim amount is defined as S X₁, where Xį are independent and i=1 identically distributed claim amounts and N is the number of claims.

And also suppose N follows a negative-binomial distribution with

E(N) = k(1 − p)/p

and variance

Var(N) = k(1 − p)/p².

Now we have to show that:

k(1 − p)

(i) [tex]E(S) = -m₁ and р k(1 − p) k(1-P)² m²,[/tex]

(ii) Var (S) = -M2 + p² -

(iii) [tex]Skew k(1 − p)m² 3k(1 − p)²m₁m2 p² + + 2k(1 − p)³m³ p³ P(i) E(S) = -m₁[/tex]

Where S = X1 + X2 + ...... + XN.

Also, N and Xi's are independent.

So, E(S) = E(E(S|N))

From the law of total expectation,

E(S|N) = E(X1 + X2 +......+XN|N)

Using linearity of expectation

,E(X1 + X2 +......+XN|N) = E(X1|N) + E(X2|N) +......+ E(XN|N) = NE(X1)Now, E(S) = E(E(S|N)) = E(NE(X1))= NE(X1) = m₁

Therefore,

E(S) = -m₁.(ii) Var (S) = -M2 + p² -Where Var(S|N) = Var(X1 + X2 +......+XN|N) = Var(X1|N) + Var(X2|N) +......+ Var(XN|N)Also, E(S|N) = NE(X1)Thus, E(S) = E(E(S|N)) = E(NE(X1)) = NE(X1) = m₁ And Var(S) = E(Var(S|N)) + Var(E(S|N))

Using independence,

[tex]Var(S|N) = Var(X1 + X2 +......+XN|N) = Var(X1|N) + Var(X2|N) +......+ Var(XN|N)Var(S|N) = N Var(X1)Using independence, E(S|N) = NE(X1)Var(E(S|N)) = Var(NE(X1)) = N²Var(X1)Hence, Var(S) = E(Var(S|N)) + Var(E(S|N))= E(N Var(X1)) + Var(NE(X1))= (k(1 − p)/p) Var(X1) + N²Var(X1)= k(1 − p)Var(X1)/p + N²Var(X1)[/tex]

Also, [tex]Var(X1) = E(X1²) - (E(X1))² = m₂ - m₁²[/tex]

Therefore,

Var(S) = k(1 − p)(m₂ - m₁²)/p + N²(m₂ - m₁²)

And N follows a negative-binomial distribution with

E(N) = k(1 − p)/p and variance

[tex]Var(N) = k(1 − p)/p². Thus, E(N²) = Var(N) + (E(N))²E(N²) = k(1-p)/p² + [k(1-p)/p]²[/tex]

Therefore,

[tex]Var(S) = k(1 − p)(m₂ - m₁²)/p + [k(1-p)/p]² (m₁² + m₂ - m₁²)(iii) Skew = 3(1 − 2p)/sqrt{k(1 − p)}[/tex]

Therefore,

[tex]k(1 − p)m² 3k(1 − p)²m₁m2 p² + + 2k(1 − p)³m³ p³ P = 3(1 − 2p)/sqrt{k(1 − p)}.[/tex]To know more about binomial distribution, visit:

https://brainly.com/question/29137961

#SPJ11

Answer:

30

Step-by-step explanation:

30

The mean, median, and mode of the given monthly salary is 1794, 1790, and 1940, respectively.

Measures of central tendency assist in the discovery of a data set's middle, or average. The mode, median, and mean are the three most popular metrics of central tendency.

Mode: It is the most common value in a given data set.

Median: In an ordered data set, the median is the number in the middle.

Mean: It is the total number of values divided by the sum of all values.

For the given data, the mean, median and the mode of the data can be found as shown below,

Sum of the Observations

= 1940 + 1660 + 1860 + 2100 + 1720 + 1540 + 1760 + 1940 + 1820 + 1600

= 17940

Number of Observations = 10

The mean of the data is,

Mean = Sum of Observations / Number of Observations

          = 17940 / 10  
          = 1794

The median of the data can be found by arranging the data in an order first. Therefore, the data can be arranged as,

The median of the data is,

Median = (Sum of the two mid values) / 2

             = (1760 + 1820) / 2

             = 1790

The mode of the data is 1940, since this is repeated twice.

b.

If the salary of each employee is increased by 5% that means that the value of each observation in the data will increase by 5%. Therefore, The raise increases the mean, median, and mode by 5% each.

c.

As it is now required to find the mean, median, and mode of the annual salary; there is a need to multiply the monthly salary of each employee by 12. Therefore, the value of each observation will be 12 times its original value. These values are 12 times the mean median, and mode of the monthly salaries.

Learn more about the Central Tendency here:

https://brainly.com/question/17330554

#SPJ3

(a) If f is uniformly continuous, then fn converges to f uniformly.

(b) Uniform continuity of f is necessary for the uniform convergence of fn to f; a counterexample is provided with a continuous f but non-uniform convergence of fn.

(a)If f is uniformly continuous, then we want to show that fn converges to f uniformly.

Given ε > 0, since f is uniformly continuous, there exists δ > 0 such that for any x, y in R, if |x - y| < δ, then |f(x) - f(y)| < ε.

Now, consider fn(x) = f(x + 1/n) for each n. We need to show that for any ε > 0, there exists N such that for all n ≥ N, |fn(x) - f(x)| < ε for all x in R.

Fix ε > 0. By the uniform continuity of f, there exists δ > 0 such that for any x, y in R, if |x - y| < δ, then |f(x) - f(y)| < ε.

Now, for any x in R, let N > 1/δ. Then for all n ≥ N and for any y = x + 1/n, we have |x - y| = |x - (x + 1/n)| = 1/n < δ.

By choosing y = x + 1/n, we have |fn(x) - f(x)| = |f(x + 1/n) - f(x)| < ε.

Since ε was chosen arbitrarily, this shows that fn converges to f uniformly.

(b) Counterexample: To show that  uniform continuity  of f is necessary for the uniform convergence of fn to f, we need to find an example where f is continuous but fn does not converge to f uniformly.

Consider the function f(x) = x on R. This function is continuous.

Now, let's examine the sequence fn(x) = f(x + 1/n). For any x in R, we have:

|fn(x) - f(x)| = |(x + 1/n) - x| = 1/n.

Notice that for any fixed x, as n approaches infinity, 1/n approaches 0. However, the convergence is not uniform since the choice of x affects the convergence rate.

For any ε > 0, no matter how large N is chosen, there will always exist x such that |fn(x) - f(x)| = 1/n ≥ ε, for n > 1/ε.

Therefore, fn does not converge uniformly to f(x) = x, despite f(x) being continuous.

This counterexample demonstrates that the assumption of uniform continuity of f is necessary for the uniform convergence of fn to f.

To learn more about uniform convergence visit : https://brainly.com/question/28169281

#SPJ11

Answer:

it could also be [tex]\frac{20}{4}[/tex] or [tex]\frac{10}{2}[/tex]

Step-by-step explanation:

Simplify.

[tex]\frac{40}{8}[/tex] ÷ 2 = [tex]\frac{20}{4}[/tex]

[tex]\frac{20}{4}[/tex] ÷ 2 = [tex]\frac{10}{2}[/tex]

Answer:

61

Step-by-step explanation:

Answer:

[tex]\frac{5}{13}[/tex]

Step-by-step explanation:

sine of A = [tex]\frac{opposite}{hypotenuse}[/tex]

opposite = 5

adjacent = 12

hypotenuse = 13

Answer:

C.) 12/13

Explanation:

trust me

Answer:

1/67

Step-by-step explanation:

Complete question

If X+2/3x is equal to 45. find the value of x​

Given the equation

x+2/3x = 45

Cross multiply

x+2 = 3x(45)

x+2 = 135x

x - 135x = -2

-134x = -2

x = 2/134

x = 1/67

Hence the value of x is 1/67

Answer:

+100 nasan yung tanong ah

To determine the probability of selecting a card that is less than 8 or a club from a standard deck of cards, we need to consider the number of favorable outcomes and the total number of possible outcomes.

First, let's calculate the number of cards that are less than 8. There are four suits (hearts, diamonds, clubs, and spades), and each suit has cards numbered 2 through 7. So, there are 4 suits * 6 cards per suit = 24 cards that are less than 8.

Next, let's calculate the number of clubs in the deck. There are 13 cards in each suit, and one of those suits is clubs. Therefore, there are 13 clubs in the deck.

To find the probability, we add the number of favorable outcomes (cards less than 8 or clubs) and divide it by the total number of possible outcomes (52 cards in a deck).

Probability = (24 + 13) / 52 = 37 / 52 ≈ 0.7115

Therefore, the probability of selecting a card that is less than 8 or a club is approximately 0.7115 or 71.15%.

To learn more about probability click here:

brainly.com/question/31828911

#SPJ11