Find the scale factor

The mean number of garage stalls per home in the sample of 200 homes is 1.09.

The mean is a measure of central tendency in statistics that represents the average value of a set of numerical data. It is calculated by summing up all the values and dividing by the total number of values.

According to the given information:

To find the mean number of garage stalls per home in the sample of 200 homes, we need to calculate the expected value or the average value of X, which is the number of garage stalls per home. We are given the probabilities of X taking the values 0, 1, and 2, which are P(X=0) = 0.06, P(X=1) = 0.45, and P(X=2) = 0.32.

The formula for calculating the expected value of X is:

E(X) = Σ [ x × P(X=x) ]

where Σ represents the sum of all values of x, and P(X=x) is the probability of X taking the value x.

Using this formula, we can calculate the expected value of X as follows:

\(E(X) = (0 * 0.06) + (1 * 0.45) + (2 * 0.32)\)

\(= 0 + 0.45 + 0.64\)

= 1.09

Therefore, the mean number of garage stalls per home in the sample of 200 homes is 1.09. Hence, the correct option is (a) 1.09.

To know more about mean visit :

https://brainly.com/question/12019147

#SPJ1

The mean number of garage stalls per home in the sample of 200 homes is 1.09.

What is mean?

The mean is a measure of central tendency in statistics that represents the average value of a set of numerical data. It is calculated by summing up all the values and dividing by the total number of values.

According to the given information:

To find the mean number of garage stalls per home in the sample of 200 homes, we need to calculate the expected value or the average value of X, which is the number of garage stalls per home. We are given the probabilities of X taking the values 0, 1, and 2, which are P(X=0) = 0.06, P(X=1) = 0.45, and P(X=2) = 0.32.

The formula for calculating the expected value of X is:

E(X) = Σ [ x × P(X=x) ]

where Σ represents the sum of all values of x, and P(X=x) is the probability of X taking the value x.

Using this formula, we can calculate the expected value of X as follows:

E(x) = (0.06*0)+(1*0.45)+(2*0.32)

= 1.09

Therefore, the mean number of garage stalls per home in the sample of 200 homes is 1.09. Hence, the correct option is (a) 1.09.

To know more about mean visit :

https://brainly.com/question/12019147

#SPJ1

Answer:

3 5,7,9,11,13,16,17 19,21,23,25,27,29

The correct way to measure the zone of inhibition is to place a known amount of an antimicrobial agent on a solid medium.

Area is a quantity that measures the size of a two-dimensional surface or shape. It is expressed in square units such as square centimetres (cm2), square metres (m2) or square kilometres (km2). Area is used to describe the size of a garden, a house, a room, a city and much more. It can also be used to calculate the amount of material required for a project, such as paint, carpet or tiles. Knowing the area of a shape can help to calculate costs, and to make sure that enough materials are ordered.

The zone of inhibition is then measured as the area surrounding the antimicrobial agent where microbial growth has been inhibited. This area is typically measured in millimeters. To accurately measure the zone of inhibition, it is important to ensure that the size of the inoculum and the amount of antimicrobial agent used remain constant. Additionally, it is important to consider the type of organism being studied, as different organisms can have different levels of susceptibility to the antimicrobial agent. Finally, the medium used should be appropriate for the organism being studied, as different media can produce different results.

To know more about area click-
https://brainly.com/question/28012687
#SPJ1

The correct order of steps to prove the inequality 3^n < (n+1)! for n = 7 is as follows: 3^k < (k+1) * k!, 3 * 3^k = 3^(k+1), 3^(k+1) < (k+1) * 3^k; For n = 7, 3^7 = 2187: 2187 < 7! + 5040.

To prove the inequality 3^n < (n+1)! for n = 7, we can follow these steps:

Start with the assumption that 3^k < (k+1) * k! is true for some positive integer k.

Multiply both sides of the inequality by 3 to get 3^(k+1) < 3 * (k+1) * k!.

Simplify the right side to obtain 3^(k+1) < (k+1) * (k+1) * k!.

Rewrite (k+1) * (k+1) as (k+1)^2.

By substitution, we have 3^(k+1) < (k+1)^2 * k!.

Now, consider the case where n = 7. We substitute k = 6 in the inequality.

Evaluating both sides of the inequality for n = 7, we find that 3^7 = 2187.

Calculate (7+1)! = 8! = 40320.

Compare the values: 2187 < 40320.

Since 2187 is indeed less than 40320, the inequality holds true for n = 7.

Therefore, we have successfully shown that 3^n < (n+1)! for n = 7.

To know more about inequality,

https://brainly.com/question/24848865

#SPJ11

To find the number of minutes it will take for both Aquarium A and Aquarium B to contain the same amount of water, we can set up an equation using the given information.

Aquarium A starts with 6 gallons and is filled at 2 gallons per minute. The equation for Aquarium A will be:

A = 6 + 2t

Aquarium B starts with 54 gallons and is filled at 1 gallon per minute. The equation for Aquarium B will be:

B = 54 + 1t

We want to find the time 't' when the amount of water in both aquariums is equal, so we can set the equations equal to each other:

6 + 2t = 54 + 1t

Now, solve for 't':
2t - 1t = 54 - 6
t = 48

After 48 minutes, both Aquarium A and Aquarium B will contain the same amount of water.

Learn more about Aquarium at https://brainly.com/question/29416802

#SPJ11

When resolving an inequality, you can, add the same amount to each side, take away the same amount from each side, multiply or divide each side by the same positive amount.

The complete question is,

How do you resolve an inequality equation?

To learn more about Inequalities refer to:

https://brainly.com/question/24372553

#SPJ1

A data set's attributes are enumerated through descriptive statistics. You can use inferential statistics to test a hypothesis or determine whether your data can be applied to a larger population.

Descriptive statistics concentrate on describing the features of a dataset that are readily evident (a population or sample). In contrast, inferential statistics concentrate on drawing conclusions or generalisations from a sample of data in a larger dataset.

The information from a research sample is described and condensed using descriptive statistics. We can draw conclusions about the larger population from which we drew our sample using inferential statistics.

The area of statistics known as descriptive statistics is focused on providing a description of the population being studied. A type of statistics known as inferential statistics concentrates on inferring information about the population from sample analysis and observation.

Hence we get the required answer.

Learn more about Statistics here:

brainly.com/question/15980493

#SPJ4

Answer:

\(5+2\sqrt6\)

Step-by-step explanation:

\((\sqrt3+\sqrt2)^2\\\\=(\sqrt3)^2+2.\sqrt3.\sqrt2+(\sqrt2)^2 \\\\=3+2.\sqrt{3(2)}+2\ \ \ \ \ \ \ \ \ \ \ \ (\sqrt{a}.\sqrt b=\sqrt{ab},\ \mathrm{if}\ a,b\ge 0)\\=5+2\sqrt6\)

The value of the given function \(log_6x+log_6(x-1)=1\) is x = 3 or x =-2

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x. In the simplest case, the logarithm counts the number of occurrences of the same factor in repeated multiplication; e.g. since 1000 = 10 × 10 × 10 = 10^3, the "logarithm base 10" of 1000 is 3, or \(log_1_01000=3\).

We know that

Log (a) + log (b) = log (ab)

So, \(log_6x+log_6(x-1)=1\)

\(log_6(x(x-1))=1\\log_6(x^2-x)=1\\x^2-x=6^1\\x^2-x-6=0\\\)

(x-3)(x+2)=0

So, x = 3 or x = -2

Therefore the value of the given Logarithmic function is x = 3 or x = -2

Learn more about Logarithmic function here

https://brainly.com/question/12708344

#SPJ1

Answer:

3/4

Step-by-step explanation:

divide both 120 nd 160 by 40

Answer:

3/4

Step-by-step explanation:

120/160

12/16

3/4

Answer:

\(\frac{1}{6}\)

Step-by-step explanation:

We require to create 2 equations with the repeating 6 placed after the decimal point. Then subtracting the equations eliminates the repeating part.

let x = 0.1666....... ( multiply both sides by 10 and 100 )

10x = 1.666...... → (1)

100x = 16.666...... → (2)

Subtract (1) from (2) to eliminate the repeating decimal, thus

90x = 15 ( divide both sides by 90 )

x = \(\frac{15}{90}\) = \(\frac{1}{6}\)

Thus

0.16666......... = \(\frac{1}{6}\)

The expanded linear expression is -56x - 11.

Given: Linear expression = - 7 (4x + 5) - 28x - 35 - 11x + 2 + 11x + 12 - 28x + 12

Step-by-step explanation: To expand, we just need to simplify the expression by combining the like terms.-7(4x + 5) = -28x - 35 [Distribute]-28x - 35 - 11x + 2 + 11x + 12 - 28x + 12 [Rearrange and Combine like terms]-28x - 28x - 11x + 11x - 35 + 2 + 12 + 12 = -56x - 11

A linear function is a function that, when plotted, creates a straight line. Typically, it is a polynomial function with a maximum degree of 1 or 0.  Nevertheless, calculus and linear algebra are also used to represent linear functions. The function notation is the only distinction. It is also important to understand an ordered pair expressed in function notation. When an is an independent variable on which the function depends, the expression f(a) is referred to as a function.

Know more about linear expression here:

https://brainly.com/question/30111963

#SPJ11

Answer:

I Guessed postive  5 and got it right

Step-by-step explanation:

So the answer is 5

NOT -5

Answer:

1160 feet

Step-by-step explanation:

The seating capacity of the stadium in city C is such that all given conditions satisfied will be 70300.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let's say the capacity in city A, city B, and city C is A, B, and C respectively.

As per the given,

A = B + 11500

C = 6800 + B

A = 75000

By substitution,

75000 = B + 11500

B = 63500

Again substitution,

C = 6800 + 63500

C = 70300

Hence "The seating capacity of the stadium in the city C such that the all given condition satisfied will be 70300".

For more about the equation,

https://brainly.com/question/10413253

#SPJ5

The variables examined in the study show the number of hospital visits for cooking-related knife injuries and their frequency during major holidays. The data compiled from emergency departments shows that there is a significant increase in the number of hospital visits for such injuries around major holidays.

This suggests that there may be a correlation between the holidays and the use of knives in cooking, possibly due to increased meal preparation and cooking during these times. Other variables that could be examined in further studies include the types of knives and cooking equipment used, the types of foods being prepared, and the demographics of those who sustain these injuries.

Variables refer to any characteristic, quantity, or attribute that can be measured and that can fluctuate or vary. Variables are of two types:

An independent variable is one that is thought to influence the dependent variable, which is the characteristic or response that is being measured.

The variables examined in the study indicate that the number of hospital visits for cooking-related knife injuries increases around major holidays. This implies that there is a direct relationship between cooking and knife injuries on major holidays. As a result, measures must be put in place to reduce the risk of knife injuries during the holidays. This includes the creation of awareness campaigns and the promotion of safety in the kitchen.

To know more about the "variables": //brainly.com/question/25223322

#SPJ11

In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

To know more about function visit:

brainly.com/question/30721594

#SPJ11

Answer:

Let's call the numbers n and n + 2.

(n + 2)² - n²

= n² + 4n + 4 - n²

= 4n - 4

= 4(n - 1)

Answer:

D. 41

Step-by-step explanation:

Answer:

The answer is C

Step-by-step explanation:

First, convert - 1/41 to a decimal - 1/41 as a decimal which is just 1 divided by 41 which = 0.024390243902439 now multiply that by -41 and you get your answer.

The confidence interval in both cases has been constructed as:

a) (26.02, 29.98)

b) (120.17, 127.83)

The formula to calculate the confidence interval is:

CI = xˉ ± z(σ/√n)

where:

xˉ is sample mean

σ is standard deviation

n is sample size

z is z-score at confidence level

a) xˉ = 28

σ = 4

n = 11

90 percentage confidence.

z at 90% CL = 1.645

Thus:

CI = 28 ± 1.645(4/√11)

CI = 28 ± 1.98

CI = (26.02, 29.98)

b) xˉ = 124

σ = 8

n = 29

90 percentage confidence.

z at 99% CL = 2.576

Thus:

CI = 124 ± 2.576(8/√29)

CI = 124 ± 3.83

CI = (120.17, 127.83)

Read more about Confidence Interval at: https://brainly.com/question/15712887

#SPJ1

The population after 1.5 years will be 360640.9.

Given that, a town's population was 345,000 in 1996. Its population increased by 3% each year.

The exponential growth =

A = P(1+r)ⁿ

A = final amount, P = initial amount, r = rate and n = time.

A = 345000(1+0.03)ⁿ

A = 345000(1.03)ⁿ

There is a growth factor of 1.03.

For n = 1.5

\(A = 345000(1.03)^{1.5\)

A = 360640.9

Hence, the population after 1.5 years will be 360640.9.

Learn more about growth factor click;

https://brainly.com/question/12052909

#SPJ1

Example that demonstrates the contrapositive of the limit comparison test. Let's consider a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges.

Let's define the series an and bn as follows:
- an = 1/\(n^2\)
- bn = 1/n

Now, let's examine the limit:
lim(n→∞)(an/bn) = lim(n→∞)((1/\(n^2\)) / (1/n))

To simplify the limit expression, we multiply both numerator and denominator by \(n^2\):
lim(n→∞)(\(n^2\)(1/\(n^2\)) / \(n^2\)(1/n)) = lim(n→∞)(n/\(n^2\)) = lim(n→∞)(1/n)

As n approaches infinity, the limit becomes:
lim(n→∞)(1/n) = 0

Now, let's check the convergence of the series an and bn:
- an = Σ(1/\(n^2\)) is a convergent p-series with p = 2 > 1.
- bn = Σ(1/n) is a divergent p-series with p = 1.

Thus, we have provided an example of a pair of series an and bn with positive terms, where lim(n→∞)(an/bn) = 0, bn diverges, but an converges. This demonstrates the contrapositive of the limit comparison test, as requested.

To know more about "Limit" refer here:

https://brainly.com/question/30761744#

#SPJ11

(i)The impulse response h(t) is a quadratic function that opens downward and has roots at t = -1. (ii)Therefore, by evaluating the convolution integral with the given input signal x(t) and impulse response h(t), we can determine the output signal y(t) and sketch its graph based on the obtained expression.

i. To sketch the signals x(t) and h(t), we can analyze their mathematical expressions. The input signal x(t) is a linear function with negative slope from t = 0 to t = 4, and it is zero for t > 4. The impulse response h(t) is a quadratic function that opens downward and has roots at t = -1. We can plot the graphs of x(t) and h(t) based on these characteristics.

ii. To determine the output signal y(t), we can use the convolution integral, which is given by the expression:

y(t) = ∫[x(τ)h(t-τ)] dτ

In this case, we substitute the expressions for x(t) and h(t) into the convolution integral. By performing the convolution integral calculation, we obtain the expression for y(t) as a function of t.

To sketch the output signal y(t), we can plot the graph of y(t) based on the obtained expression. The shape of the output signal will depend on the specific values of t and the coefficients in the expressions for x(t) and h(t).

Therefore, by evaluating the convolution integral with the given input signal x(t) and impulse response h(t), we can determine the output signal y(t) and sketch its graph based on the obtained expression.

Learn more about coefficients here:

https://brainly.com/question/1594145

#SPJ11

Answer:

Step-by-step explanation:

a.)

\(4880.76=4000(1+.04/4)^{4x}\\\\1.22019=1.01^{4x}\\\frac{\ln{1.22019}}{\ln{1.01}}=4x\\x= 4.999999= 5\)

b.)

\(5395.4=4000(1+x/12)^{12*5}\\1.34885=(1+x/12)^{60}\\\sqrt[60]{1.34885} =1+x/12\\x= 0.0599999772677= .06\)

c.)

\(\i)\\100*(1+.1255)= 112.55\\\\2)\\100*(1+.1218/2)^2= 112.550881= 112.55\)

The difference in medians (12 seconds in Year 1 vs. 18 seconds in Year 2) coupled with the difference in IQRs (1.8 seconds in Year 1 vs. 2 seconds in Year 2) suggests that the race times in Year 2 have both a higher central tendency (as indicated by the higher median) and a greater spread or variability (as indicated by the larger IQR) compared to Year 1.

The difference in medians in terms of the interquartile ranges (IQRs) indicates a change in the central tendency and spread of the race times between the two consecutive years.

In Year 1, the median race time is 12 seconds, and the IQR is 1.8 seconds. This means that the middle value of the race times is 12 seconds, and the range containing the middle 50% of the data spans from 10.6 seconds (12 - 1.8/2) to 13.4 seconds (12 + 1.8/2). The IQR represents the spread or dispersion of the data.

In Year 2, the median race time increases to 18 seconds, and the IQR increases to 2 seconds. This indicates that the middle value of the race times has shifted to 18 seconds, and the range containing the middle 50% of the data spans from 17 seconds (18 - 2/2) to 19 seconds (18 + 2/2). The larger IQR in Year 2 suggests that the spread of race times has increased compared to Year 1.

for more such questions on interquartile ranges

https://brainly.com/question/4102829

#SPJ8

The real solutions of the given equation are x = 19/16 and x = 13/10.

To find the real solutions of the given equation, let's solve it step by step.

Let's simplify the equation:

((1)/(-4x+5))²-((1)/(-4x+5))-20 = 0

To simplify further, let's substitute y = (-4x + 5):

(1/y²) - (1/y) - 20 = 0

Now, let's multiply the entire equation by y² to eliminate the denominators:

1 - y - 20y² = 0

Rearranging the terms, we have:

20y² - y - 1 = 0

To solve this quadratic equation, we can use the quadratic formula:

y = (-b ± √(b² - 4ac)) / (2a)

Using the coefficients a = 20, b = -1, and c = -1, we can substitute them into the quadratic formula and solve for y.

y = (-(-1) ± √((-1)² - 4(20)(-1))) / (2(20))

y = (1 ± √(1 + 80)) / 40

y = (1 ± √81) / 40

y = (1 ± 9) / 40

So, the possible values of y are:

y = (1 + 9) / 40 = 10/40 = 1/4

y = (1 - 9) / 40 = -8/40 = -1/5

Now, let's substitute back y = (-4x + 5) and solve for x:

For y = 1/4:

-4x + 5 = 1/4

-4x = 1/4 - 5

-4x = -19/4

x = (-19/4) / -4

x = 19/16

For y = -1/5:

-4x + 5 = -1/5

-4x = -1/5 - 5

-4x = -26/5

x = (-26/5) / -4

x = 13/10

Therefore, the real solutions of the given equation are x = 19/16 and x = 13/10.

Learn more about Quadratic Equation at

brainly.com/question/30098550

#SPJ4

Answer:

15

Step-by-step explanation:

The pertinent general formula for this arithmetic progression is

a(n) = a(1) + d(n - 1), where d is the common difference.  That difference is d = 4.

Here, a(n) = -5 + 4(n -1)

Therefore, a(6) = -5 + 4(5) = 15

Answer:

It is 15.

Step-by-step explanation:

Alright, first lets find the pattern. Since its a arithmetic sequence, it has something to do with adding/subtracting.

With the values, -5, -1, and 3. Notice something about them? -1 is 4 more than -5 & 3 is 4 more than -1. There's a pattern! The pattern is that for every new term, it is 4 more than the one before it.

With this, we can make a table to find the 6th term!

(Given)

1st Term: -5

2nd Term: -1

3rd Term: 3

Now, continue adding 4 to each term...

4th Term: 7

5th Term: 11

6th Term: 15

For the 6th term, it has been found that the answer's 15.