the owner of a local theatre is interested in the average number of attendees for weeknight shows. she knows that the average number of attendees for weeknight shows over the past 20 years has been 1550 with a standard deviation of 180. she takes a sample of 36 weeknight shows from this year and finds the average has been 1400 and the standard deviation has been 120. what are the mean and standard deviation for the sampling distribution of ?

Answer:

Yes they are equivalent, both equations equals \(15d+20\)

Step-by-step explanation:

We first simplify Olivia's equation

\(6d + 8 + 9d + 12\)

1. we combine like terms in the equation: \(6d + 8 + 9d + 12\)

\(6d+9d\)

\(8+12\)

\(15d+20\)

Now we simplify Isabella's

\(5(3d + 4)\)

1. we do distributive property

\(5*3d\)

\(5*4\)

\(15d+20\)

If you have any quesitons feel free to ask

The mean of the random variable, number of birds that survive migration, if 280 birds were randomly selected, is 238.

To compute the mean of the random variable, we need to multiply the probability of survival (85% or 0.85) by the total number of birds (280). By doing this, we can determine the expected number of birds that will survive the migration trip.

The probability of survival for each bird is independent of the others, so we can treat each bird's survival as a separate Bernoulli trial. In this case, the probability of success (survival) is 0.85, and the probability of failure (not surviving) is 0.15.

We can use the formula for the mean of a binomial distribution to calculate the expected number of successes. The formula is:

mean = \(n * p\)

Where:

- mean is the expected number of successes,

- n is the total number of trials (birds in this case), and

- p is the probability of success (probability of surviving the migration trip).

Plugging in the values, we have:

mean =\(280 * 0.85\) = 238

Therefore, the mean of the random variable, number of birds that survive migration, if 280 birds were randomly selected, is 238.

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The most appropriate choice for trigonometry will be given by -

Angle between beam and road is 0.33°

What is Trigonometry?

Trigonometry shows the relationship between sides and angles of a right angled triangle.

There are six trigonometrical functions. They are \(sin\theta, cos\theta, tan\theta, cos\theta, sec\theta, cosec\theta\)

\(sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\\)

Trigonometry is a very important tool in mathematics.

Here,

The headlights of an automobile are set such that the beam drops 2.00 in. for each 28.0 ft in front of the car.

According to the figure attached here, 2.0 inch forms the height of the triangle and 28.0 ft forms the base of the triangle

Let the angle be \(\theta\). Now trigonometry is applied here

\(tan\theta = \frac{\frac{2}{12}}{28}\\tan\theta = \frac{1}{6 \times 28}\\tan\theta = \frac{1}{168}\\\theta = tan^{-1}\frac{1}{168}\\\theta = 0.33^{\circ}\)

Angle between beam and road is 0.33°

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Marcia should leave her money in the bank for approximately 11.8957 years (or rounded to 11.8957 years) to reach a balance of $400.

To determine how long Marcia needs to leave her money in the bank for it to grow to $400, we can use the formula for compound interest:

A = P * (1 + r)^n

Where:

A is the final amount ($400)

P is the initial deposit ($200)

r is the interest rate (6% or 0.06)

n is the number of years

Rearranging the formula, we have:

n = log(A/P) / log(1 + r)

Substituting the given values, we get:

n = log(400/200) / log(1 + 0.06)

n = log(2) / log(1.06)

Using a calculator, we can evaluate this expression:

n ≈ 11.8957

Rounding the answer to four decimal places, we find that Marcia needs to leave her money in the bank for approximately 11.8957 years for it to grow to $400.

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Answer:

Point A

Step-by-step explanation:

The square root of 20 is 4.4 , And point A is directly on 4.4.

Hope this helps :)

Answer:

a= 31

b=92

c=44

Step-by-step explanation:

Over the 30 year period, the values of Minneapolis and St. Paul's values will be: Mean 1.580666667 1.769333333 and Standard Deviation 0.890741799 1.123161779

Using the R software or any other graphing software and typing in the, we get the graphs.

The commands were

qqnorm(c(0.32,0.52,0.77,0.81,0.96,1.2,1.31,1.43,1.62,1.87,1.95,2.1,2.48,3,3.37)) and qqnorm(c(0.47,0.59,0.81,0.9,1.18,1.2,1.35,1.51,1.74,1.89,2.05,2.2,2.81,3.09,4.75))

We see there's a slight difference between the two graphs.

For Minneapolis, the curve goes upwards to 0.4

and the for St. Paul the curve goes downwards to 0.4

The term "mean" refers to the mathematical average of a set of two or more numbers. The arithmetic mean and the geometric mean are two types of means that can be computed. By adding all of the numbers in a set and dividing by the total number of numbers in the set, the arithmetic mean is determined. The standard deviation is a measurement of how widely distributed or how much a group of data differ. A low standard deviation indicates that the values typically tend to be close to the set mean, while a high standard deviation suggests that the values are dispersed over a wider range.

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Answer:

the answer for this question is -3,248

Answer:

1 acre is equal to 43,560 square feet.

Step-by-step explanation:

Hope it helped!

Answer:

The bag contains $2.39

Explanation 40% of 50 coins is 20 dimes which equals 2 dollars

8 percent is 4 pennies

2.00+ .04 is 2.04

Plus 7 nickels because there are 3 more nickels than pennies 7*5= 35

2.04+.35= 2.39

Step-by-step explanation:

Break it up into two trapezoids as shown

area = trap1 + trap2

      = 2 *   (7+3) / 2   + 3 *  ( 7 + 3) / 2 = 10 + 15 = 25 units^2

The clock minutes rotate 270 degrees in 45 minutes.

While rotating, the clock's hands are seen to move at a speed of six degrees per minute.

The number of degrees for a clock minute is solved by

60 minutes  = 360 degrees

1 minute = ?

cross multiplying

60 * ? = 360

? = 360 / 60

? = 6

hence 1 minute is 6 degrees

The formula to use to get the calculation is multiplying the number of minutes by 6

Number of degrees in 45 minutes = 45 * 6

Number of degrees in 45 minutes = 270 degrees

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Answer:

344miles

Step-by-step explanation:

if 258=3/4

=1

258÷3/4=344

Answer:

344 miles

Step-by-step explanation:

258 ÷ 3/4 = 344

Answer:

m-6=x

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sophia asked 50 people which drinks they liked from tea, coffee and milk.

all 50 people like at least one of the drinks.

19 people like all three drinks.

16 people like tea and coffee but do not like milk.

21 people like coffee and milk.

24 people like tea and milk.

40 people like coffee.

1 person likes only milk.

sophia selects at random one of the 50 people.

work out the probability that this person likes tea.

The second sampling method is the most representative (option D).

A sample is a percentage or part of a population that is used to study a specific phenomenon. The purpose of selecting a sample is to avoid studying all the population but still obtain results that can represent all the population.

A sample is representative when individuals with different features are selected. For example, if you want to know if the population of a city supports recycling you will need to ask

In the case presented, for the sample to be representative the researcher will need to survey both members of the football and the soccer team. This is ideal because there can be differences between the teams.

Based on this, the best is to use the second sampling method because this will be representative.

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Answer:

Its D :-)

Step-by-step explanation:

The difference quotient for the function is 8.

The function is given by:

f ( x ) = 8 x − 9, where h ≠ 0

To find f(a), substitute a for x in the function. So we have:

f ( a ) = 8 a − 9

To find f(a + h), substitute a + h for x in the function. So we have:

f ( a + h ) = 8 ( a + h ) − 9

The difference quotient can be found using the formula:

(f(a + h) - f(a))/h

Substituting the values found above, we have:

(8 ( a + h ) − 9 - (8 a − 9))/h

Expanding the brackets and simplifying, we have:

((8a + 8h) - 9 - 8a + 9)/h

= 8h/h

= 8

Therefore, the difference quotient for the function is 8.

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Answer:

232 dollars

Step-by-step explanation:

200*0.16=32

200+32=232

Answer:

$232

Step-by-step explanation:

Jose will owe a total of two hundred thirty-two dollars at the end of two years. The total he owes is equal to the principal, two hundred dollars, plus the interest, thirty-two dollars.

Answer:

First it is adding 15 then it starts adding 3 then 1

Step-by-step explanation:

Four numbers forming a geometric sequence such that the second term is 35 less than the first term and the third term is 560 more than the fourth term are -35/3, -140/3, - 560/3, -2240/3 and 7, -28, 112, - 448  

Four numbers forming a geometric sequence can be calculate as follows

these terms: a₁, a₂, a₃, a₄

a₁ = a₂ + 35

a₃ = a₄ + 560

Use the formula for the n-term:

a₂ = a₁r

a₃ = a₁r²

a₄ = a₁r³

replace

a₁ = a₁r + 35 ⇒ a₁(1 - r) = 35

a₁r² = a₁r³ + 560  ⇒ a₁(1 - r)r² = 560

Subtracting from the first equation to  the second:

r² = 560/35

r² = 16

r = √16

r = ± 4

Use the first equation to find the first term:

a₁( 1 ± 4) = 35

1. a₁ = 35/-3 = -35/3

2. a₁ = 35/5 = 7

We have two sequences:

r = 4

-35/3, -140/3, - 560/3, -2240/3

r = -4

7, -28, 112, - 448  

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Answer:

729 square inches

Step-by-step explanation:

9^3 or 9×9×9

(im not sure but i think thats it)

To find the percentage, we can use the following formula:

Percentage = (Part / Whole) * 100

So, $131,701.32 is approximately 16.67% of $790,207.91.

In this case, the part is $131,701.32 and the whole is $790,207.91.

Percentage = ($131,701.32 / $790,207.91) * 100

Calculating the value:

Percentage ≈ 0.1667 * 100

Percentage ≈ 16.67%

Therefore, $131,701.32 is approximately 16.67% of $790,207.91.

Alternatively, we can calculate the percentage by dividing the part by the whole and multiplying by 100:

Percentage = ($131,701.32 / $790,207.91) * 100 ≈ 0.1667 * 100 ≈ 16.67%

So, $131,701.32 is approximately 16.67% of $790,207.91.

If you have any further questions, feel free to ask!

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The acceleration of the bookshelf is equal to 1.30 \(m/s^2\)

Given the following data:

To determine the acceleration of the bookshelf, we would apply Newton's Second Law of Motion:

Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on the object while being inversely proportional to its mass.

Mathematically, Newton's Second Law of Motion is given by this formula;

\(Acceleration = \frac{Net\;force}{Mass}\)

Substituting the given parameters into the formula, we have;

\(Acceleration = \frac{67}{51.5}\)

Acceleration = 1.30 \(m/s^2\)

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Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.

Answer:

data distribution: shows all possible values of data/probability of how often it occurs.

if it is good distribution, the data will be scattered equally in a way which allows you to easily come up with a conclusion upon analysis.

if distribution is poor, the data will not make sense basically.

sorry if this doesn't make sense, i tried to phrase it as best as i could, good luck x

Answer:

8 - 4 x = -(2 x - 17)

Step-by-step explanation:

Solve for x:

-4 (x - 2) = -2 (x - 17/2)

Hint: | Put the fractions in x - 17/2 over a common denominator.

Put each term in x - 17/2 over the common denominator 2: x - 17/2 = (2 x)/2 - 17/2:

-4 (x - 2) = -2(2 x)/2 - 17/2

Hint: | Combine (2 x)/2 - 17/2 into a single fraction.

(2 x)/2 - 17/2 = (2 x - 17)/2:

-4 (x - 2) = -21/2 (2 x - 17)

Hint: | In (-2 (2 x - 17))/2, divide -2 in the numerator by 2 in the denominator.

(-2)/2 = (2 (-1))/2 = -1:

-4 (x - 2) = -1 (2 x - 17)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

Answer: 8 - 4 x = -(2 x - 17)

The limit exists and equals -4 when a = 28.

From the information, we want to find the number a such that the limit exists. lim x→−2 4x² + ax + a + 12 divided by x² + x − 2.

It should be noted that this will be illustrated as:

(4x² + ax + a + 12) / (x² + x − 2)

We will substitute x = -2 into the value of x in the Illustration. This will be:

(16 - 2a + a + 12) / (4 - 2 - 2)

16 - 2a + a + 12 = 0

-a = -28

a = 28

Using lhopital rule, we'll find the derivative. This will be:

8x + a / 2x + 2

Substitute x = -2

(-16 + 28) / (-4 + 1)

= 12 / -3

= -4

Therefore the limit exists and equals -4 when a = 28.

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Complete question

find the number a such that the limit exists. lim x→−2 4x² + ax + a + 12 divided by x² + x − 2

I am very unsure what your question is, but the simple tip is to divide it by two each year as it is decreasing by a half..

To find the number of copies sold in subsequent years, you can use the formula:

N = N0 * (1/2)^t

where N is the number of copies sold in a given year, N0 is the initial number of copies sold (in this case, 600,000), t is the number of years since the book was released.

For example, to find the number of copies sold in the second year after the book was released:

N = 600,000 * (1/2)^1

N = 300,000

So, 300,000 copies were sold in the second year. To find the number of copies sold in subsequent years, you can continue to plug in values of t and solve for N.

Answer:

0.65

Step-by-step explanation:

\(13.00*5%=0.65\)

Answer:

Price before tax: $ 13.00

+ Sales tax (5%): $ 0.65

Total price including tax: $ 13.65

Good luck <33