Five years ago, a county lottery official conducted a very extensive (and expensive) study to determine the average age of lottery players in the county. From the data, he estimated the true age to be about 50 years. Five years later, the lottery official wants to know if the average age is now different from 50 years. He plans to conduct a smaller (and less expensive) survey of lottery players. From a random sample of 81 players from the county, the average age is 48. 7 years with a standard deviation of 8. 5 years.


(a) is there convincing evidence at the a = 0. 05 significance level that the present-day average age of all lottery players in the county is different from 50 years.


(b) Referring to your conclusion in part fa), what type of error may have been made? Describe the error in the context of this study

The sum of the infinite geometric series –288 –216 –144 –72 is -1152.

The sum of an infinite number of terms having a constant ratio between successive terms is called as infinite geometric series.

Given series, -288, -216, -144, -72, ...

The sum of the infinite geometric series can be calculated as:

Sum = \(\dfrac{a}{1 -r}\)

Here, 'a' is the first term of the series and 'r' is the common ratio.

a = -288

The common difference can be calculated as:

r = \(\dfrac{(-216)}{(-288)}\)

= \(\dfrac{3}{4}\)

Substitute the values in the sum formula:

Sum = \(\dfrac{-288}{1 - \dfrac{3}{4}}\)

It can be simplified as:

Sum =  -288 \(\times\) 4

             = -1152

So, the sum of the infinite geometric series is -1152.

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Answer:

(2) b is negative

Step-by-step explanation:

If b is negative then the result of a + b would actually be a - b, which is located to the left of a. For answer 1, the number would be located on the right and for 3 the answer would be in the same place. Finally, for answer 4, the number would still be located to the right of a, just a smaller distance than a away.

LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.

To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:

LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))

where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).

First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01

1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.

2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39

First Scenario Result:
LCL = 158.61
UCL = 161.39

Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05

1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.

2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35

Second Scenario Result:
LCL = 69.65
UCL = 70.35

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We are being asked the inverse of the function f(x) = 2x - 5. Now by definition of an inverse function, f(g(x)) = x. f(x) = 2x - 5, so the inverse would be in the following format:

\(=> \mathrm{f\left(g\left(x\right)\right)\:=\:2g\left(x\right)\:\:-\:5}\:\)

\(=> \mathrm{2g(x) - 5 = x}\:\)

\(=> \mathrm{2g(x) = x + 5}\:\)

\(=> \mathrm{g(x) = x + 5 / 2}\:\)

I don't understand the inverse function you gave, 'g(x)= Žx + 5' but if it is in other words 'g(x) = x + 5 / 2' then the two functions you gave are inverses.

EXPLANATION:

Given;

We are told that a baseball team scores in each of their first 5 innings. After that they do not score a run for the next 10 innings.

Let x represent the inning of the game and y represent the total number of runs.

Required;

Sketch a graph that shows the relationship between x and y.

Step-by-step explanation;

With each run the team scores points, that simply means as x increases, y also increases. That signifies a positive relationship between both variables. A positive relationship will be an upward sloping line (from left to right). At the point where the team does not score any more points, the line does not rise.

So the innings (the x-axis) moves towards the right while the runs does not move at all up till 10 innings.

This is best described by the graph labelled C.

ANSWER:

Graph C best represents the situation described

Answer:

66 feet

Step-by-step explanation:

5 1/2 times 12

Answer:

1

Step-by-step explanation:

Answer:

1152000 ft or 218.18 miles

Step-by-step explanation:

6400 x 60 (60 minutes in an hour) = 384000 ft

384000 = one hour at top speed

384000 x 3 = 1152000 ft (3 hours at speed)

There is 5280 feet in a mile

1152000 / 5280 = 218.18 miles

brainliest if this was helpful

Answer:

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Answer:

10^-5= 1/10^5

so option c is correct

Answer:

$105.22

Step-by-step explanation:

The expression is equivalent is 6x/4 + 24y/12

Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.

These expressions also consisting of mathematical operations, such as;

Given the expression;

1/4(3x+4y) + 3(1/4x+ 2/3y)

expand the bracket

3x/4 + 4y/4 + 3/4x + 3/3y

collect like terms

3x/4 + 3/4x + 4y/4 + 3/3y

add like terms

3x + 3x/4 +  12y + 12y /12

add the numerators

6x/4 + 24y/12

Hence, the expression is 6x/4 + 24y/12

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Step-by-step explanation:

for y-intercept

x=0 so,

y=8 (0)-18

y=0-18

y= -18

for x-intercept

y=0 so,

0=8x-18

8x=18

x=2.25

On using the distribution method the value could be  \(e ^ {t^{2}\)/ 2

What is the Gamma Distribution  ?

A distribution which is described as two parameters – shape parameter and inverse scale parameter, having continuous probability distributions.

Given,

Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).

Using the distribution method, find the pdf of U = Z 2.

And Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution.

Suppose e Z ∼ N (0, 1),  then

mZ (t) = 1√2πetxe−x2/2dx

= et2/21/√2π

\(e ^ {-(x-t)^{2} /2\) dx

= \(e ^ {t^{2}\)/ 2

hence, on using the distribution method the value could be \(e ^ {t^{2}\)/ 2

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Answer:

4.702 does not represent 4.701

Step-by-step explanation:

#teamtrees #WAP (Water And Plant)

Answer:

WHAT ARE THE NUMBERS?

Step-by-step explanation:

YOU DIDNT WRITE THEM

To calculate the molecular weight of a gas with a density of 1.524 g/l at STP, we can use the ideal gas law: PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 22.4 L/mol, and the temperature (T) is 273 K. The molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

Rearranging the equation, we get n = PV/RT.

Next, we can calculate the number of moles (n) of the gas using the given density of 1.524 g/l. We know that 1 mole of any gas at STP occupies 22.4 L, so the density can be converted to mass by multiplying by the molar mass (M) and dividing by the volume: density = (M*n)/V. Rearranging the equation, we get M = (density * V) / n.

Substituting the given values, we get n = (1 atm * 22.4 L/mol) / (0.0821 L*atm/mol*K * 273 K) = 1 mol. Then, M = (1.524 g/L * 22.4 L/mol) / 1 mol = 34.10 g/mol. Therefore, the molecular weight of the gas is 34.10 g/mol.

To calculate the molecular weight of a gas with a density of 1.524 g/L at STP, you can follow these steps:

1. Recall the ideal gas equation: PV = nRT

2. At STP (Standard Temperature and Pressure), the temperature (T) is 273.15 K and the pressure (P) is 1 atm (101.325 kPa).

3. Convert the density (given as 1.524 g/L) to mass per volume (m/V) by dividing it by the molar volume at STP (22.4 L/mol). This will give you the number of moles (n) per volume (V):

  n/V = (1.524 g/L) / (22.4 L/mol)

4. Calculate the molar mass (M) of the gas using the rearranged ideal gas equation, where R is the gas constant (8.314 J/mol K):

  M = (n/V) * (RT/P)

5. Substitute the values and solve for M:

  M = (1.524 g/L / 22.4 L/mol) * ((8.314 J/mol K * 273.15 K) / 101325 Pa)

6. Calculate the molecular weight of the gas:

  M ≈ 32.0 g/mol

Therefore, the molecular weight of the gas with a density of 1.524 g/L at STP is approximately 32.0 g/mol.

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The speed of boat in still water is 15 m per hour.

What is speed?

The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's motion per unit of time, making it a scalar quantity. The instantaneous speed is indeed the upper limit of a average speed as that of the length of the interval approaches zero. The average speed of the object in a period of time is equal to the distance travelled by object divided by duration of the period. Velocity and speed are not the same thing.

The dimensions of speed are time divided by distance.

Given, speed of lazy river current = 5

distance covered = 20 miles downstream

and 10 miles upstream

Let x be the speed in still water
(x+5)T = 20

(X-5)T= 10

2(X-5) = (X+5)

X = 15

Therefore, speed of the boat in still water is 15 m per hour

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Answer:

because the four units aren't all the way inside the circle.

Step-by-step explanation:

Answer: There isn't any full circles. in order to have a square you need 4 corners .they all only have 1 inside that circle.

Step-by-step explanation:

Answer:

95.9 cm^2

Step-by-step explanation:

this figure is composed of two semicircles. the area of each semicircle would be determined and then added together.

area of a semicircle = 1/2 nr^2

r = radius

n = 22/7

bigger semicircle

1/2 x (22/7) x (6^2) = 56.57cm^2

smaller circle = 1/2 x (22/7) x (5^2) =39.29cm^2

Sum of the areas = 56.6 + 39.3 = 95.9 cm^2

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

Answer:

See below

Step-by-step explanation:

Think about what happens when you rotate around a circle \(-\frac{3\pi}{4}\) radians. This means that you are going clockwise \(-\frac{3\pi}{4}\) radians.

Likewise, if you went \(\frac{5\pi}{4}\) radians counterclockwise, you'd end up in the same place, so the cosine values must be the same.

\(A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]\)

We can find the A as shown below:

Given A^2=I

We know that A^2=A×A

And \(I=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]\)

So, \(A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]\)

Let \(A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]\)

\(A^2=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right] \left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]\)

\(A^2=\left[\begin{array}{ccc}9-8&-6+6\\12-12&-8+9\end{array}\right]\)

\(A^2=\left[\begin{array}{ccc}1&0\\0&1\end{array}\right]\)

Hence, \(A=\left[\begin{array}{ccc}3&-2\\4&-3\end{array}\right]\)

Hence, option C is correct

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Disclaimer: Given question is incomplete. Complete question is attached.

The values of all integration function have been obtained.

Q2.  x²/2 tan²x - x² tan x/2 + x tan x - ln|cosx| + C

Q3.  32 ln|x + 1| + 23/15 ln|x - 2| - 41/8 ln|x + 3| + C.

Q2.

To find the integration of the given function i.e.

∫x tan²xdx,

Using the integration by parts, we use the following formula:

∫u dv = uv - ∫v du

Let us consider u = tan²x and dv = x dx.

So, du = 2 tan x sec²x dx and v = x²/2.

Using these values in the formula we get:

∫x tan²xdx = ∫u dv

                 = uv - ∫v du

                 = x²/2 tan²x - ∫x²/2 * 2 tan x sec²x dx

                 = x²/2 tan²x - x² tan x/2 + ∫x dx     (integration of sec²x is tanx)

                 = x²/2 tan²x - x² tan x/2 + x tan x - ∫tan x dx

                                                                (using integration by substitution)

                 = x²/2 tan²x - x² tan x/2 + x tan x - ln|cosx| + C

So, the integration of the given function using integration by parts is

x²/2 tan²x - x² tan x/2 + x tan x - ln|cosx| + C.

Q3.

To find the integration of the given function i.e.

∫(2x² + 9x - 35)/[(x + 1)(x - 2)(x + 3)] dx,

Using partial fraction, we have to first factorize the denominator.

Let us consider (x + 1)(x - 2)(x + 3).

The factors are (x + 1), (x - 2) and (x + 3).

Hence, we can write the given function as

A/(x + 1) + B/(x - 2) + C/(x + 3),

Where A, B and C are constants.

To find these constants A, B and C, let us consider.

(2x² + 9x - 35) = A(x - 2)(x + 3) + B(x + 1)(x + 3) + C(x + 1)(x - 2).

Putting x = -1, we get

-64 = -2A,

So, A = 32 Putting x = 2, we get

23 = 15B,

So, B = 23/15 Putting x = -3, we get

41 = -8C,

So, C = -41/8

So, we can write the given function as

∫(2x² + 9x - 35)/[(x + 1)(x - 2)(x + 3)] dx = ∫32/(x + 1) dx + ∫23/15(x - 2) dx - ∫41/8/(x + 3) dx

Now, we can integrate these three terms separately using the formula: ∫1/(x + a) dx = ln|x + a| + C

So, we get

= ∫(2x² + 9x - 35)/[(x + 1)(x - 2)(x + 3)] dx

= 32 ln|x + 1|/1 + 23/15 ln|x - 2|/1 - 41/8 ln|x + 3|/1 + C

= 32 ln|x + 1| + 23/15 ln|x - 2| - 41/8 ln|x + 3| + C

So, the integration of the given function using partial fraction is 32 ln|x + 1| + 23/15 ln|x - 2| - 41/8 ln|x + 3| + C.

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Another possible vertex of the square is determined as (2, 1).

option B is the correct answer.

The vertex of a figure is the point of intersection of two sides of the shape.

The perimeter of the square is given as 12 units, the length of each side of the square is calculated as follows;

P = 12 units

a side length = 12 units / 4 = 3 units

To determine another possible vertex of the square, the length between the points must be equal to 3.

Let's consider point A;

A = (1, 2)

given vertex = (-1, 1)

distance between the points = √ (-1 -1)² + (1 - 2)² = √5

Let's consider point B;

B = (2, 1)

given vertex = (-1, 1)

distance between the points = √ (-1 -2)² + (1 - 1)² = √9 = 3

Thus, point B is another possible vertex of the square.

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Answer:

moon and stars wonder

where have all the people gone

alone in hiding

Step-by-step explanation:

Answer:

Auto Praise for Cow - A Haiku

"The juxtaposition of cow and goat is truly inspired."

- The Daily Tale

"I don't like short poems. So why am I reviewing a haiku, you may wonder? Well, I liked the title - 'Cow'. It went down hill from there."

- Enid Kibbler

"Amazing how so few words can set a scene so perfectly. I close my eyes and all I can see is the baking christmastime."

- Hit the Spoof

"I felt that I was a cow. It was spooky. I hope to read more by Anonymous. Perhaps next time, something longer."

- Zob Gloop

"I've always wanted to write a haiku about a cow. I can't belive Anonymous has beaten me to it."

- Betty Borison

"Baking christmastime is a popular first line for a haiku. It's incredible how much diversity can be achieved with those final lines."

- Chris Critic, otherwise known as Cristic

Step-by-step explanation:

qw

Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e)  6200cm = 6200x cm. f)  403 kg = 40x kg.

a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.

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False. In a static method of a class, you cannot use the "this" keyword to reference instance variables or instance methods of the same class.

A static method belongs to the class itself, not to any particular instance of the class, so it cannot access instance-specific information. Instead, you would need to use the class name followed by the variable name to access any static or instance variables within a static method of that same class. For example, if the class had an instance variable called "f" and a static method called "myStaticMethod", you could reference the instance variable from within the static method using "ClassName.f". It is important to note that if you attempt to reference an instance variable using "this.f" within a static method, you will receive a compilation error.

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Answer:

They're all 45

Step-by-step explanation:

since the lines are perpendicular all angles are equal