consider two populations of coins, one of pennies and one of quarters. a random sample of 25 pennies was selected, and the mean age of the sample was 32 years. a random sample of 35 quarters was taken, and the mean age of the sample was 19 years. for the sampling distribution of the difference in sample means, have the conditions for normality been met?

that the statistic being collected is the mean difference in scores from the beginning and the end of the semester.

In this scenario, the fourth grade class is given a standardized math test at the beginning and end of the semester. The scores from both tests are compared, and the difference between the two scores is calculated for each student. The mean difference in scores is then considered as a statistic to evaluate the overall progress of the class.

Mean difference is a statistical measure that represents the average difference between two sets of data. It is calculated by subtracting the mean of one set from the mean of the other set and then dividing the result by the number of data points.

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1. 2x = 14 --> divide both sides by 2 --> x = 14/2 --> x = 7

2. x + 4 = 3 --> subtract 4 from both sides --> x = 3-4 --> x = -1

3. 3x + 6 = 12 --> subtract 6 from both sides --> 3x = 12-6 --> 3x = 6

4. 2x + 8 = 14 --> factor 2 out on the left side --> 2(x+4) = 14 --> divide both sides by 2 --> x + 4 = 14/2 --> x + 4 = 7

5. x + 5 = 4 --> factor -1 out on the left side --> -(-x-5) = 4 --> divide both sides by -1 --> -x-5 = 4/-1 --> -x-5 = -4

6. 2x + 4 = 3x - 5 --> subtract 2x from both sides --> 4 = 3x - 5 - 2x --> add 5 on both sides --> 4 + 5 = 3x - 2x --> 3x - 2x = 9

7. x - 8 = 24 --> add 8 on both sides --> x = 24 + 8 --> x = 32

8. 21 - 5x = 2 --> subtract 21 from both sides --> -5x = 2 - 21 --> -5x = -19 --> divide both sides by -1 --> 5x = -19/-1 --> 5x = 19

9. 4x + 2 = 8 --> add 2 on both sides --> 4x + 2 + 2 = 8 + 2 --> 4x + 4 = 10 --> factor 4 out on the left side --> 4(x+1) = 10 --> divide both sides by 4 --> x + 1 = 10 / 4 --> x + 1 = 2.5

10. (x-5) / 7 = 10 --> multiply both sides by 7 --> x-5 = 10 * 7 --> x-5 = 70

The cost of running the electric water heater for one month (30 days) would be $36, assuming the electricity costs 12 cents per kilowatt-hour.

To calculate the cost of running the electric water heater for one month, we need to determine the total energy consumption and multiply it by the cost per kilowatt-hour.

The water heater consumes 5 kW for 2 hours per day, so the daily energy consumption can be calculated as follows:

Daily energy consumption = Power (kW) × Time (hours) = 5 kW × 2 hours = 10 kWh

Next, we calculate the total energy consumption for one month (30 days):

Total energy consumption = Daily energy consumption × Number of days = 10 kWh/day × 30 days = 300 kWh

Finally, we multiply the total energy consumption by the cost per kilowatt-hour (12 cents/kWh) to find the cost of running the water heater for one month:

Cost = Total energy consumption × Cost per kilowatt-hour = 300 kWh × $0.12/kWh = $36

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The remainder after dividing 2x³ + 5x² - 3x + 1 by x+4 is 9x+1

We have to find the remainder when we divide 2x³ + 5x² - 3x + 1 by x+4

Dividend is the number which is getting divided by some other number

2x² - 3x + 15 is the dividend

Divisor is the number which divides a number

x+4 is the divisor

In the given division the

       2x² - 3x + 15

       ------------------

x + 4|2x³ + 5x² - 3x + 1

    - (2x³ + 8x²)

       --------------

            -3x²- 3x

            +(-3x² - 12x)

            --------------

                       9x + 1

Hence, the remainder  is 9x+1 when we divide 2x³ + 5x² - 3x + 1 by x+4

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Yes, the chain rule in calculus involves multiplying the derivative of the outside function by the derivative of the inside function.

The chain rule is a fundamental concept in calculus that allows us to find the derivative of a composite function. When a function is composed of two or more functions nested inside each other, the chain rule enables us to differentiate the composite function by taking into account the derivatives of the individual functions.

Mathematically, if we have a composite function f(g(x)), where g(x) represents the inside function and f(u) represents the outside function, the chain rule states that the derivative of the composite function is given by the product of the derivative of the outside function f'(u) and the derivative of the inside function g'(x). In other words, it is the prime of the outside function multiplied by the prime of the inside function.

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The value of the missing sides are;

1. 12. 9

2. 2. 0

3.  4. 6

4. 5. 3 degrees

We have that their are six trigonometric identities. These identities are;

From the information given, we have that;

Using sine identity

sin 57 = 10.8/x

cross multiply the values

x = 12. 9

2. Using cosine identity

cos 47 = x/3

cross multiply

x = 2. 0

3. Using the tangent identity;

tan 41 = 4/x

cross multiply

x = 4. 6

4. The angle of depression is ;

sin X = 27.6/300

sin X = 0. 092

X = 5. 3 degrees

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To calculate Keith's take-home pay, we need to subtract the taxes deducted from his total earnings.

Regular pay: $896

Overtime pay: $672

Total earnings: $896 + $672 = $1568

Taxes deducted: $275

Take-home pay: Total earnings - Taxes deducted

Take-home pay: $1568 - $275 = $1293

Therefore, Keith's take-home pay is $1293.

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Answer:

Step-by-step explanation:

To solve this problem, we can use the fact that a regular hexagon can be divided into six equilateral triangles.The radius of the hexagon is given as 12. Let's draw a diagram to better visualize the hexagon / \ / \ / \ /_______\ B C |\ /| | \ / | | \ / | | \ / | |____D____| | / \ | | / \ | | / \ | |/_______\| E FIn the diagram above, A, B, C, D, E, and F are the vertices of the hexagon.To find the apothem of the hexagon, we need to find the height of one of the equilateral triangles. We know that the side length of each triangle is equal to the radius of the hexagon, which is 12. Using the Pythagorean theorem, we can find the height of one of the triangles/| / | h /__| b/2 (b/2)^2 + h^2 = 12^2 b^2/4 + h^2 = 144 h^2 = 144 - b^2/4Since the hexagon is regular, each side length is equal to 12. Therefore, b = 12.scssCopy codeh^2 = 144 - 12^2/4 h^2 = 144 - 36 h^2 = 108 h = sqrt(108) h = 6*sqrt(3)So the apothem of the hexagon is 6*sqrt(3).To find the area of the hexagon, we can use the formula:makefileCopy codeArea = (1/2) * apothem * perimeterThe perimeter of the hexagon is equal to six times the length of one side, which is 6*12 = 72.scssCopy codeArea = (1/2) * 6*sqrt(3) * 72 Area = 216*sqrt(3)So the area of the hexagon is 216*sqrt(3).Finally, the length of one side of the hexagon is simply equal to the radius, which is 12.

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 = [tex]\dfrac{a}{1 -r}[/tex]

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 = [tex]\dfrac{(-216)}{(-288)}[/tex]

= [tex]\dfrac{3}{4}[/tex]

Substitute the values in the sum formula:

Sum = [tex]\dfrac{-288}{1 - \dfrac{3}{4}}[/tex]

It can be simplified as:

Sum =  -288 [tex]\times[/tex] 4

             = -1152

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

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Answer:

6.37 x 10^5

This is it

Answer: 80

Step-by-step explanation:

10x5=50      10x2=20 2x5=10

The range of the function f include the following: [-20, ∞].

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following range and domain:

Range = [-20, ∞] or -20 ≤ y ≤ ∞.

Domain = [-∞, ∞] or -1 < x < ∞.

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Answer:

See attached. ∠A is a right angle, ∠B and ∠D are acute, ∠C is obtuse.

Step-by-step explanation:

     A right angle is defined as an angle equal to 90 degrees.

     An acute angle is defined as an angle less than 90 degrees.

     An obtuse angle is defined as an angle greater than 90 degrees.

     Using this information we will classify all of the four given angles.

∠A is a right angle, 90 = 90

∠B is acute angle, 60 < 90

∠C is obtuse angle, 160 > 90

∠D is acute angle, 70 < 90

The area of the large pizza is approximately 824 square inches.

Let d be the diameter of the small pizza. We know that the area of the small pizza is 203 in².

Therefore, we can use the formula for the area of a circle to find the radius of the small pizza:

A = πr²

203 = π(d/2)²

203 = π(d²/4)

d² = 812/π

d ≈ 16.2

Therefore, the diameter of the small pizza is approximately 16.2 inches.

The diameter of the large pizza is twice that of the small pizza, so it is:

2d ≈ 32.4

Since the diameter of the large pizza is 32.4 inches, the radius is half of that:

r = 16.2

Therefore, the area of the large pizza is:

A = πr²

A = π(16.2)²

A ≈ 824 in²

Therefore, the area of the large pizza is approximately 824 square inches.

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Answer:

Step-by-step explanation:

1. Put the equations in order:

-14x+y=4(1)

-6x+y=8(2)

2. Eliminate a variable.

In this case, we want to eliminate y, so subtract the second equation from the first

(1)-(2)    -8x=-4

x=-4/8

x=1/2

3. Now that we have one variable, we can use it to solve for y:

6(1/2) + 8=y

3+8=y

y=11

(1/2,11) is the answer.

Another way to do this is to set the first equation equal to the second equation:

6x+8=14x+4

8x=4

x=1/2

y=11

(1/2,11) is the answer!

We used elimination and equal values!

To find the length of the curve r(t) = sqrt(2)ti, we need to use the arc length formula:L = ∫[a,b] ||r'(t)|| dt,where ||r'(t)|| is the magnitude of the derivative of the curve.

First, we need to find r'(t):

r'(t) = (d/dt) [sqrt(2)ti] = sqrt(2)i

The magnitude of r'(t) is ||r'(t)|| = sqrt(2).

So, the length of the curve is:

L = ∫[0,1] sqrt(2) dt = sqrt(2) * [t] [0,1] = sqrt(2)

Therefore, the length of the curve r(t) = sqrt(2)ti is sqrt(2).

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Answer:

13) 225

14) 289

15) 64

16) 8

Answer: #4- both graphs intersect the x-axis to the right of 0

Step-by-step explanation: put them in a graphing calculator or work it out by first solving for x then imputing that answer into the equation

Answer:

±0.6

Step-by-step explanation:

Pythagorean identity:

sin² x + cos² x = 1

sin² x + (0.8)² = 1

sin² x + 0.64 = 1

sin² x = 0.36

sin x = ±0.6

The corresponding IQ score for a z-score of 1.86 is 127.9.

Option A.

If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Given a z-score of 1.86, the corresponding IQ score is calculated as follows;

The formula for IQ score is given as;

IQ = (z-score x standard deviation) + mean

Substituting the given values, the value of IQ score is calculated as;

IQ = (1.86 x 15) + 100

IQ = 27.9 + 100

IQ = 127.9

Therefore, the corresponding IQ score for a z-score of 1.86 is 127.9. The answer is A.

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In school suspension

Yes, -0.614035088 is a rational number.

We know, A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers.

We have the number -0.614035088.

In this case, -0.614035088 can be expressed as the fraction -1227/1999, where both the numerator and denominator are integers.

Thus, Yes, -0.614035088 is a rational number.

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The airplane traveling from New York to Berlin, Germany, has covered 2100 miles in the first 5 hours of its 7-hour journey, leaving a remaining distance of 1860 miles to cover to reach its destination.

To determine the remaining distance that the airplane needs to cover to reach Berlin, we can subtract the distance already traveled from the total distance of the flight. In this case, the airplane has covered 2100 miles in the first 5 hours of its 7-hour journey. Therefore, the remaining distance can be calculated as:

Total distance - Distance covered = 3960 - 2100 = 1860 miles

This means that the airplane still needs to cover a distance of 1860 miles to reach Berlin. We can use this information to estimate the speed at which the airplane needs to travel for the remaining two hours to reach its destination on time. To do this, we can divide the remaining distance by the remaining time:

Speed = Distance / Time = 1860 / 2 = 930 miles per hour

Therefore, the airplane needs to maintain a speed of 930 miles per hour to reach Berlin on time. It's important to note that weather conditions, air traffic, and other factors can affect the actual speed of the airplane during the remaining two hours of the flight, which should be taken into account by the pilot and the flight crew to ensure a safe and timely arrival at the destination.

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The number of required tiles including the breakage and cut-offs are 37.

Firstly we will calculate the number of required tiles based on below mentioned formula-

Number of tiles required to cover the floor = Area covered by one tile × Total area to be tiled

Number of required tiles = 33.984

Rounding off the number

Number of required tiles = 34

Number of extra tiles required for breakage and cut-offs = 34 + 10% × 34

Number of extra tiles = 34 + 10/100×34

Performing multiplication, division, addition along with cancelling common zeroes of the number

Number of extra tiles = 34 + 3.4

Adding the values

Number of extra tiles = 37.4

Again rounding off the number

Number of extra tiles = 37

Hence, the total required number of tiles are 37 according to stated percentage of waste.

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The mason's assistant's pay for the job is $165.

To find the mason's assistant's pay for the job, we need to multiply the rate of pay per cubic foot by the number of cubic feet moved.

Rate of pay per cubic foot = $0.75
Number of cubic feet moved = 220

Pay for the job = $0.75 x 220 = $165

Therefore, the mason's assistant's pay for the job is $165.
The mason's assistant will earn $165 for this job.


To calculate the pay for the mason's assistant, follow these steps:

1. Determine the rate of pay per cubic foot: $0.75
2. Determine the total amount of cubic feet moved: 220 cubic feet
3. Multiply the rate of pay by the total cubic feet moved: $0.75 x 220

By multiplying the rate of pay ($0.75) by the total cubic feet moved (220), you get the total pay for the job:

$0.75 x 220 = $165


The mason's assistant will be paid $165 for moving 220 cubic feet of earth to dig the trench.

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The set {x∈R:[tex]x^2\geq 0[/tex]}^c is the empty set, as there are no real numbers that are not included in the set of all real numbers.

To find the set {x∈R:[tex]x^2\geq 0[/tex]}^c, we first need to understand what the statement [tex]x^2\geq 0[/tex] means. This inequality simply states that any real number squared is always non-negative. Therefore, the set {x∈R:[tex]x^2\geq 0[/tex]} is equivalent to the set of all real numbers.

Now, to find the complement of this set, we need to look for all the elements that are not in the set of all real numbers. Since the universal set is R, which is the set of all real numbers, the complement of {x∈R:[tex]x^2\geq 0[/tex]} will be the empty set, since there are no real numbers that are not included in the set of all real numbers.
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The length of KL to millimeters is  460 millimeters

To convert the measurements, we need to take into considerations the following.

We have that;

Idm = 10 cm

1000 centimeter = 1 liter

100 millimeters = 1cm

From the information given, we have that;

The length of line KL is 4.6cm

If 100 millimeters = 1cm

Then, x = 4. 6cm

cross multiply the values, we get;

x = 460 millimeters

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Vlad should sample 1733 soldiers to estimate the proportion with a margin of error of less than 0.007 and a 97% confidence level.

We can use the formula for the margin of error of a proportion:

ME = zsqrt(p(1-p)/n)

where ME is the margin of error, z is the critical value for a 97% confidence interval (which can be found using a table or calculator and is approximately 2.17), p is the estimated proportion (0.62), and n is the sample size.

We want to find n, so we can rearrange the formula and solve for n:

n = (z^2 * p * (1-p)) / ME^2

Substituting the values given, we get:

n = (2.17^2 * 0.62 * 0.38) / 0.007^2

n ≈ 1732.92

Since we need a whole number of soldiers, we round up to n = 1733.

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