Which rectangle has side lenghths of 5 units and 6 units

All four conditions have been met, the conditions for statistical inference for testing a difference in population proportions have been satisfied. The conditions for statistical inference for testing a difference in population proportions are:

Random samples: Both schools have selected simple random samples of their respective student populations, which satisfies this condition.

Large sample size: Both schools have over 2,000 students, which satisfies the large sample size condition.

Independent samples: The samples from schools A and B are independent, as the students from one school do not affect the students from the other school.

Success-failure condition: The sample sizes are large enough to satisfy the success-failure condition, which states that there should be at least 10 successes and 10 failures in each sample. Both schools have well over 10 successes and failures in their respective samples.

Since all four conditions have been met, the conditions for statistical inference for testing a difference in population proportions have been satisfied.

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Answer:

30. Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The Half-Life of the material is 13.86 hours. The mass of the material remaining at any time t can be expressed as:
M(t) = 50e^(-0.05t), where t is measured in hours.

The amount of time needed for a number (of material) to decrease to half of its original value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long steady atoms last.

The mass of the material after 4 hours is M(4) = 50e^(-0.2) ≈ 31.4 grams. The half-life of the material can be found by solving for when M(t) = 25 grams:
t = ln(2)/0.05 ≈ 13.86 hours.

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Answer:

See below.

Step-by-step explanation:

Please check the assumptions.  I did not see a graph, so made assumptions in the calculations,

Given that for 10 guests, the total cost is $20, we can calculate a rate of $2/guest ( the unit rate).  This seems too inexpensive, even for a hot dog and soft drink.  But going on that, we can establish the relationship between x (the number of guests) and y (the total cost) as y = ($2/guest)*x.

The list of numbers does not provide a clear undertanding of what is being requested,  The attached spreadheet calculates a number of guest options based on a rate of $2/guest.  The area in green are the second list of values based on the numbers of guests.

As per the given distance, the angle that is made by the ramp with the ground is 19.1 degrees

Let's call the angle we're trying to find theta (θ). We can use the tangent function to calculate θ, as follows:

tan(θ) = opposite / adjacent

We know the opposite side (height of the ramp) is 3.5ft, and the adjacent side (distance along the ground) is 10ft. Plugging these values into the tangent equation, we get:

tan(θ) = 3.5 / 10

We can solve for θ by taking the inverse tangent (also known as arctan) of both sides:

θ = arctan(3.5 / 10)

Using a calculator, we find that θ is approximately 19.1 degrees. Therefore, the ramp makes an angle of 19.1 degrees with the ground.

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Answer:

[tex]x=\frac{5}{2},\:x=3[/tex]

Step-by-step explanation:

[tex]\mathrm{Factor\:}2x^2-11x+15[/tex]

[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]

[tex]\left(2x^2-5x\right)+\left(-6x+15\right)[/tex]

[tex]\mathrm{Factor\:out}\:x\:\mathrm{from}\:2x^2-5x:\quad \:x\left(2x-5\right)[/tex][tex]\mathrm{Factor\:out}\:-3\:\mathrm{from}\:-6x+15:\quad \:-3\left(2x-5\right)[/tex]

[tex]x\left(2x-5\right)-3\left(2x-5\right)[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}2x-5[/tex]

[tex]\left(2x-5\right)\left(x-3\right)[/tex]

[tex]\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0[/tex]

[tex]2x-5=0\quad \mathrm{or}\quad \:x-3=0[/tex]

[tex]\mathrm{Solve\:}\:2x-5=0:\quad x=\frac{5}{2}[/tex]

[tex]\mathrm{Solve\:}\:x-3=0:\quad x=3[/tex]

[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]

[tex]x=\frac{5}{2},\:x=3[/tex]

The rectangular sidewalk for Liam to build the pathway, [tex]36[/tex] stones are required.

The rectangular shape in two dimensions has four aspects, four corners, & four sharp angles (90°). Equal and equal opposing sides make form a rectangle. As a two-dimensional form, the rectangles comprises length and breadth just like its 2 components.

Because a square is indeed a parallelogram with all specific corners at right angles, every square is also a rectangle. To be a square, a rectangle's sides must all have the same length, hence not all rectangles are squares.

Area of the walkway [tex]=length * width[/tex]

[tex]24*6=144[/tex] square feet

Area of each stone [tex]= length of each side * width of each side[/tex]

[tex]=2ft*2ft=4[/tex] square feet

Number of stones needed [tex]=\frac{Area of walkway }{Area of each stone}[/tex]

Number of stones needed [tex]=\frac{144}{4}=36[/tex] stones

Therefore, Liam will need [tex]36[/tex] stones to make the walkway.

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If the force is 270 Newton and the area is 0.03 square meter, the pressure is equal to 9,000 N/m².

In Mathematics, pressure can be defined as a measure of the force exerted per unit area of an object or physical body. This ultimately implies that, it is usually measured in Newton per meter square.

Mathematically, the pressure of a physical object can be calculated by using this formula:

P = F/A

Where:

By substituting the given parameters, we have:

Pressure, P = 270/0.03

Pressure, P = 9,000 N/m².

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The formula that expresses the fact that f(x, y) is a distance 8 from the origin can be found using the distance formula for two points on the coordinate plane, (0, 0) and (x, y).

The distance formula is given by d = √(x2−x1)2+(y2−y1)2where (x1, y1) = (0, 0) and d = 8. Thus, we have8 = √(x2−0)2+(y2−0)2Squaring both sides gives8^2 = (x2−0)2+(y2−0)2which simplifies to64 = x2+y2

Therefore, the formula that expresses the fact that f(x, y) is a distance 8 from the origin isx2+y2= 64.

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Answer:

x = 4

Step-by-step explanation:

- 6 + [tex]\frac{x}{4}[/tex] = - 5 ( add 6 to both sides )

[tex]\frac{x}{4}[/tex] = 1 ( multiply both sides by 4 to clear the function )

x = 4

The current yield of the bond is 11.76% and the yield to call is 19.51%.

The current yield of the bond can be calculated using the following formula:

Current Yield = (Annual Interest Payment/Bond Price) * 100

In this case, the annual interest payment is 10% of the face value of the bond (5 * $100 = $500). The bond price is $41, so the current yield is 11.76%:

Current Yield = ($500/$41)*100 = 11.76%.

The bond is callable at 103 as of 2032, so the call premium is 103 – 41 = 62. This means that if the bond is called, the investor will receive an additional payment of $62 per bond (5 * $62 = $310). The yield to call is the total annual return the investor will receive if the bond is called:

Yield to Call = (Annual Interest Payment + Call Premium)/Bond Price * 100

In this case, the yield to call is:

Yield to Call = ($500 + $310)/$41 * 100 = 19.51%.

This means that if the bond is called in 10 years, the investor will receive an annual return of 19.51%.

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A DVD club charges nonmembers $20. 50 to purchase a DVD. Members pay $18 per DVD for a one-time membership cost of $25. The cost is the same for members and nonmembers on the first purchase is 10.

Let's call the number of DVDs "d". For non-members, the cost of purchasing d DVDs is:

Cost for non-members = 20.50d

For members, the cost of purchasing d DVDs is:

Cost for members = 25 + 18d

We want to find the value of d for which the cost is the same for members and non-members. In other words, we want to find the value of d that satisfies the equation:

20.50d = 25 + 18d

To solve for d, we can start by subtracting 18d from both sides of the equation:

2.50d = 25

Then, we can divide both sides by 2.50:

d = 10

Therefore, the cost will be the same for members and non-members on the first purchase if the number of DVDs purchased is 10.

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Length οf the smaller οf the twο missing sides (the secοnd leg) is 80

In mathematics, the Pythagοrean theοrem οr Pythagοras' theοrem is a fundamental relatiοn in Euclidean geοmetry between the three sides οf a right triangle. It states that the area οf the square whοse side is the hypοtenuse (the side οppοsite the right angle) is equal tο the sum οf the areas οf the squares οn the οther twο sides.

Let x be the length οf the smaller οf the twο missing sides (the secοnd leg). Then the length οf the larger missing side (the hypοtenuse) is (x + 2), since the twο sides are cοnsecutive even integers.

By the Pythagοrean theοrem, we have:

[tex]18^2 + x^2 = (x + 2)^2[/tex]

Simplifying and expanding the right side, we get:

[tex]324 + x^2 = x^2 + 4x + 4[/tex]

Subtracting x^2 frοm bοth sides, we get:

324 = 4x + 4

Subtracting 4 frοm bοth sides, we get:

320 = 4x

Dividing bοth sides by 4, we get:

x = 80

Therefοre, the length οf the smaller οf the twο missing sides (the secοnd leg) is 80.

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The point (3, -5π/3) can be represented by the formula x = 3, y = -5π/3.

The point (3, -5π/3) can be represented by the formula x = 3, y = -5π/3. To calculate this, we first find the x-coordinate, which is simply 3. To find the y-coordinate, we must first multiply 5 and π. 5π = 15.78. We then divide 15.78 by 3, which gives us 5.26. To make this a negative number, we add a negative sign, giving us -5.26. We can then convert this to fraction form by dividing the numerator and denominator by the greatest common factor, which is 1. This gives us -5π/3.

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Complete question:

What point represents (3, negative StartFraction 5 pi Over 3 EndFraction)?

Answer:

A

Step-by-step explanation:

Answer: the very top answer -> A

The bond would pay the bondholder the following sum of $1,000 annually.

The bond being offered by Company ABC has a par value of $1,000, a fixed coupon rate of 5% per year, and a maturity of 10 years.

The coupon rate of 5% per year means that for each $1,000 bond, the bondholder will receive an annual interest payment of $50 (5% of $1,000).

Therefore, out of the given options, the correct amount that the bondholder would receive each year is $50.

It's important to note that this interest payment is fixed and does not change over the 10-year term of the bond. At maturity, the bondholder would receive the par value of $1,000 back from the company.

So, over the course of 10 years, the bondholder would receive a total of $500 ($50 per year) in interest payments, in addition to the return of the $1,000 par value at maturity.

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The measure of ik in the given equation can be calculated by subtracting the sum of IR (which is equal to jkh) and mjk from 180e degrees.

In order to calculate the measure of ik in the given equation, we must use the formula for interior angles of a triangle which is the sum of all angles in a triangle is 180 degrees. In this equation, we are given the measures of two of the angles, IR and mjk. Therefore, the measure of ik can be calculated by subtracting the sum of IR and mjk from 180 degrees.

Given that IR = jk, we can calculate the measure of ik by first calculating the measure of jk. We are given that mik = (11x + 2), so we can solve for x and use that value to calculate jk. If we solve for x, we find that x = (mik-2)/11. We can then use that value to calculate jk, which equals mik-mjk. In this equation, we are given that mjk = (12x - 7), so jk = (11x + 2) - (12x - 7). Simplifying, we find that jk = 9x + 9.

Now that we have the measure of jk, we can calculate the measure of ik by subtracting the sum of jk and IR from 180 degrees. Since IR = jk, we can substitute jk in for IR, so ik = 180

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The distance after 79 minutes is 11 miles.

We know that the distance can be modeled with a linear equation like:

y = ax + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope can be written as:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know the points (39, 45) and (61, 26.3)

Then we can write:

a = (26.3 - 45)/(61 - 39) = -0.85

So we can write:

y = -0.85*x + b

To find the value of b we can replace the values of one of the points, i will use (39, 45) to get.

45 = -0.85*39 + b

45 + 0.85*39 = b

78.15 = b

So the line is:

y =  -0.85*x + 78.15

The distance after 79 minutes is.

y =  -0.85*79 + 78.15

y = 11

The distance left is 11 miles.

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Answer:

4 th option bcoz [tex]x^{y+2}=x^{y}x^{2[/tex]

The value of the required number is - 10  

To find the unknown number represent the number with a variable 'x' and form a linear equation according to the condition given in the problem.

Solve the resultant equation for the value variable 'x' by adding or subtracting the same number on both sides.

Here we have

A number decreased by 16 and the result was -26.

Let 'x' be the number

According to the given data,

=> x - 16 = - 26

Add 16 on both sides

=> x - 16 + 16 = - 26 + 16

=> x = - 10

Hence,

The value of the required number is - 10  

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Answer:

Step-by-step explanation:

wheres the table

The area under the curve of the given function from x=1 to x=5 is -64.17.

The area under a curve is the area between the curve and the x-axis in a certain range. To calculate the area under a curve, we will use the definite integral of the function. The definite integral of a function f(x) from x=a to x=b is defined as

[tex]∫baf(x)dx[/tex]

For the given function f(x) = x^3 - 5x^2 + 2x + 8, the definite integral from x=1 to x=5 is

[tex]∫51(x^3 - 5x^2 + 2x + 8)dx = [x^4/4 - 5x^3/3 + x^2 - 8x]5[/tex]

Substituting x=1 and x=5 gives

[54 - 5(125)/3 + 25 - 8(5)] = -64.17

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Check the picture below.

[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{39}{\sin(53^o)}=\cfrac{JN}{\sin(65^o)}\implies \cfrac{39\sin(65^o)}{\sin(53^o)}=JN\implies 44.3\approx JN \\\\\\ \cfrac{39}{\sin(53^o)}=\cfrac{JS}{\sin(62^o)}\implies \cfrac{39\sin(62^o)}{\sin(53^o)}=JS\implies 43.1\approx JS[/tex]

Make sure your calculator is in Degree mode.

The 90% confidence interval for the difference in mean response times between the cell phone and control group is given as follows:

(12.6, 82.2).

The estimate of the differences is given as follows:

585.3 - 537.9 = 47.4.

The standard error for the distribution of each sample is given as follows:

Hence the standard error for the distribution of differences is given as follows:

sqrt(16.4² + 12.8²) = 20.8.

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 27 + 27 - 2 = 52 df, is t = 1.6747.

The lower bound of the interval is given as follows:

47.4 - 1.6747 x 20.8 = 12.6.

The upper bound of the interval is of:

47.4 + 1.6747 x 20.8 = 82.2.

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we can tentatively conclude that the data is reasonably well-approximated by a normal distribution, but further analysis may be needed to confirm this conclusion.

To create a normal probability plot, we need to first sort the data in ascending order and then calculate the corresponding z-scores for each observation based on the normal distribution. We can then plot the observed z-scores against the expected z-scores on a normal distribution.

Here is the sorted data:

5.04  5.08  6.09  7.55  8.04  8.32  8.51  9.34  9.7   9.74  

10.49 10.94 11.2   11.68 12.39 12.9   14.05 14.64 28.34

And here are the corresponding z-scores calculated based on the normal distribution:

diff

-1.77 -1.74 -1.53 -1.17 -1.04 -0.96 -0.90 -0.72 -0.67 -0.65

-0.41 -0.29 -0.24 -0.17 0.06  0.21  0.48  0.65  3.09

The plot appears to be fairly linear, which suggests that the data could have come from a population that is normally distributed. However, there are a few points that deviate slightly from the line, particularly the two extreme points on the right-hand side. This suggests that there may be some skewness or outliers in the data that are causing deviations from normality.

Overall, we can tentatively conclude that the data is reasonably well-approximated by a normal distribution, but further analysis may be needed to confirm this conclusion.

the complete question is :

"The following data represent a random sample of the number of shares of a pharmaceutical​ company's stock traded for 20 days in 2000. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.

4.78 9.7 11.2 8.32 14.64

6.09 10.49 9.74 12.9 14.05

5.04 9.34 12.39 7.55 28.34

8.51 10.94 5.08 8.04 11.68

Please create a normal probability plot and interpret your findings."

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Step-by-step explanation:

1. Calculate the mean for each sample.

Sample #

1

234

2

3

5

6

7

8

9

O ACCESS Virtual Learning 2022

Sample Items

(1, 1, 2, 0)

(2, 2, 0, 1)

(1, 1, 1, 2)

(2,0, 1, 0)

(2, 2, 0, 1)

(1, 1, 2, 3)

(3, 2, 0, 0)

(1, 1, 1, 1)

(3, 1, 1, 1)

x

The percentage of college seniors' undergraduate major that is engineering is 36.25%.

To calculate the percentage of college seniors' undergraduate major that is engineering, we need to find the proportion of students who majored in engineering out of the total number of students surveyed.

We see that out of the 400 college seniors surveyed, 145 majored in engineering. Therefore, the proportion of students who majored in engineering is 145/400. To convert this proportion to a percentage, we multiply it by 100. So, (145/400) x 100 = 36.25%.

Therefore, 36.25% of the college seniors surveyed had an undergraduate major in engineering.

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Method 1: Factoring

m^2 + 7m + 10

We need to find two numbers that multiply to 10 and add up to 7. These numbers are 2 and 5.

m^2 + 2m + 5m + 10

(m + 2)(m + 5)

n^2 + 9n + 18

We need to find two numbers that multiply to 18 and add up to 9. These numbers are 3 and 6.

n^2 + 3n + 6n + 18

(n + 3)(n + 6)

p^2 - 6p + 8

We need to find two numbers that multiply to 8 and add up to -6. There are no such numbers, so we cannot factor this quadratic.

Method 2: Quadratic Formula

m^2 + 7m + 10

a = 1, b = 7, c = 10

m = (-b ± sqrt(b^2 - 4ac)) / 2a

m = (-7 ± sqrt(7^2 - 4(1)(10))) / 2(1)

m = (-7 ± sqrt(9)) / 2

m = -5 or -2

n^2 + 9n + 18

a = 1, b = 9, c = 18

n = (-b ± sqrt(b^2 - 4ac)) / 2a

n = (-9 ± sqrt(9^2 - 4(1)(18))) / 2(1)

n = (-9 ± sqrt(9)) / 2

n = -3 or -6

p^2 - 6p + 8

a = 1, b = -6, c = 8

p = (-b ± sqrt(b^2 - 4ac)) / 2a

p = (6 ± sqrt(6^2 - 4(1)(8))) / 2(1)

p = (6 ± sqrt(16)) / 2

p = 2 or 4

Therefore, the solutions to the quadratics are:

m^2 + 7m + 10 = (m + 2)(m + 5) or m = -5 or -2

n^2 + 9n + 18 = (n + 3)(n + 6) or n = -3 or -6

p^2 - 6p + 8 = (p - 2)(p - 4) or p = 2 or 4

By answering the above question, we may state that expressions  Researcher A: Value Frequency 3  2 4  1

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

Researcher A:

Value Frequency

3                 2

4                 1

8                  1

10               2

12              1

13                1

14               2

16                 2

17               2

19                 1

21                 1

22               2

24                2

25               2

26                   2

27             2

29               3

31                 2

32                    1

33                  2

34                    2

35                   1

37                   1

40                 1

44                 2

47                   1

Researcher B:

Value Frequency

3                 2

4                 1

6                      1

8               2

13              1

14               3

16             2

17                 1

18                  2

21                 3

22                 2

23              2

24              2

25              2

26            1

28                  1

29                 2

31              2

33                2

34               1

35                   1

41                2

42             1

44                   1

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