Suppose you tested two age groups on the number of details they could recall from a paragraph. The mean for the older group is 16, and the mean for the younger group is 14. Further suppose that you fail to reject the null hypothesis for this independent samples t-test.

Required:
What best accounts for the difference between these sample means?

When you divide the circumference of a jack-o'-lantern by its diameter, you get the mathematical constant pi, which has many important applications in various fields of science and technology.

When you divide the circumference, you get a mathematical constant called pi, denoted by the symbol π. Pi is a non-repeating, non-terminating decimal that represents the ratio of the circumference of a circle to its diameter. Its value is approximately 3.14159, but it extends infinitely without repeating or terminating.

The fact that the ratio of the circumference of a circle to its diameter is always the same value, pi, is a fundamental concept in mathematics and has numerous applications in science, engineering, and technology.

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a) A is a hard one but here goes...

\(4cos2x + 2sinx = 3\\4cos2x + 2sinx -3 = 0\\4(1-sin^2x) +2 sinx - 3 = 0\\let w = sinx\\4(1-2w^2) + 2w -3 = 0\\8w^2 + 2w - 3 = 0\\factor\\\\(2w-1)(4w+3)=0\\\\w = sinx = \frac{1}{2},\frac{-3}{4\\}\\x= arcsin(\frac{1}{2}) = \frac{\pi}{6} + 2k\pi \\\\and \\x =arcsin(\frac{-3}{4} )+2k\pi\)

b)

\(sin2x = sin2x\\sin2x - sin2x = 0\)

x = all real numbers

c)

\(7sinx*cosx =2\\7 * \frac{sin2x}{2} = 2\\7*sin2x = 4\\sin2x = \frac{4}{7}\\2x = arcsin(4/7)\\x = \frac{arcsin\frac{4}{7} }{2}+2\pi k\) where k is an integer.  

Rounding to 4 decimal places, we expect 9.9600 of the 12 vehicles to use E-ZPass.

Rounding to 4 decimal places, the mode is 10 and the probability associated with the mode is 0.2822.

Rounding to 4 decimal places, the probability of eight or more of the sampled vehicles using E-ZPass is 0.9975.

a. We can use the binomial distribution to model the number of vehicles out of 12 that use E-ZPass. The probability of a vehicle using E-ZPass is 0.83, so the expected number of vehicles out of 12 that use E-ZPass is:

E(X) = np = 12 x 0.83 = 9.96

Rounding to 4 decimal places, we expect 9.9600 of the 12 vehicles to use E-ZPass.

b. The mode of the binomial distribution is the value of X that maximizes the probability mass function (PMF). In this case, the PMF is given by:

P(X = x) = (12 choose x) * 0.83^x * 0.17^(12-x)

We can find the mode by calculating the PMF for each possible value of X and identifying the value(s) with the highest probability. Alternatively, we can use the formula for the mode of the binomial distribution, which is:

mode = floor((n+1)p)

where n is the number of trials and p is the probability of success.

In this case, the mode is:

mode = floor((12+1) x 0.83) = floor(10.08) = 10

The probability associated with the mode is:

P(X = 10) = (12 choose 10) * 0.83^10 * 0.17^2 = 0.2822

Rounding to 4 decimal places, the mode is 10 and the probability associated with the mode is 0.2822.

c. The probability of eight or more of the sampled vehicles using E-ZPass can be found using the binomial distribution:

P(X >= 8) = 1 - P(X < 8) = 1 - P(X <= 7)

Using a binomial calculator or a cumulative binomial table, we can find:

P(X <= 7) = 0.0025

Therefore:

P(X >= 8) = 1 - 0.0025 = 0.9975

Rounding to 4 decimal places, the probability of eight or more of the sampled vehicles using E-ZPass is 0.9975.

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Answer: 30%

Step-by-step explanation:

The number of periods over which interest is calculated on the loan.

We have to determine

The following formula is used to calculate the monthly payment on a personal loan.

The formula used to calculate monthly payments are as follows;

\(\rm P = PV \times \dfrac{i}{1-(i+1)^{-n}}\)

Where,

1. PV is the present value or the amount of the loan.

2. i is the interest rate per period and is calculated by dividing the yearly percent rate by 100 and by the number of periods in a year.

3. n is the total number of periods and is calculated as the product of the number of periods in a year times the number of years.

Hence, the number of periods over which interest is calculated on the loan.

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Answer: B.

Step-by-step explanation:

edge 2023

Dan could be charged with larceny, which is a felony offense in some states.

Dan could be charged with larceny, which is the taking of another person's property without their permission or consent. In this case, Dan took money from the tip jar without the permission of the ice cream shop or its owners. In some states, this type of larceny is considered grand larceny, which is a felony offense.

Larceny is a crime of intent, meaning that the perpetrator had the intent to deprive the victim of their property permanently. In the case of Dan, he intended to take the money from the tip jar for his own use, not to return it. As such, he could be charged with larceny.

In some states, the punishment for grand larceny is prison time or fines, and the length of the sentence or amount of the fines is determined by the value of the stolen property. In this case, the stolen property was five dollar bills, so the sentence or fine could be quite severe.

It is important to note that in some states, a minor's age may be taken into account when determining the sentence for a crime such as this one. For example, if Dan was a minor, his sentence could be reduced or his charges could be dropped altogether.

In conclusion, Dan could be charged with larceny, which is a felony offense in some states. Depending on the laws of the state, the age of the perpetrator, and the value of the stolen property, Dan could face prison time, fines, or a combination of both.

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Answer:

its 4

Step-by-step explanation:

Answer:

its easy!

Step-by-step explanation:

Answer:Quadrilateral ABCD is transformed to create A′B′C′D′. Match the coordinates of A′ with the transformations that create it. (2, 4) (2, 1) (6, 12) (4, -5) (-2, 4) (2, -4) (6, -12) (-4, 5) Quadrilateral ABCD is reflected over the x-axis. arrowRight Quadrilateral ABCD is translated 2 units right and 1 unit down. arrowRight Quadrilateral ABCD is dilated by a scale factor of 3. arrowRight Quadrilateral ABCD is rotated 180° clockwise about the origin.

the first-order partial derivative of w with respect to x is:

dw/dx = [13 * (x^2 + y^2 + z^2)^(3/2) - 39x^2] / (x^2 + y^2 + z^2)^3

To compute the partial derivative dw/dx, we differentiate the function with respect to x while treating y and z as constants.

To compute the first-order partial derivative of the function w = 13x / (x^2 + y^2 + z^2)^(3/2) with respect to x, we differentiate the function with respect to x while treating y and z as constants.

Using the quotient rule and the chain rule, the derivative is calculated as follows:

dw/dx = [13 * (x^2 + y^2 + z^2)^(3/2) - 13x * (3/2) * (2x)] / (x^2 + y^2 + z^2)^3

Simplifying the derivative:

dw/dx = [13 * (x^2 + y^2 + z^2)^(3/2) - 39x^2] / (x^2 + y^2 + z^2)^3

Therefore, the first-order partial derivative of w with respect to x is:

dw/dx = [13 * (x^2 + y^2 + z^2)^(3/2) - 39x^2] / (x^2 + y^2 + z^2)^3

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The general solution is given by: y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

The most general solution to the original nonhomogeneous differential equation can be found by adding the homogeneous solution and the particular solution together. That is,

y = y_h + y_p

= c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the most general solution to the original nonhomogeneous differential equation. We can use the arbitrary constants c1 and c2 to find specific solutions for different initial conditions. The general solution is given by:

y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the final answer. Note that we have used the terms "general solution" and "arbitrary constants" in our answer, as instructed.

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The limit does exist for lim x→49 (x^2 - 7x - 49) and it approaches value of 2009.

The limit can be found using algebraic manipulation. First we will try plug in the value and see if we can determine the limit. We have:

lim x→49 (x^2 - 7x - 49) = 49^2 - 7×49 - 49 = 2009

So limit exist at x^2 - 7x - 49 and it can be found out by simple substitution.

So, as x approaches 49, the expression x^2 - 7x - 49 approaches 2009.

Therefore, lim x→49 x^2 - 7x - 49 = 343.

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Answer:

Step-by-step explanation:

m3/9=3

We move all terms to the left:

m3/9-(3)=0

We multiply all the terms by the denominator

m3-3*9=0

We add all the numbers together, and all the variables

m^3-27=0

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Answer:

n

Step-by-step explanation:

Answer:

x = 6

y = -1

Step-by-step explanation:

We have to use substitution for the system of equations.

x = -6y

4x + 10y = 14

Because we know that [x = -6y], we can get rid of the x value by substituting y into the equation, [4x + 10y = 14].

4 x -6y + 10y = 14

Simplify.

-24y + 10y = 14

-14y = 14

Divide both sides by -14.

-14y = 14

÷-14   ÷-14

y = -1

From y, we can also find out the x value, as [x = -6y].

We now know that y = -1.

Therefore, we have to substitute again.

x = -6y

y = -1

x = -6 x -1

x = 6

Hence, x = 6 and y = -1.

Sorry it took so long to answer.

Answer: The answer is B) y < 0

Answer: B

Step-by-step explanation:

Since the polynomial given has both positive and negative terms, the shaded region representing the area of the polynomial should have both positive and negative areas.

This means that the area under the curve should cross the x-axis at least once. Looking at the options, only option C has a shaded region that crosses the x-axis, which means that the area represented by the shaded region includes both positive and negative areas. Therefore, option C is the correct figure with a shaded region that has an area equal to the given polynomial.

The shaded region in the graph represents the area between the curve of the function and the x-axis, and the height of the shaded region is given by the value of the function at each point along the x-axis. When the function has both positive and negative values, it means that the area above the x-axis cancels out some of the area below the x-axis, resulting in a net area that may be positive, negative, or zero.

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Answer:

I believe it is 2

The answer is 20 - 3x.                                   

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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The Distance from point A to point B is: 3.4 ft when θ = 28° and The value of θ is: 54.8°

According to the question,

A spring is attached at one end to support B and at the other end to collar A.

Part A: Given that : Reference angle (θ) = 28°

We have to find out the distance of point A to point B.

Adjacent = 3 ft (given)

To find AB, apply the trigonometry function which is:

cos θ = adj / hypotenuse

Substituting all the values ,

=> cos 28°= 3/AB

=> AB = 3/cos 28°

=>  AB = 3.4 ft (nearest tenth of a foot)

Part B:

It is given that Distance  from point A to point B is 5.2 feet

We have to calculate the Value of θ

adj = 3 ft

hypotenuse = AB = 5.2 ft

To find θ , We will again apply the trigonometry function

cos θ = adj/hypotenuse

Substituting all the given values

=> cos θ = 3/5.2

=> θ = cos⁻¹ ( 3 / 5.2)

=> θ = 54.8°

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If the total degrees of freedom (dftotal) in an analysis of variance comparing three treatment conditions is 32, the group size for each condition needs to be determined.



To determine the number of individuals in each group, we need to divide the total number of individuals (dftotal) by the number of treatment conditions (groups).

Given that dftotal = 32 and there are three treatment conditions (groups), we can divide dftotal by the number of treatment conditions to find the number of individuals in each group.

Number of individuals in each group = dftotal / number of treatment conditions

Number of individuals in each group = 32 / 3

Number of individuals in each group ≈ 10.67

Since the groups must have the same size, we need to round the result to the nearest whole number. Therefore, there are approximately 11 individuals in each group.

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Answer:

31.5576

Step-by-step explanation:

The data set of the sample is

62 82 79 76 73 70 67 64 61 66 66 66 63 63 63 60 60 71 71

we have that

(84.5-59.5)/5=5

therefore

The classes are equal to

N 1) 59.5-64.5 ------> midpoint 62

N2) 64.5-69.5 -----> midpoint 67

N3) 69.5-74.5 -----> midpoint 72

N4) 74.5-79.5 -----> midpoint 77

N5) 79.5-84.5 -----> midpoint 82

Find out the frequency for each class

N 1) 59.5-64.5 ------> 8

N2) 64.5-69.5 ----->4

N3) 69.5-74.5 ----> 4

N4) 74.5-79.5 ------> 2

N5) 79.5-84.5 ----> 1

see the figure below to better understand the problem

Answer: B

Step-by-step explanation:

Points from the graph

Points from f(x)                         points from g(x)

(1,2)                                                (1, 1/2)

(4, 16)                                             (4, 4)

f(x) was multiplied by 1/4 to get to g(x)

Answer:

3.8

Step-by-step explanation:

1. Use sine rule

d/sin(D) = f/sin(F) (d=EF, f=DE=3)

2. cross multiply

d=f(sin(D)/sin(F)) = 3(sin(75)/sin(50))=3.783

Answer:

  (b)  3.8

Step-by-step explanation:

Often, simple relations will help you solve geometry problems. Here, you only need to know that larger angles are opposite longer sides.

__

The angle opposite side EF is angle D, which is 75°. That angle is larger than angle F, which is opposite the side marked as having length 3.

This means EF > 3.

There is only one answer choice greater than 3. Choice B is 3.8.

  EF ≈ 3.8

______

The only "work" is remembering that larger angles are opposite longer sides.

The statement A line of symmetry divides a figure into two equal halves in all aspects is true.

A line of symmetry does indeed divide a figure into two equal halves in all aspects. When a figure has a line of symmetry, it means that if you were to fold the figure along that line, both halves would match exactly. This implies that the two halves of the figure are mirror images of each other, and they are congruent in terms of shape, size, and all other aspects.

The concept of symmetry is widely used in various fields, including mathematics, art, and design. Figures that possess symmetry often have an aesthetically pleasing and harmonious appearance.

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The first five terms of the sequence will be 3, 6, 11, 18, 27. Then the correct option is C.

A sequence is a list of elements that have been ordered sequentially, such that members come either before or after.

The equation will be given below.

\(\rm a_n = n^2+2\)

Then the first five terms of the sequence will be

For n = 1, we have

a₁ = 1² + 2

a₁ = 3

For n = 2, we have

a₂ = 2² + 2

a₂ = 6

For n =3, we have

a₃ = 3² + 2

a₃ = 11

For n = 4, we have

a₄ = 4² + 2

a₄ = 18

For n = 5, we have

a₅ = 5² + 2

a₅ = 27

Then the sequence will be 3, 6, 11, 18, 27.

Then the correct option is C.

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