a private and a public university are located in the same city. for the private university, 1037 alumni were surveyed and 647 said that they attended at least one class reunion. for the public university, 808 out of 1317 sampled alumni claimed they have attended at least one class reunion. is the difference in the sample proportions statistically significant? (use α

Answer:

20

Step-by-step explanation: 20 divided by 3 is 6, so if you divided that 120 by 6 you get 20.

Answer:

Range: y ≥ -1

Step-by-step explanation:

The are no limits on the domain because x can be any value

( x-3) ^2 must be greater than or equal to zero since it is squared

0 -1 = -1

The smallest value the range can be is -1

y ≥ -1

Answer:

you might’ve already answered this but it’s 65

Step-by-step explanation:

the two sides in a triangle have to be congruent so if one angle is 65, the other has to be 65 too :)

Answer:

65

Step-by-step explanation:

the given triangle is an isoceles triangle and opposite angles of opposite equal sides of isosceles triangle are equal

Answer:

-5,-4,-3,-2,1,0,1,2

Step-by-step explanation:

Domain are all the x values. I believe this is the answer, however the open bracket o is bit confusing, if this it not correct(still should be)try -5,and forever going. But yeah im like 99% sure im right

The divisors of 60 are the numbers that evenly divide 60 without leaving a remainder. In other words, if we divide 60 by one of its divisors, the result will be a whole number.

For example, if we divide 60 by 2, we get 30. If we divide 60 by 3, we get 20. And so on.

When the teacher wants to form equal groups of students, she needs to ensure that the number of students in each group is one of the divisors of 60. This way, she can divide the class into groups with an equal number of students in each group.

So, in this case, the different groups the teacher can make are:

1 group of 60 students

2 groups of 30 students each

3 groups of 20 students each

4 groups of 15 students each

5 groups of 12 students each

6 groups of 10 students each

10 groups of 6 students each

12 groups of 5 students each

15 groups of 4 students each

20 groups of 3 students each

30 groups of 2 students each

60 groups of 1 student each

These are the 12 different options for forming equal groups of students.

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Answer:

intersection of the lines drawn to bisect each vertex of the triangle

Step-by-step explanation:

trust

Dividing the circumference of a pumpkin by its diameter gives a value approximately equal to pi (π)

When you divide the circumference of a pumpkin by its diameter, you get a value that is approximately equal to the mathematical constant pi (π), which is approximately 3.14159.

This is because pi represents the ratio of the circumference of a circle to its diameter, and a pumpkin is roughly spherical in shape. So, no matter how big or small the pumpkin is, if you measure its circumference and diameter and divide them, the result will be very close to pi.

Mathematically, this can be represented by the formula

pi ≈ circumference / diameter

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V' makes an angle of -/2 (or -90 degrees) with the positive x-axis. Let's divide this problem into two components: the size of the vector difference and the angle formed by V' with the positive x-axis.

(a) Graphical Solution:

To determine the magnitude of the vector difference V - V₂ - V₁ graphically, we can use vector addition and subtraction.

Draw vector V₁ with a magnitude of 12 units starting from the origin.

Draw vector V₂ with a magnitude of 15 units starting from the end point of V₁.

Draw vector V starting from the origin and ending at the end point of V₂.

Draw the negative vector V' (opposite direction to V) starting from the end point of V₂.

Draw the negative vector V₁ (opposite direction to V₁) starting from the end point of V'.

Draw the vector difference V - V₂ - V₁, which is the vector from the origin to the end point of V₁.

Measure the magnitude of the vector difference V - V₂ - V₁ using a ruler or measuring tool on the graph. The measured magnitude will give us the graphical solution for the magnitude of the vector difference.

(b) Algebraic Solution:

To determine the magnitude of the vector difference V - V₂ - V₁ algebraically, we can subtract the vectors component-wise and then calculate the magnitude.

V = (a, b) = (0, -18.69)

V₁ = (12, 0)

V₂ = (-15, 0)

V - V₂ - V₁ = (0, -18.69) - (-15, 0) - (12, 0)

= (0 - (-15) - 12, -18.69 - 0 - 0)

= (15 - 12, -18.69)

= (3, -18.69)

To find the magnitude of the vector (3, -18.69), we can use the magnitude formula:

|V - V₂ - V₁| = √(3^2 + (-18.69)^2)

= √(9 + 349.4761)

= √358.4761

≈ 18.944

Therefore, the algebraic solution for the magnitude of the vector difference V - V₂ - V₁ is approximately 18.944 units.

Now let's determine the angle that V' makes with the positive x-axis.

The angle θ can be calculated using the inverse tangent (arctan) function:

θ = arctan(b/a)

= arctan(-18.69/0)

= arctan(-∞)

= -π/2 (or -90 degrees)

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The angular area of the HST's field of view is 25 square degrees.

The field of view is the extent of the sky that the Hubble Space Telescope (HST) can observe at a given time. It is usually measured in degrees.

To calculate the angular area, we can use the formula for the area of a circle:

Area = π * (angular size/2)^2

Where π is a mathematical constant approximately equal to 3.14, and the angular size is in degrees.

Let's say the angular size of the HST's field of view is 10 degrees.

First, we divide the angular size by 2:

10 degrees / 2 = 5 degrees

Next, we square the result:

5 degrees * 5 degrees = 25 square degrees

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Answer:

21x2(x-3)

Step-by-step explanation:

Answer: Its C- 3(7x^2+5)(x-3)

Step-by-step explanation:

took it on edge2022

The required order will be;

⇒ -2 1/4, -11/4, 3/4, |1 1/4|, |-1 3/4|, |-2 1/4|

The numbers arrange in order to least to greatest number is called Ascending order.

Given that;

The given order is:

⇒ -2 1/4, |-1 3/4|, -11/4 , 3/4, |-2 1/4|, |1 1/4|

Now,

We know that, modulus make every number positive.

We converting mixed fraction into simple fraction as;

⇒ -9/4, 7/4, -5/4 , 3/4, 9/4, 5/4

After arranging it into ascending order, we get;

⇒ -9/4 , - 5/4, 3/4, 5/4, 7/4, 9/4

Therefore, The ascending order is,

⇒ -2 1/4, -11/4, 3/4, |1 1/4|, |-1 3/4|, |-2 1/4|

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A graph of the given quadratic equation is shown below.

The axis of symmetry is equal to 3.

The vertex is equal to (3, -1).

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).

Since the leading coefficient (value of a) in the given quadratic function y = x² - 6x + 8 is positive 1, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -1.

In conclusion, the axis of symmetry is 3 while the vertex is given by the ordered pair (3, -1).

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Answer:

85.006

hope this helps

have a good day :)

Step-by-step explanation:

When a point on a triangle is dilated, the coordinate of the vertex changes

The coordinate of the vertex after the dilation is (-1.5,4)

The given parameters are:

(x,y) = (-3,8)

k = 0.5

To calculate the coordinate of the vertex after the dilation, we make use of:

(x,y)' = k * (x,y)

So, we have:

(x,y)' = 0.5 * (-3,8)

Evaluate the product

(x,y)' = (-1.5,4)

Hence, the coordinate of the vertex after the dilation is (-1.5,4)

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The inequalities that must be true if m is greater-than-or-equal-to n are given as:

Only those operations are allowed which are sure to not modify the inequality between the expressions in the statement.

Some operations that are sure not to modify the inequalities are:

Addition, Subtraction, multiplication by positive real numbers, division by positive real numbers etc.

Example, if 5 > 2, then you can do whatever which keeps the term on the side of 5 bigger than the terms formed on side of 2.

Thus, 5 + 1  > 2 + 1 is correct, (it was addition of 1, a real number).

For the considered case, we're given that:

\(m \geq n\)

Checking all the options sequentially, we get:

It must be true, since the multiplication is done by 2.1, which is > 0

It must be true since -4 is a real number, and addition or subtraction of any real number (if done on all the sides of the statement) doesn't change the inequality

From \(m \geq n\), addition or subtraction is guaranteed to not change the inequality only if they are of same quantity on all the sides of the inequality. Thus, this inequality is not necessary to be true.
Example, if we take m = 5, n =3, then,

\(5 \geq 3\) but \(5 - 3=0 \: \rm and \: 3 + 3= 6 \implies 5-3 < 3 + 3\)

It must be true if given that \(m \geq n\) since multiplication of equal positive real number on both the sides of  \(m \geq n\) was done.

one-half of 6 = 3, thus, this inequality means \(3m \geq 9m\)

Dividing both the sides by 3, we get:

\(m \geq 3n\)

It is not  necessary to be true if  \(m \geq n\). Example

\(3 \geq 2\\but\\ 3 < 3 \times 2 = 6\)

Thus, the inequalities that must be true if m is greater-than-or-equal-to n are given as:

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The probability of a bulb lasting for at most 556 hours is 0.9693 or 96.93%

To find the probability of a bulb lasting for at most 556 hours, we need to determine the area under the normal curve to the left of 556 hours. We can achieve this by using the standard normal distribution table or by calculating the z-score and using the formula for the standard normal distribution.

The z-score is a measure of how many standard deviations an observation is away from the mean. We can calculate the z-score for 556 hours as follows:

z = (556 - 500) / 30 = 1.87

Using the standard normal distribution table, we can find that the area to the left of 1.87 is 0.9693 or 96.93%.

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A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

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Answer: 1357784

Step-by-step explanation:

Square of 660 = 435600

Multiplied by pie = 1357784

As formula of area of circle= pie r square.

The 95% confidence interval for the average GPA of all UCF students, estimated by the educational researcher, is (2.62, 3.04). This interval provides us with information about the range within which the true population mean GPA is likely to fall.

The interpretation of the interval is as follows:

1. The interval (2.62, 3.04) represents a range of possible values for the true average GPA of all UCF students.
2. We can be 95% confident that the true population mean GPA falls within this range.
3. The lower bound of the interval, 2.62, represents the lowest estimated GPA value.
4. The upper bound of the interval, 3.04, represents the highest estimated GPA value.
5. This confidence interval was created based on data collected from a random sample of 150 UCF students.
6. The educational researcher used this sample to estimate the average GPA of all UCF students, with a 95% level of confidence.

In simpler terms, the educational researcher estimated that the average GPA of all UCF students is likely to be between 2.62 and 3.04, with a 95% confidence. This means that if we were to take many samples of 150 students from the UCF population, 95% of the resulting confidence intervals would contain the true average GPA of all UCF students.

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Answer:

The best way to decompose the composite figure to determine its area is as a semicircle, a trapezoid, and two rectangles. This way, we can use the following formulas to find the area of each part:

Area of a semicircle = 21​πr2, where r is the radius of the circle.

Area of a trapezoid = 21​(b1​+b2​)h, where b1​ and b2​ are the bases and h is the height of the trapezoid.

Area of a rectangle = l×w, where l is the length and w is the width of the rectangle.

Then, we can add up the areas of each part to find the total area of the composite figure. The other options are not as convenient because they either involve more parts or more complicated shapes. For example, option A would require finding the area of a triangle, which involves using trigonometry or the Pythagorean theorem. Option B would require finding the area of four triangles, which is more tedious than finding the area of two rectangles. Option C would require finding the area of a square, which is redundant because a square is a special case of a rectangle.

Step-by-step explanation:

The composite figure can be decomposed into a semicircle, a trapezoid, and two rectangles.

Option D is the correct answer.

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as: 1/2 x sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The given figure can be decomposed into the following figure.

- Semicircle

- Trapezoid

- Two rectangles

Thus,

A semicircle, a trapezoid, and two rectangles.

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The measure of center that is the sum of a data set divided by the number of values it contains is called sample mean.

Sample mean is calculated by adding up all the values in the sample and then dividing the sum by the number of values in the sample. It is a measure of central tendency, which describes a typical value of the dataset. It is also known as the arithmetic mean or simply the mean.

The mean can be used to summarize data sets for comparison. It is useful in inferential statistics to estimate the population mean from the sample data. It is an important measure that is frequently used in many areas such as research, business, and finance.

In summary, the measure of center that is the sum of a data set divided by the number of values it contains is sample mean, and it is calculated by adding up all the values in the sample and then dividing the sum by the number of values in the sample.

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Answer:

t/7

Step-by-step explanation:

Since the ratio between the amount of water and the time should be the same, 84/12 = 7.

Hence, the ratio is t/7.

Hope this helped!

The parametric equations for the tangent line at t=2 are:
x(t) = 1 + 2t
y(t) = 3
z(t) = 16 + 12t

To find the parametric equations for the tangent line at t=2, we first need to find the derivative of each coordinate function with respect to t, and then evaluate them at t=2.

1. Differentiate x(t) = (t-1)^2 with respect to t:
dx/dt = 2(t-1)

2. Differentiate y(t) = 3 with respect to t:
dy/dt = 0 (constant function)

3. Differentiate z(t) = 2t^3 - 3t^2 with respect to t:
dz/dt = 6t^2 - 6t

Now, evaluate the derivatives at t=2:

dx/dt(2) = 2(2-1) = 2
dy/dt(2) = 0
dz/dt(2) = 6(2^2) - 6(2) = 12

Next, find the point (x, y, z) at t=2:
x(2) = (2-1)^2 = 1
y(2) = 3
z(2) = 2(2)^3 - 3(2)^2 = 16

The parametric equations for the tangent line at t=2 are:
x(t) = 1 + 2t
y(t) = 3
z(t) = 16 + 12t

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The number of different designs possible using combination is 70.

The formula to calculate combinations is given by:

where n is the total number of items, and k is the number of items to be chosen.

In this scenario, we have:

Plugging these values into the formula, we get:

C(8, 4) = 8! / (4! * (8 - 4)!)

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320

4! = 4 * 3 * 2 * 1 = 24

Substituting the values:

C(8, 4) = 40,320 / (24 * 24) = 70

Therefore, there are 70 different designs possible.

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Answer:

8

Step-by-step explanation:

Market classes and grades are used to describe the quality and characteristics of agricultural products, including meat, poultry, fruits, and vegetables.  True

They provide a common language for buyers and sellers to communicate about the characteristics, such as the age, sex, fat content, and muscling, of the product. Market classes and grades help ensure that buyers receive products that meet their quality standards and help sellers receive a fair price for their products. For example, beef is graded based on marbling, maturity, and lean color, with the highest grade being USDA Prime, followed by USDA Choice and USDA Select.

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Full Question: market classes and grades encompass descriptive terminology of carcasses and products for the understanding of different groups or buyers. T/F

This standardized system of classification allows for easier communication and understanding between buyers and sellers, and ensures consistency and fairness in the marketplace.

Market classes and grades refer to the categorization and labeling of carcasses and products based on their quality and characteristics. These classifications use descriptive terminology that is understood by different groups of buyers, such as meat packers, wholesalers, retailers, and consumers. Market classes typically group animals based on their intended use, such as beef cattle for slaughter, while grades are assigned based on factors such as maturity, marbling, and fat content. This standardized system of classification allows for easier communication and understanding between buyers and sellers, and ensures consistency and fairness in the marketplace.

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Answer:

It's d or the 4th graph

Step-by-step explanation:

A graph which represents the overall equation (inequality) represented by this scenario.

A graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).

Let the variable x represent the total number of guests.

Let the variable y represent the amount of meat

Next, we would write an inequality that represents an amount of meat that must be 2 pounds fewer than one-third (1/3) the total number of guests. Since the customer decides they want at least that amount of meat, the inequality symbol that must be used is greater than (>).

y > 1/3(x) + 2

y > x/3 + 2

In conclusion, the y-value for this inequality graph (see attachment) intersects the x-axis at 0 and 6 with the boundary line shaded upward and dashed to indicate that it is not part of the solution, which must be represented with a greater than (>) inequality symbol.

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Answer:

A rational number is any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero.

Step-by-step explanation:

In other words, a rational number can be expressed as p/q, where p and q are both integers and q ≠ 0.

An integer is a number that is not a fraction. So basically, a whole number.

Hope this helped!

Any integer that can be expressed in the form p/q, with q≠0, is referred to as a rational number in mathematics.

What are integers?

The Latin word "Integer," which means entire or intact, is where the word "integer" initially appeared. Zero, positive numbers, and negative numbers make up the specific class of numbers known as integers.

Any number that can be expressed as a fraction and has an integer denominator that is not zero and both the numerator and the numerator are integers is considered to be rational.

To put it another way, a rational number can be written as p/q, where p and q are both integers and q≠0.

Hence, rational number is any integer that can be expressed in the form p/q, with q≠0.

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The zero of the function is given as follows:

x = 1.

The function for this problem is defined as follows:

f(x) = [x² - 1]/(x² + 3x + 2)

The zeros are given as follows:

x² - 1 = 0.

x² = 1.

x = -1 or x = 1.

The zeros of the denominator are given as follows:

x² + 3x + 2 = 0.

(x + 2)(x + 1) = 0.

Hence:

The denominator cannot assume a value of zero, hence the zero is given as follows:

x = 1.

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