Determine the t critical value for a two-sided confidence interval in each of the following situations:


a. Confidence level = 95%, df = 10


b. Confidence level = 95%, df = 15


c. Confidence level = 99%, df = 15


d. Confidence level = 99%, n = 5


e. Confidence level =98%, df = 24


f. Confidence level = 99%, n = 38

Answer:

55

Step-by-step explanation:

let 'n' equal the number

(n + 11) / 3 = 22

cross-multiply to get:

n + 11 = 66

n = 55

We Proven that AB is congruent to BC in the given triangle.

Two sets of points are said to be congruent if and only if one set of points can be transformed into the other by an isometry, or a combination of rigid motions like translation, rotation, and reflection.

This indicates either object might be precisely aligned with other object by moving & reflecting it, but not by resizing it. The ability to cut out and then perfectly match up two separate plane figures on a piece of paper indicates that they are congruent. I'm allowed to turn the paper over.

Given that

BD ≅ BE

DE bisects AB

DE bisect BC

If DE bisects AB it means

BD = DA

2BD = 2DA

2BD = AB

BD ≅ AB

Also DE bisect BC meaning

BE = EC

2BE= 2EC

2BE = BC

BE ≅ BC

As it already given that BD ≅ BE, we have,

⇒ AB ≅  BD ≅ BE ≅  BC

⇒ AB ≅ BC

Hence, Proven that AB is congruent to BC in the given triangle.

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The additive inverse of -13 7/8 is +13 7/8.

The additive inverse of a number is the number that, when added to the original, equals zero. The additive inverse of -13 7/8 can be found by turning the sign of the original number into its opposite, which would be +13 7/8. This can be expressed mathematically using the formula a + (-a) = 0, where a is the original number.

When -13 7/8 is added to +13 7/8, the result is 0. This can be seen by calculation: -13 7/8 + 13 7/8 = -13 7/8 + 8/8 + 5/8 = -5/8 + 8/8 = 3/8 + 8/8 = 11/8 + 8/8 = 19/8 + 8/8 = 27/8 + 8/8 = 35/8 + 8/8 = 43/8 + 8/8 = 51/8 + 8/8 = 59/8 + 8/8 = 67/8 + 8/8 = 75/8 + 8/8 = 83/8 + 8/8 = 91/8 + 8/8 = 99/8 + 8/8 = 107/8 = 0.

Therefore, the additive inverse of -13 7/8 is +13 7/8.

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The 3 types straight line are

1. Slope-intercept form: y = mx + b

2. Point-slope form: y - y1 = m(x - x1)

3. Standard form: ax + by = c

1. Slope-intercept form: y = mx + b - This is the most common form of a straight line; it is composed of two parts: m (the slope of the line) and b (the y-intercept). To use this form, you need to know the slope (m) of the line and the y-intercept (b). From this information, you can calculate the equation of the line by substituting the values of m and b into the equation.

2. Point-slope form: y - y1 = m(x - x1) - This form of a straight line requires two points on the line and the slope of the line. To use this form, you need to know the two points on the line (x1, y1) and the slope of the line (m). Then, you can calculate the equation of the line by substituting the values of x1, y1 and m into the equation.

3. Standard form: ax + by = c - This form of a straight line is composed of three parts: a (the coefficient of x), b (the coefficient of y) and c (the constant). To use this form, you need to know the coefficients of x and y and the constant. From this information, you can calculate the equation of the line by substituting the values of a, b and c into the equation.

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Answer

15/28

Step-by-step explanation:

total no. of students in the class = 15+13

=28

no. of boys = 15

p(boy) =15/28

Answer:

219.96

Step-by-step explanation:

Do you mean the product? The term quotient is for division.

Step 3 is unnecessary (the statement is already given, plus you haven't proven the triangle is isosceles anyway).

After, omit step 5 and jump straight to 6.

After this, step 6 is the statement that used to be step 5, which is true by CPCTC.

Then, you can prove the required statement by definition from this.

A system of linear equations in two variables can have a unique solution, infinitely many solutions, or no solution.

There are three types of solutions to a system of linear equations in two variables:

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tan(x) is equivalent to 1/sin2x - cos2x/sin2x.

To determine equivalent 1/sin2x - cos2x/sin2x we use the tan(x) formula.

What is tan(x)?

tan(x) is tangent of x here, tan is trigonometric operator.

Now, evaluate the given equation

= 1/sin2x - cos2x/sin2x

use the formula of 1-cos2x and substitute in the above equation.

= (1-cos2x)/sin2x

we have the formula of sin2x=2sinxcosx and converting 1-cos2x as 2sin²x

Now, substitute in the above equation.

= (2sin²x)/2sinxcosx

By, canceling 2sinx in the numerator and denominator, we get

= sin(x)/cos(x)

= tan(x)

Thus, tan(x) is equivalent to 1/sin2x - cos2x/sin2x.

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Distance is a measure of how far an object has traveled from a starting point. Displacement is the change in position from the starting point.

It is the total distance an object has moved and is the sum of all the displacements an object has made. The formula for calculating distance is distance = speed x time. For example, if a car has traveled at a speed of 50 km/h for 4 hours, then the distance traveled is 200 km (50 km/h x 4 h = 200 km).

Displacement is the change in position from the starting point. It is the shortest distance between the starting point and the final point and does not take into account the direction of motion. The formula for calculating displacement is displacement = final position – initial position. For example, if a car starts at point A and travels to point B, the displacement is the distance between A and B (B – A).

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Answer:

The correct answer is that X < 0.

Step-by-step explanation:

Now that all the important information is covered, let's take a look at the number line.

Please let me know if this helped!!!

In the given set of data, 4/5 is the constant of proportionality in the proportional relationship.

When two or more parameters are either directly or indirectly proportional to one another, the relationship is written as a = kb or a = k/b, where k denotes the direction of the relationship between the two variables. The proportionality constant, k, is defined as follows.

The ratio of two proportional values at a constant value serves as the definition of the proportionality constant. When the product or ratio of two variables yields a constant, the relationship between the two is proportional. By comparing the ratio of the two specified quantities, we can calculate the value of the proportionality constant. A direct variation or an inverse variation of this relationship are both possible.

Given

2 : 5/2

2 = (k)5/2

also

3 : 15/4

3 = (k)15/4

This gives us

k = 2 × 2/5

k = 4/5

k = 3 × 4/15

k = 4/5

Thus, In the given set of data, 4/5 is the constant of proportionality in this proportional relationship.

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The expression (x - 10) + (3x - 6) is equivalent to the expression 4x - 16.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (x - 10) + (3x - 6)

Simplify the expression, then we have

⇒ (x - 10) + (3x - 6)

⇒ x - 10 + 3x - 6

⇒ 4x - 16

The expression (x - 10) + (3x - 6) is equivalent to the expression 4x - 16.

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The value of "x" in the algebraic equation

3(-3x - 8) = 3(-6x + 3) which makes it true is equal to 11/3 and option C is correct.

An algebraic equation is a mathematical statement that contains two equated algebraic expressions.

We shall evaluate for the value of x in the algebraic equation 3(-3x - 8) = 3(-6x + 3) as follows:

-9x - 24 = -18x + 9 {expand the bracket}

18x - 9x = 24 + 9 {collect like terms}

9x = 33

x = 33/9 {divide through by 9}

x = 11/3

Therefore, 11/3 is the value of x in the algebraic equation 3(-3x - 8) = 3(-6x + 3) that makes it true.

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An exponential function is a function in which the variable is in the exponent. The general form of an exponential function is f(x) = ab^x, where a and b are constants.

The variable x is the exponent, meaning that it is raised to a certain power, resulting in the variable being in the exponent. In this function, the value of the function increases or decreases at a rate that is proportionate to the current value of the function.

This type of function is commonly used in modeling growth or decay in various fields such as biology, economics, and physics. The exponential function generates a sequence that is exponential in nature, the rate of change of the function is directly proportional to the value of the function.

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The graph shows the different combinations of loaves of bread and rolls that the baker can sell in order to reach a total revenue of $27.

What is the slope-intercept form?

The slope-intercept form is a way of expressing a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept is the point at which the line crosses the y-axis, meaning the point at which the line intersects the y-axis when x = 0.

The given equation is in the form of y = mx + b where y =27, m = 3 and b = 1, is a linear equation and it can be represented as a straight line in a coordinate plane.

To graph this equation, we can use the following steps:

The graph shows the different combinations of loaves of bread and rolls that the baker can sell in order to reach a total revenue of $27.

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Solving the provided question we can say that the  algebraic equation the value of 'y' is 19.

The difference is that expressions, which are essentially mathematical "phrases," do not contain an equal sign. Equations have an equal sign and demonstrate that two mathematical expressions are equivalent. An algebraic equation is 2x + b = 14, but 2x + b is an algebraic expression. Complete addition and subtraction from left to right after working from left to right to complete multiplication and division.

Expressions, which are essentially mathematical "phrases," are distinguished by the lack of the equal sign. Equations have an equal sign, which indicates that two mathematical expressions are equal.

3x+2y =  -4

15x +42y =  588

32y = 608

y = 608/32

y= 19

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Answer:

triangle angle sum theorem

Answer:

3.2 hours

Step-by-step explanation:

You know that it takes him 1 hour to go 17 kilometers so you can divide 54.4 by 17 to get the hours.

Answer:

---------------------------------------

Let the number of quarters be x, then the number of dimes is x - 10.

We know that quarter is $0.25 and dime is $0.10.

The total amount is $10.90.

Set up equation and solve for x:

Najee has 34 quarters and 34 - 10 = 24 dimes.

The descriptions with the correct rule of transformation are given above.

Rotation 90° counterclockwise

(x, y) → (-x, y)

Reflection over the x-axis

(x, y) → (x, -y)

Translation 2 left and 2 up

(x, y) → (x - 2, y + 2)

Translation 2 right and 2 down

(x, y) → (x + 2, y - 2)

It is the movement of the shape in the left, right, up, and down directions.

The translated shape will have the same shape and shape.

There is a positive value when translated to the right and up.

There is a negative value when translated to the left and down.

We have,

(x, y) is in the first quadrant.

Rotation 90° counterclockwise (x, y) will be in the II quadrant.

So,

(x, y) → (-x, y)

(x, y) is in the first quadrant.

Reflection over the x-axis (x, y) will be in the IV quadrant.

(x, y) → (x, -y)

(x, y) is in the first quadrant.

Translation 2 left and 2 up we get,

(x, y) → (x - 2, y + 2)

(x, y) is in the first quadrant.

Translation 2 right and 2 down we get,

(x, y) → (x + 2, y - 2)

Thus,

The descriptions with the correct rule of transformation are given above.

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Answer:

-4.5

Step-by-step explanation:

3 × 1.5 = 4.5

Negative times positive is negative.

-3 × 1.5 = -4.5

Answer:

2x0

Step-by-step explanation:

2 rounds to 2

and 0.33 rounds to 0

2x0

I understand that the answer is 0.99 which would round to 1.
But if these are the options then 2x0 is your answer.

The sequence of rigid motion to take figure ABC to DEF given below.

Triangle is a geometric figure with three sides and three angles. It is one of the basic safe in geometry. Triangles are either write, acute or obtuse depending on the size of each angle. The sum of the angles in a triangle is 180 degrees. Triangle can be classified into equity real isosceles and triangles depending on the length of the sides.

1. Rotate figure ABC 90 degrees clockwise about the origin (point O).
2. Translate figure ABC 4 units to the right.
3. Rotate figure ABC 180 degrees clockwise about point O.
4. Translate figure ABC 2 units down.
5. Rotate figure ABC 90 degrees counterclockwise about point O.
6. Translate figure ABC 3 units to the left.
7. The figure is now in the position of figure DEF.

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Therefore ,the solution of the given problem of circle comes out to be as a result, the answer to the given circle problem is 6 + π cm

Each spot on a circle's plane is evenly spaced from the core and is a sealed, double object. The development of a ribbon of reflective symmetry is aided by each arc tracing the circle. Each angle also has an axis of symmetry centered on it.

Here,

The central angle of a 9 Pi sq millimeter circle is 60 degrees.

R² = 9 for the area of a circle.

Circumference = 2πR

=> = 6π cm = 2π*3 

(60/360)*6 cm is the length of an arc.

Following are the calculations for arc's perimeter: Radius + Arc Length + Radius = +3 + 3 = 6 + cm

Therefore ,the solution of the given problem of circle comes out to be as a result, the answer to the given circle problem is 6 + π cm

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A function example table is a tool used to organize and present information about a specific function or set of functions.

It typically includes the following columns:

Input: This column lists the inputs or arguments that the function accepts.

Output: This column lists the outputs or return values that the function produces.

Description: This column provides a brief explanation of what the function does and how it works.

Example: This column provides one or more examples of how the function can be used, along with the corresponding inputs and outputs.

Function example tables are a useful tool for documenting and understanding code, as they provide a clear and concise summary of a function's behavior.

They can also be helpful for testing and debugging code, as they can be used to quickly check that a function is behaving as expected.

In conclusion, A function example table can be used to organize and present information about a specific function or set of functions, it typically includes the following columns: Input, Output, Description and Example.

This table is a useful tool for documenting and understanding code, as they provide a clear and concise summary of a function's behavior which can also be helpful for testing and debugging code.

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Therefore , the solution of the given problem of equation comes out to be 12 pennies.

A equation is a method that links two statements and signifies equivalence with the equals sign (=). In algebra, a scientific assertion that confirms the equivalency of two schemas is referred to as an equation. For instance, the answer obd + 6 = 12 has an equal sign between the elements ptdc + 6 and 12, respectively. There is a mathematical formula that describes the relationship between two phrases on either side of a letter. Frequently, the symbol and the single variable are the same. For example, 4x – 4 = 0.

Here,

Solving once per variable is the key to this issue.

Let x equal quarters and y equal dimes.

So, x + y = 20

Now, we'll build an equation using the coin values and total quantity of cash. (Decimals have been omitted for clarity.) 25x + 10y = 320

In terms of y, let's restate the original equation: y = 20 - x

In the second equation, we will now substitute this for y. 25x + 10(20-x) = 320

Calculate the value of x: 25x + 200 – 10x = 320.

15x = 120

8 quads times x

In light of this, y = 20 - 8 = 12 pennies.

Therefore , the solution of the given problem of equation comes out to be 12 pennies.

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The domain of the composite function is the intersection of the domain of f(x) and G(x). D f(x) intersection D g(x) The range of the function is now restricted by the domain of the composite function.

Therefore, the range is found by evaluating the function at the points in the domain of f(x).

You find the domain of the function by finding all numbers that can't go into the equation. Usually all that prevents this is whether or not it contains a fraction with x on the bottom or a x under a square root .

The range is found by finding the vertex and noting that it is the minimum or maximum (depending on direction) of the graph. You can find the vertex by using -b/2a for the x value and then plugging in to get y value.

The given function f(x) = –37 is a horizontal line which goes from negative infinity to positive infinity.

In this case, the domain can be any number since there is no limit on what the x value can be.

So, the domain of the given function f(x) = –37 will be all real numbers.

And, the range will always be y = –37 because no matter what x value will equal, y will always be equal to –37 in the function of f(x) = –37.

So, the range of the given function f(x) = –37 will be y = –37.

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The number 9550000 can be arranged in a total of 8!/(4!4!) = 70 different ways.

Digits are numerals or numbers used for counting, measuring, and representing quantities. They are the building blocks of mathematics, and are used to express amounts, relationships, and orders of magnitude. Digits are also used in computers and other digital devices to store and communicate information.

The 8 digits of 9550000 can be arranged using the formula for permutation: nPr = n!/(n-r)!

In this case, n = 8 and r = 8. So, the number of permutations of the 8 digits of 9550000 will be 8!/(8-8)! = 8!/(0!) = 8! = 40320.

However, we need to account for the fact that there are 4 zeros in the number 9550000. To do this, we need to divide the number of permutations by 4! (factorial of 4) to account for the 4 identical digits.

Therefore, the total number of ways the digits in the number 9550000 can be arranged is 40320/4! = 70.

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