given a normal random variable x with mean 36 and variance 16, and a random sample of size n taken from the distribution, what sample size n is necessary in order that p(35.9≤x≤36.1)=0.95?

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Angle bisector

An angle bisector is a line segment, ray, or line that divides an angle into two congruent adjacent angles.

Line segment OC bisects angle AOB above. So, ∠AOC = ∠BOC which means ∠AOC and ∠BOC are congruent angles.

Bisecting an angle with compass and ruler

In geometry, it is possible to bisect an angle using only a compass and ruler. To do so, use the following steps:

Things to know about an angle bisector

If a point lies anywhere on an angle bisector, it is equidistant from the 2 sides of the bisected angle; this will be referred to as the equidistance theorem of angle bisectors, or equidistance theorem, for short.

In the figure above, point D lies on bisector BD of angle ABC. The distance from point D to the 2 sides forming angle ABC are equal. So, DC and DA have equal measures.

Conversely, if a point on a line or ray that divides an angle is equidistant from the sides of the angle, the line or ray must be an angle bisector for the angle.

Based on the equidistance theorem, it can be seen that when the two sides that make up an angle are tangent to a circle, the line segment or ray formed by the angle's vertex and the circle's center is the angle's bisector.

In the diagram above, the two sides of the angle are tangent to the circle and, DC and DA are the distances from the center of the circle to the sides. DC and DA are also the radii of the circle. Since all radii of a circle have equal measure, line BD bisects the angle.

Angle bisector theorem

For a triangle, like the one in the diagram below, if the bisector of angle A intersects side BC at point D, the ratio of the lengths of AB to AC equals the ratio of the length BD to DC. This can be written as: [tex]\frac{AB}{AC}=\frac{BD}{DC}[/tex]

The point at which the three interior angle bisectors intersect is known as the incenter of the triangle. Referencing the diagram below, the three bisecting rays intersect at point D. Point D is the incenter of the triangle and is a point that is equidistant from the three sides of the triangle.

Extra:

I hope this helped at all.

Answer:-3x-1

Step-by-step explanation:

First we remove the parentheses and we will get 6x+2-9x-3

second, we combined like term 6x and -9x can combine and 2 and -3 can combine we will get 6x-9x and -1

third, we mix it together and can get -3x-1

The area of the circle, considering it's diameter of 5.35, is given as follows:

22.48 units squared.

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr²

The diameter for the circle in this problem is given as follows:

5.35.

The radius is half the diameter, hence it's length is given as follows:

r = 0.5 x 5.35

r = 2.675.

Hence the area of the circle is given as follows:

A = π x (2.675)²

A = 22.48 units squared.

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Therefore , the solution of bar graph is estimated number of the pizza sold on 30 days = 1200

A bar graph is a graphical depiction of information, amounts, or numbers using bars or strips. They are employed to contrast and compare various data types, frequencies, or other measurements of various categories of data.

Here,

Given : The data set from the bar chart is

20, 30, 40, 35, 25

Total number of pizza sold on a day = 20 + 30 + 40 + 35 + 25= 150

Number of pizza of type T3 sold on a day = 40

Estimated number of pizza sales (T3) on 30 days = 40

150×4500= 1200

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The least common denominator of the given rational expressions is 2x^3(x + 4). This is the smallest expression that both denominators can be multiplied by to obtain equivalent fractions with a common denominator.

To find the least common denominator (LCD) of the rational expressions 1/(2x^2 + 8x)and 10/x^2, we need to determine the common factors in the denominators and then multiply them.

The first denominator, 2x^2 + 8x, can be factored as 2x(x + 4), where x + 4 is a linear factor.

The second denominator,[tex]x^2[/tex], is already in its factored form.

To find the LCD, we need to consider all the factors and their highest powers. In this case, we have:

2x(x + 4) and [tex]x^2[/tex]

Since the highest power of x in 2x(x + 4) is 1 and in [tex]x^2[/tex] is 2, the LCD must include both factors with their highest powers. Therefore, the LCD is:

LCD = 2x(x + 4)(x^2)

Simplifying further, we can write the LCD as:

LCD = 2x^3(x + 4)

So, the least common denominator of the given rational expressions is 2x^3(x + 4). This is the smallest expression that both denominators can be multiplied by to obtain equivalent fractions with a common denominator.

Using the LCD, we can then add or subtract the rational expressions by multiplying each term by the necessary factors to achieve the common denominator.

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Absolute change is the straightforward difference in an indicator's value between two time periods, i.e. Relative change represents absolute change as a percentage of the indicator's value in the earlier period.

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When t = π and t = 3π, the acceleration of a particle moving along the x axis with position function x ( t ) = 4 sin ( (π − t) / 2 ) for 0 ≤ t ≤ 4 π where t is measured in seconds is zero.

An acceleration of 0 means that the velocity of the particle is constant, so the derivative of the velocity function is 0. Therefore, the particle has an acceleration of 0 when the second derivative of the position function is 0.

The position function is

x(t) = 4 sin((π − t) / 2)

so the velocity function is

x'(t) = -2cos((π − t) / 2)

and the acceleration function is

x''(t) = - sin((π − t) / 2).

To find when x''(t) = 0, we set -sin((π − t) / 2) = 0 and solve for t:

- sin((π − t) / 2) = 0

sin((π − t) / 2) = 0

(π − t) / 2 = nπ, where n is an integer

t = π - 2nπ

So the particle has an acceleration of 0 when t = π - 2nπ, where n is an integer.

As t is in the interval 0 ≤ t ≤ 4π, the possible values of t is  π and 3π.

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Answer:

0.00497512437

Step-by-step explanation:

calcuator

Answer: 0.00497512437

Step-by-step explanation:

To divide a decimal number by a whole number, long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend. If it does not divide evenly, add a 0 to the end of the dividend and continue dividing until there is no remainder.

Answer:

Step-by-step explanation:

6.56

It is not possible to construct a triangle whose sides are 5.5 cm 4.5 cm and 10 cm because the sum of two sides are equal to three sides. The equal sides cannot form a triangle.

In the given question, we have to check that it is possible to construct a triangle whose sides are 5.5 cm 4.5 cm and 10 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 5.5 and 10

5.5 + 10 > 4.5

15.5 > 4.5

Now we add 4.5 and 10

4.5 + 10 > 5.5

14.5 > 5.5

Now we add 5.5 and 4.5

5.5 + 4.5 = 10

10 = 10

It is not possible to construct a triangle whose sides are 5.5 cm 4.5 cm and 10 cm because the sum of two sides are equal to three sides. The equal sides cannot form a triangle.

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Answer: 6/7 / 2/9 = 3/1 or 3 ✅

PLEASEEEE GIVE BRANLIEST

Step-by-step explanation:

To divide two fractions, you can invert the second one (the one being divided by) and then multiply the two fractions.

So:

(6/7) / (2/9) = (6/7) * (9/2)

To multiply the fractions, you just multiply the numerators together and multiply the denominators together.

(6/7) * (9/2) = (69)/(72)

= 54/14

So the final answer is 54/14.

You can also simplify the fraction by dividing the numerator and denominator by their greatest common factor.

54/14 = 3/1

So the final answer is 3/1 which is 3.

i and iv are correct  in a 45° - 45° - 90° triangle?|. The legs are congruentII. The length of the hypotenuse is twice the length of the shorter leg.

in 45 -45-90 triangle the legs are both 1 units in length and the hypotenuse is sqrt 2

sqrt2 ^2 = 1^2+1^2

this denotes our measurement is true

if the legs ofa right triangle are a and b and the hytponuse is c then

a²+b²=c²

lets say

a>b

so

longer leg is 4ft longer than shorter

a=4+b

hypotnuse is 8ft longer than shorter

c=8+b

teh equation in terms of b and solve

a²+b²=c²

subsitute

(b+4)²+b²=(b+8)²

b²+8b+16+b²=b²+16b+64

2b²+8b+16=b²+16b+64

minus (b²+16b+64) from both sides

b²-8b-48=0

what 2 numbers multiply to get -48 and add to get -8?

-12 and 4

(b-12)(b+4)=0

set equal to 0

b-12=0

b=12

b+4=0

b=-4

false, can't have negative length

b=12

so

a=4+b

a=4+12

a=16

c=8+b

c=8+12

c=2

shorter leg: 12ft

longer leg: 16ft

hypotonuse: 20ft

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Answer: All Real Numbers Except "-8" (R - {-8})

Step-by-step explanation:

The domain of a function is all possible x values that the function can be defined with.

This means that if a value does not create any indeterminate situation, we can consider this value is in the domain of a function.

For this function, "-8" is not in the domain of the function because the denominator of a rational fraction cannot be zero in any case. This creates an indeterminate situation, therefore we do not consider "-8" in the domain of the function.

But for the other values, there is no problem since the denominator cannot be zero without x = -8.

The solution to the system of equation 4g - 2h = -4  and 17 = h - 5g is g = -5 and h = -8

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Given the equation:

4g - 2h = -4   (1)

Also:

17 = h - 5g

multiplying through by 2:

-10g + 2h = 34   (2)

Solving by elimination method. Add equation 2 and 1:

-6g = 30

g = -5

Put g = -5 in eqn 1:

4(-5) - 2h = -4

-20 - 2h = -4

h = -8

The solution is g = -5 and h = -8

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Therefore , the solution of the given problem of interest comes out to be $90 is the interest earned by next summer.

Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.

Here,

Given :

Principal amount = $1800

and interest = 5%

For 1 year like  next summer

So,

=>  Simple Interest  = P*R*T/100

=>  Simple Interest  = 1800 * 5 * 1/100

=> Simple Interest  = 90

Therefore , the solution of the given problem of interest comes out to be

$90 is the interest earned by next summer.

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D) Moving Expenses is an adjustment allowed by the IRS.

The IRS allows certain deductions or adjustments to income for individuals who meet certain qualifications. Some examples of these deductions or adjustments include medical expenses, certain taxes, and certain work-related expenses.

Moving expenses are also an adjustment allowed by the IRS, if you move due to change in your job or business location, or because you start a new job or business. You can deduct certain expenses of moving to the area where you will be working, such as the cost of getting yourself and your household goods to your new home, and lodging during the move.

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The length of the side of the given square is 12.3 inches approx.

Due to the fact that this particular group of numbers makes up a square, they are known as square numbers (or squared numbers).

Finding the area of a square is easy because they all have equal sides. Just "square" (multiply by itself) one of their sides!

So, we have:

The area of the square is 151 in².

Area formula: s²

Now, calculate the length of the side as follows:

A = s²

151 = s²

s = √151

s = 12.3 approx

Therefore, the length of the side of the given square is 12.3 inches approx.

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Answer:

  10 ft

Step-by-step explanation:

You have a photo of a palm tree in which the tree is 6 inches tall. The scale of the photo is 1.5 in : 2.5 ft, and you want the know the height of the actual tree.

The heights of things in the photo are presumed to be related to their actual height by the given scale factor.

  actual height / photo height = 2.5 ft / (1.5 in)

  actual height / 6 in = (2.5 ft)/(1.5 in)

Multiplying by 6 in gives ...

  actual height = (2.5 ft)(6/1.5) = 10 ft

The actual palm tree is 10 feet tall.

__

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We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, and c are the coefficients. The formula is then updated with these coefficients:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

We observed that many real-world scenarios can be represented by quadratic equations. Let's study about the many ways to solve quadratic equations now that we are familiar with what they are.

Three basic approaches can be used to resolve quadratic equations:

(1) The use of factors

(2) Using the square approach to finish

(3) Formula for a Quadratic Equation

The two approaches mentioned above are ineffective for some equations. Such equations call for a more robust approach. A technique that is applicable to all quadratic equations.

This is the formula for a quadratic equation in general. It is described as follows: The value of x is determined by the following equation if the quadratic equation ax2 + bx + c = 0 is true:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

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Answer:

∠ CEA = 95°

Step-by-step explanation:

the chord- chord angle CEA is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

∠ CEA = [tex]\frac{1}{2}[/tex] (CA + DB) = [tex]\frac{1}{2}[/tex] (148 + 42)° = [tex]\frac{1}{2}[/tex] × 190° = 95°

The zero of the polynomial 3x³ 4x² 7 is -7/3.

In order to find the zeros of a polynomial, one must first factor the equation and then set it equal to zero. The zeros of a polynomial are the values of x that make the equation equal to zero. The zeros of a polynomial can be found by factoring the polynomial and then solving for x, which will produce the x values that make the equation equal to zero.

The zero of the polynomial 3x³ 4x² 7 is -7/3. This can be calculated by setting the polynomial equal to 0 and solving for x.

3x³ 4x² 7 = 0

3x³ 4x² = -7

3x(x² - 4) = -7

x(x² - 4) = -7/3

x² - 4 = -7/3

x² = -7/3 + 4

x² = 1/3

x = ±√(1/3)

x = ±(1/√3)

x = -7/3

Therefore, the zero of the polynomial 3x³ 4x² 7 is -7/3.

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Complete question : What is the value of the zero?

Five fundamental ideas provide the foundation for all basic geometry notions. These are the plane, line, and point.points, lines, ray, collinear, planes, and co-planar.

The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.

The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.

The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.

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Five basic ideas form the basis of all basic geometry concepts. These are points, lines, rays, colinear planes, and co-planars.

The domain of mathematics known as geometry connects the concepts relating to areas, volumes, patterns, angles, and distances. Geometry is a category that encompasses all notions that are aesthetically and spatially connected.

Euclid, the father of geometry, was a brilliant mathematician. Learn about the history of Euclid and some of the mathematical ideas we use today, and see how important they have become. The terms "ge" and "metria", meaning "survey", are of geometric origin. For over 2000 years, the Greek approach to geometry has served as its foundation.

The study of various mathematical or real shapes, figures, and sizes is called geometry. The different angles, transformations, and similarities between shapes in geometry. Points, lines, and planes are the primary building blocks of geometry.

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Interior angles on the same side The same-side interior angles are additional if a transversal connects two parallel lines.

A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.

given

The Isosceles Triangle Theorem's opposite is also accurate.

A triangle's opposite sides are congruent if two of the triangle's angles are.

Each right angle exists when two angles are complementary and congruent. Interior angles on the same side The same-side interior angles are additional if a transversal connects two parallel lines.

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The addition and subtraction of the fractions gives 9/(x+3)²(x-3)²

A fraction can be described as one part of a whole number, element or variable.

In mathematics, there are different types of fractions which includes;

From the information given, we have the fractions;

1/(x -3)² - 2/x² - 9 + 1/(x+3)²

Note that with the knowledge of difference of two squares;

x² - 9 is equivalent to (x+3)(x-3) = (x-3)²

Now, let's take the lowest common multiple

(x+3)² -2(x+3)(x-3) +(x-3)²/ (x+3)²(x-3)²

expand the bracket

x²+3x+3x+9 -2x² -6x +6x +9 + x² -3x -3x - 9/ (x+3)²(x-3)²

Add like terms

9/(x+3)²(x-3)²

Hence, the value is 9/(x+3)²(x-3)²

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The minimum and maximum possible volume for a rectangular right prism are 1221.875 and 1603.125 cubic inches.

In this problem we must determine the minimum possible and maximum possible volumes for a rectangular right prism, whose volume formula including length uncertainties is shown below:

V = (w ± Δw) · (l ± Δl) · (h ± Δh)

Where:

Please notice that minimum possible volume is found when all "±" operators are replaced by "-" operators and that maximum possible volume is found when all "±" are replace by "+" operators. Given that statement does not mention the value of every length uncertainty, we assume that Δw = Δl = Δh = 0.5 in.

If we know that w = 12 in, l = 13 in, h = 9 in and Δw = Δl = Δh = 0.5 in, then the minimum and maximum possible volumes are:

Minimum possible volume

V = (12 in - 0.5 in) · (13 in - 0.5 in) · (9 in - 0.5 in)

V = (11.5 in) · (12.5 in) · (8.5 in)

V = 1221.875 in³

Maximum possible volume

V = (12 in + 0.5 in) · (13 in + 0.5 in) · (9 in + 0.5 in)

V = (12.5 in) · (13.5 in) · (9.5 in)

V = 1603.125 in³

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a) Melissa's monthly payment for the promissory note is $133.10.

b) The total monthly payment amounts to $6,388.80.

c) The total finance charge is $388.80, which is the difference between the total payment and the promissory note amount.

The monthly payment represents the equal periodic payment made to settle the loan and the finance charge.

Using an online finance calculator, we can compute the monthly payment, total payments, and finance charges.

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 3.11%

PV (Present Value) = $6,000

FV (Future Value) = $0

Results:

PMT (Monthly Payment) = $133.10

Sum of all periodic payments (Total Payments) = $6,388.80

Total Interest (Finance Charge) = $388.80

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The angles EBI and BCJ are complementary. Show that the corresponding angles are congruent by transforming angle EB1 to angle BCJ. Orient point C at angle BCJ by 180 degrees. reflecting from line BCJ over angle BC Angle BCJ is translated by the directed line segment from C to B.

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