the incomes in a certain larger population of college teachers have a normal distribution with mean of $60,000 and standard deviation of $5,000. four teachers are selected at random from this population to serve on a salary review committee. what is the probability that their average salary exceeds $65,000.

Answer:

25 times larger

Step-by-step explanation:

given a scale factor of 5 from A → B

then the scale factor of the area is 5² = 25

area of B is 25 times larger than the area of A

The median of the distribution 34 22 13 is 22.

To find the median of a set of scores, you first need to arrange the scores in numerical order. The median is the middle score in the set. If there is an odd number of scores, then the median is the middle score. If there is an even number of scores, then the median is the average of the two middle scores.

In this case, the scores are 13, 22, and 34.

After arranging the scores in numerical order, we have 13, 22, and 34.

There are three scores in this set, so the median is the middle score, which is 22.

The median of the set is 22.

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Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.

A linear equation has the following standard form: ax + by + c = 0.

Here, variables x and y and constants a, b, and c are used.

Also, a ≠ 0, and b ≠ 0.

For linear equations, the slope-intercept formula is: y=mx+b

Where m stands for the line's slope and b represents the y-intercept.

The three types of linear equations are point-slope, slope-intercept, and standard form.

When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This is known as linear equations.

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The oldest child is a 11-year-old boy.

Three sisters have were born in 3 consecutive years. The total of their ages is 30.

Sequential numbers are those that follow one another continually, from lowest to biggest.

Here, assume that the youngest sibling is x years old.

Middle sibling's age will be (x+1) years old.

the oldest sibling's age is (x+2) years.

According to the inquiry,

x + (x+1) + (x+2) = 30

3x + 3 = 30

3x = 30-3

3x = 27

x = 27 / 3

x=  9

The oldest child is therefore (x + 2) years old, or 11 years old.

x+2 = 9+2 =11

The oldest child is a 11-year-old boy.

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Answer:

A parallelogram

Step-by-step explanation:

A parallelogram is a shape with four sides and two sets of parallel lines. A common example of a parallelogram is a square.

We can't solve 3x + 1 because eventually reach 1 if you keep performing this operation, regardless of what odd number you started with.

Even numbers are ones that can be divided into two equal parts, but odd numbers cannot be divided into two equal parts. The numbers 3, 5, 7, 9, 11, 13, and 15 are examples of odd numbers. Even numbers include 2, 4, 6, 8, 10, 12, and so on. Odd numbers are those that cannot be evenly divided by two. It cannot be evenly split into two different integers. An odd number will leave a leftover when divided by two. 1, 3, 5, 7, and other odd numbers are instances. The idea of odd numbers is identical to that of even numbers.

Given

Three times, then add one.

Divide the largest power of 2 from the resultant even number to obtain the new odd number T. (x).

Do you eventually reach 1 if you keep performing this operation, regardless of what odd number you started with? This issue has not yet been resolved, to put it simply.

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Angle-Angle-Angle (AAA) does not work because it can produce similar but not congruent triangles.

There are a few conditions for AAA:

"AAA" is when we know all three angles of a triangle, but no sides. AAA triangles are impossible to solve further since there is nothing to show us the size.

If two angles and any side of one triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.

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Answer:

Whole numbers are positive numbers including zero that dont include fractions or intergers

Step-by-step explanation:

examples of this are 73, 68, 27

A function can have an asymptote if it approaches a horizontal or vertical line but never touches it. There are several types of functions that can have asymptotes, including rational functions, exponential functions, and logarithmic functions.

For example, a rational function is a function that can be written in the form of a ratio of two polynomials. These functions can have horizontal asymptotes if the degree of the denominator is greater than the degree of the numerator, and they can have vertical asymptotes if the denominator has a factor that is not present in the numerator.

Exponential functions can have horizontal asymptotes if the base of the exponent is less than 1, and they can have vertical asymptotes if the base of the exponent is greater than 1.

Logarithmic functions can have horizontal asymptotes if the base of the logarithm is less than 1, and they can have vertical asymptotes if the base of the logarithm is greater than 1.

It's also possible for a function to have both horizontal and vertical asymptotes, depending on its form.

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If the exponent's base is less than 1, an exponential function may have a horizontal asymptote; if it is greater, a vertical asymptote may occur.

If the base of the logarithm is less than 1, a logarithmic function may have a horizontal asymptote, and if the base is greater, a vertical asymptote.

Yes, triangle inequality theorem apply to all equilateral triangles.

The triangle inequality theorem explains the relation between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.

So Triangle inequality theorem is not only valid for all equilateral traingles but it is valid for all traingles.

A Triangle is only formed is if follows Triangle inequality theorem so every equilateral triangle needs to follow this theorem.

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Answer:66.67% to the nearest whole number is 67%

Step-by-step explanation:

The total number of acres available are 30

and only 20 acres of land can be farmed

20 acres out of 30 acres is available for farming

20/30 x 100%

To do with the calculator

20 ÷30 x 100=66.67% then add the percent sign

The length of the side of the square is 12 cm.

Given that, a triangle with an area of 59 cm from a certain square, the area of the remaining shape will be 85 cm².

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

We know that, the area of a square is a².

Here, total area = Area of a square + The area of the remaining shape

= 59+85

= 144 cm²

So, a²= 144 cm²

⇒ a =12 cm

Therefore, the length of the side of the square is 12 cm.

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Answer:

1 balloon is = £2 and 1 cake is = £4

Step-by-step explanation:

this is true because 2 balloons = £4

and 3 cakes = £12 so 4 + 12 = 16 and also

4 balloons = £8

and 4 cakes = £16 so 8 + 16 = £24

this is one of the possible answers

Answer:

A cake is £3.50

A Balloon is £2.75

Step-by-step explanation:

Let b be balloons and c be cake

2 balloons and 3 cakes = £16 = 2b + 3c = 16

4 balloons and 4 cakes = £24 = 4b + 4c = 25

First times -2 to the first equation

-4b - 6c = -32

4b + 4c = 25

Now let's find c first by adding the two equations together.

-2c = -7

c = £3.50

Now put 3.50 back in the c

4b + 4(3.50) = 25

4b + 14 = 25

4b = 11

b = £2.75

A system of 3 equations can have 0, 1, 2, or infinitely many solutions.

It is possible for a system of 3 equations to have no solutions if the equations are incompatible, meaning that there is no combination of values for the variables that can satisfy all of the equations simultaneously. It is possible for a system of 3 equations to have exactly one solution if the equations are dependent, meaning that one of the equations can be derived from the other two. It is possible for a system of 3 equations to have exactly two solutions if the equations are independent, meaning that the equations are not related to each other and cannot be derived from each other. Finally, it is possible for a system of 3 equations to have infinitely many solutions if the equations are consistent and the variables are linearly dependent.

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The larger number is 8 and the smaller number is -4.

Let us assume that the larger number is x and the smaller number is y.

Now according to the question:

The sum of two numbers is 4, so

x+y= 4....(1)

A two-variable linear equation has two variables and can be represented as: ax+by=c

Here x and y are the variables, a and b are the respective cofficients of the variables and c is a constant term.

And the larger number is 12 more than three times the smaller number.

So

x=y+12 ...(2)

By equation (1) and (2)

y+12+y=4

2y= 4-12=-8

y = -4

Now put the value of y in equation (2)

x= y+12=-4+12=8

So the larger number is 8 and the smaller number is -4.

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The numeric value of the expression 4000×20÷408-44 is given as follows:

4000×20÷408-44 = 152.08.

The expression for this problem is defined as follows:

4000×20÷408-44

We have a multiplication, a division and a subtraction operation, hence the precedence of the operations is given as follows:

Then the multiplication is given as follows:

4000×20 = 80,000.

The division is given as follows:

80000/408 = 196.08.

Finally, the subtraction is calculated as follows:

196.08 - 44 = 152.08.

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The formula of current I is I=V/R.

In the field of physics, current can be described as the rate that shows the intensity of electrons that are flowing from one place to another.

The current is the measure of the potential difference from which the current moves forward when resistance is also a factor that stops it. Electric current is directly proportional to the potential difference applied and is inversely proportional to the resistance in the object in which the electric current is flowing.

Based on this fact, the formula for current, which is represented by the letter I is   I=V/R, here I is the current, V is the potential difference and R is the resistance.

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Answer:

8/9

Step-by-step explanation:

2/9 divided by 1/4 is 8/9

The numerical value of x and the length of side ST are 2 and 6 respectively.

An equilateral triangle is simply a triangle with all three sides having the same length.

Given that;

First, we determine the value of x.

Since all three sides are equal;

RS = TR

2x + 2 = 5x - 4

Solve for x

5x - 2x = 2 + 4

3x = 6

x = 6/3

x = 2

Now, for side ST.

ST = 3x

Plug in x=2

ST = 3( 2 )

ST = 6

Therefore, the value of x is 2 and side length of ST is 6.

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To find the median of a set of numbers, you first need to put the numbers in order from smallest to largest. Then, if there is an odd number of values, the median is the middle value. If there is an even number of values, the median is the average of the two middle values.

In this case, the set of numbers is already in order: [2, 4, 5, 6, 7, 8, 11]. There are 7 values, so the median is the middle value, which is 6.

So, the median of the set {7, 6, 4, 8, 2, 5, 11} is 6.

the middle number, which is obtained by sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: Because the number 4 is in the middle when the numbers are ordered (1, 4, 7), it is the median of 4, 1, and 7.

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Answer: 3

Step-by-step explanation: The median is three (3) because its the middle number

Answer:

Hey no prob!

We take 3x(2x-7) and we distribute the 3x to both of the terms inside

3x times 2x is 6x^2

and

3x times -7 is -21x

the final answer would be C

6x^2-21x

Answer:

[tex] \sf \: c) \: 6 {x}^{2} - 21x[/tex]

Step-by-step explanation:

Given expression,

→ 3x(2x - 7)

Simplifying the expression,

→ 3x(2x - 7)

→ 3x(2x) + 3x(-7)

→ (3 × 2)x² + (3 × -7)x

→ (6)x² + (-21)x

→ 6x² - 21x

Hence, option (c) is correct.

The pair of equations y=0 and y=−5 has no solution.

Since the provided variable y might take on a variety of values, the pair of equations y=0 and y=5 cannot have a solution.

A two-variable linear equation is one with the formula ax+by+c, where a, b, and c are all real numbers and a, b is not equal to zero. In a set of two linear equations in two variables, we deal with two such equations.Such equations have a point on their representational line as the solution. A two-sided statement with the same sign on both sides is called an equation.

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The values of p and q are 11 and 3 respectively.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers. Simply said, the mean is the average of the values in the given collection. It indicates that values in a certain data collection are distributed equally.

Given that,

∑f = 40

=> 26+p+q = 40

=>p+q=40-26

=> p+q = 14 .......................(i)

∵ x bar = ∑xf/∑f

=>14.7 = 408+9p+27p / 40 (since, x bar = 14.7)

=>588 = 408+9p+27p

=>588 - 408= 9(p+3p)

=>180= 9(p+3p)

=>p+3q=20......................(ii)

Solving equations (i) and (ii)

=>p+3q -(p+q)=20-14

=>p+3q-p-q=6

=>2q=6

=>q=3

Substituting this value in equation (ii)

∴p+3=14 => p = 11

Hence, the values of p and q are 11 and 3 respectively.

(Refer to the image attached for the missing data)

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The percentage of all patients who took the test and had a false positive result will be 35%. Then the correct option is D.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

Lyme illness is a disease brought about by microscopic organisms. A test for Lyme infection might be impacted by different prescriptions and ailments. The testing results are summed up in the table.

                                      Tested positive      Tested negative     Row Totals

Has Lyme disease                  53%                         17%                     70%

Doesnt have Lyme disease    12%                         18%                     30%

Column Totals                         65%                        35%                    100%

The level of all patients who stepped through the examination and had a misleading positive outcome will be 35%. Then, at that point, the right choice is D.

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The graph of the equation will be a parabola that opens upwards, starting at the y-axis and increasing in value as x increases. The vertex of the parabola will be the lowest point on the graph, and the parabola will be symmetrical about the line of symmetry.

When the degree of an equation is even and the leading coefficient is positive, the graph of the equation will be a parabola. This parabola will open upwards, meaning that it will start at the y-axis and increase in value as x increases. The vertex of the parabola will be the lowest point on the graph, and this vertex will always be located to the right of the y-axis. Additionally, the parabola will be symmetrical about the line of symmetry, which is the vertical line that passes through the vertex. To further illustrate, consider the equation y = 4x^2 + 5x + 1. In this equation, the degree is even (2) and the leading coefficient is positive (4). Therefore, the graph of this equation will be a parabola that opens upwards and has its vertex to the right of the y-axis. Additionally, the parabola will be symmetrical about the line of symmetry, which is the vertical line that passes through the vertex. The vertex of the parabola will have coordinates (2.5, -2.625), and the parabola will increase in value as x increases from this point.

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The circumference of the circle is C = 144.44 yd .

From the given figure :

we observe that the radius r = 23 yd

we know that ,

What is circumference of circle ?

Circumference is the distance around the perimeter of a circle. It is calculated by multiplying the distance across the center .

A circle's perimeter is known as its circumference.

Formula :

C = 2πr

= 2 * 3.14 * 23

= 46 * 3.14

= 46 * 314 / 100

= 14444 / 100

= 144.44 yd

Hence the circumference of the circle is 144.44 yd .

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Full question :

is in the image uploaded

Consider the behavior of the function when x approaches the value of the vertical asymptote from the left and from the right in order to locate the vertical asymptotes of a function using limits. Consider the behavior of the function when x grows very big in order to determine the horizontal asymptotes of a function using limits (in either the positive or negative direction).Similary, To find the horizontal asymptotes of a function using limits, consider the behavior of the function as x becomes very large (in either the positive or negative direction). If the y-values of the function approach a fixed value as x becomes very large, then that value is the horizontal asymptote of the function.

An asymtote is a line being approached by a curve but never touching the curve at any finite distance.It is a line that the graph approaches as either x or y in positive or negative infinity.

A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.

Consider the behavior of the function when x approaches the value of the vertical asymptote from the left and from the right in order to identify the vertical asymptotes of a function using limits. The vertical asymptote is at that value of x if the function approaches positive infinity as x approaches the asymptote from the left and negative infinity as x approaches the asymptote from the right. Consider the function f(x) = 1/x as an illustration. We may take into account how the function behaves as x approaches 0 from the left and from the right in order to determine the vertical asymptotes of this function using limits.The y-values of the function become closer to negative infinity as x moves toward 0 from the left (negative x-values). The y-values of the function get closer to positive infinity as x gets closer to 0 from the right (positive x-values). As a result, we may infer that the function's vertical asymptote lies at x = 0.

Similary, Consider the behavior of the function when x grows very big in order to determine the horizontal asymptotes of a function using limits (in either the positive or negative direction). The horizontal asymptote of the function is the point at which the y-values of the function begin to approach a fixed value when x increases significantly.

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x=3+√15/3 and x=3-√15/3 are the solutions of 3x²-6x-2=0.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is 3x²-6x-2=0

Use the quadratic formula to find the solutions.

x=-b±√b²-4ac/2a

a=3, b=-6 and c=-2.

Now plug in these values in quadratic formula to find the solutions.

x=6±√-6²-4(3)(-2)/2(3)

x=6±√36+24/6

x=6±√60/6

x=3±√15/3

Hence, x=3+√15/3 and x=3-√15/3 are  the solutions of 3x²-6x-2=0.

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Answer:

Step-by-step explanation:

I'm going to guess that the equation is really  

y = -3x +3    not   y = -34 + 3

we don't really need the point information to solve this,  we know that a perpendicular line has an inverse slope with a sign change

so we know the slope of the perpendicular line is

[tex]\frac{1}{3}[/tex]