The average annual salary for all US teachers is $48,000. Assume the distribution is normal and the standard deviation is $5700, if you apply for teaching position and were $52,000,how do you feel (based on the probability result)? Explain why you feel that way.

Answer:

94.5

Step-by-step explanation:

Use the trapezoid area formula:

[(a+b)/2]×h

a and b represent the bases. h is the height

both bases are 17.5 and 9.5. So plug them in.

17.5 plus 9.5 is 27.

27 divided by 2 is 13.5

Now, multiply 13.5 by the height.

13.5 times 7 is 94.5

\(\sf\large\red{ANSWER:-}\)

Here we've been provided with a trapezoid who is having,

The question they are looking for is what is the area of the given trapezoid. The standard formula to calculate area for trapezoid is given by,

\(:\implies\tt{( \frac{a + b}{2} ) \times h}\)

Here,

Substituting values in formula we get,

\(:\implies\tt{( \frac{17.5 + 9.5}{2} ) \times 7.2}\)

\(:\implies\tt{( \frac{27}{2} ) \times 7.2}\)

\(:\implies\tt{13.5 \times 7.2}\)

\(:\implies\tt{94.5}\)

Answer:

x = -2

Step-by-step explanation:

Answer:

The expected frequency for each category would be:

10.

Step-by-step explanation:

a) Data and Calculations:

Number of respondents = 30

Number of categories = 3

Political preferences (categories) = 3

Probability of each category or preference occurring = 1/3

Expected frequency for each category = 1/3 * 30 = 10

b) The expected frequency for each political category (political affiliation) can be calculated by multiplying the probability of each category (political preferences) by the number of respondents.  Note that the expected frequency will be different from the observed frequency, which is the actual number of times that each category of political affiliations will be preferred.

According to the given information, the correct answer is option b): (z+15)(z-15).

What is an algebraic expression?

An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent quantities or values that can vary, depending on the values assigned to the variables in the expression. Algebraic expressions can be simple or complex, and they can have one or more variables.

We can factorize the expression z² - 225 using the difference of squares formula, which states that a² - b² = (a + b)(a - b). In this case, a = z and b = 15, so we have:

z² - 225 = (z + 15)(z - 15)

Therefore, the correct answer is option b): (z+15)(z-15).

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9514 1404 393

Answer:

  3 < x < 6

Step-by-step explanation:

Use the perimeter formula to write an expression for the perimeter. Then put that in an inequality with the given limits. Solve for x.

  P = 2(L +W)

  P = 2((4x) +(2x +1)) = 2(6x +1) = 12x +2 . . . . . fill in the given values; simplify

The perimeter wants to be between 38 and 74 cm, so we have ...

  38 < 12x +2 < 74

  36 < 12x < 72 . . . . . subtract 2

  3 < x < 6 . . . . . . . . . divide by 6

_____

Additional comment

Solving a compound inequality is very much like solving a single inequality. You need to "undo" what is done to the variable. The rules of equality (ordering) still apply. If you were to multiply or divide by a negative number, the direction (sense) of the inequality symbols would reverse in the same way they do for a single inequality.

Here, our first step was to subtract 2 from all parts of the inequality:

  38 -2 < 12x +2 -2 < 74 -2   ⇒   36 < 12x < 72

The division by 12 worked the same way: all parts are divided by 12.

  36/12 < (12x)/12 < 72/12   ⇒   3 < x < 6

__

If it makes you more comfortable, you can treat the perimeter limits as two separate inequalities: 38 < 12x+2 and 12x+2 < 74. Both restrictions apply, so the solution set is the intersection of the solution sets of these separate inequalities.

Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

The value of the given fraction in mixed numbers is 6, or 36/6.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a piece or part of a whole. It symbolizes the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator.

Here,

=81/6-45/6

=(81-45)/6

=36/6

=6

The value for given fraction in mixed number will be 6 that is 36/6.

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The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer:

Pay fast, no need to store cash

Step-by-step explanation:

The equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

We can use the point-slope version of the equation, which is: to determine the equation of a line passing through two specified points.

y - y₁ = m(x - x₁)

where (x₁, y₁) are the coordinates of one of the points, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

Use the points (1,6) and (2,7) to find the equation of the line:

Using (x₁, y₁) = (1,6):

y - 6 = m(x - 1)

Now, substitute the coordinates (2,7) into the equation:

7 - 6 = m(2 - 1)

1 = m

So, the slope of the line is m = 1.

Substitute this value into the equation:

y - 6 = 1(x - 1)

y - 6 = x - 1

y = x + 5

Therefore, the equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.

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x = 6 is the value of x does f(x) = 2.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Here, we have

Given function:  f(x) = −1 + 0.5x

We have to find the value of x does f(x) = 2.

For this, we put the different values of x and see what value satisfies the given function.

For x = -6

f(x) = −1 + 0.5(-6)

f(x) = -4

For x = 5

f(x) = −1 + 0.5(5)

f(x) = 1.5

For x = 6

f(x) = −1 + 0.5(6)

f(x) = 2

Hence, x = 6 is the value of x does f(x) = 2.

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

573.33

Step-by-step explanation:

599+14.33

= 573.33

(if rounding then its  600+14.33) = 614.33

Answer:

balls

Step-by-step explanation:

balls

On solving the provided question, we can say that - by prime factorization the factors of 5 are 5 and 1

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.

The factors of 5 are -

5and 1

as 5 = 5 X 1

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Answer:

Answer is Option B.

That is the nth term of the sequence.

1/8 + 1/16 + 1/32....

You notice that all the numerators are the same. Which is (1).

so we have to both about getting the nth term of the denominator

Since all the denominator are divisible by 2... and Your intuition should tell you that they'd multiples of 2

So Lets go with 2^n

2^n

let n be all Integers

let take 1,2,3

2¹ = 2

2² = 4

2³ = 8

Now Observe that

If you multiply all these by 4... We will have all the values of the denominator

which are 4,16,32

So thats our nth term

1/4(2^n)

as n approaches positive Infinity.

The expression is \(\lim_{n \to \infty} \frac{1}{4(2^{n}) }\) , so option (B) is the correct expression.

"A series expansion is an expansion of a function into a series or infinite sum. It is a method for calculating a function that cannot be expressed by just elementary operators (addition, subtraction, multiplication, and division)".

For the given situation,

The series is given as \(\frac{1}{8} +\frac{1}{16}+ \frac{1}{32}+ \frac{1}{64}+ \frac{1}{128}+......\)

In the series, all the numerators are 1 and the denominators are even numbers so multiples of 2.

Now, we examine the denominators alone.

\(8,16,32,64,128\)

⇒ Multiples of 2. So we get \(2^{n}\) multiplied by some integers.

Put \(n=1,\)

⇒ \(2^{1}\) × \(4=8\)

Put \(n=2,\)

⇒ \(2^{2}\) × \(4=8\)

Put \(n=3,\)

⇒ \(2^{3}\) × \(4=32\)

Put \(n=4,\\\)

⇒ \(2^{4}\) × \(4=64\)

Put \(n=5\),

⇒ \(2^{5}\) × \(4=128\)

Thus \(2^{n}\) expression becomes \(2^{n}(4)\) .

Hence we can conclude that the expression is \(\lim_{n \to \infty} \frac{1}{4(2^{n}) }\) . So option (B) is the correct expression.

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The function that correctly defines S(x) is S(x) = 5x - 2(20 - x) + 20

We have the following definitions in the question

If the total questions is 20, then

Incorrect answers = 20 - x

So, the points gained/lost are

Gained = 5 * x = 5x

Lost = -2 * (20 - x) = -2(20 - x)

Bonus = 20

Add the above points to get the function S(x)

S(x) = 5x - 2(20 - x) + 20

Hence, the definition is S(x) = 5x - 2(20 - x) + 20

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Answer: 50 miles

Step-by-step explanation:

Because 25 x 2 = 50

and 1 inch is 25 miles and 2 inches is then 50 miles

Answer:

C. 50 miles

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

\(\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow\)

Make sure to always round up the required sample size to the nearest integer!

Answer: 12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Check the picture below

With  the empirical rule, we can estimate that the number of farms in the sample whose land and building values per acre are between $1100 and $1500 is approximately 50 farms.

The empirical rule (also known as the 68-95-99.7 rule) states that for data sets with a bell-shaped distribution:

68% of the data falls within one standard deviation of the mean.

95% of the data falls within two standard deviations of the mean.

99.7% of the data falls within three standard deviations of the mean.

Using this rule, we can estimate the number of farms whose land and building values per acre are between $1100 and $1500 as follows:

The mean value of land and buildings per acre from the sample of farms is $1300, and the standard deviation is $200.

$1100 is 1.5 standard deviations below the mean:

($1100 - $1300) / $200 = -1.0.

$1500 is 1 standard deviation above the mean:

($1500 - $1300) / $200 = 1.0.

Therefore, we can estimate that approximately:

68% of the farms in the sample have land and building values per acre between $1100 and $1500 plus or minus one standard deviation of $200. This is equivalent to approximately 50 farms, which is 68% of the sample size of 74 farms.

95% of the farms in the sample have land and building values per acre between $900 and $1700 plus or minus two standard deviations of $200. This is equivalent to approximately 70 farms, which is 95% of the sample size of 74 farms.

99.7% of the farms in the sample have land and building values per acre between $700 and $1900 plus or minus three standard deviations of $200. This is equivalent to approximately 73 farms, which is almost the entire sample size of 74 farms.

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Note: The full question is:-

The mean value of land and buildings per acre from a sample of farms is $1300, with a standard deviation of $200. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 74. Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1100 and $1500.

The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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Answer:

The inverse is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x) = (x+3)^5

Finding the inverse,

\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)

We replace x with y and vice versa

so,

\(x = (y+3)^5\)

Solving for y,

the the 5th root,

\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)

hence the inverse function is,

\(f^{-1}(x) = \sqrt[5]{x} - 3\)

Step-by-step explanation:

f(x)=(x+3)×5

Y=5X+15

now

interxchanging x and y we get,

x=5y+15

5y=x-15

y=x-15/5

therefor f~1(x)=x-15/5

Answer:

a)

\(4ydy = xdx\)

\(2 {y}^{2} = \frac{1}{2} {x}^{2} + c\)

\( {y}^{2} = \frac{1}{4} {x}^{2} + c \)

\( {y}^{2} - \frac{1}{4} {x}^{2} = c \)

b)

c = 4, so

\( {y}^{2} = \frac{1}{4} {x}^{2} + 4\)

\(y = - \sqrt{ \frac{1}{4} {x}^{2} + 4} \)

\(y = - \frac{ \sqrt{ {x}^{2} + 16} }{2} \)

Answer: c = 7.25r + 9.50

Step-by-step explanation:

The total cost depends on how much Cooper goes golfing. That variable, something that can change over the course of time, is r. 7.25 times the amount of rounds, r, is how much he'll be paying without the admission ticket.

The 9.50 is an unchanging amount, because he has to pay to get in. That amount is added to the end result. So:

c = 7.25r + 9.50

Answer

y=−3x+10  

The given equation is in slope-y intercept form. The slope is the coefficient of x…which is -3, and the y-intercept is the constant term…+4.

Parallel lines have the same slope. So the correct equation should have a slope of -3. The only change will be the constant term (y-intercept) which needs to be +10. which gives us the equation….y =-3x+10.

Step-by-step explanation:

The freighter is approximately 164.33 miles from the city.

We can use the Law of Cosines to solve this problem. Let's label the distances as follows:

d: distance between the city and the freighter

x: distance between the city and the island

y: distance between the island and the freighter

First, we need to find x using the given coordinates:

N23°38'W is equivalent to S23°38'E, so we have:

cos(23°38') = x/48

x = 48cos(23°38') ≈ 42.67 miles

Next, we can use the coordinates of the freighter to find y:

N11°26'E is equivalent to E11°26'N, and N12°16'W is equivalent to S12°16'E. This means that the angle between the island and the freighter is:

23°38' + 11°26' + 12°16' = 47°20'

cos(47°20') = y/d

We can rearrange this equation to solve for y:

y = dcos(47°20')

Now we can use the Law of Cosines to solve for d:

d² = x² + y² - 2xy cos(90° - 47°20')

d² = 42.67² + (d cos(47°20'))² - 2(42.67)(d cos(47°20')) sin(47°20')

d² = 1822.44 + d² cos²(47°20') - 2(42.67)(d cos(47°20')) sin(47°20')

d² - d² cos²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² (1 - cos²(47°20')) = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² sin²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² = (1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')) / sin²(47°20')

d ≈ 164.33 miles

Therefore, the freighter is approximately 164.33 miles from the city.

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Answer: 48 more monthly payments

Step-by-step explanation: