the salary of teachers in a particular school district is normally distributed with a mean of 50000 and a standard deviation of 2500. due to budget limitations, it has been decided that the teachers who are in the top 2.5% of the salaries would not get a raise. what is the salary level that divides the teachers into one group that gets a raise and one that doesn't?

The value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

The history of pi dates back thousands of years, and over time, various civilizations have attempted to calculate its value with varying degrees of accuracy. One of the most inaccurate versions of pi was recorded by the ancient Babylonians around 2000 BC.

The Babylonians calculated the value of pi as 3.125, which is off by more than 6% from the actual value. It is believed that the Babylonians arrived at this value by using a rough approximation of a circle as a hexagon. They measured the perimeter of the hexagon and divided it by the diameter to get their approximation of pi.

This value was later refined by the ancient Egyptians and Greeks, who were able to calculate pi with greater accuracy. The Greek mathematician Archimedes, for instance, was able to calculate pi to within 1% accuracy by using a method of exhaustion.

It wasn't until the development of calculus in the 17th century that mathematicians were able to derive an exact formula for pi. Today, the value of pi is known to over 31 trillion decimal places, thanks to the use of powerful computers and sophisticated algorithms.

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Answer:

$54

Step-by-step explanation:

First, we calculate the amount she paid for each pen.

$255/5 = $51

She paid $51 for each pen.

She made a profit of $3 per pen, so she sold each pen for $51 + $3 = $54

Answer: $54

Population density of the wolves is 0.156 wolves per square mile.

The term "population density" refers to the measurement of population per unit land area.

To get population density of wolves in Yellowstone park, we divide the estimated number of wolves by the park's area which give us:

= 540 / 3,471

= 0.15557476231

= 0.1557 wolves per square mile.

By rounding to the thousandth, the population density of wolves in Yellowstone park is 0.156 wolves per square mile.

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Answer:

$3686 remaining after tax

Step-by-step explanation:

Answer:

mean=81.81

median=85

Step-by-step explanation:

MEAN.

\( \frac{65 + 70 + 70 + 80 + 80 + 85 + 85 + 85 + 90 + 90 + 100}{11} \)

\( = 81.81\)

MEDIAN

Since it's already arranged in ascending order, the middle number is taken as the median

which is 85.

i hope this helps

Answer:

See below ↓↓

Step-by-step explanation:

Mean

Median

The sample mean variance of the continuous distribution will be 0.3428.

The population variance is equal to the sample size divided by the variance of the sampling distribution of the mean.

14 is the greatest and 1 is the smallest value in a uniform continuous distribution.

36-size samples are taken from the distribution.

Now,

Variance among the population = 14 – 2 = 12

The sample size is 36.

Given that the sample means' variance is defined as;

= Variation in the population / Sample Size

If you replace all the values, you get;

= 12 / 35

= 0.3428

As a result, the sample mean variance will be 0.3428.

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The total mass of the deposit is 0.12 g.

To calculate the total mass of the mineral deposit, we need to integrate the density function over the entire length of the strip:

\(m = \int 0^2 s(x) dx\)

Substituting the given density function, we have:

\(m = \int 0^2 0.09x(2-x) dx\)

Expanding the integrand and integrating, we get:

\(m = 0.09 \int 0^2 (2x-x^2) dx\)

\(m = 0.09 [(x^2) - (x^3)/3]\)|0 to 2

\(m = 0.09 [(2^2) - (2^3)/3 - 0]\)

m = 0.09 [4 - (8/3)]

m = 0.09 (4/3)

m = 0.36/3

m = 0.12 g

Therefore, the total mass of the deposit is 0.12 g.

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Answer:

The average salary is $57,500

Step-by-step explanation:

You would find the total salaries and divide that by 40 because there were 40 people: 18 + 10 +8 + 2 + 2

To find the total salaries"

18(50,000) + 10(60,000) + 8(75000) + 2(90,000) + 2(10000) = 2300000

2300000/40 = 57,500

Answer: $1,312.5 difference

Step-by-step explanation:

1050 x 1.5 = 1575

1575 x 1.5 = 2,362.5

2,362.5 - 1050 = 1,312.5

Answer:

x = - 2 and x = 6

Step-by-step explanation:

given

(x - 6)(x + 2) = 0

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

the values of x that result in the expression being equal to 0 are

x = - 2 and x = 6

When the standard deviation of a sample increases, the confidence interval option (a) becomes wider.

When we increase the standard deviation of the sample, it means that the values in the sample are more spread out from the mean. This results in a larger range of possible values for the population parameter, which makes the confidence interval wider.

To put it mathematically, the formula for the confidence interval is:

CI = X ± t*(s/√n)

Where:

X is the sample mean

s is the sample standard deviation

n is the sample size

t is the t-score, which depends on the desired confidence level and degrees of freedom.

As we can see from the formula, the standard deviation (s) is directly proportional to the width of the confidence interval (CI). This means that if the sample standard deviation increases, the width of the confidence interval also increases.

Therefore, the correct answer to the question is: a) It becomes wider.

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Alonzo rode the scooter for 44 minutes.

Let the fee to start the scooter be F, and let the cost per minute of the ride be C. We are given that Alonzo's total bill for the ride is T. With this knowledge, we can construct the following equation:

T = F + Cm

where m is the number of minutes Alonzo rode the scooter. We want to solve for m.

To find m, we may rewrite the equation as follows:

m = (T - F)/C

Therefore, the number of minutes Alonzo rode the scooter is (T - F)/C.

For example, let's say the fee to start the scooter is $2.50, and the cost per minute of the ride is $0.15. If Alonzo's total bill for the ride was $9.20, then we can plug these values into the equation above to find the number of minutes Alonzo rode the scooter:

m = (T - F)/C = (9.20 - 2.50)/0.15 = 44

Therefore, Alonzo rode the scooter for 44 minutes.

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Answer:

não entend i

Sep-by-step explanation:

Answer: \(x = \frac{3}{4}\)

Step-by-step explanation:

\(4x-2=1\\Add(2)\\4x=3\\Divide(4)\\x=3/4\)

Hope it helps <3

Answer:

\(\boxed{x=\frac{3}{4}}\)

Step-by-step explanation:

\(4x-2=1\)

Add 2 on both sides.

\(4x-2+2=1+2\)

\(4x=3\)

Divide both sides by 4.

\(\displaystyle \frac{4x}{4} =\frac{3}{4}\)

\(\displaystyle x=\frac{3}{4}\)

There are 24 different ways we can draw two red, three green, and two purple balls if the balls are considered distinct.

To determine the number of ways we can draw the balls, we can use the concept of permutations. Since the balls are considered distinct, the order in which they are drawn matters.

First, let's consider the red balls. We need to choose 2 out of the available 2 red balls, so the number of ways to choose them is 2P2 = 2! = 2.

Next, let's consider the green balls. We need to choose 3 out of the available 3 green balls, so the number of ways to choose them is 3P3 = 3! = 6.

Finally, let's consider the purple balls. We need to choose 2 out of the available 2 purple balls, so the number of ways to choose them is 2P2 = 2! = 2.

To find the total number of ways we can draw the balls, we multiply the number of ways for each color: 2 * 6 * 2 = 24.

Therefore, there are 24 different ways we can draw two red, three green, and two purple balls if the balls are considered distinct.

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The conditional probability that the size of the family is less than 6 given that it is at least 3 is 1.

To find the conditional probability that the size of the family is less than 6 given that it is at least 3, we need to use the formula for conditional probability.

Let's denote A as the event that the size of the family is less than 6, and B as the event that the size of the family is at least 3.

The conditional probability of A given B, denoted as P(A|B), is calculated as follows:

P(A|B) = P(A and B) / P(B)

First, we need to find P(B), the probability that the size of the family is at least 3. Since the family is selected at random, we can assume that all possible family sizes have an equal chance of being selected.

Let's assume the total number of possible family sizes is n. The probability of selecting a family with at least 3 members is the sum of the probabilities of selecting a family with exactly 3 members, exactly 4 members, and exactly 5 members.

P(B) = P(3) + P(4) + P(5)

Next, we need to find P(A and B), the probability that the size of the family is both less than 6 and at least 3. Since any family size less than 6 is also at least 3, P(A and B) will be the same as P(B).

Finally, we can substitute the values into the formula for conditional probability:

P(A|B) = P(A and B) / P(B) = P(B) / P(B) = 1

Therefore, the conditional probability that the size of the family is less than 6 given that it is at least 3 is 1.

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Answer:

Step-by-step explanation:

We can find the distance between line l and point P by finding the distance between point P and the closest point on line l.The slope of line l is 0, since both points have the same y-coordinate. Therefore, line l is a horizontal line. The y-coordinate of any point on line l is 1.To find the closest point on line l to point P, we need to find the point on line l that has a y-coordinate of 7. Since line l is horizontal, any point on line l with a y-coordinate of 7 will work. Let's choose the point (5, 7), which is on the same horizontal line as line l.Now we can find the distance between point P and the point (5, 7):sqrt((5-(-2))^2 + (7-1)^2) = sqrt(49 + 36) = sqrt(85)Therefore, the distance between line l and point P is sqrt(85).

The solution of the quadratic equation is x=5±√35 .

A quadratic equation is given by the equation which can be written in the form ax²+bx +c.

the given quadratic equation is :

x²-10x+25=35

Simplifying the equation we get:

or, x²-10x+25-35=0

or, x²-10x-10=0

Now we will solve the equation by completion squares method:

x²-10x-10=0

or, x²-2×x×5+5²-5²-10=0

or, (x-5)²=35

or, x-5=±√35

or, x= 5±√35

Therefore the solution of the quadratic equation is 5+√35 and 5-√35 .

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Answer:

B

Step-by-step explanation:

The equation of Nolan's line is  

The slope-intercept form of a line is given by:

Here

m is the slope of the line

and b is the y-intercept.

Given

y-intercept = b = 3

slope = m = 2

The values of m and b can be put into the equation to find the line's equation

So,

Putting the value

Hence,

The equation of Nolan's line is

The photo along with the mat will be something like this:

So, new side length = 3 + 2x

new height = 5 + 2x

Hence,

Rectangle Area (A) = length * height

Thus,

Answer:

24513

Step-by-step explanation:

Answer:

6x2 + 16x = 672

Reorder the terms:

16x + 16x2 = 672

Solving

16x + 16x2 = 672

Solving for variable 'x'.

Reorder the terms:

-672 + 16x + 16x2 = 672 + -672

Combine like terms: 672 + -672 = 0

-672 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.

16(-42 + x + x2) = 0

Factor a trinomial.

16((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

Solution

x = {-7, 6}

Step-by-step explanation:

The given quadratic function models the projectile of the object as it is

launched off the top of the building.

The interpretation of the function values are;

The appropriate domain is 0 ≤ x ≤ 7

Reasons:

The given function for the height of the object is f(x) = -16·x² + 16·x + 672

The domain is given by the values of x for which the value of y ≥ 0

Therefore, when -16·x² + 16·x + 672 = 0, we get;

-16·x² + 16·x + 672 = 0

16·(-x² + x + 42) = 0

-x² + x + 42 = 0

x² - x - 42 = 0

(x - 7)·(x + 6) = 0

x = 7, or x = -6

The minimum value of time, x is 0, which is the x-value at the top of the

building, and when x = 7, the object is on the ground.

Therefore;

The maximum value of f(x) = a·x² + b·x + c, is given at \(x = -\dfrac{b}{2 \cdot a}\)

Therefore;

We have;

\(x = -\dfrac{16}{2 \times (-16)} = \dfrac{1}{2}\)

Which gives;

\(f \left(\frac{1}{2} \right) = -16 \times \left(\dfrac{1}{2} \right)^2 + 16 \times \left(\dfrac{1}{2} \right)+ 672 = 676\)

The height of the building is given when the time, x = 0, as follows;

Height of building, f(0) = -16 × 0² + 16 × 0 + 672 = 672

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Answer:

3^5m over 3^3m = 9

Step-by-step explanation:

Heres why

First reduce and simplify

cancel the common factor M which gives you 3^5 over 3^3 then simplify the expression which gives you 3^2

second evaluate the power

3^2=9

Answer :-The interval of convergence for the given power series is (4, 14).

The power series in question is ∑n=1 to infinity [(x−9)^n]/[n(-5)^n].

To find the interval of convergence, we will use the Ratio Test:

1. Compute the absolute value of the ratio between the (n+1)th term and the nth term:

|(a_(n+1))/a_n| = |[((x-9)^(n+1))/((n+1)(-5)^(n+1))]/[((x-9)^n)/(n(-5)^n)]|

2. Simplify the ratio:

|(a_(n+1))/a_n| = |(x-9)/((-5)(n+1))|

3. Take the limit as n approaches infinity:

lim (n→∞) |(x-9)/((-5)(n+1))|

4. For the Ratio Test, if the limit is less than 1, then the series converges. In this case:

|(x-9)/(-5)| < 1

5. Solve the inequality to find the interval of convergence:

-1 < (x-9)/(-5) < 1

Multiply each side by -5 (and reverse the inequalities since we're multiplying by a negative number):

5 > x-9 > -5

Add 9 to each side:

14 > x > 4

So, the interval of convergence for the given power series is (4, 14).

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Answer:

0, -8, 2

Step-by-step explanation:

Opposite of 0 is still 0.

Opposite of 8 = -8

Opposite of the opposite of 2: -2 is the opposite, then the opposite of opposite is -(-2) = 2

Answer: 230 Marbles

Step-by-step explanation:

Let Xavier marbles be x

Let Thomas marbles be y

Let Mei marbles be z

Xavier, Thomas, and Mei had 650 marbles.

x + y + z = 650

Thomas had 3 times as many marbles as Mei.

y = 3 × z

y = 3z

Mei had 50 fewer marbles than Xavier.

x = z - 50

We can plug all the equation gotten back into the first equation

x + y + z = 650

Since y = 3z and x = z - 50

x + y + z = 650

(z - 50) + 3z + z = 650

z - 50 + 3z + z = 650

5z - 50 = 650

5z = 650 + 50

5z = 700

z = 700/5

z = 140

Mei has 140 marbles

Since x = z - 50

x = 140 - 50

x = 90

Xavier has 90 marbles

y = 3z

y = 3 × 140

y = 420

Thomas has 420 marbles

Xavier and Mei marbles = 90 + 140

= 230 marbles

Answer: 2 . (7)

Step-by-step explanation:2 7/9 equals to 2.(7)

It is, a so called, 'repeating' decimal

`~hope i helped~

Let cost be x

\(\\ \bull\sf\dashrightarrow x+0.15x=1449\)

\(\\ \bull\sf\dashrightarrow 1.15x=1449\)

\(\\ \bull\sf\dashrightarrow x=\dfrac{1449}{1.15}\)

\(\\ \bull\sf\dashrightarrow x=1260\)

Answer:

Solution given:

Vat=15%

Selling price with vat=Rs1449

Selling price with out vat=?

We have

Selling price with vat=Selling price without vat +Vat amount

Rs 1449=selling price without vat +vat % of selling price without vat

Rs1449=Selling price without vat(1+vat/%)

Selling price without vat=\(\bold{\frac{Rs1449} {1+\frac{15}{100}}}\)

Selling price without vat=\(\bold{\frac{Rs1449}{1.15}}\)

Selling price without vat=Rs1260

Answer:

16/3 or 5.3 recurring

Step-by-step explanation:

-8 times -2/3 is 16/3, and 16/3 is 5.3 recurring

Answer:

w = 2

Step-by-step explanation:

Step 1: Write equation

1.3(w + 4) = 2.1w + 3.6

Step 2: Solve for w

Step 3: Check

Plug in w to verify it's a solution.

1.3(2 + 4) = 2.1(2) + 3.6

1.3(6) = 4.2 + 3.6

7.8 = 7.8