Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 143000 dollars. Assume the distribution is normal and that the standard deviation is 31000 dollars. Enter your answers as numbers accurate to 4 decimal places.

1.Find the probability that a single randomly selected salary is less than 144000 dollars.

2.Find the probability that a sample of size n=75 is randomly selected with a mean that is less than 144000 dollars.

Answer:

Let L be the length of the rectangular garden. We know that the perimeter of a rectangle is given by: P = 2L + 2W where P is the perimeter, L is the length, and W is the width. In this case, we are given that the perimeter is 372 m and the width is 88 m. Substituting these values into the equation, we get: 372 = 2L + 2(88) Simplifying and solving for L, we get: 372 = 2L + 176 2L = 196 L = 98 Therefore, the length of the rectangular garden is 98 m.

Answer: L = 98 m

Step-by-step explanation:

The perimeter of a rectangle can be found with this formula:

      P = 2W + 2L

➜ P is Perimeter

➜ W is Width

➜ L is Length

We will input known values and solve for the length. To solve, we will use multiplication and inverse operations.

      372 m = 2(88 m) + 2L

      372 m = 176 m + 2L

      196 m = 2L

      L = 98 m

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Answer:

Question 7 is correct.

205,000 (For Question 8)

Step-by-step explanation:

First, we need to find the value of x.

We need to subtract 1995 from 2010 to find out how many years would have passed.

This gives us 15, which is our x value.

Next, we need to solve for y.

We multiply 2000 by 15 to get 30,000.

Then, add 175,000 to 30,000 to get 205,000. That leaves us with the equation y = 205,000.

The Y value is equivalent to the population in 2010.

We have shown that the sum of the elements in G is equal to zero, as required.

An abelian group, also known as a commutative group in mathematics, is a set of elements where the outcome of applying the group operation on two elements of the set does not depend on the order in which the elements are written. The group operation is hence commutative. The integers and real numbers both form abelian groups when addition is used as an operation, and the idea of an abelian group can be seen as a generalisation of these cases.

We can prove this statement using the fact that the sum of the elements in an abelian group is always equal to zero.

Since G is a finite abelian group, every element ai in G has an inverse, denoted by -ai. Furthermore, since G is abelian, the order in which we add the elements does not matter. Therefore, we can rearrange the terms in the sum a1 + a2 + ... + an so that all of the terms are paired with their inverse:

a1 + a2 + ... + an = (a1 + (-a1)) + (a2 + (-a2)) + ... + (an + (-an))

Since n is odd, we have an odd number of elements in G, which means that we have an odd number of pairs of the form ai + (-ai). Therefore, there is exactly one element in the sum that is not paired with its inverse, which is either ai or -ai for some i.

Without loss of generality, suppose that ai is the element that is not paired with its inverse. Then, we have:

a1 + a2 + ... + ai + ... + an = (a1 + (-a1)) + (a2 + (-a2)) + ... + (ai + (-ai)) + ... + (an + (-an))

= 0 + 0 + ... + 0 + ai + (-ai) + ... + 0

= ai - ai

= 0

Therefore, we have shown that the sum of the elements in G is equal to zero, as required.

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The measure of the angles are 82. 7 degrees and 97. 3 degrees

Supplementary angles are simply described as those angles whose sum is equal or equivalent to 180 degrees.

Note that pair of angles on a straight line are supplementary to each other.

From the information given, we have that;

Let the angle of one be x

Then,

Angle 1 = x

Angle 2 = 14. 6 + x

Equate the angles

x + 14. 6 + x = 180

collect the like terms, we get;

2x = 180 - 14. 6

subtract the values

2x = 165. 4

x = 82. 7 degrees

Then, the second angle = 82. 7 + 14. 6 = 97. 3 degrees

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The missing data value in the table of values is y = 14

We can use the two given data points (1,6) and (2,10) to find the equation of the linear function that represents the data.

First, we can use the slope formula to find the slope of the line:

slope = (change in y) / (change in x) = (10-6) / (2-1) = 4/1 = 4

Next, we can use the point-slope formula to find the equation of the line using one of the given points. Let's use (1,6):

y - 6 = 4(x - 1)

We can simplify this equation to slope-intercept form (y = mx + b) by solving for y:

y = 4x + 2

Now we can use this equation to find the missing data value when x = 3:

y = 4(3) + 2 = 14

Therefore, the missing data value is y = 14, and the correct answer is (d) 14.

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The formula to find the length of an arc of a circle is given by L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the angle measured in radians and the radius of the circle is 2.

To find the length of the arc, we use the formula L = rθ. Substituting the given values, we get:

L = rθ

L = r( [tex]\frac{\pi}{2}[/tex]) or ( [tex]\frac{\pi}{2}[/tex])r

We are also given that the length of the arc is 1π, so we can write:

( [tex]\frac{\pi}{2}[/tex])r = 1π

Simplifying this equation, we get:

r = (1π) ÷ ( [tex]\frac{\pi}{2}[/tex])

r = 2

We can say that the length of an arc that is intercepted by an angle of  [tex]\frac{\pi}{2}[/tex] radians is equal to half the circumference of the circle. Since the length of the arc is given as 1π, we can find the radius of the circle by dividing 1π by [tex]\frac{\pi}{2}[/tex], which gives us 2.

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The complete question is:

In a circle, an angle measuring  [tex]\frac{\pi}{2}[/tex] radians intercepts an arc of length 1π. Find the radius of the circle in simplest form.

The probability of landing on a number greater than 7 is 4÷12 or 1÷3, which is approximately 0.333 or 33.3%.

What is Probability ?

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

If the spinner has 12 sections labeled with the numbers 1 through 12, then the probability of landing on a number greater than 7 would be:

There are 12 equally likely outcomes when the spinner is spun.

Out of these 12 outcomes, 4 are greater than 7: 8, 9, 10, and 11.

Therefore, the probability of landing on a number greater than 7 is 4÷12 or 1÷3, which is approximately 0.333 or 33.3%.

So P(>7) = 1÷3 or 0.333 or 33.3%.

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The interquartile range (IQR) of the data set represented by this box plot is 24.

The interquartile range, or IQR, can be determined in four easy steps: Sort the facts in ascending order of importance. locate the centre. Do the lower and higher half of the data's median calculations. Upper and lower median differences make up the IQR.

We must determine the difference between the third quartile (Q3) and the first quartile (Q1) in order to determine the interquartile range (IQR) of the data set depicted by this box plot.

We can see from the box plot that the range of the box is 18 to 49, which implies that Q1 is 25 and Q3 is 49. Therefore,

IQR = Q3 - Q1 = 49 - 25 = 24

So, none of the choices provided are the correct response. The data collection represented by this box plot has an IQR of 24, which is 24.

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Complete question:

What is the interquartile range (IQR) of the data set represented by this box plot?

A. 55

B. 37

C. 24

D. 12

Answer:

Determine the lengths of sides and measures of angles in a right triangle by ... 9 = 12x. Cross Products Property. 9 = 3x. Subtract 9x from each side. 3 = x.

Answer:

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

Slope-intercept form is:

Use two points on the line:

The first point represents the y-intercept, b = 8.

Find the slope, using the slope equation:

Substitute the found values to get the equation of the line:

1. The rate at which the faster child is working is 1/t.

2.The rate at which the slower child is working is 1/(2t)

3.The homework done by the faster child in 45 minutes is (1/t) * (3/4), since both children can complete the homework in 45 minutes.

4.The part of the homework done by the slower child in 45 minutes is (1/(2t)) * (3/4),

5.Thus, t=30 minutes, which is the time taken by the faster child to do the homework by herself.

6. Thus, 2t=90 minutes and t=45 minutes, which is the time taken by the slower child to do the homework by herself.

Time is a concept used to describe the progression of events from the past, through the present, and into the future. It is a measure of duration or an interval between two events, and it is often represented in units such as seconds, minutes, hours, days, weeks, months, and years.

1. Let t = the time needed for the faster child to complete the homework.

The faster child completes the homework twice as fast as the partner. Therefore, the rate at which the faster child is working is 1/t.

2.The rate at which the slower child is working is 1/(2t) since the slower child takes twice as long as the faster child to complete the homework.

3.The part of the homework done by the faster child in 45 minutes is (1/t) * (3/4), since both children can complete the homework in 45 minutes. In 45 minutes, the faster child completes 3/4 of the homework because she is working at a rate of 1/t, while the slower child is working at a rate of 1/(2t).

4.The part of the homework done by the slower child in 45 minutes is (1/(2t)) * (3/4), since both children can complete the homework in 45 minutes. In 45 minutes, the slower child completes 3/4 of the homework because she is working at a rate of 1/(2t), while the faster child is working at a rate of 1/t.

5.Let's use the equation P=rt, where P=1 (since the entire homework is done by one child alone) and r=1/t (since the faster child completes the homework in t time). Thus, t=30 minutes, which is the time taken by the faster child to do the homework by herself.

6.Similarly, we can use the equation P=rt, where P=1 (since the entire homework is done by one child alone) and r=1/(2t) (since the slower child takes twice as long as the faster child to complete the homework). Thus, 2t=90 minutes and t=45 minutes, which is the time taken by the slower child to do the homework by herself.

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Answer:

V_air = V_inside = 2,600 cubic inches.

Step-by-step explanation:

To find the amount of air contained in the display case, we need to subtract the volume of the glass from the volume of the outside dimensions.

The volume of the outside dimensions of the display case is:

V_outside = 22 * 15 * 12 = 3,960 cubic inches

The glass is half an inch thick, which means it adds 1 inch to each dimension of the display case. Therefore, the inside dimensions of the display case are:

22 - 2(1) = 20 inches

15 - 2(1) = 13 inches

12 - 2(1) = 10 inches

The volume of the inside dimensions of the display case is:

V_inside = 20 * 13 * 10 = 2,600 cubic inches

The volume of the glass is the difference between the outside and inside volumes:

V_glass = V_outside - V_inside = 3,960 - 2,600 = 1,360 cubic inches

Therefore, the amount of air contained in the display case is:

V_air = V_inside = 2,600 cubic inches.

Answer:

Area = 63.2 cm²

Step-by-step explanation:

To find the area of the given shape, we can split it into two shapes: a trapezium and a rectangle (as shown in the attached diagram).

Doing so gives us a rectangle with a length of 10 cm and a breadth of 2.8 cm at the bottom of the shape. Therefore its area:

Area = length × breadth

        = 10 cm × 2.8 cm

        = 28 cm²

We also get a trapezium, whose area can be found using the following formula:

[tex]\boxed{\mathrm{Area = \frac{1}{2} \times (a + b) \times h}}[/tex]

where:

• a, b ⇒ length of the parallel sides of trapezium

• h ⇒ distance between the parallel sides a and b

From the diagram attached below, we can see that the two parallel sides have lengths of 10 cm and 6 cm. Moreover, the distance between the parallel sides is 7.2 - 2.8 = 4.4 cm.

Therefore, using the above formula and information, we can calculate the area of the trapezium:

Area = [tex]\frac{1}{2}[/tex] × (6 + 10) cm × 4.4 cm

        = [tex]\frac{1}{2}[/tex] × 16 cm × 4.4 cm

        = 35.2 cm²

Now that we have the areas of the rectangle and trapezium, we can find the area of the whole shape simply by adding those two areas:

Area of shape = 28 cm² + 35.2 cm²

                        = 63.2 cm²

Therefore, the area of the given shape is 63.2 cm².

To find the ordered pair solutions, we need to solve the system of equations by setting them equal to each other:

-x² + x + 2 = x

Simplifying:

-x² + 2x + 2 = 0

We can solve for x using the quadratic formula:

x = (-2 ± sqrt(2^2 - 4(-1)(2))) / (2(-1))

x = (-2 ± sqrt(12)) / (-2)

x = 1 ± sqrt(3)

So the x-values of the ordered pair solutions are:

x = 1 + sqrt(3)

x = 1 - sqrt(3)

To find the corresponding y-values, we can substitute these x-values into either equation. Let's use y = x:

When x = 1 + sqrt(3):

y = 1 + sqrt(3)

When x = 1 - sqrt(3):

y = 1 - sqrt(3)

As a result, the probability that a randomly selected student in Gianna's probability maths class has read or seen the movie adaptation of her favourite book is 44%.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

solve this problem,

P(A or B) = P(A) + P(B) - P(A and B)

P(A) = 28%

P(B) = 36%

P(A and B) = 20%

Using the formula, we can find:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 28% + 36% - 20%

P(A or B) = 44%

As a result, the probability that a randomly selected student in Gianna's maths class has read or seen the movie adaptation of her favourite book is 44%.

As a result, the right answer is (a) 44%.

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Step-by-step explanation:

The correct first step the student could use to solve the equation 3(x-12)=9x is to distribute 3 on the left side of the equation, resulting in 3x - 36 = 9x.

This is because the distributive property states that a(b + c) = ab + ac. In this case, we have 3(x - 12), so we can distribute the 3 by multiplying it by both terms inside the parentheses: 3(x - 12) = 3x - 36.

Then, we can simplify the equation by subtracting 3x from both sides: -36 = 6x. Finally, we can solve for x by dividing both sides by 6: x = -6.

Therefore, the correct option is: "The student can distribute 3 on the left side of the equation, resulting in 3x−36=9x."

The first step in solving the equation 3(x−12)=9x is to distribute the 3 on the left-hand side of the equation. You multiply each term inside the parentheses by 3, resulting in a simplified equation: 3x - 36 = 9x.

If you're aiming to solve the equation 3(x−12)=9x, the initial step would be to distribute the 3 into the parentheses on the left side of the equation. This is achieved by multiplying each term inside the parenthesis by 3. Here's the process in detail:

Step 1: Start with the initial equation, which is 3(x−12)=9x.

Step 2: Remove the parentheses by distributing 3, resulting in 3x - 36 = 9x.

This is a viable initial step because now you have simplified equations on both sides, which helps you to get closer towards isolating the variable x.

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Answer:

Step-by-step explanation:

F

x=weeks

5=inital

y=total money saved

Thus value of x in the given the proportion is 7.

Here, both triangles are congruent due to sss congruency,

Thus,

6 : 12

6k = 12

k = 12/6

k = 2

Also, The expressions are

(x+2) : 3x - 3

(x+2)k = 3x - 3

(x+2)2 = 3x - 3

2x + 4 = 3x - 3

3x - 2x = 4 + 3

x = 7

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Answer: -2

Step-by-step explanation:

-7w + 1 = 8

Subtract 1 from both sides

-7w + = 7

Divide -7 from both sides

w = -1

then

8(-1) = -8

-8 + 6 = -2

The value of cos (90 - x ) = sin (x) = 7/11.

option B.

In trigonometry identity, we know that sin(x) = opposite / hypotenuse. Therefore, we can draw a right triangle with an angle x and opposite side 7 and hypotenuse 11.

Using the Pythagorean theorem, we can find the adjacent side of the triangle:

adjacent² = hypotenuse² - opposite²

adjacent² = 11² - 7²

adjacent² = 120

adjacent = √(120)

adjacent = 2 √(30)

Now, we can use the definition of cosine to find cos(90 - x):

cos(90 - x) = sin(x)

Therefore, cos(90 - x) = 7/11.

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Answer: False

Step-by-step explanation:  A whale can't fly

Answer:

False

Step-by-step explanation:

Because a whale cannot fly

Answer:

1.52×10⁶ liters of water

Step-by-step explanation:

38(4×10⁴)

By answering the presented question, we may conclude that the balance  interest after 5 years is approximately $1,484.71.

In mathematics, interest is the amount of money gained or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest per year for three years, for a total of $15.

for calculating the balance

[tex]A = Pe^(rt)\\[/tex]

this formula,

[tex]A = 1000e^(0.085*5)\\A = 1000e^(0.425)\\[/tex]

A ≈ $1,484.71

the balance after 5 years is approximately $1,484.71.

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Answer:1529.59

Step-by-step explanation:

1000e^(.085)5

Answer:

the circumcenter of triangle ABC is the point (3, 7/3).

Step-by-step explanation:

To find the circumcenter of triangle ABC, we need to find the intersection point of the perpendicular bisectors of its sides.

First, let's find the midpoint and slope of each side of the triangle:

Side AB: midpoint = (0,1), slope = undefined (vertical line)

Side AC: midpoint = (3,2), slope = -1/3

Side BC: midpoint = (3,-1/2), slope = 3/2

Next, we need to find the equations of the perpendicular bisectors of each side. The perpendicular bisector of a segment is the line that passes through its midpoint and is perpendicular to the segment.

Perpendicular bisector of AB: x = 0 (it is a vertical line passing through the midpoint of AB)

Perpendicular bisector of AC: passes through the midpoint (3,2) and has a slope of the negative reciprocal of AC's slope, which is 3

Therefore, the equation of the perpendicular bisector of AC is y - 2 = -1/3 (x - 3), which simplifies to y = -x/3 + 8/3

Perpendicular bisector of BC: passes through the midpoint (3,-1/2) and has a slope of the negative reciprocal of BC's slope, which is -2/3

Therefore, the equation of the perpendicular bisector of BC is y + 1/2 = -2/3 (x - 3), which simplifies to y = -2x/3 + 7/2

Now we need to find the intersection point of any two of these perpendicular bisectors. We can choose any two, but it is usually easier to choose the ones that have equations in slope-intercept form, which are the perpendicular bisectors of AC and BC.

Solving the system of equations y = -x/3 + 8/3 and y = -2x/3 + 7/2, we get x = 3 and y = 7/3.

Therefore, the circumcenter of triangle ABC is the point (3, 7/3).

Answer:

the expected value of your gain or loss is a net loss of $0.5006.

The probability of winning is 1/10,000 = 0.0001.

Step-by-step explanation:

There are 10,000 possible four-digit numbers between 0000 and 9999. Only one of those numbers is the winning number. Therefore, the probability of winning the Pick 4 game is:

Probability of winning = 1/10,000 = 0.0001

If you bet $5 on 1234, there are two possible outcomes:

-You lose $5 with probability 0.9999

-You gain $9,995 with probability 0.0001

The expected value of your gain or loss is the sum of the products of each outcome and its probability:

Expected value = (-$5 x 0.9999) + ($9,995 x 0.0001)

Expected value = -$0.5006

Answer:

Step-by-step explanation:

Answer:

Rounding to the nearest foot, the distance from point A to point B is 719 feet.

Answer:

The given expression is divisible by both 30 and 37

Step-by-step explanation:

First, let's consider the expression (36^5-6^9). We can factor out 6^5 from both terms to get:

(36^5-6^9) = 6^5(6^10-36^3)

Next, let's consider the expression (38^9-38^8). We can factor out 38^8 from both terms to get:

(38^9-38^8) = 38^8(38-1)

Now, we can substitute these factorizations back into the original expression:

(36^5-6^9)(38^9-38^8) = 6^5(6^10-36^3)38^8(38-1)

To show that this expression is divisible by 30, we need to show that it is divisible by both 2 and 3. We can see that 6^5 is divisible by both 2 and 3, so the entire expression is divisible by 2 and 3, and hence divisible by 30.

To show that this expression is divisible by 37, we can use Fermat's Little Theorem, which states that if p is a prime number and a is any integer not divisible by p, then a^(p-1) is congruent to 1 mod p. In this case, p=37 and a=6, so we can write:

6^36 ≡ 1 (mod 37)

Multiplying both sides by 6^10 gives:

6^46 ≡ 6^10 (mod 37)

We can use this congruence to simplify the expression we are interested in:

(36^5-6^9)(38^9-38^8) ≡ (6^10-6^9)(1-38^-1) (mod 37)

Simplifying this expression further gives:

(6^10-6^9)(1-38^-1) ≡ 0 (mod 37)

Therefore, the expression (36^5-6^9)(38^9-38^8) is divisible by both 30 and 37.

Answer:

The value of x of a circle with radius x + 1.5 and diameter of 9 2 / 5 cm is 7.9 cm

Radius of a circle

Radius of a circle is half of the diameter of a circle. The radius extend from the centre of the circle to the circumference.

Mathematically,

radius = 1 / 2 (diameter)

Therefore,

radius = (x + 1.5) cm

diameter = 9 2 / 5 cm = 47 / 5 cm

let's find x with the relationship above.

Therefore,

x + 1.5 = 47 / 5

subtract 1.5 from both sides

x + 1.5 - 1.5 = 9.4 - 1.5

x = 7.9 cm

Step-by-step explanation:

The constant of proportionality of juice to blackberries is 3. This means that for every cup of blackberries, you will get 1/3 cup of juice.

The constant of proportionality is a mathematical term used to describe the relationship between two quantities that are directly proportional to each other. When two quantities are directly proportional, they vary in proportion to each other such that if one quantity doubles, the other also doubles. The constant of proportionality is the number that relates the two quantities together.

To find the constant of proportionality, we need to divide the amount of juice by the amount of blackberries.

Let x be the amount of blackberries required to make 1 cup of juice. Then we have:

4 cups of blackberries = 1 1/3 cups of juice

Divide both sides by 1 1/3 cups of juice:

4 cups of blackberries / (4/3) cups of juice = 3 cups of blackberries / cup of juice

So the constant of proportionality of juice to blackberries is 3. This means that for every cup of blackberries, you will get 1/3 cup of juice.

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