With a mean of $32,500 and a standard deviation of $2,500. The z-score for a sales associate who earns $37,500 is 2.
The z-score, also known as a standard score, is a measure of how many standard deviations a given value is from the mean. It is used to standardize the data and make it easier to compare and interpret. The formula for the z-score is:
z = (x - μ) / σ
where x is the value of interest, μ is the mean, and σ is the standard deviation.
In this case, the mean annual salary for sales associates from a particular store is $32,500 and the standard deviation is $2,500. We want to find the z-score for a sales associate who earns $37,500. Plugging in the values, we get:
z = ($37,500 - $32,500) / $2,500 = 2
This means that the sales associate's salary is 2 standard deviations above the mean.
Interpreting the z-score can help us understand how unusual or typical a given value is in comparison to the mean. In this case, a z-score of 2 indicates that the sales associate's salary is relatively high compared to the mean, but it is not an extremely high salary.
We can use a standard normal table to find the proportion of the data that falls below a given z-score, or to find the corresponding value for a given proportion of the data.
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Find the volume of a pyramid whose height is 15.7 inches and whose base is a rectangle with
dimensions of 7.6 inches and 12.4 inches.
Answer: V = 493.19
Step-by-step explanation:
V=1/3bh
7.6*12.4=94
94*15.7=1479.568
1479.568*1/3=493.19
order the given functions in increasing order of their growth rate. note: all logarithms are base-10.
When comparing exponential functions, the one with the bigger base expands more quickly. A logarithmic function grows more quickly if its argument is bigger.
Compared to polynomial functions, which in turn expand more quickly than logarithmic functions, exponential functions grow more quickly.
When comparing exponential functions, the one with the bigger base expands more quickly.
A logarithmic function grows more quickly if its argument is bigger.
We can arrange the provided functions in this manner by applying these rules:
log n, n, n log n, n, n2, n!, nn
Taking the function with the fastest rate of growth first: log n n n log n n 2
Each of these variables has a polynomial or logarithmic growth rate. The exponential functions will now be discussed:
2^n > n^2
Since polynomial functions increase more slowly than exponential functions, n2 grows more slowly than 2n.
The two categories with the fastest growth are: n! > n^2
n! grows more quickly than 2n and n2, as factorial functions expand even more quickly than exponential functions do. Finally:
n^n > n!
Therefore, nn grows more quickly than n! because exponential functions with bigger bases scale up more quickly than those with smaller bases.
Consequently, the following functions are listed in ascending order of growth rate:
log n n n log n n n log n n n! n n.
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14 tires is% of 250 tires.
(Type a whole number or decimal rounded to the nearest tenth
The complete statement is 14 tires is 5.6% of 250 tires.
How to complete the blanksFrom the question, we have the following parameters that can be used in our computation:
14 tires is% of 250 tires.
As an equation, we have
14 = x% * 250
Divide both sides of the equation by 250
So, we have the following representation
x% = 14/250
Evaluate
x% = 0.056
Multiply by 100
x = 5.6
Hence, the expression in the blank is 5.6
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Help with this question
According to the figure of the right triangle
a = b = 10How to find angle a and b in the right triangleWhen a right triangle has one of the angles as 45 degrees the angle must be 45 degrees two. Also, the sides are equal, hence we have that
a = b
Using trigonometry we solve for b as follows
cos 45 = b / 10√2
multiplying both sides by 10√2
10√2 * cos 45 = 10√2 * b / 10√2
10√2 * cos 45 = b
rearranging
b = 10√2 * cos 45
where cos 45 = 1/√2 = √2/2
b = 10√2 * 1/√2
b = 10
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Expand and simplify
1) (x+3)(x+ 5) =
2) (x+3)(x - 5) =
3) (x-3)(x - 5) =
4) (2x + 4)(x-7)=
Please help me
Answer:
x^2+8x+15
x^2-2x+15
x^2-8x+15
2x^2&10x-28
Which of the following could be the areas of
the three squares shown?
A. 40 ft², 55 ft², 95 ft²
B. 35 ft²2, 25 ft², 45 ft²
C. 10 ft2, 10 ft², 100 ft²
D. 40 ft2, 30 ft², 1200 ft²
The areas of the squares are calculated from the Pythagoras relation of right angled triangle and it is 40 ft², 55 ft², 95 ft²
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the right angle triangle be represented as ΔABC
Now , the measure of side AB = √40 feet
The measure of side BC = √55 feet
The measure of side AC = √95 feet
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
Substituting the values in the equation , we get
AC² = AB² + BC²
( √95 )² = ( √40 )² + ( √55 )²
On simplifying the equation , we get
95 = 40 + 55
95 = 95
Therefore , the area of squares formed is 40 ft², 55 ft², 95 ft²
Hence , the triangle is having sides √40 feet , √55 feet and √95 feet
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This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Show that if n is an integer and n^3 + 5 is odd, then n is even usinga proof by contradiction. Rank the options below. Suppose that n^3 + 5 is odd and that n is odd. We know that the sum of two odd numbers is even. As n is odd. n^3 is odd. Therefore, our supposition was wrong; hence n is even. As n^3 and 5 are odd, their sum n^3 + 5 should be even, but it is given to be odd. This is a contradiction.
Assume n is odd. Since n^3 is odd, n^3 + 5 should be even, but it's odd. Therefore, n is even.
The correct ranking of the options is:
As n^3 and 5 are odd, their sum n^3 + 5 should be even, but it is given to be odd. This is a contradiction.
Suppose that n^3 + 5 is odd and that n is odd. We know that the sum of two odd numbers is even. As n is odd, n^3 is odd. Therefore, our supposition was wrong; hence n is even.
The proof by contradiction shows that the assumption that n is odd leads to a contradiction with the given fact that n^3 + 5 is odd. Therefore, the assumption that n is odd must be false, and hence n is even.
The proof begins by assuming that n is odd and showing that this leads to a contradiction with the given fact that n^3 + 5 is odd. Specifically, since the sum of two odd numbers is even, n^3 + 5 should be even if n is odd. However, we know that n^3 + 5 is odd, so our assumption that n is odd must be false, meaning that n is even.
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Half of a number is seven less than the number. What is the number?
Answer: [tex]x=3.5[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the number, then
[tex]\frac{1}{2}x=x-7\\\frac{1}{2}x-x=-7\\-\frac{1}{2}x=-7\\x=3.5[/tex]
Write a function that models the data.
j k
0 3
5 28
10 53
15 78
20 103
k=[
The equation of line is y = 5x + 3 , where the slope is m = 5
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 3 )
Let the second point be Q ( 5 , 28 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 28 - 3 ) / ( 5 - 0 )
Slope m = 25 / 5 = 5
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 3 = 5 ( x - 0 )
On simplifying the equation , we get
y - 3 = 5x
Adding 3 on both sides of the equation , we get
y = 5x + 3
Hence , the equation of line is y = 5x + 3
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Evaluate 5r + p if p = 3 and r = 4
Work Shown:
5r + p
5*4 + 3
20 + 3
23
A bag contains 7 green marbles, 2 white marbles, 5 orange marbles, 9 green marbles, and 7 red marbles. A marble will be drawn from the bag and replaced 180 times. What is a reasonable prediction for the number of times a white or red marble will be drawn? Answer A 15 B 54 C 57 D 63
A Reasonable prediction for the number of times a white or red marble will be drawn is 3/10 x 180 = 54. Thus, option b is correct
If a marble is drawn and not replaced, what is the probability of drawing an orange marble on the second draw?If a marble is drawn and not replaced, the probability of drawing an orange marble on the second draw depends on the color of the marble drawn on the first draw. If an orange marble was drawn on the first draw, then there will be one less orange marble in the bag, and the probability of drawing another orange marble on the second draw will be 4 out of the remaining 29 marbles. If a non-orange marble was drawn on the first draw, then there will be 5 orange marbles in the bag, and the probability of drawing an orange marble on the second draw will be 5 out of 29.
There are a total of 30 marbles in the bag.
The probability of drawing a white or red marble is
2/30 + 7/30
= 9/30
= 3/10.
Therefore, a reasonable prediction for the number of times a white or red marble will be drawn is 3/10 x 180 = 54. Answer B.
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Arianys has $0.45 worth of pennies and nickels. She has a total of 21 pennies and
nickels altogether. Graphically solve a system of equations in order to determine the
number of pennies, x, and the number of nickels, y, that Arianys has.
Taking into account the definition of a system of linear equations, the number of pennies and nickles that Arianys has is 15 and 6 respectively.
Definition of system of linear equationsThe degrees of systems of linear equations are groupings of linear equations with the same unknowns, of which it is necessary to find a common solution.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
Number of pennies and nickelsIn this case, a system of linear equations must be proposed taking into account that:
"x" is the number of pennies that Arianys has."y" is the number of nickels that Arianys has.You know:
Arianys has $0.45 worth of pennies and nickels. She has a total of 21 pennies and nickels altogether.The system of equations to be solved is
x + y = 21
0.01x + 0.05y = 0.45
There are several methods to solve a system of equations, it is decided to solve it using the graphical method, which consists of representing the graphs associated with the equations of the system to deduce its solution. The solution of the system is the point of intersection between the graphs, since the coordinates of said point satisfy both equations.
In this case, graphing the system of equations (image attached) it is obtained that the system of intersection between both equations is (x,y)=(15,6). This means that the number of pennies that Arianys has is 15 and the number of nickels that Arianys has is 6.
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The U.S. Department of Transportation maintains statistics for mishandled bags per 1,000 airline passengers. In September 2016, Delta mishandled 1.35 bags per 1,000 passengers. What is the probability that in the next 1,000 passengers, Delta will have no mishandled bags? at least one mishandled bag? at least two mishandled bags?
Answer:
The given probability of Delta mishandling a bag is 1.35 per 1,000 passengers. This means the probability of not mishandling a bag is 1 - 1.35/1000 = 0.99865.
The probability of no mishandled bags in the next 1,000 passengers is:
P(no mishandled bags) = (0.99865)^1000 ≈ 0.716
The probability of at least one mishandled bag in the next 1,000 passengers is the complement of no mishandled bags:
P(at least one mishandled bag) = 1 - P(no mishandled bags) ≈ 0.284
To find the probability of at least two mishandled bags, we can use the binomial distribution formula:
P(at least two mishandled bags) = 1 - P(0 mishandled bags) - P(1 mishandled bag)
where P(0 mishandled bags) and P(1 mishandled bag) can be calculated using the binomial probability formula:
P(k successes in n trials) = (n choose k) * p^k * (1-p)^(n-k)
where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient.
For P(0 mishandled bags), we have n = 1000, k = 0, and p = 0.00135:
P(0 mishandled bags) = (1000 choose 0) * 0.00135^0 * 0.99865^1000 ≈ 0.716
For P(1 mishandled bag), we have n = 1000, k = 1, and p = 0.00135:
P(1 mishandled bag) = (1000 choose 1) * 0.00135^1 * 0.99865^999 ≈ 0.242
Therefore,
P(at least two mishandled bags) = 1 - 0.716 - 0.242 ≈ 0.042
4 m
/60°
5m
4m
5m
Find the area of the figure. Round your answer to the nearest tenth.
The area is about square meters.
Both measurements are below the minimum area of 169 square feet required.
What is area?Area is a measurement of size of two dimensional surface such as Square rectangle or circle. It is calculated by multiplying the length of the surface by width area also can measured in terms of square units such as square feet or square meters area is an important concept in mathematics and is used to measure the size of safe and object it is also used to find the total area of a group of shape.
The measurements of the parking spaces shown do not meet the requirements of the town. The first parking space has an area of 144 square feet, while the second parking space has an area of 128 square feet. Both measurements are below the minimum area of 169 square feet required.
The area of the figure can be found by using the formula for the area of a regular polygon. Since the figure is composed of four 60-degree angles and four sides, the formula can be expressed as:
A = (1/2) * (a * s) * n
Where a is the length of one side of the polygon, s is the length of the apothem (a line perpendicular to the center of the polygon to a corner), and n is the number of sides of the polygon.
Since the figure has four sides of equal length (5 meters each), the length of the apothem can be calculated by using the Pythagorean theorem. The equation for the apothem is:
s = [tex](4^{2} - 5^{2} ) ^{0.5}[/tex]
Plugging these values into the area formula yields:
A = (1/2) * (5 * 4.472) * 4
A = (1/2) * (22.36) * 4
A = 44.72 square meters
Rounding to the nearest tenth yields an area of 44.7 square meters.
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♫
La edad del padre de Dylan es actualmente el cuadrado de la edad de Dylan. Si Dylan tiene 6 años, ¿cuántos años tiene su papá?
Dylan's father's age would be 36 years old at the time when Dylan is 6 years old.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that Dylan's father's age is currently the square of Dylan's age. Dylan is 6 years old.
We can write Dylan's father's age as -
A{father} = A{Dylan} x A{Dylan}
A{father} = 6 x 6
A{father} = 36
Therefore, Dylan's father's age would be 36 years old at the time when Dylan is 6 years old.
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{Question in english -
Dylan's father's age is currently the square of Dylan's age. If Dylan is 6 years old, how old is his dad?}
SOMEONE HELPPPPPLLLOLLL
Using the same table as before, which was the worst month for the team in terms of results?
The worst month for the team in terms of results was October, with a total of three losses in five matches.
What is number?Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.
The team won only one match and drew one, resulting in a total of five points. This was the lowest points total of any month during the season, a stark contrast to the other months where the team achieved much higher totals. The team's form during October was a far cry from their form during the rest of the season, with only one win in five matches. This poor form contributed to the team's overall lack of success during the season and led to their eventual relegation from the top division.
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A payment on a $155,000 house is $850. If you pay this monthly for 30 years, how much interest will you have paid on this house?
To find out how much interest will be paid on a $155,000 house if a monthly payment of $850 is made for 30 years, we can use the formula for the total interest paid on a fixed-rate mortgage loan:
Total Interest = (Monthly Payment x Number of Payments) - Loan Amount
where Monthly Payment is $850, Number of Payments is 30 years x 12 months/year = 360 months, and Loan Amount is $155,000.
Plugging in these values, we get:
Total Interest = ($850 x 360) - $155,000
Total Interest = $306,000 - $155,000
Total Interest = $151,000
Therefore, the total interest paid on the $155,000 house over 30 years with a monthly payment of $850 is $151,000.
simplify 4(x+5)-x+3n
3x+3n+20 is the answer
what's the formula to find the area of a pentagon
Answer:
The formula to find the area of a regular pentagon (a polygon with five sides of equal length and equal interior angles) is:
Area = (1/4) * sqrt(5(5+2sqrt(5))) * s^2
Where s is the length of one side of the pentagon.
Step-by-step explanation:
A 1.08 km diameter asteroid has a density of 3000 kg/m3 and impact the surface at 23.0 km/sec. Assuming a spherical asteroid, what is the kinetic energy (in joule) of the asteroid? Convert the answer to megatons of TNT, where 1 megaton is about 4e15 joule. For comparison, the most energetic weapon in the human arsenal is about 100 megatons.
The kinetic energy (in joule) of the asteroid is, 33 million
What is kinetic energy ?The kinetic energy is the energy associated with the particle having mass m and moving with the velocity v.
To find the kinetic energy of the asteroid, we need to use the formula:
KE = (1/2)mv²
where KE is the kinetic energy, m is the mass of the asteroid, and v is its velocity.
The mass of the asteroid can be calculated using its density and volume:
V = (4/3)πr³
where V is the volume of the asteroid, r is its radius, and π is the mathematical constant pi.
Since the asteroid is spherical, its radius is half its diameter, which is 0.54 km.
So,
V = (4/3)π(0.54 km)³
= 0.65 km³
The mass of the asteroid is then:
m = density × volume
= 3000 kg/m³ × 10⁹ m³/km³ × 0.65 km³
= 1.95 × 10¹² kg
Now we can calculate the kinetic energy:
KE = (1/2)mv²
= (1/2) × 1.95 × 10¹² kg × (23.0 km/sec)²
= 1.32 × 10²³ joule
To convert this to megatons of TNT, we divide by the energy of one megaton:
= 1.32 × 10³ joule / (4 × 10¹⁵ joule/megaton)
= 3.3 × 10⁷ megatons
Hence, the KE of asteroid is 33 million
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Each of the following statements is true. In each case write the converse of the statement, and give a counterexample showing that the converse is false. a. If n is any prime number that is greater than 2, then n+1 is even. b. If m is any odd integer, then 2m is even. c. If two circles intersect in exactly two points, then they do not have a common center.
a. Original statement: If n is any prime number that is greater than 2, then n+1 is even.
Converse: If n+1 is even, then n is prime and greater than 2.
Counterexample: n = 4, which is not a prime number but 4+1=5 is a prime number greater than 2.
b. Original statement: If m is any odd integer, then 2m is even.
Converse: If 2m is even, then m is odd.
Counterexample: m = 2, which is not an odd integer but 2×2=4 is an even integer.
c. Original statement: If two circles intersect in exactly two points, then they do not have a common center.
Converse: If two circles do not have a common center, then they intersect in exactly two points.
Counterexample: Two identical circles with centers coinciding have a common center and intersect at all points on the circle, which is more than two points.
What is converse statement?In mathematics, the converse of a conditional statement is formed by interchanging the hypothesis and conclusion.
For example, if the original statement is "If p then q",
the converse statement is "If q then p".
The converse statement may or may not be true, and it needs to be proven separately.
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For the following situation, find the mean and standard deviation of the population. List all samples (with replacement) of the given size from that population. Find the mean and
standard deviation of the sampling distribution and compare them with the mean and standard deviation of the population.
The number of DVDs rented by each of three families in the past month is 2, 11, and 5. Use a sample size of 2
The correct comparison of the population and sampling distribution is A. Means are the same but the standard deviation of sampling distribution is smaller
How to find the mean and standard deviationX X^2
95 9025
96 9216
98 9604
Sum = 289 27845
n 3
The sample mean 96.33333333 SUM/n
Population mean 96.33333333 SUM/n
Sample standard dev [tex]1.527525232 \sqrt{((1/(n-1))(SUM(X^2)-(1/n)SUM(X)^2)}[/tex]
Population standard dev [tex]1.247219129 \sqrt{((1/n)(SUM(X^2)-(1/n)SUM(X)^2)}[/tex]
Population Mean(μ) = 96.33
Population standard deviation (σ) = 1.25
Option A) 95,96,98 and X bar = 96.33
Sampling distribution :
mean (μx = μ) = 96.33
standard deviation(σx = σ/SQRT(n)) = 1.25/SQRT(3) = 0.72
Option A) Means are the same but the standard deviation of the sampling distribution is smaller
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There are 3 second grade classrooms that are 10 packs of paper. how much should each classroom get?
By solving an expression, we can find that the number of packs of paper that each classroom should get is 10/3.
Define Expression.Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations. An example is the expression x + y, which combines the terms x and y with an addition operator. In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.
Given,
Number of classrooms= 3
Number of packs of paper= 10
Now let the number of packs of paper per class be x.
x= Number of packs of paper/Number of classrooms
= 10/3.
Therefore, each classroom will get 10/3 packs of paper.
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The strength of magnetic force varies inversely with the square of the distance between the magnets.
Suppose that when two magnets are 0.06 meters apart, there is a force of 4 newtons. Find the work, in joules, that is required to move the magnets from a distance of 0.03 meters apart to a distance of 0.1 meters apart. (1 Joule = 1 Newton * 1 meter). Round your answer to three (or more) decimal places.
We can start by using the formula for inverse square law: F = k/d^2. where F is the force, d is the distance between the magnets, and k is a constant.
We can use the given information to solve for k: 4 = k/0.06^2, k = 4 * 0.06^2, k = 0.0144
Now we can use the value of k to find the force when the magnets are 0.03 meters and 0.1 meters apart: F1 = 0.0144/0.03^2 = 16, F2 = 0.0144/0.1^2 = 0.144
The work required to move the magnets is equal to the change in potential energy between the initial and final positions.
We can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy plus its change in potential energy. Since the magnets are not moving, their kinetic energy is constant, so the work done on them is equal to their change in potential energy: W = Uf - Ui
where W is the work, Uf is the final potential energy, and Ui is the initial potential energy. The potential energy of the magnets is given by: U = -k/d
where k is the constant we found earlier and d is the distance between the magnets.
Therefore, the initial potential energy is: Ui = -0.0144/0.03 = -0.48
And the final potential energy is: Uf = -0.0144/0.1 = -0.144
So the work required to move the magnets is: W = -0.144 - (-0.48) = 0.336 Joules
Therefore, the work required to move the magnets from 0.03 meters apart to 0.1 meters apart is 0.336 Joules (rounded to three decimal places).
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Find the quotient of these complex numbers (6-7i)-(4-5i)=
2 - 2i is the quotient of these complex numbers (6-7i)-(4-5i).
What is Division?A division is a process of splitting a specific amount into equal parts.
To find the quotient of complex numbers, we need to use the formula:
(a + bi) / (c + di) = [(a + bi) x (c - di)] / (c^2 + d^2)
where a, b, c, and d are real numbers and i is the imaginary unit.
In this case, we are subtracting two complex numbers:
(6-7i) - (4-5i)
= 6 - 7i - 4 + 5i (distribute the negative sign)
= 2 - 2i
Hence, 2 - 2i is the quotient of these complex numbers (6-7i)-(4-5i).
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the rate of change in the number of americans over the age of 65 is n(t) = 0.00246t^2 + 0.118t + 0.183 million people per year
where is the number of years since 2000. in 2000, there were 34.42 million people over age 65 in the us. answer the following questions, rounding the answer to 2 decimal places: the average rate of change in the number of americans over the age of 65 from 2000 to 2015 is____
The average rate of change in the number of Americans over the age of 65 from 2000 to 2015 is approximately -2.09 million people per year.
To find the average rate of change in the number of Americans over the age of 65 from 2000 to 2015, we need to calculate the change in the number of people over 65 during that time period and divide it by the number of years:
Number of people over 65 in 2015:
n(15) = 0.00246(15)^2 + 0.118(15) + 0.183
n(15) = 2.781 million people
Change in the number of people over 65 from 2000 to 2015:
2.781 million - 34.42 million = -31.639 million people
Average rate of change:
-31.639 million / 15 years = -2.09 million people per year
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The population change for the ten most populous counties in the US from 2000 to 2010 are given in the following table:County & Percent Change: Los Angeles CA 3.1, Cook IL -3.4, Harris TX 20.3, Maricopa AZ 24.2, San Diego CA 10.0, Orange CA 5.8, Kings NY 1.6, Miami-Dade FL 10.8 Dallas TX 6.7, Queens NY 0.1a. What is the mean of the data? b. What is the median of the data? c. Which is the better description of the center of this data and why?
The mean and median of given data of population change for the ten most populous counties in the US from 2000 to 2010 is 7.2% and 6.25%.
To find the mean of the data, we need to add up all the percent changes and divide by the total number of counties:
Mean = (3.1 - 3.4 + 20.3 + 24.2 + 10.0 + 5.8 + 1.6 + 10.8 + 6.7 + 0.1) / 10 = 7.2%
Therefore, the mean percent change for the ten most populous counties in the US from 2000 to 2010 is 7.2%.
To find the median of the data, we first need to order the percent changes from smallest to largest:
-3.4, 0.1, 1.6, 3.1, 5.8, 6.7, 10.0, 10.8, 20.3, 24.2
Since there are an even number of values, the median is the average of the two middle values, which in this case are 5.8 and 6.7. Therefore, the median percent change for the ten most populous counties in the US from 2000 to 2010 is (5.8 + 6.7) / 2 = 6.25%.
The better description of the center of this data is the median, because it is less affected by outliers than the mean. In this case, the percent change for Maricopa County, AZ (24.2%) is much larger than the other values, and it pulls the mean upward. The median, on the other hand, is not affected by outliers, and it gives a better representation of the typical percent change for these counties.
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HELP!!!!!!!!!!!!!!!!
The value of x and y are 13 and 3 respectively and the measure of angle mqr is 51 degree.
What are Exterior angle ?
It is an measure of rotation between one extended side(we extend it virtually) of the polygon with its adjacent side which is not extended.
WE are given that in the diagram, Ks, LT, MU are parallel to each other.
Angle knj = (2x-5)°, Angle lpn = (2y + 15), Angle pqu = (3x+4y)°.
Sine, the corresponding angles are equal
(2x-5) = (2y+15)
2x - 2y = 15 + 5
2x - 2y = 20
x - y = 10
x = 10 + y
Now,
(3x+4y) = (2y+15)
3x + 4y - 2y = 15
3x + 2y = 15
3(10 + y) + 2y = 15
30 + 5y = 15
y = 3
x = 13
Angle mqr = (3x+4y) = 51 degree.
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What is the solution of the system of equations?
4x - 3y = 15
x+y = 2
Enter your answer in the boxes.
Answer:
x = 3, y = -1
Step-by-step explanation:
4x - 3y = 15
x + y = 2 -> y = 2 - x
4x - 3(2 - x) = 15
4x - 6 + 3x = 15
7x = 21
x = 3
y = 2 - x
y = 2 -3
y = -1
Answer: x =3, y = -1
Step-by-step explanation:
[tex]\bf{\underline{We\:solve\:by\:applying\:the\:reduction\:method.}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{The\:exercise\:is \ ---\to \ \left \{ {{4x-3y=15} \atop {x+y=2 \ \ \ \ \ }} \right. } \end{gathered}$}}[/tex]
Multiply the second equation by -4, then add both equations.
4x - 3y = 15
-4(x + y = 2)
We add these equations to eliminate x.
-7y = 7
Then we solve -7y = 7 for y. (We divide by 7)
[tex]\bf{\dfrac{-7y}{ -7}=\dfrac{7}{-7} } \\ \\ \bf{y=-1}[/tex]
We place the found value of y , in one of the original equations y in order to solve for x:
4x - 3y = 15
4x - 3(-1) = 15
3x + 4 = 15
We add (-3) to both sides.
4x + 3 + (-3) = 15 + (-3)
4x = 12
We divide both sides by 4.
[tex]\bf{\dfrac{4x}{4}=\dfrac{12}{4} } \\ \\ \bf{x=3}[/tex]
Solution: x=3,y=-1
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