Hans deposits $300 into an account that pays simple interest at a rate of 2% per year. How much interest will he be paid in the first 5 years?
Evaluate 4(a2 + 2b) - 2b when a = 2 and b = –2.
The given expression is [tex]4(a^2 + 2b) - 2b[/tex]. when a = 2 and b = –2 then the answer would be 4.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
The given expression is
[tex]4(a^2 + 2b) - 2b[/tex]
when a = 2 and b = –2.
[tex]4(2^2 + 2(-2)) - 2(-2) \\\\ =4(4-4) + 4 \\\\= 4\times 0 + 4 = 4[/tex]
Learn more about the factored form of an expression here:
https://brainly.com/question/1249625
#SPJ2
On a certain marathon course a runner reaches a big hill that is at least 10 miles into the race. If a total marathon is 26.2 miles, how can u find the number of miles the runner still has to go?
this would have to be an inequality equation.
Marathon is 26.2 miles
they get to a hill that is at least 10 miles into the race
26.2-10=16.2
so they have at most 16.2 miles to go
the equation is X<=16.2
what ithe distance from (3 1/2,5) to (3 1/2,-12)
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Questions like these are really simple to answer, for one, all you have to know is Rise over Run (or Rise/Run)...
This being:
Rise: the distance from one y value to the other...
Run: the distance from one x value to the other...
Naturally graph points are represented as (x, y).
So, all we need to is do the math....
For Rise: the distance from 5 to -12 is 17...
For Run: the distance from 3.5 (or 3 1/2) to 3.5 is 0, but because the denominator of ANY fraction can never be 0, we will change it to 1...
So, our equation looks like: 17/1 (or 17 over 1)...
And our answer is: The 2 points are EXACTLY 17 units apart...
A Ferris wheel has a diameter of 42 feet. It rotates 3 times per minute. Approximately how far will a passenger travel during a 5-minute ride?
132 feet
659 feet
1,978 feet
3,956 feet
Approximately 1978 ft a passenger travel during a 5-minute ride and this can be determined by using the formula of the perimeter of a circle.
Given :
A Ferris wheel has a diameter of 42 feet. It rotates 3 times per minute.
The following steps can be used in order to determine the total distance travel by the passenger during a 5 minutes ride:
Step 1 - First determine the perimeter of the circle. The formula of the perimeter of the circle is given by:
[tex]\rm C = 2\pi r[/tex]
Step 2 - Now, substitute the value of known terms in the above formula.
[tex]\rm C=2\pi\times(21)[/tex]
[tex]\rm C= 131.94\;ft[/tex]
Step 3 - In one minute passenger travels:
[tex]\rm =131.94\times 3=395.82\; ft[/tex]
Step 4 - So, in three minutes passenger travels:
[tex]=395.82\times5[/tex]
= 1978 ft
So, approximately 1978 ft a passenger travel during a 5-minute ride.
For more information, refer to the link given below:
https://brainly.com/question/23450266
Describe how the graph of y=|x| – 4 is like the graph of y= |x| – 4 and how it is different.
The graphs of y = |x| and y = |x| - 4 are similar in their overall V-shape and slope behavior, but differ in their vertical position due to the constant term difference in the equations. The second graph is essentially a downward translation of the first by 4 units.
Similarities:
Both represent absolute value functions.
Both graphs pass through the origin (0, 0)
Both graphs have a slope of 1 for positive values of x and a slope of -1 for negative values of x.
Differences:
The graph of y = |x| - 4 is shifted downwards by 4 units
The y-intercept is different for both graphs.
Given a polynomial function f(x), describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and the end behavior when the following changes are made. Make sure to account for even and odd functions.
-When f(x) becomes f(x) + 2
-When f(x) becomes −(1 / 2) * f(x)
Answer:
f(x) + 2 is translated 2 units up and -(1/2)*f(x) is reflected across x-axis.
Step-by-step explanation:
We have f(x) becomes f(x) + 2.
The y-intercept of f(x) is f(0), implies that y-intercept of f(x) + 2 is f(0) + 2. This means that the graph of f(x) is translated 2 units upwards.
Moreover, the region where f(x) increases will be the same region region where f(x) + 2 increases and there will not any change in the size of the figure.
Now, we have f(x) becomes -(1/2)*f(x).
The y-intercept of -(1/2)*f(x) is -(1/2)*f(0). This means that the graph is dilated by 1/2 units and then reflected across x-axis.
Moreover, the region where f(x) increases will be the opposite region region where -(1/2)*f(x) increases and the size of the figure will change as dilation of 1/2 is applied to f(x)
Answer with Explanation
Let the polynomial function which is an odd function, be
[tex]f(x)=x^5+x^3+x[/tex]
f(-x)= - f(x)
So,it is an odd function.
The function will pass through first and fourth quadrant.
Y intercept =0
Function is increasing in it's domain [-∞, ∞]
1. When f(x) becomes f(x)+2
g(x)=f(x) +2
This function will shift 2 units up, and it will not pass through the origin and has Y intercept equal to 2.
This function will also pass through first and fourth quadrant.
Function is an increasing function in it's domain [-∞, ∞]
Now, when f(x) becomes [tex]\frac{-f(x)}{2}[/tex]
The function will pass through second and fourth Quadrant,due to negative sign before it, and distance from y axis either in second Quadrant or in fourth Quadrant increases by a value of [tex]\frac{1}{2}[/tex].
Here also, Y intercept =0
Function is a decreasing function in it's domain [-∞, ∞]
Now, taking the even function
[tex]f(x)=x^6+x^4+x^2[/tex]
f(-x)= f(x)
So,it is an even function.
The function will pass through first and second quadrant equally spaced on both side of y axis.
Y intercept =0
Function is decreasing in [-∞,0) and increasing in (0, ∞]
1. When f(x) becomes f(x)+2
g(x)=f(x) +2
This function will shift 2 units up, and it will not pass through the origin and has Y intercept equal to 2.
This function will also pass through first and third quadrant.
Function is decreasing from [-∞,2) and increasing in (2, ∞]
Now, when f(x) becomes [tex]\frac{-f(x)}{2}[/tex]
The function will pass through third and fourth Quadrant,due to negative sign before it, and function expands by the value of [tex]\frac{1}{2}[/tex] on both sides of Y axis.
Here also, Y intercept =0
Function is increasing in [-∞,0) and decreasing in (0, ∞].
What is the graph of the function f(x) = the quantity of negative x squared plus 4 x plus 6, all over x plus 4? I am stressing over this question is just confusing for me help me please
Answer:
The graph of the function is given below.
We are given the function, [tex]f(x)=\frac{-x^2+4x+6}{x+4}[/tex]
We see that, when x= 0, the value of the function is,
[tex]f(0)=\frac{-0^2+40+6}{x+0}[/tex] i.e. [tex]f(0)=\frac{6}{4}=\frac{3}{2}[/tex].
So, the y-intercept is [tex](0,\frac{3}{2})[/tex].
Also, the zeroes of the function are given by,
[tex]f(x)=\frac{-x^2+4x+6}{x+4}=0[/tex]
i.e.[tex]-x^2+4x+6=0[/tex]
i.e. (x+1.162)(x-5.162)=0
i.e. x= -1.162 and x= 5.162
Thus, the x-intercept are (0,-1.162) and (0,5.162).
The graph of the function is given below.
How many arrangements of the letters in the word o l i v e can you make if each arrangement must use three letters?
A. 60
B. 5 · 4 · 3 · 2 · 1
C. 20
D. 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1
Chef Pierre can do something unique. Using a secret process, he can bake a nearly perfectly spherical pie consisting of a vegetable filling inside a thick crust. The radius of the whole pie is 12 cm, and the radius of the filling is 8 cm. What is the volume of the crust alone, to the nearest unit? Use p = 3.14.
The volume of Chef Pierre's pie crust is calculated by subtracting the volume of the vegetable filling from the volume of the entire pie, yielding approximately 5,091 cm³.
Explanation:To determine the volume of the crust of Chef Pierre's spherical pie, we need to calculate the volume of the entire pie and then subtract the volume of the vegetable filling. The formula for the volume of a sphere is V = (4/3)πr³. First, we calculate the volume of the whole pie (including crust) with a radius of 12 cm, and then the volume of the vegetable filling with a radius of 8 cm.
Volume of whole pie: Vwhole = (4/3)π(12 cm)³ = (4/3) * 3.14 * (12 cm)³ ≈ (4/3) * 3.14 * 1,728 cm³ ≈ 7,238.56 cm³
Volume of vegetable filling: Vfilling = (4/3)π(8 cm)³ = (4/3) * 3.14 * (8 cm)³ ≈ (4/3) * 3.14 * 512 cm³ ≈ 2,147.97 cm³
Subtract the volume of the filling from the volume of the whole pie to get the volume of the crust alone:
Volume of crust alone: Vcrust = Vwhole - Vfilling ≈ 7,238.56 cm³ - 2,147.97 cm³ ≈ 5,090.59 cm³
To the nearest unit, the volume of the crust is approximately 5,091 cm³.
Write an expression for the number of hours in an unknown number of minutes.
In mathematics, the nth harmonic number is defined to be 1 + 1/2 + 1/3 + 1/4 + ... + 1/n. so, the first harmonic number is 1, the second is 1.5, the third is 1.83333... and so on. write an expression whose value is the 8th harmonic number.
The nth harmonic number is defined to be 1 + 1/2 + 1/3 + 1/4 + ... + 1/n. the first harmonic number is 1.5 , the second is 1.5 the third is 1.83333... and soon, the harmonic expression will be written as follows
Given:
a1 = first term = 1
a2 = second term = 1.5
a3 = third term = 1.83333...
We will write expression in Harmonic term, as
= [tex]\rm 1.0 + \dfrac{1.0}{2.0} + \dfrac{1.0}{3.0} + \dfrac{1.0}{4.0} + \dfrac{1.0}{5.0} + \dfrac{1.0}{6.0} + \dfrac{1.0}{7.0} +\dfrac{ 1.0}{8.0}[/tex]
Learn more about Harmonic expressions here: https://brainly.com/question/12788282
Solve:The quantity 2 x minus 20 divided by 3= 2x
The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product.
The minimum cost of producing this product is:
13
Step-by-step explanation:The function which is used to represent the cost to produce x elements is given by:
[tex]f(x)=5x^2-70x+258[/tex]
Now, on simplifying this term we have:
[tex]f(x)=5(x^2-14x)+258\\\\i.e.\\\\f(x)=5(x^2+49-49-14x)+258\\\\i.e.\\\\f(x)=5((x-7)^2-49)+258\\\\i.e.\\\\f(x)=5(x-7)^2-5\times 49+258\\\\i.e.\\\\f(x)=5(x-7)^2-245+258\\\\i.e.\\\\f(x)=5(x-7)^2+13[/tex]
We know that:
[tex](x-7)^2\geq 0\\\\i.e.\\\\5(x-7)^2\geq 0\\\\i.e.\\\\5(x-7)^2+13\geq 13[/tex]
This means that:
[tex]f(x)\geq 13[/tex]
This means that the minimum cost of producing this product is: 13
You have 4500 cubic centimeters of wax. how many cylindrical candles can you make from the wax if each candle is 15 centimeters tall and has a diameter of 10 centimeters?
The number of cylindrical candles of 15cm height and 10cm diameter to be made from 4500[tex]cm^{3}[/tex] of wax is : 3.81 approximately 4
What is a cylinder?A cylinder is a solid geometrical shape with two parallel sides and two oval or circular cross-sections.
Analysis:
Given data:
Volume of wax = 4500[tex]cm^{3}[/tex]
Diameter of candle = 10cm
Radius of candle = diameter/2 = 10/2 = 5cm
Height of candle = 15cm
Volume of each cylindrical candle = π[tex]r^{2}[/tex]h
Volume of each cylindrical candle = [tex]\frac{22}{7}[/tex] x [tex](5)^{2}[/tex] x 15 = [tex]\frac{8250}{7}[/tex][tex]cm^{3}[/tex]
Volume of wax = n x volume of each cylindrical candle
n = number of candles
n = [tex]\frac{volume of wax}{volume of each cylindrical candle}[/tex]
n = [tex]\frac{4500}{\frac{8250}{7} }[/tex] = 3.81 approximately 4
In conclusion, the number of cylindrical candles to be made from 4500 cubic centimeters wax is 4.
Learn more about cylinders: brainly.com/question/9554871
#SPJ2
Final answer:
To find the number of cylindrical candles that can be made from a given volume of wax, one needs to calculate the volume of one candle with the formula for the volume of a cylinder and then divide the total wax volume by a single candle's volume.
Approximately 3 candles can be made from 4500 cm^3 of wax if each candle is 15 cm tall with a 10 cm diameter.
Explanation:
To calculate the number of cylindrical candles that can be made from 4500 cubic centimeters of wax, with each candle being 15 centimeters tall and with a diameter of 10 centimeters, we use the formula for the volume of a cylinder, V = πr^2h.
First, we need to calculate the radius of the cylinder by dividing the diameter by 2. The diameter is 10 cm, so the radius is 5 cm. Next, we apply the formula to find the volume V of one candle:
V = (π)(5 cm)^2(15 cm) = 3.14159 × 25 cm^2 × 15 cm = 1177.5 cm^3 approximately
To find out how many candles we can make, we divide the total volume of wax by the volume of one candle:
{4500 cm^3/}{1177.5 cm^3} approx 3.82
As it is not possible to make a fraction of a candle, you can make 3 complete candles with the given amount of wax.
What is the discriminant of 3x^2-10x=-2?
the discriminant of the equation [tex]\(3x^2 - 10x + 2 = 0\)[/tex] is [tex]\(76\)[/tex].
To find the discriminant of the quadratic equation [tex]\(3x^2 - 10x + 2 = 0\)[/tex], we first need to rewrite it in the standard form [tex]\(ax^2 + bx + c = 0\)[/tex].
The given equation is [tex]\(3x^2 - 10x + 2 = 0\)[/tex].
Comparing it with the standard form [tex]\(ax^2 + bx + c = 0\)[/tex], we have:
- [tex]\(a = 3\)[/tex],
- [tex]\(b = -10\)[/tex],
- [tex]\(c = 2\).[/tex]
The discriminant [tex](\(D\))[/tex] of a quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex] is given by the formula:
[tex]\[ D = b^2 - 4ac \][/tex]
Substituting the values of [tex]\(a\), \(b\)[/tex], and [tex]\(c\)[/tex], we get:
[tex]\[ D = (-10)^2 - 4 \cdot 3 \cdot 2 \][/tex]
[tex]\[ D = 100 - 24 \][/tex]
[tex]\[ D = 76 \][/tex]
So, the discriminant of the equation [tex]\(3x^2 - 10x + 2 = 0\)[/tex] is [tex]\(76\)[/tex].
The Partnership for 21st Century Learning lists core subject areas that all employees need to know about. What are two of those core subjects?
A. Economics and mathematics
B. Technology and citizenship
C. Art and Latin
D. Vocational skills and English
The Partnership for 21st Century Learning identifies Economics and Mathematics as two core subjects necessary for employee knowledge, essential for developing critical thinking and problem-solving skills in the global economy. Hence the correct answer is option A
Explanation:The Partnership for 21st Century Learning lists Economics and Mathematics as two core subject areas that are essential for all employees to have knowledge about. These subjects are foundational to understanding the global economy and are associated with the skills needed by "knowledge workers" such as engineers, scientists, doctors, teachers, financial analysts, and computer programmers. A strong grounding in Economics and Mathematics equips students with valuable skills such as critical thinking, problem-solving, and the ability to analyze complex data, which are highly sought after in the modern workforce.
As per the Partnership for 21st Century Learning, to support the quality of American education, it's crucial to prepare students with a well-rounded understanding of core disciplines, including Economics and Mathematics. This preparation is significant in light of increasing global competition and the need for American students to improve in reading, math, and critical thinking to match or exceed the capabilities of their peers in other industrialized nations.
Hence the correct answer is option A
(05.03 MC)
Eva has borrowed 200 songs from her friend. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x:
A graph titled Song Downloading shows Number of Weeks on x-axis and Number of Songs Left to Download on y-axis. The x-axis scale is shown from 0 to 5 at increments of 1, and the y-axis scale is shown from 0 to 280 at increments of 40. A straight line joins the ordered pairs 0, 200 and 1, 160 and 2, 120 and 3, 80 and 4, 40 and 5, 0.
Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points)
Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
A) The rate of change is -40 songs each week, that is because the amount of songs left to be downloaded decrease by 40 each week
B) lets use 2 points of the graph p1(0, 200), p2(1, 160)
calculate the slope:
m = (y2- y1)/(x2 - x1) = (160 - 200)/(1 - 0)
m = -40
now use line equation in form point-slope:
y - y1 = m(x - x1)
y - 200 = -40(x - 0)
y = -40x + 200
Part A:
Each week the amount of songs that need to download decreases by 40. So The rate of change is -40 songs each week. The initial value is 200 because that is the number of songs left to download.
Part B:
y = -40x + 200
Find the X intercepts of the parabola with the vertex (1,-9) and y intercept of (0,-6)
The x-intercepts of the parabola with vertex (1,-9) and y-intercept of (0,-6) are of [tex]x = 1 \pm \sqrt{3}[/tex].
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the parabola has vertex (1,-9), hence h = 1, k = -9, and:
y = a(x - 1)^2 - 9.
The y-intercept is of (0,-6), hence when x = 0, y = -6, and this is used to find a.
-6 = a - 9
a = 3.
So the equation is:
y = 3(x - 1)^2 - 9.
y = 3x² - 6x - 6.
The x-intercepts are the values of x for which:
3x² - 6x - 6 = 0.
Then:
x² - 2x - 2 = 0.
Which has coefficients a = 1, b = -2, c = -2, hence:
[tex]\Delta = b^2 - 4ac = (-2)^2 - 4(1)(-2) = 12[/tex]
[tex]x_1 = \frac{2 + \sqrt{12}}{2} = 1 + \sqrt{3}[/tex]
[tex]x_2 = \frac{2 - \sqrt{12}}{2} = 1 - \sqrt{3}[/tex]
The x-intercepts of the parabola are [tex]x = 1 \pm \sqrt{3}[/tex].
More can be learned about quadratic equations at https://brainly.com/question/24737967
#SPJ2
Solve for x and y:
28x−49y=35
4x−7y=5
Select one:
a. The solution is (0, 0).
b. There are an infinite number of solutions.
c. There is no solution.
d. x=3,y=1
If the height of Mount Everest is about 8.8×10^3 meters, and the height of the Empire State Building is about 3.8×10^2 meters, which of these statements is true?
A.There is no way to compare these heights
B.Mount Everest is about 40 times as tall as the Empire State Building
C.Mount Everest is about 23 times as tall as the Empire State Building
D.The Empire State Building is about 23 times as tall as Mount Everest
Step-by-step explanation:
Height of Mount Everest = 8.8 x 10³ m = 8800 m
Height of the Empire State Building = 3.8 x 10² m = 380 m
[tex]\frac{\texttt{Height of Mount Everest}}{\texttt{Height of the Empire State Building}}=\frac{8800}{380}\\\\\frac{\texttt{Height of Mount Everest}}{\texttt{Height of the Empire State Building}}=23.16[/tex]
Height of Mount Everest = 23 x Height of the Empire State Building.
So, Mount Everest is about 23 times as tall as the Empire State Building
Option C is the correct answer.
What is the value of y so that the line segment with endpoints A(−3, y) and B(6, −4) is parallel to the line segment with endpoints C(7, 6) and D(−2, 8)?
y = −7
y = 1
y=1/2
y = −2
To make line segment AB parallel to line segment CD, we calculate the slope of CD and ensure AB has the same slope. The slope of CD is −1/4.5, and setting the slope of AB equal to this value leads to the conclusion that y = −2 for point A.
Explanation:To determine the value of y such that the line segment with endpoints A(−3, y) and B(6, −4) is parallel to the line segment with endpoints C(7, 6) and D(−2, 8), we need to ensure that the slope of line AB is equal to the slope of line CD. The slope m of a line passing through two points (x1, y1) and (x2, y2) is given by m = (y2 − y1) / (x2 − x1).
For line CD, the slope is (8 − 6) / (−2 − 7) = 2 / (−9) = −1/4.5. To find the value of y for point A so that line AB is parallel to CD, we need to set the slope of AB equal to −1/4.5:
(−4 − y) / (6 − (−3)) = −1/4.5
(−4 − y) / 9 = −1/4.5
−4 − y = −9 / 4.5
y = −4 + 2 = −2
Therefore, the correct value of y that makes line AB parallel to line CD is −2.
When graphed,a system shows the exact same lines. How many solutions will the system have?
What is the answer to 40-2a squared when a=4?
A rectangular shipping container has a volume of 2500 cubic cm. The container is 4 times as wide as it is deep, and 5cm taller than it is wide. What are the dimensions of the contaner?
The question asks for the dimensions of a rectangular container with given volume and specific proportional relationships between its dimensions. Setting up and solving the equation 2500 = d × (4d) × (4d + 5) leads us to find the distinct depth, width, and height of the container.
Explanation:The subject matter of the student's question pertains to the mathematics concepts of volume and dimensional relationships of rectangular prisms. Let's represent the depth of the shipping container as d, the width as 4d (since it is four times the depth), and the height as 4d + 5 (since it is 5cm taller than the width). The volume of a rectangular prism (such as our shipping container) is given by the formula Volume = length × width × height. Given the volume is 2500 cubic cm, or 2500 cm³, we can set up the equation 2500 = d × (4d) × (4d + 5).
Solving this equation leads us to find the dimensions of the container, wherein the depth, width, and height are represented by the variables d, 4d, and 4d + 5
Learn more about Volume of Rectangular Prism here:https://brainly.com/question/18097475
#SPJ3
Transform (5 square root x^7)^3 into an expression with a rational exponent
In order to transform (5 square root x^7)^3 into an expression with a rational exponent, first transform square root x^7 into x^(7/2), then raise entire expression to the power of 3. So, final expression is 125x^(21/2).
Explanation:To transform (5 square root x^7)^3 into an expression with a rational exponent, firstly simplify the expression inside the bracket, then apply the exponent of 3 to the simplified expression.
Inside the brackets, square root of x^7 can be written as x^(7/2). So, the first parenthesis can be transformed into 5x^(7/2). Now, raise this to the power of 3. The rule for powers of powers is to multiply the powers. So, 5 cubed is 125 and (x^(7/2))^3 is x^(21/2).
So, the transformed expression with a rational exponent is 125x^(21/2).
Learn more about Exponent Conversion here:https://brainly.com/question/29149659
#SPJ2
Edgar started with 2 poems in his journal. Then he started writing 3 poems each day. Which of the following graphs represents Edgar's poem writing
Answer:
Let x represents the number of the days, and y represents total number of the poem.
According to the question,
Edgar started with 2 poems in his journal. Then he started writing 3 poems each day.
Thus, the line that describes the above situation is,
y = 2 + 3 x
The x -intercept of the line is [tex](-\frac{2}{3} , 0)[/tex] or (-0.667 , 0)
And, the y-intercept of the line is (0,2)
Also, if x = 1 y = 5
if x = 2 y = 8
If x = -1 y = - 1
And, if x = - 2 , y = -4
Thus, the points by which the line will pass are,
(1,5), (2,8) , (-1,-1) and (-2,-4)
Therefore, with the help of the above information we can plot the graph of the line. ( shown below)
When a pair of six sided dice is rolled , each with faces numbered 1 to 6,is rolled once,what is the probability that the result is either 3 and 4 or a 5 and a prime number?
A shipment of racquetballs with a mean diameter of 60 mm and a standard deviation of 0.9 mm is normally distributed. By how many standard deviations does a ball bearing with a diameter of 58.2 mm differ from the mean?
Answer:
By 2 standard deviations a ball does bearing with a diameter of 58.2 mm differ from the mean.
Step-by-step explanation:
It is given that a shipment of racquetballs with a mean diameter of 60 mm and a standard deviation of 0.9 mm is normally distributed.
[tex]Mean=60[/tex]
[tex]\text{Standard deviation}=0.9[/tex]
Absolute difference written diameter of 58.2 mm and average diameter is
[tex]|58.2-60|=1.8[/tex]
Divide the difference by standard deviation (i.e.,0.9), to find the by how many standard deviations does a ball bearing with a diameter of 58.2 mm differ from the mean.
[tex]\frac{1.8}{0.9}=2[/tex]
Therefore 2 standard deviations a ball does bearing with a diameter of 58.2 mm differ from the mean.
Candy Crunchers wants to see if their new candy is enjoyed more by high school or middle school students. They decide to visit one middle school and one high school in Miami, FL. After interviewing 100 students at each school, they determine that high school students like their candy more than the middle school students do. What is the sample of the population?