Answer: 30 in
Step-by-step explanation:
Multiply the length and width and divide the number you get from 2175.
Brainliest Please!
Complete the table by finding the circumference and area of a circle with a radius of 279 inches. Substitute 3.14 for pi. Express your answers to the hundredths place.
fill in the blanks
thx
Answer:
Circumference = 558π inches
= 1,752.12 inches
Area = π(279^2)
= 77,841π square inches
= 244,420.74 square inches
In circle
�
L,
�
�
=
9
LM=9 and the area of shaded sector =
27
�
27π. Find the length of
�
�
⌢
MN
⌢
. Express your answer as a fraction times
�
π.
The requried length of the arc MN is evaluated as 6π.
From the figure,
The area of the shaded sector is given as:
A = ∠NLM/360×πr²
27π= ∠NLM/360×π9²
∠NLM = 120
Now,
length MN = 120/360*2πr
= 1/3×2π×9
= 6π
Thus, the requried length of the arc MN is evaluated as 6π.
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which of the following statements appropriately describe theoretical hypotheses? check all that apply. a theoretical hypothesis is a hypothesis that can never be proved, but only confirmed. a theoretical hypothesis is a hypothesis that attempts to provide an explanation for a scientific question or phenomenon. a theoretical hypothesis is a hypothesis that can be proved with empirical evidence. a theoretical hypothesis is a hypothesis that can be proved by evidence from observation.
A theoretical hypothesis is a hypothesis that attempts to provide an explanation for a scientific question or phenomenon by proposing a theoretical framework or model. (option b).
Theoretical hypotheses are often used in scientific research to guide investigations and to help researchers make predictions about what they expect to observe. They are essential to the scientific method because they provide a basis for developing testable predictions and designing experiments to confirm or reject them.
A theoretical hypothesis is a hypothesis that attempts to provide an explanation for a scientific question or phenomenon.
This statement is accurate. As discussed earlier, a theoretical hypothesis is a type of hypothesis that proposes a theoretical framework or model to explain a scientific question or phenomenon.
Therefore, statement b is the most accurate description of a theoretical hypothesis.
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how many different normal forms as in theorem 4 are there for nilpotent endomorphisms of a 4-dimensional vector space?
There are two different normal forms, namely a single Jordan block of size 4 or two Jordan blocks of sizes 3 and 1, for nilpotent endomorphisms of a 4-dimensional vector space.
Cayley-Hamilton Theorem, states that every matrix satisfies its own characteristic polynomial. However, it is not directly related to the concept of normal forms.
To answer your question, we can use the Jordan Normal Form theorem, which states that every linear operator (or endomorphism) on a finite-dimensional vector space over an algebraically closed field (such as the complex numbers) is similar to a matrix in Jordan normal form.
For a nilpotent endomorphism on a 4-dimensional vector space, there are two possible Jordan normal forms: either a single Jordan block of size 4 with eigenvalue 0, or two Jordan blocks of sizes 3 and 1, also with eigenvalue 0.
Therefore, there are two different normal forms for nilpotent endomorphisms of a 4-dimensional vector space.
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brainliest, multiple choice, and 100 points! i really appreciate the help, and please let me know if you need help on anything, thanks!!
Answer:
Triangle congruence cannot be determined with the given information.
darren picked 25 2525 flowers that he plans to divide evenly into 3 33 vases. he will use as many flowers per vase as he can, but may have flowers left. how many flowers will be in each vase? answer must be a whole number. flowers how many flowers remain without a vase? answer must be a whole number. flowers
Each vase will have 8 flowers and there will be 1 flower remaining without a vase.
To solve the problem, we first need to determine the total number of flowers that Darren picked, which is given as 25.
Next, we need to divide the flowers into 3 vases as evenly as possible. To do this, we can use integer division to determine how many flowers will go into each vase. Integer division only considers whole numbers, so any remainder will be left over.
Dividing 25 flowers by 3 vases gives us:
25 ÷ 3 = 8 R1This tells us that each vase will have 8 flowers, with 1 flower remaining.
Therefore, the answer is that each vase will have 8 flowers, and there will be 1 flower remaining without a vase.
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Charlotte is redecorating the master bedroom in her house. She has purchased a new bedroom set and also plans to
paint the room and put in new flooring. The room is rectangular, with dimensions of (160 feet (length) by \(13\frac(1)
(210) feet (width). The walls in the room are 9 feet tall, and the room contains two doors and two windows.
Charlotte has decided to put new carpet in the bedroom. The carpet she chose costs $1.85 per square foot, not
Including the cost of labor or other related materials. She was given the following information by the local flooring store
where she is purchasing the carpet.
She is required to purchase a plece of carpet which includes a 3-inch overlap on all sides. Labor and material costs
will relate to the area of this plece.
The labor costs are $23 per hour, per person.
A two-person carpet crew can lay 50 square feet of carpet each hour.
The crew that will complete the job at Charlotte's house will be a four-person crew.
There is an additional $75 fee to cover the cost of equipment, materials, and supplies.
What are the dimensions of the plece of carpet that Charlotte must purchase? Note: Express your answer as a decimal
number and do not round.
Answer:
The dimensions of the piece of carpet that Charlotte must purchase is 160.5 feet by 13.5 feet, and the total cost of the carpet, including labor and materials, is $5088.95
Step-by-step explanation:
To determine the dimensions of the piece of carpet that Charlotte must purchase, we need to add the overlap to the length and width of the room.
The overlap is 3 inches, which is 0.25 feet (since there are 12 inches in a foot and 3/12 = 0.25).
So the length of the piece of carpet needed is 160.5 feet (160 + 0.25 + 0.25), and the width is 13.5 feet (13.25 + 0.25 + 0.25).
To find the area of the piece of carpet needed, we multiply the length by the width:
160.5 feet x 13.5 feet = 2166.75 square feet
Now we need to add the extra area needed for the overlap, which is:
0.25 feet x 0.25 feet x 4 (since there are 4 sides) = 0.25 square feet
So the total area of the piece of carpet needed is:
2166.75 square feet + 0.25 square feet = 2167 square feet
To determine the labor and material costs, we need to find the area of the plece (piece) of carpet, including the overlap.
The labor costs are $23 per hour, per person, and the crew can lay 50 square feet of carpet each hour. So the total labor cost will be:
4 people x $23 per hour per person = $92 per hour
To determine how many hours it will take to lay the carpet, we divide the total area of the plece by the rate at which the crew can lay carpet:
2167 square feet ÷ (4 people x 50 square feet per hour) = 10.835 hours
We will need to round up to the nearest whole number since the crew cannot work for a fraction of an hour. So it will take 11 hours to lay the carpet.
The cost of materials will be:
2167 square feet x $1.85 per square foot = $4001.95
The cost of labor and materials will be:
11 hours x $92 per hour = $1012
$1012 + $4001.95 + $75 equipment/materials/supplies fee = $5088.95
Therefore, the dimensions of the plece of carpet that Charlotte must purchase is 160.5 feet by 13.5 feet, and the total cost of the carpet, including labor and materials, is $5088.95.
Sam is visiting a local shopping mall that has a rectangular shape with a diagonal walkway that goes from the entrance of the mall to the food court. The floor plan is shown
1,600
Restroom,
Food Court
Entrance Electronics Sports Store
Store
Sam needs to stop at the sports store on the way to the food court. How much longer, in feet, does he walk than if he walks directly from the entrance to the food court along the diagonal
walkway? Show work to justify your answer.
BI U G X₂
=
Answer:
262.8 feet
Step-by-step explanation:
To determine how much longer Sam walks, we need to calculate the distance of his actual path compared to the diagonal walkway. Using the Pythagorean theorem, we can calculate the diagonal walkway's length as follows:
diagonal walkway = √(1600² + 400²) = √(2560000) = 1600√2 ≈ 2,262.8 feet
To find Sam's actual path, we can add the distance from the entrance to the sports store (200 feet) and the distance from the sports store to the food court (800 feet):
actual path = 200 + 800 = 1000 feet
The difference between the actual path and the diagonal walkway is:
1000 - 1600√2 ≈ -262.8 feet
Since the result is negative, it means that Sam walks approximately 262.8 feet less than if he walks directly from the entrance to the food court along the diagonal walkway.
Which inequality is represented by this graph?
A: y/2 >4-x
B:y>4-x/2
C:y<4-x/2
D:y/2<4-x
An inequality that is represented by this graph include the following: C. y ≤ (4 - x)/2.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (1 - 3)/(2 + 2)
Slope (m) = -2/4
Slope (m) = -1/2.
At data point (2, 1) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = -1/2(x - 2)
y = -x/2 + 1 + 1
y = -x/2 + 2
y ≤ (4 - x)/2 (since the solid line is shaded below)
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Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it.
lim (ln(x))²/7x
x→[infinity]
Here, x approaches infinity, the fraction 2/(7x) approaches 0. Therefore, the limit is: lim (ln(x))²/7x as x → ∞ = 0. To get the limit of (ln(x))²/7x as x approaches infinity, we can first try using l'Hospital's Rule. However, we should first check if the conditions to apply l'Hospital's Rule are met. In this case, we have:
Step:1. lim (ln(x))²/7x as x → ∞. As x goes to infinity, ln(x) also goes to infinity. So, we have an indeterminate form ∞/∞, which means we can apply l'Hospital's Rule. Taking derivatives of both numerator and denominator with respect to x, we get:
Numerator derivative: d/dx [(ln(x))²] = 2ln(x) * (1/x) = 2ln(x)/x
Denominator derivative: d/dx [7x] = 7
Step:2. Applying l'Hospital's Rule, we have:
lim (2ln(x)/x) / 7 as x → ∞
Step:3. Simplifying the expression, we get: lim (2ln(x))/(7x) as x → ∞
Step:4. Now we can apply l'Hospital's Rule again, since we still have an indeterminate form ∞/∞:
Numerator derivative: d/dx [2ln(x)] = 2/x
Denominator derivative: d/dx [7x] = 7
Applying l'Hospital's Rule, we have: lim (2/x) / 7 as x → ∞
Step:5. Simplifying the expression, we get: lim 2/(7x) as x → ∞
Now, we can see that as x approaches infinity, the fraction 2/(7x) approaches 0. Therefore, the limit is: lim (ln(x))²/7x as x → ∞ = 0
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The sum of two numbers is 45 the difference is 15 what are the numbers
The two numbers are 30 and 15.
What is equation?An equation is a statement that asserts the equality of two mathematical expressions. It typically consists of two sides separated by an equal sign (=), where each side contains one or more variables and mathematical operations.
Let's call the two numbers "x" and "y".
From the problem statement, we know:
[tex]x + y = 45[/tex] (equation 1)
[tex]x - y = 15[/tex] (equation 2)
We can solve this system of equations by adding equation 1 and equation 2:
[tex](x + y) + (x - y) = 45 + 15[/tex]
Simplifying the left side of the equation:
[tex]2x = 60[/tex]
Dividing both sides by 2:
[tex]x = 30[/tex]
Now that we know x, we can use equation 1 to solve for y:
[tex]30 + y = 45[/tex]
Subtracting 30 from both sides:
y = 15
Therefore, the two numbers are 30 and 15.
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The two numbers are 30 and 15.
What is equation?
An equation is a statement that asserts the equality of two mathematical expressions. It typically consists of two sides separated by an equal sign (=), where each side contains one or more variables and mathematical operations.
Let's call the two numbers "x" and "y".
From the problem statement, we know:
x=y=45 (equation 1)
x-y=15 (equation 2)
We can solve this system of equations by adding equation 1 and equation 2:
(x+y)+(x-y)=45+15
Simplifying the left side of the equation:
2x=60
Dividing both sides by 2:
x=30
Now that we know x, we can use equation 1 to solve for y:
30+y=45
Subtracting 30 from both sides:
y = 15
Therefore, the two numbers are 30 and 15.
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Find the area of the regular polygon with the given radius or apothem.
(Simplify your answer. Type an exact answer using radicals as needed.)
The area of the regular polygon with 4 sides and an apothem of 12 cm is 576 square cm.
The given apothem of the polygon is 12 cm.
The area of a regular polygon with 4 sides (a square):
Area = 2 × apothem × perimeter / 4
Since a square has four equal sides, the perimeter of the square is given by:
Perimeter = 4 × side length
So, the side length by using the formula for the apothem of a regular polygon with 4 sides:
Apothem = side length / 2
Solving for side length, we get:
side length = apothem × 2 = 12 × 2 = 24 cm
Now we can find the perimeter:
Perimeter = 4 × side length = 4 × 24 = 96 cm
Substituting the values of apothem and perimeter in the area formula, we get:
Area = 2 × 12 × 96 / 4 = 2 × 12 × 24 = 576 square cm
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A carpenter is framing windows in a house he used feet of wood on the project if the windows are all same size how many feet of wood on the
The total amount of wood needed would be -
X = 2w(l + b).
Assume that the total number of windows made by the carpenter are {w}.
Let the dimensions of each of the window be {l} x {b} respectively.
The total amount of wood needed for one window would be -
x = 2(l + b)
For all the windows, the total amount of wood needed would be -
X = 2w(l + b).
Therefore, the total amount of wood needed would be -
X = 2w(l + b).
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By what number should(-3) ki power upon2 be divided to give the quotient as (4) ki power3 upon27
To obtain the quotient (4/27)⁻², (-3/2)⁻³ should be divided by -128/6561, and the result is -1/27.
To solve the problem, we need to simplify (-3/2)⁻³ and (4/27)⁻², and then find the quotient between them.
First, let's simplify (-3/2)⁻³
(-3/2)⁻³ = (2/-3)³ = -8/27
Next, let's simplify (4/27)⁻²
(4/27)⁻² = (27/4)² = 729/16
Now, we need to divide -8/27 by 729/16
(-8/27) ÷ (729/16) = (-8/27) × (16/729)
Multiply the numbers
= -128/6561
Therefore, we should divide (-3/2)⁻³ by -128/6561 to get the quotient (4/27)⁻².
(-3/2)⁻³ ÷ (-128/6561) = -1/27
So, (-3/2)⁻³ should be divided by -128/6561 to get the quotient (4/27)⁻², which is equal to -1/27.
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The given question is incomplete, the complete question is:
By what number should (-3/2)⁻³ be divided so that the quotient may be (4/27)⁻²
The spinner face shown is divided into 8 equal sections. 1, 2, 1, 2, 4, 2, 5, 3. The arrow on this spinner is spun once. What is the probability that the arrow will land on a section labeled with a number greater than 3?
Answer: 1/4
Step-by-step explanation:
There are 8 possible outcomes
there are 2 possible times that the number is greater than 3
so you have a 2 out of 8 chance of getting a number greater than 3
2/8=1/4
if tan (x+y)=4/3 and tan x=5/13. evaluate tan y
What is the value of of 3 1/4 - 1 7/8
Answer:
The solution is 11/8
Step-by-step explanation:
3 1/4 - 1 7/8
= 13/4 - 15/8
= 26-15/8
= 11/8
PLEASE HELP ME I REALLY NEED TO GET MY GRADE UP I INCLUDED THE GRAPH WITH THE QUESTION!!!
Graph f(x) = -2/3x -3
Use the line tool and select two points to graph the line.
Answer:
Step-by-step explanation:
In the picture are 2 dots connect the line
I plugged in 0 for x and got (0,-3)
then i plugged in -3/2 for x and got (-3/2, -2)
plotted those 2 points and drew a line connecting those 2 dots
options:
-x=2
-y=6
-y=8.1
-w=3.8
-kh=7.6
-kn=6.3
-kr=10.6
The statements that are true based on the variables around the centroid are; 1)The value of x is 2, 2)The value of y is 6 and 3) The length of KH is 7.6
How do we find the values of x and y and the lengths of the lines around the centroid?To find the value of y with the information provided about the various lengths around centroid,
KW : KR - 1:2
(2y - 8.9)/ (0.5y + 3.2) = 1/2
4y - 17.8 = 0.5y + 3.2
3.5y = 21
y =21/3.5
y = 6
KR = 0.5 × 6 + 3.2 = 6.2.
KT : KW = 1/2
7.1 x - 11. 8/ 5x - 5.2 = 1/2
14.2x - 23.6 = 5x -5.2
9.2x = 18.4
x = 2
KW = 5 × 2 - 5.2 = 4.8
KD : KH = 1/2
9w - 23.2/ 4.5w - 5.9 = 1/2
18w - 46.4 = 4.5w -5.9
13.5w = 40.5
w = 3
KH 4.5 x 3 - 5.9 = 7.6
The length of KN
KN = (5x - 5.2)
KN = (5 × 2 - 5.2)
KN = 4.8
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at the local supermarket, 2 apples and one orange cost $1.50, while 3 apples and one orange cost $1.95. how much does an orange cost?
Answer:
The orange is 60 cents.
Step-by-step explanation:
1) Calculate the cost of an apple (45 cents).
2) Take away the cost of the 2 apples from the original problem (45+45=90 cents).
3) You get the cost of 60 cents for one apple.
3A + O - (2A + O) = 1.95 - 1.5
A = 0.45
Now we can substitute this value of A into one of the original equations to solve for O:
2(0.45) + O = 1.5
O = 0.6
Thus, an orange costs $0.60 at the local supermarket.
To find the cost of an orange, we can use the system of linear equations. Let's denote the cost of an apple as "a" and the cost of an orange as "o".
From the given information, we can write two equations:
1) 2a + o = $1.50
2) 3a + o = $1.95
Now, we can solve for "o" using the following steps:
Step 1: Subtract equation 1 from equation 2 to eliminate the "o" variable:
(3a + o) - (2a + o) = $1.95 - $1.50
a = $0.45
Step 2: Substitute the value of "a" back into equation 1 to find the value of "o":
2($0.45) + o = $1.50
$0.90 + o = $1.50
Step 3: Solve for "o":
o = $1.50 - $0.90
o = $0.60
So, the cost of an orange at the local supermarket is $0.60.
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PLEASE HELPT
Out of 100 seventh and eight grade CAVA student , there wre 35 student that chose Music as their elective course and the rest chose world language . There were a Titian of 55 eight grade student and 50 of them chose world language
In Seventh grade, 30 students chose Music and 15 students chose World language while in Eight grade, 5 students chose Music and 50 students chose World language.
Simplified solution on linear algebraTotal students is 100
Total students that chose music is 35
Total students that chose world language is 100-35 = 65
Total students in eight grade is 55
Total students in seventh grade is 100-55 = 45
Students in eight grade that chose world language is 50
Students in eight grade that chose music is 55 - 50 = 5
Students in seventh grade who chose music is 35 - 5 = 30 (total students who chose music - number of eighth grade students who chose music)
Students in seventh grade who chose world language = 45 - 30 = 15 (total student in seventh grade - students in seventh grade who chose music)
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Solve the following system of equations. What is one x-value of a solution? f(x)=2x^(2)-3x-10 g(x)=x+20
a. x = -5
b. x = -3
c. x = 0
d. x = 3
Answer: x = -3
Explanation did the test
Step 2: Switch the variables in the equation from Step 1. Then solve for y. Show your work. (2 points)
Step 3: Find the inverse of g(x)=x-2/5. What does this tell you about the relationship between f(x) = 5x + 2 and g(x)? Show your work. (3 points)
The inverse of the function is g(x) = ( x - 2 )/5 and f(x) = 5x + 2 and g(x) = x - 2/5 are inverse functions of each other
Given data ,
Step 1:
Let the function be represented as f ( x )
Now , f(x) = 5x + 2 as an equation with the variable x:
f(x) = 5x + 2
Step 2:
Switch the variables in the equation from Step 1 and solve for y
Switching x and y:
x = 5y + 2
x - 2 = 5y
Dividing both sides by 5
y = (x - 2)/5
So, the equation with y as the variable is y = (x - 2)/5
Step 3:
Now , the inverse of g(x) = x - 2/5 and f(x) = 5x + 2
The inverse of a function g(x) is denoted as g⁻¹(x) and it is obtained by interchanging x and y and solving for y
Given g(x) = x - 2/5, we can switch x and y:
x - 2/5 = g^(-1)(x)
Now, we can solve for y by isolating it on one side of the equation
x - 2/5 = y
Hence , the inverse of g(x) is y = ( x - 2 )/5
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1,6kg of bananas costR36,80 what is the cost of 1kg of bananas ?
Answer:
R23
Step-by-step explanation:
1.6kg of bananas= R36.80
1kg= 36.80×1/1.6
= R23
Geometry.
Find the length of FG
Express your answer as a fraction times π
The calculated value of the length of the arc FG is 4π
Finding the length of the arc FGFrom the question, we have the following parameters that can be used in our computation:
central angle = 60 degrees
Radius = 12
Using the above as a guide, we have the following:
Arc FG = central angle/360 * 2 * π * Radius
Substitute the known values in the above equation, so, we have the following representation
FG = 60/360 * 2 * π * 12
Evaluate
FG = 4π
Hence, the length of the arc FG is 4π
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PLEASE HELP ASAP!!!!
Given the frequency table, what percentage of the students in grades 9–10 like rap music? Round to the nearest whole percent.
Band Preference for School Dance
Grade group | Rap | Rock | Country | Row totals
Grades 9–10 | 40 | 30 | 55 | 125
Grades 11–12 | 65 | 20 | 35 | 120
Column totals | 105 | 50 | 90 | 245
A.40%
B.38%
C. 32%
D.16%
Answer:
C.32%
Step-by-step explanation:
look at the column for grades 9-10 and add all of the different band preferences together: 40 + 30 + 55 = 125. Now, to find the percentage for rap music, divide the number of students for rap music by the total number of students in that grade group. 40 ÷ 125 = 0.32. Multiply by 100 to give it as a percentage. 0.32 × 100 = 32%
________________________________
C. 32%= 40 ÷ 125 × 100= 32%The Percentage of Students In Grades 9 - 10 Who Like Rap Music Is 32%________________________________
Find 2/3 and 1/6 in it simplest form, the fraction which is exactly half way between
The fraction which exactly half-way between the fractions "2/3" and "1/6", expressed in simplest-form is "5/12".
To find the fraction exactly halfway between 2/3 and 1/6, we first convert the given fractions to fractions with a common denominator.
So, 2/3 = 8/12 and 1/6 = 2/12,
Now we have the fractions "8/12" and "2/12".
To find the fraction exactly halfway between them, we take their average.
So, Average of "8/12" and "2/12" is
⇒ (8/12 + 2/12)/2,
⇒ 5/12.
Therefore, "5/12" is the fraction exactly halfway between 2/3 and 1/6.
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The given question is incomplete, the complete question is
Find the fraction which is exactly half way between 2/3 and 1/6 in it simplest form.
A box contains eight cards labeled , , , , , , , and . One card will be randomly chosen. What is the probability of choosing a letter from to ?
The probability of choosing a letter from Q to W is : 0.875
Probability Formula:The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes. The probability formula can be expressed as,
P(A) = Number of favorable outcomes/ total no. of possible outcomes
A box contains eight cards labeled P,Q,R,S,T,U,V, and W.
There is eight in total cards.
To find the probability letter from Q to W.
From Q to W, there are 7 cards
The required probability = (7 / 8) = (3 / 5) = 0.875.
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The given question is incomplete, complete question is:
A box contains eight cards labeled P,Q,R,S,T,U,V, and W. One card will be randomly chosen. What is the probability of choosing a letter from Q to W ? Write your answer as a fraction.
what is interquartile range? What is it used for? how do you calculate the position of the quartiles?
The interquartile range (IQR) is a measure of statistical dispersion, representing the difference between the first quartile (Q1) and the third quartile (Q3) in a dataset. It is used to assess the spread of the data and to identify potential outliers. The interquartile range (IQR) can be calculated as Q3 - Q1.
Interquartile range is a measure of dispersion that measures the range of the middle 50% of a dataset. It is commonly used in statistical analysis to summarize and compare the spread of different sets of data. The interquartile range is calculated by subtracting the first quartile (Q1) from the third quartile (Q3) of a dataset.
To calculate the position of the quartiles, the dataset is first ordered from smallest to largest. The first quartile (Q1) is the value at the 25th percentile of the dataset, or the value that is one-quarter of the way through the dataset.
The third quartile (Q3) is the value at the 75th percentile, or the value that is three-quarters of the way through the dataset. The second quartile (Q2) is the median, or the value that is exactly in the middle of the dataset.
Overall, the interquartile range is useful because it is less sensitive to extreme values (outliers) than other measures of dispersion such as the range or standard deviation. This makes it a valuable tool for summarizing and comparing the spread of datasets with outliers or extreme values.
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A box of fruit candy contains 50 candy pieces in five different colors: red, orange, yellow, green, and purple. willy opened the box and found that 22% , percent of the candy pieces are purple. if the box willy opened is representative of that particular brand of fruit candy, what best estimates the total number of non-purple candy pieces in 36 boxes of the same candy?
Answer: 1,404 Non-Purple Candies
Step-by-step explanation:
First, you must figure out how many are non-purple in the box of 50:
50*0.22=11
Then, you must figure out how many are NOT purple:
50-11=39
Next, since you are trying to calculate how many non-purples are in 36 boxes of that candy, you must multiply the number of non-purple found in 1 box by 36:
39*36= 1404
So, there are 1,404 Purple Candies in 36 Boxes of Candy (approximately)
The best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1,404.
If 22% of the candy pieces in one box of fruit candy are purple, then 78% (100% - 22%) of the candy pieces are non-purple. To find the best estimate of the total number of non-purple candy pieces in 36 boxes of the same candy, we need to use proportions.
Let x be the total number of candy pieces in one box of fruit candy. Then, the number of non-purple candy pieces in one box is 0.78x. Therefore, the total number of non-purple candy pieces in 36 boxes is:
36 boxes x 0.78x non-purple candy pieces per box = 28.08x non-purple candy pieces
To find the value of x, we can use the fact that the box contains 50 candy pieces in total. Therefore:
22% of x = 0.22x purple candy pieces
78% of x = 0.78x non-purple candy pieces
Total number of candy pieces = 50
Using these equations, we can solve for x:
0.22x + 0.78x = 50
1x = 50 / 0.78
x = 64.1 (rounded to one decimal place)
Therefore, each box contains approximately 64 candy pieces. And the total number of non-purple candy pieces in 36 boxes is:
28.08x non-purple candy pieces = 28.08 x 64.1 = 1802.728 non-purple candy pieces
So the best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1803 (rounded to the nearest whole number).
Let's use the terms you've provided to solve the problem step-by-step.
Step 1: Determine the number of purple candies in one box.
22% of the 50 fruit candy pieces are purple. To find this, multiply 50 by 0.22 (the decimal equivalent of 22%):
50 * 0.22 = 11 purple candy pieces
Step 2: Determine the number of non-purple candies in one box.
There are 50 fruit candy pieces in total. Subtract the 11 purple candies to find the number of non-purple candies:
50 - 11 = 39 non-purple candy pieces
Step 3: Estimate the total number of non-purple candies in 36 boxes.
To find this, multiply the number of non-purple candies in one box (39) by the number of boxes (36):
39 * 36 = 1,404
So, the best estimate for the total number of non-purple candy pieces in 36 boxes of the same candy is 1,404.
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