The closed form for the matrix l−1 is the inverse matrix of l, which corresponds to an elementary transformation of type 1, which is a row transformation.
A closed form for the matrix L-1 is given by the following formula:
L-1 = (1/det(L)) * adj(L)
Where "det(L)" represents the determinant of the matrix L, and "adj(L)" is the adjugate matrix of L. The adjugate matrix of a matrix A is the transpose of its cofactor matrix, and is denoted as adj(A). The cofactor matrix of a matrix is the matrix of determinants of the minors of the matrix multiplied by alternating signs.
The elementary transformation of type 1 is row interchange. This means that two rows of the matrix are interchanged with each other. This transformation has the same effect when applied from the left as from the right, so when multiplying with L-1 from the left, it corresponds to a row interchange.
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your friend claims that she has 30 coins containing nickels dimes and quarters the total value of the 30 coins is $3 there are twice as many nickels as there are dimes is your friend correct explain the reasoning
The stated combination of coins is not possible as the number of quarters are highly more than the number of dimes and nickels.
Let the number of dimes be x. So, the number of an nickels will be 2x. The number of quarters will be (30 - 3x). As per the known information, the one nickel is 0.05 dollars, one dime is 0.1 dollars and one quarter is with 0.25 dollars.
Now forming the expression -
x×0.1 + 2x×0.05 + (30-3x)×0.25 = 3
Performing multiplication on Left Hand Side of the equation
0.1x + 0.1x + 7.5 - 0.75x = 3
Performing addition on Left Hand Side of the equation
0.2x - 0.75x = 3 - 7.5
On subtraction we will find the value on Left Hand Side will be negative. Thus, the stated combination is not possible.
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Let A= and B=.What value(s) of k , if any , will make AB = BA ? Select the correct choice below and. if necessary fill in the answer box within your choice. A. k = D (Use a comma to separate answers as needed.) B. No value of k will make AB = BA
The value of k = −8 for which AB = BA.
[tex]A = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right][/tex]
[tex]B = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right][/tex]
Now,
[tex]AB = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right] \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right] = \left[\begin{array}{ccc}-7&18+3k\\2&-9-k\end{array}\right][/tex]
[tex]BA = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right] \left[\begin{array}{ccc}2&3\\-1&-1\end{array}\right] = \left[\begin{array}{ccc}-7&-6\\-6-k&-9-k\end{array}\right][/tex]
Thus, in order for AB = BA, we must have that
[tex]\left[\begin{array}{ccc}-7&18+3k\\2&-9-k\end{array}\right] = \left[\begin{array}{ccc}-7&-6\\-6-k&-9-k\end{array}\right][/tex]
Equate the values, and we get
18 + 3k = -6
3k = -6 - 18
3k = -24
k = -8
and 2 = -6 - k
k = -6 - 2
k = -8
Therefore we can say that it is easy to see that these equations are satisfied if and only if k = −8, and thus k = −8 is the (unique) value for which AB = BA.
--The given question is incomplete; the complete question is
"Let [tex]A = \left[\begin{array}{ccc}2&3\\-1&1\end{array}\right][/tex] and [tex]B = \left[\begin{array}{ccc}1&9\\-3&k\end{array}\right][/tex]. What value(s) of k, if any, will make AB = BA?"--
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a. what are the mean and median number of the number of times a face will appear? b. what are the mean and median face value of the 600 rolls of the die?
The mean and median number of times a face will appear are 100 and 99.5. The mean and median face value of the 600 rolls of the die are 96.2 and 94.5
a) Mean number of appearances of each face = [tex]\frac{107+120+84+110+92+87}{6}[/tex]
= 100
Median number of appearances of each face = Average of middle two values when arranged in ascending order
Ascending order: 84, 87, 92, 107, 110, 120
Average of middle two values = [tex]\frac{92+107}{2}[/tex]
= 99.5
b) Mean and Median face values of the 600 rolls of the die:
Mean = [tex]\frac{107\times1+120\times2+84\times3+110\times4+92\times5+87\times6}{21}[/tex]
= [tex]\frac{2021}{21}[/tex]
= 96.2
Median = [tex]\frac{92\times5+107}{2}[/tex]
= [tex]\frac{567}{6}[/tex]
= 94.5
The question is incomplete. The complete question is
"The following represents the outcomes of rolling a die 600 times
Face 1 2 3 4 5 6
Number 107 120 84 110 92 87
a. What are the mean and median numbers of appearances of each face?
b. What are the mean and median face values of the 600 rolls of the die?"
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Can somebody PLEASE give me the right answer? I have been given 2 different answers 48 and 5.76 ALSO PLEASE SHOW THE WORK
Step-by-step explanation:
Not much work to show really. It's 36% of 16, which is 5.76
Consider the exponential function f(x)=(15). What is the value of the growth factor of the function?
23/1/2
23/
05
O 15
On solving the provided question, we can say that here, the function is f(x) = 1/5(15^x) and growth factor is 15.
What is function?
The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
For given question
the function is
f(x) = 1/5(15ˣ)
when f(x) = aˣ
then the growth factor of function = a
Then for f(x) = 1/5(15ˣ)
Growth factor = 15
Therefore the growth factor of function is 15.
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2 11/12x-5/6(x-2/5) what is the answer?.....
The required simplified value of the given expression is given as 11/12x² + 7/15x - 1/3.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= (11/12x-5/6) (x-2/5)
= 11/12x (x - 2/5) + 5/6 (x - 2/5)
= 11/12x² - 11/30x + 5/6x - 1/3
= 11/12x² + 7/15x - 1/3
Thus, the required simplified value of the given expression is given as 11/12x² + 7/15x - 1/3.
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50 points
How much would $400 be worth after 6 years, if it were invested at 2%
interest compounded annually? (Use the formula below and round your
answer to the nearest cent.)
If $450.46 were invested at 2% interest that is compounded annually, it would be worth after 6 years.
How is annual compound interest determined?The future value of a loan or investment may be determined using the formula FV = P*(1+R/N)(N*T), where FV is the future value, P is the original principal, R is the annual interest rate, N is the number of times interest is compounded annually, and T is the amount of time in years.
The formula to use isA = P(1+r/n)ⁿ
From the question, we have
P = $400
t = 6 year
r = 2%
r = 0.02
n = 1
Using the parameters, we haveA = P(1+r/n)ⁿ
A = 400(1+0.02/1)⁶
A = 400(1.02)⁶
A = $450.46.
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how does the hawthorne effect materialize in health services research, and what impact does this have on research objectivity?
The Hawthorne Effect can be mitigated by utilizing research designs that obscure the presence of the researcher, such as randomized controlled trials and naturalistic observation studies.
It is often seen in studies involving health services research, where individuals being studied change their behavior due to the presence of the researcher, or the knowledge that they are being observed. This can have an impact on research objectivity, as the behavior of the subjects might not be representative of the behavior they would normally exhibit while not being observed.
The Hawthorne Effect can be mitigated by utilizing research designs that obscure the presence of the researcher, such as randomized controlled trials and naturalistic observation studies. Additionally, researchers can also use methods such as questionnaires and interviews to gain insight into the experiences and behavior of the research subjects, in order to better understand the impact that the Hawthorne Effect might have on the research results.
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What is the minimum value for the function shown in the graph?
Answer:
2.5
Step-by-step explanation:
The minimum is the smallest value taken by the function.
PLEASE HELP !!
Question: what do means indicate about the vegetables weight?
Tomatoes are typically ____ (lighter or heavier) than cucumbers since the mean weight for tomatoes is ___ (less or greater) than the mean weight for cucumbers.
Tomatoes are typically lighter than cucumbers since the mean weight for tomatoes is less than the mean weight for cucumbers.
Answer:
Lighter, less
Step-by-step explanation:
The mean is also known as the average. This means that it is the sum of all values divided by the total number. Therefore it is said that on average, tomatoes weigh less than cucumbers.
When production volume exceeds the breakeven point, we can expecteda. profitb. fixed cost to decreasec. marginal revenue to decreased. a loss
When production volume exceeds the breakeven point, we can expect (a) profit.
The Breakeven Point is the level of production at which a company's total revenue equals its total expenses, and the company neither makes a profit nor incurs a loss.
When production volume exceeds the breakeven point, the company's total revenue exceeds its total expenses, which leads to a profit.
Option (b) : Fixed cost does not necessarily decrease when production volume exceeds the breakeven point.
Option (c) : Marginal revenue does not necessarily decrease when production volume exceeds the breakeven point.
Option (d) : A loss is not expected when production volume exceeds the breakeven point.
Therefore , If production volume is greater than the breakeven point, the company is expected to make a profit.
The given question is incomplete , the complete question is
When production volume exceeds the breakeven point, we can expected
(a) profit
(b) fixed cost to decrease
(c) marginal revenue to decrease
(d) a loss
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A recent survey of 250 citizens showed that 56% favored a renovation project for the local library. The survey had a margin of error of ±1.9%. If the town has 78,717 registered voters, what is the expected maximum number of voters who would support the project? Round the answer to the nearest whole number.
Maximum number of voters support renovation project is 44082.
What is margin of error?Margin of error provides a clearer understanding of what a survey’s estimate of a population characteristic means. it’s expressed with a plus and minus sign together, e.g. + or -1%.
A recent survey of 250 citizens showed that 56% favored a renovation project for the local library.
The survey had a margin of error of ±1.9%.
Total number of voters in the town = 78,717
56% of 78717= 44081.52 ⇒44082(rounded to nearest whole number)
Hence, maximum number of voters support renovation project is 44082.
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the quarter mile grounding rule for rural electric utilities for direct-buried jacketed distribution cables says that they must have at least ? grounds per mile, minimum.
The quarter mile grounding rule for rural electric utilities for direct-buried jacketed distribution cables says that they must have at least 4 grounds per mile.
A utility cooperative is a specific kind of cooperative that is responsible for providing its members with a public utility, such as power, water, or telecommunications. Profits are either distributed to members as "patronage" or "capital credits," which are dividends paid on a member's investment in the cooperative, or they are reinvested for infrastructure.
Every consumer is a shareholder and a member of the company. This means that, in contrast to investor-owned utilities where the amount of individual authority is determined by the number of shares held, all members have the same level of personal authority. Many utility cooperatives operate their business in accordance with a set of ideals based on the Rochdale Principles, just like cooperatives active in other industries.
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The drama club i elling ticket to their play to raie money for the how' expene. Each tudent ticket ell for $4. 50 and each adult ticket ell for $8. The auditorium can hold no more than 84 people. The drama club mut make at leat $560 from ticket ale to cover the how' cot. If 29 tudent ticket were old, determine all poible value for the number of adult ticket that the drama club mut ell in order to meet the how' expene. Your anwer hould be a comma eparated lit of value. If there are no poible olution, ubmit an empty anwer
If 29 student tickets were sold, then all possible values for the number of adult tickets that the drama club must sell in order to meet the show's expenses are 54 and 55 .
the price for each student ticket is $4.50 and adult is $8 ;
The number of people auditorium can hold is = no more than 84 people ;
the number of children tickets sold is = 29 tickets ;
Let "x" be number of adult tickets sold.
The total revenue from ticket sales = $4.50×29 + $8×(x)
⇒ $130.5 + $8x.
The total revenue must be at least $560,
So , $130.5 + $8x ≥ $560.
Subtracting $130.5 from both sides, we get $8x ≥ $429.5 ;
Dividing both sides by 8, we get x ≥ 53.69 ;
Since the number of adult tickets sold must be an integer, the minimum number of adult tickets that must be sold is 54.
The maximum number of people allowed in the auditorium is 84, so the maximum number of adult tickets that can be sold is 84 - 29 = 55.
Therefore, the possible values for the number of adult tickets that must be sold are 54, 55.
The given question is incomplete , the complete question is
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $4.50 and each adult ticket sells for $8. The auditorium can hold no more than 84 people. The drama club must make at least $560 from ticket sales to cover the show's costs. If 29 student tickets were sold, determine all possible values for the number of adult tickets that the drama club must sell in order to meet the show's expenses.
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Describe the inverse operation that will undo the given operation adding -6
Answer:6
Step-by-step explanation:
Question 2 of 10
Nina is careful to avoid oversharing. She makes sure what she does share is
accurate before reposting. What recommended behavior is Nina practicing?
The recommended behavior that Nina is practicing is ethical social media usage.
What is ethical social media usage ?Ethical social media usage refers to responsible and respectful behavior when using social media platforms. This includes respecting others' privacy, avoiding the spread of false information, not engaging in cyberbullying or harassment, and being mindful of one's own digital footprint. This is what Nina is doing by making sure what she shares is accurate.
Additionally, ethical social media usage also involves being transparent about one's identity and intentions, and recognizing the power of one's words and actions in the digital world.
.
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how to find perimeter of a triangular prism?
Answer:
Read below:
Step-by-step explanation:
To find the perimeter of a triangular prism, you need to add up the lengths of all three sides of the triangular base and all three sides of the rectangular lateral faces.
The formula for the perimeter of a triangular prism is P = a + b + c + 3l, where a, b, and c are the lengths of the sides of the triangular base, and l is the length of each of the rectangular lateral faces.
The perimeter of the triangular prism is solved
What is the volume of a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
The volume of a prism is the product of its base area and height
Volume of Prism = B x h
where B = base area of prism
h = height of prism
Given data ,
To find the perimeter of a triangular prism, you need to add the lengths of all the edges. The edges of a triangular prism include the three sides of the base triangle and three additional edges connecting the corresponding vertices of the two base triangles.
So, the formula for finding the perimeter of a triangular prism is:
Perimeter = (Sum of the lengths of the three sides of the base triangle) + (Sum of the lengths of the three edges connecting the corresponding vertices of the two base triangles)
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3/4 + x < 1/6.
Please help!!!!!
Original Equation:
[tex]\frac{3}{4} + x < \frac{1}{6}[/tex]
1) Subtract 3/4 from both sides:
[tex](\frac{3}{4}+x)-\frac{3}{4} < \frac{1}{6}-\frac{3}{4}[/tex]
2) Simplify:
[tex]x < \frac{1}{6}-\frac{3}{4}[/tex]
Find a common denominator for both fractions (I will use 12)
[tex]x < \frac{2}{12} -\frac{9}{12}[/tex]
Simplify:
[tex]x < \frac{-7}{12}[/tex]
We cannot simplify the expression anymore, therefore this is the answer!
Solve the equation? I really don't get it.
P = __
Answer:
Step-by-step explanation:
P = x
the sum of two positive integers is 28. when the smaller integer is subtracted from three times the larger, the result is 36. find the two integers.
The two integers required in the question are; 16 and 12
How to solve Algebraic word problems?We are told that the sum of two positive integers is 28. Now, if the two integers are x and y, then we have;
x + y = 28 ------(1)
When the smaller integer is subtracted from three times the larger, the result is 36. Thus;
3x - y = 36 ------(2)
Add eq 1 and eq 2 to get;
4x = 64
x = 64/4
x = 16
16 + y = 28
y = 28 - 16
y = 12
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Hint: The 103 degree angle is corresponding to angle 3x + 1.
Answer: x = Answer
The measure of value of x for the given set of parallel lines is found as:
x = 34.
Define the term alternate exterior angles?The pair of angles that lie outside the parallel lines yet on the other side of the transversal are known as alternate exterior angles. When two lines are split in a third line, called transversal, the phrase alternating exterior angles is frequently used. According to the Alternative Exterior Angles Theorem, pairs of alternative exterior angles become congruent if any lines k and l are parallel.From the definition of alternate exterior angles:
3x + 1 = 103°
3x = 103 - 1
3x = 102
x = 34
Thus, the measure of value of x for the given set of parallel lines is found as: x = 34.
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a. suppose the smoking habits of the parents are independent and the probability that the mother is a current smoker is 0.3, whereas the probability that the father is a current smoker is 0.4. what is the probability that both the father and mother are current smokers?
The probability that both the father and mother are current smokers is 0.12.
The probability that the mother is a current smoker is, 0.3 and the father is a current smoker is, 0.4.
The events are independent, the probability that both the events will occur is the multiplication of probability of individual events.
Therefore, the required probability is product of probability that mother is a current smoker with the probability that father is a current smoker.
P(Father and Mother are current smokers) = P(Father is a current smoker) × P(Mother is a current smoker)
P(Father and Mother are current smokers) = 0.4 × 0.3
P(Father and Mother are current smokers) = 0.12
The required probability is 0.12.
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On a coordinate plane, 3 parallelograms are shown. Parallelogram A B C D has points (3, 5), (6, 5), (4, 1), (1, 1). Parallelogram A prime B prime C prime D prime has points (3, negative 5), (6, negative 5), (4, negative 1), (1, negative 1). Parallelogram A double-prime B double-prime C double-prime D double-prime has points (negative 3, negative 4), (0, negative 4), (negative 2, 0), (negative 4, 0).
Which rule describes the composition of transformations that maps pre-image ABCD to final image A"B"C"D"?
The rule that describes the composition transformation that maps ABCD to A''B''C''D'' is;
''Translation of negative 6 units x, 1 units y composition reflection across the x-axis''.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
The given coordinates of parallelogram ABCD are;
⇒ (3, 5), (6, 5), (4, 1), (1, 1)
The coordinates of the parallelogram A'B'C'D' are;
⇒ A'(3, -5), B'(6, -5), C'(4, -1), D(1, -1)
The coordinates of the parallelogram A''B''C''D'' are;
⇒ D(-5, 0), C''(-2, 0), A''(-3, -4), B''(0, -4)
The image of the point (x, y), following a reflection about the x-axis is the point (x, -y).
And, The difference in the coordinates of the parallelogram ABCD and A'B'C'D' is the change in the sign of the y-coordinates
Therefore, the transformation that gives the parallelogram A'B'C'D' from the parallelogram ABCD is a reflection about the x-axis
Thus, The difference between the coordinates of the vertices of the parallelogram A'B'C'D' and the parallelogram A''B''C''D'', is a change in the x-value by (-6), and a change in the y-value by (+1)
Therefore, the parallelogram A''B''C''D'' can be obtained from parallelogram A'B'C'D', by a translation of -6 units (left) in the x-direction and a translation of 1 unit, x in the y-direction.
Which gives;
The composition transformation that maps the pre-image ABCD to the final image A''B''C''D'', (given that in a composition transformation, the transformation to the right is done first) are; which is the option;
''Translation of negative 6 units x, 1 units y composition reflection across the x-axis''.
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What is the arithmetic sequence if the first term is 40 and the common difference is -12
Answer:
40,28,16,4, -8,-20... keep going
Step-by-step explanation:
use 40-12, then 40-2*12, so forth
Can someone help me with this aleks question
Evaluate the following expreion when x = 4 and y = 5 Fraction with x quared plu y cubed in the numerator and 2 plu x in the denominator
When x = 4 and y = 5, the expression evaluates to 23.5.
Evaluate x and y expressionThe expression is (x² + y³)/(2 + x). Plugging in x = 4 and y = 5, we get:
(4² + 5³)/(2 + 4) = 16 + 125/(2 + 4) = 141/(6) = 23.5.
So when x = 4 and y = 5, the expression evaluates to 23.5.
The method of substituting values for variables in an expression to find its numerical value is a fundamental concept in algebra and mathematics. When evaluating an expression, we simply replace the variables with the given values and perform the arithmetic operations according to the rules of arithmetic. This process allows us to find the numerical result of the expression for a specific set of inputs.
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Find the circumference of a circle with a radius of 3 miles
The circumference of the circle with radius 3 miles is 18.85 miles.
What is a circle ?All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
The following are some of the circle's crucial characteristics:
If the circles have equal radii, they are said to be congruent.The longest chord in a circle is its diameter.In the center of a circle, equal chords subtend equal angles.The chord is divided in half by the radius drawn perpendicular to the chord.Circles with various radii are comparable.A circle can encircle a kite, triangle, square, trapezium, rectangle, and more.You may encircle a square, triangle, or kite with a circle.Equal in length are the chords that are equally spaced from the center.The longest chord's (diameter) distance from the circle's center is equal to zero.As the chord length rises, the perpendicular distance from the circle's center decreases.The tangents are parallel to one another if they are drawn at the diameter's end.The radii connecting the ends of a chord to the center of a circle create an isosceles triangle.The radius of the circle is 3 miles
Circumference of the circle 2π(radius) = 2*π*3 = 18.85 miles.
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Simplify each expreion. |6- 10| i don't know if it -4 ince it an abolute expreion
Absolute value of expression | 6 - 10 | can be simplified into 4.
The absolute value of a number is its distance from zero on the number line, regardless of its sign. It is represented by enclosing the number inside two vertical bars (| |) and is always a non-negative number.
In mathematical terms, the absolute value of x is defined as:
|x| =
a) x if x >= 0
b) -x if x < 0
So, for any number x, its absolute value is always positive or zero.
The expression |6 - 10| represents the absolute value of the difference between 6 and 10. To find the absolute value, we need to consider only the magnitude of the result and ignore its sign. In this case, the difference between 6 and 10 is -4, which is a negative number. Therefore, to find the absolute value, we need to take the absolute value of -4, which is 4. So, the simplified expression is:
|6 - 10| = 4
Hence the result for |6-10| is 4
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An 8-ounce serving of apples contains 8% of your daily vitamin C. How many ounces of apples would you need to get 100% of our daily vitamin C?
Answer:
Step-by-step explanation:
You would need 100 ounces of apples to get 100% of your daily vitamin C.
We know that 8 ounces of apples contains 8% of your daily vitamin C.
To find out how many ounces of apples are needed to get 100% of your daily vitamin C, we can use the following proportion:
(8 ounces / 8%) = (x ounces / 100%)
where x represents the number of ounces needed for 100% of the daily vitamin C.
To solve for x, we can cross-multiply and divide:
8 ounces * 100% = 8% * x ounces
8 ounces * 100 = 8 * x ounces
800 = 8x
x = 100
Therefore, you would need 100 ounces of apples to get 100% of your daily vitamin C.
Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?
A stratified random sample size is being used by Donald. He is segmenting the population into groups and choosing a representative sample of pupils from each category at random.
To examine the eating patterns of all pupils attending his school, Donald is utilising stratified random sampling. In this kind of sampling, the population is divided into strata, or groups, and a proportionate number of people from each category are randomly chosen to make up the sample. To make sure the sample is representative of the total community, Donald in this instance is grouping the pupils by grade level. Then he gathers information from the sample in order to make generalisations about the eating patterns of all the pupils enrolled in his school. A representative sample can be obtained and reliable population inferences can be made using stratified random sampling
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