The money shared by Natasha and Trisha is $160.
What is defined as the term ratio?A ratio is a measure of 2 or more numbers which indicates their relative sizes. A ratio compares two amount by dividing them, with the dividend or number divided referred to as the antecedent and thus the divisor or number divided referred to as the consequent.Let the amount paid by the Natasha is 'x'
And the amount Paid by Trisha is 'y';
Their amounts are in the ratio of 5:3
Thus, x/y = 5/3
Trisha shares a amount of $120.
y = $12.
Then, put y = 120 in the ratio.
x/y = 5/3
x = 5y/3
x = (5×12)/3
x = 5×4
x = 40 (amount shared by Natasha)
Total amount = Natash's share + Trisha's share
Total amount = 40 + 120
Total amount = 160
Thus, the total amount of money shared is $160.
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the number that is 7 more than -9
Hey there!
Guide:
• Negatives are BELOW 0
• Negatives are SMALLER than 0
• Negatives are also on the LEFT side of 0.
• Positives are ABOVE 0
• Positives are BIGGER than 0
• Positives are also on the RIGHT side of 0.
Thus, this means 7 is bigger than -9 because, your -9 is a negative number and 7 is a positive
That being said 7 > -9 (7 is the greater number out of the two numbers)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Suppose that the random variable F follows an F distribution with 11 numerator degrees of freedom and 15 denominator degrees of freedom. E(F) = __ E(F) = , and V(F) = , and V(F) = - F0.005 ,11,15 =
We are asked to find the F value that has a probability of 0.005 to its right, or a probability of 0.995 to its left. The answers are: E(F) = 1.3636, V(F) = 1.5097, and F0.005,11,15 = 2.91.
In statistics, an F distribution is a probability distribution that arises from the ratio of two independent chi-squared distributions. The F distribution is defined by two parameters, the numerator degrees of freedom and the denominator degrees of freedom.
In this case, we are given that the random variable F follows an F distribution with 11 numerator degrees of freedom and 15 denominator degrees of freedom. To find E(F) and V(F), we can use the following formulas:
E(F) = d2 / (d2 - 2), where d1 and d2 are the numerator and denominator degrees of freedom, respectively.
V(F) = [2d22(d1 + d2 - 2)] / (d12(d2 - 2)2(d2 - 4)), where d1 and d2 are the numerator and denominator degrees of freedom, respectively.
Substituting the given values, we have:
E(F) = 15 / (15 - 2) = 1.3636
V(F) = [2(15^2)(11 + 15 - 2)] / (11^2(15 - 2)^2(15 - 4)) = 1.5097
Finally, we are asked to find the F value that has a probability of 0.005 to its right, or a probability of 0.995 to its left. To do this, we can use a table or a calculator that provides F-distribution probabilities. For the given degrees of freedom, we find that F0.005,11,15 = 2.91.
Therefore, the answers are: E(F) = 1.3636, V(F) = 1.5097, and F0.005,11,15 = 2.91.
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a) Determine the area of the region D bounded by the curves: x = y³, x+y = 2, y = 0. b) Find the volume of the solid bounded by the paraboloid z = 4 x² - y². and the xy-plane. (5 marks) (5 marks)
The area of the region D bounded by the curves x = y³, x + y = 2, and y = 0 is 4/15 square units. The volume of the solid bounded by the paraboloid z = 4x² - y² and the xy-plane cannot be determined without specific information about the region of integration.
To determine the area of the region D bounded by the curves x = y³, x + y = 2, and y = 0, we can use integration. By setting up the integral and evaluating it, we find that the area of region D is 4/15 square units.
To find the volume of the solid bounded by the paraboloid z = 4x² - y² and the xy-plane, we can set up a triple integral. By integrating the appropriate function over the region, we find that the volume is 16/3 cubic units.
a) To determine the area of the region D bounded by the curves x = y³, x + y = 2, and y = 0, we can set up the integral using the formula for calculating the area between two curves. The area is given by A = ∫[a,b] (f(x) - g(x)) dx, where f(x) and g(x) are the functions defining the curves and [a,b] is the interval of x-values over which the curves intersect.
In this case, the curves x = y³ and x + y = 2 intersect at the points (1, 1) and (-1, 1). To find the limits of integration, we need to determine the x-values where the curves intersect.
From x + y = 2, we can solve for y to get y = 2 - x. Substituting this into x = y³, we have x = (2 - x)³. Expanding and rearranging the equation, we get x³ - 3x² + 3x - 2 = 0. This equation can be factored as (x - 1)(x + 1)(x - 2) = 0. Therefore, the curves intersect at x = 1 and x = -1.
To calculate the area, we set up the integral as follows:
A = ∫[-1,1] (y³ - (2 - y)) dx.
Evaluating the integral, we find:
A = ∫[-1,1] (y³ - 2 + y) dx = [y⁴/4 - 2y + y²/2]│[-1,1].
Substituting the limits of integration, we get:
A = [(1/4 - 2 + 1/2) - ((1/4 + 2 + 1/2)] = 4/15.
Therefore, the area of region D is 4/15 square units.
b) To find the volume of the solid bounded by the paraboloid z = 4x² - y² and the xy-plane, we need to set up a triple integral. The volume can be calculated by integrating the appropriate function over the region.
Since the solid is bounded by the xy-plane, the limits of integration for z are from 0 to z = 4x² - y².
The volume V is given by V = ∭R (4x² - y²) dV, where R represents the region in the xy-plane.
To evaluate the triple integral, we need to determine the limits of integration for x and y. However, the region R is not specified in the question, so we cannot provide the exact limits without that information.
Assuming that R is a region that extends infinitely, we can set the limits of integration for x and y as (-∞, ∞). Thus, the volume V becomes:
V = ∬R ∫[0, 4x² - y²] (4x² - y²) dz dA = ∬R (4x
² - y²)(4x² - y²) dA.
Evaluating this integral would require specific information about the region R in order to determine the limits of integration. Therefore, without further information about the region, we cannot calculate the exact volume.
In conclusion, the area of the region D bounded by the curves x = y³, x + y = 2, and y = 0 is 4/15 square units. The volume of the solid bounded by the paraboloid z = 4x² - y² and the xy-plane cannot be determined without specific information about the region of integration.
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Qa.) State the contrapositive of the following implication. If G is a connected planar graph then G has at least one vertex of degree <= 5.
Qb.) Prove the contrapositive stated in part (a). Hint: use the fact that if G is a connected Planar graph , then e <= 3v-6.
Qc.) Use part (a) to show that every planar graph can be colored with 6 (or less) colors. Hint: Use a proof by Induction on the number of vertices G.
We assume that G is a connected planar graph with no vertex of degree <= 5. We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices. Let d be the maximum degree of G.
Qa. Contrapositive of an implication is a new implication formed by negating both the hypothesis and the conclusion.
The contrapositive of the implication "If G is a connected planar graph, then G has at least one vertex of degree <= 5" is "If G has no vertex of degree <= 5, then G is not a connected planar graph."
Qb. Proof: We assume that G is a connected planar graph with no vertex of degree <= 5.
We will use e <= 3v - 6 to prove that G is not a planar graph. By handshaking lemma, we know that 2e = sum of degrees of all vertices.
Let d be the maximum degree of G. Since G has no vertex of degree <= 5, then d >= 6.
Thus, the sum of degrees of all vertices in G is greater than or equal to 6v/2, which is equal to 3v.
Hence, 2e >= 3v.
Substituting this inequality in e <= 3v - 6, we get 2e >= 3e - 6, which implies that e >= 6.
Since e >= 6, it follows that G is not planar.
Qc. Proof: We use proof by induction on the number of vertices of G. For a graph with one vertex, the statement is trivially true.
For a graph with n > 1 vertices, assume that every planar graph with at most n - 1 vertices can be colored with 6 (or less) colors.
Let G be a planar graph with n vertices.
By part (a), there exists a vertex v of G with degree <= 5.
We remove v and all its edges from G to get a new graph G' with n - 1 vertices.
By the induction hypothesis, we can color G' with 6 (or less) colors.
We add back v and its edges to G.
Since v has degree <= 5, at most 5 colors are used on its adjacent vertices.
We use a new color for v.
Thus, G can be colored with 6 (or less) colors.
Therefore, by induction, the statement is true for all planar graphs.
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A model of a statue has a height of 4 cm. The volume of the model is 12 cm3 . 3 The volume of the statue is 40 500 cm
Answer:Pencil, pen, ruler, protractor, pair of compasses and eraser ... Work out the volume of prism B. me x3' (X27). 15X27 = 405. 405 ..cm3 ... 3. Below are two similar parallelograms. X1.5. 4cm / A /. 6cm. B. The area of ... bon Area: 120 cm? 3 ... Two clay models of the Statue of Liberty are mathematically similar.
Step-by-step explanation:
Sorry If It Dont Help But It Helped Meh...Come Back To Meh If Its Wrong♀️....
1.Make an industry analysis using either PESTEL or Five forces
model.
2. Prepare a strategic group map using updated information. Use
three parameters-for x axis, for y axis and for the diameter of th
Industry Analysis using five forces model which are Political, Economic, Social, Technological, Environmental, Legal. A strategic group map visually represents the competitive positioning of companies within an industry.
1. Industry Analysis using PESTEL Model:
The PESTEL analysis examines the external factors that impact an industry:
Political: Government regulations, stability, and policies affecting the industry.
Economic: Economic growth, inflation, exchange rates, and consumer purchasing power.
Social: Demographic trends, cultural factors, and consumer behavior.
Technological: Technological advancements, innovation, and automation in the industry.
Environmental: Environmental regulations, sustainability practices, and climate change impact.
Legal: Legal frameworks, industry-specific regulations, and intellectual property protection.
By conducting a PESTEL analysis, one can gain insights into the industry's overall environment, identify opportunities and threats, and understand the factors influencing its growth and competitiveness.
2. Strategic Group Map:
A strategic group map visually represents the competitive positioning of companies within an industry. It uses parameters to plot companies on an x and y axis, and the diameter of the circle represents their market share or another relevant metric.
Parameters for x-axis: Price range (e.g., low to high)
Parameters for y-axis: Product differentiation (e.g., basic to premium)
Diameter of the circle: Market share (e.g., small to large)
By plotting companies based on these parameters, the strategic group map helps identify market segments, competitive dynamics, and potential areas for differentiation or strategic alliances.
3. Reconstructed Vignette 5: Cost of Operation for GP (2019 and 2020):
In 2019, the cost of operation for the GP (General Practitioner) increased due to rising expenses such as rent, salaries, and medical supplies. This was influenced by factors such as inflation and increased demand for healthcare services.
In 2020, the COVID-19 pandemic significantly impacted the cost of operation for GPs. The costs surged due to additional expenses related to personal protective equipment (PPE), sanitation measures, and telehealth infrastructure. Simultaneously, some costs decreased as patient visits reduced temporarily.
The increased costs challenged GPs' profitability, especially for independent practitioners or smaller clinics with limited resources. Adapting to new operational requirements and investing in technology further added to the financial burden.
4. Agreement with the Idea in the Case:
As the case or specific idea isn't provided, it's challenging to agree or disagree without context. Please provide more information or details about the case or idea so that I can offer a justified answer based on logic or data.
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COMPLETE QUESTION - 1.Make an industry analysis using either PESTEL or Five forces model.
2. Prepare a strategic group map using updated information. Use three parameters-for x axis, for y axis and for the diameter of the circle.
3. Reconstruct Vignette 5: Cost of operation for GP. Make it for 2019 and 2020.
4. Do you agree with the idea described in the case? Justify your answer in brief (you may use logic or data in support of your answer).
Ben and Juliette are going to the movies with two friends. Movie tickets cost $8 each. Each person purchases a soda for $2 each and a candy for $1 each. Ben also buys a popcorn for $5. How much did they spend in all at the movie theater?
symplify the expression 3⁴÷3⁹. Select all that apply.
Answer:
C and D
Step-by-step explanation:
When you divide exponents with the same base, you just subtract the exponents.
3^4 / 3^9
4-9 = -5
3^-5
That can be rewritten into 1/3^5 and 1/243.
TRUE OR FALSE: The alternative hypothesis states that there is no difference/no effect.
The answer is FALSE. The alternative hypothesis is a statement that there is a difference or an effect in the population being studied, and it contradicts the null hypothesis, which is a statement that there is no difference or no effect in the population being studied.
The alternative hypothesis is a statement that contradicts the null hypothesis and is generally the hypothesis that the researcher wants to support. It is a statement that there is a difference or an effect in the population being studied.
In hypothesis testing, the null hypothesis is a statement that there is no difference or no effect in the population being studied. The null hypothesis is typically the default hypothesis, which is assumed to be true unless evidence suggests otherwise. The alternative hypothesis, on the other hand, is a statement that there is a difference or an effect in the population being studied, and it is typically the hypothesis that the researcher wants to support.
For example, if a researcher wants to test the effectiveness of a new drug, the null hypothesis might be that the drug has no effect on the condition being treated, while the alternative hypothesis might be that the drug has a positive effect on the condition being treated.
In summary, the alternative hypothesis is a statement that there is a difference or an effect in the population being studied, and it contradicts the null hypothesis, which is a statement that there is no difference or no effect in the population being studied.
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What are the factors of -24 that have a sum of 5?
Answer:
Step-by-step explanation:
5 Easy as 1-2-3
5 is a prime number.
Prime factorization: 5 is prime.
The exponent of prime number 5 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 5 has exactly 2 factors.
Factors of 5: 1, 5.
Factor pairs: 5 = 1 x 5.
5 has no square factors that allow its square root to be simplified. √5 ≈ 2.236.
solve for v: 16.8-v=6v
___________
\( \: \)
16.8 - v = 6v
128 - v = 6v
-v - 6v = -128
-7v = -128
7v = 128
v = 128 ÷ 7
v = 18 2/7
Evaluate: 12+(-16)+24-18
Answer:
2.
Step-by-step explanation:
12 + (-16) + 24 - 18
= 36 - 34
= 2.
The value of the expression 12+(-16)+24-18 is 2, which can be computed using the commutative property.
What is the commutative property?The commutative property signifies that the order of terms in mathematical expressions does not matters. It applies only to addition and multiplication operations, and not to subtraction and division operations.
How to solve the given question?In the question, we are asked to evaluate: 12 + (-16) + 24 - 18.
By using the commutative property, we can write the expression
12 + (-16) + 24 - 18, as
= 12 + 24 + (-16) - 18
= 12 + 24 -16 - 18
= 36 - 34
= 2
∴ The value of the expression 12+(-16)+24-18 is 2, which can be computed using the commutative property.
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Which of the following sets of numbers could represent the three sides of a triangle? { 7 , 10 , 18 } {7,10,18} { 6 , 19 , 25 } {6,19,25} { 11 , 17 , 26 } {11,17,26} { 8 , 16 , 24 } {8,16,24}
The set of numbers that could represent the sides of a triangle is
{ 11, 17, 26 }.
Option E is the correct answer.
We have,
To determine whether a set of three numbers can represent the sides of a triangle, we need to check if the sum of the two shorter sides is greater than the longest side.
This is known as the Triangle Inequality Theorem.
So,
{ 7, 10, 18 }:
7 + 10 = 17, which is less than 18.
Therefore, this set cannot represent the sides of a triangle.
{ 6, 19, 25 }:
6 + 19 = 25, which is equal to 25.
Therefore, this set cannot represent the sides of a triangle.
{ 11, 17, 26 }:
11 + 17 = 28, which is greater than 26. 17 + 26 = 43, which is greater than 11. Therefore, this set can represent the sides of a triangle.
{ 8, 16, 24 }:
8 + 16 = 24, which is equal to 24.
Therefore, this set cannot represent the sides of a triangle.
Thus,
The set of numbers that could represent the sides of a triangle is
{ 11, 17, 26 }.
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Rewrite this as a function: y + 5x = 16
Answer:
y=-5x+16
Step-by-step explanation:
Which statement describes the relationship between x and y in these 2 equations?
Y = 4x Y = x + 4
In y = 4x the value of y is 4 times the value of x, and in y = x + 4 the value of y is 4 more than the value of x.
Thus option D is Correct.
what is linear equation?
A linear equation is an equation in which the highest power of the variable is 1, and the equation can be graphed as a straight line. It is of the form y = mx + b, where m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis. The variable y represents the dependent variable, while x represents the independent variable.
The relationship between x and y in these two equations is that they both represent a linear equation but with different slopes and y-intercepts.
The first equation, Y = 4x, is in slope-intercept form, where the slope is 4, and the y-intercept is 0. This means that as x increases by 1, y increases by 4, and the line passes through the origin.
The second equation, Y = x + 4, is also in slope-intercept form, where the slope is 1, and the y-intercept is 4. This means that as x increases by 1, y increases by 1, and the line intercepts the y-axis at (0, 4).
Therefore, In y = 4x the value of y is 4 times the value of x, and in y = x + 4 the value of y is 4 more than the value of x
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Complete Question :
Which statement describes the relationship between x and y in these two equations? y = 4x and y = x + 4
A. In y = 4x the value of y is 4 more than the value of x, and in y = x + 4 the value of y is twice the value of x.
B. In y = 4x and in y = x + 4, the value of y is 4 more than the value of x.
C. In y = 4x and in y = x + 4, the value of y is twice the value of x
D. In y = 4x the value of y is 4 times the value of x, and in y = x + 4 the value of y is 4 more than the value of x
T/F: since the square matrix that represents the dct coefficient is an orthogonal matrix, inverse and transpose are the same.
True. Since the square matrix that represents the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same. This property is a fundamental characteristic of orthogonal matrices and holds true for all orthogonal matrices.
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False While it is true that the square matrix that represents the DCT coefficient is orthogonal, it does not mean that its inverse and transpose are the same.
the inverse of an orthogonal matrix is its transpose. However, the transpose of the matrix does not necessarily mean that it is the same as the inverse of the matrix. In the statement is false because the inverse and transpose of an orthogonal matrix are not always the same.
The Discrete Cosine Transform (DCT) coefficient matrix is an orthogonal matrix. In the case of orthogonal matrices, the inverse matrix is indeed equal to the transpose of the original matrix. This is because the product of an orthogonal matrix and its transpose results in the identity matrix.
Since the square matrix representing the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same.
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need help with all of these questions you see on the top. there the red squares. please someone smart ( dose not show rn ). this is one of the problems I need to finish this tonight.
Answer:
402.1 in^3
Step-by-step explanation:
To find the area of a cylinder, you multiply the base by the height. Given a base area of \(32\pi\) in^2 and a height of 4 in results in the following equation:
V = 32π x 4
This comes out to be 402.123859659 which is 402.1 when rounded to the nearest tenth.
to its 4. RST maps to AR'S'T'.
Preimage
R(1, 1)
S(1,-1)
T(2,-2)
(197
dixes 180x
↑
↑↑
The coordinate rule is:
The transformation is:
Image
R'(3,2)
S'(3,-2)
T'(6,-4)
The coordinate rule for each point is;
R'(x, y) → (x + 2, y + 1)
S'(x, y) → (x + 2, y - 1)
T'(x, y) → (x + 4, y - 2)
How to Interpret Transformations?Coordinate plane rules is simply (x, y) → (x ± h, y ± k)
where h and k are the horizontal and vertical shifts.
Thus, the coordinate rule for each point is;
R'(x, y) → (x + 2, y + 1)
S'(x, y) → (x + 2, y - 1)
T'(x, y) → (x + 4, y - 2)
The transformation is (x, y) = (x, y) for Point R
The transformation is (x, -y) = (x, -y) for Points S and T
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A dime weighs about 0.08 ounce. About how many dimes weigh a pound?
(I will mark brainliest)
Answer:
200
Step-by-step explanation:
Well, 1 pound is 16 ouces, so you would just need to do 16/0.08 and it should give you the awnser!
16/0.08=200
200 dimes would be a pound
Answer:
200 dimes = 16 ounces
step-by-step explanation:
16 ounces in a pound
16 = .08 * d where d = number of dimes
d = 16/.08 = 200 dimes
what is the slope between (4,-17), (-20,-1)?
The rational number
number ———————
is equal to its negative
The first step in analyzing numeric data of two variables is to __________. Please choose the correct answer from the following choices, and then select the submit answer button. Answer choices measure the strength of the linear relationship determine whether the variables are quantitative create a scatterplot model a linear relationship with a regression line
Answer:
Create a scatterplot
Step-by-step explanation:
What is the inequality shown? -6 -5 -4 -3 Inequalities - Introduction A201/ Farringdo Construction 28/74 Marks -2 -1 0 1 2 Q Search 3 4 X 5 6 Overview DLDLC 181
The notation of the inequality is -6 ≤ x ≤ -3
How to determine the inequality shownFrom the question, we have the following parameters that can be used in our computation:
-6 -5 -4 -3
From the above we can see that the numbers are between -6 and -3
This means that they are greater than of equal to -6 but less than or equal to -3
So, we can use the following inequality
-6 ≤ x ≤ -3
Hence, the inequality is -6 ≤ x ≤ -3
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Please help! I will give brainliest! The first container of milk contains twice as much milk as the secound container of milk.After John uses 2 gallons of milk from the second container and 3 gallons from the first, the first contains 4.5 times as much milk as the secound. How many gallons of milk were in each container originally?
John had 4.8 gallons of milk in the first container and 2.4 gallons of milk in the second container
How to find the gallons of milk in each container originallyThe first container of milk contains twice as much milk as the second container of milk
let the quantity of milk in the first container be x
let the quantity of milk in the second container be y
x = 2y
After John uses 2 gallons of milk from the second container and 3 gallons from the first, the first contains 4.5 times as much milk as the second
x - 3 gallons = 4.5 (y - 2 gallons)
x - 3 = 4.5(y - 2)
x - 3 = 4.5y - 9
x = 4.5y - 6
substituting the value of x
2y = 4.5y - 6
4.5y - 2y = 6
2.5y = 6
y = 2.4 gallons
x = 2y = 4.8 gallons
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ok I got it but I think im not sure plsss help!!!
Answer:
7 and 8: these are both proportional relationships because they grow at a constant rate of change
9: for every 40 miles that the car travels, it uses 2 gallons of gas.
10: y= 20x
11: the graph would be steeper and have a greater rate of change. This car would be able to go farther on less fuel.
Find the magnitude of the vector that begins at (1,1) and ends at (-8,12).
a. 15.81
b. 14.76
c. 14.21
d.04
Answer the answer is a 15.81
Step-by-step explanation:
if the sum of two number is 37 and the greater number exceeds the smaller by 5, find the numbers.
Answer:
21 and 16
Step-by-step explanation:
x= big number
x`-5 = small number
x + x-5 = 37
2x-5 =37
2x= 42
x = 21
21-5 = 16
21+16 = 37
A side of the triangle below has been extended to form an exterior angle of 158°. Find the value of x.
Answer:
x =22
Step-by-step explanation:
158 and x from a straight line so they add to 180
158+x = 180
x = 180-158
x =22
price money of R4000 must be shared among the first three winners in the ratio 5:3:2, calculate how much each winner will receive?
Answer: Explanation below
Step-by-step explanation:
R4000 is the money to be split
5:3:2 is the ratio
We can add the ratios together.
5+3+2=10
The first winner = 5/10 x 4000
= R2000
The second winner = 3/10 x 4000
= R1200
The third winner = 2/10 x 4000
= R800
Hope this helped :)
MaryAnn and Nana conduct surveys to determine which potential new menu item would be most popular among customers. Surveys will provide MaryAnn and Nana with what type of data?
MaryAnn and Nana's surveys will provide them with quantitative data, which is numerical data that can be measured and analyzed using mathematical or statistical methods.
Quantitative data refers to numerical information that can be measured and expressed in terms of numbers or quantities. It is often obtained through structured research methods such as surveys, experiments, and statistical analyses. This type of data is objective, reliable, and precise, and can be easily analyzed using statistical techniques.
Quantitative data can be divided into two main categories: discrete data and continuous data. Discrete data can only take specific values, such as the number of people in a room or the number of cars in a parking lot. Continuous data, on the other hand, can take any value within a certain range, such as height, weight, or temperature. Quantitative data can provide valuable insights into patterns, trends, and relationships between variables, making it an essential tool for decision-making in various fields, including business, science, and social research.
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