Answer:
6x² + 7x - 49
53×47 = 2491
Step-by-step explanation:
(3x-7)(2x+7)
6x² + 21x - 14x - 49
combine like terms:
6x² + 7x - 49
A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? hint: look at the difference between number of people and cost to get cost per person and then cost without people
How much does each person cost?
Write an equation to show cost, c, of a bus with x number of people on it.
1) The base rate for the empty bus is $120.
2) The variable cost (slope) for each person on board the bus is $2.
3) An equation to show the cost, c, of a bus with x number of people on it is C = 120 + 2x.
How the base rate and slope for the equation are derived:The total charge for taking 30 people aboard = $180
The total charge for taking 50 people on board = $220
The differences in the number of people and charges are 20 and $40, respectively.
Let x = the number of people boarding the bus and n = the fixed rate per bus.
30x + n = 180 ... Equation 1
50x + n = $220 ... Equation 2
Subtract Equation 1 from Equation 2:
20x = $40
x = $2 ($40/20)
The variable cost per person = $2 ($40/20)
The base rate for the empty bus = 30(2) + n = $180, where n is the base rate or fixed cost per bus.
= 60 + n = $180
n = $120
OR:
50(2) + n = $220
100 + n = $220
n = $120
The equation for the cost, c, of a bus with x number of people:
C = 120 + 2x
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2. Which system has an infinite number of solutions?
a. x+2=y
4= 2y-x
b. 2y + 6 = 4x
-3=y-2x
c. y+3=2x
4x=2y-3
d. y = 2x - 5
-2 = y - 2x
Answer: B
Step-by-step explanation:
Substitution method
solve the equation for Y by putting the variable on the left. -3 = y - 2x would become y = 2x - 3
Plug Y into the top equation. 2(2x - 3) + 6 =4x
4x - 6 + 6 = 4x
Combine like terms
4x - 0 = 4x
4x = 4x
Infinite Solutions
Sheryl creates a scatter plot to analyze how an increase in the outside temperature above 52°F affects the sale of hot chocolate at her shop. The line shown on the graph is the line of best fit for the data. Which statements are true about the graph? Select all that apply.
1. The y-intercept represents the orders for hot chocolate on a day when the outside temperature was 52°F.
2. Sheryl gets 160 orders for hot chocolate on a day when the outside temperature is 52°F.
3. Sheryl gets 2 fewer orders for each degree increase above 52°F in the outside temperature.
4. Sheryl gets 16 fewer orders for each degree increase above 52°F in the outside temperature.
The true statement about the graph include:
1. The y-intercept represents the orders for hot chocolate on a day when the outside temperature was 52°F.
2. Sheryl gets 160 orders for hot chocolate on a day when the outside temperature is 52°F.
What are the true statement about the graph?It is clearly mentioned on graph above 52 degrees fahrenheit. So y-intercept represents the orders for hot chocolate when the outside temparature was 52 F.
For every 16° increase in temparature above 52°F there is a decrease of 32 orders. Therefore for each degree increase above 52°F decrease in order = 32/16 => 2
So Sheryl gets 2 few orders for each degree decrease in temperature above 52°F. The slope of the line represents the decrease in numbers of order per degree increase in temparature.
As graph starts with 52oF and the number of orders on it is 160; So, Sheryl gets 160 orders when outside temparature is 52°F.
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Amelia has two sheets of construction people with length accent meters one piece of construction paper has a width of X +4. 5 cm and the other has a width of X +6. 25 cm right and expression to represent the the two pieces of construction paperwork cover
x² + 6.25x + 4.5x + 28.125, this expression represents the area the 2 pieces of construction paper will cover.
What is the quadratic equation?
A quadratic equation is any equation in algebra that can be rearranged in standard form as where x represents an unknown value and a, b, and c represent known numbers, with a 0.
We have,
Amelia has 2 sheets of construction paper with length x centimeters.
One piece of construction paper has a width of x+4.5 centimeters, and the other has a width of x+6.25 centimeters.
expression to represent the area the 2 pieces of construction paper will cover.
To find the area(A) of a paper:
multiply its height by its width:
A = (x + 4.5) * (x + 6.25)
A = x² + 6.25x + 4.5x + (4.5) * (6.25)
A = x² + 6.25x + 4.5x + 28.125
hence, x² + 6.25x + 4.5x + 28.125, this expression represents the area the 2 pieces of construction paper will cover.
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Conner and Darian made a profit of $40,021.50 on day 1 of the hot chocolate sale. They donated $10,050.25 to their school so their school could purchase more good books. Then Conner gave his dad $25.00 and Darian gave his dad $25.00. Conner and Darian invested the rest of the money so that they can make their hot chocolate shop even better! How much money did they invest?
Answer:29,921.25
Conner and Darian made a profit of $40,021.50 on the first day of their hot chocolate sale. They donated $10,050.25 of that money to their school, which leaves them with $40,021.50 - $10,050.25 = $29,971.25.
Conner and Darian each gave their dad $25.00, which means they gave a total of $25.00 * 2 = $<<25*2=50.00>>50.00 to their dads.
This means that Conner and Darian had $29,971.25 - $50.00 = $29,921.25 left to invest in their hot chocolate shop.
Graph the line with y-intercept 6 and slope 1/3
Answer:
y = 1/3x + 6
Step-by-step explanation:
3. What is the slope of the following line?
1/2 is the slope of the following when you simplify
It is the process by which people are separated from social participation as well as economic, social, cultural and political opportunities.
The process by which people are separated from social participation is known as social exclusion.
¿What is social exclusion?This term refers to the process in which people or groups are separated or not allowed to participate.
Exclusion is considered a negative process or phenomenon, since:
It does not allow social development in general.It strengthens many negative values and elements such as inequality and lack of participation.In this sense, what must be done is to fight to eliminate exclusion and promote inclusion.
¡Hope this helped!
|2x - 1|> 7.
|7-5x|<3
Answer:
1)x=2
2)4<x
3)x<4/5
4)1<x
Can someone please answer this problem for me.
Length of each Plan A workout: 4 hours and Length of each Plan B workout: 8 hours.
To find the length of each workout plan, we need to know the total amount of time that Deshaun spent on each plan. We can find this by adding up the number of clients who did each plan on Friday and Saturday and then multiplying by the total amount of time that Deshaun spent training his clients on each day.
On Friday, Deshaun had 4 clients who did Plan A and 8 who did Plan B, for a total of 4 + 8 = 12 clients.
On Saturday, Deshaun had 2 clients who did Plan A and 3 who did Plan B, for a total of 2 + 3 = 5 clients.
In total, Deshaun had 12 + 5 = 17 clients who did his workout plans.
Since Deshaun trained his Friday clients for a total of 17 hours and his Saturday clients for a total of 7 hours, the total amount of time that he spent on Plan A was 4 × 17 = 68 hours.
The total amount of time that he spent on Plan B was 8 × 17 = 136 hours.
Since there were 17 clients in total, the length of each Plan A workout is 68 / 17 = 4 hours.
The length of each Plan B workout is 136 / 17 = 8 hours.
Thus, the length of each Plan A workout is 4 hours, and the length of each Plan B workout is 8 hours.
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Henri paid $10.75 for a calculator, $4.98 for copier paper, and $3.21 for folders. He paid with a $20 bill and got $1.06 in change. Which shows by sung estimation that Bradley’s change is reasonable?
A. Add 11 and 5 and 3 to get $19; $20-$19=$1, which is very close to the amount of change received by Bradley
B. Add 11 and 5 and 4 to get $20; $20-$20=$0, which is very close to the amount of change received by Bradley
C. Add 10 and 4 and 3 to get $17; $20-$17=$3, which is very close to the amount of change received by Bradley
D. Add 10 and 5 and 3 to get $18; $20-$18=$2, which is very close to the amount of change received by Bradley
The option that shows the estimation that Bradley’s change is reasonable is A. Add 11 and 5 and 3 to get $19; $20-$19=$1, which is very close to the amount of change received by Bradley
How to estimate the value?Estimation is the process of determining an estimate or approximation, which is a value that can be used for a specific purpose even when the input data is incomplete, uncertain, or unstable. Nonetheless, the value is usable because it is based on the best available information.
In this situation, Henri paid $10.75 for a calculator, $4.98 for copier paper, and $3.21 for folders. He paid with a $20 bill and got $1.06 in change.
The correct estimation is option A.
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Search
When solving a word problem using a system of equations, how many equations
must you create when there are two unknowns?
a) 1
b) 2
c) 3
d) 4
Answer:
The answer for the above question is:
b)2
When solving a word problem using a system of equations with two unknowns, you must create two equations. So, correct option is B.
The reason is that each unknown in the problem requires an equation to represent its relationship with the other variables.
For example, let's say you have two unknowns, x and y. You need two equations to define the relationships between these variables. These equations can be represented as:
Equation 1: x + y = 10 (This equation represents the relationship between x and y based on the given information in the problem.)
Equation 2: 2x - y = 4 (This equation represents another relationship between x and y based on additional information provided in the problem.)
With a system of two equations involving two unknowns, you can use algebraic methods such as substitution or elimination to solve for the values of x and y.
Having only one equation would not be enough to determine unique values for both x and y, as there would be an infinite number of possible solutions. On the other hand, having more than two equations might lead to over-determining the system, making it inconsistent or redundant.
Therefore, two equations are the minimum required to solve for two unknowns effectively. So, correct option is B.
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Anyone explain please
The relation between variables is represented by an equation ; y = 2.5x+15
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Alexa joined a program at some coffee shop which offers her $15 per month, after which she will get her coffee at a discount rate which $2.5
We can represent the relationship as ;
y = 2.5x+15
Where, x (number of coffee) is an independent variable because it does not depend on any condition, and y (cost) is a dependent variable because it depends on the value of x.
Hence, the relation is described as y = 2.5x+15
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The distance is 1,163 miles and the driving is 17 hours and 38 minutes
Answer:
Step-by-step explanation:
17 hours multiplied by 60 (60 seconds in 1 minute) = 1020 minutes + 38 minutes = 1058 minutes.
Miles per hour = distance/time
1163/1058 = 1.10 miles per hour
based on the graph how many tiles are im figure 0
For figure {0}, the number of tiles will be equal to 2.
What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is a graph as shown in the image.
The line passes through point -
(3, 8) and (4, 10)
So, the slope of the line will be -
m = (10 - 8)/(4 - 3)
m = 2
y = 2x + c
For the point (3, 8), we can write -
8 = 6 + c
c = 2
For figure {0}, the number of tiles will be equal to 2.
Therefore, for figure {0}, the number of tiles will be equal to 2.
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Which ordered pair is included in the solution set to the following system?
y < x² + 3
y > x² - 2x + 8
a) (-4,2)
b) (0,6)
c) (1,12)
d) (4,16)
Answer: D
Step-by-step explanation:
(4,16)
A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 13% chose chocolate pie, and the margin of error was given as 5 percentage points. Given specific sample data, which confidence interval is wider the 95% confidence interval interval? Why is it wider? r the 80% confidence Choose the correct answer below A. An 80% confidence interval must be wider than a 95% confidence interval in order to be more confident that it captures the true value of the population proportion. B. A 95% confidence interval must be wider than an 80% confidence interval because it contains 95% of the true population parameters, while the 80% confidence interval only contains 80% of the true population parameters B. C. An 80% confidence interval must be wider thant> 95% confidence interval because it contains pr 100%-80%-20% of the true population parameters, while the 95% confidence interval only contains 100%-95%-5% of the true population parameters. D. A 95% confidence interval must be wider than an 80% confidence interval in order to be more confident that it captures the true value of the population proportion. D.
The correct answer is D. A 95% confidence interval must be wider than an 80% confidence interval in order to be more confident that it captures the true value of the population proportion.
The width of a confidence interval reflects the degree of uncertainty about the estimate of the population parameter. A wider interval indicates a higher degree of uncertainty, while a narrower interval indicates a lower degree of uncertainty.
The confidence level of a confidence interval is the probability that the interval contains the true population parameter. For example, a 95% confidence interval means that there is a 95% probability that the interval contains the true population parameter. Similarly, an 80% confidence interval means that there is an 80% probability that the interval contains the true population parameter
Since a 95% confidence interval is more confident that it captures the true value of the population parameter than an 80% confidence interval, the 95% confidence interval must be wider in order to capture the true value with a higher degree of confidence.
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Which function has a y-value of 6, if the x-value is 3?
Oy= 3 x
Oy=x-3
Oy=x+2
O y = 2 x
Option (d) i.e y = 2x is correct option as this function is satisfying given values of y and x.
What is a function in mathematics?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Peter Dirichlet initially offered the standard concept of function in 1837.
y and x are coupled in such a way that there is a distinct value of y for each value of x, and this relationship is frequently represented as y = f(x), or "f of x." In other words, the same x cannot have more than one value for f(x).
We need to check by substituting value of y in every equation to check correct option.
(a) Substituting y=6 and x=3 in function
L.H.S = 6
R.H.S = 3x= 3×3=9
L.H.S≠R.H.S
So, it is not a correct option.
(b) Substituting y=6 and x=3 in function
L.H.S = 6
R.H.S = x-3= 3-3=0
L.H.S≠R.H.S
So, it is not a correct option.
(c) Substituting y=6 and x=3 in function
L.H.S = 6
R.H.S = x+2= 3+3=5
L.H.S≠R.H.S
So, it is not a correct option.
(d) Substituting y=6 and x=3 in function
L.H.S = 6
R.H.S = 2x= 2×3=6
L.H.S=R.H.S
So, it is correct option.
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Assuming independent assortment, how many different gametes can be formed by an organism that is homozygous for 3 and heterozygous for 2 genes?a. 2 b. 3 c. 2 + 2 = 4 d. 2 + 3 = 6 e. 3 + 3 = 9
The correct answer is (D) 2 + 3 = 6. If an organism is homozygous for 3 genes and heterozygous for 2 genes, it can produce a total of 2 + 3 = 5 different gametes.
When an organism is homozygous for a gene, it means that it carries two copies of the same allele for that gene. When an organism is heterozygous for a gene, it means that it carries two different alleles for that gene.
In this case, the organism is homozygous for 3 genes, which means that all its gametes will carry the same alleles for these 3 genes. It is also heterozygous for 2 genes, which means that it can produce gametes that carry either one of the two alleles for these 2 genes.
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A time-and-motion study measures the time required for an assembly-line worker to perform a repetitive task. The data show that the time required to bring a part from a bin to its position on an automobile chassis varies from car to car according to a Normal distribution with mean 11 seconds and standard deviation 2 seconds. The time required to attach the part to the chassis follows a Normal distribution with mean 20 seconds and standard deviation 4 seconds. The study finds that the times required for the two steps are independent. A part that takes a long time to position, for example, does not take more or less time to attach than other parts. Management's goal is for the entire process to take less than 30 seconds. Find the probability that this goal will be met for a randomly selected part.
The amount of time required for an assembly line worker to complete a repetitive task is measured using a time and motion study.
According to the data, the average time it takes to move apart from the bin to its place on a car's chassis is 11 seconds, while the standard deviation is 2 seconds.
If XX and YY are independent, the property mean and variance are as follows: X 1 = 11; sigma_X_1 = 2, X 1 = 2, mu_X_2 = 20, X 2 = 20, sigma_X_2 = 4, and X 2 = 4.
aX+bY = a X + b Y; sigma_aX+bY = a X + b Y; aX+bY 2 = a 2 X 2 + b 2 Y 2; and finally, we have the following results:
X 1 + X 2 = X 1 + X 2 = 11+20=31 sigma_X_1+X_2=sqrtsigma_X_1+sigma_X_2=sqrtsigma_X_1+sigma_X_2=sqrtsigma_X_2=sqrtsigma_X_2=sqrtsigma_X_2=sqrtsigma_X_1+
The value reduced by the mean and divided by the standard deviation is the z-score:
z=\dfrac{x-\mu} {\sigma} =\dfrac{30-4.4721} \approx - 0.22
z=σx−μ =4.472130−31
≈−0.22
Decide the relating esteem utilizing table A:
P (X_1+X_2 30) = P(Z-0.22) = 0.4129 P (X 1 30) = P(Z-0.22) = 0.4129
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A 4-cylinder engine with 543 Cubic Centimeters volume per cylinder has what approximate displacement?
Answer:
you would times them both so 4x543 =2172
Step-by-step explanation:
543 cubic centimeters has 0.543 L approximate displacement.
What is Engine displacement?Engine displacement means the displacement of the piston inside cylinder from Bottom Dead Center into Top Dead Center in one cycle.
Basic formula to calculate engine displacement is =
V = π/4 x D² x H x N
Where :
D = Bore Diameter
H = Length of Stroke
N = Number of Cylinder
Since the question has already stated cubic centimeter, it has already shown the displacement. So, we can ignore above formula and the 4-cylinder engine information.
First, we state what is known. It is the displacement at cubic centimeter.
Cubic centimeter = 543 cc
Next, we change the unit of cubic centimeter (cc) into liter (L)
Displacement = cc / 1000 L
= 543 / 1000 L = 0.543 L
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A bank teller hourly wage will increase from $18 to $21.60. What percent increase does this represent?
The percentage increase is about 16.66%.
What is a percentage increase?
The percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in the percentage.
The initial amount was $18 and the final amount is $21.60.
By using the percentage increase formula, we can write
Percentage increase = (final value - initial value)/|Final value| * 100
= ((21.60 - 18)/21.60)*100
= 16.66%
Hence, the percentage increase is about 16.66%.
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One angle measures 18°, and another angle measures (6d − 6)°. If the angles are complementary, what is the value of d? d = 2 d = 13 d = 31 d = 36.2
The value of d for the given angles will be equal to d = 13. The correct option is B.
What is the complementary angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
Complementary angles are formed when the sum of two angles equals 90 degrees. 30 degrees and 60 degrees, for example, are complementary angles.
Given that one angle measures 18° and another angle measures (6d − 6)°.
The value of d will be calculated as,
18 + 6d - 6 = 90
6d + 12 = 90
6d = 90 - 18
6d = 78
d = 78 / 6
d = 13
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Given BD is the segment bisector of AC, complete the flowchart proof below. Note
that the last statement and reason have both been filled in for you.
D
The triangle ΔADB is congruent to the triangle ΔCDB by the ASA postulate.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangles are said to be congruent if two points and the contained side among one triangle match two angles and the contained side of another triangle.
In triangles ΔADB and ΔCDB, then we have
∠BAD = ∠BCD (Given)
∠BDA = ∠BDC (Given)
AD = AD (Common side)
The triangle ΔADB is congruent to the triangle ΔCDB by the ASA postulate.
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(100 POINTS!)
Create a proportion using the form %/100= is/of to represent the following word problem:
15 is 1 1/2 % of what number?
Answer:
To create a proportion using the form %/100 = is/of, we can first write the given information in the form %/100 = is/of. In this case, we know that 1 1/2% represents 15, so we can write:
1 1/2%/100 = 15/of
Next, we need to solve for the "of" value, which is the number we are trying to find. To do this, we can multiply both sides of the equation by 100 and then divide both sides by 1 1/2% to get:
(1 1/2%/100) * 100 = (15/of) * 100
of = (15/1 1/2%) * 100
Finally, we can evaluate the right-hand side of the equation to find the value of "of". Since 1 1/2% is the same as 1.5%, we can substitute 1.5 for 1 1/2% in the equation to get:
of = (15/1.5%) * 100
of = (15/0.015) * 100
of = 1000
Therefore, the number we are trying to find is 1000.
In summary, the proportion that represents the given word problem is:
1 1/2%/100 = 15/1000
Answer:
[tex]\textsf{Proportion}: \quad \sf \dfrac{1.5}{100}=\dfrac{15}{x}[/tex]
[tex]\textsf{Solution}: \quad \sf x=1000[/tex]
Step-by-step explanation:
Given proportion formula:
[tex]\sf \dfrac{\%}{100}=\dfrac{is}{of}[/tex]
Given word problem:
15 is 1¹/₂% of what number.Let the unknown number be x.
Therefore:
% = 1.5is = 15of = xSubstitute these into the proportion formula to create a proportion to represent the given word problem:
[tex]\sf \dfrac{1.5}{100}=\dfrac{15}{x}[/tex]
To solve the proportion, cross multiply:
[tex]\implies \sf 1.5x=15 \cdot 100[/tex]
[tex]\implies \sf 1.5x=1500[/tex]
Divide both sides by 1.5:
[tex]\implies \sf \dfrac{1.5x}{1.5}=\dfrac{1500}{1.5}[/tex]
[tex]\implies \sf x=1000[/tex]
I’ll give BRAINLIEST if correct pls answer need ASAP question is in the photo attached
Answer:
Part A: 2 Part B: 2- and 4-Part C: 8 The graph shows at 8 seconds the slope starts to decrease rapidly. Part D: I believe at 14 seconds the water balloon would be o the ground.
Step-by-step explanation:
Find the rate of change
1/5
-5
5
-1/5
The rate of change of the table of values is calculated as: A. 1/5.
How to Find the Rate of Change?Given the table above, the rate of change can be calculated using the formula below:
Rate of change (m) = change in y / change in x.
Using two pairs of values from the table, (10, 2) and (20, 4):
Change in y = 4 - 2 = 2
Change in x = 20 - 10 = 10
Therefore:
Rate of change (m) = 2/10
m = 1/5
Therefore, the rate of change is determined as: A. 1/5.
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Given rectangle EFGH below, EI = 35. If FH = 2z+8, solve for z.
Answer:
N
65
Ex
Submit Answer
By using the properties of rectangle, it can be calculated that-
Value of z is 31°
What is a rectangle?
Rectangle is a four sided two dimensional figure which satisfies the properties of a parallelogram and whose every angle is 90°
FH = 2z + 8
EG = 2z + 8 [Diagonals of a rectangle are equal]
EI = 35
EG = [tex]35 \times 2 = 70[/tex] [Diagonals of rectangle bisect each other]
So,
2z + 8 = 70
2z = 70 - 8
2z = 62
z = [tex]\frac{62}{2}[/tex]
z = 31
Value of z is 31°
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Bookwork code: A99
The table shows the hair colours of the
students in a sports team.
Hair colour
Black
Blonde
Brown
Frequency
1
< Back
a) What fraction of the students have brown
hair? Give your answer in its simplest form.
b) How many sections on this pie chart
would you shade to show the students with
brown hair?
4
2
Scroll down
Watch video
Answer >
A fraction of the students who have brown hair is equal to 1/7.
You should shade only one (1) section on the pie chart to show the number of students with brown hair.
What is a pie chart?In Mathematics, a pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors or sections.
Based on the information provided in the table (see attachment), we can logically deduce the following parameters about the various hair color;
Number of brown hair = 1 brown hair.
Number of blonde hair = 4 blonde hair.
Number of black hair = 2 black hair.
Therefore, the total number of hairs is equal to 7 hairs.
For the fraction of students with brown hair, we have;
Fraction = 1/7.
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I kinda get it and i kinda do pleas help
Answer:
Step-by-step explanation:
first things first go back in the lesson or your notes if you wrote down some and if not go right some down and in the notes there would be the answer between pages 1-5 or maybe 6 IDR ( i dont remember ) but look thru those pages and you will find the answer hope this helped. please mark me brainiest please.