Answers
Therefore , the solution of the given problem of graph comes out to be
option c is correct it shows an association of the distribution of different mode of transportation among the same age of group.
What is graph ?Academics use graphs to visually represent or chart happenings or quantities in a logical manner. The interaction between a number of objects is frequently represented by a graph point. A graph is a non-linear storage structure made up of nodes, also known as vertices, and edges. The vertices, sometimes referred to as nodes, should be joined together with glue. Vertex numbers in this graph are 1, 2, 3, or 5, while edge numbers are 1, 2, 1, 3, 2, 4, etc. (2.5). (3.5). (4.5). (4.5). (4.5).
Here,
Given : A graph having choices of adult , child , teen and senior mode of transportation ,
In different age the mode of transportation preferred by among the same ages .
Thus ,
it shows an association of the distribution of different mode of transportation among the same age of group.
So , option c is the correct answer.
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Related Questions
y=100000(0.25)^8 exponential decay
Answers
y=100000(0.25)^8 exponential decay is 1.526.
How to find the exponential decay?The formula represents exponential decay with a decay factor of 0.25 and an initial value of 100,000. To evaluate the formula, you can simply substitute 8 for the variable x (since the formula has y in terms of x) and calculate the result:
y = 100000(0.25)^8
y = 100000(0.00001525878906)
y ≈ 1.526
Therefore, the value of y for x = 8 is approximately 1.526. This means that after 8 units of time, the initial value of 100,000 has decayed to around 1.526.
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Answer please, I'll give brainliest
Answers
Answer:
1st one
Step-by-step explanation:
Answer: A. (2/5,-3)
Step-by-step explanation:
in order to find the solution to the set of equations, you need to find one variable first, lets fing y first
10x+3y=-5
10x = -5 - 3y
x = (-5 -3y)/10
substitute this in for x in the other equation
-5((-5 - 3y)/10) -4y = 10
(25 + 15y)/10 -4y = 10
25/10 + 15y/10 -4y = 10
make all fractions on the left side
25/10 + 15y/10 - 40y/10 = 10
combine
25/10 -25y/10 = 10
multiply both sides by 10 to get rid of the denominator
25 - 25y = 100
combine like terms
-25y = 75
divide
y = -3
plug y into the first equation to find x
10x + 3(-3) = -5
10x -9 = -5
10x = 4
x = 4/10
simplify
x = 2/5
hope this helps!
Which correctly describes how the graph of the inequality 6y − 3x > 9 is shaded?
Group of answer choices
Above the solid line
Below the solid line
Above the dashed line
Below the dashed line
Answers
Explanation
A dashed line is used in inequalities to show the solution is above or below the line but not ON the line (more than or less than symbols).
A solid line is used for solutions that are more than or equal, or less than or equal to the points on that line.
So 6y -3x > 9 tells us the solution is more than 9 but not equal to 9 so it’s above the dashed line
x > -3 and y > 1.5
See attached graph
2x - (-4x + 5b). x = 2. b = -5
Answers
Answer:
37
Step-by-step explanation:
2x - (-4x + 5b); x = 2; b = -5
2(2) - (-4 × 2 + 5 (-5)) = 4 - (-8 - 25) = 37
I hope this helps
The measures of the angles of △ABC are given by the expressions in the table.
Answers
The angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.
Define triangles.A triangle is a closed geometric shape with three sides, three angles, and three line segments. Three non-collinear points are joined by line segments to create the simplest polygon, which has three non-collinear points.
Triangles can be categorized according to the size of their sides and angles. Triangles can be categorized as equilateral (all sides are equal in length), isosceles (both sides are equal in length), or scalene based on their sides (all sides are different in length). Triangles can be categorized as acute (all angles are less than 90 degrees), obtuse (one angle is greater than 90 degrees), or right (one angle is greater than 90 degrees) (one angle is exactly 90 degrees).
In any triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can write:
a + b + c = 180
Substituting the given values, we get:
(6x-1) + 20 + (x+14) = 180
Simplifying and solving for x, we get:
7x + 33 = 180
7x = 147
x = 21
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their values:
angle a = (6x-1) = (6*21-1) = 125 degrees
angle b = 20 degrees
angle c = (x+14) = (21+14) = 35 degrees
Therefore, the angles of the triangle are 125 degrees, 20 degrees, and 35 degrees.
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A supply chain manager faced with choosing among four possible locations has assessed each location according to the following criteria, where the weights reflect the importance of the criteria. How can he use this information to choose a location? Can you develop a quantitative approach to do this?
Criteriia Weight 1 2 3 4
Raw material availability 0.15 G P OK VG
Infrastructure 0.1 OK OK OK OK
Transportation cost 0.35 VG OK P OK
Labor relations 0.2 G VG P OK
Quality of life 0.2 G VG P OK
VG = Very good
G = Good
OK = Acceptable
P = Poor
Answers
The best option is Location 2, which you can determine by adding up the points for each site using the information below.
What is meant by reflect?An image of the shape reflected in a mirror. A line, called the line of reflection, is where an image will reflect. Every point in one figure is equal distance from every corresponding point in the other, and this is what is meant when one figure is said to reflect the other.Reflection is a type of transformation that reverses a shape in a mirror line, also known as a line of reflection, such that each point is the same distance from the mirror line as its mirrored point. For instance, Triangle P has Triangle Q as a reflection on the line x = 4 x = 4 x = 4. Representing the reverse of a figure, a reflection is a change.The complete question is:
A supply chain manager faced with choosing among four possible locations has assessed each location according to the following criteria, where the weights reflect the importance of the criteria. Use the information below to calculate total points for each location and choose the best option. Round your answers to two decimal places.
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What is the probability of flipping a coin 11 times and getting heads 4 times? Round your answer to the nearest tenth of a percent. O A. 8.1% O B. 22.6% O C. 16.1% ) D. 0.5%
Answers
Answer:
The answer is (A) 8.1%.
Step-by-step explanation:
The probability of flipping a coin and getting heads is 1/2 or 0.5. Assuming the coin is fair, the probability of getting heads 4 times in 11 flips is given by the binomial probability formula:
P(4 heads in 11 flips) = (11 choose 4) * (0.5)^4 * (0.5)^(11-4) = 330 * 0.5^11
Using a calculator, we get:
P(4 heads in 11 flips) ≈ 8.1%
Therefore, the answer is (A) 8.1%.
The left-hand and right-hand derivatives of f at a are defined byf′−(a)=limh→0−f(a+h)−f(a)h�′−(�)=limℎ→0−�(�+ℎ)−�(�)ℎand f′+(a)=limh→0+f(a+h)−f(a)h�′+(�)=limℎ→0+�(�+ℎ)−�(�)ℎif these limits exist. Then f'(a) exists if and only if these one-sided derivatives exist and are equal.(a) Find f' ^- (4) and f' ^+ (4) for the functionf(x)=⎧⎪⎨⎪⎩0 if x⩽05−x if 0
Answers
Answer:
Step-by-step explanation:
To find the left-hand derivative of f at x = 4, we need to evaluate:
f′−(4) = limh→0−f(4+h)−f(4)h
Since f(x) = 0 for x ≤ 0 and f(x) = 5 - x for 0 < x < 5, we have:
f(4 + h) = 0 for h < -4
f(4 + h) = 5 - (4 + h) = 1 - h for -4 < h < 1
f(4 + h) = undefined for h > 1
Therefore, we can rewrite the limit as:
f′−(4) = limh→0−f(4+h)−f(4)h = limh→0−(1 - h) - 0h = -1
To find the right-hand derivative of f at x = 4, we need to evaluate:
f′+(4) = limh→0+f(4+h)−f(4)h
Using the same reasoning as before, we can rewrite the limit as:
f′+(4) = limh→0+(5 - (4 + h)) - 0h = -1
Since the left-hand derivative and the right-hand derivative are equal, we can conclude that f'(4) exists and is equal to:
f'(4) = f′−(4) = f′+(4) = -1
Therefore, the derivative of f at x = 4 is -1.
Solve the following and list any extraneous solutions
1. √30- x = x
2. x = √42 - x
3. √12-r=r
4. m = √56 - m
5. r = √-1-2r
6. √4n+8 = n +3
7. -n+√6n + 19 = 2
8. 4+√-3m + 10 = m
9. x-5=√x+1
10. n-7= √√3n - 21
Answers
Due to length restrictions, we kindly invite to check the explanation for further detail on the solution of radical equations and existence of extraneous solutions.
How to solve radical equations
In this question we have ten cases of radical equations, whose roots can be found by algebra properties. The solutions to each equation is listed below: (Please notice that a solution is extraneous when an absurdity is found)
Case 1
√(30 - x) = x
30 - x = x²
x² + x - 30 = 0
(x + 6) · (x - 5) = 0
x = - 6
√[30 - (- 6)] = - 6
- √36 = - 6
- 6 = - 6
x = 5
√[30 - 5] = 5
√25 = 5
5 = 5
Case 2
x = √(42 - x)
x² = 42 - x
x² + x - 42 = 0
(x + 7) · (x - 6) = 0
x = - 7
7 = √[42 - (- 7)]
7 = √49
7 = 7
x = 6
6 = √(42 - 6)
6 = √36
6 = 6
Case 3
√(12 - r) = r
12 - r = r²
r² + r - 12 = 0
(r + 4) · (r - 3) = 0
x = - 4
√[12 - (- 4)] = - 4
- √16 = - 4
- 4 = - 4
x = 3
√(12 - 3) = 3
√9 = 3
3 = 3
Case 4
m = √(56 - m)
m² = 56 - m
m² + m - 56 = 0
(m + 8) · (m - 7) = 0
m = - 8
- 8 = √[56 - (- 8)]
- 8 = - 8
m = 7
7 = √(56 - 7)
7 = √49
7 = 7
Case 5
r = √(1 - 2 · r)
r² = 1 - 2 · r
r² + 2 · r + 1 = 0
(r + 1)² = 0
r = - 1
- 1 = √[1 - 2 · (- 1)]
- 1 = √3 (EXTRANEOUS)
Case 6
√(4 · n + 8) = n + 3
4 · n + 8 = (n + 3)²
4 · n + 8 = n² + 6 · n + 9
n² + 2 · n + 1 = 0
(n + 1)² = 0
n = - 1
√[4 · (- 1) + 8] = (- 1) + 3
√4 = 2
2 = 2
Case 7
- n + √(6 · n + 19) = 2
√(6 · n + 19) = n + 2
6 · n + 19 = (n + 2)²
6 · n + 19 = n² + 4 · n + 4
n² - 2 · n - 15 = 0
(n - 5) · (n + 3) = 0
n = 5
- 5 + √(6 · 5 + 19) = 2
- 5 + √49 = 2
- 5 + 7 = 2
2 = 2
n = - 3
- (- 3) + √[6 · (- 3) + 19] = 2
3 + √1 = 2
4 = 2 (EXTRANEOUS)
Case 8
4 + √(- 3 · m + 10) = m
√(10 - 3 · m) = m - 4
10 - 3 · m = (m - 4)²
10 - 3 · m = m² - 8 · m + 16
m² - 5 · m + 6 = 0
(m - 6) · (m + 1) = 0
m = 6
4 + √(- 3 · 6 + 10) = 6
4 + √(- 8) = 6 (EXTRANEOUS)
m = - 1
4 + √[- 3 · (- 1) + 10] = - 1
4 + √13 = - 1 (EXTRANEOUS)
Case 9
x - 5 = √(x + 1)
(x - 5)² = x + 1
x² - 10 · x + 25 = x + 1
x² - 11 · x + 24 = 0
(x - 3) · (x - 8) = 0
x = 3
3 - 5 = √(3 + 1)
- 2 = - 2
x = 8
8 - 5 = √(8 + 1)
3 = √9
3 = 3
Case 10
n - 7 = √(3 · n - 21)
(n - 7)² = 3 · n - 21
n² - 14 · n + 49 = 3 · n - 21
n² - 17 · n + 70 = 0
(n - 7) · (n - 10) = 0
n = 7
7 - 7 = √(3 · 7 - 21)
0 = 0
n = 10
10 - 7 = √(3 · 10 - 21)
3 = 3
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use the definition of derivative. find the derivative of f(x)=cosx
Answers
For the given function f(x) = cos x, f '(x) = -sin x.
By the definition of the derivative, this means that -sin x provides the rate of change of cos x at a specific angle.
What is meant by the derivative of a function?
The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. It is described as the fluctuating rate at which a function changes in relation to an independent variable. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised. The sensitivity of the dependent variable to the independent variable is assessed using the derivative. Calculus's core tool is derivative.
We are given the function f(x) = cos x
The derivative of cos x is -sin x.
That is, f '(x) = -sin x
Therefore, by definition of the derivative, this means that -sin x provides the rate of change of cos x at a specific angle.
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The bricks on the warehouse of the museum are crumbling. The community needs to hire a contractor
to replace the bricks with siding because it is more cost efficient. You have chosen the siding that will
replace the bricks. Each piece of siding is 4 ¾ inches x 24 inches. Estimate the cost to replace the
brick with siding with siding priced at 22.65 a piece.
The Warehouse
sides:
17ft
25ft
33ft
A. Determine the surface area of the warehouse.
B. What is the area of the surfaces that need siding? Justify your reasoning.
C. How many pieces of siding need to be purchased? Justify your reasoning.
D. What is the approximate cost of siding that will be needed to cover the outside of the
warehouse? Justify your reasoning.
Answers
Answer:
Step-by-step explanation:
here is a step by step answer:
A. To determine the surface area of the warehouse:
Identify the dimensions of each side of the warehouse. In this case, we know that the sides are 17 ft, 25 ft, and 33 ft in length, and the height is 10 ft.
Calculate the area of each side by multiplying the length and height. For example, the area of the first side is 17 ft x 10 ft = 170 sq ft.
Add up the areas of all the sides to get the total surface area of the warehouse. In this case, the total surface area is 170 + 250 + 330 = 750 sq ft.
B. To determine the area of the surfaces that need siding:
Since all sides of the warehouse need to be covered with siding, the area of the surfaces that need siding is equal to the total surface area of the warehouse. In this case, we calculated the total surface area to be 750 sq ft.
C. To determine how many pieces of siding need to be purchased:
Identify the size of each piece of siding. In this case, we know that each piece of siding is 4 ¾ inches x 24 inches.
Convert the size of each piece of siding to square feet. To do this, we can divide the length and width by 12 to convert to feet, and then multiply the two dimensions to get the area. In this case, 4 ¾ inches is approximately 0.3958 feet, and 24 inches is 2 feet, so the area of each piece of siding is approximately 0.7916 sq ft.
Divide the total surface area of the warehouse by the area of each piece of siding to get the number of pieces needed. In this case, we calculated that the total surface area is 750 sq ft, and each piece of siding covers approximately 0.7916 sq ft. So, the number of pieces needed is 750 sq ft ÷ 0.7916 sq ft/piece = 946.84 pieces. We must round up to the nearest whole number because we can't purchase a fraction of a piece of siding. So, we need to purchase 947 pieces of siding.
D. To determine the approximate cost of siding needed to cover the outside of the warehouse:
Identify the price per piece of siding. In this case, we know that the siding is priced at $22.65 per piece.
Multiply the number of pieces of siding needed by the price per piece to get the total cost of siding. In this case, we calculated that we need 947 pieces of siding, so the total cost of siding is 947 x $22.65 = $21,465.55. So, the approximate cost of siding needed to cover the outside of the warehouse is $21,465.55.
help with maths problem please
Answers
The area of the shaded region is 73.5 cm square.
How to find the area of a region?Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.
We are given the dimension of the shaded region.
Length = 15 cm
Breadth = 7 cm
The area of the trapezium is
Area = 1/2(sum of non parallel sides)height
Area = 1/2 (12 + 9) 7
Area = 1/2 x 21 x 7
Area = 73.5
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According to Statistics Canada, approximately 29% of all St. Marys residents are in the 45–64 age range. Suppose that 97% of the people who used the new bins, once they were introduced for the first time during the initial two-month period, were in the 45–64 age category. Use this information to determine whether age is independent of the initial use of the bins during the introductory two-month time period. Explain your answer.
Answers
To determine whether age is independent of the initial use of the bins, we need to compare the actual proportion of people in the 45-64 age range who used the new bins during the initial two-month period with the expected proportion if age and bin use were independent.
First, we need to calculate the expected proportion. If age and bin use were independent, the proportion of people in the 45-64 age range who used the new bins during the initial two-month period would be equal to the overall proportion of people in the 45-64 age range in the population, which is 0.29.
The actual proportion of people in the 45-64 age range who used the new bins during the initial two-month period is 0.97.
We can use a chi-square test to determine whether the difference between the observed and expected proportions is statistically significant. The null hypothesis is that age and bin use are independent, and the alternative hypothesis is that they are not independent.
Using the chi-square test with one degree of freedom and a significance level of 0.05, we obtain a critical value of 3.84. The test statistic is:
(0.97 - 0.29)^2 / 0.29 + (0.03 - 0.71)^2 / 0.71 = 196.64
Since the test statistic is greater than the critical value, we reject the null hypothesis and conclude that age and bin use are not independent. In other words, there is a significant association between age and the initial use of the new bins.
Identify the solution to the system of linear equations.
y = -3x + 2
y = x - 6
A. (2, -4)
B. (4, -2)
C. (0, 2)
D. (1, -1)
Answers
The system of linear equations is solved by finding x = 2 and y = -4, making the solution (2, -4).
To find the solution to the system of linear equations,
find the values of x and y that satisfy both equations simultaneously.
The equations are,
y = -3x + 2
y = x - 6
To find the solution, set the right-hand sides of both equations equal to each other:
-3x + 2 = x - 6
Now, let's solve for x:
-3x - x = -6 - 2
-4x = -8
x = -8 / -4
x = 2
Now that the value of x, we can find y by substituting x back into one of the equations.
Let's use the second equation:
y = 2 - 6
y = -4
Therefore, the solution to the system of linear equations is equal to option A. (2, -4).
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Calculate the cubic roots of the complex number Z:
Z=-27
(number 6)
Answers
The cubic root of z = -27 is -3
What is the cubic rootA real cube and tree roots may be the first images that come to mind when we hear the terms "cube" and "root." Is it not? Well, the concept is the same. Root refers to the main source or starting point. So, all we need to do is consider "which number's cube should be taken to get the given number." The cube root definition in mathematics is expressed as The cube root is the quantity that must be three times multiplied to yield the initial quantity. Let's look at the cube root equation: ∛x = y, where y is the cube root of x. Every number with a little 3 inscribed on it can be represented by the radical sign as the cube root symbol.
In this problem, the cubic root of z = -27 can be calculated as;
z = -∛-27
z = -3
This is because 27 is a perfect cube
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P is the point (2, 5) and Q is the point (6, 0).
A line l is drawn through P perpendicular to PQ to meet the y-axis at the point R. Find the coordinates of the point R.
Answers
The coordinates of the point R: (0, 3.4)
What is the slope?
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line
Slope PQ 5–0/ 2–6 = 5 /-4
equation of PQ y =-5/4 x +c ;
this passing through 2,5
5 =-5/4*2 +c ; C = 5 -5/2 =5/2
y =-5x/4+5/2 =-5x+10/4 ; 4y =-5x +10 ;
equation of PQ =5x +4y-10 =0 ;
slope of PR : m1 *m2 =-1 ;m2 = -1/ [-5/4 ] = 4/5
equation of PR y = mx +c this passes through [2,5]
5 = 4/5*2 +C so C = 5- 8/5 =17/5
y =4 x /5 +17/5 so coordinates of R = [0, 3.4]
Hence, the coordinates of the point R: (0, 3.4)
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What mixed number is equivalent to 27/4
Answers
Answer: 6 3/4 I hope this helps
Step-by-step explanation:
27/4
Convert the improper fraction into a mixed number
6 3/4
Mixed number-A number written as a whole number and a fraction.
Answer please, I'll give you brainliest
Answers
Answer:
pretty sure its "A"
Step-by-step explanation:
A store is offering 20% discounts on new laptops and 10% discounts on new printers when the two are purchased together. The original prices of the two together is at least $1,050. The discounted price exceeds $860. Which system of inequalities can be used to find the possible original prices of a laptop, x, and of a printer, y?
Answers
The system of inequalities that can be used to find the possible original prices of a laptop, x, and of a printer, y is: x + y ≥ 1050 and 0.8x + 0.9y > 860
How to determine the system of inequalitiesLet x be the original price of the laptop and y be the original price of the printer.
So, the discounted price of the laptop is 0.8x and the discounted price of the printer is 0.9y
If the two are purchased together, the total discounted price is:
0.8x + 0.9y
This exceeds $860
0.8x + 0.9y > 860
The original prices of the two together is at least $1,050.
This can be written as:
x + y ≥ 1050
So, we have
x + y ≥ 1050 and 0.8x + 0.9y > 860
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The stock price of Alps Co. is $53.50. Investors require a return of 13 percent on similar stocks. If the company plans to pay a dividend of $3.40 next year. what groeth rate is expected for the company's stock price?
Answers
Answer:
The expected growth rate for the company's stock price is 9.7%. This is calculated by subtracting the dividend yield (3.40/53.50 = 0.0635) from the required return (13%).
A carpenter is building a rectangular table. He wants the perimeter of the tabletop to be no more than 28 feet. He also wants the length of the tabletop to be greater than or equal to the square of 2 feet less than its width. Create a system of inequalities to model the situation, where x represents the width of the tabletop and y represents the length of the tabletop. Then, use this system of inequalities to determine the viable solutions.
Answers
The option is (B) The entire solution region is viable is correct when both the inequalities are solved.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
Let's first translate the given information into mathematical inequalities -
The perimeter of the tabletop to be no more than 28 feet -
Perimeter = 2(length + width) ≤ 28
The length of the tabletop to be greater than or equal to the square of 2 feet less than its width -
Length ≥ (Width - 2)²
We can combine these two inequalities to form the system -
2(length + width) ≤ 28
Length ≥ (Width - 2)²
Now, let's solve for y in terms of x (so that we can graph the solution region) -
2(y + x) ≤ 28
y ≥ (x - 2)²
Simplifying the first inequality -
y ≤ -x + 14
Now graph both the inequalities -
The viable solutions are the points that satisfy both inequalities, which lie in the shaded region above.
Therefore, there is no part of the solution region that includes negative length or negative width.
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A shipping container is in the form of a right rectangular prism, with dimensions of 35 ft by 8 ft by 7 ft 6 inches. How many cubic feet of shipped goods would it hold when it is full? Round your answer to the nearest tenth if necessary.
Answers
Answer:
1110
Step-by-step explanation:
Charles had m yards of material. He used 0.4m yards of material to make a costume, 0.2m yards to make pillows and 0.3m yards to make a bag. Which expression shows how many yards of fabric Charles has left? Check all that apply.
(A) 0.1m
(B) 0.9m
(C) m – 0.9m
(D) (0.4 + 0.2 + 0.3)m
(E) (1 – 0.4 – 0.2 – 0.3)m
(F) m – (0.4 + 0.2 + 0.3)m
(G) m – 0.4m – 0.2m – 0.3m
(H) m – (0.4m + 0.2m + 0.3m) check all that apply
Answers
Answer:
(A) [tex]0.1m[/tex](C) [tex]m - 0.9m[/tex](E) [tex](1 - 0.4 - 0.2 - 0.3)m[/tex](F) [tex]m - (0.4 + 0.2 + 0.3)m[/tex](G) [tex]m - 0.4m - 0.2m - 0.3m[/tex](H) [tex]m - (0.4m + 0.2m + 0.3m)[/tex]Step-by-step explanation:
To determine how many yards of fabric Charles has left, we need to subtract the total amount of fabric used for the costume, pillows, and bag from the initial amount of fabric (m yards). The total amount of fabric used is:
[tex]0.4m + 0.2m + 0.3m = 0.9m.[/tex]Now, we can subtract the total used fabric from the initial amount of fabric:
[tex]m - 0.9m[/tex]The correct expressions that show how many yards of fabric Charles has left are:
(A) [tex]0.1m[/tex](C) [tex]m - 0.9m[/tex](E) [tex](1 - 0.4 - 0.2 - 0.3)m[/tex](F) [tex]m - (0.4 + 0.2 + 0.3)m[/tex](G) [tex]m - 0.4m - 0.2m - 0.3m[/tex](H) [tex]m - (0.4m + 0.2m + 0.3m)[/tex]Why are the options correct/incorrect?(A) 0.1m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(B) 0.9m: This option is incorrect because it represents the amount of fabric Charles used, not the amount he has left.(C) m - 0.9m: This option is correct because it represents the initial amount of fabric (m) minus the total amount of fabric used for the costume, pillows, and bag (0.9m), which gives the remaining amount of fabric.(D) (0.4 + 0.2 + 0.3)m: This option is incorrect because it represents the total amount of fabric Charles used to make the costume, pillows, and bag, not the amount he has left, like option (B).(E) (1 - 0.4 - 0.2 - 0.3)m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(F) m - (0.4 + 0.2 + 0.3)m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(G) m - 0.4m - 0.2m - 0.3m: This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.(H) m - (0.4m + 0.2m + 0.3m): This option is correct because it represents the amount of fabric Charles has left after using 0.9m of fabric.Final answerSo, the correct options are (A), (C), (E), (F), (G), and (H).
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how many ways can we distribute 20 distinct exams to grade among 4 people: a,b,c,d, if a has to grade 3 exams, b has to grade 4 exams, c has to grade 5 exams, and d has to grade 8 exams? there might be more than one correct answer
Answers
Answer:
Step-by-step explanation:
the answer is
B
and
C
Select the total number of possible permutations.
On a separate piece of paper, draw tree diagrams to show all possible outcomes if you match the letters in box 1 to the numbers in box 2.
Answers
The first node in set 1 should represent the element.
For each potential value in set 2, create a branch.
Create a new node to represent the following set 1 element at the end of each branch.
Steps 2-4 must be repeated for each additional Set 1 component.
All potential outcomes are represented by the final nodes.
The appropriate line of best fit for the scatter plot is y hat equals 67 hundredths times x plus 4 and 5 hundredths.
What is number?The number is a mathematical entity used to represent a computer's magnitude it can be a symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three, or eight numbers are used to verify the context including counting measuring and computing.
This line of best fit indicates that the number of households with cable television will increase by 67 hundredths (or 0.67) each year. This line of best fit is based on the data points on the scatter plot, which suggest that the number of households with cable television has been steadily increasing over the years.
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The height
y
(in feet) of a ball thrown by a child is
y
=
−
1
14
x
2
+
6
x
+
5
where
x
is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand?
feet
(b) What is the maximum height of the ball?
feet
(c) How far from the child does the ball strike the ground?
feet
Answers
a) The ball is at 5 feet height when it leaves the child's hand
b) The maximum height of the ball is 131 feet
c) 84.825 ft far from the child, the ball strike the ground
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.
(a)
At the beginning when the ball leaves the hand of the child, the horizontal distance was 0, so putting x=0 we can get the height of the ball.
at time zero, t=0, the distance is 5 feet, so the ball is at 5 feet height
(b)
the max occurs at the average of the solutions, which is 28.
or -b/2a = -6/(2*-1/14) = -6/ (-1/7) = 42 ft
-(1/14)*42^2 +6*42 + 5 = 131
so the max height is 131 feet after 42 feet
(c)
(-1/14) x^2 + 6x + 5 =0
x^2 - 84x - 70 = 0 <--- after multiplied by -14
x = 84.825, x = -0.825
the ball will hit the ground at (56 + sqrt(3416)) / 2 = 84.825 ft
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which expression is equivalent to -24-12w
Answers
The given algebraic expression (24 - 12w) is equivalent to
6(4 - 2w).
What is algebraic expressions?An algebraic expression is a combination of terms both constants and variables. For example -
2x + 3y + z
4x + 5z
Given is the algebraic expression as -
24 - 12w
We can rewrite the expression above as -
24 - 12w
24 - 12w = 6 x 4 - 6 x 2w
24 - 12w = 6(4 - 2w)
Therefore, the given algebraic expression (24 - 12w) is equivalent to
6(4 - 2w).
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The equivalent expression to -24 - 12w is -6 (4 + 2w).
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.
Variable: A symbol without a set value is referred to as a variable.
Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.
Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.
Given:
We have the Expression as -24 - 12w.
So, Prime factorizing
24 = 2 x 2 x 2 x 3
12 = 2 x 2 x 3
So, -24 - 12w.
= - (2 x 2 x 2 x 3) - (2 x 2 x 3)w
= -2 x 3 ( 2 x 2 + 2w)
= -6 (4 + 2w)
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Let's do a couple of similar examples with the tan function.
The figure below, shows the graph of a function.
f(x)=
Answers
The domain are the possible input while the range are the possible output of a function.
(a) The domain = [-√2, √2], the range = [0, 2]
(b) The domain = [-1, 1], the range = [0, 1]
(c) The domain = [-1, 1], the range = [0, -1]
(d) The domain = [0, 2], the range = [0, 1]
(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]
Reasons:
The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1
Therefore, we have;
(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2
The x-intercept of the above function are, x = √2, and x = -√2
Which gives;
The domain = [-√2, √2]
The range = [0, 2]
(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3
At the x–intercepts, we have;
-3·x² + 3 = 0
x = ±1
The domain = [-1, 1]
The maximum value of y is given at x = 0, therefore;
= -3 × 0² + 3 = 3
The range = [0, 1]
(c) y = -f(x) = -(-x² + 1) = x² - 1
At the x–intercepts, x² - 1 = 0
x = ± 1
The domain = [-1, 1]
The minimum value of y is given at x = 0, which is y = -1
The range = [0, -1]
(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x
At the x–intercepts, we have; -x² + 2·x = 0, which gives;
(-x + 2)·x = 0
Which gives, x = 0, or x = 2
The domain = [0, 2]
The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1
y = f(1) = -1² + 2×1 = 1
Therefore;
The range = [0, 1]
(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2
At the x–intercepts, we have; -x² - 4·x - 2 = 0, which gives;
x = -(2 + √2) or x = x = √2 - 2
The domain = [-(2 + √2), (√2 - 2)]
The maximum value of y is given when x = -4/(2)) = -2
Which gives;
-(-2)² - 4·(-2) - 2 = 2
The range = [0, 2]
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What is the factorization of the polynomial below? x2 - x - 42 A. (x + 7)(x + 6) B. (x + 7)(x - 6) C. (x - 7)(x + 6) D. (x - 7)(x - 6)
Answers
The factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.
What is factorization?The breaking or breakdown of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication yields the original number, matrix, etc., is known as factorization or factoring in mathematics.
The given polynomial is:
x² - x - 42 = 0
Expand the quadratic equation:
x² + 6x - 7x - 42 = 0
Take the common terms out from the equation:
x(x + 6) - 7(x + 6) = 0
(x - 7)(x + 6) = 0
Hence, the factorization of the polynomial is (x - 7)(x + 6). Option C is the correct answer.
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Warren measured a rectangular window
to find out how much wood he would
need for a new frame. What is the total
length of wood that Warren needs? Write
your answer in feet and inches.
2 feet 9 inches
5 feet 6 inches
Answers
The equation is (4.5-0.7)/5 and length of each piece is 0.74
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
He has a piece of wood that is 4.5 feet long.
After cutting five equal pieces of wood from it, he has 0.7 feet of wood left over
an equation that could be used to determine the length of each of the five pieces of wood he cut
legth of each piece is = (4.5-0.7)/5
The total length is 4.5 and the leftover is 0.7, so used wood is total minus left ove
Length of each piece is used woof by number if pieces
(4.5 - 0.7)/5 = 3.7/5 = 0.74
Therefore, the equation is (4.5-0.7)/5 and legth of each piece is 0.74
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