A group of cyclists recorded the distance they have traveled.
Draw a line plot and answer the questions below.
Name
Gina
Rey
Faye
Mark
John
James
Albert
William
Nathan
Kate
Mary
Risa
Paul
Abi
Joan
Distance in
miles
40 1/2
50
35 3/4
60
45
55 1/4
60
45
40 1/2
50
45
40 1/2
60
40 1/2
35 3/4
Title:
1. How many cyclists were there?
2. What was the longest distance traveled?
3. How many cyclists traveled less than 50 miles?
4. What was the most common distance traveled by
the cyclists?
5. How many more cyclists traveled 45 miles than
55 1/4 miles?
6. How many cyclists traveled more than 45 miles
A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.
A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.
The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.
Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.
Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.
A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.
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1.Glenda wants to glue glitter over a piece of felt shaped like a parallelogram with a height of 52 in. and a base of 58 in.
If the glitter costs $1.10 per ft², how much will it cost to cover the felt?
2.The shape of a patio is trapezoidal with a height of 10 ft. and bases of 19 ft. and 13 ft.
What is the cost of outdoor carpeting to cover the patio if the carpeting costs $1.50 per ft².?
The cost of covering the felt with glitter is $3,317.60.
The cost of the outdoor carpeting to cover the patio is $240.
What are the costs?The first step is to determine the area of the parallelogram. A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length
Area = base x height
52 x 58 = 3,016 in²
Cost of covering the felt = cost of the glitter per feet are of the felt
$1.10 x 3,016 = $3,317.60
A trapezoid is a shape that has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height
Area of a trapezoid = 1/2 x (19 + 13) x 10
Area of a trapezoid = 1/2 x 32 x 10 = 160 ft²
Cost of the outdoor carpeting =cost per square feet x area of the patio
$1.50 x 160 = $240
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The minimum number of parallel faces that a prism should have is
Answer:
The minimum number of parallel faces that a prism should have is three pairs
Answer:
The minimum number of parallel faces that a prism should have is three faces
A right circular cone is intersected by a plane that passes through the cone's
vertex and is parallel to its base, as in the picture below. What is produced
from this intersection?
OA. A pair of intersecting lines
OB. A point
OC. A pair of parallel lines
OD. A parabola
Answer:
B. A point
Step-by-step explanation:
You want a description of the intersection between a plane and a cone given that the plane is parallel to the base and passes through the vertex of the cone.
VertexThe vertex of a cone is a single point. If a plane passes through that, but does not intersect the base of the cone, it will not intersect anywhere else.
The intersection is one point.
__
Additional comment
Figure f in the attachment illustrates this case.
Santa has many toy to deliver on elm street. If there are 48 kids that live on elm street and 12 of them are boys, what is the ratio of girls to boys ?
Answer:
36 to 12
Step-by-step explanation:
subtract 12 from 48 an you get 36 girls
The sum of 3x and 70 exceeds 13x
The algebraic representation of the sentence the sum of 3x and 70 exceeds 13x is: 3x + 70 > 13x.
What is algebraic expression?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Given that the sum of 3x and 70 exceeds 13x, this is represented as:
3x + 70 >13x
Hence, the algebraic representation of the sentence the sum of 3x and 70 exceeds 13x is: 3x + 70 > 13x.
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I need help on this question I have attached it on this assignment. THX
Answer:
I) 5575
ii) 312.50
b) 345
Step-by-step explanation:
I)11.15(500)=5575
ii) 1.25(250)=312.50
b) 407.10/1.18 = 345
a motorboat takes 4 hours to travel 128 km going Upstream. the return trip takes 2 hours going Downstream. what is the rate of the boat in still water and what is the rate of the current? rate of the boat in still water: __km/hrate of the current: __km/h
Distance = rate * time
r= rate of the boat in still water
c= rate of current
Upstream = r - c
Downstream= r+c
Upstream
r-c = 128/4 = 32
r-c= 32 (a)
Downstream
r+c=128/2=64
r+c=64 (b)
Add both equations (a)+(b)
r-c=32
+
r+c= 64
_______
2r= 96
r= 96/2
r=48 km/h
Substitute r in (b)
48+c =64
c= 64-48
c= 16km/h
What is h(x) = f(x)g(x)?
h(x) = f(x)g(x) represents the product of two functions, combining their behaviors into a new function.
In mathematics, the expression h(x) = f(x)g(x) represents the product of two functions, f(x) and g(x). When evaluating h(x) for a given value of x, it involves multiplying the corresponding values of f(x) and g(x).
The product of two functions allows for the combination of their individual behaviors and characteristics. The resulting function, h(x), inherits properties from both f(x) and g(x). The behavior of h(x) will depend on the specific functions involved.
For example, if f(x) represents a linear function and g(x) represents an exponential function, their product h(x) = f(x)g(x) will exhibit a combined behavior reflecting both linearity and exponential growth. The specific form of the functions will determine the precise behavior of h(x) and its graph.
It is important to note that the product of two functions assumes that the functions are defined for the given values of x and that the multiplication operation is valid for the corresponding function values.
h(x) = f(x)g(x) represents the product of two functions, combining their behaviors to form a new function. The specific nature of h(x) depends on the characteristics of f(x) and g(x).
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Isabelle is taking a survey to find the most popular music group of students in her community. Which of these is not a way for her to get a representative sample of this information?
A. ask every tenth student she sees ac a concert
B. ask every fifth student entering her school in the morning
C. ask every third student she encounters at the mall
D. ask every student at a local movie theater
the option that is not a way for Isabelle to get a representative sample of the most popular music group of students in her community is D. ask every student at a local movie theater.
The reason is that asking every student at a local movie theater is a form of convenience sampling, where the sample is chosen based on convenience and accessibility, rather than being selected randomly from the entire population of interest. It may not provide a representative sample of the community's music preferences since the population of students who attend a movie theater may not be the same as the general population of students in the community. In contrast, options A, B, and C suggest a form of systematic sampling, where every nth student is selected from a randomly chosen starting point, which can help to ensure that the sample is more representative of the general population of students in the community.
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What is the solution to the equation below?
7/8 (x - 1/2) = -49/80
a
1/5
b
6/5
c
-6/5
d
-1/5
Answer:
hence the value of x is -⅕
4x + 9y =36 Convert the standard form to slope intercept form (y= mx+b)
Answer:
4x+9y-36=0
Step-by-step explanation:
Use the slope-intercept form
y
=
m
x
+
b
to find the slope
m
and y-intercept
b
.
Slope:
−
4
9
y-intercept:
(
0
,
4
)
I need help with this math question.
x^3-8x^2<0
Answer:
X>8
Step-by-step explanation:
Dudbdksjhdkdkfisk
Pls Help! Worth 5 Points Will give brainlest
Answer:
d
Step-by-step explanation:
What is the constant of the following:
19x - 4y - 2?
at the zoo the length of each iguana is measured which statement is best supported by the information below
1.) Over half of the iguanas measure 14 centimeters or more in length.
Why is the above statement relevant?The assertion that is most supported by the data is, "More than half of the iguanas measure 14 centimeters or more in length." According to this claim, more than 50% of the iguanas are 14 cm or longer in length. The other two claims describe precise iguana lengths (12 centimeters and 11 centimeters or less, respectively), but they do not mention how common such lengths are in comparison to other lengths. Therefore, out of the available probability, the first statement is the one that is most illuminating and best substantiated.
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Complete question is :
At the zoo, the length of each iguana is measured. Which statement is best supported by the information below?
Over half of the iguanas measure 14 centimeters or more in length.25% of the iguanas measure 12 centimeters in length.The number of iguanas that measure 15 centimeters or more is equal to the number that measure 11 centimeters or less.In AMNO, the measure of 20=90°, MN = 99 feet, and OM = 52 feet. Find the
measure of M to the nearest degree.
Answer:
x = 58 degrees
Step-by-step explanation:
Using the SOH CAH TOA trigonometry identity
hypotenuse =99
adjacent = 52
angle of elevation = x
cos theta = adj/hyp
cos x = 52/99
x = arccos (52/99)
x = arccos(0.5253)
x = 58 degrees ( to the nearest degree)
Use the rule to write the first twelve numbers in the pattern Describe another pattern in the numbers Rule add 15 subtract 7 first term 4
HELP HOMEWORKKK ;C
Answer:
4, 19, 12, 27, 20, 35, 28, 43, 36, 51, 44, 59 and even, odd, even,...
Step-by-step explanation:
Rule add 15 subtract 7 first term 4
4
4 +15 = 19
19 -7 = 12
12 +15 = 27
27 -7 = 20
20 +15 =35
35 -7 = 28
28 +15=43
43 -7=36
36 +15 = 51
51- 7=44
44 +15=59
Describe another pattern in the numbers
even, odd, even, odd,...
Students are designing a new town as part of a social studies project on urban planning. ey want to place the town’s high school at point A and the middle school at point B. they also plan to build roads that run directly from point A to the mall and from point B to the mall. the average cost to build a road in this area is $550,000 per mile. . c. Draw the road from point A to the mall and find its length. d. Draw the road from point B to the mall and find its length. e. How much farther from the mall is point B than point A? How much more will it cost to build the longer road?
Answer:
c, d. see attached
e. about 2.96 miles; about $1.63 million
Step-by-step explanation:
e. The x-coordinates of points A and B are 1/3 and 2/3 of the x-coordinate of "Downtown", respectively. The y-coordinates of A and B are 2/3 and 1/3 of the y-coordinate of "Town pool", respectively. Then the distances from A and B to the Mall can be found using the Pythagorean theorem:
A to Mall = √(4² +(10/3)²) = √(244/9) ≈ 5.20683 . . . miles
B to Mall = √(8² +(5/3)²) = √(601/9) ≈ 8.17177 . . . miles
The difference in distance is ...
(BM -AM) = 8.17177 -5.20683 = 2.96493 . . . miles
The mall is about 2.96 miles farther from point B than from point A.
The additional cost is the difference in miles multiplied by the cost per mile:
(2.96 mi)($0.550 M/mi) = $1.63 M
The additional cost of the longer road is about $1.63 million.
Explain why the two figures show equivalent graphs. Then draw a third equivalent graph.
B
G
K
M
Why are the two graphs equivalent? Select all that apply.
A. The graphs have a number of edges that matches the number of vertices.
B. The graphs have the same number of edges.
C. The vertices are connected in the same way.
D. The graphs have the same number of vertices.
The two figures show equivalent graphs because:
A. The graphs have several edges that match the number of vertices.
B. The graphs have the same number of edges.
C. The vertices are connected in the same way.
D. The graphs have the same number of vertices.
The third equivalent graph is at option D.
What are equivalent graphs?The graphs that have the same number of vertices connected in the same way are called equivalent graphs. If they are connected in the same way then their count of edges will be the same for both graphs. They are also said to be isomorphic graphs.
Calculation:The given graphs have
Graph1: vertices BCJK
Graph2: vertices BCJK
So, there is the same number of vertices for both graphs.
The connection between the vertices:
Graph1: J - B - C - K - B
Graph2: J - B - C - K - B
So, they are connected in the same way.
The edges formed by these vertices:
Graph1: JB; BC; CK; KB
Graph2: JB; BC; CK; KB
So, there is the same number of edges for both graphs.
Here the number of edges = the number of vertices i.e., (4 = 4)
From all these comparisons, the given graphs are equivalent.
The third equivalent graph made from these graphs is at option D in the diagram attached below.
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Disclaimer: The given question is incomplete. There is no image attached in the given question. Here the image is attached.
Ryan buys lunch for $16.83. If sales tax is 8.4%, How much money does Ryan need total for lunch
\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.4\% of 16.83}}{\left( \cfrac{8.4}{100} \right)16.83} ~~ \approx ~~ 1.41~\hfill \underset{ Total~for~lunch }{\stackrel{ 16.83~~ + ~~1.41 }{\approx\text{\LARGE 18.24}}}\)
How does finding a pattern for a rule change if you subtract instead of add?
Answer:
When you subtract, the numbers decrease however when you add the numbers increase.
Step-by-step explanation: Theres the answer but is it multiple choice? if so than you can give me the choices and ill tell you the answer. But i hope this helped and if u need anything u can ask!
3x + 18y = 1 what is the slope intercept form?
Answer:y=-1/6*x-1/18
Step-by-step explanation:answer = y=-1/6*x-1/18
18y=1-3x
y=1/18-3/18x
y=-1/6*x-1/18
Which function is equivalent to g(x)= x2 +11x-60?
The table represents two liner functions in a system
What is the solution to this system
Please answer
A) 1,0
B)1,6
C) 8,26
D)8,-22
Inequalities - Introduction
Answer:
Step-by-step explanation:
This number line says that we can take all values of x that are less than or equal to 2. That is, the solution is
\(x\leq 2\)
NOTE: if the circle at 2 were not filled in then that would mean x<2 (2 would not be an accepted value of x)
f(x) =x(x-1) on R to R
find A and B such that g: A to B defined by g(x)=f(x) is bijective
this is an algebra question, help.
details are needed
Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.
To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.
So, let's assume that g(x1) = g(x2). Then, we have:
f(x1) = f(x2)
x1(x1-1) = x2(x2-1)
x1^2 - x1 = x2^2 - x2
x1^2 - x2^2 - x1 + x2 = 0
(x1 - x2)(x1 + x2 - 1) = 0
Since x1 and x2 are distinct, we must have x1 + x2 = 1.
But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.
To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.
So, let's solve the equation f(x) = y for x:
x(x-1) = y
x^2 - x - y = 0
Using the quadratic formula, we get:
x = (1 ± √(1 + 4y))/2
Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.
Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.
A circular sprinkler system is installed and waters an area of 28.26 square yards. What is the radius of the circle?
Answer:
The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the area of the circle watered by the sprinkler system is 28.26 square yards, we can set up the equation:
28.26 = πr^2
To solve for r, we need to isolate it on one side of the equation. We can do this by dividing both sides by π and then taking the square root:
r = √(28.26/π)
Using a calculator to evaluate this expression, we get:
r ≈ 3 yd
Therefore, the radius of the circle is approximately 3 yards.
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Answer: 2.99924
Step-by-step explanation:
If 11% of x is equal to 66, what is the value of x ?
Answer: The value of x is 6
Step-by-step explanation:
Given:
11x = 66
To Find:
The value of x.
Solution:
11x = 66
x = 66/11
11 multiplied by 6 gives 66 therefore,
x = 6/1
The value of x is 600.
Explanation:To find the value of x, we need to solve the equation: 11% of x = 66. To do this, we can set up the equation as: 0.11x = 66. We can solve for x by dividing both sides of the equation by 0.11: x = 66 / 0.11 = 600.
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Solve by Factoring:
2x^2 - x - 3 = 0
Answer:
x = 3/2 or x = -1
Step-by-step explanation:
2x² - x - 3 = 0
2*(-3) = -6
Factors of -6:
(-1, 6), (1, -6), (-2, 3), (2, -3)
We need to find a pair that adds up to the co-eff of x which is (-1)
Factors :(2,-3)
2 - 3 = -1
so, 2x² - x - 3 = 0 can be written as:
2x² + 2x - 3x - 3 = 0
⇒ 2x(x + 1) -3(x + 1) = 0
⇒ (2x - 3)(x + 1) = 0
⇒ 2x - 3 = 0 or
x + 1 = 0
⇒ 2x = 3 or x = -1
⇒ x = 3/2 or x = -1