Answers
The length of the course is 480 m.
Length is used to measure distance. According to the International System of Quantities, length has the dimension of distance. In most measurement systems, length is represented by a base unit from which all other units are derived. The International System of Units (SI) system's fundamental unit of length is the meter.
Nevertheless, depending on the item's position, this is not always the case. A fixed object's length is commonly understood to be its greatest extended dimension.The length of a fixed object is referred to by a number of names, including height, also referred to as vertical length or vertical extension, and width, breadth, or depth.From the given figure we can infer that W is the mid-point of AB. Therefore we know that AW = WB
Now the distance is given by
5x -110 = 2x +100
or, 5x - 2x = 100 + 110
or, 3x = 210
or, x = 70
Therefore total length = 5x -110 + 2x +100 = 7x - 10 = 490 - 10 = 480 m
Therefore the length is 480 m.
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Related Questions
Find the volume of a solid bounded by the paraboloids [tex]\displaystyle{z=4x^2+4y^2}[/tex] and [tex]\displaystyle{z=5-6x^2-y^2}[/tex]
Answers
The two surfaces meet in an ellipse in some plane with [tex]0\le z\le5[/tex], since
[tex]4x^2 + 4y^2 = 5 - 6x^2 - y^2 \implies 10x^2 + 5y^2 = 5 \implies 2x^2 + y^2 = 1[/tex]
so the solid is bounded by the elliptical cylinder with this equation. In cylindrical coordinates, with
[tex]\begin{cases}x = \frac1{\sqrt2} r \cos(\theta) \\ y = r \sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = \frac1{\sqrt2} r \, dr \, d\theta \, d\zeta\end{cases}[/tex]
the solid is the set
[tex]\begin{array}{c} R = \left\{(r,\theta,\zeta) ~:~ 0\le r\le1 \text{ and } 0 \le\theta\le2\pi \text{ and } \right. \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \left.3r^2 - r^2 \cos(2\theta) \le \zeta \le 5 - 2r^2 - r^2 \cos(2t)\right\} \end{array}[/tex]
and the volume is given by the integral
[tex]\displaystyle \iiint_R dV = \frac1{\sqrt2} \int_0^{2\pi} \int_0^1 \int_{3r^2 - r^2 \cos(2\theta)}^{5 - 2r^2 - r^2 \cos(2\theta)} r \, d\zeta \, dr \, d\theta \\\\ ~~~~ = \frac1{\sqrt2} \int_0^{2\pi} \int_0^1 r(5 - 5r^2) \, dr \, d\theta \\\\ ~~~~ = \frac{10\pi}{\sqrt2} \int_0^1 (r - r^3) \, dr \\\\ ~~~~ = 5\sqrt2\,\pi \left(\frac12 - \frac14\right) = \boxed{\frac{5\pi}{2\sqrt2}}[/tex]
HELP!!!! HELP HELP HELP HELP
Answers
The matchings are:
3x - y = -5 ⇒ table C.
x - 3y = 12 ⇒ table A.
3x - y = -2 ⇒ table D.
2x - 3y = 9 ⇒ table B.
How to match each equation to the correspondent table?The first equation we have is:
3x - y = -5
Evaluating in x = 0, we have:
3*0 - y = - 5
y = 5
So we have the point (0, 5).
Evaluating in x = -2 we get:
3*-2 - y = -5
6 + y = 5
y = 5 - 6 = -1
So we have the point (-2, -1)
The only table with that point is table C, so we conclude that it is the correct option.
2) The second equation is:
x - 3y = 12
Evaluating in x = 0 we get:
0 - 3y = 12
y = 12/-3 = -4
So we have the point (0, -4)
if x = 3 we have:
3 - 3*y = 12
-3*y = 12 - 3 = 9
y = 9/-3 = -3
So we have the point (3, -3)
The only table with these two points is table A, so that is the correct one.
3) The next equation is:
3x - y = -2
The tables left are B and D.
Now, let's evalaute this equation in x = 3.
3*3 - y = -2
9 - y = -2
9 + 2 = y
11 = y
So we have the point (3, 11)
Notice that on table B,the value associated to x = 3 is y = -1, so we discard table B, and we conclude that this equation relates to table D.
Trivially, the last equation:
2x - 3y = 9
Matches table B.
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Dante buys candy that costs $7 per pound. He will spend at least $42 on candy. What are the possible numbers of pounds he will buy? Use p for the number of pounds Dante will buy. Write your answer as an inequality solved for p
Answers
Answer:
p [tex]\geq[/tex] 6
Step-by-step explanation:
If one pound costs $7 and he's going to spend at least $42, then he will buy at least as many pounds as what costs $42.
42 divided by 7 equals 6, so he will buy at least 6 pounds of candy.
4. Mrs. Sparks is a 9th grade Algebra 1 teacher. She teaches three
Algebra 1 courses and all the classes recently took a chapter exam.
Below are the scores.
Class 1
45
68
77
90
90
95
100
100
86
90
50
55
Class 2
64
65
70
40
100
87
84
88
90
90
95
80
Class 3
70
75
75
90
100
80
55
65
76
80
88
99
a. Find the mean, median, mode and range of Class 1.
b. Find the mean, median, mode and range of Class 2.
c. Find the mean, median, mode and range of Class 3.
d. Find the standard deviation of Class 1.
e. Find the standard deviation of Class 2.
f. Find the standard deviation of Class 3.
g. Which class had a higher standard deviation and what does that mean?
h. In your opinion, which class did better on the exam? Explain your answer.
Answers
The mean of Class 1 is 78.83.
The median of Class 1 is 88
The mode of Class 1 is 90
The mean of Class 2 is 79.42
The median of Class 2 is 85.50
The mode of Class 2 is 90
The mean of Class 3 is 79.42
The median of Class 3 is 78
The mode of Class 3 are 75 and 80
The standard deviation of Class 1 is 18.81
The standard deviation of Class 2 is 16.15
The standard deviation of Class 3 is 12.70.
The class that had the higher standard deviation is class 1.
The class that did better on the exam is class 3 because it has the higher mean and the lowest standard deviation.
What is the mean, median and mode?Mean is the average of a set of numbers.
Mean = sum of numbers / total number
Mean of Class 1 = (45 + 50 + 55 + 68 + 77 + 86 + 90 + 90 + 90 + 95 + 100 + 100) / 12 = 78.83
Mean of Class 2 = (40 + 64 + 65 + 70 + 80 + 84 + 87 + 88 + 90 + 90 + 95 + 100) / 12 = 79.42
Mean of Class 3 = (55 + 65 + 70 + 75 + 75 + 76 + 80 + 80 + 88 + 90 + 99 + 100) / 12 = 79.42
Median is the number that is at the center of the dataset that is arranged in either ascending or descending order.
Median of Class 1 = (86 + 90) / 2 = 88
Median of Class 2 = (84 + 87) / 2 = 85.50
Median of Class 3 = (76 + 80) / 2 = 78
Mode is the number that occurs most frequently in a dataset.
Standard deviation is used to calculate the average variation of a dataset.
Standard deviation = [tex]\sqrt{\frac{(x - u)^{2} }{n} }[/tex]
Where:
x = number in the dataset u = mean n = total numbers in the dataset.Standard deviation of Class 1 = 18.81
Standard deviation of Class 2 = 16.15
Standard deviation of Class 3 = 12.70
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Answer:
Down below!
Step-by-step explanation:
A.
The mean 78.83.
The median 88
The mode 90
The range 55
B.
The mean 79.42
The median 85.50
The mode 90
The range 60
C.
The mean 79.42
The median 78
The mode 75 and 80
The range 45
D. 18.81
E. 16.15
F. 12.70
G. The class that had the higher standard deviation is class 1.
H. The class that did better on the exam is class 3 because it has the higher mean and the lowest standard deviation.
If Aaron buys 5 watermelons for 9 how much would 4 cost at the same rate?
Answers
Answer: $ 7.20
Step-by-step explanation:
(9x4)/5
36/5
= 7.2
= $7.20
The subtraction of 8 from a number is 2. What is the number?
Answers
Answer:6
Step-by-step explanation:
8-6 = 2
Answer:
10
Step-by-step explanation:
Let the number be equal to y
y-8=2y=8+2y=10The area and perimeter
Answers
Answer:
N/A
Step-by-step explanation:
the area and perimeter for what exactly?
True value received an invoice dated may 08, 2020. the invoice had a $5,800 balance that included $800 freight. terms were 3/10, 2/30, n/60. true value pays the invoice on may 22. what amount does true value pay?
Answers
True value received an invoice dated may 08, 2020. the invoice had a $5,800 balance that included $800 freight true value pays the invoice on may 22. then true value pay amount is $4900
Invoice dated 08/may/2020. Amounting to $5,800 which includes $800 freight.
Terms:
3/10 ; 2/30 ; n/60
The term 3/10 means that True value can avail of 3% discount if it pays within 10 days from date of issuance. The 10th day would be 18/may/2020
The term 2/30 means that True value can avail of 2% discount if it pays from the 11th day up to the 30th day from the date of issuance.
may 22 is beyond the 10th day but within the 30 days discount period. True Value can avail of the 2% discount.
5,800 - 800 = 5,000 The freight can't be subjected to discount thus it is deducted from the total invoice amount.
5,000 * 2% = 100
5,000 - 100 = 4900 amount True Value has to pay.
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Determine the angle of rotation
Answers
Answer: b
Step-by-step explanation:
:)
What is the value of r in the equation 6(1 + 2r) - 3(1 - 8r) = 75?
Answers
Answer:
2
Step-by-step explanation:
[tex]6(1+2r)-3(1-8r)=75 \\ \\ 6+12r-3+24r=75 \\ \\ 3+36r=75 \\ \\ 36r=72 \\ \\ r=2[/tex]
answer these 2 questions for a cookie
Answers
Answer:
1. C
2. D
5. C
Step-by-step explanation:
Answer:
C as j is a variable
D
C as 13+9+1.9= 23.9
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Three consecutive positive odd integers such that 5 times the square of the
middle integer exceeds the product of the other two by 488.
By letting the smallest integer equal x, set up and solve a quadratic equation
to find the middle integer.
A solution by trial and improvement will not be accepted.
Answers
An analogous equation can be created by factoring a quadratic equation. 5x^2 = (x-2) * (x+2) + 488 can give integers 9, 11,13.
What is a quadratic equation?In algebra, quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as
[tex]{ax^{2}+bx+c=0}[/tex]
where a 0 and x denotes an unknown and a, b, and c denote known numbers, Since there is no ax2 term, the equation is linear (and not quadratic) if a = 0 (and b 0). The coefficients of the equation, denoted by the numbers a, b, and c, are the quadratic coefficient, linear coefficient, and constant or free term, respectively.
The roots or zeros of the expression on the left-hand side of the equation are the values of x that fulfill the equation. There can only be two solutions to a quadratic problem. One claims that a problem is a double root if there is just one solution. There are either two real solutions, one real double root, two complex solutions that are complex conjugates of one another, or two real solutions if all the coefficients are real values. If complex roots are included, a quadratic equation will always have two roots; a double root counts as two. An analogous equation can be created by factoring a quadratic equation.
According to the formula, if 5x2 = x2 - 4 + 488, then 5x2 = x2 + 484.
For 4x2 = 484, subtract x2 from each side, resulting in x2 = 121.
For x = 11, square root each side.
TEST: 5*121 = 9*13 + 488, so 605 is equal to 117 plus 488.
The middle odd number, x, is equal to 11.
The figures are 9, 11, and 13.
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A saleswoman earns 9% commission on all the merchandise that she sells. Last month she sold $6000 worth of merchandise. How much commission (in dollars) did she earn last month?
Answers
Answer: she gets 540
Step-by-step explanation:
She earns 540 dollars since the saleswoman only gets 9% of it and she sold $6000 dollars worth of merchandise you divide by percentage
Example: 1. Find the percentage of the original or real number. In this case, it's 500.
2. Multiply the final number by 100. 500 x 100 = 50,000.
3. Divide the result of the multiplication by the percentage. 50,000 divided by 40% = 1,250. Thus, 500 is 40% of 1,250.
True or false? A corollary is a statement that can be easily proved using a
theorem.
O A. True
OB. False
SUBMIT
answer to this question for anyone who needs it
Answers
The theorem can be used to readily show the corollary because, according to its statement, it considerably depends on it. Consequently, the assertion is accurate.
The given statement is True.
Is the meaning of corollary?The term "corollary" refers to an outcome that follows logically from another action. You could claim that your rediscovered passion of reading is a corollary to the recent opening of a bookstore in your area. The term corollary describes the result of an action, such as the need to study more as a corollary to receiving a poor grade.
Briefing:A theorem states that two angles that add up to 180° and form a straight line are regarded as "supplementary."
A corollary of this is known as the "Vertical Angle Theorem," which asserts that where two lines intersect, their angles across from each other are equal (in the diagram, a=c and b=d).
The theorem can be used to readily show the corollary because, according to its statement, it considerably depends on it. Consequently, the assertion is accurate.
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3 5/11 as a decimal exspansion
Answers
Answer: 3 5/11 should be 3.4545454545 as a decimal
Hope this helps!
Answer:
3 + 0.4545454545454545 = 3.454545454545455
Step-by-step explanation:
3 5/11 as a decimal exspansion
3 + (5 : 11) =
3 + 0.4545454545454545 =
3.454545454545455
Kaj needs to order some new supplies for the restaurant where she works. The restaurant needs at least 736 knives. There are currently 155 knives. If each set on sale contains 12 knives, what is the minimum number of sets of knives Kaj should buy?
Please hurry! :D
Answers
Answer:
736 - 155 = 581.
581 divided by 12 is 48.416.
that means the minimum number of sets of knives Kaj should buy is 49.
Step-by-step explanation:
Fav Sport
volleyball (12)
Basketball (18)
Ping Pong (8)
Softball (10)
Football (24)
(#s in brackets are the frequencies of their individual sports)
Answers
It should be noted that the angle sector for each sport will be:
volleyball (12) = 60°
Basketball (18) = 90°
Ping Pong (8) = 40°
Softball (10) = 50°
Football (24) = 120°
How to illustrate the information?From the information given, the following can be illustrated:
volleyball (12) = 12/72 × 360° = 60°
Basketball (18)= 18/72 × 360° = 90°
Ping Pong (8) = 8/72 × 360° = 40°
Softball (10) = 10/72 × 360° = 50°
Football (24) = 24/72 × 360° = 120°
Total = 72
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Name the reciprocal that you will use to multiply
(Equations in picture)
I only need the reciprocals
Answers
Answer: 9/4 and -2/1 (or -2)
Step-by-step explanation: Reciprocals are just the fraction flipped
let’s review some basics of probability. a bag of skittles has 9 reds, 10 oranges, 7 yellows, 8 purples, and 6 greens. what is the probability of a red skittle if one is selected at random?
Answers
Answer:
7/20
Step-by-step explanation:
is always right use without the s
Evaluate the expression when a = 2 and x = -4.
2a-x
Answers
The expression when a = 2 and x = -4, given 2a-x. The value will be 8.
What are mathematical operations?In mathematics, an operation is a function that transforms zero or more arguments or operands into a clearly defined output value. The number of operands in the operation determines how difficult it is.
Unary operations (i.e., operations of arity 1), which include additive inverse and multiplicative inverse, as well as binary operations (i.e., operations of arity 2), which include addition and multiplication, are the operations that are most frequently studied. The nullary operation, also referred to as a zero-arity operation, is a constant. The mixed product is an example of a ternary operation, also referred to as an operation of arity 3.
The arity is typically assumed to be limited. Even yet, infinitary operations are occasionally taken into account, in which case the "typical" operations of finite dimensionality are referred to as finiteary operations.
Similar to an operation, but with partial function in place of a function, is the definition of a partial operation.
Since, a= 2 and x= -4, then,
2(2)-(-4)= 8
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Evaluate m + (n-1)^2 if m = 3 and n = -4
Answers
Answer:
Step-by-step explanation:Answer: using identity[(a+b)(a-b) = a^2 - b^2]. (m+n)(m-n) = m^2 - n^2. m^2 - n^2 = (3)^2 - (4)^2 = -7.
3+(-5)^2
3+25
28
A match-seller arranges his matchboxes in a
triangular pattern as shown in Fig. 18.4. He
continues until there are 11 matchboxes in
the bottom row of the triangle. How many
matchboxes are in the complete pattern?
MATO
MATCHES
MATCHES
Fig. 18.4
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
MATCHES
Answers
Using the properties of an arithmetic sequence we can conclude that the total number of match boxes is 66.
There is a consistent distinction between the words in a sequence of numbers known as a "arithmetic progression" or "arithmetic sequence" (AP).
In an arithmetic series, the space between subsequent terms is constant. The numbers 3, 5, 7, and 9 come to mind. because there is always a two-term difference between two succeeding terms, it is arithmetic.We know that the bottom row of the pyramid has 11 matchboxes .
As we can see in the figure that the each succeeding step has one matchbox less.
Therefore the number of matchboxes in each row is in an AP.
Therefore the AP has a common difference of -1 and the first term is 11
The last term of the AP is 1.
Therefore
aₙ = a + (n-1)d
or, 1 = 11 + (n-1)(-1)
or, n = 11
We know that the sum of all terms of an AP is given by
S=n/2{2a+(n-1)d}
or, S = 11/2 {2×11 + (10)(-1)}
or, S = 66
Therefore from the arithmetic progression we calculate that the total number of match boxes is 66.
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Select the correct answer from each drop down-menu.
Which are the best definitions for theorem, conjecture, and axiom?
A statement that is assumed to be true without proof is a(n)
. A statement that has been shown to be true by vigorous application of logic is a(n)
. A(n)
is a statement that is believed to be true but hasn't been proven.
Answers
A statement that is assumed to be true without proof is a(n) Theorem
A statement that has been shown to be true by vigorous application of logic is a(n) ---> Conjecture
A(n) Axiom is a statement that is believed to be true but hasn't been proven.
What's the big difference between a definition and a theorem?A definition is both a precise and a general statement of the significance of a mathematical term.
It does this by laying down all of the characteristics of the word together with the structures that need to be true.
This is how the meaning of the word is defined. A mathematical assertion that can be demonstrated using logically sound mathematical reasoning is called a theorem.
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Information is given about a polynomial f(x) whose coefficients are real
numbers. Find the remaining zeros of f.
Degree 3; zeros: -4, -2- i
The remaining zero(s) of f is
(Use a comma to separate answers as needed.)
Answers
Answer: -2+i
Step-by-step explanation:
By the conjugate root theorem, since the coefficients are real, the complex conjugate of a root must also be a root.
Solve the following...
4x+10=-26
Answers
Answer:
x = -9
Step-by-step explanation:
the goal is to get x by itself, so subtract 10 from both sides: 4x=-36
divide both sides by 4: x = -9
|-----4x+10=-26 |
|ANSWER= x=-9-------|
happy fall!
explanation ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
When we have questions like this, and the x is just THROWN in there, we have to "combine our like terms."
STEP ONE ✨: "How do we do that..if one is on the other side?"
We have to make it disappear. +10-10 equals zero, right? right! So do that!
4x+10=-26
-10
But what we do to one side, we do to the other! Subtract 10 from the numbers on the equal side.
4x+10=-26
-10 -10
-26-10
4x=-36
STEP TWO : What do we do when a number has an X beside it?
Since this number is being multiplied to the x, we have to DIVIDE the 4x by 4, so we just get the x alone. It always works like this. Don't doubt yourself!!
4x=-36
/4 /4
-36/4=-9
x=-9!
----------------
i hope this helped! || much love! <33
How many sheets of metal are in a stack 4.00 in. high if each sheet is 0.0146 in. thick?
The number of metal sheets in the stack is
(Round to the nearest whole number as needed.)
Answers
The number of metal sheets in the stack is 274 metal sheets
Ratio and proportionFractions are written as a ratio of two integers. For instance a/b is a fraction.
Given the following parameters
Height of metal sheet = 4.00in
Height of each sheet= 0.0146 in
Number of metal sheet = height of metal sheet/height of each sheet
Substitute
Number of metal sheet = 4.00/0.0146
Number of metal sheet = 274 metal sheets
This gives the required number of sheets
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The graph of a function f(x) passes through the following points:
(0,-2), (1,0), (-1,0)
Which of the following could be f(x)?
> f(x) = -2x - 2
> f(x) = 2x - 2
> f(x) = (2\sqrt[x])-2
> f(x) = 2x^2 - 2
Answers
*109
eight feral 103721
what is the maximum number of balls of clay of radius 2 that can completely fit inside a cube of side length 7 assuming the balls can be reshaped but not compressed before they are packed in the cube?
Answers
Answer:
Number of balls of clay: 10
Step-by-step explanation:
The volume of the cube is [tex]$V_{\text{cube}}=7^3=343,$[/tex]
and the volume of a clay ball is: [tex]$V_{\text{ball}}=\frac43\cdot\pi\cdot2^3=\frac{32}{3}\pi.$[/tex]
Since the balls can be reshaped but not compressed, the maximum number of balls that can completely fit inside a cube is
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor=\left\lfloor\frac{343}{\frac{32\pi}{3} }\right\rfloor.\][/tex]
Approximating with [tex]$\pi\approx3.14[/tex]
We have:
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor=10.23565228[/tex]
We simplify to get:
[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor\approx10[/tex]
So:
[tex]\boxed{number\ of\ balls = 10}.$[/tex]
if u know this please help
Answers
Answer:
alternate angles and corresponding angles.
and vertical opposite angles
Step-by-step explanation:
#G o o g l e
6. Joshua took a bus from Orlando to Atlanta. The bus traveled 420 miles in 6 hours. What was the
average speed of the bus?
a) 60 miles per hour
b) 65 miles per hour
c) 70 miles per hour
d) 75 miles per hour