Answers
A + B = 12 miles
Beth and Candace combined ran 34% of the total distance.
B + C = 10.2 miles
Candace and John combined ran 40% of the total distance.
C + J = 12 miles
John and Pat combined ran 41% of the total distance.
J + P = 12.3 miles
A + B + C + J + P = 30
A + (10.2-C) + C + J + (12.3-J) = 30
A + 10.2 + 12.3 = 30
A = 7.5 miles
B = 12 - 7.5 = 4.5 miles
C = 10.2 - 4.5 = 5.7 miles
J = 12 - 5.7 ] = 6.3 miles
P = 12.3 - 6.3 = 6 miles
Related Questions
pls help me uwuwuwuuwuwuww
Answers
Answer:
128
6
12
48
Step-by-step explanation:
Three students are sitting in a playground to make a circular path. They are sitting on the circumference, the co-ordinates of their position on the circle are (1, 2), (3, 4) and (3, 2). Find the co-ordinates of the point equidistant from their position. Also, find the equation of the locus.
Answers
The coordinates of the point equidistant from their position is C(x,y) = (2, 3) and the equation of the locus is (x - 2)² + (y - 3)² = 2.
How to derive the equation of the circunference associated with a playground
The center is the point that is equidistant to every point on the circumference. First, we need to determine the coefficients of the general equation of the circle, whose form is described below:
x² + y² + D · x + E · y + F = 0 (1)
We need three distinct points of the circumference to determine one solution.
If we know that (x₁, y₁) = (1, 2), (x₂, y₂) = (3, 4) and (x₃, y₃) = (3, 2), then the system of linear equations is:
D + 2 · E + F = -5 (2)
3 · D + 4 · E + F = - 25 (3)
3 · D + 2 · E + F = - 13 (4)
The solution of the linear system is D = - 4, E = - 6 and F = 11.
Now we proceed to transform the expression into its standard form by completing the squares:
x² + y² - 4 · x - 6 · y + 11 = 0
(x² - 4 · x + 4) + (y² - 6 · y + 9) - 2 = 0
(x - 2)² + (y - 3)² = 2
The coordinates of the point equidistant from their position is C(x,y) = (2, 3) and the equation of the locus is (x - 2)² + (y - 3)² = 2.
To learn more on circumferences, we kindly invite to check this verified question: https://brainly.com/question/4268218
Can yo solve this ones, please? in adittion, can you put answers and the process. The topic are area down the curve
Answers
1) The net area between the two functions is 2.
2) The net area between the two functions is 4/3.
3) The net area between the two functions is 17/6.
4) The net area between the two functions is approximately 1.218.
5) The net area between the two functions is 1/2.
How to determine the area between two functions by definite integrals
The area between the two curves is determined by definite integrals for a interval between two values of x. A general formula for the definite integral is presented below:
[tex]A = \int\limits^{b}_{a} {[f(x) - g(x)]} \, dx[/tex] (1)
Where:
a - Lower limitb - Upper limitf(x) - "Upper" functiong(x) - "Lower" functionNow we proceed to solve each integral:
Case I - [tex]f(x) = \sqrt{x}[/tex] and [tex]g(x) = x^{2}[/tex]The lower and upper limits between the two functions are 0 and 1, respectively. The definite integral is described below:
[tex]A = \int\limits^1_0 {x^{0.5}} \, dx - \int\limits^1_0 {x^{2}} \, dx[/tex]
[tex]A = 2\cdot (1^{1.5}-0^{1.5})-\frac{1}{3}\cdot (1^{3}-0^{3})[/tex]
[tex]A = 2[/tex]
The net area between the two functions is 2. [tex]\blacksquare[/tex]
Case II - [tex]f(x) = -4\cdot x[/tex] and [tex]g(x) = x^{2}+3[/tex]The lower and upper limits between the two functions are -3 and -1, respectively. The definite integral is described below:
[tex]A = - 4 \int\limits^{-1}_{-3} {x} \, dx - \int\limits^{-1}_{-3} {x^{2}} \, dx - 3 \int\limits^{-1}_{-3}\, dx[/tex]
[tex]A = -2\cdot [(-1)^{2}-(-3)^{2}]-\frac{1}{3}\cdot [(-1)^{3}-(-3)^{3}] -3\cdot [(-1)-(-3)][/tex]
[tex]A = \frac{4}{3}[/tex]
The net area between the two functions is 4/3. [tex]\blacksquare[/tex]
Case III - [tex]f(x) = x^{2}+2[/tex] and [tex]g(x) = -x[/tex]The definite integral is described below:
[tex]A = \int\limits^{1}_{0} {x^{2}} \, dx + 2\int\limits^{1}_{0}\, dx + \int\limits^{1}_{0} {x} \, dx[/tex]
[tex]A = \frac{1}{3}\cdot (1^{3}-0^{3}) + 2\cdot (1-0) +\frac{1}{2}\cdot (1^{2}-0^{2})[/tex]
[tex]A = \frac{17}{6}[/tex]
The net area between the two functions is 17/6. [tex]\blacksquare[/tex]
Case IV - [tex]f(x) = e^{-x}[/tex] and [tex]g(x) = -x[/tex]The definite integral is described below:
[tex]A = \int\limits^{0}_{-1} {e^{-x}} \, dx+ \int\limits^{0}_{-1} {x} \, dx[/tex]
[tex]A = -(e^{0}-e^{1}) + \frac{1}{2}\cdot [0^{2}-(-1)^{2}][/tex]
[tex]A \approx 1.218[/tex]
The net area between the two functions is approximately 1.218. [tex]\blacksquare[/tex]
Case V - [tex]f(x) = \sin 2x[/tex] and [tex]g(x) = \sin x[/tex]This case requires a combination of definite integrals, as f(x) may be higher that g(x) in some subintervals. The combination of definite integrals is:
[tex]A = \int\limits^{\frac{\pi}{3} }_0 {\sin 2x} \, dx - \int\limits^{\frac{\pi}{3} }_{0} {\sin x} \, dx + \int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin x} \, dx -\int\limits^{\frac{\pi}{2} }_{\frac{\pi}{3} } {\sin 2x} \, dx[/tex]
[tex]A = -\frac{1}{2}\cdot (\cos \frac{2\pi}{3}-\cos 0)+(\cos \frac{\pi}{3}-\cos 0 ) -(\cos \frac{\pi}{2}-\cos \frac{\pi}{3} )+\frac{1}{2}\cdot (\cos \pi-\cos \frac{2\pi}{3} )[/tex]
[tex]A = \frac{1}{2}[/tex]
The net area between the two functions is 1/2. [tex]\blacksquare[/tex]
To learn more on definite integrals, we kindly invite to check this verified question: https://brainly.com/question/14279102
if p + 2q = 40 find Q when p = 16
Answers
Plug in the value of p:-
16+2q=40
Subtract 16 from both sides:-
2q=40-16
2q=24
Divide both sides by 2:-
q=12 ✓
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Find the slope of the line passing through the points (7, -3) and (3, -7)
Answers
Answer:
The slope of the line is -1
Step-by-step explanation:
You need to use the slope formula
Slope Formula: y2 - y1 / x2 - x1
**The numbers represent subscripts but the subscripts aren't on computers**
Your Coordinate Points:
(7, -3) and (3, -7)
Do -7 - (-3) / 3-7
First, do -7 - (-3)
The negatives cancel to an addition problem.
-7 + 3
Now do -7 + 3. This is a subtraction problem that should be negative.
-7 + 3 = -4
Next, do 3 - 7
That should be 4
-4/4 is what we have right now.
Do -4 divided by 4 which has to contain a negative.
That is simply -1.
The slope of the line is -1
Adam earns $36 for every four hours of work how long will it take him to earn $144
Answers
Answer:
It will take 16 hours to earn $144.
Step-by-step explanation:
If Adam earns $36 in 4 hours,
36 = 4k
k = 9
Therefore, expression for total earnings will be,
y = 9x
a). For y = $144, 144 = 9x x = 16 hours
which has a greater magnitude 17 ft above sea level or 11 ft
Answers
Answer:
1 - 52= 52 33= 33 52 > 33, so -52 dollars has the greater magnitude. 1 - 141 = 14 [23] = 23 14 < 23, so 23 feet has the greater magnitude.
Step-by-step explanation:
Hope This Helps
meter and Area
1
Casey wants to put new carpet in her bedroom. A drawing of Casey's room is below. It consists of two sections: a square and a
rectangle
The rectangular section has the same width as the square section, but wice the length. If one side of the square section measures 3
yards, how many square yards of carpet should Casey buy for her room?
A 36 square yards
OB 24 square yards
OC 18 square yards
D. 27 square yards
Answers
Answer:
18 square yards
Step-by-step explanation:
because if you do 3x3 twice then add the two numbers you get you will get 18.
Select ALL of the expressions that are equivalent to 4√5.
A. 2√20
B. 6^1/2-5^1/2
c. 3*5^1/2+5^1/2
D.4*5^1/2
E.2√10
F.3*5^1/2
Answers
Answer:
A, C, D
All 3 of those simplfiy to 4√5
14,15,3,15,14,14,18,15,8 mean ,mode,median determine which measure of center best represenrs the data
Answers
Answer:
Mean: 12.9
Mode: 14,15
Median: 14
Step-by-step explanation:
in addition to the diagram, which statement is necessary to prove that the two triangles are congruent by the SAS criterion?
A . AC=DE
B. m
C.BC=EF
D. m
Answers
Answer:
BC = FE
Step-by-step explanation:
given ,
BA = FD and the measure of angle ABC = the measure of angle DFE
If we have BC = FE then according to the SAS criterion the two triangles are congruent
Over the last 16 years Johanna saved some of her pay each month. She now has $46,000. She decides to invest some
of it at 5.25% annual interest and the rest at 3.75% annual interest. After one year, her total interest earned from both
accounts is $2001. How much did she invest in each account? (Clearly label which amount is for which account in
your answer.
Answers
The amount invested in the account that gives a 5.25% interest is $18400.
The amount invested in the account that gives a 3.75% interest is 27600.
What are the linear equations that represent this question?0.0525a + 0.0375b = 2001 equation 1
a + b = 46000 equation 2
Where:
a = amount invested in the account that gives a 5.25% interest
b = amount invested in the account that gives a 3.75% interest
What is the amount invested in the account that gives a 3.75% interest?
Multiply equation 2 by 0.0525
0.0525a + 0.0525b = 2415 equation 3
Subtract equation 1 from equation 3
414 = 0.015b
b = 27600
What is the amount invested in the account that gives a 5.25% interest ?Subtract 27600 from 46000
46000 27600 = $18400
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
Find the distance between the two points in simplest radical form.
(3,9) and (-2,4)
Answers
Here we would be using distance formula to calculate the distance between those two points.
★ Points are,
(3 , 9)(-2 , 4)★ Distance Formula :
[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]★ We have :
x1 = 3
x2 = -2
y1 = 9
y2 = 4
★ Substituting the values :
Refer the attachment.Additional Information :Centroid of a triangle :-
[tex]\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} }} \: \pink\bigstar[/tex]Midpoint of two points:-
[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]60 = y-3 divided by 10
Answers
Answer:
y = 60.3
Step-by-step explanation:
What are the solution to the equation below? 4x^2+ 9 = 25
Answers
that is the complete answer to the question
Using the formula S = P(1 + r)t, where P is the original principal, r is the annual interest rate, and t is the number of years, what is the investment savings, S, if P = $14,500.00, r = 7.5%, and t = 5 years?
Answers
[tex]~~~~~~ \textit{Savings Earned Amount} \\\\ S=P\left(1+r\right)^{t} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$14500\\ r=rate\to 7.5\%\to \frac{7.5}{100}\dotfill &0.075\\ t=years\dotfill &5 \end{cases} \\\\\\ S=14500\left(1+0.075\right)^{5}\implies S=14500(1.075)^5\implies A\approx 20816.63[/tex]
What are the zeros of the function below?
F(x) = 8x(x-6)/(x+2)(x+9)
Answers
Answer:
x = 0, 6
Step-by-step explanation:
8x(x-6) = 0
x = 0, 6
Simplify the expression. 16 • 4–4
a)256
b)–256
c)1/16
d)–4,096
Answers
Answer: C) 1/16
Hope this helps :)
Help picture below problem 12
Answers
Answer:
isosceles triangle is shown in fig
QUESTION 1 Which one of the following is an ordered pair? O {-3,5} O (2, 4,0) 0 (0, 6) 0 1,3
Answers
PLEASE HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
Consider this dilation.
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain and show your work.
ANSWER BOTH PARTS YOU MAY GET EXTRA POINTS!
Answers
Step-by-step explanation:
1) if the initial figure ABCD, then the figure A'B'C'D' is reduction of the initial one.
2) the scale factor is 0.5: the ratio of all the corresponded coordinates is 2:1 [D(8;4) - D'(4;2); C(4;0)-C'(2;0); B(0;-2)-B'(0;-1) and A(-4;4)-A'(-2;2)].
Mark the quadrilaterals ABcD and A'B'C'D'
The image is reduced in size hence it's reduction
Take 2 sides two calculate scale factor
AD=12unitsA'D'=6unitsScale factor:-
6/121/2What is the area of the obtuse triangle given below?
6, 18
Answers
Answer:
54
Step-by-step explanation:
A = 1/2 bh
A = 1/2 (6)(18)
A = 1/2 (108)
A = 54
Area of the Obtuse triangle whose measures are 6 and 18 is 54 square units.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
We need to find the area of the obtuse triangle whose base is six units and height is eighteen 18 units.
A triangle whose any one of the angles is an obtuse angle or more than 90° is called Obtuse.
The area of triangle is 1/2×Base×Height
Half base times of height
Area of triangle=1/2×6×18
=54 square units
Area is 54 square units.
Hence, Area of the Obtuse triangle whose measures are 6 and 18 is 54 square units.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ7
Which economic system has no government involvement in the market?
a capitalism
.. communism
C. socialism
l. No economic system is free from government involvement.
Please select the best answer from the choices provided
Answers
Answer: I.
Step-by-step explanation:
Capitalism is clearly not the answer. Capitalist governments such as America have their fingers into the economic trading.
Socialism and Communism sound plausible, but Communism is giving people money by their work, and Socialism is everything is owned by the public. Both still involve themselves in markets, so the answer is I
Answer:
d.
No economic system is free from government involvement.
Step-by-step explanation:
i need help 100 points for a question
Answers
Answer:
34.28 ftStep-by-step explanation:
Find the length of semicircle
C = πd, circumference of circleC/2 = πd/2 = 3.14*4/2 = 6.28 ftFind the perimeter
P = 4 + 6.28 + 2*12 = 34.28 ftFor rectangle
L=12B=4Perimeter:-
2(L+B)2(12+4)2(16)32ftFor semicircle:-
radius=r=4/2=2ftPerimeter:-
πr2π6.28ftTotal:-
6.28+32-438.28-434.28ftPark
Avenue
Describe the lines that intersect at Park Avenue and Hawthome Boulevard. Explain.
Answers
Answer:
make it clearer
Step-by-step explanation:
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
160
Step-by-step explanation:
FEJ angle is the large angle and the number in red shows how big it is. Remember the whole thing is 180 degrees.
160°
It is an obtuse angle because it is greater than 90°
Hope this helps :)
Enter the solution (x, y) to the system of equations shown.
y=4x−3
y=−x−13
Answers
Answer:
x=-2
y=-11
Step-by-step explanation:
4x-3=-x-13
5x-3=-13
5x=-10
x=-2
y=4(-2)-3
y=-11
Find the sum of the first 21 terms of the arithmetic progression.
−7, −11, −15, . . .
Answers
We are given with an AP (Arithmetic Progression) with first term being -7, and the common difference being the difference between any succeding term from any term and the term itself, so common difference = -11 - (-7) = -11 + 7 = -4, so now before finding the sum of 21 terms, let's recall that ;
[tex]{\boxed{\bf{S_{n}=\dfrac{n}{2}\{2a+(n-1)d\}}}}[/tex]Where, d is the common difference, a is the first term, and n is the number of terms and [tex]{\bf S_n}[/tex], being the sum of n terms, so putting all the values in the formula, we will have ;
[tex]{:\implies \quad \sf S_{21}=\dfrac{21}{2}\{2\times -7+(21-1)-4\}}[/tex]
[tex]{:\implies \quad \sf S_{21}=\dfrac{21}{2}(-8+20\times -4)}[/tex]
[tex]{:\implies \quad \sf S_{21}=\dfrac{21(-8-80)}{2}}[/tex]
[tex]{:\implies \quad \sf S_{21}=\dfrac{21(-88)}{2}}[/tex]
[tex]{:\implies \quad \sf S_{21}=-21\times 44}[/tex]
[tex]{:\implies \quad \boxed{\bf{S_{21}=-924}}}[/tex]
=) A student is taking a standardized test
consisting of multiple choice questions for
which there are five options for each question.
Four points are awarded for each correct
answer, but the student loses 2 points for an
incorrect answer. Questions left blank neither
receive nor lose points. Is it in the student's
best interest to guess?
Answers
Answer:
in this problem. Not that the total number of ways of taking one or more alternative out of ...
Step-by-step explanation:
Answer:
No.
Step-by-step explanation:
Well, honestly not sure how to solve this but I'll try.
Each correct answer is giving 4 points but the probability to choose the correct one is 1/5
Each incorrect one gives -2 points and the chance to pick a wrong answer is 4/5.
Obviously, the chance to lose points is more. But is taking the risk and guessing worth it? Well, it depends on how many points the correct answer gives. If it makes up for the possible loss of points, then it is in his interest to guess, otherwise he will end up losing more than they win.
If we sum the two chances to find averagely how many points the student will get, then I guess that would be the correct answer:
4(1/5) + (-2)(4/5) = 4/5 - 8/5 = -4/5
He will get averagely -4/5 points, so I believe it isn't in his interest. It means that the points he gets don't make up for the possible loss of points if you choose answers randomly. (Wow, I'm glad teachers don't do this on tests 0_0)
This is my theory though, not sure how to go for solving this, just thinked logically. I hope this helps, but don't trust me and copy paste my answer on your test or whatever. Think if this is correct first because I'm not sure
1 point
2. Three boards are unloaded into the factory.
А
B
С
Board A is three times the length of board C, plus 5 inches. Board B is two
times the length of board C, plus 3 inches. The total length of all three boards
is 104 inches. How long is each board?
Your answer
??
