Answer:
Step-by-step explanation:
2005 AMC 8 Problems/Problem 20
Problem
Alice and Bob play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Alice moves clockwise and Bob, counterclockwise. In a turn of the game, Alice moves 5 points clockwise and Bob moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
$\textbf{(A)}\ 6\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 12\qquad\textbf{(D)}\ 14\qquad\textbf{(E)}\ 24$
Solution
Alice moves $5k$ steps and Bob moves $9k$ steps, where $k$ is the turn they are on. Alice and Bob coincide when the number of steps they move collectively, $14k$, is a multiple of $12$. Since this number must be a multiple of $12$, as stated in the previous sentence, $14$ has a factor $2$, $k$ must have a factor of $6$. The smallest number of turns that is a multiple of $6$ is $\boxed{\textbf{(A)}\ 6}$.
See Also
2005 AMC 8 (Problems • Answer Key • Resources)
Preceded by
Problem 19 Followed by
Problem 21
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
Mattie Evans drove 350 miles in the same amount of time that it took a turbopropeller plane to travel 1350 miles. The speed of the plane Has 200 mph faster than
the speed of the car. Find the speed of the plane.
(Simplify )
let
d1 = 250 mi the distance that Mattie Evans drove
v1 = the speed of Mattie Evans
d2 = 1300 mi the distance the plane traveled
v2 = the speed of the plane
The speed of the plane was 190 mph faster than the speed of the car:
v2 = v1 + 190
since time = distance/speed and they both traveled the same time we have
d1/v1 = d2/v2
250/v1 = 1300/v2 cross multiply
250v2 = 1300v1 divid eboth sides by 50
5v2 = 26v1
by solving the system of equations:
v2 = v1 + 190
5v2 = 26v1
we find
v1 = 45.24 mph
v2 = 235.24 mph
Can someone help me please?
Answer: a=(3,-4)
B=(3,-1)
C=(5,-2)
Step-by-step explanation:
A Coke can has a radius of 4 cm and a height of 11 cm. What is the volume of the can?
Answer:
V ≈ 552.9 cm³
Step-by-step explanation:
The volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius and h the height ) , then
V = π × 4² × 11 = π × 16 × 11 = 176π ≈ 552.9 cm³ ( to the nearest tenth )
Answer:
The volume of Coke can is 552.64 cm².
Step-by-step explanation:
Given :
✧ Radius of Coke can = 4 cm.✧ Height of Coke can = 11 cm.To Find :
✧ Volume of Coke canUsing Formula :
[tex]{\star{\small{\underline{\boxed{\sf{\red{V_{(Can)} = \pi{r}^{2}h}}}}}}}[/tex]
✧ V = Volume ✧ π = 3.14 ✧ r = radius ✧ h = heightSolution :
Here's the Coke can is in cylindrical form.
So, finding the volume of Coke can by substituting the values in the formula :
[tex]{\dashrightarrow{\pmb{\sf{Volume_{(Can)} = \pi{r}^{2}h}}}}[/tex]
[tex]{\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {(4)}^{2} \times 11}}}[/tex]
[tex]{\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {(4 \times 4)}\times 11}}}[/tex]
[tex]{\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {(16)}\times 11}}}[/tex]
[tex]{\dashrightarrow{\sf{Volume_{(Can)} = 3.14 \times {16}\times 11}}}[/tex]
[tex]{\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{314}{100} \times {16}\times 11}}}[/tex]
[tex]{\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{314 \times 16 \times 11}{100}}}}[/tex]
[tex]{\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{5024 \times 11}{100}}}}[/tex]
[tex]{\dashrightarrow{\sf{Volume_{(Can)} = \dfrac{55264}{100}}}}[/tex]
[tex]{\dashrightarrow{\sf{Volume_{(Can)} \approx 552.64 \: {cm}^{2}}}}[/tex]
[tex]\star{\red{\underline{\boxed{\sf{Volume_{(Can)} \approx 552.64 \: {cm}^{2}}}}}}[/tex]
Hence, the volume of Coke can is 552.64 cm².
Chang made $156 for 13 hours of work at the same rate, how many hours would he have to work to make $108?
Answer:
9 hours
Step-by-step explanation:
"At the same rate" means time and wages are proportional.
time/wages = t/$108 = (13 h)/$156
t = 108(13 h)/156 . . . . . . . . . . . . . . . units of dollars cancel
t = 9 h
Chang would have to work 9 hours to make $108.
What polygon is shown below?
O A. Square
O B. Rhombus
Answer:
The answer is Option B, Rhombus
Step-by-step explanation:
The picture shows that it is indeed a Rhombus.
The given below is rhombus.
what is polygon?
A polygon is a two-dimensional geometric figure that has a finite number of sides.
As, per the figure the given figure is a quadrilateral.
As its four sides are equal.
So, it can be a side or rhombus but the corner angle are not 90 degrees,
Hence, the given figure is Rhombus.
Learn more about polygon here:
https://brainly.com/question/10441863
#SPJ5
Which point is located at (Negative 1, 1 and one-fourth)? A B C D
Answer:
Point A
Step-by-step explanation:
Look along the x axis (horizontal) and find -1. Then look on the y axis and find 1 and 1/4. Finally, find where the two coordinates meet and that's your point - A.
Hope this helps!
Meg visited her Aunt Clare for lunch. After they ate, Aunt Clare made tea. She put the same amount of black tea and milk in both their cups, but Meg decided to add some extra milk to hers. Which cup of tea was darker after they had finished adding milk?
Answer:
Aunt Clare
Step-by-step explanation:
Milk makes tea weaker, therefore the one with less milk (Aunt Clare's) is darker.
Answer:Aunt clares is darker
hi please help, I can't understand.
If the sides of a rectangle with area 12cm² are (3x-2) and (x+1)
a)X-? b)P-?
[tex](3x - 2)(x + 1) = 12 \\ = > {3x}^{2} - 2x + 3x - 2 = 12 \\ = > {3x}^{2} + x - 2 = 12 \\ = > {3x}^{2} + x - 12 - 2 = 0 \\ = > {3x}^{2} + x - 14 = 0 \\ = > {3x}^{2} + 7x - 6x - 14 = 0 \\ = > x(3x + 7) - 2(3x + 7) = 0 \\ = > (x - 2)(3x + 7) = 0 \\ = > x = 2 \: \: \: or \: \: \: \frac{ - 7}{3} \\ [/tex]
But a negative number cannot be the side of a rectangle.So, x = 2 cmNow, length = (3x - 2) = (3 × 2 - 2) cm = (6 - 2) cm = 4 cmBreadth = (x + 1) = (2 + 1) cm = 3 cm.We know, perimeter of a rectangle = 2( length + breadth)Therefore, the perimeter of the rectangle[tex] = 2(4 + 3)cm \\ = 2 \times 7cm \\ = 14cm[/tex]
Answer:
The value of x is 2 cm and the perimeter of the rectangle is 14 cm.
Hope you could get an idea from here.
Doubt clarification - use comment section.
Chanel says the sequence of transformations that maps trapezoid PQRS onto trapezoid KLMN is: rotate it 90 degrees counterclockwise, and then dilate it by a scale factor of .
Preston says the sequence of transformations that maps trapezoid PQRS onto trapezoid KLMN is: reflect it across the x-axis, and then dilate it by a scale factor of .
Answer:
it changes it by putting it into quadrant 2.
Step-by-step explanation:
(x,y) → (x,-y)
KLMN is an upside down image of PQRS So it was reflected across the x axis and then scaled by 1/2
Preston is correct
Simplify the expression: 4 + 5(2x - 3) - 6x *
16x + 19
-16x -11
4x -9
4x + 9
Step-by-step explanation:
4+5 (2x-3)-6x
9 (2x-3)-6x
18x-27-6x
12x-27
Answer:
[tex] \sf \: 4x - 11 [/tex]
Step-by-step explanation:
Given expression,
→ 4 + 5(2x - 3) - 6x
Let's simplify the expression,
→ 4 + 5(2x - 3) - 6x
→ 4 + 10x - 15 - 6x
→ (10x - 6x) + (4 - 15)
→ (4x) + (-11)
→ 4x - 11
Hence, the answer is 4x - 11.
Need to review this problem for finals help pls
Answer:
Step-by-step explanation:
Slope form: y=mx+b
given slope and x intercept:
y=3x+b
let y=0
0=3(7)+b
b=-21
so:
ANSWER: y=3x-21
plss help me with this:(((
Answer:
11) 7 ( Answer A)
12) (-2) ( Answer D)
Step-by-step explanation:
You can use y = m x + c to answer these questions.
In the equation y = m x + c,
m = slope
c = y - intercept
According to the question,
they have given the equation,
y = 7 x - 2
So, you can replace it with y = m x + c like this.
y = 7 x - 2
↑ ↑
m c
There fore,
slope = 7
y - intercept = ( - 2)
And now let's write the answers for the question.
11) 7 ( Answer A)
12) (-2) ( Answer D)
Hope this helps you :-)
giving brainliest to anyone who solves this question CORRECTLY WITH NO LINKS
5 ti the fifth power + 16 divided by 19 times 20 plus one equals ?????
Answer:
3307.31578947
Step-by-step explanation:
Answer:
I believe it's [tex]\frac{62839}{19}[/tex], or 3307.31578947
Step-by-step explanation:
hope this helps! :D
have a miraculous day!! <3
brainliest will be immensely appreciated uwu
I will give brainiest to the best answer.
what is half of the square root of 72?
Plz answer in square root form. Thank you
Answer:
3sqrt(2)
Step-by-step explanation:
72=6^2 x 2 so sqrt(72)=6sqrt(2)
divide by 2 to get 3sqrt(2)
Answer:
[tex]answer \: is \: = \: \sqrt[6]{2} [/tex]
[tex]to \: know \: the \: answer \: with \: proof[/tex]
[tex]refer \: to \: the \: above \: attatchmet \: [/tex]
Hope this helps you !!Simplify, and Write answer without parentheses
Answer:
w^18
Step-by-step explanation:
exponents are multiplied when there is a parenthesis between them
Answer:
[tex]w^{18}[/tex]
Step-by-step explanation:
the "power to a power" rule allows you to multiply those two exponents. [tex](x^{a} )^{b} =x^{ab}[/tex] is the formula for this rule. in this question, x is w, a is 3, and b is 6. we can multiply the 3 and 6 and get 18 and keep the base the same.
Please help me its due tommorow
Answer:
read below for answers
Step-by-step explanation:
7. 4d + 6 =42
d = 9
8. -3y + 12 = -48
y = 20
9. k/2 + 9 = 30
k = 42
10. g/3 - 7 = 15
g = 66
11. z/5 + 3 = -35
z = -190
12. -9h - 15 = 93
h = -12
13. -3(n + 5) = 12
n = -9
14. -17 + b/8 = 13
b = -32
15. 7( c- 12 ) = -21
c = 9
16. -3 + p/7 = -5
p = -14
17. 46 = -6t - 8
t = -9
Find the total surface of :
Answer:
=2112cm²
Step-by-step explanation:
radius=14cm
height=10cm,
Curved surface area of cylinder=2πrh
=2×22÷7×14×10
=880cm²
Base area of cylinder=πr²
=22÷7×14×14
=616cm
Whole surface area of cylinder=2πr(r+h)
=2×22÷7×14(14+10)
=2×22÷7×14(24)
What is the solution to the system of equations?
Answer:
(-2, 5/3)
Step-by-step explanation:
Substitute x with -2 and solve
y = 2/3(-2) + 3
Multiply 2/3 and -2
y = -4/3 + 3
Add
-4/3 + 3 = 5/3
y = 5/3
Final answer:
(-2, 5/3)
x^2=x+2
Please solve by factoring
But I’ll take anything honestly
Answer:
Step-by-step explanation:
[tex]\sf x^2=x+2[/tex]
Subtract x+2 from both sides of the equation:
[tex]\sf x^2-(x+2)=x+2-(x+2)[/tex]
[tex]\sf x2-x-2=0[/tex]
Now, factor left side of equation:
[tex]\sf (x+1)(x-2)=0[/tex]
Set the factors equal to zero:
[tex]\sf x+1=0[/tex] [tex]\sf x-2=0[/tex]
[tex]\boxed{\sf x=-1}[/tex] [tex]\boxed{\sf x=2}[/tex]
_____________________________________
What is 4/6 divided by 3/12 what is the quotient
Answer: 8/3, 2 2/3
Step-by-step explanation:
reciprocal of 3/12 is 12/3
soooooo
4/6 x 12/3
which is 48/18
u can divide that by 6
which is 8/3
or 2 2/3
help me with this question plz with an explanation
Answer:
374mm squared
Step-by-step explanation:
Bottom rectangle can be cut off to equal 52mm, by multipling 4 by 13
the rest is 14*23, which equals 322mm
add those together to get 374mm squared
Answer:
374 square millimeters
Step-by-step explanation:
First, we can split the shape into 2 rectangles.
This will give us a rectangle with a width of 13 and 10.
Let's work out 1 rectangle at a time.
Area of a rectangle=Width times by legth
13*18=234- This is the area of 1 of the rectangles.
10*14=140- This is the area of the second rectangle
Now we add the areas together to get 374 square millimeters, which is the area of this figure.
Answer the following.
1 Bharat borrows a certain sum of money at
5% pa. If he pays 2000 as simple interest
at the end of the first year, find the sum he
borrowed
Answer:
40000
Step-by-step explanation:
Simple interest (I) is calculated as
I = [tex]\frac{PRT}{100}[/tex]
P is the amount borrowed , R is the interest and T the time in years
Here I = 2000 , R = 5 and T = 1 with P to be found , then
2000 = [tex]\frac{P(5)(1)}{100}[/tex] ( multiply both sides by 100 )
5P = 200000 ( divide both sides by 5 )
P = 40000
Answer:
The sum (Principal) is Rs.4000.
Step-by-step explanation:
Given :
Simple interest = Rs.2000Time = 5% per annum Time = 1 yearTo Find :
PrincipleUsing Formula :
[tex]\star\small{\underline{ \boxed{\sf{\red{S.I = \dfrac{P \times R \times T}{100}}}}}}[/tex]
S.I = Simple Interest P = Principle R = Rate T = TimeSolution :
Substituting all the given values in the formula to find the Simple Interest :
[tex]{\dashrightarrow{\small{\sf{S.I = \dfrac{P \times R \times T}{100}}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{2000= \dfrac{P \times 5 \times 1}{100}}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{2000= \dfrac{P \times 5}{100}}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{2000= \dfrac{5P}{100}}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{P = 2000 \times \dfrac{100}{5}}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{P = 2000 \times \cancel{\dfrac{100}{5}}}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{P = 2000 \times 20}}}}[/tex]
[tex]{\dashrightarrow{\small{\sf{P =Rs.40000}}}}[/tex]
[tex]\star\small{\underline{ \boxed{\sf{\red{P = Rs.40000}}}}}[/tex]
Hence, the sum Bharat borrowed is Rs.40000.
[tex] \rule{190}1[/tex]
Solve the quadratic equation 2x2 – x = 15 using the quadratic formula.
Question 6 options:
A)
x = –3, x = –5∕2
B)
x = –3, x = 5∕2
C)
x = 5∕2, x = 3
D)
x = – 5∕2, x = 3
which one is right. keep it simple
Answer:
B) x = 3 or x = -5/2
Step-by-step explanation:
Solve for x over the real numbers:
2 x^2 - x = 15
Subtract 15 from both sides:
2 x^2 - x - 15 = 0
x = (1 ± sqrt((-1)^2 - 4×2 (-15)))/(2×2) = (1 ± sqrt(1 + 120))/4 = (1 ± sqrt(121))/4:
x = (1 + sqrt(121))/4 or x = (1 - sqrt(121))/4
sqrt(121) = sqrt(11^2) = 11:
x = (1 + 11)/4 or x = (1 - 11)/4
(1 + 11)/4 = 12/4 = 3:
x = 3 or x = (1 - 11)/4
(1 - 11)/4 = -10/4 = -5/2:
Answer: x = 3 or x = -5/2
How i can answer this question
Answer:
6x
Step-by-step explanation:
7x-x = x ( 7-1) = 6x
Answer:
6 x
Step-by-step explanation:
Subtract x from 7 x .
What is the distance from 5,1 and 2,1
Answer:
2.0
Step-by-step explanation:
This question has 3 parts: subject (distance), and numbers (5.1 and 3.1).
Distance means subtraction. Between means to 5.1 and 3.1 .
So 5.1 - 3.1 = 2.0
f(x) is graphed below. If g(x)=f(x+2)-4, what are the roots of g(x)?
Answer:
fortnit 90s
Step-by-step explanation:
crank and c until u get too 90 height
A study is testing the effectiveness of a new allergy medication. Sixty people who reported they experience allergies were randomly assigned to one of two groups: one with the new medication, and another with a placebo. After two weeks, the subjects were surveyed by technicians to determine their level of allergic symptoms.
Which of the following would benefit this experiment the most?
This experiment should be double blind. Neither the subject nor the technician should know which group is receiving the new medication and which is receiving the placebo. This method would control for the placebo effect and prevent any effect on the response.
This experiment should be single blind. The subjects do not know which treatment they are receiving to control for the placebo effect, but the technicians need to know which group received which treatment.
This experiment should be single blind. The subjects know which treatment they are receiving but the technicians do not know which group received which treatment, so the response being measured is not affected.
This experiment should not use blinding. It is unethical for the subjects not to know which treatment they are receiving, placebo or new medication, and for the technicians not to know which group received which treatment.
The best method that would lead to a more effective study is:
This experiment should be double blind. Neither the subject nor the technician should know which group is receiving the new medication and which is receiving the placebo. This method would control for the placebo effect and prevent any effect on the response.Double blind experiments are usually better than single blind experiments because they will account for experimenter bias which is where the technicians influence the project whether knowingly or unknowingly.
The placebo effect is also better studied because the participants will not know whether they are receiving a placebo or the real thing.
In conclusion, option A is correct.
Find out more about double blind experiments at https://brainly.com/question/9292513.
Answer:
A ON EDGE2022 :)))))))
Step-by-step explanation:
Could someone answers these! I Really NEED HELP
Answer:
(3x + 5) (x - 3)
Step-by-step explanation:
This is the quadratic expression
What is a bond and how do you make money from it?
Answer:
Bonds are among a number of investments known as fixed-income securities. They are debt obligations, meaning that the investor loans a sum of money (the principal) to a company or a government for a set period of time, and in return receives a series of interest payments (the yield).
Step-by-step explanation:
5/12 of the pupils in yr9 say their favourite colour is red. There are 180 pupils in yr9. How many students said red is their favourite colour?
Answer:
75 students
Step-by-step explanation:
180*5/12=75