It is found that Ken will have run 3 laps and Hamid will have run 4 around a track.
What is prime factorization?Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities. Prime factorization is when all those factors are prime numbers.Thus, prime factorization expresses an integer in terms of multiples of prime numbers.
Prime factorization is unique for each integer.
To determine the number of seconds that will have passed when they meet again. We will use the LCM, or least common multiple, for this.
Thus the prime factorization of each number:
80 = 10(8)
10 = 5(2)
8 = 2(4)
4 = 2(2)
80 = 2(2)(2)(5)(2)
60 = 10(6)
10 = 5(2)
6 = 2(3)
60 = 2(2)(3)(5)
For the LCM,
2(2)(5)(2)(2)(3) = 240
This means every 240 sec; they will both be at the start line.
Since Ken completes a lap in 80 seconds, then he will completes
240/80 = 3 laps in 240 seconds.
Since Hamid completes a lap in 60 seconds, then he will completes 240/60 = 4 laps in 240 seconds.
Hence, It is found that Ken will have run 3 laps and Hamid will have run 4.
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Two angles are complementary. The measure of the larger angle is 14° less than 3 times the measure of the smaller angle.
The measure of the smaller angle is ____
degrees and the measure of the larger angle is ____ degrees.
Answer:
Step-by-step explanation:
Comment
2 angles are complementary means together they = 90 Degrees.
Let the smaller angle be x
The complement = 3*x - 14 It is the larger angle.
Givens
<1 = x
<2 = 3x - 14
<1 + <2 = 90
Solution
x + 3x -14 = 90 Combine the left
4x - 14 = 90 Add 14 to both sides
4x - 14+14 = 90 + 14 Combine
4x = 104 Divide both sides by 4
4x/4 = 104/4
x = 26
Answer
<1 = 26
<2 = 3*26 - 14
<2 = 78 - 14
<2 = 64
In simple interest, a principle of money doubles itself in 10 years. Find the number of years it will take to triple itself.
Help me pls
Answer: 20 years
Step-by-step explanation:
Let M be the sum of money invested.
Given Sum of money doubles itself in 10 years.
Then, M will become 2M in 10 years.
Now we can calculate interest for ten years as given below.
From the above calculation, M is the interest for the first 10 years.
In simple interest, interest earned will be the same every year.
So, interest earned in the next 10 years also will be M.
So it will take 20 years.
Thank you if you can give me a brainliest.
please help!! will mark branliest if correct!!!
Answer:
Remove the negative from the 1 on the first increasing interval
Please answer the 2 question in photo [ Brainliest + points ]
Answer:
second is obtuse angle .
Step-by-step explanation:
5. 160°
6. 120°
[im not sure what they're asking for but if its degree then this is the answer]
(15y - 48)
(8r - 1)(11x - 25)
The measure of the angles ( 15y - 48 )°, ( 8x - 1 )°, and ( 11x - 25 )° are 165°, 15°, and 63° respectively.
The lines j and k are parallel and lines l and m are parallel.
Consider the figure,
( 8x - 1 )° ≅ 1, corresponding angles
1 ≅ 9, corresponding angles
9 ≅ ( 11x - 25 )°, vertical angles
Therefore,
m∠ 1 = m∠ 9
m∠9 = ( 8x - 1 )°
So,
( 8x - 1 )° = ( 11x - 25 )°
Subtracting 8x from both sides of the equation.
11x - 25 - 8x = 8x - 1 - 8x
3x - 25 = - 1
Adding 25 on both sides of the equation.
3x - 25 + 25 = - 1 + 25
3x = 24
Dividing each side of the equation by 3
( 3x/3 ) = ( 24/3 )
x = 8
Now, the angle made by a straight line is 180°.
Therefore,
( 8x - 1 )° + ( 15y - 48 )° = 180°
( 8 × 8 - 1 )° + ( 15y - 48 )° = 180°
15° + 15y - 48° = 180°
15y - 33° = 180°
Adding each side of the equation by 33°.
15y - 33° + 33° = 180° + 33°
15y = 213°
Dividing each side of the equation by 15
( 15y/15 ) = ( 213/15 )°
y = 14.2°
So, the measure of the angles are:
( 15y - 48 )° = ( 15 × 14.2 - 48 )° = ( 213 - 48 )° = 165°
( 8x - 1 )° = ( 8 × 8 - 1 )° = 15°
( 11x - 25 )° = ( 11 × 8 - 25 )° = ( 88 - 25 )° = 63°
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Self balancing scooter travels 12 miles per hour, all terrain vehicle can travel 6 times as fast as the scooter,a go kart can travel 67 miles per hour,which vehicle can travel the fastest
The fastest vehicle is: the all terrain that can travel at a speed of 72 mi/h
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
v(scooter) = 12mi/hv(all terrain vehicle) = 6 * 12mi/hv(go kart) = 67 mi/hwhich is the faster=?Calculating the velocity of the all terrain vehicle we get:
v(all terrain vehicle) = 6 * 12mi/h
v(all terrain vehicle) = 72 mi/h
By ordering the velocities from highest to lowest we have:
(all terrain vehicle)72 mi/h >(go kart)67 mi/h >(scooter)12mi/h
Due to the all terrain vehicle has the highest velocity it is the faster vehicle.
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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Bookwork code: L64
Calculator
not allowed
This is a new version of the question. Make sure you start new workings.
Spinner A has pink, black and blue sections.
Spinner B has pink and black sections only.
Annabelle spins each spinner once.
Work out how many possible ways there are for at least
one of the spinners to land on pink.
(Hint: copy and complete the tree diagram first.)
Possible ways there are for at least one of the spinners to land on the pink is 2 / 3.
Given spinner A has pink, black, and blue sections.
The number of possible outcomes of spinner A to land not on pink is 2/3
Given spinner B has pink and black sections.
So, the number of possible outcomes of spinner B to land not on pink is 1/2
Annabelle spins each spinner once
possible ways not land on pink = 2/3 * 1/2 = 1/3
Possible ways there are for at least one of the spinners to land on the pink is
= 1 - possible ways not to land on the pink
= 1 - 1/3
= 2 / 3
Possible ways there are for at least one of the spinners to land on the pink is 2 / 3.
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Solve for j in the literal equation
h - 10/j
=k.
The value of j from the equation h-10/j=k is equal to 10/(h-k).
Given that the equation is h-10/j=k.
We are required to find the value of j from the given equation.
Equation is a relationship between two or more variables that are expressed in equal to form. It may be a linear equation,quadratic equation, cubic equation and many more depending on the power of the variables present in that equation.
The equation is h-10/j=k.
-10/j=k-h
1/j=(k-h)/-10
j=-10/(k-h)
j=10/(h-k)
(We can eliminate the negative sign by taking negative out from the denominator.)
Hence the value of j from the equation h-10/j=k is equal to 10/(h-k).
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Jason considered two similar televisions at a local electronics store. the cheaper version was 12 inches by 24 inches. the more expensive version was \large \frac{8}{3} the size of the cheaper one. what are the dimensions of the expensive television? a 4.5 inches by 9 inches b 28 inches by 56 inches c 7.5 inches by 15 inches d 32 inches by 64 inches
The dimensions of expensive television is 32 inches through 64 inches.
This trouble may be solved if we understand the idea of fraction and a way to calculate the part of a fragment.
right here it is for the reason that the inexpensive tv is 12 inches by means of 24 inches.
Also it is given that the expensive television is [tex]\frac{8}{3}[/tex] of the cheaper one.
Now taking the length into consideration the length of the television is
=[tex]\frac{8}{3}*12[/tex]
= 32 inches
Now taking the width into consideration the width of the television is
=[tex]\frac{8}{3}*24[/tex]
= 64 inches
So, the dimension of the expensive television is 32 inches by 64 inches.
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A triangle has base 7 m and area 17.5 m². What is the height?
Answer: Height = 5m
Step-by-step explanation: To solve the height of the triangle we can use the Area formula and substitute the values given to solve for heigh.
A = ( b * h ) / 2
17.5 = (7 * h) / 2
17.5 (*2) = 7 * h
(Remember that everything done to one side has to be done to both. We can multiply by 2 on both sides to eliminate the 2.)
35 = 7 * h
35/7 = h
5 = h
The height of the triangle equals 5.
Can you help me i really dont get it
By using Pythagorean theorem, the shortest distance between planet Q and planet R is 1.25 × 10⁷ kilometers (12.5 million kilometers).
How to find the distance between two planets
The picture shows the geometry between three planets, which represents the three vertices of a right triangle, the straight line distance between the points Q and R represents the hypotenuse of the right triangle. The hypotenuse can be found by using the Pythagorean theorem:
QR = √(PQ² + PR²)
Where QR is the hypotenuse of the right triangle, in kilometers.
If we know that PQ = 3.5 × 10⁶ km and PR = 1.2 × 10⁷ km, then the distance between planet Q and planet R is:
QR = √[(3.5 × 10⁶ km)² + (1.2 × 10⁷ km)²]
QR = 1.25 × 10⁷ km
The shortest distance between planet Q and planet R is 1.25 × 10⁷ kilometers (12.5 million kilometers).
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Form linear equations in two variables using suitable variables for the unknowns.
The perimeter of a rectangle is 98 cm. [Take length as x and breadth as y.]
Answer:
2(x+y)=98 is the answer.
18% of the car inn the parking lot are blue . If there are 150 cars in the parking lot how many cars are blue
Answer:
27
Step-by-step explanation:
27
Explanation:
"Percent" or "%" means "out of 100" or "per 100", Therefore 18% can be written as
18 /100 .
When dealing with percentage, the word "of" means "times" or "to multiply".
Finally, lets call the number we are looking for "n".
Putting this altogether we can write this equation and solve for "n "
while keeping the equation balanced:
n = 18 /100 × 150
n = 2700 /100
n = 27
27 is 18% of 150
olivia and yixing are volunteering at a cat rescue shelter. the shelter supervisor asks them to clean out kennels and haul bags of cat food from the donation area into storage. it takes olivia 6 minutes to clean out a kennel and 6 minutes to move a bag of food. it takes yixing 10 minutes to clean out a kennel and 12 minutes to move a bag of food. for the following questions, round each answer to the nearest tenth. a. has an absolute advantage in completing both tasks.
The correct option is A which is Yixing should clean out the kennels, and Olivia should move the food bags.
What is an expression?Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
All the parts will be solved below:-
a. Olivia has an absolute advantage as she takes less time for completing both the tasks
b. Olivia's opportunity cost of cleaning a kennel is
= 6 ÷ 6
= 1 bag of food moved.
c. Olivia's opportunity cost of moving one bag of food is
= 6 ÷ 6
= 1 kennel cleaned
d. Yixing's opportunity cost of cleaning a kennel is
= 10 ÷ 12
= 0.83 bags of food moved.
e. Yixing's opportunity cost of moving one bag of food is
= 12 ÷ 10
= 1.2 kennels cleaned
f. From the above calculations, we can see that the opportunity cost of kennel cleaning would be less sin Yixing so here Yixing should have a comparative advantage and Olivia should have moved the food bags
The complete question is given below:-
Olivia and Yixing are volunteering at a cat rescue shelter. The shelter supervisor asks them to clean out kennels and haul bags of cat food from the donation area into storage. It takes Olivia 6 minutes to clean out a kennel and 6 minutes to move a bag of food. It takes Yixing 10 minutes to clean out a kennel and 12 minutes to move a bag of food.
A. ____has an absolute advantage in completing both tasks.
B. Olivia's opportunity cost of cleaning a kennel:___bags of food moved.
C. Olivia's opportunity cost of moving one bag of food:_____kennels cleaned.
D. Yixing's opportunity cost of cleaning a kennel:____bags of food moved.
E. Yixing's opportunity cost of moving one bag of food:____kennels cleaned.
F. Yixing says it does not matter which task each of them performs because Olivia is faster at both tasks. Is she correct?
A) No, Yixing should clean out the kennels, and Olivia should move the food bags.
B) No, Olivia should clean out the kennels, and Yixing should move the food bags.
C) Yes, Olivia should do both tasks because she is faster at both.
D) No, Yixing should do both tasks so that she can practice and become more efficient.
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Can somebody help wit this I’m failing geometry rn and it makes no sense .
By definition of vertical angles, the value of the variable x behind the geometric system is equal to 12. The measure of the labeled angle is 48°.
What is the measure of variable within a geometric system generated by two lines intersecting each other?
The image shows a geometric system generated by two non-parallel lines that intersect each other and consequently two pairs of vertical angles are therefore created. In geometry, two vertical angles are opposite to each other and have the same measure. Then, the following mathematical relationship is found:
4 · x = 48
In addition, we must clear the variable x within the equation:
4 · x = 48 Given
x = 48 / 4 Compatibility with multiplication / Commutative, associative and modulative properties / Existence of multiplication
x = 12 Definition of division / Result
The value of the variable x behind the geometric system is equal to 12.
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a cup of coffee at 160 degrees is placed in a room where the temperature of 70 degrees. after 5 minutes, the coffee’s temperature is 112.5 degrees.
The coffee reaches t ≈ 12 minutes a temperature of 150◦F.
(t) = Ts + (T0 - Ts)e-kt, according to Newton's Law of Cooling.
T(t) = temperature of the coffee cup t minutes after being placed in the roomTs is the ambient temperature.T0 indicates the coffee cup's beginning temperature.
(a). Using the given information, we have T(t) = 70 + (160 - 70)e-kt
= 70 + 90e-kt
T(5) = 70 + 90e-k(5) = 112.5
So, 90e-5k = 42.5
e-5k = 0.47222222
-5k = ln(0.47222222)
k = 0.15 Temperature after 10 minutes = T(10) = 70 + 90e-0.15(10)
≈ 90.1
-------------------------------------------------------------------------------------
(b). When will the temperature of the coffee reach 85°?
Find t so that T(t) = 85: 70 + 90e-0.15t = 85
90e-0.15t = 15
e-0.15t = 0.16666666
-0.15t = ln(0.166666666)
t ≈ 12 minutes
what do you mean by newton's law of cooling?According to Newton's law of cooling, a body's rate of heat loss is inversely related to the temperature difference between it and its surroundings. The law is frequently qualified to state that the tiny temperature differential and the consistency of the heat transmission mechanism must exist. As a result, it is the same as asserting that the heat transfer coefficient, which mediates between heat losses and temperature variations, is constant. Due to the fact that the thermal conductivity of the majority of materials very slightly depends on temperature, this requirement is typically satisfied in heat conduction (where it is guaranteed by Fourier's law). Newton's Law is applied in convective heat transfer for forced air or pumped fluid cooling.
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Select the correct answer. The difference of two numbers is 8. When twice the first number is added to three times the second number, the result is 51. What are the two numbers? A. 12 and 4 B. 15 and 7 C. 20 and 12 D. 23 and 15 Reset Next
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The numbers are 15 and 7.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
We have,
Let the two numbers be M and N.
The difference between the two numbers is 8.
i.e M - N = 8
M = 8 + N ____(1)
When twice the first number is added to three times the second number, the result is 51.
Let the first number = M
i.e 2M + 3N = 51 _____(2)
Now,
2 ( 8 + N ) + 3N = 51
16 + 2N + 3N = 51
5N = 51 - 16
5N = 35
N = 7 put in (1)
M = 8 + 7 = 15
Thus the numbers are 15 and 7.
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Convert 549/999 to a decimal. 5.495— .549 .549— .549–..please help
Answer:
.549 (all under bar/repeted)
Step-by-step explanation:
Multiply (4.12 × 10−9)(8.3 × 1015). write the final answer in scientific notation. 34.196 × 10−134 3.4196 × 107 3.4196 × 10−135 34.196 × 106
The product, in scientific notation, can be rewritten as:
3.4196*10²⁵
How to get the product in scientific notation?We want to find the product between the two numbers:
(4.12*10⁹)*(8.3*10¹⁵)
To take it, we can rewrite the product as:
(4.12*8.3)*(10⁹*10¹⁵)
(34.196)*(10⁹⁺¹⁵)
(34.196)*10²⁴
Now, to get this in scientific notation, we need to have only one digit in the left side of the decimal point, then we can rewrite:
(34.196)*10²⁴ = 3.4196*10²⁵
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Make r the subject of 5r+1= a(m + r)
Answer:
See below
Step-by-step explanation:
xpand R sid to get
5r+1 = am + ar subtract 'ar' from both sides
5r - ar + 1 = am factor out 'a'
r ( 5-a) + 1 = am
r (5-a) = am-1 divide both sides by ' 5-a'
r = (am-1 ) / (5-a)
5 $17.00 3-66. Randall and Stephano work in a restaurant. Randall earned $27.50 one day, $25.00 the next day, and $32.50 on the third day. Stephano works fewer hours, but more days. He earned $17.50 one day, $22.50 the next day, $12.50 the third day, $15.00 the fourth day, and $17.00 the fifth day. Who earned the most money? How much more?
Answer:
Randall and the most money. she earned 50 cents more than Stephano did.
Step-by-step explanation:
so it's Randall makes $27.50 on his first day and $25 on a second date and and 32.50 on his third day you would add those up to get $85 in all. now Stefano gets 7.50 22.50 12.50 15.00 and 17.00 dollars , and when you add all those together he gets 84.50 and all. meaning that random made more money by .50 cents.
Karen reads a book at a rate of 10 chapters per hour.
How many chapters does she read in 5 hours?
Please answer the question in photo [ Brainliest + points ]
Answer:
EQ = 47
Step-by-step explanation:
Since Q is midpoint, EQ = QF
or EQ = EF/2
5x + 2 = (9x + 13)/2
10x + 4 = 9x + 13
10x - 9x = 13 - 4
x = 9
EQ = 5x + 2 = 5(9) + 2 = 45 + 2 = 47
0.39 repeating as a fraction in simplest form
It depend on the repeating part.
If x = 0.393939… (the repeating part is underlined), then 100x = 39.393939…, and
100x - x = 39.393939… - 0.393939…
99x = 39
x = 39/99 = 13/33
On the other hand, if you mean x = 0.3999…, then 10x = 3.999… and 100x = 39.999…, so that
100x - 10x = 39.999… - 3.999…
90x = 36
x = 36/90 = 2/5
This entire concept is difficult for me to understand but I have some grasp of what I’m doing if it’s graphing the equation but doing the reverse, however, is somehow difficult for me. (and yes i need help on all 4 of them)
(5) Set up a system of equations and solve:
38 people are playing pickle-ball in a park. 13 matches are in progress. How many double and
how many single matches are being played?
Step-by-step explanation:
Assume the number of double matches is x (matches)
the number of single matches is y (matches)
(Condition: x > 0 and y > 0)
Because there are 13 matches in progress, so:
x + y = 13 (1)
Because there are 38 people playing (4 people on each double match and 2 people on each single match), so:
4x + 2y = 38 (2)
A system of equation is made by combining (1) and (2):
x + y = 13 (1)
4x + 2y = 38 (2)
Take (2) - 2×(1):
=> 2x = 12
=> x = 6
Substitute the result on (1)
=> y = 7
So there are 6 double matches and 7 single matches being played
The sum of two-thirds a
number and eighteen is twenty-three. What is the number?
number = x
2/3x + 18 = 23
2/3x = 5
x = 15/2 = 7.5
What is the slope of the line that passes through the points (1, -1) and (-8, -7) Write your answer in simplest form
Answer:
2/3
Step-by-step explanation:
Compute the slope of the line through the following points:
p_1 = (1, -1) and p_2 = (-8, -7)
The slope of the line through (x_1, y_1) and (x_2, y_2) is:
(y_2 - y_1)/(x_2 - x_1)
Substitute (x_1, y_1) = (1, -1) and (x_2, y_2) = (-8, -7):
= (-7 - -1)/(-8 - 1)
-8 - 1 = -(8 + 1):
= (-7 - -1)/(-(8 + 1))
8 + 1 = 9:
= (-7 - -1)/(-9)
(-1)^2 = 1:
= (-7 + 1)/(-9)
-7 + 1 = -6:
= (-6)/(-9)
The gcd of -6 and -9 is -3, so (-6)/(-9) = (-3×2)/(-3×3) = (-3)/(-3)×2/3 = 2/3:
Answer: = 2/3
how to simplify 4x +5(-3x +6)
Answer:
-11x + 30
Step-by-step explanation:
distribute the 5 into the parenthesis
= 4x -15x + 30
combine like terms
= -11x + 30
Answer:
-11x + 30
Step-by-step explanation:
4x + 5(-3x + 6) Distribute the 5
4x + (5)-3x + (5)6
4x -15x + 30 Combine the x's
-11x + 30
help with this please
Answer:
-4-9=-13
Step-by-step explanation:
the small arrow has moved 4 times to the left that makes 4 negative-4..and the large arrow moved 10 times to the left that makes it negative too but the big arrow arised from the tip of the small arrow that means it is -9 NOT -10 be careful.Keep in mind that if arrows face to the left that means subtraction but if moving to the right it means additionthat means as a conclusion the equation is subtraction and it will be[tex]-4-9=-13[/tex]