If each of these runners travels the indicated number of spaces in the same amount of time, at which numbered spot will all of the runners be next to one another?
The numbered spot at which all the runners will be next to one another is spot 19.
What is the LCM?Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.
Starting with the runner on the outside track, the provided parameters are;
The runner covered n₁ = 5 places on the outside track, which is the number of spaces.
Next, the inner runner will traverse n₂ spaces, which equals one space.
The following inner runner will cover n₃ = 3 spaces.
The subsequent runner will traverse n₄ = 2 spaces.
The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.
LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.
Time = 30/ = 6
Consequently, when the first runner has covered 30 places, we have;
Six time units have been expended.
The runner comes to a stop at position 30- (30 -19) = Position 19.
First runner's new destination is Spot 19.
The distance covered simultaneously by runner 2 is 6 x 1 = 6.
The distance covered by two runners running simultaneously equals six spaces.
Second runner's new position: 6 spaces plus spot 13 equals spot 19.
The combined distance covered by the three runners is 6 x 3 = 18.
The distance runner 3 covers 18 spaces simultaneously.
Third runner's new position: 18 spaces + Spot 1 = 19 spaces
Runner 4 covers a distance of 6 x 2 = 12 at the same time.
Distance runner 4 journeys equals 12 spaces
Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.
Therefore, all the runners will be next to one another is spot 19.
To learn more about the LCM;
https://brainly.com/question/20739723
#SPJ1
A coffee pot holds 6 quarts of coffee. How much is it in cups?
Answer:
24 cups
Step-by-step explanation:
Hope this helps :)
The following are the annual incomes (in thousands of dollars) for 8 randomly chosen, U.S. adults employed full-time.
44, 44, 54, 54, 65, 39, 54, 44
Send data to calculator
(a) What is the mean of this data set? If your answer is not an
integer, round your answer to one decimal place.
(b) What is the median of this data set? If your answer is not
an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are
their values? Indicate the number of modes by clicking in the
appropriate dircle, and then indicate the value(s) of the
mode(s), if applicable.
0
Zero modes
one mode:
Two modes:
Answer:
(a) To find the mean of the data set, sum up all the values and divide by the total number of values.
44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398
Mean = 398 / 8 = 49.75
Rounded to one decimal place, the mean of this data set is 49.8.
(b) To find the median of the data set, i need to arrange the values in ascending order first:
39, 44, 44, 44, 54, 54, 54, 65
The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:
(44 + 54) / 2 = 98 / 2 = 49
Rounded to one decimal place, the median of this data set is 49.0.
(c) To determine the modes of the data set, identify the values that appear most frequently.
In this case, the mode refers to the value(s) that occur(s) with the highest frequency.
From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.
Find the surface area of this triangular prism.
3 cm
5 cm
11 cm
4 cm
Step-by-step explanation:
The area of a triangular pyramid is 5 cm.
Five people bought raffle tickets,
They bought 8 tickets each. How
many raffle tickets did they buy in all?
Answer:
\(\pink{\rule{1pt}{900000pt}}\)
Answer:
40 tickets because, you multiply 8 and 5 so you get 40.
Step-by-step explanation:
Martin a une table ronde de 1 ,10m de diamètre il peut ajouter jusqu'à 5 rallonge de 40 cm chacune pour son repas d'anniversaire 10 personne seront présentes autour de cette table En comptant 60 cm par personne quel est le nombre minimal de rallonge qu'il doit installé
PLEASE HELP
Dennis read 30% of his book on Tuesday and 1/5
of his book on Wednesday. If he started the book on Tuesday, what fractional part of the book did he have left to read after Wednesday?
Answer:
50%(1/2) I geuss
Step-by-step explanation:
1/5=0.2=20%
20%+30%=50%
50%=1/2(or 2/4,or 3/6)
Mara is playing a game. There are two marbles in a bag. Ifshe chooses the purple marble, she will win $10. If she chooses the orange marble, she will win $200. What is the expected value of Mara's winnings from the game?
Answer:
Step-by-step explanation:
Mara has a 50% chance of getting the purple marble and 50% of getting an orange marble, since there's 2 marble; 1 purple and one orange; 1/2 = 50%
So she has a 50% chance of receiving $10 and a 50% chance of receiving the $200.
IMPORTANT GUYS please help
Answer:
x=3,y=7
Step-by-step explanation:
8x+3y=45
2x+3y=27
8x-2x=6x
45-27=18
6x=18
6. 6
x=3
2x+3y=27
2(3)+3y=27
6+3y=27
3y=27-6
3y = 21
3. 3
y=7
Which relationships describe angles 1 and 2?
Select each correct answer.
vertical angles
supplementary angles
adjacent angles
complementary angles
Answer:
choice 4
Step-by-step explanation:
complementary angles sum to 90
Two houses on the same side of the street have house numbers that are consecutive
even integers. The sum of the integers is 58. What are the two house numbers?
Answer:
28 and 30
Step-by-step explanation:
'x' = 1st consecutive #
'x+2' = 2nd consecutive #
x + x+2 = 58
2x + 2 = 58
2x = 56
x = 28
x+2 = 30
How many different possible outcomes are there if you spin 4 spinners labeled Red,
Blue, Yellow?
From the information given, there are 81 different possible outcomes if you spin 4 spinners labeled Red, Blue, Yellow.
A permutation is an arrangement of objects in a specific order, and spinning involves generating a random outcome from a set of possible outcomes.
When spinning the spinner, each outcome has an equal chance of occurring, so we can say that the set of possible outcomes is being randomly permuted.
Spinning can be thought of as a way to generate a random permutation of a set of possible outcomes.
Each spinner has three possible outcomes, so the total number of different possible outcomes for all four spinners is:
3 x 3 x 3 x 3 = 81
Learn more about permutations here: brainly.com/question/1216161
#SPJ4
What’s the difference between 126 1/4 and 78 7/12
The difference between 126 1/4 and 78 7/12 is 143/3 or 47 2/3.
The is the difference between the two mixed fraction?To find the difference between the numbers simplify means;
to subtract 78 7/12 from 126 1/4 .
126 1/4 - 78 7/12
First, convert the mixed fractions into improper fractions.
( 126 × 4 + 1 )/4 - ( 78 × 12 + 7) /12
505/4 - 943/12
Multiply first term by 3/3 which is the same as 1.
( 505/4 × 3/3 ) - 943/12
1515/12 - 943/12
( 1515 - 943) / 12
572 / 12
143/3 or 47 2/3.
Therefore, the difference is 143/3 or 47 2/3.
Learn more about common factors here:https://brainly.com/question/11221202
#SPJ1
Write an exponential equation with (1, 8) and (2,32)
Answer:
y=2(4^x)
Step-by-step explanation:
exponential equation in form y=ab^x
sub both point and solve
8=a(b^1)=ab...(1)
32=a(b^2)....(2)
equation (2)/(1):
32/8=b
b=4
a=2
Why is FOQZ the odd one out in
these sets of letters?
BCDEGPTV AJK FOQZ IY
The odd one out in the set is "FOQZ." It deviates from the pattern by the other sets, where the letters are arranged in Alphabetical order.
The set of letters "BCDEGPTV AJK FOQZ IY" seems to follow a specific pattern. If we examine the letters in each group, we can identify a difference that sets "FOQZ" apart from the others.
In the first group "BCDEGPTV," the letters are arranged in alphabetical order. Similarly, in the second group "AJK," the letters are also in alphabetical order. However, when we look at the third group "FOQZ," the letters do not follow alphabetical order.
Based on this pattern, we can conclude that the odd one out in the set is "FOQZ." It deviates from the pattern followed by the other sets, where the letters are arranged in alphabetical order.
It's worth noting that the pattern could be based on different criteria, such as the position of the letters in the alphabet or some other sequence. Without additional information or context, it is difficult to determine the exact pattern or reason for the deviation.
To know more about Alphabetical order.
https://brainly.com/question/27870403
#SPJ11
HELP PLSS I WILL GIVE BRAINLYEST
I SUCK AT MATH
Answer:
W=11
Step-by-step explanation:
Just trust me with this one :3
You work independently as a copier salesperson. Last month, you sold 26 printers at a cost of $1,750 each. The cost of goods sold for each printer is $975. Additional operating expenses include your salary ($3,000/month), advertising ($50/month), and office lease ($550/month). Use this information to calculate (a) your gross profit and (b) your net income.
To calculate the gross profit, we need to subtract the cost of goods sold (COGS) from the revenue generated by sales. The revenue generated by sales can be found by multiplying the number of printers sold by the selling price of each printer, which is $1,750.
Revenue generated by sales = 26 x $1,750 = $45,500
The cost of goods sold for each printer is $975, so the total cost of goods sold for all 26 printers is:
Total cost of goods sold = 26 x $975 = $25,350
Therefore, the gross profit can be calculated as:
Gross profit = Revenue generated by sales - Total cost of goods sold
Gross profit = $45,500 - $25,350
Gross profit = $20,150
The gross profit is $20,150.
To calculate the net income, we need to subtract all operating expenses from the gross profit. The operating expenses include your salary ($3,000/month), advertising ($50/month), and office lease ($550/month).
Total operating expenses = $3,000 + $50 + $550
Total operating expenses = $3,600
Therefore, the net income can be calculated as:
Net income = Gross profit - Total operating expenses
Net income = $20,150 - $3,600
Net income = $16,550
The net income is $16,550.
In summary, the gross profit is the revenue generated by sales minus the cost of goods sold, which in this case is $20,150. The net income is the gross profit minus all operating expenses, which in this case is $16,550.
To learn more about gross profit click:
https://brainly.com/question/942181
#SPJ1
I’m am so lost please help thank you all
Answer:
Step-by-step explanation:
148 people
0.0605 in standard form?
Step-by-step explanation:
Actually 0.0605 is already in standard form and it can be expressed in scientific notations as given below.
\( \huge0.0605 = 6.05 \times {10}^{ - 2} \\ \)
You have a bag of 10 marbles. Three of them are red, five are blue, and two are green. What is the probability of NOT picking a green marble out of the bag randomly?
Answer:
hey there
The answer is 7/10
this is true because we have two green marbles and five blue
2+5=7
Step-by-step explanation:
Answer:
20% or 2/10
Step-by-step explanation:
10 marbles in total. We want to find the probability of not picking a green marble. 10marbles-3red-5blue=2marbles left.
So the probability of picking a green marble is 2/10 or 20%
Peter baked 64 loaves of bread in three days. How many loaves did he bake each day, if he baked 3 more loaves on the second day than on the first day, and 4 more loaves on the third day than on the first day?
Answer:
19
Step-by-step explanation:
1st day: x
2nd day: x+3
3rd day: x+4
Equation: x+(x+3)+(x+4)=64
3x+7=64
3x=57
x=19
I hope you found this answer helpful!!!!!!(sorry if instructions aren't clear)
what does this even mean
if you were to graph the inequality would the circle be open or closed?
x > 45
Answer:
The "circle" you are referring to is only for inequality graphing.
A closed circle means that the "circle" is less than or greater than AND EQUAL TO wherever that point is on the graph.
A open circle means that the "circle" is less than or greater than wherever it is on the graph.
For your example,
X > 45 would be an open circle, because the alligator doesn't have an underline indicating it is also equal to 45.
The alligator indicates the direction and whether it also includes "equal to".
An example of a closed circle is this.
\(x \geq 45\); the line below the alligator indicates that it is also equal to 45.
Eric has 7 red shirts and 11 black shirts what is the ratio of red and black shirts.
Answer:
7:11
Step-by-step explanation:
Hope this helps! God bless.
a shape is rotated 180 about the origin and then its image is reflected in the y-axis
if sample of size 40 and sampl of size 10, sample mean from larger sample closer to to true popuation is?
Yes,The law of large number says that if you take sample of larger and larger size forming population than the mean of the sampling distribution u-x tend to get closer to true population.
What is the relationship between sample size and sample mean?As a sample size increases, the sample mean and standard deviation will be closer in value to the population mean μ and standard deviation σ.Very large samples tend to transform small differences into statistically significant differences.
How do you find the sample size for a sample mean?There are following steps for finding sample mean
Add up the sample items. Firstly we will need to count how many sample items you have within a data set and add up the total amount of items.
Divide sum by the number of samples.
The result is the mean.
Use the mean to find the variance.
Use the variance to find the standard deviation.
To learn more about sample mean visit;
https://brainly.com/question/30023845
#SPJ4
"I have a 40% chance of being selected as the captain of the volleyball team and a 75% chance of being elected student body president." What is the probability that Cara will be selected as the captain of the volleyball team and will be elected student body president?
Answer:
30% chance of them both happening
Answer:
thats going to be and exact 85%!
I used the probability calculater on cal.net
Find the range and standard deviation of the set of data.
11 8 5 11 25
Answer: The range is 20, Standard Deviation, σ: 6.8702256149271
Step-by-step explanation:
I hope it helped!
<3
Levi buys eggs and lemons at the store.
• He pays a total of $29.33.
• He pays a total of $5.39 for the eggs.
• He buys 6 bags of lemons that each cost the same amount.
How much does each bag of lemons cost?
Answer:
Each bag of lemons cost $3.99.
Step-by-step explanation:
29.33 - 5.39 = 23.94
23.94 / 6 = 3.99
PLEASE HELP MEEEEEEE! JUSTIFY
Answer:
Step-by-step explanation:
a.12÷36/7=7/3
12*7/36
84/36
7/3
b.let the number be x
x*1/2=x/2
x*1/2
x/2
A- True
12÷36/7 = 2.333...
7/3 = 2.333....
Hence it's true
B- True
Consider Any random number eg 10
multiplying it by 1/2 gives 5
and dividing by 2 also gives 5
hence it's true.
C- False
3/2 = 1.5
multiplying it to any number will produce half of the number more.
Evaluate the logarithmic expression without using a calculator. Answer exactly. log 2 ( 1/16 ) + 4 =
\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{we'll use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)+4\implies \log_2\left( \cfrac{1}{2^4} \right)+4\implies \log_2(2^{-4})+4\implies -4+4\implies \text{\LARGE 0}\)
\(\rule{34em}{0.25pt}\\\\ \textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_2\left( \cfrac{1}{16} \right)=y\implies 2^y=\cfrac{1}{16}\implies 2^y=2^{-4}\implies y=-4\)