Final answer:
To determine the first time Carly and Matt will have a soccer game on the same day, we find the least common multiple (LCM) of 4 and 5, which is 20. Thus, they will both have a game on the 20th day.
Explanation:
The question is asking when Carly, who has a soccer game every 4th day, and Matt, who has a soccer game every 5th day, will both have a game on the same day. This is a problem that can be solved using the concept of the least common multiple (LCM). The LCM of two numbers is the smallest number that is a multiple of both numbers. To find when Carly and Matt will have a soccer game on the same day, we need to find the LCM of 4 and 5.
List the multiples of 4 (4, 8, 12, 16, 20, ...) and 5 (5, 10, 15, 20, ...).
Identify the smallest multiple that is common to both lists, which would be 20.
Therefore, the first day Carly and Matt will have a game on the same day is the 20th day.
A mail truck traveled 82 miles in 412 hours. The distance is the product of the rate and the time. To the nearest tenth, what was the average speed of the mail truck?
Answer:
18.2
Step-by-step explanation:
in how many ways can 5 men and 5 woman sit alternately in a row of 10 seats?
the men can be arranges in 5! ways
and the women in 5! ways
so (5*4*3*2) = 120
120 *120 = 14,400 ways
Niko bought 4 stamps each week for 3 weeks. He wants to put 6 stamps on each page of his album how many pages will niko use
If Argyl earns $93.00 for 7.75 hours of work, how many must he work to earn $571.50?
Hans needs to memorize words on a vocabulary list for Latin class. He has memorized 20 of the words which is 1/4 of the list. How many words are in the list?
Exact product of 379 and 8
what is an expression for twice a number,increased by 5
If candies have a cost X cents less per dozen, it would have cost 3 cents less for x+3 candies then if they had cost x cents more per dozen. What is x?
The answer is obtained by setting up a mathematical equation corresponding to the details given in the word problem. It is found that if the candies were 36 cents cheaper or dearer per dozen, it would affect the price by 3 cents for 39 candies.
Explanation:The problem can be solved by translating the words into a mathematical equation. Let's denote the original price of a candy as Y cents. Therefore, a dozen candies would cost 12Y cents.
First, we acknowledge that if candies are X cents less per dozen, each candy will be X/12 cents cheaper. And if you buy x+3 such candies, you will pay (x+3)*X/12 cents less.
Simultaneously, the problem also mentions that x+3 candies would have cost 3 cents less if they had been X cents *more* per dozen. This implies that buying x+3 candies would cost an extra (x+3)*X/12 cents, yet it is still 3 cents less.
Therefore, these two costs should be equal: (x+3)*X/12 = (x+3)*X/12 +3. By solving this equation: X = 36. Therefore, if candies were 36 cents cheaper or dearer per dozen, it would affect the cost by 3 cents for x+3 or 39 candies.
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The equation d = can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an equivalent equation solved for V?
dm = V
= V
= V
m – d = V
The equivalent equation solving for volume is v = mass/density
Data;
Mass = mdensity = dvolume = volumeDensity of an ObjectThe density of an object can be calculated using the formula
[tex]density = \frac{mass}{volume}[/tex]
Making the volume the subject of formula here
[tex]density = \frac{mass}{volume}\\ volume = \frac{mass}{density}[/tex]
The equivalent equation solving for volume is v = mass/density
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which of the following describes a simple event ?
A. Tossing a coin 5 times and getting heads twice
B. spinning "back 2spaces" on a spinner
C. Spinning “back 2 spaces” on a spinner and drawing a blue or red marble from a box
D. Rolling an odd number on a die and getting tails on the toss of a coin
Option B, spinning "back 2 spaces" on a spinner, describes a simple event as it represents a single outcome from the experiment, in contrast to the other options which describe compound events.
A simple event is an event that consists of a single outcome of an experiment. When tossing a coin 5 times and getting heads twice, we're looking at a compound event because it involves a combination of outcomes. In the options given, option B, spinning "back 2 spaces" on a spinner represents a simple event because it describes a single outcome that can occur from the experiment. The other options involve multiple outcomes or combinations and are therefore not simple events.
Considering the additional information provided:
Coin tosses and the outcomes of 5 coin tosses just give us a set of possible results which help illustrate compound events. The idea of grouping real world observations into outcomes or events shows us that a simple event is a single, specific outcome, such as getting an even number when rolling a die, which can be defined as an event with a single characteristic and has a calculable probability.
the price of a technology stock was $9.53 yesterday. Today, the price rose to $9.66. Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer to this problem
54 3/11 as a decimal
Tony has $727.29 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $248.50 today. Write and solve an inequality to solve for the least amount of money he needs to deposit to avoid a fee.
The diagram shows a rhombus ABCD. The points B and D have coordinates (2, 10) and (6, 2) respectively, and A lies on the x-axis. The mid-point of BD is M. Find, by calculation, the coordinates of each of M, A and C.
The coordinates of the midpoint M, point A, and point C in the rhombus can be found using formulas. The coordinates of M are (4, 6), the coordinates of A are (0, 0), and the coordinates of C are (4, 2).
Explanation:To find the coordinates of the midpoint of BD, we can use the midpoint formula:
M = ( (x1+x2)/2, (y1+y2)/2 )
Substituting the coordinates of B and D into the formula, we get:
M = ( (2+6)/2, (10+2)/2 )
Simplifying, we get:
M = (4, 6)
Since A lies on the x-axis, its y-coordinate is 0. Therefore, the coordinates of A are:
A = (0, 0)
To find the coordinates of C, we can use the fact that a rhombus has opposite sides equal in length and parallel. Since B and D have the same y-coordinate, the y-coordinate of C will also be the same. The x-coordinate of C will be the average of the x-coordinates of B and D. Therefore, the coordinates of C are:
C = ( (2+6)/2, 2 )
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what's the property of 34+0+18+26
Write an even number between 7 and 16. Draw a picture and then write a sentence to explain why it's an odd number
Answer:
9, 11, 13 and 15
Step-by-step explanation:
Given numbers,
7 and 16,
In the number line the numbers are arranged in ascending order from left to right,
Thus, the numbers greater than 7 are,
8, 9, 10, 11, 12, 13, 14, 15, 16, 17....
Also, the number less than 16,
.......6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
So, the numbers between 7 and 16,
8, 9, 10, 11, 12, 13, 14, 15
Now, a number with 1, 3, 5 or 7 in the ones place is an odd number.
Hence, the odd number between 7 and 16 are,
9, 11, 13 and 15
help me
2y = x + 2
x – 3y = –5
Paulita reads an average of 20 pages each day. She has 6 days to read 100 pages. Will she finish her reading in 6 days? Explain
Decimals from 7.0 to 8.4, with an interval of 0.2 between each pair of decimals
what is 1.086 rounded to the nearest whole number
A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 469 tickets overall. It has sold 112 more $20 tickets than $10 tickets. The total sales are $8300 How many tickets of each kind have been sold?
Final answer:
The basketball team has sold 155 $10 tickets, 267 $20 tickets, and 47 $30 tickets. This was determined by setting up a system of linear equations based on the information given and solving for the variables representing the number of tickets of each kind.
Explanation:
The problem at hand is a classic example of a system of linear equations in the world of numerical problems. We need to find the number of $10, $20, and $30 tickets sold by the basketball team based on the given conditions. Let's denote the number of $10 tickets as x, the number of $20 tickets as y, and the number of $30 tickets as z.
The total number of tickets sold is 469: x + y + z = 469.The team has sold 112 more $20 tickets than $10 tickets: y = x + 112.The total sales amount to $8300: 10x + 20y + 30z = 8300.Substituting y from the second equation into the first and third equations, we get two new equations:
x + (x + 112) + z = 469, which simplifies to 2x + z = 357.10x + 20(x + 112) + 30z = 8300, which simplifies to 10x + 20x + 2240 + 30z = 8300, and further to 30x + 30z = 6060 by combining like terms and subtracting 2240 from both sides.Dividing the last equation by 30, we obtain x + z = 202. Now, we have a system of two equations with two variables:
2x + z = 357x + z = 202Subtracting the second equation from the first, we find x = 155. We can then substitute x into the second equation to find z = 202 - 155 = 47.
Finally, we substitute x into the second original equation to find y = 155 + 112 = 267.
Therefore, the team has sold 155 $10 tickets, 267 $20 tickets, and 47 $30 tickets.
-4(c)+5=-6-30????????????????
What is the sum of the geometric series in which a1 = 4, r = 3, and an = 324?
Hint: cap s sub n equals start fraction a sub one left parenthesis one minus r to the power of n end power right parenthesis over one minus r end fraction comma r ≠ 1, where a1 is the first term and r is the common ratio.
The sum of the geometric series is approximately 324.
Explanation:The sum of a geometric series can be found using the formula:
Sn = a1(1 - rn) / (1 - r)
Where Sn is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.
Plugging in the given values, we have:
Sn = 4(1 - 3n) / (1 - 3)
Now we can solve for n by plugging in the given value of an:
324 = 4(1 - 3n) / (1 - 3)
Cross-multiplying and simplifying:
324(1 - 3) = 4(1 - 3n)
324 - 972 = 4 - 12n
-648 = -8n
Dividing both sides by -8, we get:
81 = 2n
Taking the logarithm base 2 of both sides:
n = log2(81)
Using a calculator, we find that n is approximately 6.3398.
Now we can plug this value back into the formula:
Sn = 4(1 - 36.3398) / (1 - 3)
Simplifying further:
Sn ≈ -648 / -2
Sn ≈ 324
At a local school supply store, a highlighter costs $1.25, a ballpoint pen costs $0.80, and a spiral notebook costs $2.75. Explain how you can use the Commutative Property of Addition to find the total cost if three of each item are purchased!
The addition of all costs using commutative property will be $4.8.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Summation = addition of two or more numbers or variable
For example = 2 + 8 + 9
Subtraction = Minus of any two or more numbers with each other called subtraction.
For example = 4 - 8
Division = divide any two numbers or variable called division.
For example 4/8
Multiplication = to multiply any two or more numbers or variables called multiplication.
For example 5 × 7.
Given,
Cost of one highlighter = $1.25
Cost of one ballpoint pen = $0.80
Cost of one spiral notebook = $2.75
The cumulative property states that the resultant of summation or multiplication does change by changing order.
Addition = 1.25 + 0.80 + 2.75
Total cost = $4.8.
Hence"The addition of all costs using commutative property will be $4.8".
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will give BRAINEST
Use the elimination method to solve the system of equations. Choose the correct ordered pair.
20d + 13 - 12d = -14
20d +13 -12d = -14
combine like terms
20d-12d = 8d
8d+13 = -14
subtract 13 from each side:
8d =-27
divide both sides by 8
d = -27/8
Suppose a card is drawn from a deck of 52 playing cards. what is the probability of drawing a 4 or an ace?
A number and it's absolute value are equal. If you subtract 2 from the number, the new number and it's absolute value are not equal. What do you know about the number? What is a possible number that satisfies these conditions?
What fraction of £2 is 50p