There were 110 children and 237 adults whο swam at the public pοοl that day.
Let's assume that the number οf children whο used the swimming pοοl is x, and the number οf adults is y.
Accοrding tο the prοblem, the tοtal number οf peοple whο used the swimming pοοl is 347. Therefοre, we have:
x + y = 347 ....(1)
Alsο, the tοtal amοunt cοllected in admissiοn fees is $785.00. We knοw that the admissiοn fee fοr children is $1.75 and fοr adults is $2.50. Therefοre, we can write anοther equatiοn as:
1.75x + 2.5y = 785 ....(2)
We nοw have twο equatiοns with twο unknοwns. We can sοlve fοr x and y by using any suitable methοd. Here, we will use the substitutiοn methοd.
Frοm equatiοn (1), we can express y in terms οf x as:
y = 347 - x
We can substitute this expressiοn fοr y in equatiοn (2), and sοlve fοr x:
1.75x + 2.5(347 - x) = 785
1.75x + 867.5 - 2.5x = 785
-0.75x = -82.5
x = 110
Therefοre, the number οf children whο used the swimming pοοl is 110. We can use equatiοn (1) tο find the number οf adults:
110 + y = 347
y = 237
Therefοre, the number οf adults whο used the swimming pοοl is 237.
Therefοre, there were 110 children and 237 adults whο swam at the public pοοl that day.
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find the mode of the data set: 10, 18, 13, 22, 10, 13, 10, 19
Answer: The mode in this data set would be 10.
Step-by-step explanation: Mode is the most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.
Answer: The mode is 10.
Step-by-step explanation: To find the mode of a data set, you need to determine which number appears most frequently. In your case, the number 10 occurs three times, but all other numbers appear only once or twice. So, the mode is 10.
Help a girl out pleasee it’s math
The solution set for x + 10 ≥ 14 is x ≥ 4, and it can be represented as graph as a shaded region to the right of x = 4 on a number line.
The inequality [tex]x + 10 \geq 14[/tex] can be solved algebraically as follows:
[tex]x + 10 \geq 14[/tex]
Subtracting 10 from both sides, we get:
[tex]x \geq 4[/tex]
This means that any value of x that is greater than or equal to 4 will satisfy the inequality. To graph the solution, we can draw a number line and shade in all the values of x that satisfy the inequality. Since x is greater than or equal to 4, we can represent the solution set as follows:
────●────●────●────●────●───> x
0 1 2 3 4
The dot at x = 4 indicates that 4 is included in the solution set (since the inequality is "greater than or equal to"), and the shaded region to the right of the dot represents all values of x that are greater than 4 and satisfy the inequality.
Therefore, the solution set for [tex]x + 10 > = 14[/tex] is[tex]x \geq 4[/tex], and it can be represented as graph as a shaded region to the right of x = 4 on a number line.
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please help , its making me mad
Answer: 282.6 [tex]cm^{2}[/tex]
Step-by-step explanation:
as the TSA of Cylinder is [tex]2\pi r[r+h][/tex] so here r = 3cm & h = 12cm so by putting values in the above formula we get the answer
Enter the resulting inequality.
10 > −1; Subtract 10 from both sides.
whats the resulting inequality ?
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru is able to estimate their wait time more consistently and why?
Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
The drive-thru that is able to estimate their wait time more consistently and why is: A. Burger Quick, because it has a smaller IQR.
Which drive-thru is able to estimate their wait time more consistently and why?The IQR is a measure of the spread of the middle 50% of the data, and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). A smaller IQR indicates that the data is less spread out around the median, and therefore more consistent.
In this case, the IQR for Super Fast Food is 15.5 - 12 = 3.5, while the IQR for Burger Quick is 24 - 15.5 = 8.5. Therefore, Burger Quick has a larger range (24 - 2 = 22) than Super Fast Food (27 - 3 = 24), but a smaller IQR, indicating that their wait time estimates are more consistent.
Therefore Quick is able to estimate their wait time more consistently because it has a smaller interquartile range (IQR).
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in the game of roulette, a steel ball is rolled onto a wheel that contains 18 red, 18 black, and 2 green slots. If the ball is rolled 23 times, find the probability of the following events.
A. The ball falls into the green slots 2 or more times.
Probability =
B. The ball does not fall into any green slots.
Probability = .288359853
C. The ball falls into black slots 14 or more times.
Probability =
D. The ball falls into red slots 12 or fewer times.
Probability
The probability of the ball falling into red slots 12 or fewer times in 23 rolls is approximately 0.3486.
A. Using the binomial probability formula, we can determine the likelihood that the ball will land in the green slots two or more times out of 23 rolls:
[tex]P(X > = 2) = 0 - 1 - P(X = 0)[/tex]
where P(X): likelihood that X will occur and X is the number of times the ball has fallen into the green slots.
The chances of the ball landing in a green slot on one roll are 2/38, whereas the chances of it not landing there are 36/38. This allows us to compute:
[tex]P(X = 0) = (36/38)^(23) = 0.288359853[/tex]
[tex]P(X = 1) = 23 * (2/38) * (36/38)^(22) = 0.357973143[/tex]
With the binomial probability formula substituted, we obtain:
[tex]P(X > = 2) = 1 - 0.288359853 - 0.357973143 = 0.353666004[/tex]
As a result, there is a roughly 0.3537 percent chance that the ball will land in the green slots two or more times during the course of 23 rolls.
B. The likelihood that the ball will not land in any green slots after 23 rolls is:
[tex]P(not green) = (36/38)23, or 0.288359853[/tex]
Hence, there is a roughly 0.2884 percent chance that the ball won't land in any green slots after 23 rolls.
B. Using the binomial probability formula, we can determine the likelihood that the ball will land in the black slots 14 or more times:
[tex]P(X > = 14) = 1 - P(X < = 13)[/tex]
where P(X): likelihood that X will occur and X is the number of times the ball has fallen into the black slots.
The odds of the ball not falling into a black slot in one roll are 20/38, while the odds of the ball going into a black slot are 18/38. This allows us to compute:
[tex]P(X = 13) = sum of (23 pick I (18/38)*i* (20/38)*(23-i) from i=0 to 13 = 0.829288657[/tex]
With the binomial probability formula substituted, we will get:
[tex]P(X > = 14) = 1 - 0.829288657 = 0.170711343[/tex]
The likelihood of the ball landing in the black slots 14 or more times during the course of 23 rolls is therefore roughly 0.1707.
D. Using the binomial probability formula once more, we can determine the likelihood of the ball landing in the red slots 12 or fewer times:
[tex]P(X = 12) = sum of (23 pick I from i=0 to 12 * (18/38) * I * (20/38) * (23-i) = 0.348609995[/tex]
The likelihood that the ball will land in a red slot 12 or fewer times in 23 rolls is therefore roughly 0.3486.
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An investor puts $4,500 into a life insurance policy that pays 6.5% simple annual interest. If no additional investment is made into the policy, how much accumulated interest should the investor expect at the end of 6 years?
The accumulated interest the investor should expect at the end of 6 years is $1,755.00.
19 The weight, y, of a carton of books
containing x books can be modeled using
a linear function. The packaging carton
weighs 14 ounces. Each book weighs
8 ounces. The carton can hold from 0 to
6 books.
What is the domain of the function for
this situation?
A {8, 16, 24, 32, 40, 48}
B (14, 22, 30, 38, 46, 54, 62}
C
{0, 1, 2, 3, 4, 5, 6}
D
{0, 14, 28, 42, 56, 70, 84}
Find the area of the trapezoid by decomposing it into other shapes.
The area of the trapezoid by decomposing it into other shapes is 55 sq. cm.
What is a trapezoid?A quadrilateral with at least one set of parallel sides is known as a trapezium. The trapezoid's other two sides are referred to as its legs, and its parallel sides are known as its bases. The distance between the bases of a trapezium measured perpendicularly is its height. By multiplying the average of the bases (the total of the bases divided by 2) by the height, one may get the area of a trapezium. A = (b1 + b2)h/2, where b1 and b2 are the lengths of the bases and h is the height, is the formula for a trapezoid's surface area.
The trapezoid can be divided into one right angles triangle and a trapezium.
The area of the triangle is given as:
A1 = 1/2 bh
A1 = 1/2(5)(4)
A1 = 10 sq. cm.
Now, the area of trapezium is given as:
A2 = 1/2 h (a + b)
Here, a = 12, b = 15 - 5 = 10, and h = 4.
A2 = 1/2 (4) (12 + 10)
A2 = 2(22) = 44 sq. cm
The total area of the trapezoid is:
A = A1 + A2
A = 10 + 44
A = 55 sq. cm.
Hence, the area of the trapezoid by decomposing it into other shapes is 55 sq. cm.
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brandon rolls a six sided die twenty times, and records the result in the table below. how many times did brandon roll above the average?
The expected value for each roll is [tex](1+2+3+4+5+6)/6 = 3.5.[/tex]
The average of Brandon's rolls, we simply add up all the results and divide by the number of rolls:
[tex](1+2+2+3+4+6+2+1+5+6+1+6+2+6+4+6+2+6+4+6)/20 = 3.6[/tex]
So the average of Brandon's rolls is 3.6.
Now we need to count how many times he rolled above the average. To do this, we simply count how many rolls were greater than 3.6:
4, 6, 5, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 6
There were 18 rolls that were greater than 3.6, so Brandon rolled above the average 18 times.
In summary, Brandon rolled a six-sided die 20 times and recorded the results in a table. To find out how many times he rolled above the average, we first calculated the average roll to be 3.6. We then counted how many times he rolled above this value and found that he did so 18 times.
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Choose the correct measurement of the paper clip to the nearest 1/8 inch
1 1/2 inch
7/8 inch
1 2/8 inch
1 4/8 inch
1 3/8 inch
Choose the correct measurement of the paper clip to the nearest 1/8 inch
1 1/2 inch
7/8 inch
1 2/8 inch
1 4/8 inch
1 3/8 inch
Identify the shapes that make up the figure at the left. Then find the perimeter and area of the figure to the nearest hundredth
The required Perimeter and area of the shape is 27.42 units and 64.26 sq units.
What is Perimeter of the shape?The circumference of a shape is its perimeter. How is a perimeter calculated? The border can be found by including the lengths of each side of a shape.
According to question:We have given a shape which made up of two circle and rectangle
diameter of circle = 12 - 6 = 6
then radius = 3 units
Perimeter = 3+3+3+3+3+3+π(3)
= 18 + 3.14(3)
= 18 + 9.42
= 27.42 units
and
Area = area of rectangle + area of two half circles
= 12(3) + π(3)²
= 36 + 28.26
= 64.26 sq units.
Thus, required Perimeter and area of the shape is 27.42 units and 64.26 sq units.
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help asap assignment closes soon!
The volume of the cone is approximately 12π cubic feet
What is the volume of a cone?
[tex]V = \frac{1}{3} \pi {r}^{2}h[/tex] where r is the radius of the base and h is the height of the cone.
In this case, the base of the cone is a square with a side length of b = 4 ft. The radius of the base is half the length of a side of the square, so:
[tex]r = \frac{b}{2} = \frac{4}{2} = 2 \: ft[/tex]
The height of the cone is h = 9 ft.
Now we can substitute these values into the formula for the volume of a cone:
[tex]V = \frac{1}{3} \times \pi {r}^{2} h \\V = \frac{1}{3} \pi {2}^{2} \times 9 \\ V = \frac{1}{3}\pi \times 4 \times 9 \\ V = \frac{1}{3} \times \pi \times 36 \\ V = 12\pi[/tex]
So the volume of the cone is approximately 12π cubic feet.
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which of the following lists of data has the smallest standard deviation? select the correct answer below: 6, 19, 9, 18, 19, 9, 17, 18, 17, 15 31, 30, 26, 28, 18, 28, 18, 21, 23, 32 20, 21, 20, 19, 25, 24, 19, 14, 21, 15 14, 20, 16, 14, 28, 13, 17, 21, 12, 22 16, 12, 13, 16, 14, 15, 16, 14, 14, 13
The list with the smallest standard deviation is the following: 16, 12, 13, 16, 14, 15, 16, 14, 14, 13.
What is standard deviation?
Standard deviation is a statistical measure of the variability of a set of data values. It's a step-by-step process for determining how far each value is from the mean. It is important since it may reveal the amount of variability in a set of data. The formula for calculating standard deviation is as follows:
σ=√∑(x−μ)²nσ=√∑(x−μ)²n
In this equation, x represents the values in the data set, μ represents the mean of the data set, and n represents the number of values in the data set. Let us now compute the standard deviation of each of the given data sets, starting with the first one. We can utilize the formula given above to do so:
6, 19, 9, 18, 19, 9, 17, 18, 17, 15 μ = 15.8,σ = 4.83 (rounded to two decimal places)
31, 30, 26, 28, 18, 28, 18, 21, 23, 32 μ = 25.5,σ = 5.93 (rounded to two decimal places)
20, 21, 20, 19, 25, 24, 19, 14, 21, 15 μ = 19.8,σ = 3.98 (rounded to two decimal places)
14, 20, 16, 14, 28, 13, 17, 21, 12, 22 μ = 17.7,σ = 4.96 (rounded to two decimal places)
16, 12, 13, 16, 14, 15, 16, 14, 14, 13 μ = 14.3,σ = 1.96 (rounded to two decimal places)
The list with the smallest standard deviation is the following: 16, 12, 13, 16, 14, 15, 16, 14, 14, 13.
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how many 6-digit numbers (using 1,2,3 , ... ,9) are there if repetition is not allowed? how many are there which have at least one digit repeated?
Total 6-digit numbers that can be made from 1 to 9 will be 60480 and without repetition will be 84. The numbers that have at least one digit repeated will be 60396.
There are 9 digits from 1 to 9. If the digits are not repeated, the combination is called simple combination and is calculated using the formula
C(n, r) = n!/ r!(n-r)!
Here n= 9 and r = 6
C(9, 6) = 9!/6!(9-6)! = 9!/ (6! × 3!) = 84
So without repeating the digits there are 84 six digit numbers using 1 to 9.
Total numbers that can be made with or without repetition of digits is calculated by using permutations. The formula is
P( n, r) = n!/(n-r)!
= 9!/(9-6)! = 60480
So total number without repetition = 84
Number with or without repetition = 60480
So the total numbers that have at least one digit repeated will be = 60480 - 84 = 60396
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Cynthia has earned $1,000 and wants to put it in a savings account that earns 5% simple interest. Assuming she makes no additional deposits or withdrawals, which represents the total value of Cynthia’s account after 48 months?
Answer:
1,200
Step-by-step explanation:
The formula for Simple Interest is I=prt p=principal r=rate expressed as decimal t=time in years
I=1,000*0.05*4
0.05 because 5% in decimal form it’s 0.05
4 because 48months dived by 12= 4 years
200=1,000*0.05*4 The interest is 200 but they are asking for the total value so then you add the amount you initiated with 1,000+200=1,200
Which of the following is not a solution to sin x − cos 2x = 0 on the interval [0, 2π)? A. pi over 6
B. pi over 2
C. 5 times pi over 6
C. 3 times pi over 2
None of the given options (A, B, C, or D) is a solution to sin x − cos 2x = 0 on the interval [0, 2π).
What is solution of a trigonometric equation ?The solution of any trigonometric equation represents the value of the parameter which satisfies the given equation. The solution should lie within a given range and it should have the same value as ±π .
To find the solutions to sin x − cos 2x = 0 on the interval [0, 2π), we can start by using the identity cos 2x = 1 - 2sin² x, which gives:
sin x - (1 - 2sin² x) = 0
Simplifying this equation, we get:
2sin² x - sin x + 1 = 0
We can solve this quadratic equation using the quadratic formula:
sin x = [1 ± √(1 - 8)] / 4
sin x = [1 ± √(-7)] / 4
Since the square root of a negative number is not a real number, this equation has no real solutions. Therefore, none of the given options (A, B, C, or D) is a solution to sin x − cos 2x = 0 on the interval [0, 2π).
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Pls help 1/6 (x + 18) = -5.
Answer:
x= -48
Step-by-step explanation:
go step by step with this problem.
The missing angle m∠U of the quadrilateral is calculated as: 117°
How to find the angle of a quadrilateral?From the given quadrilateral, we see that the angle m∠R is given as 117°.
We also see that the sides TU and RS are congruent to each other. No, we know that the sum of angles of a quadrilateral is 360 degrees.
However, we see that since TU and RS are congruent, this can be likened to an isosceles trapezium and as such the angle m∠U must be equal to the angle m∠R.
Thus:
m∠R = m∠U = 117°
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The data in this graph represent how long it took a child to complete a puzzle based on its number of pieces.
How many pieces were in the puzzle that took the child 30 seconds to complete?
Enter your answer in the box.
pieces
Coordinate plane titled Puzzle Completions with five points. The x-axis extends from 0 to 13 by ones and is labeled Number of pieces. The y-axis extends from 0 to 50 by fives and is labeled Time (seconds). Points are above the 4 on the x-axis and to the right of the 15 on the y-axis, above the 5 on the x-axis and to the right of the 15 on the y-axis, above the 7 on the x-axis and to the right of the 30 on the y-axis, above the 8 on the x-axis and to the right of the 25 on the y-axis, and above the 12 on the x-axis and to the right of the 40 on the y-axis.
There were 7 number of pieces that were in the puzzle that took the child 30 seconds to complete,that can be found using the data given & the coordinates on the graph (7,30) which indicates the number of pieces as 7 and time as 30 sec.
What is data?
Data is the collected information that can be arranged and used for analysing or interpretation. The collected data is also called as raw data, which further needs to be arranged. The data can be represented visually, in tabular form , grouped or ungrouped form. Pictographs, bargraphs, box-whisker plot, line plot, histogram, pie chart are the visual representations.
Here given that the data is arranged in the form of graph containing x-axis & y-axis. Data collected/arranged represents the number of pieces contained in the puzzle & the time taken to solve it.
X-axis represents the number of pieces in the puzzle & Y-axis represents the time taken to complete that.
The points plotted on graph are:
(4,15): Number of pieces=4
Time taken to complete=15 seconds
(5,15):Number of pieces=5
Time taken to complete=15 seconds
(7,30): Number of pieces=7
Time taken to complete=30 seconds
(8,25): Number of pieces=8
Time taken to complete=25 seconds
(12,40): Number of pieces=12
Time taken to complete=40 seconds
∴The puzzle that was completed by child in 30 seconds contained 7 pieces.
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PLEASE HELP ME WITH QUESTION 15 PLEASEEE IT DUES TODAY, SOON!!!
Answer:
[tex]14. \: \: \: m {}^{4} - 16 \\ = (m {}^{2} -4)(m {}^{2} + 4) \\ = (m - 2)(m + 2)(m {}^{2} + 4) \\15. \: \: \: x {}^{2} + 4xy + 4y {}^{2} - 4z {}^{2} \\ (x + 2y) {}^{2} - 4z {}^{2} \\ (x + 2y - 2z)(x + 2y + 2z) \\ 16. \: \: m {}^{4} + m {}^{2} - 12 \\ (m {}^{4} + 4m {}^{2} )( - 3m {}^{2} - 12) \\ m {}^{2} (m {}^{2} + 4) - 3(m {}^{2} + 4) \\ (m {}^{2} + 4)(m {}^{2} - 3) \\ [/tex]
A convex polygon looks like it collapsed or has indentations.
True
False
Answer:
False
Step-by-step explanation:
Because it is convex, that is, it has bulges
Solven16. Which of the following must be true about the inequality and the resulting graph? Select three
options.
Ons-24
Onz-24
OThe circle is open.
OThe circle is closed.
OThe arrow points right.
The true statements about the inequality are
n > -24.
The circle is open.
The arrow points right.
How to solve the inequalityTo solve for n in the inequality -2/3n < 16, we need to isolate the variable n on one side of the inequality.
First, we can multiply both sides by -3/2 to get rid of the fraction:
(-3/2) * (-2/3n) > (-3/2) * 16
n > -24
Therefore, the solution for n in the inequality -2/3n < 16 is n > -24.
The circle is open means that the inequality sign is either less than or greater than
Having greater that means it points to the right
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Grace always brings her own shopping bags to buy fruits. a bag with 68 guavas in it has a mass of 7.55 kg. the same bag with 62 guavas in it has a mass of 6.95 kg. find the mass of the bag when it is empty in grams.
To solve the problem, we can use the following steps:
Determine the difference in mass between the two bags with different numbers of guavas:
Mass of bag with 68 guavas = 7.55 kg Mass of bag with 62 guavas = 6.95 kg Difference in mass = 7.55 kg - 6.95 kg = 0.6 kg
Determine the mass of the 6 extra guavas:
Mass of 6 guavas = ? We can assume that the mass of each guava is roughly the same, so the mass of 6 guavas is proportional to the difference in mass between the two bags:
Difference in mass = 0.6 kg Mass of 6 guavas / 6 = 0.6 kg / 6 Mass of 6 guavas = 0.1 kg
Subtract the mass of the 6 extra guavas from the mass difference to get the mass of the bag:
Mass of bag with no guavas = ? Mass of bag with 68 guavas - mass of bag with 62 guavas = Mass of 6 extra guavas + Mass of bag with no guavas 0.6 kg - 0.1 kg = Mass of bag with no guavas Mass of bag with no guavas = 0.5 kg
Convert the mass of the bag from kilograms to grams:
Mass of bag with no guavas = 0.5 kg = 500 g
Therefore, the mass of the bag when it is empty is 500 grams.
What is the Standard Form after distribution of (x+3) (x-3)
Answer (Please mark as brainliest):
x^2 - 9
Step-by-step explanation:
To distribute (x+3) (x-3), we use the FOIL method:
(x+3)(x-3) = x(x) + x(-3) + 3(x) + 3(-3)
= x^2 - 3x + 3x - 9
= x^2 - 9
The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a is not equal to 0.
In this case, the equation is already in standard form since there is only one term with x^2 and no x or constant terms:
x^2 - 9
Choose the expression that would best fit the situation below:
Andy walked down five flights of stairs, and then he walked back up three floors.
The expression that would best fit the situation is: "Andy descended five flights of stairs, and then ascended three floors."
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
Andy walked down five flights of stairs, and then he walked back up three floors.
The expression that would best fit the situation would be:
Andy descended five flights of stairs, and then ascended three floors.
Therefore, the expression that would best fit the situation is: "Andy descended five flights of stairs, and then ascended three floors."
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Which operation should be completed first to find the value of the expression below
The order of operations that should be completed first to find the value of given expression 12+30÷(6-3)+1 is (6-3) which is option-B
What is the correct order of operations?
To solve any given expression the rule applied is PEMDAS or the BODMAS . PEMDAS acronym for-
P indicates the parentheses that are the brackets to be solved first in an expression.
E which indicates exponents or powers to be solved.
M refers to Multiplication
D refers to divide
A refers to add
S indicates subraction
BODMAS is similar to PEMDAS whose sequence of solving stands for
B- brackets
O-Order/Of
D-Divide
M-Multiply
A-Add
S-Subtract
Here in the given expression: 12+30÷(6-3)+1 , the order would be
=12+30÷(6-3)+1
=12 + 30 ÷ (3) + 1 { brackets/parentheses}
= 12 + 30 ÷ 3 + 1
=12 + 10 + 1 {divide}
=23
∴ the first operation was to solve brackets/parentheses (6-3)
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In the expression 5xy7, what value of y would make a product greater than 5
According to the given information, any value of y greater than 1/35 would make the product 5xy7 greater than 5 when x = 1.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
The expression 5xy7 can be interpreted as 5 times x times y times 7. To make the product greater than 5, we need to find a value of y such that:
5xy7 > 5
Dividing both sides by 5 and 7, we get:
xy > 1/7
So, we need to find a value of y such that the product xy is greater than 1/7. The value of x is not given, so we can assume that it is a positive number.
For example, if we choose x = 1, then we need to find a value of y such that:
y > 1/35
Therefore, any value of y greater than 1/35 would make the product 5xy7 greater than 5 when x = 1.
If we choose a different value of x, we would get a different inequality, but the general idea is the same: we need to find a value of y such that the product xy is greater than a certain value (in this case, 1/7 divided by 5 times 7).
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every day, kymere takes the same street from his home to the university. there are multiple traffic lights with patterns along the way. if there is a green light while passing through an intersection, then 60% of the time the next light is also green and 25% of the time the next light is red. if the light is yellow, then there is a probability of 1 that the next light is red. if there is a red light, then 30% of the time the next light is green and 50% of the time the next light is red. (a) does this situation represent a markov chain? explain. (b) set up the transition probability matrix and diagram. (c) determine the number of classes and classify them. (d) the first light is green. compute and interpret all probabilities after three more lights. (e) if kymere has many street lights between home and the university, what proportion of these lights are green, yellow, and red? [no technology estimations permitted. solve this problem with a system of equations showing every step and fraction answers only.]
a) Yes. (b) G Y R
G [0.60 0.00 0.40]
Y [1.00 0.00 0.00]
R [0.30 0.20 0.50]
(c) P(G, G, G, G) = 0.216. P(G, G, G, Y)= 0.144. P(G, G, G, R) = 0.120. P(G, G, Y, R) = 0.000. P(G, Y, R, R) = 0.000. P(Y, R, R, R) = 0.000
(a) Yes, this situation represents a Markov chain because the probabilities of moving to the next state (traffic light) depend only on the current state (traffic light) and not on any previous states.
(b) The transition probability matrix is:
G Y R
G [0.60 0.00 0.40]
Y [1.00 0.00 0.00]
R [0.30 0.20 0.50]
where G represents green, Y represents yellow, and R represents red. The transition diagram can be drawn with arrows between states labeled with the transition probabilities.
(c) There are two classes: {G, Y} and {R}, where {G, Y} is a transient class and {R} is an absorbing class.
(d) Starting with the first light being green, the probabilities after three more lights are:
P(G, G, G, G) = 0.60 * 0.60 * 0.60 = 0.216
P(G, G, G, Y) = 0.60 * 0.60 * 0.40 = 0.144
P(G, G, G, R) = 0.60 * 0.40 * 0.50 = 0.120
P(G, G, Y, R) = 0.60 * 0.00 * 0.50 = 0.000
P(G, Y, R, R) = 0.00 * 0.50 * 0.30 = 0.000
P(Y, R, R, R) = 0.00 * 0.50 * 0.50 = 0.000
The interpretation of these probabilities is, for example, that the probability of passing through four consecutive green lights is 0.216, and the probability of passing through three consecutive green lights followed by a yellow light is 0.144.
(e) Let p_G, p_Y, and p_R be the proportions of green, yellow, and red lights, respectively. Then we have the system of equations:
0.60 p_G + 0.00 p_Y + 0.40 p_R = p_G
1.00 p_Y + 0.00 p_Y + 0.00 p_R = p_Y
0.30 p_G + 0.20 p_Y + 0.50 p_R = p_R
p_G + p_Y + p_R = 1
Solving this system of equations, we get:
p_G = 0.44
p_Y = 0.14
p_R = 0.42
Therefore, approximately 44% of the street lights are green, 14% are yellow, and 42% are red.
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a snack hut is selling fruit smoothies at the beach. the cost of a smoothie is 3 dollars and an additional 1.50 for each fruit you add. your friend writes the equation y=3+1.5x and says the slope of the line that represents this relationship is 3.
The y-intercept (b) represents the starting cost of the smoothie (when no fruits are added), which is $3 in this case.
What is Algebraic expression?An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.
The equation y = 3 + 1.5x represents the relationship between the total cost of a fruit smoothie (y) and the number of fruits added to it (x).
The slope of this line is not 3, as your friend suggests. The slope of the line is actually 1.5, which represents the cost per fruit added.
To see this, we can rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:
y = 1.5x + 3
In this form, we can clearly see that the slope (m) is 1.5, not 3. The slope represents the rate of change of the y variable (cost) with respect to the x variable (number of fruits added), which is $1.50 per fruit.
Therefore, The y-intercept represents the starting cost of the smoothie (when no fruits are added), which is $3 in this case.
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Complete question:
A snack hut is selling fruit smoothies at the beach. the cost of a smoothie is 3 dollars and an additional 1.50 for each fruit you add. your friend writes the equation y=3+1.5x and says the slope of the line that represents this relationship is 3. What does the y-intercept represent here.