Answer with explanation:
Number of oak trees =54
Number of pine trees =27
→Abe would like to plant the trees in rows that all have the same number of trees and are made up of only one type of tree.
We, will take H CF that is highest common factor of 54 and 27.
54 = 2×3×3×3
27=3×3×3
→H CF(54,27)=3 × 3×3=27
So, greatest number of trees Abe can have in each row =27,and there will be maximum of 3 rows, 2 containing oak tree because [tex]\frac{54}{27}=2[/tex], and one containing pine tree because[tex] \frac{27}{27}=1[/tex].
The greatest number of trees in each row is 27.
What are factors?
The factors of a number are numbers that divide the original number into equal numbers. They are numbers that when they are used to divide another number, the result is an integer.
What is the greatest number of trees that can be in each row?
In order to determine the required value, we have to determine the common factors of 27 and 54.
Factors of 27 = 1, 3, 9 and 27Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54.Common factors = 1, 3, 9, 27To learn more about factors, please check: https://brainly.com/question/26073850
At a wedding reception, the bride and groom and five attendants will form a receiving line. How many ways can they be arranged in each of following cases? a) Any order will do. b) The bride and groom must be the last two in line. c) The groom must be last in line with the bride next to him.
A. In this case, they can be arranged at any order. Since there are 7 people all in all, therefore the number of arrangements is:
number of arrangements = 7P7 = 5040 ways
B. In this case, only the 5 people can be arranged in any order therefore 5P5. However the groom and bride can be interchanged on 2 places, therefore:
number of arrangements = 5P5 * 2 = 240 ways
C. In this case, only the 5 people can be arranged in any order while the groom and bride can no longer be interchanged, therefore:
number of arrangements = 5P5 = 120 ways
Final answer:
The arrangements for the wedding reception receiving line can be calculated using permutations: a) Any order will do, giving 7!, b) The bride and groom must be the last two in line, giving 5!, c) The groom must be last in line with the bride next to him, giving 6! x 2.
Explanation:
The question asks about the number of ways a bride and groom along with five attendants can be arranged in a receiving line at a wedding reception under different conditions. This is a permutations problem where we calculate the arrangements using factorial notation.
Case a: Any order will do.
In this case, we have a total of 7 people (bride, groom, and five attendants) who can be arranged in any order. The number of arrangements is the factorial of 7, which is calculated as 7! (7 factorial). So, the number of ways they can be arranged is 7! (which is 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040 ways).
Case b: The bride and groom must be the last two in line.
Since the bride and groom's positions are fixed at the end of the line, we only need to arrange the five attendants. This is equivalent to 5! arrangements for the attendants. Thus, the number of ways they can be arranged is 5! (which is 5 x 4 x 3 x 2 x 1 = 120 ways).
Case c: The groom must be last in line with the bride next to him.
Here, the bride and groom are fixed in the last two positions, but the bride must be next to the groom. We consider the bride and groom as a single unit in addition to the five attendants. This gives us 6! arrangements for the attendants and the bride-groom unit, multiplied by 2 because the bride and groom can switch places within their unit. So, the number of ways they can be arranged is 6! x 2 (which is 6 x 5 x 4 x 3 x 2 x 1 x 2 = 1,440 ways).
(2.03)
Below are the steps to solve an equation:
Step 1: |x − 2| + 3 = 7
Step 2: |x − 2| = 7 − 3
Step 3: |x − 2| = 4
Which of the following is a correct next step to solve the equation? (1 point)
Connor drives an an eighteen-wheeler. It cost Conner $456 to fill the truck up with diesel fuel. If diesel fuel cost $3 a gallon, how many gallons of fuel were bought?
What is 45122 to the nearest ten thousand
A coffeepot contains 1 1/2 quqarts of coffee. After Tonya pours an equal amount of coffee into two cups, 3 1/2 cups of coffee still remain in the pot. How much coffee did Tonya pour into each cup?
what is 8x-27-10-6x=15
A student measured the lead content of a paint sample 4 times. the standard deviation of the measurements was found to be 1.1% of the average. can this student be 90% confident that the true value is within 1.8% of the measured average?
Figure ABCD is a parallelogram. What is the value of n?
3
5
17
25
Answer: the answer to this question is
choice c. 17
how do i solve 2 1/7 ÷ 1 1/4
At a recent boat show, Boater's Paradis sold five more boats than Pelican Marine sold. If together they sold 33 boats, how many were sold by each company?
In this mathematics problem about boat sales, Pelican Marine sold 14 boats and Boater's Paradis sold 19 boats. This conclusion was achieved by forming and solving a simple algebraic equation based on the provided problem information.
Explanation:To solve this problem, let's visualize it first. Pelican Marine sold a certain number of boats, and Boater's Paradis sold 5 more than that. If we call the number of boats sold by Pelican Marine as x, and adding Boater's Paradis' sales (x + 5), together they sold 33 boats. So we form the equation as x + (x+5) = 33.
Solving that equation, we will get 2x + 5 = 33, then simplify it to 2x = 28 after subtracting 5 from both sides. Finally, we divide both sides by 2 we get x = 14.
So, Pelican Marine sold 14 boats and Boater's Paradis sold 19 boats (14 boats Pelican Marine sold plus an additional 5 Boater's Paradis sold).
Learn more about Math Problem Solving here:https://brainly.com/question/11526758
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7times blank equals 56
Round 992,449 to the nearest hundred thousand
867,000 rounded to the nearest hundred thousand
For questions #6-8, use this data set and show your work 5, 10, 12, 4, 6, 11, 13, 5
Calculate the mean.
Type answer here
Calculate the median.
Type answer here
Calculate the mode.
Susan and Mark are standing at different places on a beach and watching a bird. The angles of elevation they make are 20º and 50º, respectively. If Susan and Mark are 7 kilometers apart and the bird is between them, the bird is at a height of kilometers from the ground. NextReset
Answer:
The bird is at a height of 1.95 km from the ground.
Step-by-step explanation:
It is given that the distance between susan and mark is 7 km and bird is between susan and mark. The angles of elevation they make are 20º and 50º, respectively.
Draw a perpendicular line from the bird on base.
Let the distance of susan from and the altitude be x.
In triangle ABS,
[tex]tan(20^{\circ})=\frac{AB}{x}[/tex]
[tex]tan(20^{\circ})x=AB[/tex]
[tex]0.364x=AB[/tex] ..... (1)
In triangle ABM,
[tex]tan(50^{\circ})=\frac{AB}{7-x}[/tex]
[tex]1.192(7-x)=AB[/tex] ..... (2)
From (1) and (2), we get
[tex]0.364x=1.192(7-x)[/tex]
[tex]1.556x=8342[/tex]
[tex]x=5.36[/tex]
The length of AB is,
[tex]AB=0.364(5.36)=1.95147\approx 1.95[/tex]
Therefore, the he bird is at a height of 1.95 km from the ground.
290 in expanded notation
This is the answer. 200 + 90 + 0
The place value chart can help us to write a number in expanded notation. When we put 290 into the place value chart, we can recognize that our number is equal to
2 hundreds + 9 tens + 0 units
Image is provided.
The table shows the cost of a ski rental package for a given number of people. People Cost ($) 4 160 5 200 6 240 7 280 The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. A. 1/40 dollars per room; the cost is $40 for each person. B. 40/1 dollars per person; the cost is $40 for each person. C. 1/280 dollars per person; the cost is $1 for 280 people. D. 160/1 dollars per person; the cost is $160 for each person.
The answer is B. 40/1 dollars per person; the cost is $40 for each person.
Gymnast Clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. Its cost (in dollars) for a run of x pairs of cleats is C(x) = 2750 + 8x + 0.1x2 (0 ≤ x ≤ 500). Gymnast Clothing sells the cleats at $100 per pair. Find the revenue and profit functions. How many should Gymnast Clothing manufacture to make a profit?
Answer:
Revenue function: [tex]R(x)=100x[/tex]
Profit function: [tex]P(x)=-0.1 x^2 + 92 x - 2750[/tex]
31 to 500 Gymnast Clothing are manufactured to make a profit.
Step-by-step explanation:
The cost (in dollars) for a run of x pairs of cleats.
[tex]C(x)=2750 + 8x + 0.1x^2[/tex]
Gymnast Clothing sells the cleats at $100 per pair.
The Revenue (in dollars) for a run of x pairs of cleats.
[tex]R(x)=100x[/tex]
Profit = Revenue - Cost
[tex]P(x)=R(x)-C(x)[/tex]
[tex]P(x)=100x-(2750 + 8x + 0.1x^2)[/tex]
[tex]P(x)=-0.1 x^2 + 92 x - 2750[/tex]
We need to find how many should Gymnast Clothing manufacture to make a profit.
[tex]P(x)\geq 0[/tex]
[tex]-0.1 x^2 + 92 x - 2750\geq 0[/tex]
From the given figure it is clear that P(x) is greater than or equal to 0 for 30.931 ≤ x ≤ 889.069.
The value of x can not be more than 500.
31 ≤ x ≤ 500
31 to 500 Gymnast Clothing are manufactured to make a profit.
Multiply and simplify -12i x 3i
Student to faculty is 17:3 The total is 740 how many students and faculty are at the college
17+3 =20
so for every 20 people there are 17 students and 3 faculty
740/20 = 37
37*3 = 111 faculty
37 *17 = 629 students
Suppose you randomly select a letter from BURGER AND STARBIRD. Imagine writing these letters on Ping- Pong balls—one letter per ball—then putting them all in a barrel and remov- ing one. What is the probability of pulling out an R?
How do I use the info given in the table to figure out the answers?
Given that (-2,-5) is on the graph of f(x), find the corresponding point for the function f(-2/3x).
The corresponding point for the function f(-2/3x) given the point (-2,-5) on the graph of f(x) is (3,-5), where the x-coordinate is transformed by multiplying -2 by -3/2 and the y-coordinate remains unchanged.
The question asks about finding a corresponding point for the function f(-2/3x) given that the point (-2,-5) is on the graph of the original function f(x). To find the corresponding point, we need to apply the transformation to the x-coordinate of the given point. Since the function is f(-2/3x), this represents a horizontal stretch by the reciprocal of -2/3, which is -3/2. Therefore, we multiply the x-coordinate of the given point by -3/2.
Let's calculate this step by step:
Start with the original point (-2,-5).Apply the transformation to the x-coordinate: -2 multiplied by -3/2 equals 3.The y-coordinate remains unchanged because the transformation applies only to the x-coordinate.Agnes scored 87 on the first test 73 on the second test, 81 on the third test. supoise Agbes has one more test in the semester ajd wants to finish with a mean of at least 80. what does she need to get on her last test?
Find all 6 trigonometric ratios of the angle θ =7∏/ 6
1)Solve for x.
5+x+(−2)=−8
2)Solve for h.
6.51−9.32+h=1.02
3)Solve for y.
2/3+y−1/9=7/9 ( the ones with slashes are fractions (: )
4 )Solve for x.
−2/3(3x−4)+3x=5/6
5)
What is the value of s?
0.7(3s+4)−1.1s=7.9
see attached picture for answers:
replaced picture with correct answer for #1
A 3x3x4 cuboid is painted blue and cut into 1x1 cubes. what is the expected value for the painted sides of a randomly selected cube?
A 3 x 3 x 4 cuboid can be cut into 3(3) (4) = 36 pieces of 1 x 1 cubes.
Out of the 36 pieces of 1 x 1 cubes, there are no 1 x 1 cube with the four
sides painted, there are eight 1 x 1 cubes with simply 3 sides painted, there
are twenty 1 x 1 cubes with only 2 sides tinted, there are 6 cubes with only 1
side painted and there are 2 cubes with no side painted.
The chance that the four sides of a randomly selected cube is painted is 0.
The likelihood that only 3 sides of a randomly selected cube is painted is 8 / 36 = 2 / 9.
The chance that only 2 sides of a randomly selected cube is painted is 20 / 36 = 5 / 9.
The likelihood that only 1 side of a randomly selected cube is painted is 6 / 36 = 1 / 6.
The probability that no side of a randomly selected cube is
painted is 2 / 36 = 1 / 18.
Thus, the expected value for the painted sides of a randomly selected cube is
given by 4(0) + 3(2 / 9) + 2(5 / 9) + 1(1 / 6) + 0( 1 / 18) = 2 / 3 + 10 / 9 +
1 / 6 = 35 / 18 = 1.94
The sum of the square of a positive number and the square of 5 more than the number is 37. What is the number?
Find the derivative of f (x)=(x^2+1)^3 (x^2+2)^6 using chain rule.
Alan is 14 years old. This is twice as old as his brother James. How old is James?