Grant can arrange 3 of his 10 plants on a window ledge in 720 ways.
Determine the number of the waysTo find the answer, we need to use the formula for permutations:
Permutations = n! / (n-r)!
Where:
- n is the total number of items
- r is the number of items to be arranged
- ! means factorial (e.g. 5! = 5 x 4 x 3 x 2 x 1)
In this case:
- n = 10 (the total number of plants)
- r = 3 (the number of plants to be arranged on the window ledge)
Plugging these values into the formula, we get:
Permutations = 10! / (10-3)! = 10! / 7! = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (7 x 6 x 5 x 4 x 3 x 2 x 1) = (10 x 9 x 8) / 1 = 720
Therefore, Grant can arrange 3 of his 10 plants on a window ledge in 720 ways.
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Draw the graph of the equation y=6-x-x² and find the gradient at x=2 x=-3+0+3
The graph of equation y = 6 - x - x² is shown in figure.
And, The value of gradient at x = 2 is, - 5.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The equation is,
⇒ y = 6 - x - x²
Now, The graph of equation y = 6 - x - x² is shown in figure.
Which represent the graph of parabola.
And, The value of gradient at x = 2 is,
⇒ y = 6 - x - x²
⇒ y' (x) = 0 - 1 - 2x
⇒ y' (x) = - 1 - 2x
At x = 2;
⇒ y' (2) = - 1 - 2 × 2
⇒ y ' (2) = - 1 - 4
⇒ y' (2) = - 5
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Question 5 of 10
The area of the triangle below is_____
Sq.units.
A. 34
B. 42
C. 21
D. 68
The area of the triangle below is 34 Square per units. The Option A is correct.
How do we find area of the triangle?The area of a triangle is total region that is enclosed by the three sides of any particular triangle. It is equal to half of the base multiplied by the height.
The area of a triangle is given as: Area of triangle= 1/2 * Base of triangle * Height of Triangle where the height is 4 and base is 17
The calculation of our area:
= 1/2 * 17 * 4.
= 34²
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what will be the value of |2-3i| ?
The value of complex number |2 - 3i| will be, 3.605
What is a complex number ?A complex number is one that has the formula a + bi, where I is the imaginary unit and a and b are real numbers. A and b are the real and imaginary halves of a complex number, respectively.
In order to expand the real number system to include answers to polynomial equations that couldn't be solved with just real numbers, complex numbers were first introduced. Many branches of mathematics and science, such as computer science, physics, and engineering, are based on the idea of a complex number.
The absolute value of a complex number "a + bi" can be calculated as the square root of the sum of the squares of its real and imaginary parts:
|a + bi| = √(a² + b²)
In this case, a = 2 and b = -3, so:
|2 - 3i| = √(2 + (-3)²)
= √(4 + 9)
= √(13)
= approximately 3.6055
So, the value of |2 - 3i| is approximately 3.6055.
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A product is marked down to 15%; the sale price is $127.46. What was the original price?
Answer:
The original price is $ 149.95
Solve the equation AB=BC for A, assuming that A,B and C are square matrices and B is invertible.
The solution of AB = BC for A, assuming that A,B and C are square matrices and B is invertible is [tex]A = BCB^{-1}[/tex]
We have to solve the equation
AB = BC , given that these all are square matrices and B is invertible.
Write the required Equation:
AB = BC
Multiply both sides by inverse of B
The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.
Matrix multiplied by an identity matrix, the result is always the same original non-identity (non-unit) matrix, and thus, as explained before, the identity matrix gets the nickname of "unit matrix"
[tex]ABB^{-1} = BCB^{-1}\\AI = BCB^{-1}\\A = BCB^{-1}[/tex]
so the solution of AB = BC is [tex]A = BCB^{-1}[/tex]
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14 cm
2 cm
18 cm
2 cm
What is the approximate area of the remaining cardboard? Use 3.14 for and round to the nearest whole number.
O 227 cm²
O 246 cm²
O258 cm²
O276 cm²
The approximate area of the remaining cardboard would be = 246 cm². That is option B.
How to calculate the area of the remaining cardboard?To calculate the area of the remaining cardboard = (area of rectangle) - 2(area of circle)
The formula that is used to calculate the area of rectangle = length×width
where length = 14 cm
width = 18cm
area = 14×18 = 252 cm²
The area of the 2 circle formula;
= 2(πr²)
where π = 3.14
r = 2/2 = 1
area = 2(3.14) = 6.28
Area of the remaining cardboard
= 252 cm²- 6.28
= 245.72
= 246 cm²
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Solve the first word problem .Will mark brainliest.
Answer: Area of path = 1492 m^2 Area of "no path" = 123508 m^2
Step-by-step explanation:
Probably wrong
Consider the data set.
91, 91, 92, 97, 99, 108, 110, 112, 119, 132, 150
Which box plot represents the data set?
The box plot that represents the data-set is given as follows:
Option B.
What is shown by the box and whisker plot?From left to right, the five features of the box and whisker plot are listed as follows
Minimum value.Lower quartile.Median.Upper quartile.Maximum value.The data-set in this problem has 11 elements, hence:
The first half is 91, 91, 92, 97, 99.The second half is 110, 112, 119, 132, 150.The median is 108.The quartiles are the mean of each half, hence:
First quartile: 92.Second quartile: 119.Meaning that the second plot is correct.
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what is 5.76 divide by 16
Answer:
0.36
Step-by-step explanation:
and I got this answer by using calculator
Which equation does the graph below represent? (5 points)
O
A
-5-4-3 -2 -10 1 2 3 4 5
Ob
Oc
Od
20
16
12
22
280
4
ܬܬ ܣ ܘ ܗ 8
-8
-12
-20
1
y-¼+x
y= +X
1
y = 4x
y=4+x
y = 4x
If two events are collectively exhaustive, what is the probability that both occur at the same time?
a) 0. b) 0.50. c) 1.00. d) Cannot be determined from the information given
If two events are collectively exhaustive, then the probability that both occur at the same time is 1.00 (Option c)
What do you mean by Probability?Probability is a quantification of how likely an event is to occur. Typically, probabilities are defined as the chances that a specific outcome will occur out of a given selection of outcomes. A probability is expressed mostly in decimal form, taking values between 0 and 1. Probabilities cannot exceed this particular range of values.
Firstly, To clarify : You are confusing mutually exclusive and jointly collectively exhaustive.
The former describes condition which cannot both (or all) obtain. and so exclude one another.
i.e., "not - (both A and not - A)"
The latter describes conditions, one of which must obtain, and so exhaust the field of possibilities. i.e., "either A or not - A"
I presume you intend to refer to the latter.
Second, to answer your question: If two events - are jointly exhaustive, their probabilities must by definition sum to 1.
It is thus certain, not merely probable, that one or the other will obtain.
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Given: (x+y)^2 evaluate the expression if x=6 and if y=9
Answer:
225
Step-by-step explanation:
(x+y)^2, if x=6 and y=9
Put 6 in place of x and 9 in place of y.
(6+9)^2 According to order of operations, add the 6+9 first.
(6+9)^2
= 15^2
= 225
Adam and Shane are competing to see who can save the most money
in one month. Which statement gives a correct comparison of their
rate of savings?
The slope in both equations shows the rate of their savings per week, is Adma saves 3$ per week while Shane saves $4 per week.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees. And also it is defined as the rate of change of a function.
Here,
Adam and Shane are competing to see who can save the most money in one month. From the graph, Adam's linear function of saving is given as by slope-intercept form of equation as,
y = 3x + 3
While the linear function for Shane is not given, so we assume the function as y = 4x.
The slope in both equations shows the rate of their savings per week, is Adma saves 3$ per week while Shane saves $4 per week.
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Plss help its due today
(a) The angle measurement of first unknown angle is c = 80 degrees
(b) The angle measurement of second unknown angle is y = 110 degrees
How to find the angle measurement of first unknown angle?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees
The angle measurement of first unknown angle will be:
a + b + c = 180 (sum of angles in a triangle is 180 degrees)
c = 180 - a - b
c = 180 - 30 - 70
c = 80 degrees
(b) The angle measurement of second unknown angle will be:
y = 180 - b (sum of angles on a straight line is 180 degrees)
y = 180 - 70
y = 110 degrees
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PLEASE HELP ASAP‼️‼️ I’ve been wasting my points and I don’t know the answer
The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
In given two triangles,
RST and NLM
In the triangle RST ,
The sum of angles is 180
so,
44 + 15 + S = 180
S = 180 - 59
S = 121
And similarly in the triangle NLM,
N + 121 + 44 = 180
N = 180 - 165
N = 15
Therefore, The values of given angles S and N are 121 , 15 respectively
SR / ML = 3.61 / 5.415 = 0.667
ST / MN = 9.71 / 14.565 = 0.667
Hence, The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .
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Factory A has produced 120 pairs of shoes
and produces 40 more each week. Factory B
has produced 70 pairs of shoes and produces
50 more each week. How many weeks (w)
will it be before Factory B produces as many
pairs of shoes (s) as Factory A?
s = 40w + 120
s = 50w + 70
[?] weeks
Answer:
5 weeks
Step-by-step explanation:
Let factory B produce the same amount of shoes as factory A in w weeks.
then,
70+50w = 120+40w
50w - 40w = 120 - 70
10w = 50
w = 50/10
w = 5
Therefore, in 5 weeks factory B will produce the same amount of shoes as factory A will produce in 5 weeks time.
There used to be 60 teachers at RWMS, in 2019 there are 72 teachers. What is the percent increase of teachers this year?
Find the difference between the starting and ending values:
72 - 60 = 12
Divide that difference by the starting value:
12 ÷ 60 = 0.2
Convert that to a percent:
0.2 = 20%
The number of teachers increased by 20%.
The key is to divide the difference by the original number, not the ending number.
How do you validate a min-heap?
To validate a min-heap, you can follow these steps: Start at the root, Check each subtree, Repeat the process recursively, If any node violates the min-heap property, then the heap is not valid.
Start at the root: Verify that the value at the root node is the minimum value in the heap. This is the defining property of a min-heap. Check each subtree: For each subtree, check that the value at the root of the subtree is less than or equal to the values of its child nodes. If this property holds true for all subtrees, the heap is a valid min-heap. Repeat the process recursively: Continue the above steps for each subtree until all nodes have been checked. If any node violates the min-heap property, then the heap is not valid. In that case, you can either rebuild the heap or identify the specific node or subtree that violates the property and fix it. In summary, to validate a min-heap, you need to check that the root node contains the minimum value, and each subtree obeys the min-heap property. You can check the property recursively until all nodes have been verified, and identify any nodes that violate the property for correction.
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PLEASE HELP 20 POINTS 1. Jack, Art, Fran, and Megan work as volunteers at the local kennel. Jack gives the dogs baths every 4 days; Art cleans out cages every 6 days; Fran feeds the animals in Section Bevery 2 days; and Megan helps the receptionist every 3 days. How many times in 12 weeks will all 4 helpers be at the clinic on the same day? Show all work and explain how you got your power Due date
All 4 helpers will be at the clinic on the same day 7 times in 12 weeks.
What is Prime Factorization?
"Prime Factorization" is the process of determining which prime numbers multiply together to get the original number.
To find the number of times in 12 weeks that all 4 helpers will be at the clinic on the same day, we need to find the least common multiple (LCM) of the numbers 4, 6, 2, and 3.
First, we can find the prime factorization of each number:
4 = 2 x 2
6 = 2 x 3
2 = 2
3 = 3
Next, we can find the LCM by taking the highest power of each prime factor that appears in the factorizations:
LCM = 2 x 2 x 3 = 12
Therefore, all 4 helpers will be at the clinic on the same day every 12 days. Since 12 weeks is equivalent to 84 days, we can divide 84 by 12 to get the number of times:
84 ÷ 12 = 7
So, all 4 helpers will be at the clinic on the same day 7 times in 12 weeks.
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Esteban's family buys a new car. For the next five years, the car's value decreases
by about 20% per year
Answer:
If the Esteban's car continues to decrease 20%, by five years the car will be worthless.
20 x 5 is 100. This means that 100% of the car will have lost its value and will be worthless.
I hope this helps & Good luck <3 !!!
3x + y = -8 -2x - y = 6
Answer:
x=-2
Step-by-step explanation:
if we find sum of same variables ,
3x-2x+y-y=-8+6
x=-2
A marine biologist was interested in seeing the relationship between a manatee's weight and height. She gathered data and wanted to construct a graph to display the data in order to observe this relationship.
Is a scatter plot or a line graph more appropriate to construct for the data, given the context of the problem? Explain.
A scatter plot, because it would show the association or relationship between two variables
A scatter plot, because it would show how a variable changes over time between each data point given
A line graph, because it would show the association or relationship between two variables
A line graph, because it would show how a variable changes over time between each data point given
Answer:
(c) A line graph, because it would show the association or relationship between two variables
Step-by-step explanation:
You want to know if scatter plot or a line graph more appropriate to construct for seeing the relationship between a manatee's weight and height.
VariablesThe variables involved are "weight" and "height". Notice that "time" is not involved. (This eliminates choices B and D.)
GraphA line graph is useful for showing how one variable relates to another as the value of one variable changes. It would be useful for plotting the weight and height of one animal as it changes during the animal's lifetime.
When multiple animals are involved, a scatter plot might be more helpful for showing the relationship.
The context is given as "a manatee's weight and height", not "manatees' weight and height." Hence it seems we can assume that we're looking at data for only one animal.
The appropriate graph would be ...
A line graph, because it would show the association or relationship between two variables — choice C.
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You randomly choose one marble from the jar. What is the theoretical probability of choosing a green marble.
What is Simpson's 1 3rd rule?
Simpson's 1/3rd rule is a method of numerical integration that is used to approximate the value of a definite integral.
It is based on the idea of approximating the area under a curve by dividing it into a series of trapezoids and calculating the area of each trapezoid. The formula for Simpson's 1/3rd rule is:
∫abf(x)dx ≈ (b-a)/6 [f(a) + 4f((a+b)/2) + f(b)]
In this formula, a and b are the limits of integration, and f(x) is the function being integrated. The rule is called the "1/3rd rule" because the coefficient of the middle term is 4/3, which is equal to 1/3 when multiplied by the 3 in the denominator.
To use Simpson's 1/3rd rule, you first need to divide the interval [a,b] into an even number of subintervals. Then, you can apply the formula to each subinterval to get an approximation of the integral over that subinterval. Finally, you can add up the approximations for each subinterval to get an approximation of the integral over the entire interval.
Simpson's 1/3rd rule is a more accurate method of numerical integration than the trapezoidal rule, but it is still an approximation. The accuracy of the approximation depends on the number of subintervals used and the smoothness of the function being integrated.
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Describe how the graph of
g(x) = 4(0.5)x - 3
compares to the graph of
f(x) = 4(0.5)x .
Answer:
the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.
Step-by-step explanation:
The functions g(x) = 4(0.5)^x - 3 and f(x) = 4(0.5)^x are both exponential functions with the same base of 0.5 and the same coefficient of 4.
However, the graph of g(x) will be shifted downward by 3 units compared to the graph of f(x), because of the constant subtraction of 3 at the end of the function. This shift will occur for all values of x, meaning that the distance between the two graphs will remain constant as x changes.
In other words, the graph of g(x) will be the same shape as the graph of f(x), but shifted downward by 3 units.
liz is writing a report on adult male otters . she is analyzing two data sets that compare the amount of food two adult male otters eat each day for one mounth at the local zoo.
a. The median of Otter 2 's data is greater than the median of Otter 1's data. b. The variability in the data for Otter 1 is greater than the variability in the data for Otter 2.
c. Liz can conclude that Otter 2 generaily eats more food.
How to convey the informationIn statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution.
The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median.
The median for A is 25.5 and 26 for B. This implies that B has higher median than A.
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11. Given the four points, A(-3, 5), B(1, 13), C(4, 2), and D(10, 5) are AB and CD parallel? Use
mathematical evidence to justify your answer.
AB and CD are not parallel lines.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
If the slope of AB and CD are equal then the lines are parallel.
A(-3, 5), B(1, 13), C(4, 2), and D(10, 5)
AB=13-5/1+3
=8/4=2
CD=5-2/10-4
=3/6=1/2
As the slope of lines are different, the lines are not parallel.
Hence, AB and CD are not parallel lines.
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Find the product. Simplify, if needed. 1/8×5/6×4/5
A. 5/48
B. 1/12
C. 1/16
D. 10/240
PLEASE HELP!!
Answer:
B. 1/12
Step-by-step explanation:
1/8 × 5/6 = 5/48 × 4/5 = 1/12
how problem solving with algorithms and data structures using python?
The algorithms are a problem solving tool in Python because it provides a wide range of built-in algorithms that can be used to solve many common problems.
The Algorithms are a fundamental problem solving tool in Python . An algorithm is a set of instructions that are executed in a specific order to solve a particular problem. In Python, algorithms can be implemented in the form of functions or methods.
So , In addition to the built in algorithms, Python also provides a rich collection of third party libraries that contain various algorithms that can be used to solve complex problems.
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The given question is incomplete , the complete question is
How are algorithms a problem solving tool in Python ?
The temperature in Toronto, Canada was 12° F at noon. For the remainder of the day, the temperature dropped 5° every hour. What equation could be used to represent the relationship between x, the number of hours past noon, and y, the temperature outside?
WHAT IS THE GRAPH?
Answer:
y=12-5x
Step-by-step explanation:
We know that 12 is our original number so we put that first. X represents the number of hours. And 5 is how much its dropping per hour. Y would be our final answer. If you sub in for x the amount of hours outside and multiply it by 5, that's how many degrees it dropped.