Mike cannot attain a mean grade of 85% for every one of his studies since a grade higher than 100% is not feasible.
What does the math mean?The sum of all numbers divided by the entire number of values determines the mean (also known as the arithmetic mean, which differs from of the median) of a dataset. This central tendency is usually referred to as the "average".
How can you calculate the mean?Just dividing the total amount of information in a data collection even by sum of all of the values yields it. Both raw data and data that have been compiled into a frequency distribution table can be used for the computation.
mean = (sum of all numbers) / (number of numbers)
80% = (82% + 75% + 78% + 80% + m) / 5
85% = m
The another equation is,
85% = (82% + 75% + 78% + 80% + m) / 5
425% = 315% + m
110% = m
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need help with part A part B and part c
Answer:
4,20,C
Step-by-step explanation:
1/7 of 28 is 4
5/7 of 28 is 20
and if you multiply 4 times 5 you get 20
hope this helped
*See image *The number of foxes in a forest increases
by 20% each year.
This year, there are 500 foxes in the
forest.
Calculate the number of foxes that there
will be in the forest
a) after 1 year.
b) after 2 years.
Answer:
a) 600 foxes
b) 720 foxes
Step-by-step explanation:
See attached spreadsheet.
The rate of population increase is 20% each year. To find a new year's population, multiply the previous year's population by 0.20 (20%) and add that to the previous year. Year 1 would be (500)*(0.20) = 100 new foxes which are added to the year 0 population of 500, which means there are (500+100) or 600 foxes in year 1.
Year 2: (0.20)*(600) = 120 new foxes
Add 120 to the existing 600 to find 720 foxes in year 2,
============
A formula that can be used to predict the fox population for any year, n, would be:
P(n) = 500*(1+0.20)^n
where P(n) is the popluation at year n. The 500 is the population at year 0 (the starting population). (1+0.20) is the growth for each year (120%, which means the original population plus 20%). That is raised to the year of interest, n. [When n=0, (1+0.20)^0 = 1]
−
2
x
+
2
y
=
8
6
x
+
y
=
11
If
(
x
,
y
)
is the solution to the system of equations above, what is the value of
7
y
?
Answer:
7y=-91
Step-by-step explanation:
-2x + 2y = 8 (multiply the second equation by 2)
12x + 2y = 22
Adding the two equations, we get:
10x = 30
Therefore, x = 3.
Substituting x = 3 into the second equation, we get:
6(3) + y = 11
Simplifying, we get:
y = -13
Finally, we can find the value of 7y:
7y = 7(-13) = -91
Find the missing information for the triangle. *not drawn to scale
The measure of the angle x is 60 degrees and the sides of the triangle is 4√3 and 8.
What is sum of interior angles of triangle?According to the triangle sum theorem, a triangle's internal angles can be added up to 180 degrees. The triangle sum theorem, often referred to as the angle sum theorem of the triangle, states that the total of the measures of a triangle's internal angles in a Euclidean space adds up to 180 degrees, whether the triangle is acute, obtuse, or right. The smallest polygon with three sides and three internal angles, one at each vertex, and bordered by two neighbouring sides is a triangle.
Given that, angle B = 30 degrees and angle m = 90 degrees.
The sum of all the angles of a triangle is 180 degrees.
Thus,
30 + 90 + angle x = 180
120 + angle x = 180
angle x = 180 - 120
angle x = 60
The sides is thus a triangle with angle 30-60-90.
For this case the sides are in the ratio:
x : x√3 : 2x
From the figure we see that, x = 4.
Thus, the remaining sides are:
x√3 = 4√3 and 2x = 2(4) = 8
Hence, the measure of the angle x is 60 degrees and the sides of the triangle is 4√3 and 8.
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HEELLPPPP!!!! quickly im being timed.
Find the Primeter and area
For rectangle type books, the difference in the heights of their stacks of books is 15 3/4 inches.
What exactly is a rectangle?
A rectangle is a type of quadrilateral (a four-sided polygon) that has four straight sides and four right angles. It is a two-dimensional shape, meaning it lies flat in a plane, and is defined by its two sets of parallel sides, each pair of which are equal in length.
In a rectangle, opposite sides are parallel and congruent (equal in length), and adjacent sides are perpendicular (meet at a right angle). The diagonals of a rectangle bisect each other (divide each other into two equal parts) and are congruent.
The area of a rectangle is calculated by multiplying its length and width, while its perimeter is found by adding the lengths of all its sides. The area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width.
Now,
To solve this problem, we need to first find out the height of Rick's stack of books. We know that his stack is 3 times as tall as Trevor's stack, so:
Rick's stack = 3 x Trevor's stack
Rick's stack = 3 x 7 7/8 inches
Rick's stack = 23 5/8 inches
Now that we know the height of both stacks, we can find the difference between them:
Difference = Rick's stack - Trevor's stack
Difference = 23 5/8 inches - 7 7/8 inches
Difference = 15 6/8 inches
Difference = 15 3/4 inches
Therefore, the difference in the heights of their stacks of books is 15 3/4 inches.
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for the next olympic winter games, the organizers wish to expand the number of teams competing in curling. they wish to have teams enter, divided into two pools of seven teams each. right now, they're thinking of requiring that in preliminary play each team will play seven games against distinct opponents. five of the opponents will come from their own pool and two of the opponents will come from the other pool. they're having trouble setting up such a schedule, so they've come to you. by using an appropriate graph-theoretic model, either argue that they cannot use their current plan or devise a way for them to do so.
The organizers can use their current plan and have each team play 7 games against distinct opponents, with 5 of the opponents from their own pool and 2 of the opponents from the other pool.
To answer this question, we can use a bipartite graph as a model. A bipartite graph is a graph that has two sets of vertices, X and Y, with edges only between vertices from different sets. In this case, we can have one set of vertices representing the teams in one pool and the other set of vertices representing the teams in the other pool.
We can start by drawing a bipartite graph with 14 vertices, 7 in each set. Each vertex represents a team, and we can label them as T1, T2, ..., T14. Now, we need to add edges to represent the games that each team will play.
For each team in one pool, we can add 5 edges to connect it to 5 different teams in the same pool, and 2 edges to connect it to 2 different teams in the other pool.
After adding all the edges, we can see that each team has 7 edges connected to it, representing the 7 games that it will play. However, we also need to make sure that each team plays against distinct opponents. To do this, we can check if there are any duplicate edges in the graph.
If there are no duplicate edges, then the schedule can be used as it is. But if there are duplicate edges, then the schedule cannot be used and the organizers need to come up with a different plan.
In this case, we can see that there are no duplicate edges in the graph, which means that the schedule can be used as it is. Therefore, the organizers can use their current plan and have each team play 7 games against distinct opponents, with 5 of the opponents from their own pool and 2 of the opponents from the other pool.
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A bank offers two interest account plans. Plan A gives you 6% interest compounded annually. Plan B gives you 13% annual simple interest. You plan to invest $2,000 for the next 4 years. Which account earns you the most interest (in dollars) after 4 years? How much will you have earned?
Answer:
Plan A
The formula is
A=p (1+r)^t
A=2,000×(1+0.06)^(4)
A=2,524.95 ( future value )
Interest earned=A-p
Interest earned=2524.95-2000
Interest earned=524.95
Plan B
Use the simple interest formula
I=prt
I interest earned?
P principle 2000
R interest rate 0.13
T time 4years
I=2,000×0.13×4
I=1,040
The Answer is
Plan B; $1,040
Step-by-step explanation:
Do you mind if someone would answer number 21 part a and b
I would really appreciate if you would
The value at the 60th percentile is 72°F. According to the given question.
What is whisker plot?
A whisker plot, also known as a box and whisker plot, is a graphical representation of a dataset that shows the distribution of values. It is often used to summarize and compare datasets, and to identify outliers or extreme values.
The plot is constructed using a rectangular box that represents the middle 50% of the data (the interquartile range or IQR). The box extends from the lower quartile (the value below which 25% of the data falls) to the upper quartile (the value below which 75% of the data falls). A line inside the box represents the median (the value below which 50% of the data falls).
Part A:
Here is a box and whisker plot representing the given data:
| + |
75 -+ + |
| | |
70 -+ | |
| | |
65 -+-------------+-------------------+
| S M T W | T F S |
The plot is divided into four sections: the lowest 25% of the data (the lower quartile), the next 25% of the data (the second quartile or median), the next 25% of the data (the third quartile), and the highest 25% of the data (the upper quartile). The box represents the middle 50% of the data, and the whiskers extend to the lowest and highest values that are not outliers.
Part B:
To determine which value is at a given percentile, we need to sort the data in ascending order and count how many values are less than or equal to the percentile we are interested in. Then we find the corresponding value in the sorted list.
For example, to find the value at the 60th percentile, we first calculate 60% of the total number of values, which is:
0.60 * 7 = 4.2
Since we cannot have a fraction of a value, we round up to the next integer, which is 5. This means that the value at the 60th percentile is the fifth value in the sorted list:
65, 66, 68, 70, 72, 74, 75
Therefore, the value at the 60th percentile is 72°F.
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The system of linear equations below has the solution (3, 3), where F, G, H, P. Q, and R are non-zero real numbers.
Fr+ Gy=H
Pr+Qy= R
Which system must also have the solution (3,3) ?
3Fx - 3Gy= H
Pr + Qy = R
[ 3Fx + 3Gy = H
13Px +3Qy = R
((F+3P) x + (G+ 3Q) y = H + 3R
Pr+Qy = R
((F+3G) x + (P+3Q) y = H + 3R
Pr+Qy = R
Answer:
3Fx - 3Gy= H
Step-by-step explanation:
The diameter of a circle is 6 kilometers. What is the length of a 30 degree arc
Hence, in answering the stated question, we may say that As a result, the circle length of a 30-degree arc of a 6-kilometer-diameter circle is approximately 1.57 kilometers.
What is circle?Each spot that is a particular distance from yet another point creates a circle in the plane (center). As a result, it is a curve composed of points separated in the plane by a given distance. Furthermore, at all angles, it is circumferentially symmetric the about centre. Every couple of points in such a circle's closed, two at least plane is evenly spaced out from the "centre." A round symmetry line is formed by tracing a line through circle. Furthermore, at all angles, it is rotationally equal about the centre.
The circumference of a circle can be calculated using the formula C = d, where d is the circle's diameter. Because the diameter in this case is 6 kilometres, the circumference is:
C = d = (6) = 18.85 km (rounded to two decimal places)
1/12 = 30 degrees / 360 degrees
As a result, the length of the 30 degree arc is:
1.57 km length = (1/12) * C = (1/12) * 18.85 km (rounded to two decimal places)
As a result, the length of a 30-degree arc of a 6-kilometer-diameter circle is approximately 1.57 kilometres.
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a bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. if you pick six letters one at a time, what is the chance that you spell c-h-a-n-c-e? (in this order)
The chance of spelling C-H-A-N-C-E in this order with a bag of 15 scrabble tiles containing three each of the letters A, C, E, H, and N is 3/40040.
The chance of spelling C-H-A-N-C-E in this order with a bag of 15 scrabble tiles containing three each of the letters A, C, E, H, and N can be calculated by multiplying the probabilities of picking each letter in the correct order.
we need to calculate the probability of picking the letter C. There are three C's in the bag and a total of 15 tiles, so the probability of picking C is 3/15 or 1/5.
Next, we need to calculate the probability of picking the letter H. After picking the first letter, there are 14 tiles left in the bag and three H's, so the probability of picking H is 3/14. We can calculate the probabilities of picking the letters A, N, C, and E in the correct order:
- Probability of picking A: 3/13
- Probability of picking N: 3/12 or 1/4
- Probability of picking C: 2/11
- Probability of picking E: 3/10
To find the overall probability of spelling C-H-A-N-C-E in this order, we multiply all of these probabilities together:
[tex](1/5) * (3/14) * (3/13) * (1/4) * (2/11) * (3/10) = 18/240240 = 3/40040[/tex]
Therefore, the chance of spelling C-H-A-N-C-E in this order with a bag of 15 scrabble tiles containing three each of the letters A, C, E, H, and N is 3/40040.
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When women were allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ACES-II ejection seats were designed for men weighing between 140LB and 211LB. Weights of women are now normally distributed with a mean of 165LB and a standard deviation of 45.6LB
a. If 1 woman is randomly selected, find the probability that her weight is between 140LB and 211LB
b. If 36 different women are randomly selected, find the probability that their mean weight is between 140LB and 211LB
The probability that the mean weight of 36 different women is between 140LB and 211LB is approximately 0.9874.
Is it possible for a random variable to have 0 probability across the board?There can only be one value for a random variable. A random variable's value could be zero with a probability of zero. A probability distribution's total probabilities are always equal to one.
a. We must convert the weight to a typical normal distribution using the following formula in order to determine the likelihood that a randomly chosen woman weighs between 140LB and 211LB.
z = (x - μ) / σ
If the weight x, the mean weight, and the standard deviation are all given. The probability can then be determined using a calculator or a typical normal table.
When x=140LB, we get:
z = (140 - 165) / 45.6 = -0.5461
x = 211LB results in:
z = (211 - 165) / 45.6 = 1.0096
The area under the standard normal curve between z = -0.5461 and z = 1.0096 is found to be roughly 0.6267 using a typical normal table or calculator.
Hence, the likelihood that a lady chosen at random weighs between 140LB and 211LB is roughly 0.6267.
b. We must normalise the sample mean to a standard normal distribution using the following method in order to determine the likelihood that the mean weight of 36 individual women is between 140LB and 211LB.
z is equal to (x - ) / (n / sqrt(n)).
When n is the sample size, x is the sample mean weight, is the mean weight, and is the standard deviation. The probability can then be determined using a calculator or a typical normal table.
To solve this issue, we have:
μ = 165LB
σ = 45.6LB
n = 36
If x = 140 LB, we get:
z = (140 - 165) / (45.6 / sqrt(36)) = -2.4994
With x = 211LB, we get:
z = (211 - 165) / (45.6 / sqrt(36)) = 2.4994
The area under the standard normal curve between z = -2.4994 and z = 2.4994 is found to be around 0.9874 using a standard normal table or calculator.
Hence, there is a roughly 0.9874 percent chance that the average weight of 36 individual women falls between 140LB and 211LB.
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enter your answer and show all the steps that you use to solve this in the space provided.
find the surface area of the cone. Use 3.14 for π height 7in diameter 8in and below it says drawing not to scale??
The surface area of the cone is 305.30 inches squared.
How to find the surface area of a cone?The height of the cone is 7 inches and the diameter of the cone is 8 inches. Therefore, let's find the surface area of the cone as follows:
surface area of the cone = πr(r + l)
where
r = radiusl = slant heightHence,
r = 8 / 2 = 4 inches
l² = 7² + 4²
l = √49 + 16
l = √65
l = 8.0622577483
l = 8.06 inches
Therefore,
surface area of the cone = 3.14 × 8.06(4 + 8.06)
surface area of the cone = 25.3154893297(12.06)
surface area of the cone = 305.304801316
surface area of the cone = 305.30 inches squared
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ALGEBRA 2 HELP
(Please show work!)
A student wrote the arithmetic series 8 + 11 + ... + 29 in summation notation as (picture below)
a. Describe and correct the error in the notation.
b. Evaluate the corrected summation of the arithmetic series above.
[tex]S_8=[/tex]
c. Write the explicit and recursive formulas for the arithmetic series above,
Explicit:
[tex]a_n=[/tex]
Recursive:
If [tex]a_1=[/tex]
Then for n > 1
[tex]a_n=[/tex]
Step-by-step explanation:
ALGEBRA 2 HELP
(Please show work!)
A student wrote the arithmetic series 8 + 11 + ... + 29 in summation notation as (picture below)
a. Describe and correct the error in the notation.
b. Evaluate the corrected summation of the arithmetic series above.
�
8
=
S
8
=
c. Write the explicit and recursive formulas for the arithmetic series above,
Explicit:
�
�
=
a
n
=
Recursive:
If
�
1
=
a
1
=
Then for n > 1
�
�
=
a
n
=
14. EXTENSION QUESTION
A GIVE WAY sign in the shape of an equilateral triangle is 110cm in height. Find the length of one
of its sides. Include a diagram.
The length of one of the sides of the GIVE WAY sign, equilateral triangle is approximately 200.89cm.
What is an equilateral triangle?
An equilateral triangle in geometry is a triangle with equally long sides. The three angles opposing the three equal sides are equal in size because the three sides are equal. As a result, with each angle measuring 60 degrees, it is sometimes referred to as an equiangular triangle. Equilateral triangles have the same area, perimeter, and height formula as other kinds of triangles.
Given that the triangle is an equilateral triangle, thus all sides are equal.
Let us suppose the sides = x.
The height of the equilateral triangle is given by:
height = (√3/2) x side length
Substituting the values:
110 = (√3/2) x (x)
x = 110 / (√3/2)
x ≈ 200.89cm
Hence, the length of one of the sides of the GIVE WAY sign is approximately 200.89cm.
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Mrs. Smitherman is coordinating the third- and fourth-grade program. She wishes to arrange the children to the fewest number of rows that contain the same number of children. She also does not wish to mix be classes within a row. If there are 60 third graders and 48 fourth graders, how many children should be aced in each row? How many rows will be needed?
Answer:
Number of students in each row = 12
Total number of rows = 9
Step-by-step explanation:
We have to assume that each row can seat the same number of students
Find the GCF(greatest common factor) of 60 and 48 to find the number of students in each row
60 = 12 x 5
48 = 12 x 4
The GCF = 12
So there are 12 students per row
If there are 60 third-grade students they will occupy 60/12 = 5 rows
48 fourth grade students will occupy 48/12 = 4 rows
Therefore the total number of rows = 5 + 4 = 9 rows
AD and EC are diameters of 0. OB is a radius. Classify each statement as true or false. AOC = 100
Therefore , the solution of the given problem of circle comes out to be this statement is true ∠AOC = 100° .
Circle – what is it?Each area of a plane with a specific distance from this additional spot forms a circle (center). Thus, it comprises of curved spots that are separated from one another and separated by the surface. Additionally, it rotates evenly around the centre from all sides. Every set of endpoints in a circular, constrained double sphere is uniformly spaced apart from the "centre."
Here,
Given :
AD and EC are diameters as we can see they are passing through centre .
So , there are diameter.
=> ∠AOC = ∠A0B + ∠BOC
=> ∠AOC = 100°
thus , this statement is true ∠AOC = 100° .
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Which is better? 8"A" students out of 40, or 9 "A" student out of 50
The first group has a higher proportion of "A" students 0.2
To determine which is better, we need to compare the proportions of "A" students in each group.
For the first group, the proportion of "A" students is:
8/40 = 0.2
For the second group, the proportion of "A" students is:
9/50 = 0.18
Therefore, the first group has a higher proportion of "A" students, and we can say that it is "better" in terms of producing "A" students. However, it is important to note that this is just one aspect of performance and there may be other factors to consider as well.
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Hi. I need to know the answer because one of my friends wanted to know the answer and I knew the answer, but not how to explain it well enough: Adrienne and Evelyn have a pet cat. When they got it as a kitten, as much as it it weighed 0.6 kilograms. Now it weighs 7.3 times did when it was a kitten. How much does their cat weigh now?
So their cat weighs 4.38 kilograms now.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
Algebraic expressions can take many different forms, but some common examples include:
3x + 7
2a^2 + 5ab - 3b^2
(x + 2)(x - 5)
4x^2 - 9.
Let's start by figuring out how much the cat weighs now. We know that the cat weighs 7.3 times what it did when it was a kitten, and it weighed 0.6 kilograms when it was a kitten.
To find out how much the cat weighs now, we can multiply its original weight by 7.3:
0.6 kilograms x 7.3 = 4.38 kilograms
Therefore, So their cat weighs 4.38 kilograms now.
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Trey and matt each have a rectangular prism the base if treys is 4 by 7 by 12 the base of matts prism is 6 by 10 by 3 whose rectangular prism will require more material to construct
Trey's rectangular prism will require more material to be constructed.
To determine which rectangular prism will require more material to construct, we need to calculate the surface area of each prism.
The surface area of a rectangular prism is given by the formula,
SA = 2×l×w + 2×l×h + 2×w×h
where l, w, and h are the length, width, and height of the prism, respectively.
For Trey's prism, the length is 12, the width is 7, and the height is 4. Therefore, the surface area of Trey's prism is:
SA of Trey = 2(12 x 7) + 2(12 x 4) + 2(7 x 4) = 336
For Matt's prism, the length is 10, the width is 6, and the height is 3. Therefore, the surface area of Matt's prism is,
SA of Matt = 2(10 x 6) + 2(10 x 3) + 2(6 x 3) = 192
Comparing the surface areas, we see that Trey's prism requires more material to construct since its surface area is larger than Matt's prism. Therefore, Trey's rectangular prism requires more material to construct than Matt's rectangular prism.
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Graph f(x) = -x. Click on the graph until the graph of f(x) = -x appears.
The graph of f(x) = -x is attached.
What is the x-intercept?The intersection of a function or equation's graph with the x axis is known as the x intercept. This can be compared to a point having a value of 0.
For any given curve, the x-intercept is a coordinate that is plotted on the x-axis. To put it another way, the x-intercept is the value of the x coordinate at the point where the graph crosses the x-axis, or we can say that it is the value of the x coordinate at a point where the value of the y coordinate equals zero.
f(x) = -x ----------(1)
Equation (1) can be written as f(x) = -x+0
This is in the form of f(x)=mx+b,
where , m= -1, b=0
this represents a line
Find the x and y-intercepts: ( consider f(x)=y)
Find x-intercept when y=0
=> 0=-x
=> x=0
Thus, x-intercept is (0,0)
Find y-intercept when x=0
=> y=-0 = 0
Thus, y-intercept is (0,0)
We need another point, because both intercepts are same
When x= 1, y= -1
The point is (1,-1)
Plot these points and join them with a line.
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Complete Question:
Which of the following is the graph of f(x) = x2?
Click on the graph until the correct graph appears.
2p - 5q= 8
3p - 7q = 11
Solve the simultaneous equation using elimination method
Step-by-step explanation:
Paul behavior is not unethical is that the information is firsthand hand factual and
how is a condominium different than a single family dwelling
a. occupants pay rent to the landlord who owns the property
b.occupants are investors who own shares in the entire property and not individual unit
c.occupants individually own both the home and the land
b.occupants jointly own the common parts of the property and individually own their own units
Option d. occupants jointly own the common parts of the property and individually own their own units is the correct answer .A condominium is a type of housing where individuals own their own unit or apartment
what is condominium?
A condominium, often shortened to "condo," is a type of housing arrangement where individuals own their own unit or apartment within a larger building or community, and jointly own the common areas and facilities of the property with other owners.
In the given question,
A condominium is a type of housing where individuals own their own unit or apartment and jointly own the common areas of the property, such as hallways, elevators, and recreation areas. This is different from a single-family dwelling where the occupant individually owns both the home and the land.
In a condominium, occupants are not renting from a landlord who owns the property, nor are they investors who own shares in the entire property. Instead, each occupant owns their own individual unit and has a shared interest in the common areas of the property.
Additionally, in a condominium, occupants are typically required to pay fees to the condo association to cover the maintenance and upkeep of the common areas, which is not typically required in a single-family dwelling.
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Solve 19(1.12^x)=8(1.18^x). Show work.
Answer:
x≈12.6
Step-by-step explanation:
We have the equation:
19(1.12^x) = 8(1.18^x)
Divide both sides by 8:
19/8 (1.12^x) = (1.18^x)
Take the natural logarithm of both sides:
ln[19/8 (1.12^x)] = ln[1.18^x]
Using the properties of logarithms, we can simplify the left side:
ln(19/8) + ln(1.12^x) = x ln(1.18)
Substituting y = 1.12^x, we get:
ln(19/8) + ln(y) = ln(1.18) y
Now we can solve for y:
ln(y) = ln(1.18) y - ln(19/8)
Using a numerical method or a graphing calculator, we can find that y ≈ 10.584.
Substituting back to solve for x:
1.12^x ≈ 10.584
Taking the logarithm base 1.12 of both sides:
x ≈ ln(10.584)/ln(1.12)
x ≈ 12.6
Therefore, the solution to the equation is x ≈ 12.6.
to decrease a number by 37% you multiply by 0.63
to decrease a number by 16% what do you multiply it by
To decrease a number by 16%, you should multiply it by 0.84.(1 - 0.16 = 0.84).
When you reduce a number by a percentage, you are subtracting that percentage from it. For example, if you were to decrease 100 by 16%, you would subtract 16 from 100 to get 84.
This is also known as a percentage decrease, which is the opposite of a percentage increase.
Using the formula for percentage decrease, we get:
Percentage decrease = (Decrease in value / Original value) × 100
We're told that to decrease a number by 37%, you multiply it by 0.63.
Therefore, we can write:
0.63 = (Decrease in value / Original value) × 1000.63 × Original value = Decrease in value
We want to find what you multiply a number by to decrease it by 16%, so let's call that value x.
So: x = (Decrease in value / Original value) × 100%
So, we can substitute in the values we know to solve for x:
x = (0.16 × Original value / Original value) × 100%x = 0.16 × 100%x = 16%
Therefore, to decrease a number by 16%, you should multiply it by 0.84.
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Let X be a geometric random variable with so that P(X=k)=(1=p)^k-1 p over k=1,2,…and p is the probability of success taking a value between 0 and 1. a) Let
P(A) be the event that X assumes an even number. Compute P(A) . b) Compute the expectation and variance of e^X. c) Compute P(e^x >10)
0.0472 (approx.)
Anwer:
a) P(A) = P(X is even) = P(X = 2) + P(X = 4) + P(X = 6) + ...Let us take p = 1/3, thus P(X = k) = (1 - p)^(k - 1)p, for k = 1, 2, 3, .... Therefore, P(X = 2) = (2 - 1)p(1-p), P(X = 4) = (4 - 1)p(1 - p)^3, P(X = 6) = (6 - 1)p(1 - p)^5, ...So, we haveP(A) = [(2-1)p(1-p)] + [(4-1)p(1-p)^3] + [(6-1)p(1-p)^5] + ...= p(1-p)[1 + 3(1-p)^2 + 5(1-p)^4 + ...]= p(1-p)/(1-(1-p)^2)= 2p(1-p) = 2/9.b) For a geometric random variable, we have E(X) = 1/p and Var(X) = (1 - p)/p^2.The expected value of e^X is:E(e^X) = Σ e^k (1-p)^(k-1) p= p Σ [e^(ln(1-p))]^(k-1) = p Σ (1-p)^(k-1)= p/(1-(1-p)) = 1/pAnd the variance of e^X is:Var(e^X) = E((e^X)^2) - [E(e^X)]^2= E(e^(2X)) - (1/p)^2= Σ e^(2k) (1-p)^(k-1) p - 1/p^2= p Σ [e^(2ln(1-p))]^(k-1) - 1/p^2= p Σ (1-p)^(2(k-1)) - 1/p^2= p/[1-(1-p)^2] - 1/p^2= (2-p)/(p(1-p)^2).c) P(e^X > 10) = P(X > ln(10)) = (1-p)^[ln(10)] = 0.0472 (approx.)
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(09.02 MC)
What step is needed when constructing a circle circumscribed about a triangle? (1 point)
Group of answer choices
Construct the angle bisectors of each angle in the triangle.
Construct the perpendicular bisectors of each side of the triangle.
Construct the midpoints of each side of the triangle.
Construct the altitude of each angle in the triangle.
The step needed when constructing a circle circumscribed about a triangle is option B: Construct the perpendicular bisectors of each side of the triangle.
What is the triangle construction about?When constructing a circle circumscribed about a triangle, the center of the circle must lie at the intersection of the perpendicular bisectors of the sides of the triangle.
To construct the perpendicular bisector of a side, you need to find its midpoint and then draw a line perpendicular to the side passing through that midpoint.
By constructing the perpendicular bisectors of all three sides, you can find their point of intersection, which will be the center of the circle. Then, the radius of the circle can be found by measuring the distance from the center to any of the vertices of the triangle.
Therefore, Once you have the center and radius, you can draw the circle circumscribed about the triangle.
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F(x)=4x^2+2
a) F(1)=
B) F(-1)=
C) F(-4)
D) F(-7/2)=
Answer:
F(1) = 6
F(-1) = 6
F(-4) = 66
F(-7/2) = 51
What is the x-coordinate of the midpoint of line segment AB with points A(21, 5) and B(-9, -13).
Answer:
6
Step-by-step explanation:
You want the x-coordinate of the midpoint of segment AB with endpoint coordinates A(21, 5) and B(-9, -13).
MidpointThe midpoint of a line segment has coordinates that are the average of the endpoint coordinates:
M = (A +B)/2
M = ((21, 5) +(-9, -13))/2 = (12, -8)/2
M = (6, -4)
The midpoint of AB is (6, -4).
The x-coordinate of the midpoint is 6.