according to the question,
given data in the question'
there are 51 houses on a street'
each hoses has an address between 1000 and 1099
There are 51 residences and 1000 possible addresses, according to the pigeon hole principle. There must be at least one address between each house in order for there to be no houses with consecutive addresses. To do this, only give houses even numbers (leaving odd addresses as the buffer address)
Giving houses even numbers (leaving odd addresses as the buffer address) There are now 1000=50 addresses that can be used.
According to the pigeon hole principle, there must be at least one box that contains at least N
k things if N objects are put into k boxes.
Because of this, it is impossible to assign 50 distinct addresses to 51 separate homes without utilising a single consecutive integer.
So, at least one instance of a home must have consecutive integers, which.
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There are 2 houses that have at least consecutive integers .
What is meant by the pigeonhole principle?According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m.
Why is pigeonhole principle important?According to the pigeonhole principle, if there are more pigeons than there are pigeonholes, then at least one pigeonhole must hold more than one pigeon. Although the underlying idea is clear, the ramifications are staggering. The explanation is that the principle establishes the reality (or absence) of a certain phenomena.
There are potential residences and addresses. There must be at least one address between each house in order for there to be no houses with consecutive addresses. To do this, only give houses even numbers (leaving odd addresses as the buffer address)
Houses are given even numbers, leaving odd addresses as the buffer address. As a result, we now have
50
addressable addresses
According to the "pigeon hole concept," if items are put into boxes, then there must be at least one box that contains at
[N/k]object.
As a result, it is impossible to assign distinct addresses to several dwellings without using at least one consecutive number.
Since there must be at least two homes with consecutive integer addresses, there must be at least one instance of consecutive integer addresses for houses.
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phil dunphy, a real estate agent, is considering whether he should list an unusual $774,395 house for sale. if he lists it, he will need to spend $5,747 in advertising, staging, and fresh cookies. the current owner has given phil 6 months to sell the house. if he sells it, he will receive a commission of $16,870. if he is unable to sell the house, he will lose the listing and his expenses. phil estimates the probability of selling this house in 6 months to be 49%. what is the expected profit on this listing?
The required expected profit on this listing with 49% probability in 6 months.
What is Probability?A probability is a number that mirrors the opportunity or probability that a specific occasion will happen. Probabilities can be communicated as extents that reach from 0 to 1, and they can likewise be communicated as rates going from 0% to 100 percent.
According to question:We have,
he will need to spend $5,747 in advertising, staging, and fresh cookies.he will receive a commission of $16,870 on selling.Then, there is 49% chances in 6 months = 49% of $16,870
⇒ $8266.3
And 51% of expenditure = 51%of $5,747
⇒ $29.3
So, required profit = $8266.3 - $29.3 = $8237
Thus, required profit is $8237.
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What is limit of a function in maths?
The limit of a function is a value of the function as the input of the function gets closer to some number.
We know that, a limit is a value toward which an expression converges as variable approaches certain values.
The limit of a function at m point is nothing but the value that the function approaches as its argument(variable) approaches m.
When a function is said to have a limit L at point p if it is possible to make the function arbitrarily close to L by choosing values to point p.
It is a value of the function as the input of the function gets closer to some number.
Therefore, the limit of a function is nothing but a value of the function as the input of the function gets closer to some number.
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What is 1/2 in a number?
Answer: 1/2, or half of something, is 0.5.
Step-by-step explanation: 1/2 means half, as you are halfway to 2 and to a whole number. This means the value of 1/2 is 0.5.
for the transition matrix P = [0.9 0.1 0.3 0.7], solve the equation SP = S to find the stationary matrix S and the limiting matrix P.
The limiting matrix is [tex]\bar{P}[/tex]=[tex]\left[\begin{array}{ccc}0.75&0.25\\0.75&0.25\\\end{array}\right][/tex].
What is meant by transition matrix?Mathematicians frequently refer to "transition matrices" in a variety of situations. The term "change of coordinates matrix" is occasionally used in the context of linear algebra. As an alternative term for a stochastic matrix, or a matrix that describes transitions, it is employed in the theory of Markov chains. Use row operations to try to create the identity matrix to the left while augmenting the matrix of the second basis with the matrix of the first basis. Afterward, the transition matrix will be on the right. Row 1 should be multiplied by 1 as follows: R1=R1 R 1=-R 1 R1=R1.
The given transition matrix is:
P=[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex]
Let S=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9a+0.1b\\0.3a+0.7b\\\end{array}\right][/tex]=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
Here, 0.9a+0.1b=0, 0.3a-0.3b=0
So, a=b
a+b=1
a=b=1/2
S=[tex]\left[\begin{array}{ccc}0.5\\0.5\\\end{array}\right][/tex]
This S is called the stationary matrix
P=[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex]
P=det[tex]\left[\begin{array}{ccc}0.9-\lambda&0.1\\0.3&0.7-\lambda\\\end{array}\right][/tex]=0
λ²-1.6λ+0.6=(λ-1)(λ-0.6)=0
λ₁=1, λ₂=0.6
x=[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
Px=λx
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =1[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
0.9a+0.1b=a
a=b
v₁=[tex]\left[\begin{array}{ccc}1\\1\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}0.9&0.1\\0.3&0.7\\\end{array}\right][/tex][tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex] =0.6[tex]\left[\begin{array}{ccc}a\\b\\\end{array}\right][/tex]
0.9a+0.1b=0.6a
b=-3a
v₂=[tex]\left[\begin{array}{ccc}1\\-3\\\end{array}\right][/tex]
V=[tex]\left[\begin{array}{ccc}1&1\\1&-3\\\end{array}\right][/tex]
V⁻¹=(1/4)[tex]\left[\begin{array}{ccc}3&1\\1&-1\\\end{array}\right][/tex]
D=[tex]\left[\begin{array}{ccc}\lambda_{1} &0\\0&\lambda_{2}\\\end{array}\right][/tex]
D=[tex]\left[\begin{array}{ccc}1&0\\0&0.6\\\end{array}\right][/tex]
P=VDV⁻¹
Pⁿ=VDⁿV⁻¹
[tex]\bar{P}[/tex]=[tex]\left[\begin{array}{ccc}0.75&0.25\\0.75&0.25\\\end{array}\right][/tex]
This is the required limit matrix.
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-3/4 x 4/3 x -3/7
Just need the answer. Need by next Friday. 30 points for whoever answered.
Answer:-3/4x=-3x/4
4/3x -3/7 = 4x/3 - 3x
Step-by-step explanation:
The bar graph shows the number of reserved campsites at a campground for one week. What percent of the reservations were for Friday or Saturday?
Reservations: Monday=5
Tuesday=3
Wednesday=4
Thursday=7
Friday=26
Saturday=30
Sunday=9
The percentage of the reservations were for Friday or Saturday is 67%
How to determine the percentage of the reservations were for Friday or Saturday?From the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following data values for reservation
Monday = 5Tuesday = 3Wednesday = 4Thursday = 7Friday = 26Saturday = 30Sunday = 9The total number of reservations in the bar chart is then calculated as
Total number of reservations = 5 + 3 + 4 + 7 + 26 + 30 + 9
Evaluate the sum
So, we have the following representation
Total number of reservations = 84
The total number of reservations for Friday or Saturday is then calculated as
Total number for Friday or Saturday = 26 + 30
Evaluate the sum
So, we have the following representation
Total number for Friday or Saturday = 56
The percentage of the reservations were for Friday or Saturday is then calculated as
Percentage = Total number for Friday or Saturday/Total number of reservations
This gives
Percentage = 56/84
Evaluate
Percentage = 67%
Hence, the percentage is 67%
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please solve this question
If [tex]$\tan \theta=\frac{a}{b}$[/tex], then [tex]$\frac{a \sin \theta+b \cos \theta}{a \sin \theta-b \cos \theta}$[/tex] is equal to the [tex]\frac{a^2+b^2}{a^2-b^2}[/tex].
What is Hypotenuse?
The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, may be used to determine the length of the hypotenuse.
Given: [tex]$\tan \theta=\frac{a}{b}$[/tex]
We have to find the value of following expression in terms of a and b
We know that: [tex]$\tan \theta=\frac{\text { Perpendicular }}{\text { Base }}$[/tex]
[tex]$\Rightarrow$[/tex] Base [tex]$=b$[/tex]
[tex]$\Rightarrow$[/tex] Perpendicular[tex]$=a$[/tex]
[tex]$\Rightarrow$[/tex] Hypotenuse [tex]$=\sqrt{(\text { Perpendicular })^{2}+(\text { Base })^{2}}$[/tex]
[tex]$\Rightarrow$[/tex] Hypotenuse[tex]$=\sqrt{a^{2}+b^{2}}$[/tex]
Now we find,
[tex]$\frac{a \sin \theta+b \cos \theta}{a \sin \theta-b \cos \theta}=\frac{a\left(\frac{a}{a^{2}+b^{2}}\right)+b\left(\frac{b}{a^{2}+b^{2}}\right)}{a\left(\frac{a}{a^{2}+b^{2}}\right)-b\left(\frac{b}{a^{2}+b^{2}}\right)}$[/tex]
[tex]$=\frac{\frac{a^{2}+b^{2}}{a^{2}+b^{2}}}{\frac{a^{2}-b^{2}}{a^{2}+b^{2}}}$[/tex]
[tex]$=\frac{a^{2}+b^{2}}{a^{2}-b^{2}}$[/tex]
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Step-by-step explanation:
i can't read acruse please some one help me I am trying to answer it
Scientists studying dolphin echolocation simulate the projection of a bottlenose dolphin's clicking sounds using computer
models. The models originate the sounds at the focus of a parabolic reflector. The parabola in the graph shows the cross
section of the reflector with focal length of 1.3 inches and aperture width of 8 inches. Write an equation to represent the cross
section of the reflector. What is the depth of the reflector? Round your answer to the nearest hundredth.
The equation __ represents the cross section.
The depth is about __ inches.
Step-by-step explanation:
The equation of a parabola with focus at (h, k) and the directrix y = p is given by the following formula:
(y - k)^2 = 4 * f * (x - h)
In this case, the focus is at the origin (0, 0) and the directrix is the line y = -1.3, so the equation representing the cross section of the reflector is:
y^2 = 4 * f * x
= 4 * (-1.3) * x
= -5.2x
The depth of the reflector is the distance from the vertex to the directrix. In this case, the vertex is at the origin, so the depth is simply the distance from the origin to the line y = -1.3. Since the directrix is a horizontal line, this distance is simply the absolute value of the y-coordinate of the line, which is 1.3 inches. Therefore, the depth of the reflector is approximately 1.3 inches.
two dice are rolled what is the probability that the sum of the dice is atleast 5, given that one die is showing a 2
Answer:
Step-by-step explanation:
the sum of the dice is at least 5
one die is showing a 2
2 and 3
2 and 4
2 and 5
2 and 6
4 out of 36 ways to get the sum at least 5 and one die is always 2
Probability = 4/36 = 1/9
If it is known that one die is showing a 2, then the probability that the sum of the dice is at least 5, is the probability that the other die shows 3 or 4 or 5 or 6, i. e. 4/6=2/3=0.666.
in october, marshal drove 217 miles ,which was 62% of the distance he drove in september. How far in miles did marshal drive in september?
Answer:
350 miles
Step-by-step explanation:
62 : 100 = 217 : x
x = 217 · 100 / 62
x = 21 700 / 62
x = 350
Required
Question 1- Which parallelogram has an area of 60 square units? *
A
12
15
10
C
15
15
12
B
10
10.2
6
D
6
6
10
Show your reasoning
Answer:
To find the area of a parallelogram, we can use the formula A = bh, where A is the area, b is the base, and h is the height. In this case, we are given that the area is 60 square units, so we can use this information to find the value of b and h for each of the options given.
Option A: 12 15 10
In this option, we can see that the base is 12 units and the height is 15 units, so we can plug these values into the formula to find the area: A = 12 * 15 = 180 square units. This is much larger than the given area of 60 square units, so option A cannot be correct.
Option B: 10 10.2 6
In this option, we can see that the base is 10 units and the height is 6 units, so we can plug these values into the formula to find the area: A = 10 * 6 = 60 square units. This matches the given area of 60 square units, so option B could be correct.
Option C: 15 15 12
In this option, we can see that the base is 15 units and the height is 12 units, so we can plug these values into the formula to find the area: A = 15 * 12 = 180 square units. This is much larger than the given area of 60 square units, so option C cannot be correct.
Option D: 6 6 10
In this option, we can see that the base is 6 units and the height is 10 units, so we can plug these values into the formula to find the area: A = 6 * 10 = 60 square units. This matches the given area of 60 square units, so option D could be correct.
Therefore, the correct answer is either option B or option D.
You are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 28 inches long. The first bend is made 10 inches from one end. Describe two ways you could complete the triangle.
Answer:
2 ways below
Step-by-step explanation:
To complete the triangle, you would need to bend the other end of the strip of metal so that it is also 10 inches from the first bend. One way to do this would be to measure 10 inches from the first bend and mark the spot, then use a bending tool to carefully bend the metal at the mark.
Another way would be to hold the metal strip against a ruler or measuring tape, aligning the first bend with the 10-inch mark, then use the bending tool to make the second bend at the 20-inch mark. In either case, the resulting triangle would have two equal sides that are 10 inches long, and a base that is 8 inches long.
24 3/5 +4^3x(8 1/5 -2)
Answer: i believe it is 123/5 + 1984x/5
Step-by-step explanation:
pls answer this questions for 15 points
Answer:
B
Step-by-step explanation:
by plugging in f, you can see that B, is the only correct answer
A fails at values greater than or equal to f = 2
C fails for all values
and D fails for all values
B works for all given values
2(1) + 3 = 5
2(2) + 3 = 7
2(3) + 3 = 3
2(4) + 3 = 11
2(5) + 3 = 13
How do you calculate raw data?
Raw data can be calculated by using mathematical operations such as addition, subtraction, multiplication, and division.
This can be done manually or by using a calculator or a computer program .Additionally, statistical methods such as mean, median, mode, and standard deviation can be used to calculate raw data.Raw data can also be manipulated in various ways. For example, data can be sorted, filtered, and organized into categories or hierarchies. Data can also be visualized in graphs, charts, and diagrams to make patterns and trends easier to identify. Statistical methods such as correlation and regression can also be used to analyze and interpret raw data. Additionally, data can be combined with other data sets to create new insights and relationships. Finally, machine learning and predictive analytics can be used to make predictions about future outcomes based on existing data.
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Another question I need help with
The expanded form of the given exponential expression -z³ is -(z×z×z).
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given expression is -z³.
Here, -z raised to 3, so multiply -z times itsef
-z³=(-z)×(-z)×(-z)
= -(z×z×z)
Therefore, the expanded form of the given exponential expression -z³ is -(z×z×z).
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Use the Distributive Property to simplify 6x²[(3x - 4) + (4x + 2)]
Answer: 0
Step-by-step explanation:
Simplifying
6x2[(3x + -4) + (4x + 2)] = 0
Reorder the terms:
6x2[(-4 + 3x) + (4x + 2)] = 0
Remove parenthesis around (-4 + 3x)
6x2[-4 + 3x + (4x + 2)] = 0
Reorder the terms:
6x2[-4 + 3x + (2 + 4x)] = 0
Remove parenthesis around (2 + 4x)
6x2[-4 + 3x + 2 + 4x] = 0
Reorder the terms:
6x2[-4 + 2 + 3x + 4x] = 0
Combine like terms: -4 + 2 = -2
6x2[-2 + 3x + 4x] = 0
Combine like terms: 3x + 4x = 7x
6x2[-2 + 7x] = 0
[-2 * 6x2 + 7x * 6x2] = 0
[-12x2 + 42x3] = 0
Solving
-12x2 + 42x3 = 0
Solving for variable 'x'.
Factor out the Greatest Common Factor (GCF), '6x2'.
6x2(-2 + 7x) = 0
Ignore the factor 6.
Please help me, it’s asap
The interquartile range of the given data set is 2.16.
What is median?When a group of values is sorted from smallest to greatest, the median is the number in the middle of the range.
The given set of data,
2.35, 1.56, 1.77, 2.45, 6.92, 4.38, 2.77, 5.23, 2.22, 3.26
To find the interquartile, range of the given data set,
First find median of the set,
Arrange the given date in lowest to highest order,
1.56, 1.77, 2.22, 2.35, 2.45, 2.77, 3.26, 4.38, 5.23, 6.92.
There are 10 terms in the set,
The median will be middle term,
median = (2.45 + 2.77) / 2 = 2.61
The lower half of the set = 1.56, 1.77, 2.22, 2.35, 2.45.
The upper half of the set = 2.77, 3.26, 4.38, 5.23, 6.92.
Here, Q₁ = Middle term of the lower half = 2.22
And Q₂ = Middle term of the upper half = 4.38
The interquartile range = Q₂ - Q₁ = 4.38 - 2.22 = 2.16
The interquartile range of the data set is 2.16
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what was the prices of oranges this week
last week the price of oranges at te farmers market was 1.75 er pound the price was decreased by 20%
The decreased amount of oranges will be equal to $1.4.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the price of oranges at the farmers' market was 1.75 pounds the price was decreased by 20%.
The decreased price of the oranges will be calculated as,
Decreased price = 1.75 x (1 - 0.2)
Decreased price = 1.75 x 0.8
Decreased price = $1.4
The reduced number of oranges will equal $1.4.
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within the third step of the control process, ______ is a principle that states that managers should be informed of a situation only if data show a significant deviation from standards.
Within the third step of the control process, management by exception is a principle that states that managers should be informed of a situation only if data show a significant deviation from standards.
The third step of the process of controlling is to compare the actual performance of the organization with the established standards. By comparing the actual performance with the standards, an organization can determine the deviation between them.
The final step of the control process is the correction of deviations to improve the performance so that in the future it matches with the plan. Establishing standards and methods for measuring performance. Measuring performance. Determine if performance is up to par. take corrective action. The marginal rate of return reduction is set to reduce the factor's marginal rate of return.
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Find the correct expression to solve for z. A. z=8tan22° z = 8 tan 22 ° B. z=tan22°8 z = tan 22 ° 8 C. z=22(tan8) z = 22 ( tan 8 ) D. z=8tan22° z = 8 tan 22 °
Answer:
The correct expression to solve for z is z = 8 tan 22°. This expression uses the tangent function and the angle measure in degrees to find the value of z. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle, and the angle measure must be in degrees in order to use the tangent function. The other answer choices do not use the tangent function or the angle measure in degrees, so they are not correct.
Step-by-step explanation:
Your model train i 18 inche long. It i an exact model of a train that i 72 feet long. A window on the train i how many time wider than a window on the model?At the movie, ticket for a night how cot $9, and ticket for a day how cot $6. 75. What percent i the dicount you get for going to a day how?
The window on the train will be 48 times wider than a window on the model .
In the question ,
it is given that ,
the length of the model train is = 18 inches and
the length of the exact train is = 72 feet ,
on comparison , we need to convert it into inches .
we know that 1 feet is = 12 inches ,
So , 72 feet is = 72×12 inches = 864 inches
So , the length of the original train is = 864/18 = 48 times the model train .
the ratio will remain same for the width of the window .
So , the window on the train is 48 times wider than a window on the model .
Therefore , the window of the train is 48 times wider.
The given question is incomplete , the complete question is
Your model train is 18 inches long. It is an exact model of a train that is 72 feet long. A window on the train is how many time wider than a window on the model ?
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The numbers of trading cards owned by 10 middle-school students are given below.
(Note that these are already ordered from least to greatest.)
361, 408, 414, 417, 498, 505, 519, 520, 530, 548
Send data to calculator
Suppose that the number 361 from this list changes to 401. Answer the following.
(a) What happens to the mean?
(b) What happens to the median?
It decreases by
13. It increases by
It stays the same.
It decreases by
It increases by
It stays the same.
Answer:
a. It increases by 4
b. It stays the same.
what is mean and median? how can be calculate it?Mean is the average of a set of values. It is calculated by adding up all the values in the set and dividing by the number of values in the set.
Median is the middle value of a set of values. It is calculated by arranging all the values from smallest to largest and then finding the middle value in the set. Mean and median are used to measure the center of a set of values. Mean and median are often used to identify trends and patterns in data sets, as they are useful in describing the “average” or “typical” value of a set of data. They are also used in hypothesis testing and various statistical tests.
Formula for mean:
Mean = (Sum of all values) / (Number of values)
Formula for median:
Median = (Middle value of sorted set)
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Melvin plays tennis and swims for a total of 110 minutes every day. He plays tennis for 40 minutes longer than he swims. Part A: Write a pair of linear equations to show the relationship between the number of minutes Melvin plays tennis (x) and the number of minutes he swims (y) every day. Part B: How much time does Melvin spend swimming every day? Show your work. Part C: Is it possible for Melvin to have spent 70 minutes playing tennis if he plays and swims for a total of exactly 110 minutes and plays tennis for 40 minutes longer than he swims? Explain your reasoning.
The answers to all the subparts using equations are shown:
(A) pair of linear equations: y + 40 = x and x + y = 110
(B) 75 minutes every day of swimming.
(C) The given statement is false as a result.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, (A):
Y indicates the volume of swimming
X denotes the quantity of tennis.
Making two equations now:
y + 40 = x
x + y = 110
(B)
X in the other equation is changed to match the first equation.
Please plug this in:
y + 40 + y = 110
2y = 70
35 minutes of swimming equals Y.
Including: 35
35 + 40 = 75 minutes every day of swimming.
(C)
No, given that equation: 70 + (70 - 40) = 100
This statement is false as a result.
Therefore, the answers to all the subparts using equations are shown:
(A) pair of linear equations: y + 40 = x and x + y = 110
(B) 75 minutes every day of swimming.
(C) The given statement is false as a result.
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see attached please thank you
After solving for the angles, the resultant answers are as follows:
(A) ∠L = 55°
(B) ∠LMN = 62°
What are angles?When two consecutive lines or rays intersect at a single endpoint, an angle is created.
The vertex of an angle is the point where two points come together.
The Latin word "angulus," which means "corner," is from which the term "angle" originates.
The intersection of two planes also creates angles.
We refer to these as geometric angles.
So, according to the given diagram:
KMN = LMN + 118
180 = LMN + 118
LMN = 180 - 118
LMN = 62°
Now,
6x - 9 + 4x + 7 + 62 = 180
10x + 60 = 180
10x = 180 - 60
10x = 120
x = 120/10
x = 12
Then,
∠L = 4x + 7
∠L = 4*12 + 7
∠L = 55°
Therefore, after solving for the angles, the resultant answers are as follows:
(A) ∠L = 55°
(B) ∠LMN = 62°
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f(d) = 0.0071d³ - 0.090d² + 0.48d,
where d is the diameter of the diamond.
Find the domain of the function in the
context of the situation. (Lesson 4-1)
A. The domain is all real numbers.
B. The domain is {dl d > 0).
C. The domain is {dl d < 0).
D. The domain is (dld > 0.48).
Evaluate 0.3k-4m k = 20 and m=-2
State the vertex and the axis of symmetry
y = 3(x-5)^2
Answer:
Vertex = (5,0)
Axis of symmetry = x = 5
Explanation:
Y = 3(x-5)^2
Equal 3(x-5) to 0
y = 3 = 0
x-5 = 0
x = 5
Vertex = (5,0)
Formula for Axis of symmetry: x = -b/2a
Write 3(x-5)^2 in standard form
Y = 3x^2 - 30x + 75
x = -b/2a
x = -(-30)/2(3)
x = 30/6
x = 5
find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms.
the sum of all positive rational numbers that are less than 10 and that have a denominator 30 is 400.
What is Rational Number?
Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.
So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that the numerator or denominator doesn't have commonly divisible.
As a small addition, you get 4+12+20+…+76, which is an arithmetic sequence. There are ten terms, so you can use
So the sum will be 10(4+76)/2 = 400
Hence the sum of all positive rational numbers that are less than 10 and that have a denominator 30 is 400.
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28 seconds to 23 seconds
Answer:
5 if your doing subtraction or Percent Change from 28 to 23 ≈ -17.86%
Step-by-step explanation:
Here's a explanation for % of change.
1) Find the difference between 28 and 23 as a number.
2) Divide the result from Step 1 by the starting number 28.
3) Multiply the result from Step 2 by 100 to get it in terms of percent.
I hope this helped.