The perimeter of a triangle is 100cm and the angles are in the ratio: 1:3:5 find the length of each side triangle
Answers
By applying the rule of sin, it can be concluded that the length of the sides of the triangle is 15.48 cm, 39.68 cm, and 44.84 cm.
Triangle is a 2D shape that is bounded by three sides and has three vertices. The perimeter of a triangle is the sum of the lengths of the three sides of the triangle.
Perimeter = a + b + c, where a, b, and c are the sides of the triangle
One of the most important properties of a triangle is that the sum of the angles in a triangle equals 180°.
The rule of sin describes the ratio of the angles corresponding to the side lengths of the sine function.
a / sin A = b / sin B = c / sin C, where A, B, and C are the angles of the triangle
If the ratio of the angles is 1 : 3 : 5 and let x be the smallest angle, then we can put this information into the following equation:
Total angle = A + B + C
180° = x + 3x + 5x
180° = 9x
x = 20°
Then we can calculate the other angles:
A = 20°
B = 3x = 3 * 20° = 60°
C = 5x = 5 * 20° = 100°
Now we put the value of A, B, and C into the rule of sin equation:
a / sin A = b / sin B
a / sin 20° = b / sin 60°
a / 0.34 = b / 0.87
a = 0.34 * b / 0.87
a = 0.39b
c / sin C = b / sin B
c / sin 100° = b / sin 60°
c / 0.98 = b / 0.87
c = 0.98 * b / 0.87
c = 1.13b
Then we go back to the perimeter formula:
perimeter = a + b + c
100 = 0.39b + b + 1.13b
100 = 2.52b
b = 39.68 cm
Then we can calculate the length of the other sides, a and c:
a = 0.39b
= 0.39 * 39.68
= 15.48 cm
c = 1.13b
= 1.13 * 39.68
= 44.84 cm
Thus, the length of the sides of the triangle is 15.48 cm, 39.68 cm, and 44.84 cm.
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Related Questions
Points D, B, and E are collinear. Find the value of x so that points A, B, and C are collinear
Answers
The value of x in the figure is calculated using the linear pair theorem to be 6 degrees
What is linear pair theorem?The linear pair postulate or linear pair theorem in mathematics states that the sum of the measurements of two angles that make up a linear pair is 180°.
Because o the linear pair postulate we have that
150 + 5x = 180
collecting like terms
5x = 180 - 150
5x = 30
Isolating x
5x / 5 = 30 / 5
x = 6
hence x is solved to be 6
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This design began from the construction of a regular hexagon.
Name 2 pairs of congruent figures.
Answers
The true statements regarding the construction are statement 2) and statement 5)
What is construction?"Construction" in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge (i.e. ruler) and a pencil.
Given that, A design began from the construction of a regular hexagon.
The true statements made on the construction is;
2) When JKLO is reflected across segment OJ, JKLO is taken to JIHO. So, quadrilateral JKLO is congruent to quadrilateral JIHO.
5) When JKLO is reflected across segment OL, JKLO is taken to HGLO. So, quadrilateral JKLO is congruent to quadrilateral HGLO.
Hence, The true statements regarding the construction are statement 2) and statement 5)
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Identify the kind of sample that is described.
A football coach randomly selected the varsity or junior varsity team and then asks all players from that team their opinion on a new logo.
A. Stratified
B. Simple Random
C. Voluntary Response
D. Cluster
E. Systematic
Answers
The given sample of the randomly selected players from the teams as described is a stratified sample. Hence, the right answer is option A.
In a stratified sample, the population is divided into groups (or strata) based on some characteristic, and a random sample is selected from each group. In this case, the population is the football players, and the groups are the varsity and junior varsity teams. The coach randomly selects one of these teams and then asks all players from that team their opinion on a new logo.
This type of sampling is used when the population is divided into subgroups that are different in some way, and the researcher wants to ensure that these subgroups are represented in the sample. In this case, the coach wants to ensure that both varsity and junior varsity players are represented in the sample, as they may have different opinions on the new logo.
It's not a simple random sample because he selected the team first and then the players. Also, it's not a voluntary response sample because the coach is selecting the players.
It's not a cluster sample because the coach is not selecting the players based on location or geographic proximity, and it's not a systematic sample because he is not selecting the players based on the order in which they appear in a list or a database.
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Part A What descriptive words, units, and intervals would you choose to label the x-axis and the y-axis?
Answers
Answer:
x on the horizontal axis and y on the vertical axis.
Use the grouping method to factor x^3 + x^2 + 2x + 2.
A. (x + 1)(x + 2)
B. x(x + 2)(x + 1)
C. (x + 1)(x2 + 2)
D. (x^2 + 1)(x + 2)
Answers
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the system using elimination.
5x + 4y = 12
3x - 3y = 18
▸ Math symbols
▸ Relations
▸ Geometry
▸ Groups
▸ Trigonometry
▸ Statistics
Answers
By solving the system using elimination method 5x + 4y = 12 and 3x -3y = 18 we get x = 4 and y = -2.
What is Elimination Method?
To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
Now solving the both equation by using elimination method;
5x +4y = 12 ----------------------------eq(1)
3x - 3y = 18 ----------------------------eq(2)
Multiply equation (1) by 3 and equation (2) by 4, we get;
15x + 12y = 36
12x - 12y = 72
Now, same equation will beb together;
15x + 12y + 12x - 12y = 36 + 72
15x + 12x = 36 + 72
27x = 108
x = 108/27
x = 4
Now, we calculate for the y ;
3x - 3y = 18
3 * 4 - 3y = 18
12 - 3y = 18
12 - 18 = 3y
3y = -6
y = -6/3
y = -2
(x, y) = (4, -2)
So, by solving the system using elimination method 5x + 4y = 12 and 3x -3y = 18 we get x = 4 and y = -2.
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A polling organization contacts 1398 teenagers who are 13 to 17 years of age and live in the United States and asks whether or not they had attended a concert this past year. What is the population in the study? A. Teenagers who are 13 to 17 years of age and have attended a concert. B. Teenagers who are 13 to 17 years of age and live in the United States. C. Teenagers who are 13 to 17 years of age and live in the United States and have attended a concert. D. Teenagers who are 13 to 17 years of age. What is the sample in the study? A. Teenagers who are 13 to 17 years of age and live in the United States. B. The 1398 teenagers who are 13 to 17 years of age and live in the United States. C. Teenagers who are 13 to 17 years of age. D. The 1398 teenagers who are 13 to 17 years of age and have attended a concert.
Answers
The population of the given study in the polling organization contacts is given by :
Option B. Teenagers who are 13 to 17 years of age and live in the United States.
Total number of people attended by the polling organization = 1398
1398 are the teenagers .They are in the age group of 13 to 17 years of age.They all live in the United States .It was asked whether they have attended any concert in the past year.Population is represented by all teenagers of United States in the age group of 13 to 17 years of age.
Those who attended the concert represents the sample of particular category.
Therefore, the population of the required study is given by :
Option B. Teenagers belongs to 13 to 17 years of age and live in the United States .
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Mrs. Flanagan has these cans of soup in her kitchen cabinet: 2 cans of tomato soup, 3 cans of chicken noodle soup, 2 cans of Italian wedding soup, 2 cans of potato soup, & 1 can of split pea soup. If Mrs. Flanagan randomly chooses 1 can of soup, what is the probability she selects chicken noodle soup?
Answers
Answer:
3/10
Step-by-step explanation:
2 cans of tomato soup, 3 cans of chicken noodle soup, 2 cans of Italian wedding soup, 2 cans of potato soup, & 1 can of split pea soup = 10 cans of soup
P( chicken noodle soup) = cans of chicken noodle soup / total cans
= 3/10
A manufacturer of cell phone screens has found that 5 percent of all screens produced have defects. Let pd represent the population proportion of all cell phone screens with a screen defect, therefore pd=0.05. For the sampling distribution of the sample proportion of cell phone screens from this manufacturer with a screen defect for sample size 400, μpˆd=0.05. Which of the following is the best interpretation of μpˆd=0.05 ?For a randomly selected cell phone screen from this population, the mean number of screen defects for the selected screen will be equal to 0.05.A For a randomly selected cell phone screen from this population, the mean number of screen defects for the selected screen will be equal to 0.05.B For every sample of size 400 from this population, the proportion of cell phone screens with a screen defect will be 0.05.C For every sample of size 400 from this population, the proportion of cell phone screens with a screen defect will be 0.05.D For all samples of size 400 from this population, the mean number of screen defects for the samples is 0.05.F For all samples of size 400 from this population, the mean number of screen defects for the samples is 0.05.G For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.H For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.I For all samples of size 400 from this population, the standard deviation of all resulting sample proportions of cell phone screens with a screen defect is 0.05.
Answers
Using the Central Limit Theorem, it is found that the correct option is: C
For all samples of size 400 from this population, the mean of all resulting sample proportions of cell phone screens with a screen defect is 0.05.
By the Central Limit Theorem, for a proportion p in a sample of size n, the mean of the sampling distribution of sample proportions is u=5, while the standard error is [tex]SE=\sqrt{\frac{p*(1-p)}{n} }[/tex]
In this problem, the mean of the sampling distribution of sample proportions is 0.05, that is, the mean proportion of all samples, hence, the correct option is C.
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1. 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why
2. The name of each contestant is written on a separate card, the cards are placed in a bag, and three names are picked from the bag. Identify which type of sampling is used and why
3. An education expert is researching teaching methods and wishes to interview teachers from a particular school district. She randomly selects ten schools from the district and interviews all of the teachers at the selected schools. Does this sampling plan result in a random sample? Simple random sample? Explain.
4. A polling company obtains an alphabetical list of names of voters in a precinct. They select every 20th person from the list until a sample of 100 is obtained. They then call these 100 people. Does this sampling plan result in a random sample? Simple random sample? Explain.
5. The personnel manager at a company wants to investigate job satisfaction among the female employees. One evening after a meeting she talks to all 30 female employees who attended the meeting. Does this sampling plan result in a random sample? Simple random sample? Explain.
Case Assignment Expectations:
Use information from the modular background readings as well as any good quality resource you can find. Please cite all sources and provide a reference list at the end of your paper.
The following items will be assessed in particular:
Your ability to identify situations when sampling is appropriate.
Your ability to draw the proper inferences about the population after the sample has been evaluated.
Your ability to describe the process of selecting and evaluating a samp
Answers
the ability to identify situations when sampling is appropriate and to draw the proper inferences about the population after the sample has been evaluated. The answer describes the process of selecting and evaluating a sample, including examples of stratified, random, and systematic sampling. It also discusses the limitations of not using a random sample in order to obtain unbiased results.
1. This is an example of stratified sampling, since the students are divided into three groups (Sophomores, Juniors, and Seniors) and a sample is taken from each group. This allows for a more representative sample of the overall population.
2. This is an example of random sampling, since each name has an equal chance of being selected from the bag. This ensures that the sample is unbiased and allows for a fair representation of the population.
3. This sampling plan results in a random sample, since the schools were randomly selected from the district. A random sample ensures that every member of the population has an equal chance of being selected.
4. This sampling plan results in a systematic sample, since the polling company selected every 20th person from the list. Systematic sampling allows for a more representative sample of the population, since it ensures that each person in the population is equally likely to be selected.
5. This sampling plan does not result in a random sample, since only the female employees who attended the meeting were selected. This means that those who did not attend the meeting had no chance of being selected in the sample, thus biasing the results.
This answer demonstrates the ability to identify situations when sampling is appropriate and to draw the proper inferences about the population after the sample has been evaluated. The answer describes the process of selecting and evaluating a sample, including examples of stratified, random, and systematic sampling. It also discusses the limitations of not using a random sample in order to obtain unbiased results.
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a student drove to the university from her home and noted that the odometer reading of her car increased by 8.00 miles. the trip took 20 min. (note: 1 mile
Answers
Vector of the average velocity = 3.33 km\hr towards the south.
Distance covered by the student=7miles 7*6 = 42km
Total displacement = 10km in the south.
Total time is taken = 20mins 20/60=0.33hr
Note:
Odometer reading is the distance covered while straight-line distance is the displacement which is the shortest route
Distance is a scaler where as displacement is a vector quantity.
Scaler has only magnitude while vector has magnitude and direction.
We have to find the average velocity.
Average velocity = Ratio of total displacement and total time.
⇒ Average velocity (v) = displacement/time.
⇒ Plugging the values.
⇒ (v) = 10/0.33
⇒ (v) =3.33 km\hr
So the vector of the average velocity = 3.33 km\hr towards the south.
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jake has 16 toy cars. lydia has five fewer toy cars than jake. how many toy cars do they have in all?
Answers
16+11=27 toy cars
7.) +9 – +16 = N
8.) +85 – +12 = N
9.) –6 –2 = N
10.) +13 – +12 = N SOMEONE PLEASE ANSWER
Answers
Answer:
here are the answers to the questions in order
Step-by-step explanation:
7. -7
8. 73
9. -8
10. 1
-6z - 18z + 2z + 6z = 16
nvm don't answer
Answers
The value of z in the given linear equation in one variable is -1.
What is a single-variable linear equation?By equating it to zero, a linear polynomial over a field, from which the coefficients are extracted, can be converted into a linear equation.
The values that, when employed as stand-ins for the unknowns in such an equation, lead to the equality being true are the solutions.
When there is just one variable, there is just one solution. The term "linear equation" is generally understood to relate to this particular circumstance, when the variable is accurately referred to as the "unknown."
It is possible to interpret each solution as the Cartesian coordinates of a specific point on the Euclidean plane when there are only two variables.
-6z -18z + 2z +6z = 16
-16z = 16
z = -1
Hence, the value of z is -1
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you win the lottery and get 1000000. the bank you invest your winnings in gives you a 6% interest rate compounded quaterly. how much will you have in 3 years ?
Answers
The amount that you will have in 3 years, given the interest rate and the amount won, is 1, 195, 618. 17 currency units
How to find the amount earned ?To find the amount earned in three years as a result of your lottery being invested, use the future value formula which is:
= Amount won x ( 1 + periodic rate ) ^ number of periods
Periodic rate :
= 6 % / 4 quarters per year
= 1. 5 %
The number of periods is:
= 3 years x 4 quarters per year
= 12 quarters
The amount you will have in 3 years is:
= 1,000,000 x ( 1 + 1. 5 %) ¹²
= 1, 195, 618. 17 currency units
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HELP PLEASE FAST i'm not understanding how to do this (i'll give brainiest to whoever has best answer) The bar below is 7 inches long and divided into 2 equal parts. What is the length of one of those parts? Fill in the blanks in the equation using fractions or mixed numbers to show the length of one of the parts. X 7 inches = inches
Answers
The length of each bar is given as follows:
3.5 inches.
As a mixed number, the length of each bar is given as follows:
3 and 1/2 inches.
How to obtain the length of each bar?The length of each bar is obtained applying the proportions in the context of this problem.
The bar that is 7 inches long is divided into two equal parts, hence the length of each part is given as follows:
7/2 = 3.5 inches.
The fraction equivalent to a decimal of 0.5 is given as follows:
1/2.
(which is used to construct the mixed number).
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Marty buys 12 ounces of granola what fraction of a pound of granola did Marty buy? Please help
Answers
The fraction of a pound of granola Marty buys is 3/4.
What is a fraction?A fraction is a part of a whole number, value, and variable.
There are proper and improper fractions, including complex fractions.
Proper fractions are those with the numerator less than the denominator. An improper fraction produces a whole number with a remainder when the denominator divides the numerator.
On the other hand, complex fractions are rational expressions that have some fractions in their numerators, denominators, or both.
1 pound = 16 ounces
The quantity of granola Marty buys = 12 ounces
The fraction of a pound of granola Marty buys = 3/4 (12/16)
Thus, we can conclude that Marty buys 3/4 or 75% of a pound of granola.
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use dynkin's theorem to prove that the infinite product measure is uniquely defined on the product measure space
Answers
The infinite product measure [tex]$\mu$\\[/tex] is uniquely defined on the product measure space[tex]$(\Omega, \mathcal{A}, \mu)$[/tex] by Dynkin's theorem, since [tex]$\mu$\\[/tex] is finitely additive, countably subadditive, and [tex]$\sigma$[/tex]-finite.
Let [tex]$\mathcal{A}_1, \mathcal{A}_2, \ldots$[/tex] be a sequence of sigma algebras defined on [tex]$\Omega_1, \Omega_2, \ldots$[/tex] respectively. Let [tex]$(\Omega, \mathcal{A}, \mu)$[/tex] be the product measure space, where [tex]\Omega = \prod_{i=1}^{\infty} \Omega_i$ and $\mathcal{A} = \bigotimes_{i=1}^{\infty} \mathcal{A}_i$[/tex].
We want to prove that the infinite product measure [tex]$\mu$[/tex] is uniquely defined. To do this, we will use Dynkin's theorem.
According to Dynkin's theorem, a measure [tex]$\mu$[/tex] is uniquely determined on a product measure space [tex]$(\Omega, \mathcal{A}, \mu)$[/tex] if the following conditions are satisfied:
1. [tex]$\mu$[/tex] is finitely additive on [tex]$\mathcal{A}$[/tex]
2. [tex]$\mu$[/tex] is countably subadditive on [tex]$\mathcal{A}$[/tex]
3. [tex]$\mu$[/tex] is [tex]$\sigma$[/tex]-finite on [tex]$\mathcal{A}$[/tex]
It is easy to see that the infinite product measure [tex]$\mu$[/tex]satisfies these conditions, since it is defined as a product of finitely additive, countably subadditive, and [tex]$\sigma$[/tex]-finite measures. Thus, by Dynkin's theorem,[tex]$\mu$[/tex] is uniquely determined on the product measure space [tex](\Omega, \mathcal{A}, \mu)$.[/tex]
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For groups of 80 or more people, a charter bus company determines the rate r (in dollars per person) according to the formula
r = 8 − 0.05(n − 80), n ≥ 80
where n is the number of people.
(a) Express the revenue R for the bus company as a function of n.
(b) Complete the table.
(c) Criticize the formula for the rate. Would you use this formula? Explain your reasoning.
Answers
The formula for rate given is not ideal, as it does not take into account factors like the distance traveled or additional services offered by the bus company. It also does not account for additional fees or taxes. Therefore, it does not provide an accurate representation of the price and should not be used.
(a) R(n) = r(n) * n = (8 − 0.05(n − 80)) * n
(b)
n r (dollars per person) R (dollars)
80 8 640
90 7.5 675
100 7 700
(c) This formula for the rate is not ideal, as it does not take into account factors like the distance traveled or any additional services that the bus company may offer. It also does not account for any additional fees or taxes. I would not use this formula, as it does not provide an accurate representation of the price the bus company should charge for its services.
The formula for rate given is not ideal, as it does not take into account factors like the distance traveled or additional services offered by the bus company. It also does not account for additional fees or taxes. Therefore, it does not provide an accurate representation of the price and should not be used.
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PLEASE HELP I WILL GIVE YOU BRAINLIEST AND 10 POINTS!! SHOW WORK PLS
Answers
Equate the slopes of the opposite lines with (x,y) as the coordinates of the missing vertex.
How to find vertex of a parallelogram?
we know that in parallelogram, opposite sides are parallel and are of equal lengths. So, we can say that line joining vertices ( 5, -2 ) and ( 6, 2 ) and line joining vertices ( x, y ) and ( 0, 2 ) will be parallel, that is line AB and DC will be parallel and equal to each other in length.We know that interior angles on the same side of a transversal are supplementary. Similarly, ∠B + ∠C = 180°, ∠C + ∠D = 180° and ∠A + ∠B = 180°. Therefore, the sum of any two adjacent angles of a parallelogram is equal to 180°.The distance formula enables us to calculate the distance between two points on a coordinate grid. If those points have coordinates one, one and two, two, then the distance between them is the square root of two minus one all squared plus two minus one all squared.To learn more about parallelogram refers to:
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Equate the slopes of the opposite lines with (x,y) as the coordinates of the missing vertex.
How to find vertex of a parallelogram?We are aware that a parallelogram has two opposed sides that are equally long and parallel. As a result, we may infer that the lines connecting the vertices (5, -2) and (6, 2) as well as the lines connecting the vertices (x, y) and (0, 2) will be parallel, making lines AB and DC parallel and of identical length. Interior angles on the same side of a transversal are understood to be supplementary. Similarly, B + C, C + D, and A + B all add up to 180 degrees. As a result, the sum of any two adjacent parallelogram angles equals 180°.The distance formula enables us to calculate the distance between two points on a coordinate grid. If those points have coordinates one, one and two, two, then the distance between them is the square root of two minus one all squared plus two minus one all squared.To learn more about parallelogram refers to:
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Which of the following refers to the type of statistical methods used to draw conclusions about the population based on a sample?
Population methods
Sampling methods
Descriptive statistics
Inferential statistics
Answers
The type of statistical methods used to draw conclusions about the population based on a sample is called inferential statistic.
Statistical inference refers to the process of generating inferences about a population from a sample or subset of the data. The goal of inferential statistics is to extrapolate from sample data to the population as a whole by comparing the parameters of multiple samples. Two major categories of inferential statistics use distinct strategies to extrapolate information from samples of the population. These are regression analysis and hypothesis testing. Inferential statistics, including hypothesis testing, examines sample data to draw conclusions about the whole population. It entails establishing a null hypothesis and an alternative hypothesis, then doing a statistical test of significance to determine which one is more likely to be correct. The impact of one variable on another can be measured with the use of regression analysis.
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Explica que procedimiento se tiene que hacer primero para hallar la solución de la expresión: 8 - 6 ÷ 3 x 7 + 2
Answers
Answer:
dividir
Step-by-step explanation:
PEMDAS
you must Divide first, since its's left most
the possible answers in the question mark are half or twice or eight times for both of the question marks. ASAP I NEED HELP
Answers
The size of each group will be half as big.
There will be twice as many groups.
How to divide fractions?We want to find out what is going to happen if we divide by 8/4 instead of 4/5.
The total of the tape diagram is 3¹/₅ = 16/5 and as such if we are going to divide by 4/5 we will have;
16/5 ÷ 4/5 = 4
However if we are dividing by 8/5, it means that the solution is;
16/5 ÷ 8/5 = 2
Thus, the solution will be half as big.
There will be twice as many groups.
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Now Jimmy wants to save money to buy concert tickets, so he draws up a new savings plan. Each week, he will raise $3 to the number of weeks he has been working and add that amount to his savings during the first 3 weeks of his new job. Use summation notation to write the sum and find the total amount he will save.
Answers
a) Using the summation notation to write the sum is 3∑n=1 3n.
b) The total amount that Jummy will save during the first 3 weeks of his new job is $18.
What is the summation notation?The summation notation is the representation of a series in a compact form, using the capital sigma symbol (Σ) to indicate the sum of a number of similar terms.
Using the summation notation, one can write a long sum in a single expression.
In this situation, the expression can be read as the sum of 3n as n goes from week 1 to week 3, representing the first three weeks Jimmy will spend on the job.
3∑n=1 3n
= 3 x 1 + 3 x 2 + 3 x 3
= 3 + 6 + 9
= 18
Thus, we have used the summation notation to find that Jimmy will save $18 during the first three weeks at his new job.
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Answer:
Step-by-step explanation:
Let m = 3.
Enter >, <, or = to compare the expressions.
4m−145m−4
Answers
Answer:
=
Step-by-step explanation: Please mark brainliest
Substitute 3 in for m and solve
4m - 1 = 4(3) - 1 = 11
5m - 4 = 5(3) - 4 = 11
Answer:
Step-by-step explanation:
P&R3 model and solve
problems using linear
equations of the form:
ax = b *
x
a
= b, a ≠ 0*
ax + b = c *
x
a
+ b = c ,a ≠ 0*
a x( ) + b = c *
ax + b = cx + d *
* a bx ( ) + c = d ex ( ) + f
*where a, b, c, d, e, and f [C,
CN, PS, V]
1. Introduction to Solving Linear Equations (pg. 4-7)
• Model the solution of a given linear equation using concrete or
pictorial representations, and record the process.
Algebra stones and Algebra Tiles.
Solve x + 5 = 10 , x − 7 = 10 , 2x = 10 , x
3 = 10
2. Solving equations of the form ax+b=c and a/c +b=c (pg. 8-10)
• Solve a given linear equation symbolically.
• Solve a given problem using a linear equation and record the
process.
Solve. 4m+3=31 & 2
5
m − 5 = 3
3. Solving equations of the form a(x+b)=c and ax+b=cx+d(pg. 11-14)
• Determine, by substitution, whether a given rational number is a
solution to a given linear equation.
Solve. 4(m+3)=40 & 6m+3=2m+15
Is m=5 a solution to the equation 2(m + 2) = 14 ?
4. More practice with ax+b=cx+d (Pg. 15-18)
• Identify and correct an error in a given incorrect solution of a
linear equation
Solve. 2(m+1)+4m=4(m-2)+6.
5. Solve equation with fractions. (Pg. 19-23)
• Solve a given linear equation symbolically. Solve m
3 + 2m
5 − 1
2
= 2
6. Solve Linear equations without numbers. (Pg. 24-28)
• Solve a given linear equation symbolically.
Solve for m. )( =+ BnmA
P&R4 explain and illustrate
strategies to solve single
variable linear inequalities with
rational coefficients
within a problem-solving
context.
7. Introduction to linear inequalities (Pg. 29-33)
• Translate a given problem into a single variable linear inequality
using the symbols ≥, >, < , or ≤ .
• Determine if a given rational number is a possible solution of a
given linear inequality.
Write an expression to represent the following
statement: Melanie needs at least $280 for snow
boarding.
8. Inequalities that Include Addition and Subtraction (Pg. 34-37)
• Generalize and apply a rule for subtracting a positive or
negative number to determine the solution of a given inequality.
• Generalize and apply a rule for multiplying or dividing by a
positive or negative number to determine the solution of a given
inequality.
• Solve a given linear inequality algebraically and explain the
process orally or in written form.
• Verify the solution of a given linear inequality using
substitution for multiple elements in the solution.
Solve 2x + 5 < 25 and verify your solution.
True or False.
If −2x > −10 then x > 5 .
9. Solving Problems with Linear Inequalities (Pg. 38-41)
• Compare and explain the process for solving a given linear
equation to the process for solving a given linear inequality.
• Graph the solution of a given linear inequality on a number line.
• Compare and explain the solution of a given linear equation to
the solution of a given linear inequality.
• Solve a given problem involving a single variable linear
inequality and graph the solution.
Vertical Wireless charges $50/ month plus $0.25 for
all minutes above 400 minutes per month. Frue Gal has
decided that she does not want to pay more than $70
per month. Write an inequality to represent how many
minutes she can use per month without going over her
$70 limit. Approximate your solution on the number
line
10. Chapter Review and Practice Test
• Help students develop sound study habits.
• Many students will graduate high school saying they do not
know how to study for math tests.
11. Go over Practice Test
12. Unit Evaluation
The average distance between the Sun and Neptune is 4450 x 100 km. Express this distance in AU
with two significant figures.
Answers
The distance 4450× 10⁶ km between the Neptune and the sun in AU is 29.75 AU
What is Astronomical unit?The astronomical unit is a unit of length, roughly the distance from Earth to the Sun and approximately equal to 150 million kilometres or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum to a minimum and back again once each year.
An astronomical unit is the average distance between the Earth and the Sun. Estimates of this distance have varied over time. It is now defined as exactly 149,597,870.7 kilometers.
if 149,597,870.7 kilometers = 1 AU
then 4450× 10⁶ km = 4450× 10⁶ ÷149,597,870.7
= 29.75 AU
Thefore the distance between the sun and neptune is 29.75 AU
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a 24/7 calling center works as follows: every agent works 5 days in a row and has two days rest, e.g., every week works tuesday-saturday and rests on sunday and monday. the numbers of agents working every day of a week should be at least given numbers d1; :::; d7. the manager wants to meet this requirement with the minimal possible total number of agents employed, by deciding what will be the days o of the agents. assuming that di are large, so that we can ignore integrality restrictions, formulate manager's problem as an lo program.
Answers
A call center required the number of agents is equal to 18.
One of the most frequent themes in quantitative aptitude that is tested in government exams is time and work. One of the subjects that candidates are knowledgeable about even before they begin preparing for competitive exams.
The idea of time and effort is still the same, but there may be some variation in the questions that are posed. The majority of the questions on this topic are 1-2 word problems, but candidates should also be ready for questions about data sufficiency and data interpretation that may come up over the course of their work.
A 24/7 calling center works as follows: every agent works 5 days in a row and has two days rest, e.g., every week works Tuesday Saturday and rests on Sunday and Monday.
total working day of call center = 7
agent's working day =5
so, required the minimal number of agents-
[tex]=\frac{7!}{2!.5!}\\\\=\frac{35}{2}\\\\= 17.5 = 18[/tex]
So, at least required number of agents = 18.
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Which statement best describes a graph of paired points that form a proportional relationship? Responses A straight line can be drawn through all the points, and the line passes through the point (3, 0). A straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 3 comma 0 end ordered pair, . A straight line can be drawn through all the points, and the line passes through the point (0, 3). A straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 0 comma 3 end ordered pair, . A straight line can be drawn through all the points, and the line passes through the point (0, 0). A straight line can be drawn through all the points, and the line passes through the point , begin ordered pair 0 comma 0 end ordered pair, . A straight line cannot be drawn through all the points, but the line passes through the point (0, 0).
Answers
The proportional relationship is given by the equations -
y = mx or y = kx or y = mx + b or y = kx + b.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the statements describing proportional relationship.
Direct variation of {y} with {x} means that as {x} increases, the value of {y} increases uniformly with it. Mathematically →{K} = y/x = constant.
Scale factor {K} is a dimensionless value that indicates the constant ratio value indicating direct variation.The proportional relationship is given by the equation -y = mx or y = kx or y = mx + b or y = kx + b
Therefore, the proportional relationship is given by the equations -
y = mx or y = kx or y = mx + b or y = kx + b.
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Write an equation to match this graph.
Answers
The equation for the line is y=x+7.
What is a linear equation's solution?The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation.
In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.
Given, the line's points are (2,9), (3,10), (4,11), and (5,12). (6,13)
Assuming that the line's equation is y=x+7, adding the points to the equation results in
(2,9) 9=2+7
(3,10) 10=3+7
The equation is also valid for every point on the graph.
Hence, The line's equation is y=x+7.
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Complete Question -
The integral with respect to time of a force applied to an object is a measure called impulse, and the impulse applied to an object during a time interval determines its change in momentum during the time interval. The safety of a t-shirt launcher, used to help get crowds cheering at baseball games, is being evaluated. As a first step in the evaluation, engineers consider the design momentum of the launched t-shirts. The springs in the launcher are designed to apply a variable force to a t-shirt over a time interval of tL=0.5s. The force as a function of time is given by F(t)=at2+b, where a=−28N/s2 and b=7.0N. The momentum of the t-shirt will be its initial momentum (p0=0) plus its change in momentum due to the applied impulse: pf=p0+∫t=tLt=0F(t)dt. By applying the given time dependent function for F(t) and performing the integration, which of the following is the correct expression for pf?
Answers
The impulse equation is given by pf = p0 + ∫tL₀F(t)dt. With the given information, the integral is ∫tL₀(-28t² + 7.0)dt.
This integral can be solved using the power rule for integration, which states that the integral of xⁿ is xⁿ⁺¹/(n+1). Thus, the integral of -28t² + 7.0 is -28/3t³ + 7t. This can be evaluated from t=0 to t=0.5 to get the change in momentum due to the applied impulse. Substituting the values into the impulse equation, pf = 0 + (-28/3(0.5)³ + 7(0.5)) = -2.167. Thus, the correct expression for pf is pf = -2.167.
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