[tex]\bold{n + (n+1)^{2}}[/tex]
Step by step explanation:An unknown number can be interpreted with any letter of the alphabet, they will be our unknowns to be able to form an algebraic expression.
Well, in this case, I will use the variable n, to name the unknown number.
Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.
(grouping the data the following algebraic expression is obtained):
[tex]\bold{n + (n+1)^{2}}[/tex]
Answer:
(n + 1 )
Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.
..
During the past year, Mrs. Singh purchased 29 books at a wholesale club store. She purchased softcover books for $3.50 each and hardcover books for $11.50
each. The total cost of the books was $205.50. How many of each type of book did she purchase?
Part 1 of 2
Mrs. Singh purchased (blank) softcover books
Part 2 of 2
Mrs. Singh purchased (blank) hardcover books.
Answer:
Step-by-step explanation:
Let's assume the number of soft-cover books Mrs. singh purchased as y.
let's assume the number of hard-cover books Mrs. singh purchased as x.
Total number of books purchased = 29 (given)
i.e. (hardcover books) + (softcover books) = 29
x + y = 29 ........................(i)
Total amount spent on books = Rs.205.50
i.e. (cost of hardcover books) + (cost of softcover books) = 205.50
(price * no. of hardcover books) + (price * no. of softcover books) = 205.50
(11.50*x) + (3.50*y) = 205.50 ......................(ii)
from eq(i),
we find x,
x = 29-y
putting the value of x in eq(ii),
(29-y)11.50 + 3.50y = 205.50
333.50 - 11.50y + 3.50y = 205.50
8y = 128
y = 16
so, x = 29 - 16 = 13
Therefore, the number of soft cover books purchased by Mrs. Singh is 16 and the number of hardcover books purchased by Mrs. Singh is 13.
Given the following probabilities for choosing 2 marbles from a bag of 10 marbles, determine if the events are dependent or independent.
P(blue) = 3/10 , P(green) = 1/5 , and P(blue and green) = 3/100
probabilities for choosing 2 marbles from a bag of 10 marbles is Dependent events
Given the following probabilities for choosing 2 marbles from a bag of 10 marbles are:-
P(blue) = 3/10, P(green) = 1/5, P(blue and green) = 3/100
We know the fact that two event are independents if we have following:-
P(X and Y) = P(X) times P(Y)
For this problem, we must have P(blue and green) = P(blue) times P(green).
P(blue and green) = (3/10) * (1/5) = 3/50
But given P(blue and green) = 3/100
Since we have 3/100 ≠ 3/50
Hence, the events are not independent events.
So, they are dependent events.
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The number N of locations of a popular coffeehouse chain is given in the table. (The numbers of locations as of October 1 are given.)(a) Find the average rate of growth between each pair of years.(b) Estimate the instantaneous rate of growth in 2006 by taking the average of the last two rates of change in part (a). locations/year(c) Estimate the instantaneous rate of growth in 2006 by measuring the slope of the tangent line through(2005, 10236) and (2007, 15005).locations/year(d) Estimate the instantaneous rate of growth in 2007 by measuring the slope of the tangent line through(2006, 12441) and (2008, 16683). locations/yearCompare the growth rates you obtained in part (c) and (d). What can you conclude?The rate of growth is constant.There is not enough information. The rate of growth is increasing.The rate of growth is decreasing.
The average rate of growth between each pair of years was calculated in part (a). The instantaneous rate of growth for 2006 was estimated in part (b) and (c), and the instantaneous rate of growth for 2007 was estimated in part (d). Comparing the growth rates from parts (c) and (d), it can be concluded that the rate of growth is constant.
In part (a), the average rate of growth between each pair of years was calculated by dividing the difference between the number of locations in two consecutive years by the number of years between them. For example, to find the average rate of growth between 2005 and 2006, the difference in the number of locations (12441-10236) was divided by the number of years (1). The result was 22.05 locations/year. In part (b), the instantaneous rate of growth in 2006 was estimated by taking the average of the last two rates of change from part (a). This was done by adding the rates of growth from 2005 to 2006 (22.05 locations/year) and 2006 to 2007 (27.64 locations/year) and then dividing by two. The result was 24.85 locations/year. In part (c), the instantaneous rate of growth in 2006 was estimated by measuring the slope of the tangent line through (2005, 10236) and (2007, 15005). This was done by finding the difference in the number of locations (15005-10236) and dividing by the number of years (2). The result was 22.85 locations/year. In part (d), the instantaneous rate of growth in 2007 was estimated by measuring the slope of the tangent line through (2006, 12441) and (2008, 16683). This was done by finding the difference in the number of locations (16683-12441) and dividing by the number of years (2). The result was 22.21 locations/year. Comparing the growth rates from parts (c) and (d), it can be concluded that the rate of growth is constant.
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Sandy used a virtual coin toss app to show the results of flipping a coin 50 times, 400 times, and 2,000 times. Explain what most likely happened in Sandy's experiment.
A. Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
B. Sandy's experimental probability was closest to the theoretical probability in the experiment with 400 flips.
C. Sandy's experimental probability was closest to the theoretical probability in the experiment with 50 flips.
D. Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The correct option regarding the probabilities for Sandy's is given as follows:
A. Sandy's experimental probability was closest to the theoretical probability in the experiment with 2,000 flips.
How to obtain the probability?A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.
For the theoretical probability, the outcomes are considering without any experiment, while for an experimental probability the outcomes are taken from previous experiment.
This means that for a large number of trials, these probabilities should be very close, meaning that the correct option is given by option A.
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Its A...............
Step-by-step explanation:
The GDP in Canada is $1.65 trillion. The rate of
inflation is 2.5%. If the population of Canada is
36,732,000, find the per capita GDP in this country.
per capita GDP = $ [?]
Round to the nearest hundredth.
Enter
PH
The per capita GDP can be calculated by dividing the total GDP by the population.
How is this calculated?$1.65 trillion (GDP) / 36,732,000 (population) = $45,073.58 (per capita GDP)
This means that, on average, each person in Canada has a GDP of $45,073.58. However, it's important to note that this number doesn't necessarily reflect the distribution of wealth within the country. It's just a way of measuring the overall economic output of a country on a per person basis.
Additionally, it's worth noting that this number only takes into account the GDP and population at the time of the calculation. The inflation rate of 2.5% would increase the GDP but not the population so it's not considered in this calculation
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the gini coefficients for countries a and b are 0.25 and 0.30, respectively. we can definitely conclude that group of answer choices none of the above the lowest 20 percent family income group receives a greater share of total income in country a than in country b. the lowest 50 percent family income groups in a and b receive 25 percent and 30 percent of total income, respectively. the lowest 20 percent family income group receives a greater share of total income in country b than in country a. the lowest 20 percent family income groups in a and b receive 25 percent and 30 percent of total income, respectively.
The Gini coefficients for countries A and B are 0.25 and 0.30, respectively. This situation is justified by the option E: None of the above.
What is Gini coefficient?
The Gini coefficient, commonly referred to as the Gini index or Gini ratio, is a measure of demographic distribution used in economics to estimate the average income of a population. The most often used method for estimating inequality is the Gini coefficient.
The Italian statistician and sociologist Corrado Gini is honoured as the creator of the Gini Coefficient.
If everyone has the same wealth or income, then a Gini coefficient of 0 implies complete equality, whereas a value of 1 indicates perfect inequality (that is, where one person owns all the wealth in a country).
For most nations, the value actually ranges between 0 and 1. It would be close to 1 in nations with significant levels of inequality.
The options are -
The lowest 20 percent family income groups in A and B receive 25 percent and 30 percent of total income, respectively.
The lowest 50 percent family income groups in A and B receive 25 percent and 30 percent of total income, respectively.
The lowest 20 percent family income group receives a greater share of total income in country A than in country B.
The lowest 20 percent family income group receives a greater share of total income in country B than in country A.
These all are incorrect as for country A, 0.25 Gini coefficient means that the 25% of the country's population has all the wealth and for country B, 0.30 Gini coefficient means that the 30% of the country's population has all the wealth.
Therefore, none of the options justify the answer.
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The Gini coefficients for countries A and B are 0.25 and 0.30, respectively. We can definitely conclude that
a) the lowest 20 percent family income groups in A and B receive 25 percent and 30 percent of total income, respectively.
b) the lowest 50 percent family income groups in A and B receive 25 percent and 30 percent of total income, respectively.
c) the lowest 20 percent family income group receives a greater share of total income in country A than in country B.
d) the lowest 20 percent family income group receives a greater share of total income in country B than in country A.
e) none of the above
The sales for products sold at an electronic store are below. What percent of the products sold were speakers?
1 point
Captionless Image
The percentage of speakers that were sold is equal to 24%.
How to calculate the percent of speakers sold?First of all, we would determine the total number of products that were sold by this electronic store. From the information provided in the table shown in the image attached below, we can logically deduce the following sales for products sold at an electronic store;
Product Unit sold
Cables 180
Computers 1,180
Televisions 540
Speakers 600
Total number of products = 180 + 1,180 + 540 + 600
Total number of products = 2,500
Now, we can calculate the percentage of speakers that were sold:
Percentage of speakers = 600/2500 × 100
Percentage of speakers = 0.24 × 100
Percentage of speakers = 24%.
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PLS HELP -
transponder for a toll bridge costs $22.50. With the transponder, the toll is $4 each time you cross the bridge. The only other option is toll-by-plate, for which the toll is $5.25 each time you cross the bridge with an additional administrative fee of $1.25 for each crossing. How many times would you need to cross the bridge for the costs of the two toll options to be the same?
You need to cross the bride _ times?
Using linear function you would need to cross the bridge 30 times for the costs of the two toll options to be the same.
What is meant by linear function ?To find out how many times you would need to cross the bridge for the costs of the two toll options to be the same, we need to set up an equation.Let x be the number of times you need to cross the bridge.For the transponder option: 22.50 + 4x = costFor the toll-by-plate option: 5.25x + 1.25x = costSince the costs of the two options need to be equal, we can set the two equations equal to each other and solve for x:22.50 + 4x = 5.25x + 1.25x + 22.504x = 5.25x + 1.25x0.75x = 22.50x = 30So you would need to cross the bridge 30 times for the costs of the two toll options to be the same.To learn more about linear function refer:
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Felipe has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
The number of different votes that are possible are = 120
What is permutation?Permutation is defined as the expression that shows the number of ways a data can be arranged.
The permutation of the the list of 5 bands will determine the number of different votes that are possible which is as follows:
5!= 5×4×3×2×1 = 120
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The dimensions of square A are three times the dimensions of square B. The area of square B is 256 cm2.
What is the area of square A?
A. 2,432 cm squared
B. 768 cm squared
C. 2,304 cm squared
D. 64 cm squared
The area of the square A would be calculated for the area of the given square B which would be = 768cm². That is option B.
What is a square?A square is defined as the quadrilateral that has equal four sides with a total of four equal 90° angles.
The dimensions of square A = 3× dimensions of square B
The given area for B = 256 cm2
Area of A = 3× 256
= 768cm²
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) draw a chord that goes between points a and b. 2) identify how many points along the curve have a tangent line parallel to the chord through . watch for rules about when there are and aren't tangent lines to the curve.
There are no points along the curve that have a tangent line parallel to the chord through A and B.
1) The chord between points A and B is a straight line connecting those two points.
2) There are no points along the curve that have a tangent line parallel to the chord through A and B, since the chord is a straight line and the curve is curved.
1) To draw the chord between points A and B, you must use a straight line to connect those two points.
2) Since the chord is a straight line and the curve is curved, there are no points along the curve that have a tangent line parallel to the chord through A and B.
To draw the chord between points A and B, draw a straight line connecting those two points. However, since the chord is a straight line and the curve is curved, there are no points along the curve that have a tangent line parallel to this chord. This is due to the fact that tangent lines only exist at points where the curve changes direction, and the chord is a straight line, not affected by the curvature of the curve. Therefore, there are no points along the curve that have a tangent line parallel to the chord through A and B.
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Dr. Rasp selects four students at random from the students in STAT 301. What is the probability that at least two of the students were born on the same day of the week? [HINT: it’s easier to begin with the probability that they all four were born on different days. Why?]
The answer is 0.650, but I don`t understand how this number was gotten
The probability that at least two of the students were born on the same day of the week is 0.6501.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Total students = 4
So, Total number of possible outcomes = 7 x 7 x 7 x 7
Number of ways of choosing 4 from 7 = C(7, 4) = 35
So, number of outcomes in which no day is repeated
= 4! x 35 = 840
P(girls all born on different days) = 840/(2401) = 0.3498
P(at least two born on same day) = 1 - 0.3498
= 0.6501
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Choose 1 answer:
A
B
C
D
-7≤ x ≤7
The x-values -7, -2, 5, and 7
0≤x≤7
The x-values 0, 2, 4, 5, and 7
the domain of the function 0≤x≤7.
What is the domain and range of function?
A function's domain and range are its components. A function's range is its potential output; its domain is the set of all conceivable input values. Domain, Function, and Range. If a function f: A B exists that maps every element in A to an element in B, then A is the domain and B is the co-domain. The image of an element 'a' under a relation R is provided by 'b,' where (a,b) R. The set of photographs makes up the function's range.
From the graph, the value of x varies from The x-values -7, -2, 5, and 7
So the domain of the function will be
0≤x≤7
Hence, the domain of the function 0≤x≤7.
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There are 24 four-digit whole numbers that use each of the four digits 2, 4, 5 and 7 exactly once. Only one of these four-digit numbers is a multiple of another one. Which of the following is it?
O 5724 O 7245 O 7254 O 7425
O 7542
The average four-digit number 7254 is the only one that is a multiple of another one, as it is composed of the digits 2, 4, 5 and 7 used exactly once.
To find the four-digit number that is a multiple of another one using the digits 2, 4, 5 and 7, we can list all the possible combinations of these digits:
2457, 2475, 2547, 2574, 2745, 2754, 4257, 4275, 4527, 4572, 4725, 4752, 5247, 5274, 5427, 5472, 5724, 5742, 7245, 7254, 7425, 7452, 7524, 7542. as it is composed of the digits 2, 4, 5 and 7 used exactly once.
Next, we can check to see which of these numbers is a multiple of another one. 7254 is the only one that is a multiple of another one, as it can be divided by 2, 4, 5 and 7. Therefore, the answer is 7254.
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Thank you to anyone that can help I am ever so appreciative!!
Answer:
C. Angle Bisector Theorem
x = 5
PO = 34
Step-by-step explanation:
The theorem used is C: Angle bisector theorem
A can be eliminated because there is no midsegment here
B can also be eliminated - no perpendicular bisector
D relates to a median and there is no median here
C is the best choice. You can see in the figure that EO bisects ∠NEP.
Because of this angles ∠NEO and ∠OEP are equal
That makes the triangles congruent since we have one common side and two angles that are equal to each other
Therefore PO = NO
8x - 6 = 6x + 4
8x - 6x = 4 + 6
2x = 10
x = 5
PO = 8(5) - 6 = 40 - 6 = 34
The data were collected from a statistics class. The column heads give the variable, and each of the row
Eye Shoe Height
Color Size (inches)
Brown 10
65
Blue 8.5
67
Blue 8.5
69
Blue
7
73
Male Age
31
30
30
20
0
1
1
1
There are
variables.
(Type a whole number.)
Weight
(pounds)
150
150
200
145
Number College Units
of Siblings This Term
3
232
2
2
5
15
13
15
Handedness
Left
Left
Right
Right
The statistics class was where the data were gathered. The variable is indicated by the column headers, along with each row's Eye Shoe Height 9.
Is the variable handedness numerical or categorical?5 different variables are present. Category-specific characteristics include gender, handedness, and field side. Quantitative factors include height and the distance covered when walking. Numbers are used to express variables like the number of siblings and student height. It is discrete since it is a count of siblings. As a continuous numerical variable, height varies throughout time.
There are three primary types of variables: controllable, dependent, and independent. His realization that shoe size is an interval variable came later. Eureka! There is no zero point in an interval variable, but there is a defined range between values. If we take shoe sizes into consideration,
we can conclude that the difference between
a size 2 and a size 3 = size 8 - a size 7
Two major categories—categorical and numeric—can be used to group variables.
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Full question:
shown below is a regular octagon. each of the four red regions has area $12$. what is the area of the blue region?
Area of the blue region = A - B = (2+ 2*√(2))/2 * (side length)^2 - 48 square units.
What is the area of congruent right triangles?
Two right-angled triangles are said to be congruent to each other if the hypotenuse and one side of the right triangle are equal to the hypotenuse and the corresponding side of the other right-angled triangle.
The blue region is a square, and the four red regions are congruent right triangles.
The blue square is formed by connecting the midpoints of the four sides of the octagon. Since it is an octagon, each of its angles is 135 degrees, and the four red regions are 45-45-90 triangles.
Thus the area of the blue region is equal to the area of the square which is (side length)^2.
The four red regions have a combined area of 124 = 48 square units.
Since the octagon is a regular polygon, all its sides are congruent.
The area of the octagon can be found by multiplying the square of the length of one side by (2+ 2√(2))/2.
If we call the area of the octagon A, and the area of the four red regions B then:
A = B + 4 * 12
Now we can solve for the area of the blue region (A - B)
Area of the blue region = A - B = (2+ 2*√(2))/2 * (side length)^2 - 48 square units
Since we know the area of the red regions we can find the area of the blue region.
Hence, the Area of the blue region = A - B = (2+ 2*√(2))/2 * (side length)^2 - 48 square units.
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When x = 3, what is the correct function notation?
Responses
A ƒ(3) = −12
ƒ(3) = − 1 2
B ƒ(−12
) = 3ƒ(− 1 2 ) = 3
C ƒ(12
) = 3ƒ( 1 2 ) = 3
D ƒ(3) = 12
The correct function notation when x = 3 is
D. ƒ(3) = 12
This is because ƒ(3) represents the output of the function when the input is 3. The equation states that when the input is 3, the output is 12.
A, B and C are not correct because the input is not 3 in those equations.
A hose fills a hot tub at a rate of 2.82 gallons per minute. How many will it take to fill a 270-gallon hot tub
It takes 95.75 minutes to fill a 270-gallon hot tub.
Given,
A hose fills a hot tub in 1 minute = 2.82 gallons
Time taken to fill a 270-gallon hot tub,
[tex]= \frac{270}{2.82}[/tex]
= 95.75 minutes
Therefore, It takes 95.75 minutes to fill a 270-gallon hot tub.
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Translate the expression:
Six subtracted from the opposite of the sum of three times a number and five
Answer:
6--(3x+5)
Step-by-step explanation:
Answer:
Translation: -3x + 5 - 6
Identify the pattern in the list of numbers. Then use this pattern to find the next number. 5,7,12,19,31,50
The next number in the sequence is 81.
The pattern in the list of numbers is that each number is the sum of the previous two numbers in the sequence. It is a Fibonacci sequence.
The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1.
So, to find the next number, we add the two last numbers of the sequence:
50 + 31 = 81
Therefore, the next number in the sequence is 81.
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Find the surface area of the soild.
The surface area of the square pyramid shown is 466.56 in²
What is an equation?An equation is an expression showing the relationship between numbers and variables.
The shape shown is a square pyramid with 5 surfaces. The surface area is the sum of each individual area surface. It is given as:
Surface area = base² + 4(1/2 * base * height)
base = 10.8 in, height = 16.2 in, hence:
Surface area = 10.8² + 4(1/2 * 10.8 * 16.2) = 466.56 in²
The surface area of the solid is 466.56 in²
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what is the angle between the given vector and the positive direction of the x-axis? (round your answer to the nearest degree. i + sqrt (15) j
The angle between the given vector and the positive direction of the x-axis is found by taking the inverse tangent of the vector components. The angle is equal to arctan(i/sqrt(15)) = 90°.
The angle between the given vector and the positive direction of the x-axis is found by taking the inverse tangent of the vector components. The angle is equal to arctan(i/sqrt(15)) = 90°.
90°
The angle between the given vector and the positive direction of the x-axis is found by taking the inverse tangent of the vector components. The angle is equal to arctan(i/sqrt(15)) = 90°.
The angle between the given vector with components i and sqrt(15) j and the positive direction of the x-axis is equal to arctan(i/sqrt(15)) = 90°. To calculate this angle, we take the inverse tangent of the components of the vector, which is equal to 90°. This angle is then rounded to the nearest degree, resulting in an angle of 90° between the two.
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(a) Calculate a confidence interval at confidence level approximately 95% for the difference between population mean height for the younger women and that for the older women. (Use μ 20−39 −μ 60 and older.)Interpret the interval. O We cannot draw a conclusion from the given information. O We are 95% confident that the true average height of younger women is greater than that of older women by an amount outside the confidence interval. O We are 95% confident that the true average height of younger women is less than that of older women by an amount within the confidence interval. O We are 95% confident that the true average height of younger women is greater than that of older women by an amount within the confidence interval.
We have a 95% confidence interval around the real average height of younger women being greater than that of older women.
What is meant by real average?You will make the same amount of money if you earn $50,000 this year as you did last year. The purchasing power you previously had will be impacted if inflation changes. The cost of things increases by 2% if inflation does as well. An estimated $54,132 is the annual take-home pay for the average American worker. According to location, education level, and other criteria, salaries might vary widely. Along with net worth and assets, income is a crucial component of your total financial wellness. A reference base period's average hourly wage rate expressed in USD. It demonstrates how much merchandise and services one hour of labour can acquire. Real wage rate is calculated as follows: 100% x (current-year nominal wage rate / current-year CPI).To learn more about real average, refer to:
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the box plot shows weights of all team members of a football team. the middle 50% of the weights for the box plot are from
This suggests that the majority of the team members have an average weight of between 90 and 100 lbs.
1. A box plot is a chart that displays the distribution of a dataset by showing the median, quartiles, and extremes of the data.
2. In this box plot, the middle 50% of the weights for the team members range from 90 to 100.
3. This means that the majority of the team members have an average weight of between 90 and 100 lbs.
The box plot shows that the majority of the team members have an average weight between 90 and 100 lbs.
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a jet airplane reaches 769. km/h on a certain flight. how long does it take to cover 272 m?Set up the math. But don't do any of it. Just leave your answer as a math expression. Also be sure your answers includes all the correct unit symbols.
The airplane will take 0.0095 seconds to cover 272 meters at a rate of 769 kilometers per hour, which is equivalent to 213.6 meters per second.
(272 m) / (769 km/h) x (1 h/3600 s) = 0.0095 s
1. Convert km/h to m/s: 769 km/h x (1000 m/1 km) x (1 h/3600 s) = 213.6 m/s
2. Divide the distance to travel (272 m) by the rate (213.6 m/s): 272 m / 213.6 m/s = 0.0095 s
The airplane's speed on this certain flight is 769 kilometers per hour. In order to calculate how long it will take to cover a distance of 272 meters, we must first convert the speed to meters per second. 769 kilometers per hour is equivalent to 213.6 meters per second. Once we have the rate, we can divide the distance by the rate, which is 272 meters divided by 213.6 meters per second. This calculation yields a result of 0.0095 seconds. Therefore, the airplane will take 0.0095 seconds to cover 272 meters.
The airplane will take 0.0095 seconds to cover 272 meters at a rate of 769 kilometers per hour, which is equivalent to 213.6 meters per second.
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I uploaded the question to simplify an equation
The value of expression after simplify is,
⇒ (w⁻⁴ x³⁶ y⁻⁶ z²⁰) / 9
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ (6w³x⁻⁸y⁻¹z⁻¹⁰ / 2wx³y⁻⁴x⁷) ⁻²
Now, We can simplify as;
⇒ (6w³x⁻⁸y⁻¹z⁻¹⁰ / 2wx³y⁻⁴x⁷) ⁻²
⇒ ( 3 w³⁻¹ x⁻⁸⁻³⁻⁷ y⁻¹⁺⁴ z⁻¹⁰ )⁻²
⇒ ( 3 w² x⁻¹⁸ y³ z⁻¹⁰ )⁻²
⇒ (3⁻² w⁻⁴ x³⁶ y⁻⁶ z²⁰)
⇒ (w⁻⁴ x³⁶ y⁻⁶ z²⁰) / 9
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find the quadratic polynomial, the sum of whose zeroes is 8 and their product is 12. hence, find the zeroes of the polynomial.
The required quadratic polynomial is [tex]x^{2} - 8x + 12 =0[/tex] and roots of this quadratic polynomial are 2 and 6.
Let the roots of the quadratic equation be [tex]\alpha[/tex] and [tex]\beta[/tex] .
Given,
Sum of zeroes, [tex]\alpha +\beta = 8[/tex]
Product of Zeroes, [tex]\alpha *\beta = 12[/tex]
we know that,
Quadratic Equation can be written as :
[tex]x^{2} - (\alpha + \beta )x + \alpha \beta =0[/tex]
Substituting the values in the above Equation,
[tex]x^{2} - (8)x + (12) =0[/tex]
[tex]x^{2} - 8x + 12 =0[/tex]
Hence, The required quadratic equation is [tex]x^{2} - 8x + 12 =0[/tex] .
Now, let's factorize the equation to find its root:
[tex]x^{2} - 8x + 12 =0[/tex]
[tex]x^{2} - 6x -2x+ 12 =0[/tex]
[tex]x(x-6) -2(x-6)=0[/tex]
[tex](x-6)(x-2)=0[/tex]
⇒ [tex]x= 2,6[/tex]
Therefore roots of the quadratic equation [tex]\alpha ,\beta[/tex] are [tex]2,6[/tex] .
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The sum of two numbers is 71. The second number is 6 more than 4 times the first number. What are the two numbers?
We can start solving the problem by using algebra. Let's call the first number x and the second number y. From the problem statement, we know that:
y = 4x + 6 (because the second number is 6 more than 4 times the first number)
x + y = 71 (because the sum of the two numbers is 71)
We can substitute the first equation into the second equation:
x + (4x + 6) = 71
5x + 6 = 71
5x = 65
x = 13
Now that we know the value of x, we can substitute it back into the first equation to find the value of y:
y = 4(13) + 6
y = 54
So the two numbers are 13 and 54.
Can you help me please
The expression 12 *3/4 is 9.
Exactly how do you solve a fraction expression?By multiplying both sides of the equation by the least common denominator (LCD) of each term, a fractional equation can be solved by first eliminating the fractions. This is possible because an equation cannot become unbalanced when both sides are multiplied by the same number, in this case, the LCD.Using mathematical operations like subtraction, addition, multiplication, and division, terms are joined to form an expression. Mathematical expressions contain the following terms: Constant: An absolute number is a constant.Explanation:
12 * 3/4 = 91 = 9.
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The expression 12 *3/4 is 9.
Exactly how do you solve a fraction expression?By multiplying both sides of the equation by the least common denominator (LCD) of each term, a fractional equation can be solved by first eliminating the fractions. This is possible because an equation cannot become unbalanced when both sides are multiplied by the same number, in this case, the LCD.
Using mathematical operations like subtraction, addition, multiplication, and division, terms are joined to form an expression. Mathematical expressions contain the following terms: Constant: An absolute number is a constant.
12 * 3/4 = 91 = 9.
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