Answer:
In a right triangle, the angle opposite the hypotenuse (side c) is always 90 degrees, so we can use the trigonometric function sine to find the length of side c.
sin(A) = opposite / hypotenuse
sin(50) = b / c
so c = b / sin(50)
c = 13 m / sin(50)
c ≈ 22.361 m
So the length of side c is approximately 22.361 meters
Which graph represents the solution set of the compound inequality below?
x+3<= (4x-12) < 20
OH
4 5 6 7 8 9 10 11 12
4 5 6 7 8 9 10 11 12
6 7 8 9 10 11 12 13 14
6 7 8 9 10 11 12 13 14
A graph that represents the solution set of the compound inequality is: graph D.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).Next, we would solve the given compound inequality by making x the subject of formula as follows;
x + 3 < 1/2(4x - 12) < 20
Multiplying all through by 2, we have the following:
2x + 6 < 4x - 12 < 40
Next, we would solve the compound inequality in parts:
2x + 6 < 4x - 12
4x - 2x < 12 + 6
2x < 18
x < 18/2
x < 9.
4x - 12 < 40
4x < 40 + 12
4x < 52
x < 52/4
x < 13.
In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).
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Cement cost $76 per cubic yard. What is the cost of cement for a sidewalk that is 4" thick, 3' wide, and 40' long.
If cement costs $76 per cubic yard, the total cost of cement for a sidewalk with a volume of 480 inches³ is $1,013.
How is the total cost determined?The total cost of cement for the sidewalk is determined using unit conversions and multiplication.
After determining the volume in inches and converting it to yards, the result is multiplied by the unit cost of cement per cubic yard.
Dimensions of the Sidewalk:
Length = 40 inches
Width = 3 inches
Thickness = 4 inches
Volume = 480 inches³ (40 x 3 x 4)
36 Inches = 1 Yard
480 cubic inches = 13.33 cubic yards
Cost of cement per cubic yard = $76
Cost of the sidewalk = $1,013 ($76 x 13.33)
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c x 3 c 9 7. followingis a statement of a theorem which can be proven using the quadratic formula. for this theorem, a, b, and c are real numbers. theorem if f is a quadratic function of the form f .x/ d ax2 c bx c c and ac < 0, then the function f has two x-intercepts. using only this theorem, what can be concluded about the functions given by the follo
The conclusion about given functions are given below.
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
We have the following theorem:
If f is a quadratic function of the form f(x) = ax²+bx+c and ac < 0 , then the function f has two x-intercepts.
(a) g(x) = -8x²+5x-2
For this function a = -8 and c = -2, then -8 × -2 = 16 is greater than zero. Therefore, we cannot conclude anything.
(b) h(x) = [tex]-\frac{1}{3}x^{2} + 3x[/tex]
For this function a = -8 and we don't know the value of c. Therefore, we cannot conclude anything.
(c) k(x) = 8x²-5x-7
For this function a = 8 and c = -7, then 8 × -7 = -56 is less than zero. Therefore, we can conclude that the function k has two x-intercepts.
(d) j(x) = [tex]-\frac{71}{99}x^{2} + 210[/tex]
For this function a = [tex]-\frac{71}{99}[/tex] and c = 210, then [tex]-\frac{71}{99}[/tex] × 210 = [tex]-\frac{4970}{33}[/tex] is less than zero. Therefore, we can conclude that the function k has two x-intercepts.
(e) f(x) = 4x²-3x+7
For this function a = 4 and c = 7, then 4×7 = 28 is greater than zero. Therefore, we cannot conclude anything.
(f) F(x) = [tex]-x^{4} + x^{3} + 9[/tex]
We cannot conclude anything because this is not a quadratic function.
The conclusion about given functions are given above in explanation.
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complete question : Following is a statement of a theorem which can be proven using the quadratic formula. For this theorem, a, b, and c are real numbers. Theorem If f is a quadratic function of the form f .x/ D ax2 C bx Cc and ac < 0, then the function f has two x-intercepts. Using only this theorem, what can be concluded about the functions given by the following formulas(a) g (x) = -8x^2 + 5x - 2 (b) h (x) = -(1/3)x^2 + 3x (c) k (x) = 8x^2 - 5x - 7 (d) j (x) = -(71/99)x^2 + 210 (e) f (x) = 4x^2 - 3x + 7 (f) F (x) = -x^4 + x^3 + 9
help asap! Giving brainliest
The table below shows the ratio of a bird's brain to body weight.
Brain (part) 0.6 B 1.8 E
Body (part) A 14.3 19.8 33
Total (whole) 7.2 C D 36
Which table shows the correct missing values?
Brain (part) 0.6 1.3 1.8 3
Body (part) 6.6 14.3 19.8 33
Total (whole) 12.6 27.3 37.8 36
Brain (part) 0.6 1.2 1.8 3
Body (part) 1.2 14.3 19.8 33
Total (whole) 7.2 15.6 21.6 36
Brain (part) 0.6 1.2 1.8 3
Body (part) 6.0 14.3 19.8 33
Total (whole) 6.6 15.5 37.8 36
Brain (part) 0.6 1.3 1.8 3
Body (part) 6.6 14.3 19.8 33
Total (whole) 7.2 15.6 21.6 36
The complete table is given as follows -
Brain (part) 0.6 1.3 1.8 3
Body (part) 6.6 14.3 19.8 33
Total (whole) 7.2 15.6 21.6 36
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 is that an interior designer recently spent £1359.55 buying 25 kettles and 20 toasters for a smaller group of new houses. For her current assignment she needs 80 kettles and 56 toasters.
The given table is -
Brain (part) 0.6 B 1.8 E
Body (part) A 14.3 19.8 33
Total (whole) 7.2 C D 36
We can write the expressions as -
0.6 + A = 7.2 .... Eq( 1 )
A = 6.6
1.8 + 19.8 = D .... Eq( 2 )
21.6 = D
E + 33 = 36
E = 3 .... Eq( 3 )
Therefore, the complete table is given as follows -
Brain (part) 0.6 1.3 1.8 3
Body (part) 6.6 14.3 19.8 33
Total (whole) 7.2 15.6 21.6 36
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Linear Equations CHECK POINT 1 University of Arkansas researchers discovered that we underestimate the number of calories in restaurant meals. The next time you eat out, take the number of calories you think you ate and double it. The researchers concluded. that this number should be a more accurate estimate. The actual number of calories in one portion of hamburger and fries and two portions of fettuccine Alfredo is 4240. The actual number of calories in two portions of hamburger and fries and one portion of fettuccine Alfredo is 3980. Find the actual number of calories in each of these dishes. (Source: Consumer Reports, January/February, 2007) Test Your Calorie I.Q.
Answer:
hamburger and fries: 1240 caloriesfettuccine Alfredo: 1500 caloriesStep-by-step explanation:
You want the number of calories in each dish if 1 portion of hamburger and fries with 2 portions of fettuccine Alfredo has 4240 calories, and 2 portions of hamburger and fries with 1 portion of fettuccine Alfredo has 3980 calories.
SetupThe equations describing the calories in each dish can be written using h and f for the calories in a portion of hamburger and in a portion of fettuccine, respectively:
1h + 2f = 4240
2h +1f = 3980
SolutionSubtracting the first equation from twice the second gives ...
2(2h +f) -(h +2f) = 2(3980) -(4240)
3h = 3710 . . . . . . . simplify
h = 1240 . . . . . . . divide by 3
Then the calories in the fettuccine can be found from the second equation:
f = 3980 -2h = 3980 -2480 = 1500
The actual number of calories in a portion of hamburger and fries is 1240.
The actual number of calories in a portion of fettuccine Alfredo is 1500.
__
Additional comment
The attachment shows a calculator solution using matrix methods.
10. Some people who have never smoked develop lung cancer. Does this disprove the evidence?
(1 point)
I
The fact that some people who smoked never develop lung cancer does not disprove the evidence.
Why can some people smoke and not develop lung cancer ?The fact that some people who have never smoked develop lung cancer does not disprove the evidence linking smoking to lung cancer.
Smoking is a major risk factor for lung cancer, and the overwhelming majority of people who are diagnosed with the disease are smokers or former smokers. However, it is important to note that other factors, such as exposure to radon and other pollutants, can also increase the risk of lung cancer, and that some people may be more genetically susceptible to the disease. So, it is possible for people who have never smoked to develop lung cancer as well.
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A town has a population of 1600 people at time t=0. In each of the following cases, write a formula for the population P, of the town as a function of year t.(a) The population increases by 70 people per year.(b) The population increases by 9 percent a year.
The population of the town at any given time t can be determined using the formulas provided. For example, if the town's population at time t=5 years is desired, the population can be calculated as follows:(a) P(5) = 1600 + 70(5) = 2100 people (b) P(5) = 1600(1.09)^5 = 2266.05 people
(a) P(t) = 1600 + 70t
(b) P(t) = 1600(1.09)^t
(a) In this case, the population increases by 70 people per year, so the formula for the population as a function of time is P(t) = 1600 + 70t. This means that the population is 1600 people at time t=0 and increases by 70 people for each additional year.
(b) In this case, the population increases by 9 percent each year, so the formula for the population as a function of time is P(t) = 1600(1.09)^t. This means that the population is 1600 people at time t=0 and increases by a factor of 1.09 (9 percent) for each additional year.
The population of the town at any given time t can be determined using the formulas provided. For example, if the town's population at time t=5 years is desired, the population can be calculated as follows:
(a) P(5) = 1600 + 70(5) = 2100 people
(b) P(5) = 1600(1.09)^5 = 2266.05 people
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exercise 1.2.3 the augmented matrix of a system of linear equations has been carried to the following by row operations. in each case solve the system.1 2 1 3 1 | 10 1 -1 0 1 | 1c = 0 0 0 1 -1 | 00 0 0 0 0 | 0
The presented system of linear equations has no solution.
The final form of the augmented matrix suggests that the system of linear equations has no solution, as the last row represents an equation with 0 = 0, which is always true but doesn't provide any information about the variables.
To see this more clearly, let's use the augmented matrix to write out the system of linear equations:
1x - 1y + 2z = 4
2y + 1z = -1
z = 1
The first two equations are consistent and have a unique solution, but the last equation is trivial and provides no information about x and y. In other words, infinitely many pairs of x and y satisfy the first two equations, but none satisfy the third equation. Therefore, the given system of linear equations has no solution.
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PLEASE HELP FOR 30 POINTS ITS A UNIT TEST!!!!!!!
The coordinates of the vertices of a polygon are shown on the graph below.
What is the name of the polygon?
hexagon
octagon
quadrilateral
triangle
Answer: Quadrilateral
Step-by-step explanation:
hexagon: 6 sides
octagon: 8 sides
quadrilateral: 4 sides
triangle: 3 sides
The quadrilateral is the only one that makes sense.
The life span of fruit fly have a bell shaped distribution, with a mean of 32 days and a standard deviation of 5 days. What is the Z score of the fruit flys at 37 ,30 and 47 days
Answer:
The Z-score (also known as a standard score) represents the number of standard deviations a value is away from the mean of a distribution. The formula for the Z-score is:
Z = (X - μ) / σ
Where X is the value of interest, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Given the information in the problem, we know that the mean of the fruit fly's lifespan is 32 days and the standard deviation is 5 days.
To find the Z-score of a fruit fly whose lifespan is 37 days:
Z = (37 - 32) / 5 = 1
To find the Z-score of a fruit fly whose lifespan is 30 days:
Z = (30 - 32) / 5 = -0.4
To find the Z-score of a fruit fly whose lifespan is 47 days:
Z = (47 - 32) / 5 = 2.4
Therefore, a fruit fly whose lifespan is 37 days has a Z-score of 1, a fruit fly whose lifespan is 30 days has a Z-score of -0.4, and a fruit fly whose lifespan is 47 days has a Z-score of 2.4.
Olivia earns $12 an hour at the grocery store. She kept track of her hours per week and how much she earned in the following table. Graph the values in the table on the coordinates plane shown. what will you label the x-axis?
Answer:
12 times y = x
Step-by-step explanation:
I see on you paper you want to do intervals of 2 so just take 12 and multiply it by the desired number. Equation: 12 x # = the y axis point. This is where #=x-axis and plugging it in the equation gives you the y point.
You mix 1 half cup of salt with 3 cups of sugar. Which below is the ratio of salt to sugar.
In a case whereby you mix 1 half cup of salt with 3 cups of sugar the ratio of salt to sugar.
What is ratio?The concept that will be used is ratio. An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
we were told that there were 1 half cup of salt with 3 cups of sugar
Then the ratio can be written as
salt/sugar
= (1 1/2)/3
Since the amount of the salt is in mixed fraction, we can reduce to improper fraction for easy calculation.
=( 3/2)/ 3
= 3/6
=1/2
Hence, the ratio is 1:2
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missing options:
A. 2:3
B.1:2
C.2:1
D. 5:6
Which difference is 4.517?
The difference between 4.507 and 4.517 can be expressed as -0.010.
What is difference in mathematics?The concept that will be used here is substraction. The outcome of subtracting one integer from another is difference. While we frequently discuss differences in how objects appear, feel, or even taste, mathematics demonstrates how much two numbers vary from one another in terms of quantity. Difference is what is left behind after subtracting one number from another.
the outcome of subtraction of two numbers. the difference between two numbers. For instance: There is a 5 difference between 8 and 3.
We were to find the difference between 4.507 and 4.517 whichg implies the substraction between the values and can be done as
(4.507 - 4.517)= -0.010
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complete question:
What is the difference between 4.507 and 4.517
when the population mean and standard deviation are known, we can generally assume the following about the sample mean and standard deviation (check all that apply
When σ is known, hypothesis tests are performed for one population mean. The one-mean z-test, or simply z-test, is a hypothesis test carried out for a single population mean when the population standard deviation is known.
A data distribution's spread is measured by standard deviation. It calculates the average separation between each data point and the mean.
Whether we consider the data to be a population unto itself or a sample of a broader population affects the method we use to calculate standard deviation.
Statistics is the parent topic for the Population Mean notion. In a nutshell, statistics addresses the issues of gathering data as well as its analysis, interpretation, and presentation. The population mean formula calculates the average of all the values in the population or set of data.
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What is the circumference of the circle in terms of π?
circle with a segment drawn from one point on the circle through the center to another point on the circle labeled 7 yards
3.5π yards
7π yards
21.98π yards
49π yards
Circumference of circle = 7π yards
The correct option is B.
What is circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Given,
Segment drawn from one point on the circle through the center to another point = diameter of circle = 7 yards
Circumference of the circle = π × Diameter
= 7π yards
Hence, 7π yards is the circumference of the circle
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Answer:
b
Step-by-step explanation:
42.735 rounded to the nearest ones places
Answer: 43 because 7 is greater than 5 so you round up. Have a nice day ;)
The correct answer is 43. 0.735 is greater than 0.5, so you round it up to 43
_____ refers to the technology that allows data, collected from sensors in all types of machines, to be sent over the Internet to repositories where it can be stored and analyzed. A. Hadoop B. MapReduce C. Advanced analytics D. Internet of Things
Internet of Things refers to the technology that allows data, collected from sensors in all types of machines, to be sent over the Internet to repositories where it can be stored and analyzed.
Internet of Things refers to the collective network of connected devices and the technology that facilitates communication between devices and the cloud, as well as between the devices themselves.
There are some Advantages of IOT:
It can assist in the smarter control of homes and cities via mobile phones. It enhances security and offers personal protection.
Automating activities saves us a lot of time. Information is easily accessible, even if we are far away from our actual location, and it is updated frequently in real time.
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what is a system of linear equations whose solution is (6,19)
Answer:
A system of linear equations is a set of two or more equations containing two or more variables. The solution to a system of linear equations is the set of values for the variables that makes all the equations in the system true.
For example, a system of linear equations whose solution is (6,19) could be represented by the following equations:
x + 2y = 25
3x - 4y = 6
Solving this system would yield x = 6 and y = 19 as the solution.
Consider the weighted voting system [20: 9,7,5,3,1] Find the weight of the coaltion P1,P2,P3
The weight of the coalition P1, P2, P3 is 36
How to determine the weight coalitionFrom the question, we have the following parameters that can be used in our computation:
weighted voting system [20: 9,7,5,3,1]
The variable P1, P2 and P3 are the first three values
So, we have
P1 = 20
P2 = 9
P3 = 7
The weight of the coalition P1, P2, P3 is the sum of the points
So, we have
Coalition = 20 + 9 + 7
Coalition = 36
Hence, the weight coalition is 36
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FILL IN THE BLANK When aligning tow shafts, the reason to rotate the coupling hubs before making each measurement is so each measurement is ____________
When we are aligning two shafts, the reason behind rotating the coupling hubs before taking each measurement is so that each of the measurements is taken from the same place on the hub every time.
Shafts are basically a component of circular cross section which rotates and transmits the power from a driving device like an engine or a motor through a particular machine. Coupling hubs are basically the attachment of the coupling to shaft in a device.
During the alignment of two shafts, the angular as well as parallel misalignment is thoroughly checked. The coupling hubs are rotated before taking each measurement is so that each of the measurements is taken from the same place on the hub every time.
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Use the motion map to answer the question. A motion map. The position line is a long black arrow pointing right with x as the reference point at left. Above the line are 3 dots with short vector arrows moving toward x, then a dot, then 2 dots with longer vector arrows moving away from x. Describe the position and velocity of the object based on the motion map.
The direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.
What are Motion maps?Motion maps are used to illustrate the direction and position of an object. Using the motion map, the description of the object position and velocity is as follows:
The object starts its movement from the origin with a large velocity, before moving back to the origin with a smaller velocity. It stops for 1 second in the origin, then moves away with a larger velocity, Finally, it moves back towards the origin with a smaller velocity.
See attachment for the motion map, where the number on each arrow in the map, represents the position of the object.
Note that; the long arrow means large velocity while the short arrow means small velocity.
We analyze the direction and position using the arrows
The first arrow shows that the object starts from the origin with a large velocity.The direction and length of the second arrow show that, the object then returned to the origin with a smaller velocity.There is a dot in front of the second arrow. This dot indicates that the object stops for one second.The third arrow means that, the object moved from the origin with a larger velocityThe direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.Therefore, the direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.
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Answer:
Based on the motion map, the object starts at the reference point "x" on the left side of the position line. The three dots with short vector arrows moving toward "x" indicate that the object is moving in the direction of the reference point and gaining speed. This suggests that the object is accelerating. Then, there is a single dot, which might indicate a momentary pause or a constant velocity. Afterward, the two dots with longer vector arrows moving away from "x" suggest that the object is decelerating or slowing down. In summary, the motion map shows an object that starts from rest, accelerates towards the reference point, maintains a constant velocity for a brief moment, and then decelerates away from the reference point.
Step-by-step explanation:
Use chat gpt to give you unique answer.
amanda got a train ticket valid for the five cities listed below. she can choose to visit some or none of these cities. she doesn't have time to visit all of them. amsterdam, brussels, lille, paris, rotterdam
As per the permutation method, the number of possible way for here travel is 5.
The term permutation in math is known as an arrangement of objects in a definite order and the members or elements of sets are arranged here in a sequence or linear order.
Here we have given that Amanda got a train ticket valid for the five cities listed below.
There are Amsterdam, brussels, Lille, Paris, Rotterdam.
So, the given number of ways is 5.
Then the value of n = 5 and the value of r = 1 because here we have given that she can choose to visit some or none of these cities which means that she must chose at least one city.
Then the number of ways is calculated as,
=> ⁵P₁ = 5!/ (5 - 1)!
=> ⁵P₁ = 5!/4!
=> ⁵P₁ = 5
Complete Question:
Let us consider that Amanda got a train ticket valid for the five cities listed below. she can choose to visit some or none of these cities. she doesn't have time to visit all of them.
They are Amsterdam, brussels, Lille, Paris, Rotterdam
Find out the number of ways to visit each cites using permutation method.
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what are the factors and zeros of the function f(x)=x2-5x+6
The factors and zeros of the function f(x)=x2-5x+6 are x-3, x-2 and 3 and 2 respectively
How to determine the zeros of the functionGiven the quadratic function as;
f(x) = x² - 5x + 6
Using the factorization method of solving quadratic function, we have to multiply the coefficient of x² by the constant of the function
Then find the pair factors of the function that sums up to -5
The pair factors area -2 and -3
Substitute the values, we get;
x²- 2x - 3x + 6
Pair the expression
(x² -2x) - (3x + 6)
Factorize the value
x(x -2) -3(x - 2)
The zeros are;
x-3 = 0
x = 3
Then,
x -2 = 0
x =2
Hence, the values are 2 and 3
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a) Using the 2" zn rule, construct a frequency distribution for these data. Select the correct choice below and fill in the answer boxes to complete your choice.O A. Credit Card Balances Frequency $0 to less than $1,000 $1,000 to less than $2,000 $2,000 to less than $3,000 $3,000 to less than $4,000 $4,000 to less than $5,000 $5,000 to less than $6,000 O B. Credit Card Balances Frequency $0 to less than $1,200 $1,200 to less than $2,400 $2,400 to less than $3,600 $3,600 to less than $4,800 $4,800 to less than $6,000 Credit Card Balances$2,368 $5,789 $1,754 $5,927 $5,815 $349 $3,522 $3,888 $5,323 $1,039 $1,247 $2,429 $461 $1,464 $4,505 $2,667 $5,425 $669 $911 $750 $1,007 $1,706 $300 $410 $4,650 $3,770 $4,502 $4,056 $1,020 $158 $168 $4,565 $1,557 $924 $524 $1,669
If k is the number of classes and n is the number of observation then for class intervals, select the smallest k such that 2k >= n using statistics.
n = 36
2^5 = 32< 36
2^6 = 64 > 36
So k = 6
a) Frequency distribution: Answer A.
Class interval Frequency
0 to less than 1000 11
1000 to less than 2000 9
2000 to less than 3000 3
3000 to less than 4000 3
4000 to less than 5000 5
5000 to less than 6000 5
b) Relative frequency distribution: Answer B.
Class interval Relative frequency
0 to less than 1000 11 / 36 = 0.306
1000 to less than 2000 9 / 36 = 0.250
2000 to less than 3000 3 / 36 = 0.083
3000 to less than 4000 3 / 36 = 0.083
4000 to less than 5000 5 / 36 = 0.139
5000 to less than 6000 5 / 36 = 0.139
c) Cumulative relative frequency:
Class interval Cumulative Frequency
less than 1000 11
less than 2000 20
less than 3000 23
less than 4000 26
less than 5000 31
less than 6000 36
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in problems 21 through 30, first verify that the given vectors are solutions of the given system. then use the wronskian to show that they are linearly independent. finally, write the general solution of the system. 25
It is verified that the given vectors x₁ and x₂ are solutions of the given system. Using Wronskian it is shown that they are linearly independent. Then, [tex]W(t)=7e^{-3t}[/tex]. The general solution of the given system is written as [tex]x(t)=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right][/tex].
Wronskian analysis helps to determine whether a solution is linearly dependent or independent.
Given the system is [tex]x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x[/tex].
Let's differentiate x₁ concerning t, and we get,
[tex]\begin{aligned}x_1'&=\left[\begin{array}{c}\frac{d}{dt}(3e^{2t})&\\\frac{d}{dt}(2e^{2t})&\end{array}\right] \\&=\left[\begin{array}{c}6e^{2t}&\\4e^{2t}&\end{array}\right] \end{aligned}[/tex]
Now,
[tex]\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_1&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}12e^{2t}-6e^{2t}\\18e^{2t}-14e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}6e^{2t}\\4e^{2t}\end{array}\right]\\&=x_1'\end{aligned}[/tex]
From this, we can write,
[tex]x_1'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_1[/tex]
Therefore, we conclude that x₁ is a solution to the given system.
Let's differentiate x₂ concerning t, and we get,
[tex]\begin{aligned}x_2'&=\left[\begin{array}{c}\frac{d}{dt}(e^{-5t})&\\\frac{d}{dt}(3e^{-5t})&\end{array}\right] \\&=\left[\begin{array}{c}-5e^{-5t}&\\-15e^{-5t}&\end{array}\right] \end{aligned}[/tex]
Now,
[tex]\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_2&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}4e^{-5t}-9e^{-5t}\\6e^{-5t}-21e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}-5e^{-5t}\\-15e^{-5t}\end{array}\right]\\&=x_2'\end{aligned}[/tex]
From this, we can write,
[tex]x_2'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_2[/tex]
Therefore, we conclude that x₂ is also a solution to the given system.
Now, find the Wronskian of x₁ and x₂, we get,
[tex]\begin{aligned}W(t)&=\text{det}[x_1\;x_2]\\&=\text{det}\left[\begin{array}{cc}3e^{2t}&e^{-5t}\\2e^{2t}&3e^{-5t}\end{array}\right] \\&=(3e^{2t}\times3e^{-5t})-(e^{-5t}\times2e^{2t})\\&=9e^{2t-5t}-2e^{2t-5t}\\&=9e^{-3t}-2e^{-3t}\\&=7e^{-3t}\\&\neq0\end{aligned}[/tex]
From this, we can conclude that x₁ and x₂ are independent.
Finally, we write the general solution of the system as follows,
[tex]\begin{aligned}x(t)&=c_1x_1+c_2x_2\\&=c_1 \left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right] +c_2\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right] \\&=\left[\begin{array}{c}3c_1e^{2t}\\2c_1e^{2t}\end{array}\right] +\left[\begin{array}{c}c_2e^{-5t}\\3c_2e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right] \end{aligned}[/tex]
The complete question is -
First, verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system.
[tex]x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x;\; x_1=\left[\begin{array}{ccc}3e^{2t}\\2e^{2t}\end{array}\right], \;x_2=\left[\begin{array}{cc}e^{-5t}\\3e^{-5t}\end{array}\right][/tex]
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The image includes the questions
Answer:
a.
b. 35/100 of 76 = 26 to 27 remained
c.
d. statistic
e. experiment
f. I don't think so
Step-by-step explanation:
which if the following definitions is not correct? which if the following definitions is not correct? raw data is data that have been collected but are not processed, cleaned or analyzed. statistics is the branch of math that deals with collection, analysis and interpretation of large masses of data. you generally use some form of statistics to get to a useful data visualization. qualitative data is data that cannot be counted easily using numbers. social scientists often used qualitative data which includes text, observations, interviews, and open questions. the y-axis is the horizontal number line and the x-axis is the vertical number line in a chart.
Qualitative data is data that cannot be counted easily using numbers is not have the correct definitions.
Qualitative data is used to address the research questionnaire regarding whats and how many(s) or also for research procedures to quantify a problem. This data can be used to compare or count data on a numerical scale.
This type of research typically involves in-depth interviews, focus groups, or observations in order to collect data that is rich in detail and context. This data is used for Qualitative research which is very helpful when understanding social reality and the attributes, beliefs, and motivations of people.
The main importance of this kind of project come into the limelight when someone is trying to understand the reason behind one's beliefs or behaviors.
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event a occurs with probability 0.. teh conditional probability that event b occurs, given that a occurs is 0.5. the probability that both a and b occurs is
The probability of event a occurring is 0 and the conditional probability of event b occurring given that event a has occurred is 0.5.
The probability that both event A and event B occur is calculated using the formula P(A and B) = P(A) x P(B|A).
In this case, P(A) = 0 and P(B|A) = 0.5. When we plug these values into the equation, P(A and B) = 0 x 0.5 = 0. Therefore, the probability of both event A and event B occurring is 0. The probability that both events a and b occur is determined by multiplying the probability of event a occurring with the conditional probability of event b occurring given that event a has already occurred. This can be expressed mathematically as P(A∩B)=P(A)*P(B|A). In this case, the probability of both events a and b occurring is 0.5*0.5=0.25, since the probability of event a occurring is 0 and the conditional probability of event b occurring given that event a has occurred is 0.5.
This makes sense, since event A has a probability of 0 and cannot occur in the first place, so the probability of both events occurring together is 0.
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What is (f/g)(x)?
f(x) = -x
g(x) = -5x + 2
Write your answer as a polynomial or a rational function in simplest form.
The rational function in the simplest form of (f/g)(x) is x / 5x - 2.
How to solve functions?Composite functions are when the output of one function is used as the input of another. A typical example of a composite function is (f/g)(x).
Therefore, let's solve the rational function in the simplest form.
Hence,
f(x) = -x
g(x) = -5x + 2
(f/g)(x) = f(x) / g(x)
Therefore,
(f/g)(x) = - x / -5x + 2
Hence,
(f/g)(x) = - x / - (5x - 2)
Finally,
(f/g)(x) = x / 5x - 2
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in a given year, approximately 30% of children and adolescents in the united states display serious psychological disturbances and need clinical treatment.
It can be concluded that in 2018, approximately 21.7% of children and adolescents in the United States displayed serious psychological disturbances and needed clinical treatment.
The percentage of children and adolescents in the United States displaying serious psychological disturbances is calculated by dividing the number of children and adolescents with serious psychological disturbances by the total number of children and adolescents in the United States. This can be expressed mathematically as:
% = (Number of children and adolescents with serious psychological disturbances / Total number of children and adolescents in US) x 100
Using estimates from 2018, approximately 48.5 million children and adolescents in the United States, and 10.5 million of them displaying serious psychological disturbances, the percentage of children and adolescents in the United States displaying serious psychological disturbances in 2018 can be calculated as:
% = (10.5 million / 48.5 million) x 100 = 21.7%
Therefore, it can be concluded that in 2018, approximately 21.7% of children and adolescents in the United States displayed serious psychological disturbances and needed clinical treatment.
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