The given equation is
\(w=\frac{va}{r^2+a^2}\)We need to solve it for a
let us cross multiply the two sides
\(w(r^2+a^2)=va\)Divide both sides by w
\(r^2+a^2=\frac{va}{w}\)Subtract r^2 from both sides
\(a^2=\frac{va}{w}-r^2\)Factor 3x+11y if the expression cannot be factored
The expression 3x+11y cannot be factorized.
What is factorization?
To factorise an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse. The same way, as the product of their factors, are the algebraic expressions written in algebra. The only difference is that in an algebraic expression, variables and integers are combined to perform mathematical operations like addition or subtraction.
Here the given expression 3x+11y didn't have any common factors.
The given expression has two variables 3x and 11y and they didn"t have any common terms.
Hence the expression 3x+11y cannot be factored.
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Prove or disprove that for all n, there exists a positive integer t such that a set of n elements can be partitioned into a number of subsets where all the subsets have size t or t - 1
The purpose of the SUBSET-SUM issue is to determine whether a subset from a list of integers may add up to a certain value.
A dynamic programming approach that takes repeating, positive, and negative numbers into account. The purpose of the SUBSET-SUM problem is to determine whether a subset of a list of integers may add up to a certain value. As an example, consider the list of numbers [1, 2, 3, 4]. If the target is set to that number, there are two subsets, 3, and 1, 2, 4, that both add up to 7. If the target is equal to 11, there are no solutions.
If there are t integers in the sums list, then there are usually (t -1) subsets that need to be checked to see if there are even any solutions to SUBSET-SUM. This post will look at a technique for using dynamic programming to solve issues more successfully. though, in contrast
Let is SUBSET-SUM (arr, t, sum/2) be the function that returns true if there is a subset of arr [0..t-1] with sum equal to sum/2
The is SUBSET-SUM problem can be divided into two subproblems
is SUBSET-SUM() without considering last element (reducing t to t-1)
is SUBSET-SUM considering the last element (reducing sum/2 by arr[t-1] and t to t-1)
If any of the above subproblems return true, then return true.
is SUBSET-SUM (arr, t, sum/2) = is SUBSET-SUM (arr, t-1, sum/2) || is SUBSET-SUM (arr, t-1, sum/2 – arr[t-1])
Therefore,
The purpose of the SUBSET-SUM issue is to determine whether a subset from a list of integers may add up to a certain value.
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Julie wants to buy a car and is deciding how she should invest her money. To best meet her needs she should
Answer:
buy a car
Step-by-step explanation:
To the best meet her needs, she should keep her money Julie must keep her money in savings account for easy access.
What is the benefit of a savings account?Savings accounts provide people to easily open a bank account with a moderate amount of interest on it as well. This offers withdrawal flexibility to people along with keeping minimum balance features as well.
Given that;
Julie wants to buy a car.
Now, We know that
When people do not require to spend their money on immediate basis then they may use savings account as there is easy deposit and withdrawal facility.
Hence, To the best meet her needs, she should keep her money Julie must keep her money in savings account for easy access.
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Complete question is this,Julie wants to buy a car and is deciding how she should invest her money. To best meet her needs, she should keep her money
A) In a checking account for easy access.
B) Invest in US savings bonds because of its short term.
C) Invest in a commodity because of its low risk.
D) Keep her money in a savings account for easy access.
Determine the shaded area
The shaded area is 40 square centimeters.
What is the triangle?
A triangle is a clοsed twο-dimensiοnal geοmetric shape with three straight sides and three angles. It is οne οf the basic shapes in geοmetry and is used in many fields οf mathematics and science. The three sides οf a triangle may have different lengths, and the three angles may alsο have different measures.
Tο determine the shaded area, we need tο find the area οf the trapezοid and the area οf the triangle and then subtract the area οf the triangle frοm the area οf the trapezοid.
First, let's find the area οf the trapezοid:
The height οf the trapezοid is 10 cm (the distance between the twο parallel bases), and the length οf the twο parallel bases are 8 cm and 16 cm. Therefοre, the area οf the trapezοid is:
A = (b1 + b2)h / 2
A = (8 cm + 16 cm) x 10 cm / 2
A = 120 cm²
Next, let's find the area of the triangle:
The base of the triangle is 16 cm, and the height is 10 cm. Therefore, the area of the triangle is:
A = bh / 2
A = 16 cm x 10 cm / 2
A = 80 cm²
Finally, we can determine the shaded area by subtracting the area of the triangle from the area of the trapezoid:
Shaded area = 120 cm² - 80 cm²
Shaded area = 40 cm²
Therefore, the shaded area is 40 square centimeters.
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A house blueprint has a scale of 1in : 10ft the length and width of each room in the actual house are shown in the table complete the table by finding the length and width of each room on the blueprint
Help me with this one
Answer:
30x40=3inx4in
50x50=5inx5in
40x20=4inx2in
30x40=3inx4in
30x30=3inx3in
35x40=3.5inx4in
Step-by-step explanation:
According to this diagram, what is tan 62 degrees ?
Answer:
According to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.
What is the right angle triangle property?
In a right-angle triangle ratio of the opposite side to the adjacent side is equal to the tangent angle between the adjacent side and the hypotenuse side.
Here, (b) is the opposite side, (a) is the adjacent side, and is the angle made between the adjacent side and the hypotenuse side.
The sides of the triangle are 8, 15, and 17 units long and the measure of the angles of the right angle triangle is 62, 90, and 28 degrees.
Re-draw, the Here in the given triangle, the base is the side which is 15 units long. Re-draw the triangle as shown below.
In the attached triangle below, the opposite side of the triangle is 15 units and the adjacent side of the triangle is 8 units long.
The angle between the opposite side and the adjacent side is 62 degrees. Thus using the right angle triangle property as,
Thus, according to this diagram, the tan 62 degrees, is the ratio of the opposite side and the adjacent side of the triangle which is equal to 1.875 units.
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What is the solution to this equation?
7x-3(x-6)= 30
A. X= 3.
B. x = 12
C. X= 9
D. x=6
Answer:
A
Step-by-step explanation:
To solve the equation 7x-3(x-6)=30, we need to use the distributive property to simplify the left-hand side of the equation:
7x - 3(x-6) = 30
7x - 3x + 18 = 30
4x + 18 = 30
Next, we need to isolate the variable term on one side of the equation. To do this, we can subtract 18 from both sides:
4x + 18 - 18 = 30 - 18
4x = 12
Finally, we can solve for x by dividing both sides by 4:
4x/4 = 12/4
x = 3
Therefore, the solution to the equation 7x-3(x-6)=30 is x = 3. Answer A is correct.
Given f(x) = x² - 5x - 6 and g(x) =
x² - 6x, what are the domain restrictions
for (-)(x)?
A) x # +6
B) x = 0
C) x = 0,6
D) x = -2,6
The domain restrictions for (f/g)(x) are (c) x = 0, 6
How to determine the domain restrictions for (f/g)(x)?From the question, we have the following parameters that can be used in our computation:
f(x) = x² - 5x - 6
g(x) = x² - 6x
The composite function (f/g)(x) is calculated as
(f/g)(x) = f(x)/g(x)
substitute the known values in the above equation, so, we have the following representation
(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)
For the domain restriction, we have
x² - 6x = 0
When solved, we have
x = 6 or x = 0
Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6
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Question
Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions
for (f/g)(x)?
A) x = +6
B) x = 0
C) x = 0,6
D) x = -2,6
3(y+1/4)>3/4 determine the value of y for the inequality
Therefore, the solution to the inequality 3(y + 1/4) > 3/4 is y > 0.
What is inequality?An inequality is a mathematical statement that shows a relationship between two values, which are not necessarily equal. Inequalities are represented using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to). Inequalities are commonly used in algebra and other areas of mathematics, as well as in real-world applications such as finance, economics, and science. They can be used to represent constraints or limits on a variable, such as the maximum or minimum value that it can take.
Here,
We can solve the inequality 3(y + 1/4) > 3/4 by first distributing the 3 to the expression inside the parentheses:
3y + 3/4 > 3/4
Next, we can simplify by subtracting 3/4 from both sides:
3y > 0
Finally, we can solve for y by dividing both sides by 3:
y > 0/3
y > 0
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Using 50 random numbers given below, compute the mean and standard deviation. 0.937776 0.270012 0.243785 0.590701 0.824982 0.131805 0.879337 0.741998 0.254683 0.080259 0.419321 0.928220 0.958430 0.980182 0.263900 0.063119 0.762096 0.485612 0.662900 0.362242 0.724796 0.307736 0.305021 0.417052 0.054337 0.323357 0.069662 0.843387 0.353107 0.074262 0.735596 0.175095 0.390508 0.668932 0.029861 0.205228 0.387740 0.962169 0.646565 0.423914 0.754782 0.156719 0.773113 0.546335 0.323573 0.649740 0.214082 0.382383 0.383982 0.030539 Mean = (to 6 decimals) Standard deviation = (to 6 decimals)
The mean is 0.477514 (rounded to 6 decimal places).
The standard deviation is 0.288919 (rounded to 6 decimal places).
How to Solve the Problem?To calculate the mean and standard deviation, we will use the following formulas:
Mean = (sum of all values) / (number of values)
Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]
Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:
Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514
Therefore, the mean is 0.477514 (rounded to 6 decimal places).
Now we will calculate the standard deviation:
Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919
Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).
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how many feet long is the airplane
Answer:
Well dam
Step-by-step explanation:
theres no info ab no plane lol
Evaluate the expression when c=4 and d=40
D-5c
Solve the inequality: 14-0.6t>2
Answer:
t > 20
Step-by-step explanation:
14 - 0.6t > 2
14 - 14 - 0.6t > 2 - 14
- 0.6t > - 12
- 0.6t ÷ - 0.6 > - 12 ÷ - 0.6
t > 20
Answer:
t<20
Step-by-step explanation:
move the constant to the right- hand side and change its sign
-0.6>2-14
calculate the differnce
-0.6> -12
divide both sides of the inequality by -.06 and flip the inequality sign
t>20
so your solution is t>2o
Mateo scored in the 55th percentile of his class on the latest math exam. What does this mean in relation to the data set, and what did he score on the exam?
Answer:
d. Mateo scored as well as or better than 55% of his classmates, with a score of 82.Step-by-step explanation:
Mateo scored in the 55th percentile of his class on the latest math exam. What does this mean in relation to the data set and what did he score on the exam?{35, 42, 55, 68, 69, 72, 72, 77, 78, 78, 82, 85, 87, 88, 90, 93, 94, 96, 96, 99)
a. Mateo scored a 55% on his exam. b. Mateo scored as well as or better than 55% of his classmates, with a score of 78. c. Mateo scored worse than 55% of his classmates, with a score of 78. d. Mateo scored as well as or better than 55% of his classmates, with a score of 82. e. Mateo scored worse than 55% of his classmates, with a score of 82. SolutionThere are scores of 20 students. Each score is equivalent of 100%/20 = 5%
The easy way to understand Mateo' s place is to compare scores against 5% slots.
See attached.
We can also get the average score
Sum
∑ {35, 42, 55, 68, 69, 72, 72, 77, 78, 78, 82, 85, 87, 88, 90, 93, 94, 96, 96, 99) = 1556Average or mean score:
1556/20 = 77.8This is matching the 50% score.
As we see Mateo scored 82 which is matching 55%.
Correct option is d.
In the diagram, m∠1=45° and m∠3=57.5°.
What is m∠4?
Enter your answer as a decimal in the box.
Check the picture below.
what is 10 divided by 0.38
Answer:
the answer is 26.3157895
Step-by-step explanation:
Let me know if this helps
Juan buys candy that costs $8 per pound. He will spend at least $48 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Juan will buy.
Write your answer as an inequality solved for p.
In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).
How can these number be determined?Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.
From the question, p = number of pounds Juan will buy.
candy=costs $8 per pound
$20/$4 = 5 pounds
p>5
at least 5 pounds
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Marvin wages are
for moving 480 crates at a piecework rate of $1.50 per crate.
$720
O $150
None of these
$481.50
$320
Answer:
The answer to your question is 320
Question 7(Multiple Choice Worth 5 points)
(04.02 MC)
The two-way frequency table contains data about students' preferred exercise.
Likes running 28
Does not like running 46
Column totals 74
What is the joint relative frequency of students who do not like to run and enjoy swimming?
O23%
37%
Enjoys swimming Enjoys cycling Row totals
62
90
64
110
126
200
46%
072%
The joint relative Frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.
The joint relative frequency of students who do not like to run and enjoy swimming, we need to find the intersection of the row and column corresponding to those categories in the two-way frequency table.
Given the following information from the table:
Likes running: 28
Does not like running: 46
Column totals: 74
Enjoys swimming: 62
Enjoys cycling: 90
Row totals: 110
The joint relative frequency, we divide the number of students who do not like running and enjoy swimming by the total number of students:
Joint relative frequency = (Number of students who do not like running and enjoy swimming) / (Total number of students)
From the table, the number of students who do not like running and enjoy swimming is given as 46.
Total number of students is given as 74.
Joint relative frequency = 46 / 74
Calculating this value, we find that the joint relative frequency is approximately 0.6216, which is equivalent to 62.16%.
Therefore, the joint relative frequency of students who do not like to run and enjoy swimming is approximately 62.16%.
In conclusion, the joint relative frequency of students who do not like to run and enjoy swimming, based on the given two-way frequency table, is approximately 62.16%.
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how did the greeks defend themselves from dorian rules?
Answer: the Dorians were far less advanced then the Mycenaean Greeks; economy collasped and trade stopped
what is an equation in point-slope form of the line that passes through the point (4,-1) and has a slope of 6
Answer:
y = 6x + (-1) or y = 6x - 1
Step-by-step explanation:
y = mx + b
M = Slope = 6
B = y-intercept = -1
personal income (in billions of dollars) in the united states was 12,430 in 2008 and 14,167 in 2013. assume that the relationship between the personal income y and the time t (in years) is linear. let t = 0 represent 2000.
The personal income in the United States can be modeled by a linear equation in the form y = mt + b, where m is the slope of the line and b is the y-intercept. We can use the given information to find the slope and y-intercept of the line.
First, we need to find the slope of the line. We can use the formula m = (y2 - y1) / (t2 - t1), where (t1, y1) and (t2, y2) are two points on the line. Using the given information, we can plug in the values to get:
m = (14,167 - 12,430) / (2013 - 2008)
m = 1,737 / 5
m = 347.4
Next, we need to find the y-intercept of the line. We can use the equation y = mt + b and plug in the values for one of the points and the slope to solve for b. Using the point (2008, 12,430), we get:
12,430 = 347.4(2008) + b
b = 12,430 - 696,691.2
b = -684,261.2
Therefore, the equation for the personal income in the United States is y = 347.4t - 684,261.2. We can use this equation to find the personal income for any given year. For example, to find the personal income in 2010, we can plug in t = 10 and solve for y:
y = 347.4(10) - 684,261.2
y = 3,474 - 684,261.2
y = -680,787.2
So the personal income in 2010 was approximately $680,787.2 billion.
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suppose a candy bar weighs 3.89 ounces how much does 8 bars weigh
Answer:
31.12 ounces
Step-by-step explanation:
3.89 x 8 = 31.12
The area of a circle is 100pi m2. What is the circumference, in meters? Express your
answer in terms of pi.
Answer: 20pi
Step-by-step explanation:
I need help someone plz help me with this
Answer:
F your welcome pls make me brainliest and follow me please!
Refer to the relation below to answer the following questions
ANSWER
The minimum value of y = -16
The maximum value of y = 6
The minimum value of x = -12
The maximum value of x = 10
STEP-BY-STEP EXPLANATION:
Given information
The following data sets were provided from the question given
{(-6, -16,), (-12, -2), (-6, -6), (10, 6)}
From the data sets given, we can determine our range and domain
The range is defined as all the y values in the data sets
The domain is defined as all the x values in the data sets
Therefore, we can determine our range and domain from the above information.
Range = {-16, -2, -6, 6)
Domain = {-6, -12, -6, 10}
The next thing is to determine the minimum and maximum values of x and y values
Therefore, the maximum and minimum values of y and x
The minimum value of y = -16
The maximum value of y = 6
The minimum value of x = -12
The maximum value of x = 10
Zack is on his school's color guard and is practicing throwing and catching his flag. He throws the flag into the air from a height of 5 feet at a velocity of 30 feet per second. After the flag starts to come back down, he catches it 7 feet above the ground.
To the nearest tenth of a second, how long is the flag in the air before Zack catches it?
Hint: Use the formula h=16t2+vt+s.
The Nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.
To determine the time the flag is in the air before Zack catches it, we can use the kinematic equation for vertical motion:
h = 16t^2 + vt + s
Where:
h is the height of the flag,
t is the time in seconds,
v is the initial vertical velocity of the flag,
s is the initial height of the flag.
In this case, the flag is thrown into the air from a height of 5 feet (s = 5) with an initial vertical velocity of 30 feet per second (v = 30). Zack catches it at a height of 7 feet (h = 7).
We can rewrite the equation as:
7 = 16t^2 + 30t + 5
To find the time (t) when the flag is at a height of 7 feet, we can rearrange the equation and solve for t. However, since this is a quadratic equation, we can also use the quadratic formula.
The quadratic equation in this case is:
16t^2 + 30t + 5 - 7 = 0
16t^2 + 30t - 2 = 0
Now, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Applying the values from the quadratic equation, we have:
t = (-30 ± √(30^2 - 4 * 16 * (-2))) / (2 * 16)
Simplifying further:
t = (-30 ± √(900 + 128)) / 32
t = (-30 ± √1028) / 32
Using a calculator, we find two solutions:
t ≈ -1.08 seconds or t ≈ 0.06 seconds
Since time cannot be negative in this context, we discard the negative solution.
Therefore, to the nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.
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At a factory, a machine puts tops on bottles at a rate of 90 bottles per minute. How many tops can be put on bottles between 10:00 AM and 2:30 PM?
Answer:
24300Step-by-step explanation:
Rate:
90 tops/minTime:
2:30 PM - 10:00 AM = 14:30 - 10:00 = 4:30 hours 4:30 hours = 4*60 + 30 min = 270 minNumber of tops can be put in 270 min:
270*90 = 24300Determine a series of transformations that would map Figure X onto Figure Y.
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The Cross Bayou Bridge in Shreveport, Louisiana has trusses that form triangles. The exterior angle of one triangle has a measure of (5 - 3)°. If the two nonadiacent interior angles of the triangle are 43° and (3x)°, what is the value of the exterior angle, in degrees?
The exterior angle of the triangle is 62°.
What is triangle?
A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.
Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.
Let us take the triangle as ABC.
Here \(m\angle C\)= 180-(5x-3)° [Because straight line angle is 180°].
We know that sum of all angles in triangle is add upto 180° Then,
=> \(m\angle A+m\angle B+m\angle C\)=180
=> 43°+3x°+180-5x+3=180°
=> -2x=180-180-43-3
=> -2x=-46
=> x=13°
Now exterior angle ,
=> 5x-3
=> 5*13-3
=> 65-3
=> 62°
Hence the exterior angle of the triangle is 62°.
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