Every number between 3 and 5 is included in the Union where x∈R of [3− x^2,5+ x^2], and no number outside of that range is included. The union is equal to [3,5].
To prove that the Union where x∈R of [3− x^2,5+ x^2] = [3,5], we need to show that every number between 3 and 5 is included in the union, and no number outside of that range is included. First, let's consider any number between 3 and 5. Since x can be any real number, we can choose a value of x such that 3− x^2 is equal to the chosen number. For example, if we choose the number 4, we can solve for x by subtracting 3 from both sides and then taking the square root: 4-3 = 1, so x = ±1. Similarly, we can choose a value of x such that 5+ x^2 is equal to the chosen number. If we choose the number 4 again, we can solve for x by subtracting 5 from both sides and then taking the square root: 4-5 = -1, so x = ±i. Therefore, any number between 3 and 5 can be expressed as either 3- x^2 or 5+ x^2 for some value of x. Since the union includes all such intervals for every possible value of x, it must include every number between 3 and 5. Now, let's consider any number outside of the range 3 to 5. If a number is less than 3, then 3- x^2 will always be greater than the number, since x^2 is always non-negative. If a number is greater than 5, then 5+ x^2 will always be greater than the number, again because x^2 is always non-negative. Therefore, no number outside of the range 3 to 5 can be included in the union. In conclusion, we have shown that every number between 3 and 5 is included in the Union where x∈R of [3− x^2,5+ x^2], and no number outside of that range is included. Therefore, the union is equal to [3,5].
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Last year, wind turbines along a hilly ridge had an average output of 340 kilowatt hours per year. The turbines were upgraded, and now their average annual output is 90% more. What is the new average yearly output
The required new average is 646-kilowatt hours per year,
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Last year, wind turbines along a hilly ridge had an average output of 340-kilowatt hours per year. The turbines were upgraded, and now their average annual output is 90% more.
So,
new average = 340 + 90% of 340
new average = 340 + 0.90 × 340
new average = 340 + 306 = 646 kilowatt hours per year,
Thus, the required new average is 646-kilowatt hours per year,
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part b pls
This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Javier bought 3 bags of balloons for a party. He used 8 balloons from each bag.
Which equation can be used to determine how many balloons, b, were originally in each bag if there were 21 balloons left over?
Multiple choice question.
cross out
A)
3b−8=21
cross out
B)
8b−3=21
cross out
C)
3(b−8)=21
cross out
D)
8(b−3)=21
Part B
Determine how many balloons were originally in each bag.
__ balloon(s)
The equation which is used to determine number of balloons were originally in bag is 3(b-8)=21 and the number of balloons in each bag on?
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Based on the given conditions, formulate: 3×(b-8)=21
Reduce the greatest common factor on both sides of the equation:
b-8 =7
Rearrange unknown terms to the left side of the equation: b = 7+8
Calculate the sum or difference: b=15
The equation which is used to determine number of balloons were originally in bag is 3(b-8)=21 and the number of balloons in each bag is 15.
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In Problems 15-18, write each relation as a set of ordered pairs. Then
identify the domain and the range of the relation. See Objectives 1
and 2.
15.
Newspaper
USA Today
Wall Street Journal
New York
Daily Circulation
(in millions)
2.28
2.06
1.1
Los Angeles Times
0.82
Washington Post
0.70
SOURCE: Information Please Almanac
Times
Times
On solving the provided question, we can say that the domain of the following data will be domains = [ (( 2.28 , 2.06) to ( 1.18 , 0.70) ] and [ (( 9 , 11) to ( 11 , 17) ]
what is domain?The domain of a function is the set of possible values that it can accept. The x-values of a function like f are represented by these integers (x). A function's domain is the set of possible values on which it can be used. This set is the value that the function returns after the insertion of the x value. Y = f is the definition of a function with x as the independent variable and y as the dependent variable (x). A value of x is said to be in a function's domain if it can be successfully utilised to produce a single value of y by using the value of x.
the domain of the following data will be
domains = [ (( 2.28 , 2.06) to ( 1.18 , 0.70) ]
domains = [ (( 9 , 11) to ( 11 , 17) ]
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what number should be added to 8000 to make it a perfect square
Answer:
100 should be added as 8100 is square root of 90 ...
Draw a histogram for each data set.
4) Age at First Job
17 15 16 16 13 18 16 17 18 17 14 16 18 22 15 16
The histogram for the data-set in this problem is given by the image presented at the end of the answer.
How to draw the histogram?The histogram of a data-set shows the number of times that each item was observed in the data-set.
For this problem, we have that:
4 observations were between 13 and 16.11 observations were between 16 and 19.0 observations were between 19 and 22. 1 observation was between 22 and 25.Hence the histogram is given by the image at the end of the answer.
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What is double prime called?
Double prime is called by different names as per the topics used in Mathematics :
Inches in length , second order derivative in differentiation, conjugate points, transformed coordinates etc.
As given in the question,
In Mathematics double prime is represented by ". Double prime is used to represent different types of function as per the topic.Double prime is used to represent the second derivative of the given function in differentiation.Double prime is used to represent the measure of length in inches.Double prime is also used to represent the transformed coordinates in the coordinate geometry.Sometimes double prime also represents the conjugate points.It also represents the number of arc seconds in the measure of any angle.Therefore, the double prime is known by many names such as inches in length, second order derivative, conjugate points, transformed coordinates etc.
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which quadrant does the point (2, 3) lie?A I B IIC III D III
The quadrant of the given point (2,3) is given A I ( that is first quadrant ).
As given in the question,
Given point is equal to :
Point ( 2, 3 )
Conditions of the quadrant in the coordinate plane is given by :
Let ( x ,y ) be the coordinates in the coordinate plane.
In the first quadrant : ( x , y ) both x and y are positive.
In the second quadrant : ( -x , y ) x is negative and y is positive.
In the third quadrant : ( -x , -y ) x is negative and y is negative.
In the fourth quadrant : ( x , -y ) x is positive and y is negative.
Here in the given point ( 2,3 ) both x and y are positive.
Given point lies in the first quadrant.
Therefore, the quadrant of the given point (2,3) is equal to A I ( that is first quadrant ).
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Rewrite each expression as a single power of 10
The solution using laws of exponents are;
A) 10⁻⁵
B) 10³
C) 10⁻²
D) 10⁻²⁰
E) 10⁻¹
F) 10⁻¹⁴
How to use laws of exponents?Some of the laws of exponents are;
1) Product of powers rule:
When multiplying two bases with the same value, keep the bases the same and then add the exponents together to get the solution
2) Quotient of powers rule; When trying to divide two bases of the same value, keep the base the same, and then subtract the exponent values.
3) Power of a power rule; This rule tells how to solve equations where a power is being raised by another power.
4) Power of a product rule; Whenever any base is being multiplied by an exponent, then we distribute the exponent to each part of the base.
A) 10⁻³ × 10⁻²
= 10⁻³⁻²
= 10⁻⁵
B) 10⁴ × 10⁻¹
= 10⁴⁻¹
= 10³
C) 10⁵/10⁷
= 10⁵⁻⁷
= 10⁻²
D) (10⁻⁴)⁵
= 10⁻⁴*⁵
= 10⁻²⁰
E) 10⁻³ × 10²
= 10⁻³⁺²
= 10⁻¹
F) 10⁻⁹/10⁵
= 10⁻⁹⁻⁵
= 10⁻¹⁴
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A movie studio keeps 240 dresses in its wardrobe for historical films. Three-fifths of them can be used for movies that take place in the 1700s and 15% of them can be used for movies in the civil war era.
What percent of the dresses are for films set in the 1700s or during the civil war era? Explain how you found your answer
The percent of the dresses that are for films set in the 1700s or during the civil war era is; 75%
How to find the percentage?Percentage is normally calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by the expression; Percentage = (value / total value) * 100%
Now, we are told that;
Number of movie dresses kept = 240 dresses
Fraction used for movies that take place in the 1700s = 3/5
Percentage used for movies in the civil war era = 15%
Thus;
Number of dresses in the 1700 = 3/5 * 240 = 144
Number of dresses for the civil era = 15% * 240 = 36
Thus;
Total for civil era and in the 1700s = 144 + 36 = 180
Thus;
Percentage for either period = 180/240 * 100% = 75%
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What does an r value of 0.7 mean?
According to the following interpretation, a correlation value of 0.7 between two variables denotes a significant and favorable association between them.
What is Correlation Coefficient?Correlation coefficients demonstrate how strongly two independent variables, x and y, are connected linearly.
A linear correlation coefficient greater than zero indicates a relationship that is favorable.
A value less than zero denotes a bad relationship. To summarize, when x and y have values of 0, there is no link between them.
A statistic that describes how closely two variables' movements are related to one another is the correlation coefficient (r2).
The most widely used correlation coefficient is the Pearson product-moment correlation, which is used to detect if two variables are linearly related.
This correlation value, however, might not always be an accurate predictor of reliance in a non-linear link.
Hence, According to the following interpretation, a correlation value of 0.7 between two variables denotes a significant and favorable association between them.
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If f(x)=4-x^2 and g(x)=6, which expression is equal to (g-f)(3)
The value of the function (g - f)(x) = 6 - 4 + x² at x = 3 will be 11.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
f(x) = 4 - x² and g(x) = 6
The function (g - f)(x) will be given as,
(g - f)(x) = 6 - 4 + x²
(g - f)(x) = 2 + x²
The value of the function (g - f)(x) at x = 3 will be give as,
(g - f)(x) = 2 + (3)²
(g - f)(x) = 2 + 9
(g - f)(x) = 11
The value of the function (g - f)(x) = 6 - 4 + x² at x = 3 will be 11.
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how many different digits are used in the hexadecimal number system?
Answer:16
Step-by-step explanation:
Write down a quadratic equation in the form $x^2 + bx + c = 0$ whose solutions are $x = -7$ and $x = 1. $.
Answer:
an average weight of 10student was calculated to be 75. later it was discovered thatone weight wss insread as 35 instead of 50k.g. calculate the correct average weight
The sides of the triangle shown increase in such a way that
dz/dt=1, and dx/dt=3 dy/dt At the instant when x = 12 and y= 5, what is the value of dx/dt?
Therefore , the solution of pythgoras theorem is the value of is dx/dt = 0.95, when x = 12 and y =5.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Here,
It is given that -
dz/dt = 1,
dx/dt = 3(dy/dt)
⇒dy/dt = 1/3 (dx/dt)
As shown in the diagram x = base, y = perpendicular and z = hypotenuse.
According to the Pythagoras theorem -
z² = x² + y²
Differentiating both sides -
d/dt (z²) = d/dt (x² + y²)
2z dz/dt = 2x dx/dt + 2y dy/dt
z dz/dt = x dx/dt + y dy/dt
Substituting the value of dy/dt -
z dz/dt = x dx/dt + y/3 (dx/dt)
z dz/dt = dx/dt (x + y/3)
dx/dt = (z dz/dt)/(x + y/3)....equation 1
So, when x = 12 and y = 5, the value of z -
z = √[(12)² + (5)²]
z = √(144+25)
z = √169
z = 13
Substituting the value of x, y, z and dz/dt in equation 1 -
dx/dt = (13 × 1)/(12 + 5/3)
dx/dt = 13 / 41/3
dx/dt = (13 × 3)/41
dx/dt = 39/41
dx/dt = 0.95
Therefore, the value of dx/dt = 0.95.
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Therefore , the solution of pythgoras theorem is the value of is dx/dt = 0.95, when x = 12 and y =5.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.
Here,
It is given that -
dz/dt = 1,
dx/dt = 3(dy/dt)
⇒dy/dt = 1/3 (dx/dt)
As shown in the diagram x = base, y = perpendicular and z = hypotenuse.
According to the Pythagoras theorem -
z² = x² + y²
Differentiating both sides -
d/dt (z²) = d/dt (x² + y²)
2z dz/dt = 2x dx/dt + 2y dy/dt
z dz/dt = x dx/dt + y dy/dt
Substituting the value of dy/dt -
z dz/dt = x dx/dt + y/3 (dx/dt)
z dz/dt = dx/dt (x + y/3)
dx/dt = (z dz/dt)/(x + y/3)....equation 1
So, when x = 12 and y = 5, the value of z -
z = √[(12)² + (5)²]
z = √(144+25)
z = √169
z = 13
Substituting the value of x, y, z and dz/dt in equation 1 -
dx/dt = (13 × 1)/(12 + 5/3)
dx/dt = 13 / 41/3
dx/dt = (13 × 3)/41
dx/dt = 39/41
dx/dt = 0.95
Therefore, the value of dx/dt = 0.95.
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Solve for x and graph the solution on the number line below. x−9≤ −4
Answer: x ≤ 5
Step-by-step explanation:
x - 9 --> x + (-9)
-9 + 5 = -4
12 students play on the schools basketball team 36 students play on the football team.what is the ratio of basketball players to football players
A rope of length 205 m is cut into 10 pieces of one length and 5 pieces of another
length. The total length of three of the first 10 lengths exceeds that of two the second
length by 2 m. Find the lengths of the pieces.
12 m length rope of 10 pieces and 17 m rope of 5 pieces.
What is equation with two variables?
The equation that has two variable terms and another equation is needed to solve both equations simultaneously is called equation with two variables.
What is the length of the rope pieces?
Given, total length of rope = 205 m.
The rope is cut into 10+5 = 15 pieces, in where 10 pieces rope are the same size, and the remaining 5 pieces are different size.
assume, length of first 10 piece = X m
length of last 5 piece = Y m
As per the first condition, total length of three of the first 10 length exceeds that of two the second length by 2 m.
hence, 3X - 2Y = 2
again, we know the total length = 205 m
10X + 5Y = 205
from the first equation, 3X = 2 +2Y
X = (2+2Y) / 3
putting the X value to the 2nd equation and we get
10(2+2Y)/3 + 5Y = 205
20+ 20Y+15Y = 615
35Y = 595
Y = 17 m
X = (2+2×17) /3 = 12 m
10 pieces of X length = 10 pieces of 12 m length
5 pieces of Y length = 5 pieces of 17 m length
10×12 = 120m
5×17 = 85m
120m + 85m = 205m
hence, verified.
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Is it true that the square root of a sum is equal to the sum of the square roots?
A number's square root multiplied by another number's square root does not always equal the total of these two numbers' square roots.
Why is it called sum of squares?A statistical method called the sum of squares (SS) is used in regression analysis to determine how well the data can fit the model and how dispersed the data are. Since it is determined by adding up the squared differences, the sum of squares is how it is calculated.
A sum's square is equal to the product of its summands' squares and its double products' sums of summands in twos.
So, it is not always true that the square root of a sum is equal to the sum of the square roots.
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A number's square root multiplied by another number's square root does not always equal the total of these two numbers' square roots.
Why is it called sum of squares?In regression analysis, the sum of squares (SS), a statistical technique, is used to assess how well the data fit the model and how distributed they are. The sum of squares is used to compute it as it is obtained by combining together the squared differences.
The product of a sum's square and its double products' sums of its summands in twos is known as the summands' square. Hence, the square root of such a sum is not necessarily equal to the total of the square roots.
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what is the diameter of the semi circle whose perimeter is 54
Perimeter of a semi circle = ñr + d(2r),ñ=22/7,r=?, d=2r
54=22/7 × r +2r
54=3.142r +2r
54=5.142r
r=54/5.142
r=10.5
d=2r
d=2×10.5017
d=21.00cm
HELLPPPP ME RIGHT AWAY PLEASE?
Answer: 3 = 12 , 4 = 2 , 2 = 22
Step-by-step explanation: Since t represents the number of tickets purchased, we need to plug that into our equation.
d = -10t + 42
d = -10(3) + 42
We know that d is the balance of the bank account, so if we plug in the number of tickets purchased, we will solve to get the balance of the bank account.
d = -10(3) + 42
d = -30 + 42
d = 12
In this equation, If we purchase 3 tickets, the balance of the bank account would be 12 dollars.
Let's do the last 2 equations using d = -10t + 42.
d = -10(4) + 42
d = -40 + 42
d = 2
In this equation, If we purchase 4 tickets, the balance of the bank account would be 2 dollars.
d = -10(2) + 42
d = -20 + 42
d = 22
In this equation, If we purchase 2 tickets, the balance of the bank account would be 22 dollars.
Breanna bikes 84 miles in 6 hours at a constant rate. The formula d = rt gives the relationship between distance (d), rate (r), and time (t). At what rate was Breanna biking?
Breanna was biking at a constant rate of 14 miles per hour.
What does rate means?A rate can be defined as the speed at which something happens or changes or the amount or number of times it happens or changes in a particular period.
The formula that describes the relationship between distance (d), rate (r), and time (t) is d = rt.
Now, we will solve for r. From d = rt. Our r will equals to:
= d/t.
Now we compute the rate at which Breanna was biking.
= 84 miles/6 hours
= 14.
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Use the long division method to find the result when 2x³+4x2 + 7x + 5 is divided
by x + 1.
Solving the provided question, we can say that the quadratic equation 2x³+4x2 + 7x + 5 is divided by (x+1) = -2+4-7+5 = 0
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation
2x³+4x2 + 7x + 5 is divided by (x+1)
which means X+1 is factor
so, x = -1
2x³+4x2 + 7x + 5 = -2+4-7+5 = 0
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Brooo this is sooo hard please helpppo
Answer:
Step-by-step explanation:
divided by nine ;)
The area of the curved surface of a cylindrical jar is 1,584 square centimeters. The height of the jar is 28 centimeters. a) What is the circumference of the jar? b) What is the radius of the jar?
please help this is due soon
The circumference of the jar is 56.57cm.
The radius of the jar is 9 cm.
What is the circumference of the jar?A cylinder is a three-dimensional object. It is a prism with a circular base.
The curved surface area of a cylinder = 2πrh
Where:
π = 3.14r = h = 281584 = 2 x 3.14 x 28 x r
r = 1584 / (2 x 3.14 x 28)
r = 9 cm
Circumference = 3.14 x diameter
diameter = 2 x radius
3.14 x 2 x 9 = 56.57cm
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Use the data to complete this statement. Any non-integer answers should be entered as decimals, rounded to the tenths place. The mean of the data set is , and the sample proportion of numbers less than the mean is %.
The mean of the given data set is 21.7 and the sample proportion of numbers less than the mean is 60%.
Consider the given data set (in the image attached to this answer). We have to find the mean of the data set is, and the sample proportion of numbers. We have been told that any non-integer answers should be entered as decimals, rounded to the tenth place. The means is the average of any data set.
Here, mean = (20.5 +24.2 +18.3 + 1.3 +27+25.5 +21+19.8+27.3+18·4 + 20.5+17-6 +25.5 +23.4 +20.2)/15
Mean = 325.5/15 =21.7
The sample proportion of numbers less than
Mean = 9/100 * 15 %
Answer: 21.7 60%
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How do you find the equation of the line of best fit?
A line of best fit can be described by the equation y=mx+b, where m denotes the slope and b the y-intercept. For a better understanding of the idea of approximating the equation of a line of best fit and making predictions, we will look at two examples that show a scatter plot with a line of best fit.
What is a line, exactly?
Having only length and no width, a line is a one-dimensional figure. A line is created from a collection of points that are endlessly stretched in the opposing directions.
A two-dimensional plane's two points serve as its determining factors. Collinear points are two points that are located on the same line.
What is the equation for a straight line?
. A straight line has the equation y=mx+c, where c is the height at which the line crosses the y-axis, also known as the y-intercept, and m is the gradient.
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What is residual value formula?
Residual=actual y value−predicted y value,ri=yi−^yi. Residual = actual y value − predicted y value , r i = y i − y i ^ . Having a negative residual means that the predicted value is too high, similarly if you have a positive residual it means that the predicted value was too low..
What Exactly Is Residual Value?
The estimated value of an asset that is fixed at the end of its useful life or lease term is its residual value, which is often referred to as salvage value. In lease agreements, the residual value is one of the lessor's main methodologies for calculating the lessee's periodic lease payments.
A good residual value is what?
Check out the Car Lease Ratings section of our Lease Kit for a complete list of high-residual vehicle brands and models.
A car is probably not a good lease deal if the lease-end residual value is less than 50% of the MSRP (for a 36-month lease). 55% to 65% of MSRP would be a nice residual.
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What is the domain of f/x )= x?
The domain of f(x) = x is all real numbers. This is because the input (x) is the same as the output (f(x)).
This means that any value that is inputted into the function will result in the same value as the output, regardless of the value. The domain of the function can be expressed mathematically as:
Domain of f(x) = x = {x ∈ R}
This means that the domain of f(x) is all real numbers, as any real number put into the function will result in that same real number being outputted. For example, if x = 5, then f(x) = 5. This illustrates that the domain of f(x) = x is all real numbers.
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Help me find the value of Y!
ABCD is an isosceles trapezoid with legs AB and CD and base BC. If the length of AB is 7y-4, the length of BC is 4y-6, and the length of CD is 8y-18, find the value of y.
I know 2 lengths are equal and I know algebra but I just don't know where to start. Please explain it. Sorry there's no diagram
======================================================
Explanation:
You are correct in thinking you'll set two things equal to one another. This type of thing happens often in algebra. The question you probably have is: what two things do I set equal?
The key term is "isosceles" which tells us we have two non-parallel sides equal in this trapezoid. In other words, we ignore the parallel sides.
The non-parallel sides of a trapezoid are known as the legs.
The legs in this case are
AB = 7y-4CD = 8y-18Set those expressions equal to one another and solve for the variable y.
AB = CD
7y-4 = 8y-18
-4+18 = 8y-7y
14 = y
y = 14 is the final answer
----------------------
Check:
AB = 7y-4 = 7*14-4 = 98-4 = 94CD = 8y-18 = 8*14-18 = 112-18 = 94Both legs AB and CD are 94 units long to confirm this trapezoid is indeed isosceles. The answer is confirmed.
Side note: as mentioned earlier, we completely ignore BC = 4y-6. It was probably put in there as a distraction.
8-2 practice multiplying a polynomial by a monomial
Find each product
1. x(5x + x^2)
2. x(4x^2 + 3x + 2)
Answer:
Skills Practice. Multiplying a Polynomial by a Monomial. Find each product. 1. a(4a + 3). 2. -c(11c + 4). 4a2 + 3a. -11c2 - 4c. 3. x(2x - 5). 4. 2y( y - 4).
Step-by-step explanation: