Answer:
if x is an unknown number you know that it is 6 more than the unknown number
Step-by-step explanation:
Solve the following initial value problem for the function y(x).
y'=2xy^2 ; y(1)=1/2
y(x) = [tex]\frac{1}{3-x^2}[/tex] is the solution of the given differential equation.
what is differential equation?A differential equation is an equation that relates a function and its derivatives; it describes how a quantity changes with respect to another. and its solution is a function that satisfies the equation for all values of the independent variable
y'=2x[tex]y^2[/tex]
where y' is dy/dx
so dy/dx = 2x[tex]y^2[/tex]
=> dy/ [tex]y^2[/tex] =2xdx
integrating on both side we get:
-1/y = [tex]x^2[/tex] +c --- (i)
where c is a constant
given that y(1) =2
putting the value of y = 1/2 and x=1 in equation (i) we get
so -2 = 1+c
=> c= -3
y(x) = 1/(3-[tex]x^2[/tex]) is the required solution of the differential equation.
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Please help
7. There are two towns, Appleville and Bananaville. Appleville had a population of 3,000
people in the year 2000. Bananaville had a population of 1,000 in the same year.
Appleville's population has increased by 500 each year since. Bananaville's population
increases by 30% each year.
a. Write an equation to represent the population of Appleville, a, in x years after the year
2000.
b. Write an equation to represent the population of Bananaville, b, in x years after the year
2000.
c. What year will the population of Bananaville be larger than the population of Appleville?
On solving the provided question, we can say that the solution of the System of Equation 3000 + 500x = 1000*
What is System of Equation ?A finite collection of equations for which common solutions are sought is referred to as a set of simultaneous equations, often known as a system of equations or an equation system.
A system of equations consists of two or more equations and looks for common answers. "A collection of equations fulfilled by the same set of variables is called a system of linear equations."
The point provides a singular solution to the system of equations if the two lines cross at the same location. There are an endless number of solutions in the situation when the two lines meet, and there is none in the case where the two lines are parallel.
The equation for Appleville is
3000 + 500x, in x years after the year 2000
The equation for Bananaville is
1000* , in x years after the year 2000
The solution of the equations
3000 + 500x = 1000*
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Question 15 of 46
Which of the following statements about the polynomial function
F(x) = 2x³ - 2x² +1 is true?
The given polynomial function has 1 relative minimum and 1 relative maximum.
What are the relative minimum and relative maximum?The relative minimum is the point on the graph where the y-coordinate has the minimum value.The relative maximum is the point on the graph where the y-coordinate has the maximum value.To determine the maximum and the minimum values of a function, the given function is derivated(since the maximum or minimum is obtained at slope = 0)Calculation:The given function is
f(x) = 2x³ - 2x² + 1
derivating the above function,
f'(x) = 6x² - 4x
At slope = 0, f'(x) = 0 (for maximum and minimum values)
⇒ 6x² - 4x = 0
⇒ 2x(3x - 2) = 0
2x = 0 or 3x - 2 = 0
∴ x = 0 or x = 2/3
Then the y-coordinates are calculated by substituting these x values in the given function,
when x = 0;
f(0) = 2(0)³ - 2(0)² + 1 = 1
So, the point is (0, 1)
when x = 2/3;
f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27
So, the point is (2/3, 19/27)
Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.
So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.
Thus, option A is correct.
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A shopkeeper buys a quantity of oranges. On Thursday 2/7 were sold, on Friday 3/8 and on
Saturday 1/5. If 156 oranges remain unsold, how many were sold on Friday? *
There is a total of 420 Oranges were sold on Friday.
What is a fraction?
A fraction is a mathematical expression that represents a ratio of two numbers. It is written as a ratio of two integers, with the numerator (top number) representing the number of parts being considered and the denominator (bottom number) representing the total number of parts in the whole. The fraction can be written with a slash (/) or a horizontal line.
let the original number of orange be x
total orange sold = 2x/7 + 3x/8 + x/5 = 241x/280
Oranges left = x - 241x/280 = 39x/280
now, 39x/280 = 156
x = 1120 were there.
According to question
number of oranges sold on Friday = 3/8 * 1120
= 420 Oranges were sold on Friday.
Hence, there is a total of 420 Oranges were sold on Friday.
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A balloon attached to an atmospheric data-gathering device must be at least 1000 m high to begin recording information. Two spotters, Mary and Nathan, walk the same distance from the launch site at an angle of 70° to each other until they are 225 m apart. From these positions, they watch the rise of the balloon with instruments that record the angle of elevation. What angles of elevation must the instruments record in order for the balloon to be at the correct height for atmospheric data gathering?
The angle of elevation that the instruments have to record to be at the correct height is given as 79°
How to solve for the angle of elevationWe have 2x + 70 = 180
We have to find the value of x
2x = 110
x = 55
y/sin x = 225/sin70
This is the use of sine rule
From here we would have
y = 225(sinx/sin70)
Remember x = 55
y = 225(sin55/sin70)
y = 196.1378
tanθ = 1000/y
tan θ = 1000/196.1378
tanθ = 5.098
θ = tan⁻¹5.098
= 78.90°
Hence the conclusion is that the angle of elevation has to be 78.9 degrees for it to be at the correct height.
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Why is 6 a prime number?
No, 6 is not considered as a prime number, it is a composite number.
As given in the question,
Given number is equal to :
6
Prime numbers are those numbers which has only two factors one and the number itself.
Example of prime numbers are :
2, 3, 5, 7, 11, 13,... so on.
Here six has more than two factors .
Factors of 6 are equal to :
1, 2, 3, 6
There are four factors of six.
When a number has more than two factors then it is considered as composite number.
Example of composite factors are :
4, 6, 8, 9, 10, ... so on.
6 is a composite number.
Therefore, 6 is not a prime number it is a composite number.
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What are the 6 types of algebraic expressions?
The six types of algebraic expressions are:
Monomial: An expression with only one term, such as 5x or 2[tex]y^3[/tex].
Binomial: An expression with two terms, such as 3x + 4y or 7a - 5b.
Trinomial: An expression with three terms, such as 2[tex]x^2[/tex] + 4x - 6 or 5[tex]a^2[/tex] + 3ab - 2[tex]b^2[/tex].
Polynomial: An expression with more than one term, such as 2[tex]x^3[/tex] + 4[tex]x^2[/tex] - 6x + 8 or 5[tex]a^4[/tex] - 3[tex]a^2[/tex]b + 2[tex]b^3[/tex].
Rational expression: An expression that is the ratio of two polynomials, such as (2x+3)/(x-4) or (5[tex]a^2[/tex]-3b)/(a-2b).
Radical expression: An expression that contains a square root, cube root, or any other root of a number or a variable, such as √x or 3√(2y+5)
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What is the area of a triangle with base 16 cm and height 8 cm?
the area of a triangle with base 16 cm and height 8 cm is 64 cm^2
What is triangle?
" Triangle is defined as the two dimensional geometric shape with three vertices, three sides, and three interior angles enclosed in it."
Standard formula A= 1/2 bh
Area of the triangle =1/2 bh
According to the question,
Given,
Given formula of the area of the triangle
b represents the base of a triangle=16
h represents the height of a triangle
Area of the triangle =?
Height of the triangle =8
Substitute the value in the given formula we get,
=1/2*8*16
= 64
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The length of each edge of a cube is decreased by $40\%$. By what percent does the volume of the cube decrease
University Data
Receiving
Not Receiving
Total
Financial Aid
Financial Aid
Undergraduates
4222
3898
8120
Graduates
1879
731
2610
Total
6101
4629
10730
If a student is selected at random, what is the
probability that the student is a graduate
(rounded to the nearest percent)? [ ? ]%
Answer:
[tex] [/tex] [tex] [/tex] [tex] [/tex] [tex] [/tex]
How do you find the rule of an XY table?
if we plug in different values for the input, we get corresponding values of output. There is always a pattern in the way input values x and the output values y are related which is given by the function rule.
What are the Slope and intercepts ?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction of function
The slope expresses how quickly the dependent variable changes when the independent variable changes. The Greek capital letter D or D is frequently used by mathematicians and economics to represent change. Slope contrasts the change in the vertical axis, y, with the change in the horizontal axis, x.
On the x-axis, negative numbers are below the origin, and on the y-axis, they are to the left of the origin. If the x-value is negative, begin at the origin and go to the left; if the y-coordinate is negative, move downward.
Line graphs, also known as XY graphs, are used to visually represent data (the outcomes of an experiment) in order to demonstrate the link between various factors, such as the severity of the disease and time.
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A man deposited ghc 1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.
Calculate the
a.simple interest for the 4 years
b.amount at the end of the 4 types
a. The simple interest for 4 years would be $960.
b. The amount at the end of the 4 years would be $2160.$
A man deposited $1200 in his bank account. A simple interest of 20% per annum was paid on his deposit.
a. For calculating simple interest for the 4 years
We have been given data as:
Principal (P) = $1200
Rate of Interest (R) = 20%
Time (T) = 4 years
⇒ Simple interest = P × R × T
Substitute the value of P, R, and T in the above formula,
The simple interest for 4 years would be:
⇒ 1200 x 20% x 4 = 960
b. For calculating the amount at the end of the 4 years
The amount at the end of the 4 years would be:
1200 + 960 = 2160
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HELP. This is due today and I am so lost on how to do this without the side length.
Answer:
Photo 1:
Question 4:
If the angles are the same (two 45° and one 90°) the vertical side is equal to side C. the Pythagorean theorem states that A²+B²=C².
if Side C is equivalent to 4, both sides of the right angle are 4 (Because they are equivalent to each other.) so 4²+4²= 4 x [tex]\sqrt{2}[/tex] (5.8) so D=5.8, C=4
D is roughly 1.45 C
Step-by-step explanation:
The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments: investigate further whether the proportions of furnished apartments differ be- tween apartments with different numbers of bedrooms, it is useful to test formally whether the number of bedrooms in an apartment and whether it is furnished or not are independent (a) State the null hypothesis the relevant form of the test statistic and the approximate distri- bution of the test statistic for carrying out this text (b) Provide cross-tabulation of the apartment data by these two factors (you should generate this table using R)
(c) Carry out a formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv. the resulting p-value for the test, or rejection region You should also ensure that you conclude your formal test by interpreting the p-value (or rejection region and your observed test statistic) in terms of the original question discussed above:'
The students were interested in the proportion of rental apartments in these suburbs that were leased as furnished apartments and whether this varied with the number of bedrooms in these apartments 500x + 900y + 1500z = 750,000
formal test, using a = 0.05,of whether the proportions of furnished apartments varies across number of bedrooms, that is, whether the furnishing status of an apartment independent of the number of bedrooms in the apartment You may use R to carry out these calculations, but please state the following information from this test: i. the table of expected frequencies ii. the observed value of the test statistic iii. the relevant degrees of freedom for the distribution of the test statistic iv
500x + 900y + 1500z = 750,000 - - - (1)
x + y + z = 1000 - - - - (11)
x = 200 + y + z - - - - (111)
x + 2y + 3z = 1550 - - - (1V)
I bedroom = x
2 bedroom = y
3 bedroom = z
All the condition s gjvbbs'
500x + 900y + 1500z = 750,000 - - - (1)
x + y + z = 1000 - - - - (11)
x = 200 + y + z - - - - (111)
x + 2y + 3z = 1550 - - - (1V)
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x+y=5:3 and x+y=56
Work out x-y
The value of x-y from the given condition is 14.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
The given ratio is x:y=5:3.
So, x/y =5/3
3x=5y
To the equation x+y=56, multiply 5 on both side, we get
5x+5y=280
5x+3x=280
8x=280
x=35
Substitute x=35 in equation x+y=56, we get
35+y=56
y=21
Now. x-y is
35-21=14
Therefore, the value of x-y from the given condition is 14.
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jamal measured the height of a flower growing in his garden at the beginning of the month the flowerwas 3 1/4 inches tall the flower grew h inches during the month at the end of the month it 4 1/8 inches tall what equation models this situation
The equation that models the situation is 33 / 4 = h + 13 / 4.
How to find the equation that models a situation?Jamal measured the height of a flower growing in his garden at the beginning of the month. The flower was 3 1 / 4 inches tall . The flower grew h inches during the month.
At the end of the month it was 4 1 / 8 inches tall.
Hence, the equation to model the situation can be represented as follows:
Let's convert the mixed fractions to improper fractions.
3 1 / 4 inches = 13 / 4 inches
4 1 / 8 inches = 33 / 4 inches
Hence, the equation is as follows:
33 / 4 = h + 13 / 4
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Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of cosines, what is the measure of angle A? Round your answer to the nearest whole number, if necessary.
a = 20 cm
b = 13 cm
C = 139°
Answers:
126°
16°
25°
38°
The measure of angle A rounded to the nearest whole number is 25°.
Hence, option C is the correct answer.
What is the measure of angle A?Given that?
side a = 20cmside b = 13cmAngle C = 139°side c = ?Angle A = ?First, we determine the length of side c using the law of cosines.
c = √( a² + b² - 2ab( cosC ) )
We substitute in our values
c = √( 20² + 13² - 2×20×13( cos 139° ) )
c = √( 400 + 169 - 520( cos 139° ) )
c = √( 569 + 392.44898 )
c = √961.44898
c = 31 cm
Next, we find Angle A, using the law of cosines.
A = cos⁻¹[ ( b² + c² - a² ) / 2cb ]
We substitute in our values
A = cos⁻¹[ ( 13² + 31² - 20² ) / ( 2 × 31 × 13 ) ]
A = cos⁻¹[ ( 169 + 961 - 400) / 806]
A = cos⁻¹[ 730 / 806]
A = cos⁻¹[ 0.9057 ]
A = 25°
The measure of angle A rounded to the nearest whole number is 25°.
Hence, option C is the correct answer.
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PLEASE HELP
1/2 (2x - 4) + 2 = 4(x + 2) - 11
SHOW WORK!!
Answer:
x = 1-------------------------------------
Solve the following equation:
1/2 (2x - 4) + 2 = 4(x + 2) - 11 Given1/2(2x) - 1/2(4) + 2 = 4x + 4(2) - 11 Distributex - 2 + 2 = 4x + 8 - 11 Simplifyx = 4x - 3 Simplify4x - x = 3 Collect like terms3x = 3 Simplifyx = 1 Answerthe spoke of a bicycle is 1 foot long. How many revolutions will the tire make when it is ridden one mile? Circumference and pi
They spoke of a bicycle that is 1-foot long. the revolutions the tire will make when it is ridden one mile is 1681.52 revolutions.
What are revolutions?Generally, The circumference of a tire is equal to the diameter times pi
C = d * pi.
Since the spoke of the bicycle is 1 foot long, the diameter of the tire is also 1 foot.
Therefore, the circumference of the tire is 1 * pi = approximately 3.14 feet.
To find out how many revolutions the tire will make when it is ridden one mile, you need to divide the distance traveled (1 mile) by the circumference of the tire.
One mile is equal to 5280 feet, so to find out how many times the tire will revolve, you would divide
5280/ 3.14
=1681.52 revolutions.
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Which equation can be simplified to find the inverse of y = 2x²?
0-2x²
O
y-1x²
O -y = 2x²
O x = 2y²
O
Answer:
D.) x = 2y²
Step-by-step explanation:
You can find the inverse of an equation by swapping the positions of the "x" and "y" variables. Then, you would need to rearrange the equation to re-isolate the "y" variable.
As such, D.) is the correct option because it is identical to the original equation except that the variables are swapped.
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.
[tex]y = 2x^2\hspace{5em}\stackrel{\textit{quick switcheroo}}{\boxed{x = 2y^2}}\implies \cfrac{x}{2}=y^2\implies \sqrt{\cfrac{x}{2}}=\stackrel{f^{-1}(x)}{y}[/tex]
Discuss the difference between r and p. Choose the correct answers below. r represents the : p represents the: 1. sample correlation coefficient thing 2. critical value for the correlation coefficient. 3. population correlation coefficient. Discuss the difference between r and p. Choose the correct answers below. r represents the: p represents the: 1. critical value for the correlation coefficient. 2. population correlation coefficient. 3. sample correlation coefficient. Click to select your answers)
The linear correlation coefficient unknown population is denoted by the statistic r and correlation strength is denoted by the parameter p, respectively.
As a result, correlations are generally portrayed by the two integers r and p. A number of +1 denotes a fully linearly positive correlation, while a number of -1 denotes a fully linearly negative connection. The correlation coefficient has a range of -1 to +1. The linear correlation becomes weaker as r approaches closer to zero.
The sample correlation coefficient evaluates the scatter plot points and a linear regression line constructed from those points (r). The correlation coefficient, denoted as r, ranges in value from -1 to 1. A p-value is a measure of statistical significance.
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You are saving $5 per week. Write and Solve and inequality that represents how many weeks (w) you need to save in order to save at least $75
Answer:
w is greater than or equal to 15
Step-by-step explanation:
15(5)=75
What is the best description of range of function?
The domain of a relation or function are the input values. In this image the domain is represented by the begining of the arrows (the values on the x column).
What is a one one function?
In Maths, an injective function or injection or one-one function is a function that comprises individuality that never maps discrete elements of its domain to the equivalent element of its codomain. We can say, every element of the codomain is the image of only one element of its domain.
The range are the output values. In this case they are the ends of the arrows (the values on the y column
• Domain: {5, 10, 15, 20}
• Range: {-3, -1, 1, 3}
• Description: ,this is an injective function, because it is a one to one relation
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Which of the following is an example of Commutative Property w.r.t. Addition ?A.5+ 9 = 9 + 5B. (9 + 2) + 8 = 9+ (2 + 8)C. 4+ 7 = 3 +4D. 6 x 1 = 6
The correct answer is A. 5 + 9 = 9 + 5 is an example of the commutative property of addition.
The commutative property of addition states that the order of the numbers being added does not affect the sum. In other words, for any two numbers a and b, a + b = b + a. In this example, 5 + 9 = 9 + 5, which shows that the order of the numbers being added does not change the sum.
B. (9 + 2) + 8 = 9+ (2 + 8) is an example of the associative property of addition.
C. 4+ 7 = 3 +4 is not an example of commutative property as its not true 4+7 != 3+4
D. 6 x 1 = 6 is an example of identity property of multiplication.
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Which of the following describes the effect of the transformation given by (x, y) -› (-x, y) on points in the coordinate plane?
Can someone help me please
Answer:
1/9, 3, 27
(A / the first option listed)
Step-by-step explanation:
Here, we are given an expression with an "x" in it, and we are to evaluate possible x values, which means we plug them in as the x in the expression
first,
x = -2
3ˣ → 3⁻²
when we raise something to a negative power, we simply find the positive version of that power, and put a 1 over it:
3² = 3 · 3 = 9
so, 3⁻² = [tex]\frac{1}{9}[/tex] (1/9)
next,
x = 1
3ˣ → 3¹
now, here we have something raised to the power of 1, which is always itself, so 3¹ = 3
(think of ^to the power of as how many times we multiply that number, so 3² = 3 · 3, 3¹ = 3)
and finally,
x = 3
3ˣ → 3³
here, we can multiply 3 by itself 3 times:
3 · 3 · 3 = 27
so, 3³ = 27
[important note: when we raise something to a power, we are not multiplying the base number by that number, but this is a common mistake. but the exponent is how many times we are multiplying that number, which is confusing at first}
So, our answers in order are:
1/9, 3, 27 (the first option listed)
hope this helps! let me know if I should clarify anything :)
Look in the picture, please help me, I will mark brainliest!!!
Answer:
My idea is to look all at the left side of the graph, and whatever number without the decimal is lowest, label first, and do the same for the right side, for instance, if the lowest is 161, then label from lowest to highest across the x-axis, if it is something like 7 as the lowest on the right side of the graph, lowest to highest up the y-axis
Step-by-step explanation:
Instructions: Find the missing side. Round your answer to the nearest tenth.
X
-
16
65⁰
X
Answer:
Maybe the answer must be 90°
On Monday Marco practiced the piano for 7/10 hour. On Tueday he practiced for 1 and 5/6 hour he i uppoed to practice 1 and 1/4 hour each day
Marco practiced 1.13 hours more on Tuesday than on Monday.
In mathematics, a fraction is used to denote a portion or component of the total. It stands for the proportionate pieces of the whole. The numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, while the denominator is the number at the bottom.
Given that,
Marco practiced for only 7/10 hours on Monday (less than the expected [tex]1\frac{1}{4}[/tex]hours)
He practiced for [tex]1\frac{5}{6}[/tex] hours on Tuesdays.
He is supposed to practice [tex]1\frac{1}{4}[/tex] hours each day.
Finding the difference between the hours he practiced each day:
[tex]1\frac{5}{6} - 7/10 = 11/6-7/10= (110-42)/60 = 68/60 = 1.13 hours[/tex]
Thus, Marco practiced 1.13 hours more on Tuesday than on Monday.
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I need help please. Does any one know how to do this
The probability that a randomly selected muffin will be a banana nut muffin is; P(banana nut muffin) = 0.5
What is the probability of selection?From the table in the question, we are given;
Number of blackberry muffins = 10
Number of banana nut muffins = 25
Number of Chocolate chip muffins = 1
Number of blueberry muffins = 11
Number of pumpkin spice muffins = 3
Total number of muffins = 10 + 25 + 1 + 11 + 3
= 50
Probability = number of successful outcomes/Total number of outcomes
Thus;
P(banana nut muffin) = 25/50
= 0.5
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