J is a maximal ideal.
1. To prove that A/J is a commutative ring with unity, note that the operations of addition and multiplication on A/J are well-defined and are commutative since they are inherited from the commutative ring A. Furthermore, the additive identity of A is the same as the additive identity of A/J, and therefore A/J has a unity.
2. Suppose first that J is a prime ideal of A. Then, if A/J is not an integral domain, there exist two nonzero elements x,y of A/J such that xy=0. This means that x and y are in the same coset of J in A. Thus, x-y is an element of J. Since J is prime, either x or y must be in J, which is a contradiction. Therefore, A/J is an integral domain. Conversely, if A/J is an integral domain, then the same argument can be reversed to show that J is a prime ideal.
3. If J is a maximal ideal of A, then A/J is a field by the fact proved in this chapter. Since a field is an integral domain, J is a prime ideal.
4. Suppose that A/J is a field. Then, for any ideal I of A, either I is contained in J or J is contained in I. This implies that J is a maximal ideal.
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The solutions to the equation x^2 + 8x +4 = 0 are x1 and X2 (a) Without solving the equation write down the value of (i) x1 + x2 (ii) x1x2 The solutions to the equation ax^2 + bx+c=0 where a,b,c E Z are 1/x1 and 1/x2 (b) Use part (a) to find the value of (i) b/a (ii) c/a Find the values of a, b and c where a is the smallest possible positive value.
The solutions to the equation x^2 + 8x +4 = 0 are x1 and X2.
(a) Without solving the equation write down the value of
(i) x1 + x2 = -8 (The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, so in this case, -8/1 = -8)
(ii) x1x2 = 4 (The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a, so in this case, 4/1 = 4)
The solutions to the equation ax^2 + bx+c=0 where a,b,c E Z are 1/x1 and 1/x2
(b) Use part (a) to find the value of
(i) b/a = -(1/x1 + 1/x2) = -(-8) = 8 (The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a, so in this case, -b/a = -8)
(ii) c/a = 1/x1 * 1/x2 = 1/4 (The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a, so in this case, c/a = 4)
Find the values of a, b, and c where a is the smallest possible positive value.
Since a is the smallest possible positive value, let a = 1. Then, b = 8 and c = 4. So the values of a, b, and c are 1, 8, and 4, respectively.
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Use P=PV(i1−(1+i)−n)
to determine the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0%.
Answer:
$1,111.88
Step-by-step explanation:
To calculate the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0% interest rate, we can use the formula:
P = PV(i / (1 - (1 + i)^(-n)))
where:
P = monthly payment
PV = present value or loan amount
i = interest rate per period
n = total number of periods
In this case, the loan amount is $60,000, the interest rate per period is 4.0% / 12 = 0.00333, and the total number of periods is 5 years x 12 months/year = 60 months.
Substituting these values into the formula, we get:
P = 60000(0.00333 / (1 - (1 + 0.00333)^(-60)))
P = $1,111.88 (rounded to the nearest cent)
Therefore, the monthly payment for a $60,000 loan compounded monthly for 5 years at a 4.0% interest rate is $1,111.88.
The table of values below represents a linear function and shows Marco’s progress as he is pumping gas into his car. What is the output for the initial value?
Gas in Marco’s Car
Seconds Spent Pumping Gas
0
12
24
36
48
Gallons of Gas in Car
3
5
7
9
11
3 gallons are the starting value determined by the slope-intercept relation.
What is slope intercept form?One of the most popular ways to represent a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfils.
To determine how much gas is entering his car each second, we must determine the rate of change:
Rise / Run is the rate of change.
Rate of change: (11 - 3 - 11) / (48 - 0)
Change rate: 8/48 = 1/6 gallons
Making use of the slope-intercept relationship:
Y = b(x) + c(slope); c(initial gas amount)
Choose any (x, y) point pair on the table:
(0, 3)
3 = 1/6x + c 3 = 1/6(0) + c\s3 = 0 + c\sc = 3
As a result, the starting point is 3 gallons.
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The diameter of a circle is 32 cm. Find its area to the nearest whole number.
Answer:
804 cm^2
Step-by-step explanation:
The area of a circle is given by the formula:
A = πr^2
where r is the radius of the circle. Since we are given the diameter of the circle, which is 32 cm, we can find the radius by dividing the diameter by 2:
r = d/2 = 32/2 = 16 cm
Substituting this value into the formula for the area of a circle, we get:
A = πr^2 = π(16)^2 = 256π
To find the approximate value of this expression in square centimeters, we can use the approximation π ≈ 3.14. Therefore:
A ≈ 256(3.14) ≈ 804
Rounding this value to the nearest whole number, we get:
A ≈ 804
Therefore, the area of the circle to the nearest whole number is 804 square centimeters.
Suppose sin θ = - 3/5, sin ɸ = 20/29 Moreover, suppose θ is in Quadrant IV and ɸ is in Quadrant l. Find the following. sin(θ + ɸ) = ____ cos(θ + ɸ) = ____
sin(θ + ɸ) = 17/145 and cos(θ + ɸ) = 144/145.
Suppose sin θ = -3/5, sin ɸ = 20/29. Moreover, suppose θ is in Quadrant IV and ɸ is in Quadrant l. We can find sin(θ + ɸ) and cos(θ + ɸ) by using the following formulas: sin(θ + ɸ) = sin θ cos ɸ + cos θ sin ɸ and cos(θ + ɸ) = cos θ cos ɸ - sin θ sin ɸ.
First, we need to find cos θ and cos ɸ. Since θ is in Quadrant IV, cos θ is positive. We can use the Pythagorean identity, sin² θ + cos² θ = 1, to find cos θ:
cos² θ = 1 - sin² θ
cos² θ = 1 - (-3/5)²
cos² θ = 1 - 9/25
cos² θ = 16/25
cos θ = √(16/25)
cos θ = 4/5
Similarly, since ɸ is in Quadrant l, cos ɸ is also positive. We can use the Pythagorean identity to find cos ɸ:
cos² ɸ = 1 - sin² ɸ
cos² ɸ = 1 - (20/29)²
cos² ɸ = 1 - 400/841
cos² ɸ = 441/841
cos ɸ = √(441/841)
cos ɸ = 21/29
Now we can plug in the values of sin θ, sin ɸ, cos θ, and cos ɸ into the formulas for sin(θ + ɸ) and cos(θ + ɸ):
sin(θ + ɸ) = sin θ cos ɸ + cos θ sin ɸ
sin(θ + ɸ) = (-3/5)(21/29) + (4/5)(20/29)
sin(θ + ɸ) = -63/145 + 80/145
sin(θ + ɸ) = 17/145
cos(θ + ɸ) = cos θ cos ɸ - sin θ sin ɸ
cos(θ + ɸ) = (4/5)(21/29) - (-3/5)(20/29)
cos(θ + ɸ) = 84/145 + 60/145
cos(θ + ɸ) = 144/145
Therefore, sin(θ + ɸ) = 17/145 and cos(θ + ɸ) = 144/145.
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What values should x and y have to complete the proportion xa = ay, where x is a hypotenuse?
The value of x is 18 and y is 16. The solution has been obtained by using concept of similar triangles.
What are similar triangles?If two triangles have the same number of corresponding sides and corresponding angles, they are said to be similar. Similar figures are objects that have the same shape but various sizes, like two or more figures.
We are given that in ΔABC and ΔBDC,
∠ABC ≅ ∠BDC (right angles)
BC ≅ BC (common side)
∠ACB ≅ ∠BCD (common angle)
So, ΔABC ≅ ΔBDC.
We know that in similar triangles, the ratio of the corresponding sides is same.
So,
AC / BC = BC / CD
Now, by substituting the given values in the relation, we get,
⇒18/a = a/16
We are given proportion as x/a = a/y.
On comparing both, we get
x = 18 and y = 16
Hence, the value of x is 18 and y is 16.
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a library has fiction and nonfiction books. The ration of the number of fiction books to the total number of books is 5:8. What is the ratio of the fiction to the nonfiction books in the library?
The ratio of fiction books to nonfiction books in the library is 5:3.
What are Ratios?
A ratio is a comparison of two or more quantities that have the same units or are of the same kind. It is expressed as a fraction, using a colon or as a quotient of the two quantities.
Let the number of fiction books in the library be 5x and the total number of books be 8x (since the ratio of fiction books to total books is 5:8).
Then, the number of nonfiction books in the library is 8x - 5x = 3x.
Therefore, the ratio of fiction books to nonfiction books in the library is 5x : 3x, which simplifies to:
5x/3x = 5/3
So, the ratio of fiction books to nonfiction books in the library is 5:3.
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Emmett is planning a party at an escape room. The escape room will charge Emmett a booking fee and an additional cost per person attending the party.
This situation can be modeled as a linear relationship.
Emmett is planning a party at an escape room. The escape room will charge Emmett a booking fee and an additional cost per person attending the party.
This situation can be modeled as a linear relationship.
What does the slope of the line tell you about the situation?
A. The booking fee is $50
B. After the booking fee the party will cost $20 per person
C. After the booking fee the party will cost $25 per person
D. Including the bookin fee it would cost emmett $250 total for 10 people to attend
The provide situation can be modeled as a linear equation, y = 50 + 20x, where y is total cost and x is number of person who will attend the party. The slope of line tells me that the additional cost per person attending the party is $20. Thus, write option is option (b).
Emmett wants to through a party at an escape room. There are two charges for
escape room, one is booking fee and other one is additional cost per person attending the party. Let the booking fee and additional cost per person who attended the party of escape room be 'a ' and 'b'. Also, consider total person who will attend the party are equal to 'x'. So, total cost = booking cost + additional cost per person × number of people's who will attend the party. Let total cost of escape room for x people be 'y'. Then,
y = a + bx --(1)
it is act as modeled linear relationship, see above graph, which represents it graphically. In the graph initial total cost is 50, when no additional cost occur, that is booking fee equals to $50 or a = $50. After that, number of people increase total cost also increases. When there are 10 people in party then total cost is $250 and the additional cost = $200 for 10 people. So, additional cost per person
= 200/10 = 20 , i.e., b = $20 and equation(1) is rewrite, y = 50 + 20x.
If we compare it with standard linear equation, y = mx + c
where m --> slope of line
c --> y-intercept
then slope of equation (1) is equals to 'b' and b = 20. In this situation, the slope of line tell me that except the booking fee, the additional cost per person who will attend the party is equals to $20. Hence, the required answer is option(b).
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Complete question:
Emmett is planning a party at an escape room. The escape room will charge Emmett a booking fee and an additional cost per person attending the party.
This situation can be modeled as a linear relationship, see above graph. What does the slope of the line tell you about the situation?
A. The booking fee is $50
B. After the booking fee the party will cost $20 per person
C. After the booking fee the party will cost $25 per person
D. Including the bookin fee it would cost emmett $250 total for 10 people to attend.
B. After the booking fee the party will cost $20 per person
e synthetic division and the Remainder Theorem to evaluate P(C). P(x)=3x^(3)+15x^(2)-10x+9,c=2
P(2) = 73.
To evaluate P(C) using synthetic division and the Remainder Theorem, we will follow the following steps:
Set up the synthetic division table with the value of C on the left and the coefficients of P(x) on the right.
Bring down the first coefficient to the bottom row.
Multiply the value of C by the first coefficient in the bottom row and place the result in the next column.
Add the values in the second column and place the result in the bottom row.
Repeat steps 3 and 4 for the remaining columns.
The last value in the bottom row is the remainder. According to the Remainder Theorem, this is the value of P(C).
Therefore, P(2) = 73.
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what x-value makes the set of ratios equivalent
The following values of x, makes the set of ratios equivalent:
2: 3 = 6: 9
4: 7 = 24: 42
(6*2)12: 48 = 3: 12
12: 15 = 16: 20
What are ratios?The ratio can be used to determine how much of one item is contained in the other by comparing two sums of the same units. Ratios fall into two different groups.
Whereas the second is a part to whole ratio, the first is a part-to-part ratio. The part-to-part ratio demonstrates the link between two independent entities or organisations.
Now here in the 1st set:
2:3 = 6:x
Now, x = 6×3/2
⇒ x = 9
Similarly,
4:7=x:42
⇒ x = 24
The next ratio we have:
2x:48= 3:12
⇒ x = 6
Now, the last ratio,
12:15 = x:20
⇒ x = 16
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Two weather stations are aware of a thunderstorm located at point c. The weather stations A and B are 34 miles apart. How far is weather station A from the storm?
The distance between weather station A and the storm is [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles, which can be calculated using the Pythagorean theorem.
What is the Pythagorean theorem?The Pythagorean Theorem is an equation in geometry which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse.
Weather station A is 34 miles away from the thunderstorm located at point c. To measure the distance between weather station A and the storm, we must calculate the hypotenuse of a right triangle. The right triangle is formed by the two points of the storm and weather station A, with the 34 miles between them forming the base of the triangle. The hypotenuse of the triangle is the distance between the two points, which can be calculated using the Pythagorean theorem. The equation for the Pythagorean theorem is a² + b²= c², where a and b are the sides of the triangle, and c is the hypotenuse.
Therefore, the distance between weather station A and the storm is [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles.
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What would be the MOST immediate effect of competition in car manufacturing?
an increase in prices of U.S. cars
an increase in U.S. car production
additional auto workers hired in the U.S.
more choices for U.S. consumers
An increase in U.S. car production would be the most immediate effect of competition in car manufacturing.
As there will be an increase in the competition in car manufacturing the manufacturer will try to produce more and more cars of different types to attract customers. More market competition will provide consumers with more options to buy whatever products they desire, which will lead to a drop in the number of devoted customers for a given product line. Competitive markets have several advantages. Businesses that must constantly compete with one another for customers and market share are motivated to do so by offering products and services that are better than those of their rivals. In this market, businesses must constantly compete with one another by offering products and services that are more innovative, superior, and affordable.
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PLEASE HELP! THIS IS MY LAST QUESTION, BUT I DON'T KNOW HOW TO DO IT!
The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. A sample increases continuously at a relative rate of 7% per day. Find the mass of the sample after six days if there were 552 grams of the substance present at the beginning of the study.
Do not round any intermediate computations, and round your answer to the nearest tenth.
Also, may you please explain how you got the answer, it would be very helpful because I don't understand how to solve this. Thank you!
Answer:
864.3
Step-by-step explanation:
Since the substance is increasing continuously at a relative rate of 7% per day, we can use the continuous exponential growth formula:
P(t) = P(0) * e^(rt)
where:
P(t) is the mass of the substance after "t" days
P(0) is the initial mass of the substance (552 grams in this case)
e is the mathematical constant e (approximately equal to 2.71828)
r is the relative growth rate (0.07 per day in this case)
Substituting the given values, we get:
P(t) = 552 * e^(0.07t)
To find the mass after 6 days, we can substitute t = 6:
P(6) = 552 * e^(0.07*6)
Using a calculator, we get:
P(6) ≈ 864.3 grams
Therefore, the mass of the substance after 6 days is approximately 864.3 grams rounded to the nearest tenth.
5(y+25)=−13
y = ??
Please answer this if you can!!
Answer:
y = - 125/18
Step-by-step explanation:
okay so here what i got when i was doing the equation
5 ( y + 25) = - 13y
5 y + 125 = - 13y
then you subtract 125 from both sides
subtract the numbers
and my solution was y = - 125 / 18 trust me!
Hope that helped
A person places $741 in an investment account earning an annual rate of 5.8%, compounded continuously. Using the formula =V=Pe^rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 13 years.
again yea im putting my hw here
Step-by-step explanation:
Using the formula V = Pe^(rt), we have:
P = $741
r = 0.058 (since the interest rate is 5.8%)
t = 13
So, V = 741e^(0.05813) = $1613.87 (rounded to the nearest cent)
Therefore, the amount of money in the account after 13 years is $1613.87.
Answer:
Step-by-step explanation:
Big ideas 7.5 question
The measure of m∠G of the trapezoid is 60°
What is a trapezoid?The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.
There are three types of trapezoids , and those are given below:
a) Isosceles Trapezoid
b) Scalene Trapezoid
c) Right Trapezoid
The area of the Trapezoid is given by
Area of Trapezoid = ( ( a + b ) h ) / 2
where , a = shorter base of trapezium
b = longer base of trapezium
h = height of trapezium
Given data ,
Let the trapezium be represented as EFGH
Now , the measure of m∠F = 150°
The measure of m∠H = 90°
Now , the measures of the sides EF = measure of side FG
So , the measures of angles are also equal
Now , the total internal angle of trapezoid is 360°
So , 2x + 150° + 90° = 360°
On simplifying , we get
2x = 360° - 240°
2x = 120°
x = 60°
Therefore , the measure of n = 60°
Hence , the measure of the angle of trapezoid ∠G = 60°
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Suppose vector d = vector a - vector b where vector vector a has components ax = 4, ay = 5 and vector vector b has components bx = -4, by = -4
The vector representing D = A - B has following values,
1. x- component of vector D = 9 and y- component of vector D = 9.
2. Magnitude and direction of vector D is equal to 12.73 and 45° above the positive x-axis.
Here, Vector D= A-B __(1)
Components of vector A are,
Ax=5
Ay=5
Components of vector B are,
Bx= -4,
By= -4
1. Subtract the x- and y-components of vector B from vector A, respectively by substituting in (1) we get,
Dx = Ax - Bx
= 5 - (-4)
= 5 + 4
= 9
Dy = Ay - By
= 5 - (-4)
= 5 + 4
= 9
2. Magnitude of vector D, use the Pythagorean theorem,
|D| = √(Dx² + Dy²)
= √(9² + 9²)
= √(162)
≈ 12.73
Direction of vector D, use trigonometry.
Angle θ represents vector D makes angle with positive x-axis is ,
θ = tan⁻¹(Dy / Dx)
= tan⁻¹(9 / 9)
= tan⁻¹(1)
= 45°
Therefore, required value of the vectors are,
1. x- and y-components of vector D are 9 and 9, respectively.
2. Magnitude of vector D is 12.73, and direction is 45° above the positive x-axis.
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The above question is incomplete , the complete question is:
Suppose D= A-B where vector A has components Ax=5, and Ay=5 and vector B has components Bx= -4, By= -4.
1. What are the x- and y- components of vector D?
2. What are the magnitude and direction of vector D?
Help this is urgent is a chemistry question I need help I will award brainliest
Answer:
The second answer is correct
Step-by-step explanation:
The first image shows nuclear fusion, combining two lighter nuclei to make a helium and a heavy nucleus, and the second image shows nuclear fission, taking a large unstable nucleus and turning it into two lighter nuclei.
what is the answer to this?
Answer: D
Step-by-step explanation:
[tex]3n^3-4n+3n+6n^3=-3[/tex]
Group together the like terms:
[tex]3n^3+6n^3+3n-4n=-3[/tex]
Combine like terms:
[tex]9n^3-n=-3[/tex]
The answer is D.
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5-6 MathXL for School: Practice and Application Cop Solve the equation by factoring. v^(2)-2v+1=0
The equation v^(2)-2v+1=0 can be solved by factoring. Factoring is a process of breaking down a number or expression into its component parts. In this case, we can factor the equation into (v-1)(v-1), which is equal to zero. Therefore, the solution to the equation is v = 1.
Factoring is a useful tool for solving equations. By factoring, we can break a complex equation into simpler parts, which makes it easier to solve. It can also be used to identify solutions that are not obvious by looking at the equation. It is a valuable skill to have in mathematics, as it can be used to solve many equations quickly and efficiently. It is also an important skill to have when working with polynomials, as it allows us to identify the zeros of a polynomial.
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George looks at Kara's work and says she made a mistake.
He says she should have divided by 2 before she added.
Which student is correct? Explain how you know.
Answer:
George will be right by the rule of BODMAS
Step-by-step explanation:
If the students use BODMAS rule, division comes before addition
For which value(s) ofcdoes the equationx+4−c=0has a solution. (A)c=−4(B)c=0(C)0
For none of the option the linear equation x+4=c have solution.
The equation x + 4 - c = 0 can be rearranged to isolate the variable c on one side of the equation. This gives us:
c = x + 4
Now, we can see that the value of c depends on the value of x. In other words, there are infinitely many values of c that make the equation true, as long as they are equal to x + 4.
So the answer to the question is that there are infinitely many values of c that make the equation x + 4 - c = 0 true. None of the given options (A) c = -4, (B) c = 0, or (C) 0 are correct.
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i need help with this problem
Answer:
4
Step-by-step explanation:
compare the coordinates of each point:
G: (1,2) x4→ G': (4,8)
H: (3,0) x4→ H': (12,0)
I: (2,-2) x4→ I': (8,-8)
As you can see the scale factor is 4
Each x and each y coordinate of the small triangle GHI is multiplied by 4 to get the image triangle G'H'I'
19. A ball is dropped from a height of 30 feet. At the same time, a ball is thrown straight into the air from a height of 5 feet with an initial velocity of 20 feet per second. The polynomials -16t2 + 30 and -16t2 + 20t + 5 represent the heights (in feet) of the balls after t seconds.
a. Write a polynomial that represents the distance between the heights of the balls after t seconds.
b. Interpret any coefficients and constants of the polynomial in part (a.)
A polynomial that represents the distance between the heights of the balls after t seconds. Time t =15/20=0.75 seconds
a. Change of speed versus acceleration and time:
v = u + at
20 = -16t2 + 30 +16t2 + 20t + 5
20= 20t + 35
20t=35-20=15
b. We now interpret this polynomial as follows:Δh(t)=[tex]h_{0} -u_{y} t[/tex]
This shows how far apart the two balls are at time t. The two terms can be interpreted as follows: The initial separation between the two balls at time t=0 is represented by the constant term, h0 (in fact, the first ball is still at the top of the building, while the second ball is on the ground). For this issue[tex]h_{0} =30 feet.[/tex] The second ball's initial velocity, which serves as the coefficient of the linear term, [tex]u_{y}[/tex]tells us that the gap between the two balls closes by [tex]u_{y}[/tex] feet every second.
Time t =15/20=0.75 seconds. Time is the continuous pattern of existence and the events that take place in what appears to be an unbroken progression from the past through the present and into the future. It is a component number of various measurements that are used to compare the lengths of events or the pauses between them, to compare the order in which they occur, and to gauge the rates at which certain quantities in the physical world or in conscious experience change.
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The LA Dodgers hit the most
homeruns in 2014. The number of
homeruns accounted for 6% of the entire
Major League Baseball homerun count. If 583
total homeruns were hit, approximately how
many did the LA Dodgers hit?
show work plsss
The number of home-runs LA Dodgers hit is 35.
What is Percentage?Percentage is a number or ratio that can be expressed as a fraction of 100.Thus y percentage of some value x is x * (y/100)Given,
Total home runs in Major league = 583
Home - runs accounted by LA Dodgers = 6 %
Number of home-runs by LA Dodgers
= 6% of 583
= 6/100 * (583)
= 0.06 * 585
= 34.98
= 35 approximately
Hence, the total number of homeruns that did the LA Dodgers hit are 35 approximately.
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System of Equations
y = (x-2)² + 35
y = -2x + 15
been trying to figure this one out for hours, please help
The solution of the system of equations is ([2+9.48i]/2, 17+9.48i).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of equations are y=(x-2)²+35 ----(i) and y=-2x+15 ----(ii).
Here, equation (i) = (ii)
(x-2)²+35= -2x+15
x²-4x+4+35= -2x+15
x²-4x+39= -2x+15
x²-4x+39+2x-15=0
x²-2x+24=0
x²-2x+24=0
By using quadratic formula, we get
x = [-b ± √(b² - 4ac)]/2a
x=[2±√((-2)² - 4×1×24)]/2×1
x=[2±√(-90)]/2
x=[2±9.48i]/2
Here, x=[2+9.48i]/2 and x=[2-9.48i]/2
So, y=2+9.48i+15=17+9.48i
Therefore, the solution of the system of equations is ([2+9.48i]/2, 17+9.48i).
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Jai went to the store to buy some chicken. The price per pound of the chicken is $3.75 per pound and he has a coupon for $1.75 off the final amount. With the coupon, how much would Jai have to pay to buy 5 pounds of chicken? Also, write an expression for the cost to buy p pounds of chicken, assuming at least one pound is purchased.
Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥ 1.
what is unitary method ?The unitary method in mathematics is a strategy for resolving proportional issues. Finding the value of one unit of a quantity and using that value to calculate the value of a second quantity that is proportional to the first includes this technique. The unitary technique is frequently employed in a variety of real-world contexts, including engineering, finance, and food preparation. The unitary method can be used to determine the amount of flour required to make a different number of cookies, for instance, if a recipe asks for 2 cups of flour to make 12 cookies.
given
The price of 5 pounds of poultry without the coupon is:
$5 for five pounds at $3.75 per pound.
Jai saves $1.75 thanks to the coupon, making the total price for 5 pounds of chicken:
$18.75 - $1.75 = $17.00
Jai would therefore need to spend $17.00 in order to purchase 5 pounds of poultry using the coupon.
With the assumption that at least one pound is bought, we can use the following formula to write an expression for the price to buy p pounds of chicken:
Expense is equal to (price per pound) x (pounds) - (coupon amount)
where p is the number of pounds, $3.75 is the price per pound, and $1.75 is the value of the voucher.
Therefore, this is how much it would cost to purchase p pounds of chicken: Cost is equal to $3.75p – $1.75, with p≥ 1.
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Lucky Duck
What is the probability you will choose each duck described below?
Write the answer as a fraction in lowest terms and place it in the appropriate
box (certain, likely, unlikely, impossible).
The ducks are
numbered from one
through twelve!
Even Unlikely Impossible
The answer response are:
A duck with wings: Likely Duck number 7: Unlikely A duck with a number greater than 3: Certain Duck number 15: Impossible A duck with a number greater than 10: Unlikely A duck with a number: Certain Duck number 4: Likely A duck with sunglasses: Impossible A duck with a hat: Unlikely An even-numbered duck: LikelyHow do you explain the probability?A duck with wings: Likely
There is a high likelihood that all the ducks have wings since it is a natural characteristic of ducks.Duck number 7: Unlikely
There are 12 ducks in total, and only one of them is duck number 7, so the probability of choosing duck number 7 is 1/12, which is unlikely.A duck with a number greater than 3: Certain
There are 9 ducks with numbers greater than 3 (4, 5, 6, 7, 8, 9, 10, 11, 12), so it is certain that you will choose a duck with a number greater than 3.Duck number 15: Impossible
There are only 12 ducks, and none of them are numbered 15, so it is impossible to choose duck number 15.A duck with a number greater than 10: Unlikely
Only two ducks have numbers greater than 10 (11, 12), so the probability of choosing a duck with a number greater than 10 is 2/12 or 1/6, which is unlikely.A duck with a number: Certain
All ducks have numbers from 1 to 12, so it is certain that you will choose a duck with a number.Duck number 4: Unlikely
There is only one duck numbered 4, so the probability of choosing duck number 4 is 1/12, which is unlikely.A duck with sunglasses: Impossible
There is no information given that any of the ducks have sunglasses, so it is impossible to choose a duck with sunglasses.A duck with a hat: Unlikely
There is no information given that any of the ducks have hats, so the probability of choosing a duck with a hat is unlikely.Lastly, An even-numbered duck: Likely
There are six even-numbered ducks (2, 4, 6, 8, 10, 12), so the probability of choosing an even-numbered duck is 6/12 or 1/2, which is likely.Learn more about probability here:
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See transcribed text below
Date:
Period:
What is the probability you will choose each duck described below? Write the answer as a fraction in lowest terms and place it in the appropriate box (certain, likely, unlikely, impossible).
33
1. A duck with wings
2. duck number 7
3. a duck with a number greater than 3
4. duck number 15
5. a duck with a number greater than 10
6. a duck with a number
7. duck number 4
8. a duck with sunglasses
9. a duck with a hat
10. an even-numbered duck
The ducks are numbered From one through twelve!
Kibb
Certain
Likely
Even
Unlikely Impossible
ว
Hi there,
Can you help me? I need help on The given equation involves a power of the variable. Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION. I don't understand. Can you show your work to understand
thank you , in advance
3x^5/3 + 96 = 0
x =
x = -4 - 4√2/6 and x = -4 + 4√2/6.
Hi there! The equation 3x5/3 + 96 = 0 can be rewritten as x5 + 32 = 0. In order to solve for the real solutions of this equation, we can use the Quadratic Formula, which states that for the equation ax2 + bx + c = 0, the real solutions are given by x = (-b ± √b2 - 4ac)/2a. Substituting the values for a, b, and c, we get x = (-32 ± √322 - 4*3*0)/6, which simplifies to x = (-32 ± √1024)/6, or x = -4 ± 4√2/6. Therefore, the real solutions for the equation are x = -4 - 4√2/6 and x = -4 + 4√2/6.
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Question 4 Solve the inequality and write your answer in interval notation 16+12x<19x+12
The solution to the inequality 16 + 12x < 19x + 12 is all the values of x between the interval notation (4/7, ∞).
To solve the inequality 16 + 12x < 19x + 12, we need to isolate the variable x on one side of the inequality. We can do this by subtracting 12x from both sides and subtracting 12 from both sides:
16 + 12x - 12x - 12 < 19x + 12 - 12x - 12
4 < 7x
Solving for x, we can divide both sides by 7:
4/7 < x or x > 4/7
In interval notation, this would be (4/7, ∞). Therefore, the solution to the inequality is (4/7, ∞) in interval notation.
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