The equation for Tomas and Emilio birthday party's celebration is 200 = 45.99 + 17p
In math the term called equation is defined as a mathematical statement that shows that two mathematical expressions are equal.
Here we have know that seven friends accept the invitation to the twins' birthday party.
Where the possible equation that can be set up will have the total budget equal to total expenses.
So it can be written as the Total Cost of party is 200,
Then the amount can be divided as
=> Cost of Party Room + Cost of Movie Tickets + Cost of popcorns
Let us consider that if p people attend the party, then the cost of movie tickets will be $12.50p and cost of popcorns will be $4.50p, assuming that each person get a small popcorn bag.
Hence the equation will be written as
=> 200 = 45.99 + 12.50p + 4.50p
=> 200 = 45.99 + 17p
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Greg forms two numbers with digits 1,2,3,4,5 and 6. Both numbers have three digits, and each digit is used only once. Greg adds these two numbers. What is the greatest sum Greg can obtain?
The greatest sum Greg can obtain is 975 by adding two numbers. Greg should use the digits 6,5 and 4 for the first number and 3,2 and 1 for the second number
Greatest sum :
654 + 321 = 975
To get the greatest sum, Greg should use the digits 6,5 and 4 for the first number and 3,2 and 1 for the second number. This is because these are the largest digits and by putting them in the leftmost side of the number, it will make the number the largest possible number.
What is the greatest sum?The greatest sum is the maximum value that can be obtained from adding two or more numbers. It is the largest possible outcome from an addition operation. The answer or result obtained by adding two or more numbers or terms is known as the sum. As a result, the sum is a way to combine things. To put it another way, adding two or more numbers together to get a new total is called the sum.
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Joanne made emi-annual depoit of ₱820 into a aving account with an interet of 5% compounded emi-annually. How much i the account balance after eleven year?
The account balance after eleven years would be ₱14,925.08. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08. total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.
The account balance after eleven years would be ₱14,925.08.
1. Calculate the compounded interest rate: 5% per year compounded semi-annually = 2.5% per semi-annual period.
2. Calculate the total number of semi-annual periods: 11 years x 2 semi-annual periods per year = 22 semi-annual periods.
3. Calculate the future value of the account: FV = PV x (1 + r)^n = 820 x (1 + 0.025)^22 = ₱14,925.08.
The account balance after eleven years would be ₱14,925.08.
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the towers of a suspension bridge are 800 feet apart and rise 160 feet above the road. the cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. what is the height of the cabl...
As the cable between the towers has the shape of a parabola, the height of the cable 200 feet from a tower is 40 feet.
Consider the origin of coordinate system at the bridge level midway between the towers and the cable has the shape of a parabola. It is the vertex of the parabola. The general equation of a parabola is given by y = a(x – h)^2 + k where (h, k) denotes the vertex. Hence, based on the provided information, the equation is;
y = a^x^2
The height of the tower above the road is 160 feet which is 400 feet from the vertex. Hence, x = 400 feet and y = 160 feet.
Substituting the values,
160 = a^(400)^2
a = 0.001
Hence, the equation of the given parabola is:
y = 0.001x^2
In order to calculate the height of the cable at 200 feet from the tower, the value of x = 400 – 200 = 200 feet
y = 0.001(200)^2 = 40 feet
Note: The question is incomplete. The complete question probably is: The towers of a suspension bridge are 800 feet apart and rise 160 feet above the road. The cable between the towers has the shape of a parabola and the cable just touches the sides of the road midway between the towers. What is the height of the cable 200 feet from a tower?
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35% of the dogs at a dog show are German shepherds. 10% of the dogs are poodles, 45% of the dogs are spaniels, and the rest were retrievers.
Witch statement is not true
A) There are more spaniels than any other type of dog at the show.
B) Retrievers account for 15% of the dogs at the show.
C) Retrievers and German shepherds account for 45% of the dogs at the show.
D) There are more German shepherds than retrievers at the show.
6th grade mathematics.
The information in assertion 2 that says Retrievers make up 15 percent of the dogs at the event is untrue.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, 35% of the dogs at a dog show are German shepherds. 10% of the dogs are poodles, 45% of the dogs are spaniels, and the rest were retrievers.
Since the rest dog breed was retrievers,
Thus, retrievers = 100- 45-35-10
retrievers = 10%
Therefore, statement 2 which states Retrievers account for 15 percent of the dogs at the show is incorrect.
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The coordinates of equilateral triangle ABC are A(0,-6) B(0,0) and C(x,y). Find the coordinates of c if the triangle is in the fourth quadrant
The coordinates of point C are C(0,-sqrt(36 - x²))
An equilateral triangle has all sides of equal length and all angles of 60 degrees. Since the triangle is in the fourth quadrant, so we know that both the x and y coordinates of point C must be negative.
We can use the distance formula to find the length of the sides of the triangle:
AB = sqrt((0 - 0)² + (-6 - 0)²) = 6
BC = sqrt((x - 0)²+ (y - 0)²) = AC = sqrt((x - 0)² + (y - (-6))²) = sqrt(x² + (y + 6)² = 6
We may now use the notion that all angles in an equilateral triangle equal 60 degrees. We know that point A is at (0,-6) and point B is at (0,0), therefore we can use the slope of line AB and the length of the side to compute point C's coordinates.
Line AB has a slope of (0 - (-6))/(0 - 0) = 6/0 = undefined.The slope of a line perpendicular to AB is the negative reciprocal of AB's undefined slope; so, line AB is parallel to the x-axis. So C(x,y) has the same x-coordinate as B(0,0) but a different y-coordinate.
The length of the side is 6, so we can use this information to find the y-coordinate of point C:
y = sqrt(6² - x²) = sqrt(36 - x²)= -sqrt(36 - x²)
So, the coordinates of point C are C(0,-sqrt(36 - x²))
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David and James are at the Famous Nathan's Hot Dog Eating
Championships of the world in New York. David was late starting, so
James already had 6 hotdogs before David started eating. From then on,
James ate a hot dog every two minutes while David stuffed 1.25 hot dogs
a minute. How many minutes does it take David to catch up with James?
Answer: We can start by using the following formula to find the time it takes for David to catch up with James:
time = (James' lead) / (David's rate - James' rate)
In this case, James' lead is 6 hotdogs, and we know that James eats 1 hotdog every 2 minutes, so his rate is 1/2 hotdog per minute. David's rate is 1.25 hotdogs per minute.
So, substituting these values into the formula:
time = (6) / (1.25 - (1/2))
time = 6 / (0.75)
time = 8 minutes
So it takes David 8 minutes to catch up with James.
Step-by-step explanation:
Determine if the graph shows a proportional relationship. Graph with x axis labeled distance miles and y axis labeled time hours. A line begins at point 0 comma 0 and continues to the right. Yes, it is proportional because it is a line that intersects with the origin. Yes, it is proportional because the x-axis and y-axis are labeled correctly. No, it is not proportional because the line does not intersect with the origin. No, it is not proportional because the x-axis and y-axis are not labeled correctly.
The correct alternatives are -
Yes, it is proportional because it is a line that intersects with the origin. Yes, it is proportional because the x-axis and y-axis are labeled correctly.What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the proportional relationship.
A line begins at point (0, 0) and continues to the right.
Direct variation of {y} with {x} means that as {x} increases, {y} increases uniformly with it. Mathematically -
{K} = y/x = constant
Scale factor {K} is a dimensionless value that indicates the constant ratio value indicating direct variation.
Therefore, the correct alternatives are -
Yes, it is proportional because it is a line that intersects with the origin. Yes, it is proportional because the x-axis and y-axis are labeled correctly.To solve more questions on scale factor , visit the link below -
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Jamie has white, blue, and pink shirts. She has black, white, and beige pants. She has black and brown shoes. If she chooses one shirt, one pair of pants, and one pair of shoes, how many unique outfits can she make?
6
8
9
18
Show your work pls
micromedia offers computer training seminars on a variety of topics. in the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting. micromedia is currently planning a two-day seminar on the use of microsoft excel in statistical analysis. the projected fee for the seminar is $575 per student. the cost for the conference room, instructor compensation, lab assistants, and promotion is $6,930. micromedia rents computers for its seminars at a cost of $130 per computer per day. (a) develop a model for the total cost (c) to put on the seminar. let x represent the number of students who enroll in the seminar. c
The total cost (c) to put on the seminar is c = 6,930 + 130x + 575x, where x represents the number of students who enroll in the seminar.
The total cost (c) to put on the seminar can be modeled using the following equation -
c = 6,930 + 130x + 575x
here, x represents the number of students who enroll in the seminar.
The above equation takes into account the fixed costs of the conference room, instructor compensation, lab assistants, and promotion (6,930), as well as the variable costs of renting computers (130x) and the seminar fee charged to each student (575x).
As more students enroll in the seminar, the total cost will increase due to the additional computer rental and seminar fee costs.
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given f(x) = 2x^2, find f(-5)
Answer:
Step-by-step explanation:
Answer:
f(-5)=50
Brief explanation:
Well we plug -5 for x
f(x)=2x^2
f(-5)=2(-5)^2
f(-5)=2(25)
f(-5)=50
hence the answer
study hard
A truck tire is about 20 inches in diameter. What is the approximate distance the truck tire will travel in 1 full rotation?
The approximate distance the truck tire will travel in 1 full rotation is 62.8 inches.
The total distance travelled by truck on completing one full rotation will be equal to the circumference of the circle. The circumference of the circle is given by the formula -
Circumference = 2πr, where r refers to radius of truck tire.
Radius = diameter/2
Radius = 20/2
Radius = 10 inches
Keep the values in formula to find the distance travelled on full rotation of truck tire.
Circumference = 2×3.14×10
Performing multiplication on Right Hand Side of the equation
Circumference = 62.8 inches
Hence, the distance covered will be 62.8 inches.
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The Sahas were reading a best-selling novel as a family. After the first week, they checked in with each other to see how much of the book each had read
The father had read the most, having finished half the book. The mother had read a third of it, while the daughter was still in the first chapter. The son had only read a few pages.
They discussed their progress and made an agreement to read a certain number of chapters each week to ensure they finished the book at the same time.
Therefore, the father had read the majority of the book, having completed it. While the daughter was still in the first chapter, the mother had already read about a third of it. Only a few pages have been read by the son.
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a placebo is an actual treatment. question content area bottom part 1 choose the correct answer below. a. the statement is false. a placebo is giving the subjects no treatment at all. b. the statement is false. a placebo is a fake treatment. c. the statement is true. d. the statement is false. a placebo is a process of randomly assigning subjects to treatment groups.
Answer:
The answer is B.
Step-by-step explanation:
A placebo is a fake medicine
You can learn more about a placebo by reading a book called Mesmerized. It basically talks about the origin of the placebo effect and all that.
A cylindrical rod measures 10 inches long and the circumference of one of its bases is 8π inches. The rod is cut into two equally-sized pieces and then all surfaces are painted.
What is the area that is painted?
Use π≈3.14.
Enter your answer, rounded to the nearest tenth, in the box.
in²
Answer:
see below
Step-by-step explanation:
length = 10
circumference = 2πr = 8 π, so r=4
8π=25.12
cut half so length = 5, so lateral surface = 8π*5 = 40π =125.6
top circle area = πr² = 3.14*4² = 3.14 *16 = 50.24
top & bottom = 2*50.24 = 100.5
so total surface of EACH after cut in half = 100.5+125.6 =226.1
TWO of them = 2*226.1 =452.2
Please i need urgent help here right now
For the imaginary roots, the value of c must be greater than the value of d that is c > d. Then the correct option is A.
What is the discriminant?The discriminant of a quadratic is a number that depends on the components and allows some characteristics of the roots to be deduced without calculating them.
The quadratic equation is ax² + bx + c = 0. Then the discriminant is given as,
D = b² - 4ac
If D > 0, then the roots are real and distinct root.If D = 0, then the roots are real and equal roots.If D < 0, then the roots are imaginary roots.The equation is given as,
2(c² + d²)x² + (c - d)x + 9 = 0
Then the discriminant is given as,
D < 0
(c - d)² - 4 × 2(c² + d²) × 9 < 0
(c - d)² > 72 (c² + d²)
The expresssion (c - d)² must be positive. Then we have
(c - d)² > 0
c - d > 0
c > d
For the imaginary roots, the value of c must be greater than the value of d that is c > d. Then the correct option is A.
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a triangle is the shape used to represent the components of total health. rue or false
A triangle is a shape used to represent the components of total health. True
Minimum wage at Ben's Burger Bar was $8.10 an hour, and later increased to $15 an hour. What was the percent increase?
The increase in the minimum wage from $8.10 to $15, indicates that the percentage increase in the minimum wage is 85.[tex]\overline{185}[/tex]%
What does a percentage of an amount represent?A percentage represent the number, amount, proportion or ratio of an item to another (possibly larger) item per hundred (100) units of the comparison or larger item.
Percentages, quantitatively describes the idea of the amount of a substance. It is a measure of the amount or occurrence of an item.
The specified original minimum wage at Ben's Burger = $8.10
The new amount to which the minimum wage is increased = $15
The percentage increase can be obtained using the formula;
[tex]\% \ increase = \frac{New - Original}{Original} \times 100[/tex]
The percentage increase is therefore; ((15 - 8.10)/8.1) × 100 = 85.[tex]\overline{185}[/tex] %
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GEOMETRY 9.3.5 POINT ON A CIRCLE ASSIGNMENT
RLLY NEED HELP
FULL DOCUMENT??
Suppose that this grid represents the customer’s yard. The bottom left corner is the origin point, (0, 0), and the x- and y- axes represent the two fences. The rose bush is at point (16, 18).
The area of the customer's yard is 580π.
What is distance formula?The distance formula is given as -
d = √(x₂ - x₁)² + (y₂ - y₁)²
Given is that this grid represents the customer’s yard. The bottom left corner is the origin point O(0, 0), and the x- and y- axes represent the two fences. The rose bush is at point P(16, 18).
We can write the area of the customer's yard -
A = πr²
Here -
r = d
r² = d²
We can write -
A = πd²
A = π {(x₂ - x₁)² + (y₂ - y₁)²}
A = π{16 x 16 + 18 x 18}
A = 580π
Therefore, the area of the customer's yard is 580π.
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the list below tracks owners and their dogs. we sometimes need to change an owner's phone number. if we change the phone number for the owner in row 1 (johnson, james), but forget to change his phone number in row 9 also we now have a mistake in our list. what is this term for this type of mistake?
If row 3 were to be deleted, it would show a deletion anomaly. This is so that this entry won't be deleted along with the entire database for the Legend book.
This oddity happens when we change a few rows in the database, and if it causes the table to become inconsistent. Updation anomalies are this kind of abnormality.
Due to the duplicate data in each of these rows, this is an update anomaly. If that data is altered in one row but not the other, there will be an update anomaly. There will be two addresses if we miss even one row during the update, which will result in inconsistent and incorrect databases.
If row 3 were to be deleted, it would show a deletion anomaly. This is so that this entry won't be deleted along with the entire database for the Legend book. There is nothing about this book in any other row. Deleting one row wouldn't result in the entire disappearance of the book data because all other books are represented in at least two rows.
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Answer these please!!!
The graph of 3x-2y≤6 is the third graph, for 3x-2y<6 is the first graph, for 3x-2y>6 is the fourth graph and for 3x-2y≥6 is the second graph. The solution has been obtained using concept of linear inequality.
What is linear inequality?
A linear inequality is one that would produce a linear equation if the equals relation were used instead of the inequality. When multiplying or dividing both sides by a negative number in order to solve the inequality, the direction of the inequality is reversed. The entire set of solutions to an inequality is known as the solution set.
We are given for graphs, of which two graphs are dotted and two are simple straight line graphs.
The dotted graphs are drawn for the inequalities having < or >
Whereas the simple straight line graphs are drawn for the inequalities having ≤ or ≥.
Now, to notice the shaded pattern, we will see whether the equations are true for (0,0) or not
1. 3x-2y≤6
⇒ 0≤6
So, the equation is true for the point.
Hence, the third graph represents this equation.
2. 3x-2y<6
⇒ 0<6
So, the equation is true for the point.
Hence, the first graph represents this equation.
3. 3x-2y>6
⇒ 0>6
So, the equation is false for the point.
Hence, the fourth graph represents this equation.
4. 3x-2y≥6
⇒ 0≥6
So, the equation is false for the point.
Hence, the second graph represents this equation.
Hence, the graphs are matched with the inequalities.
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Since, there are multiple questions so, the question answered above is attached below.
I need help with this question please and thank you .
The figure does not represent a dilation, as the scale factors for the two sides of the right triangle are different.
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The scale factors for this problem are given as follows:
Horizontal side: 4/6 = 2/3.Vertical side: 2/4 = 1/2.They are different, meaning that the figure in this problem is not a dilation.
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The Magsanoc family was having pizza for snacks. Mrs.
Magsanoc had just placed the toppings on 3
8
of the pizza
when the phone rang and she stopped to answer the phone.
While she was away, Mr. Magsanoc came in and decided to
help his wife complete the pizza. He covered 1
3
before she
returned. How much of the pizza was covered when Mrs.
Magsanoc returned?
urgent answer quick
Answer: We can start by figuring out how much of the pizza was covered before Mrs. Magsanoc returned by adding the portion that she covered before the phone rang to the portion that Mr. Magsanoc covered while she was away.
Mrs. Magsanoc covered 3/8 of the pizza before the phone rang.
Mr. Magsanoc covered 1/3 of the pizza while she was away.
To add the two portions, we need to find a common denominator, which is the least common multiple of 8 and 3. That is 24.
3/8 of the pizza is (3/8) * (24/8) = 3/24
1/3 of the pizza is (1/3) * (24/3) = 8/24
So, the total portion of the pizza that was covered before Mrs. Magsanoc returned is 3/24 + 8/24
Which is 11/24 or 0.458 of the pizza.
Step-by-step explanation:
4. The two trapezoids below are similar. What
is the length of segment EF?
24 am
A
D
30 cm
B
C
G.
7.5 cm
X
E
H
Help please
The length of segment EF is 6 cm.
What is Length of Segment?The distance between two ends determines the length of a segment.
A segment may be straight, curved, or both straight and curved.
As the distance between two points on a line, a straight segment is the most basic kind of segment. The positions at the segment's ends are known as the endpoints.
It is possible to determine the length of a straight segment by first calculating the difference between the x- and y-coordinates of the two endpoints.
To determine the overall length of the segment, this information is then combined together. It is slightly more difficult to measure a piece that is curved.
This is so because a curved segment's length is frequently different at each location.
Both trapezoids are similar,
⇒ AB / DC = FE / GH [Sides are in same ratio]
⇒ 24 / 30 = x / 7.5
⇒ x = 6
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Today only, a table is being sold for $282 . This is 30% of its regular price. What was the price yesterday?
Answer: $940
Step-by-step explanation:
30% can also be represented as 0.3.
You can solve and find 100%, or the original price, by cross-multiplying.
282 x 1 = 282
282 / 0.3 = 940
The price yesterday was $940.
The ratio of length to diagonal of a rectangular table is 3:14.
If the actual length is 6 feet, what is the measure of the width of the
table to the nearest hundredth?
Rectangle with the given ratio of length to diagonal has measure of the width equals to 27.35 feet.
Actual length of the rectangle = 6 feet
Ratio of the length to diagonal = 3 : 14
⇒Length/ diagonal = 3:14
⇒6/ diagonal = 3:14
⇒Diagonal = (14×6)/3
⇒Diagonal = 28 feet
Let 'x' be the width of the rectangle.
Length , width , and diagonal forms a right angle triangle in a rectangle.
Using Pythagoras theorem ,
Width² = Diagonal² - length²
⇒x² = 28² - 6²
⇒ x = √784 -36
⇒x = 27.35 feet ( nearest hundredth )
Therefore, the width of the given rectangle with the given ratios and dimensions is equal to 27.35 feet.
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In building a tent, Jada ties a rope from the top of a pole 3 meters high to a stake that is 4 meters away from the base of the pole. Jada draws this diagram to help; find the angle made between the rope and the ground.
Indicate whether Jada could use each of the equations to find the value of x.
The equations that enable us to compute x are tanx=3/4 and x=tan⁻¹(3/4)
What are trigonometric functions?In mathematics, trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. The six trigonometric functions are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent.
Given here: length of the pole=3m and distance of the stake from the pole=4m and the angle that the rope makes with the pole is x
We know Arctan function is the inverse of the tangent function. It is usually denoted as arctan x or tan⁻¹x. The basic formula to determine the value of arctan is θ = tan-1(Perpendicular / Base).
Thus we have the value of x as
x=tan⁻(perpendicular/Base)
=tan⁻¹(3/4)
=36.87°
Thus the two possible ways to compute the angle x are:
tanx=3/4 and x=tan⁻¹(3/4)
Hence, The equations that enable us to compute x are tanx=3/4 and x=tan⁻¹(3/4)
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A middle school has 1200 students. Of these, 25% are in the
eighth grade. How many students are in the eighth grade?
Answer: 300
Step-by-step explanation:
Step 1:
Multiply:
1200*0.25=300
Answer: 300
Step-by-step explanation: Just multiply 1200 x 1/4 and that's your answer
PLEASE HURRY TEST QUESTION LIMITED TIME!!!
Question-Write the standard form equation of a circle given the center of (-7, -15) and an area of A = π. Show all work for your calculations using the equation editor.
The standard form equation of a circle given the center of (-7, -15) is (x+7)^2+(y+15)^2 = 9.
What is Circle?
All points in a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
What is equation of circle?
(x - h)^2+ (y - k)^2 = r^2 is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius. A circle touches the x-axis at (3,0) if it is tangent to the x-axis at that location.
Given;
center (-7,-15) and A = 9π
[tex]S = \pi r^2[/tex]
[tex]r = \sqrt{\frac{A}{\pi} }[/tex]
r = [tex]\pi ^{2}[/tex]
From the equation of circle, we get;
⇒(x - h)^2+ (y - k)^2 = r^2
⇒(x+7)^2+(y+15)^2 = [tex]\pi ^{2}[/tex]
So,The standard form equation of a circle given the center of (-7, -15) is (x+7)^2+(y+15)^2 = 9.
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If a polynomial is divided by (x+3), the quotient is x^2-x+8, and the remainder is -5. Find the original polynomial
The polynomial divided by (x + 3), with quotient is x² - x + 8, and remainder of -5 is f(x) = x³ + 2x² + 5x + 19
What is the polynomial division algorithmThe polynomial division algorithm states that for two polynomials, f(x) and g(x), where the degree of g(x) a divisor is less than or equal to the degree of f(x), there exist unique polynomials, q(x) the quotient and r(x) the remainder, such that f(x) = g(x)q(x) + r(x) and the degree of r(x) is less than the degree of g(x). This is also known as synthetic division.
f(x) = (x + 3)(x² - x + 8) + (-5)
but expansion;
f(x) = x³ + 3x² - x² + 8x - 3x + 24 - 5
f(x) = x³ + 2x² + 5x + 19
Therefore, the polynomial f(x) = x³ + 2x² + 5x + 19 divided by (x + 3), will give the quotient x² - x + 8, and remainder of -5.
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Design a situation where the probability of one event is 1/5 and another event is 1/10
We have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10.
How to quantify probability?To quantify the probability of each event, we can define the following events:
Event A: selecting a unit of product A at random and finding that it is defective.Event B: selecting a unit of product B at random and finding that it is defective.Then, the probability of event A is 1/5, since 1 in every 5 units of product A is defective. Similarly, the probability of event B is 1/10, since 1 in every 10 units of product B is defective.
Now, let's consider a scenario where the company receives an order for 100 units of products, with 60 units of product A and 40 units of product B. The company wants to determine the probability of the following events:
Event C: selecting a unit from the order at random and finding that it is defective.Event D: selecting a unit from the order at random and finding that it is not defective.To calculate the probability of event C, we need to consider the probability of selecting a defective unit from product A and from product B, and the proportion of each product in the order. Since the order has 60 units of product A and 40 units of product B, the probability of selecting a unit of product A is 60/100 = 3/5, and the probability of selecting a unit of product B is 40/100 = 2/5.
Using the probabilities of event A and event B, we can calculate the probability of selecting a defective unit from product A or from product B as follows:
Probability of selecting a defective unit from product A: 1/5Probability of selecting a defective unit from product B: 1/10Therefore, the probability of event C can be calculated as follows:
P(C) = P(A) * P(A in order) + P(B) * P(B in order)
= (1/5 * 3/5) + (1/10 * 2/5)
= 3/25
So the probability of selecting a defective unit from the order is 3/25.
To calculate the probability of event D, we can use the complement rule, which states that the probability of an event and its complement (i.e., the event not happening) add up to 1. Therefore, the probability of event D can be calculated as follows:
P(D) = 1 - P(C)
= 1 - 3/25
= 22/25
So the probability of selecting a unit from the order at random and finding that it is not defective is 22/25.
In summary, we have designed a situation where the probability of one event (event A) is 1/5 and the probability of another event (event B) is 1/10. We have also calculated the probability of two other events (event C and event D) in a scenario where a manufacturing company produces two types of products, with different probabilities of defects, and receives an order with a certain proportion of each product.
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