The calculated value of the ratio of the radii of A and B is 2.
Calculating the ratio of the radii of A and BThe ratio of the areas of two circles A and B is equal to the square of the ratio of their radii.
Therefore, if the ratio of the areas of A and B is 4, then the ratio of the radii of A and B is the square root of 4, which is 2.
In other words, if the radius of circle A is rA and the radius of circle B is rB, then:
Area of A / Area of B = (rA)^2 / (rB)^2 = 4
Taking the square root of both sides, we get:
rA / rB = 2
So, the ratio of the radii of A and B is 2.
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In ΔSTU, s = 210 cm, ∠S=115° and ∠T=23°. Find the area of ΔSTU, to the nearest square centimeter.
The area of ΔSTU is approximately 6358 cm², to the nearest square centimeter.
How did we find the area of triangle STU?We can find the area of ΔSTU using the given side and angles by applying the formula:
Area = (1/2)ab x sin(C)
Where a and b are the lengths of two sides of the triangle and C is the angle between them.
We have one side, s, which is 210 cm. We also have two angles, ∠S = 115° and ∠T = 23°. We can find the third angle, ∠U, by using the fact that the sum of angles in a triangle is 180°:
∠U = 180° - ∠S - ∠T
∠U = 180° - 115° - 23°
∠U = 42°
Now, we have ∠S = 115°, ∠T = 23°, and ∠U = 42°. We can use the Law of Sines to find the other two sides of the triangle. Let side t be opposite ∠T and side u be opposite ∠U. Then:
s / sin(S) = t / sin(T) = u / sin(U)
We can now find t and u using the known values:
t / sin(23°) = 210 / sin(115°) = 90.5
S = 1/2 x 90.5 x 210 x sin 42°
=6358 cm²
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x+7=20, x=13 please help quickly
Answer:
hope this helps
Step-by-step explanation:
1. Rewrite:
x + 7 = 20
2. Subtract 7 from both sides:
x = 13
So it is true x = 13, or 13 = 13
Answer:
x=13
Step-by-step explanation: x+7=20, x = 13 : x=13
Steps:
x+7=20
x=13
Subsitute x = 13
[13+7=20]
Check
[20-x=7]
x=13
Simplify
[20 = 20]
The solutions to the system of equations are x=13.
Hope this helped
Find tn for the geometric sequence where t3 = 24 and t9 = 1536. Why are there 2 answers? (4 marks)
I need help pls, I don't understand
Answer:
Step-by-step explanation:
40 de grese
Answer:
52°
Step-by-step explanation:
The angle between two secants drawn from the point outside the circle is half the difference of the intercepted arcs.
[tex]\sf \boxed{\bf \angle \ Y =\dfrac{far \ arc - near \ arc}{2}}[/tex]
[tex]\sf \angle Y = \dfrac{m\overset{\frown}{GK} - m\overset{\frown}{CE}}{2}\\\\50 = \dfrac{152-m\overset{\frown}{CE}}{2}[/tex]
[tex]50*2 = 152 - m\overset{\frown}{CE}\\\\100 = 152 - m\overset{\frown}{CE}[/tex]
[tex]100 + m\overset{\frown}{CE} = 152\\\\[/tex]
[tex]\sf m\overset{\frown}{CE}= 152 - 100\\\\m\overset{\frown}{CE} = 52^\circ[/tex]
Given this equation what is the value of y at the indicated point?
Value of indicated point is 2.
Define straight lineIn mathematics, a straight line is a geometric object that extends infinitely in both directions and is perfectly straight, meaning that it does not curve or bend. A straight line is defined by any two points on the line, which can be connected by a line segment that lies entirely on the line.
The equation of a straight line can be written in various forms, such as slope-intercept form, point-slope form, or standard form, but they all describe the same line. The equation of a straight line is y = mx + b in slope-intercept form.
Given equation;
3x-y=1
Given coordinate (1,y)
Putting the value of coordinate in equation, we get
3-y=1
3-1=y
y=2
Hence, value of indicated point is 2.
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What is 400000+234538=?
Answer:
634538
Step-by-step explanation:
Add 4+2 since in the rest of the columns, we have to add 0 to all of the rest of the numbers.
4+2=6
0+(3, 4, 5, 3, and 8 will equal the same thing)
0+3=3
0+4=4
And so on.
400000
+ 234538
_______
634538
I hope this has helped!
I need to know the answers to number 7, 8, 9, 10
From given box plot that represents average minute time per night spent on homework
Min = 0
Q1 = 20
Q2 = 48
Q3 = 60
Max = 190
7. percent of the sophomores spend more than 60 minutes on homework per night= 25% because 60 represent the Q3 that is 75th percentile , so above that 25 % are remains.
8. range of times that the middle 50% of the sophomores spend on homework per night= 20 to 60 minutes Middle 50% that is from Q1 to Q3
60 - 20 = 40
9. No of sophomores do not do homeworkHere given box plot is for average Time sophomores spend on homework per night. So it not gives the information about number of students. So we can not identify No of sophomores do not do homework from box plot .
10. percent of the sophomores spend less than 20 minutes per night on homework = 25% because 20 represents the Q1 that is 25th percentile so below that value 25% of data are fall.
7)25%
8)40
9) can not decide
10)25%
7. Sophomores that spend more than 60 minutes are 25%. 8. The range of times that the middle 50% of the sophomores spend on homework per night = 40.
What is box plot?A box plot, also called a box-and-whisker plot, is a statistical graph that shows how a dataset is distributed. As it enables a visual comparison of their median, range, and distribution, it is very helpful when comparing several datasets.
Two whiskers extend from a rectangular box that makes up a box plot. The whiskers reflect the minimum and maximum values that are not outliers, while the box represents the interquartile range (IQR), which is the middle 50% of the data. Each solitary point outside the whiskers represents an outlier.
From the given box plot that the five number summary can be calculates as follows:
Min = 0
Q1 = 20
Q2 = 48
Q3 = 60
Max = 190
7. Now, the percent of the sophomores that spend more than 60 minutes on homework per night= 25%.
As 60 represent the Q3 that is 75th percentile. Above this the remaining value is 25%.
Thus, sophomores that spend more than 60 minutes are 25%.
8. The range of times that the middle 50% of the sophomores spend on homework per night= 20 to 60 minutes
Middle 50% that is from Q1 to Q3
60 - 20 = 40
9. Time sophomores spend on homework per night is not given. So we can not identify number of sophomores do not do homework from box plot .
10. The percent of the sophomores spend less than 20 minutes per night on homework = 25%
As 20 represents the Q1 that is 25th percentile so below that value 25% of data are fall.
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The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
15,9, 27/5
Find the 10th Term
Therefore , the solution of the given problem of sequence comes out to be the sequence's roughly 10th term is 0.049 (rounded to the closest thousandth).
What is sequence?A sequence is a grouping of range numbers, or "terms." There are phrases like 2, 5, but choose 8. Certain narrative arcs can be made to go on forever by choosing to capitalise on a certain pattern that they exhibit. Use the designs 2, 5, 8, and then 3 to lengthen it. In a list of words for words, there exist formulas that show where to look. In mathematics, a sequence is a group of items that are ordered in some way.
Here,
The first three terms in the given sequence are 15, 9, and 27/5.
We must determine the pattern or rule that underlies the sequence in order to determine the tenth word.
=> 9 = 15 * (27/5) / 15
=> 27/5 = 9 * (27/5) / 9
Thus, each term is obtained by multiplying the constant value by (27/5) / 15, which may be written as 9/25.
In order to get the next phrase in the series, we can keep multiplying the preceding term by 9/25 using this constant value:
=> 9 * (9/25)⁷
When we compute this expression, we obtain:
=> (Rounded to the closest thousandth) 9 * (9/25)⁷
As a result, the sequence's roughly 10th term is 0.049 (rounded to the closest thousandth).
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Which expresion has the greatest value when n is equal to 4
The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.
How do we calculate?To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.
A. 5n = 5(4) = 20
B. n + 30 = 4 + 30 = 34
C. 50 - n = 50 - 4 = 46
D. 80 ÷ n = 80 ÷ 4 = 20
The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n
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ii) The door is 0.9 m wide and 2.1 m high. Each of the four windows is 1.5 m wide and 1.2 m high work out the toral area of the door and the four windows
Answer: The area of the door can be calculated as:
Area of door = width x height
= 0.9 m x 2.1 m
= 1.89 square meters
The area of one window can be calculated as:
Area of window = width x height
= 1.5 m x 1.2 m
= 1.8 square meters
Since there are four windows, the total area of the four windows is:
Total area of four windows = 4 x Area of window
= 4 x 1.8 square meters
= 7.2 square meters
Therefore, the total area of the door and the four windows is:
Total area = Area of door + Total area of four windows
= 1.89 square meters + 7.2 square meters
= 9.09 square meters
Hence, the total area of the door and the four windows is 9.09 square meters.
Step-by-step explanation:
Rewrite 6x2 + 2xy + 9x + 3y in factored form. (2x + 3)(3x + y) (2x + y)(3x + 3) (3x + 2)(3x + y) (3x + y)(2x + 1)
Answer:
(3x + y)(2x + 3)
Step-by-step explanation:
Factorizing the expression:6x² = 2 * 3 * x * x
2xy = 2*x * y
Common factor = 2x.
9x = 3 * 3 * x
3y = 3 * y
Common factor = 3
Take out the common factor 2x from the first and second term & take out the common factor 3 from third and fourth term.
6x² + 2xy + 9x + 3y = 2x(3x + y) + 3(3x + y)
= (3x + y)(2x + 3)
The owner of a stereo store wants to advertise that she has many different sound systems in stock. The store carries 5 different CD players, 8 different receivers, and 10 different speakers. A sound system consists of one of each item. How many different sound systems can the store owner advertise?
The owner can advertise 400 different sound systems. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
All real numbers can be explained using the four fundamental operations, generally known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.
We are given that the owner of a stereo store carries 5 different CD players, 8 different receivers, and 10 different speakers and each sound system consists of one of each item.
So, the different sound systems that the owner can advertise is obtained by using the multiplication operation, which gives:
⇒ Different sound systems = 5 * 8 * 10
⇒ Different sound systems = 400
Hence, the owner can advertise 400 different sound systems.
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Please help me please tysm and have a great day :)
Answer:
mean: 20mins
Step-by-step explanation:
add them all together to get 240
then divide by how many there are
240÷12=20
so the mean is 20mins
write a polynomial function of least degree with rational coefficients, so that P(x)=0 has the given roots.
x=-2,x=8
P(x)=
A polynomial function of least degree with rational coefficients, so that P(x)=0 has the given roots is P(x) = x^2 - 6x - 16.
What is roots?If the roots of P(x) are -2 and 8, then the factors of P(x) are (x+2) and (x-8), since if we plug in -2 or 8 for x, one of these factors will be equal to zero, making the whole expression equal to zero.
To find the polynomial with these roots, we can multiply these factors together:
P(x) = (x+2)(x-8)
Multiplying this out, we get:
P(x) = x^2 - 6x - 16
Therefore, the polynomial function of least degree with rational coefficients that has roots of -2 and 8 is:
P(x) = x^2 - 6x - 16
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The polynomial function of least degree with rational coefficients and roots at x=-2 and x=8 is P(x) = x² - 6x - 16.
What is polynomial?A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using only the operations of addition, subtraction, and multiplication, and in which the variables appear only with positive integer exponents. The degree of a polynomial is the highest power of the variable in the expression.
Define roots?Roots refer to the values that satisfy an equation, making it equal to zero.
Using the zero product property, we know that a polynomial with roots at -2 and 8 can be written as:
P(x) = (x + 2)(x - 8)
Expanding this expression, we get:
P(x) = x² - 6x - 16
Therefore, the polynomial function of least degree with rational coefficients and roots at x=-2 and x=8 is P(x) = x² - 6x - 16.
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Chloe claims that Point A=−6 and Point B=1 . Which of the following statements provide support for Chloe's claim? Select ALL that apply. A A<0 because A is to the left of zero B A>0 because A is to the left of zero C A 0 because B is to the left of zero F B>0 because B is to the right of zero
The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.
Describe Comparison Algebra?Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.
Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.
In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.
The statements that provide support for Chloe's claim are:
A. A<0 because A is to the left of zero.
F. B>0 because B is to the right of zero.
Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.
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Divide and give your answer as a decimal. Round your answer to the nearest thousandth (3 digits behind the decimal).
2/9
Answer:
0.222
Step-by-step explanation:
2 divided by 9 is:
0.222 (rounded to the nearest thousandth)
You take out a loan in the amount of your tuition and fees cost $70,000. The loan has a monthly interest rate of 0.25% and a monthly payment of $250. How long will it take you to pay off the loan? Use the formula N= (-log(1-i*A/P))/(log(1+i)) to determine the number of months it will take you to pay off the loan. Let N represent the number of monthly payments that will need to be made, i represent the interest rate in decimal form, A represent the amount owed (total amount of the loan), and P represent the amount of your monthly payment. Be sure to show your work for all calculations made.
It will take 4.645 months to pay off the loan, which rounds up to 5 months.
Define interest rateInterest rate is the percentage of the principal amount charged by a lender or creditor for the use of borrowed money. In other words, it is the cost of borrowing money, usually expressed as an annual percentage rate (APR) or as a periodic rate for a specific time period.
Given:
Total amount of the loan (A) = $70,000
Monthly interest rate (i) = 0.25% = 0.0025
Monthly payment (P) = $250
We need to find the number of monthly payments (N) needed to pay off the loan.
Using the given formula:
N = (-log(1 - i×A/P))/(log(1+i))
Substituting the values we get:
N = (-㏑(1 - 0.0025×70000/250))/(log(1+0.0025))
N = (-㏑(0.72))/(㏑1.0025))
N = (-(-0.337))-4.308
N = 4.645 (approx.)
Therefore, it will take approximately 4.645 months to pay off the loan, which rounds up to 5 months.
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find the factors to this polynomials i need help SHOW YOUR WORK.
Answer:
hope this will help you...
7.) Adult tickets for Disney on Ice are $6.50 while a child's ticket is only $2.50. At Tuesday night's
performance, 435 people were there in attendance. The box office brought in $1667.50 for that evening.
How many of each type of ticket were sold?
There were 145 adult tickets and 290 child tickets sold at Tuesday night's Disney on Ice performance.
How many of each type of ticket were sold?Let's assume that the number of adult tickets sold is "x" and the number of child tickets sold is "y".
From the problem, we know that the price of an adult ticket is $6.50 and the price of a child ticket is $2.50.
Therefore, the total revenue from adult tickets is 6.5x and the total revenue from child tickets is 2.5y.
We also know that the total attendance for the evening was 435 people, so:
x + y = 435
Finally, we know that the box office brought in $1667.50 in revenue for the evening, so:
6.5x + 2.5y = 1667.5
First, we can use the first equation to solve for one of the variables in terms of the other:
y = 435 - x
Substituting this expression for y into the second equation, we get:
6.5x + 2.5(435 - x) = 1667.5
Simplifying and solving for x, we get:
6.5x + 1087.5 - 2.5x = 1667.5
4x = 580
x = 145
To find the number of child tickets sold, we can use the equation we derived earlier:
y = 435 - x
y = 435 - 145
y = 290
Therefore, 290 child tickets were sold.
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In order to develop a more appealing cheeseburger, a franchise uses taste tests with 11 5 different buns, 3 different cheeses, 4 types of lettuce, and types of tomatoes. If the taste tests were done at one restaurant by one tester who takes 10 minutes to eat each cheeseburger, approximately how long would it take the tester to eat all possible cheeseburgers?
It would take approximately 1,980 minutes (33 hours) for the tester to eat all possible cheeseburgers.
Find the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum.
Answer: The formula for compound interest is:
A = P(1 + R/100)^t
where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.
Here, P = Rs. 3,500, R = 8%, and t = 2 years.
So, the amount after 2 years will be:
A = 3,500(1 + 8/100)^2
= 3,500(1.08)^2
= 3,892.32
Therefore, the compound interest for 2 years will be:
CI = A - P
= 3,892.32 - 3,500
= 392.32
Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.
Step-by-step explanation:
The Greenfield Community Picnic is today. The organizers are making 2 pulled-pork sandwiches for every 5 barbeque chicken sandwiches.
Answer: What is the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic?
Let's call the number of pulled-pork sandwiches "P" and the number of barbeque chicken sandwiches "C". According to the problem, the organizers are making 2 pulled-pork sandwiches for every 5 barbeque chicken sandwiches. This means that:
P/C = 2/5
To simplify this ratio, we can multiply both sides by a common factor that will make the denominators the same. In this case, the smallest common multiple of 2 and 5 is 10, so we can multiply both sides by 10:
10(P/C) = 10(2/5)
Simplifying this expression, we get:
2P = 4C
Dividing both sides by 2, we get:
P/C = 2/4
Simplifying this fraction, we get:
P/C = 1/2
Therefore, the ratio of pulled-pork sandwiches to barbeque chicken sandwiches at the Greenfield Community Picnic is 1:2.
Step-by-step explanation:
28) The number of hours per week that high school students spend on computers is normally distributed, with a mean
of 5 hours and a standard deviation of 2 hours. 70 students are chosen at random. Let y represent the mean number
of hours spent on the computer for this group. Find the probability that y is between 5.1 and 5.7.
The probability that y is between 5.1 and 5.7 is approximately 0.4292.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.
According to question:Since the sample size is large (n = 70), we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean as normal with mean μ = 5 and standard deviation σ/sqrt(n) = 2/sqrt(70) ≈ 0.24.
Now we want to find the probability that y, the sample mean, is between 5.1 and 5.7. We can use the standard normal distribution to do this by standardizing y:
z = (y - μ) / (σ / sqrt(n)) = (y - 5) / 0.24
The probability that y is between 5.1 and 5.7 is equivalent to the probability that z is between:
z1 = (5.1 - 5) / 0.24 ≈ 0.42
and
z2 = (5.7 - 5) / 0.24 ≈ 2.92
Using a standard normal distribution table or calculator, we can find that the probability of z being between z1 and z2 is approximately 0.4292.
Therefore, the probability that y is between 5.1 and 5.7 is approximately 0.4292.
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Mohal plans to repaint some classroom bookcases. He has 1 1 /8 gallons of paint. All of the bookcases are the same size and each requires 1/8gallon of paint. How many bookcases will he be able to paint?
Mohal will be able to paint 9 bookcases for the amount of paint.
What is fraction?An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.
Given that, he has 1 1 /8 gallons of paint.
Thus, number of bookcases are:
1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9
Hence, Mohal will be able to paint 9 bookcases for the amount of paint.
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find the reduced racial form of each expression:
1: 3^√4/9m^2 ?
2:√63-√700–√112 ?
3: (a^2b^8/a^1/3)^3/4 ?
4: ^4√1024x^9y^12 ?
5:4^3√81 - 2^3√72 - ^3√24 ?
6: ^5√2pq^6 • 2 √2p^3q ?
HELP PLEASE ILL DO ANYTHING. (show explanation pls)
The reduced radical forms of the expressions provided are as follows:
1. 3^(4/9m)
2. -11√7
3. a^(1/2) * b^6
4. 2x^(9/4) * y^3
5. 16 - ^3√24
6. 4p^(9/10)q^(7/10)
What is a reduced radical form?A reduced radical form is a way of simplifying expressions that contain radicals such as square roots and cube roots, as much as possible. In a reduced radical form, the radical is simplified to its lowest possible terms.
To obtain the reduced radical forms of the expresions, we can proceed with the workings:
1. 3^(√4/9m^2) = 3^(2/3 * 1/3√4m^2) (since √4 = 2)
= (3^(2/3))^(1/3√4m^2)
= (3^(2/3))^(2/3m)
= 3^(4/9m)
2. √63 = √(9 * 7) = 3√7
√700 = √(100 * 7) = 10√7
√112 = √(16 * 7) = 4√7
√63 - √700 - √112 = 3√7 - 10√7 - 4√7
= -11√7
3. (a^2b^8/a^1/3)^3/4 = (a^2/1/3√a)^3/4 * b^8^3/4
= (a^(2/3))^3/4 * b^6
= a^(1/2) * b^6
4. ^4√1024x^9y^12 = (^4√1024) * (^4√x^9) * (^4√y^12)
= 2 * x^(9/4) * y^(12/4)
= 2x^(9/4) * y^3
5. 4^3√81 = 4^3 * 3 = 64
2^3√72 = 2^3 * 2√9 = 16√9 = 48
^3√24 can't be simplified any further
4^3√81 - 2^3√72 - ^3√24
= 64 - 48 - ^3√24 or 16 - ^3√24.
6. ^5√2pq^6 • 2 √2p^3q
= 2p^(3/5)q^(6/5) * 2p^(3/2)q^(1/2)
= 4p^(9/10)q^(7/10)
So, the results are the simplified or reduced forms of the expressions.
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Determine the equation of the circle with center (-7, -4) containing the point
(-1,-8).
Answer:
(-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52
Step-by-step explanation:
i literally just learned this today so here we go:
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
We are given the center of the circle as (-7, -4), so we can substitute these values for h and k:
(x - (-7))^2 + (y - (-4))^2 = r^2
(x + 7)^2 + (y + 4)^2 = r^2
We also know that the circle contains the point (-1, -8).
We can substitute these values for x and y, and solve for r:
(-1 + 7)^2 + (-8 + 4)^2 = r^2
36 + 16 = r^2
r^2 = 52
Substituting this value of r^2 into the equation for the circle, we get:
(x + 7)^2 + (y + 4)^2 = 52
Therefore, the equation of the circle with center (-7, -4) containing the point (-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52
Nick's new home had a purchase price of $145,500. He got a 30-year fixed mortgage for 75% of the purchase price. The interest rate on the loan is 3.15%. What is his monthly payment?
Nick's monthly mortgage payment is $482.16.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To calculate Nick's monthly mortgage payment, we first need to find out the amount he borrowed from the bank, which is 75% of the purchase price:
$145,500 x 0.75 = $109,125
Next, we need to calculate the monthly interest rate. We can do this by dividing the annual interest rate (3.15%) by 12:
3.15% / 12 = 0.002625
Now we can use the following formula to calculate Nick's monthly payment:
M = P [ [tex]i(1 + i)^{n}[/tex] ] / [ [tex](1 + i)^{n}[/tex] – 1]
Where:
M = Monthly payment
P = Loan amount (principal)
i = Monthly interest rate
n = Number of payments (in months)
Plugging in the values we have:
M = $109,125 [ 0.002625 [tex](1 + 0.002625)^{360}[/tex] ] / [ [tex](1 + 0.002625)^{360}[/tex] – 1]
M = $482.16
Therefore, Nick's monthly mortgage payment is $482.16.
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1) A local restaurant owner surveyed 100 of his customers to determine what type of salad
they preferred. He discovered that 41 people preferred ranch dressing over Italian. He
also found that 38 customers like Italian dressing and cheese on their salad. 22 customers
prefer no cheese at all. Construct a two-way table summarizing the data.
Italian
Ranch
Total
Cheese
No Cheese
Total
If a local restaurant owner surveyed 100 of his customers to determine. the two-way table summarizing the data is
Italian Dressing Ranch Dressing Total
Cheese 38 18 56
No Cheese 0 22 22
Total 38 41 100
Constructing a two-way table ?Here is the two-way table summarizing the data:
Italian Dressing Ranch Dressing Total
Cheese 38 ? ?
No Cheese ? ? 22
Total ? 41 100
To fill in the missing values, we can use the information given in the problem:
38 customers like Italian dressing and cheese on their salad.
41 people preferred ranch dressing over Italian.
22 customers prefer no cheese at all.
From this information, we can deduce that:
The total number of customers who prefer Italian dressing is 38 + the number of customers who prefer Italian dressing without cheese. The total number of customers who prefer Ranch dressing is 41 + the number of customers who prefer Italian dressing with cheese. The total number of customers who prefer cheese is 38 + the number of customers who prefer Italian dressing with cheese. The total number of customers who do not prefer cheese is 22 + the number of customers who prefer Ranch dressing without cheese.Using these deductions, we can fill in the missing values:
Italian Dressing Ranch Dressing Total
Cheese 38 18 56
No Cheese 0 22 22
Total 38 41 100
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Ryan wants to find the favorite video game of the fifth grade boys at his school. Which group would be best for Ryan to survey?
The BEST group for Ryan to survey would be the 25 fifth grade boys since they are the specific group that he is interested in studying.
Describe Statistics?Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of various methods and techniques to gather data from a sample or population and to draw conclusions or make predictions based on that data.
There are two main branches of statistics: descriptive statistics and inferential statistics. Descriptive statistics is the process of summarizing and presenting data in a meaningful way, such as by calculating measures of central tendency (e.g. mean, median, mode), variability (e.g. range, variance, standard deviation), and correlation. Inferential statistics involves using probability theory to make inferences about a larger population based on a sample of data.
Statistics is used in a wide variety of fields, including business, economics, psychology, social sciences, medicine, and engineering. It is often used to test hypotheses, identify trends, and make predictions based on data. The field of statistics has evolved over time, with the development of new techniques and technologies for collecting and analyzing data.
The BEST group for Ryan to survey would be the 25 fifth grade boys since they are the specific group that he is interested in studying. Surveying a larger group of fifth grade students or every teacher at the school would not be as effective since it would include girls and boys who are not in the fifth grade, and teachers who may not have as much knowledge about the specific video game preferences of fifth grade boys. Surveying every boy who will pass to fifth grade next year would also not be as effective since they are not currently in the fifth grade and their preferences may change by the time they reach that grade. Therefore, surveying the 25 fifth grade boys would provide the most relevant and accurate data for Ryan's study.
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The complete question is:
Ryan wants to find the favorite video game of the fifth grade boys at his school. Which group would be BEST for Ryan to survey? 25 fifth grade boys 25 fifth grade students every teacher at his school every boy who will pass to fifth grade next year
carpet is sold in square yards how much carpet would a person need to buy for a rectangle that has dimensions of 10 yards by 18 feet
A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
How to determine the amount of carpet needed for a rectangular room?
To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.
The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),
18 feet ÷ 3 feet/yard = 6 yards
So the dimensions of the room in yards are 10 yards by 6 yards.
To find the total area of the room, we need to multiply the length and width,
10 yards × 6 yards = 60 square yards
Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
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