The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.
What is the scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2. The new figure we receive will resemble the first figure, but every dimension will be double that of the first rectangle. The scale factor in this case will be denoted by the number 2.
Let us take the radius of the circle to be r
We know that circumference = 2πr and the area of a circle is πr²
As, Scale factor = Original circle / Scaled circle
From the question, scale factor = 2
Thus,
2 = Circumference of the Original circle / Circumference of the Scaled circle.
⇒ Circumference of the Scaled circle = (1/2) * Circumference of the Original circle
For the area as well, scale factor = 2
2 = Area of the Original circle / Area of the Scaled circle
⇒ Area of the scaled circle = (1/2) * Area of the original circle
Thus,
The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.
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The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.
What is the scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2. The new figure we receive will resemble the first figure, but every dimension will be double that of the first rectangle. The scale factor in this case will be denoted by the number 2.
Let us take the radius of the circle to be r
We know that circumference = 2πr and the area of a circle is πr²
As, Scale factor = Original circle / Scaled circle
From the question, scale factor = 2
Thus,
2 = Circumference of the Original circle / Circumference of the Scaled circle.
⇒ Circumference of the Scaled circle = (1/2) * Circumference of the Original circle
For the area as well, scale factor = 2
2 = Area of the Original circle / Area of the Scaled circle
⇒ Area of the scaled circle = (1/2) * Area of the original circle
Thus,
The circumference of the scaled circle is half the circumference of the original circle and the area of the scaled circle is half the area of the original circle.
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Because a Rectangle is a parallelogram the properties that were true for a parallelogram are also true for a rectangle. TRUE OR FALSE ?
Yes, it's true.
Every rectangle is a parallelogram, but not every parallelogram is rectangle.
So, every parallelogram's properties will be same to rectangle, but not every rectangle's property will be same as parallelogram.
Hope it helps ya!
f(x)=1/3x+2 when x is equal to 6
Answer: f(6)=4
f(x)=1/3x+2
f(6)=1/3(6)+2
f(6)=6/3+2
f(6)=2+2
f(6)=4
URGENT:Two publishers have offered Dr. Spencer Lewis, a noted dietician, a deal on his new book Don't Dig Your Grave with Your Knife and Fork. The first has offered to pay him $50,000 up front and a $3 royalty for every book it sells. The second has offered to pay $20,000 up front and a $5 royalty for every book it sells. Over what range of sales will Dr. Lewis make more from the deal with the second company than he will from the deal with the first?
The range of sales Dr. Spencer Lewis must exceed to profit the most from the second deal is 15,000 sales.
How to find the range of sales that favors Dr. more with the second deal?To find the range that will benefit Dr. Spencer Lewis the most with the second deal, we must perform the following operation:
A. X × 5 + 20,000B. X × 3 + 50,000We must replace the X with several numbers and buy the result, when the result of operation B exceeds the result of operation A, it means that it will be more profitable.
According to the above, if we replace the X with 15,000, the values will be the same, however, each number that we increase will mean a greater profit in agreement B.
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What governing body rules most counties?
Answer:
County boards
Step-by-step explanation:
I got this answer right on my quiz :-)
Answer:
County Boards
Step-by-step explanation:
1. County boards are commonly particular of counties in the United States.
And that's all.
Luca eats 3/6 of his submarine sandwich. Riley eats 5/6 of his submarine sandwich. Riley said he ate 2/6 more than Luca. Is he correct, if the sandwich sizes are different.
Answer:
Riley is correct
Step-by-step explanation:
Luca eats 3/6 of his submarine sandwich. Riley eats 5/6 of his submarine sandwich. Riley said he ate 2/6 more than Luca.
To find out the fraction of how much more Riley ate than Luca, we carry out Subtraction operation
= Fraction of what Riley ate - Fraction of what Luca ate
= 5/6 - 3/6
Lowe's Common Denominator = 6
= 5 - 3/6
= 2/6
Therefore, Riley is correct
Solve the equation. then check your solution. a â€"" one-half = three-fifths a. negative 1 and startfraction 1 over 10 endfraction c. startfraction 9 over 16 endfraction b. 1 and startfraction 1 over 10 endfraction d. startfraction 1 over 10 endfraction
The left side of the equation is equal to the right side, which confirms that a = 11/10 is the correct solution.
To solve the equation, we need to isolate the variable "a". The equation is given as a - 1/2 = 3/5.
To eliminate the fraction, we can multiply both sides of the equation by the least common denominator (LCD), which is 10. This will clear the fractions and make the equation easier to solve.
Multiplying the left side of the equation by 10, we get:
10(a - 1/2) = 10(3/5)
10a - 5 = 6
Next, we can simplify the equation by adding 5 to both sides:
10a - 5 + 5 = 6 + 5
10a = 11
Finally, we can solve for "a" by dividing both sides of the equation by 10:
(10a)/10 = 11/10
a = 11/10
Therefore, the solution to the equation is a = 11/10 or a = 1 1/10.
To check the solution, substitute a = 11/10 back into the original equation:
11/10 - 1/2 = 3/5
(11/10) - (5/10) = 3/5
6/10 = 3/5
In summary, the solution to the equation a - 1/2 = 3/5 is a = 11/10 or a = 1 1/10. This solution has been checked and is correct.
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a group of fish is called a school . there are twenty-five in the small school.there are one hundered twelve fish in the big school. how many fewer fish are in the small school
There are 87 fewer fish in small school compared to big school.
We solve addition and subtraction problems by focusing on either the action (joining or separating) or the relationship in the problem. Many problems involve monetary relationships.
This week, we looked at COMPARISON problems, which involve determining the similarities and differences between sets.
Difference Unknown: One type of compare problem entails determining how many more items are in one set than another. James, for example, has six mice. Joy has eleven mice. Joy has how many more mice than James?
Given,
Number of fish in small school = 25
Number of fish in big school = 112
then,
Number of fewer fish does small school have 112 -25 = 87
Thus, there are 87 fewer fish in school than big school.
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Between 1954 and 2003, swimmers have crossed Lake Ontario 43 times. Both women andmen have made the crossing. Here are some plots (we’ve omitted a crossing by Vikki Keith, who swam a round trip—North to South to North—in 3390 minutes): The summary statistics are:How much difference is there between the mean amount of time (in minutes) it would take female and male swimmers to swim the lake?a) Construct and interpret a 95% confidence interval for the difference between female and male times. B) Comment on the assumptions and conditions
(a) 95% confidence interval for the difference between female and male times is (11.954, 255.591).
(b) The assumptions and conditions for the two-sample t-test are met, so we can use the results of the test and confidence interval.
a) To construct a 95% confidence interval for the difference between female and male times, we can use a two-sample t-test. Let's denote the mean time for female swimmers as μf and the mean time for male swimmers as μm. We want to test the null hypothesis that there is no difference between the two means (i.e., μf - μm = 0) against the alternative hypothesis that there is a difference (i.e., μf - μm ≠ 0).
The formula for the two-sample t-test is:
t = (Xf - Xm - 0) / [sqrt((s^2f / nf) + (s^2m / nm))]
where Xf and Xm are the sample means for female and male swimmers, sf and sm are the sample standard deviations for female and male swimmers, and nf and nm are the sample sizes for female and male swimmers, respectively.
Using the data from the plots, we get:
Xf = 917.5, sf = 348.0137, nf = 15
Xm = 783.7273, sm = 276.0625, nm = 28
Plugging in these values, we get:
t = (917.5 - 783.7273 - 0) / [sqrt((348.0137^2 / 15) + (276.0625^2 / 28))] = 2.4895
Using a t-distribution with (15+28-2) = 41 degrees of freedom and a 95% confidence level, we can look up the critical t-value from a t-table or use a calculator. The critical t-value is approximately 2.021.
The confidence interval for the difference between female and male times is:
(917.5 - 783.7273) ± (2.021)(sqrt((348.0137^2 / 15) + (276.0625^2 / 28)))
= 133.7727 ± 121.8187
= (11.954, 255.591)
Therefore, we can be 95% confident that the true difference between female and male times is between 11.954 and 255.591 minutes.
b) Assumptions and conditions for the two-sample t-test:
Independence, We assume that the observations for each group are independent of each other.
Normality, We assume that the populations from which the samples were drawn are approximately normally distributed. Since the sample sizes are relatively large (15 and 28), we can rely on the central limit theorem to assume normality.
Equal variances, We assume that the population variances for the female and male swimmers are equal. We can test this assumption using the F-test for equality of variances. The test statistic is,
F = s^2f / s^2m
where s^2f and s^2m are the sample variances for female and male swimmers, respectively. If the p-value for the F-test is less than 0.05, we reject the null hypothesis of equal variances. If not, we can assume equal variances. In this case, the F-test yields a p-value of 0.402, so we can assume equal variances.
Sample size, The sample sizes are both greater than 30, so we can assume that the t-distribution is approximately normal.
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On Jerry's text message phone plan, she paid $0.30 for every 20 messages she sent. what is the cost per message? ___ dollars
which graph best approximates Jerry's text message plan? (on the y-axis each mark is $1
The cost of each message is $0.015.
Option C graph best approximates Jerry's text message plan.
Given,
On Jerry's text message phone plan, she paid $0.30 for every 20 messages she sent.
We need to find what is the cost per message in dollars.
How do we find the unit cost of an item?We divide the total cost by the number of items.
Example: 10 pieces cost $20
1 pieces cost = $20/10 = $2
We have,
$0.30 for every 20 messages.
The cost of each message:
= $0.30/20
= $0.300
= $0.015
We can see that in the graph x-axis represents the number of messages and the y-axis represents the cost of each message.
We have,
$0.30 = 20 messages
3 x $0.30 = 3 x 20 messages
$0.90 = 60 messages.
We need a graph that has a point that intersects $0.90 and 60 messages.
We see that in the graph of Option C.
Option C graph best approximates Jerry's text message plan.
Thus,
The cost of each message is $0.015.
Option C graph best approximates Jerry's text message plan.
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Explain the relationship between an inda vidual and a society
Answer:
The relation between individual and society is very close. Essentially, “society” is the regularities, customs and ground rules of antihuman behavior. ... Man is biologically and psychologically equipped to live in groups, in society. Society has become an essential condition for human life to arise and to continue.
27 is 30% of what number?
A 8585
B 9292
C 1212
D 90
Answer:
27 is 30% of what number?
D. 90
Step-by-step explanation:
You're welcome.
each tile in the model represents 1/4. How many titles make a group of 3/4
Answer:
3 tiles
because 1/4+1/4+1/4=3/4
I hope this helps you!
If the sphere shown above has a radius of 14 units then what is the approximate volume of the sphere
Answer:
About 11494.04
Step-by-step explanation:
There is no sphere shown above but I can still get you the answer:
The formula for the volume of a sphere is \(\frac{4}{3} *\)π*r³
Putting in the radius, we get:
\(\frac{4}{3}\)*π*14³=
\(\frac{4}{3}\)*π*2744=
\(\frac{10976}{3}\)*π=
3658.66*π≈11494.04
What solid figure is shown below? triangular pyramid square pyramid rectangular prism cylinder
the answer is rectangular prism
The solid figure shown below is a rectangular prism.
Option C is the correct answer.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
A rectangular prism is a three-dimensional shape with six faces that are all rectangles.
It is also sometimes called a rectangular parallelepiped or a rectangular cuboid.
Here are some examples of objects that can be represented as rectangular prisms:
Shoebox
Cereal box
Brick
Book
Computer keyboard
Television set
Refrigerator
Building blocks
Shipping container
Tissue box.
Thus,
The solid figure shown below is a rectangular prism.
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What is the solution to the equation below?
3log X= log 32+ log 2
X=-8
X=-4
X= 8
With the options:
X=-8
X=-4
X=4
X=8
The correct answer is x=4
The required solution of the given expression is x = 4.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
3log X= log 32+ log 2
logx³ = log 2⁵ + log 2
logx³ = log 2 ⁶
x³ = 2⁶
x = ∛2⁶
x = 4
Thus, the required solution of the given expression is x = 4.
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20. Given the area, find the side length.
Answer:
Step-by-step explanation:
Area of a square = 49a⁸b¹⁰
Side = √49a⁸b¹⁰
= √7²*(a⁴)²*(b⁵)²
= (7a⁴b⁵)²
Side = 7a⁴b⁵
let A be an n x n matrix with an eigenvalue of λ multiplicity n. show that A is diagonalizable if and only if A = λI.
If A is an n x n matrix with an eigenvalue of λ with multiplicity n, we want to prove that A is diagonalizable if and only if A = λI, where I is the n x n identity matrix.
To show the forward implication, assume A is diagonalizable. Since A has an eigenvalue of λ with multiplicity n, its characteristic polynomial can be written as (λ - λ)^n = 0.
This implies that A has only one eigenvalue, which is λ, and all other eigenvalues must be zero. Since A is diagonalizable, it can be written as A = PDP^(-1), where D is a diagonal matrix containing the eigenvalues of A.
As A has only one eigenvalue, D will have a single entry λ on its diagonal. Therefore, A = λI, where I is the n x n identity matrix.
For the reverse implication, assume A = λI. In this case, the characteristic polynomial of A is (λ - λ)^n = 0, indicating that λ is the only eigenvalue of A with multiplicity n. Moreover, A can be easily diagonalized since it is already in diagonal form.
In summary, if A is an n x n matrix with an eigenvalue of λ with multiplicity n, A is diagonalizable if and only if A = λI, where I is the n x n identity matrix.
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A'roll of cookie dough is 8.4 inches long. If we want to cut out 12 equal sections to make
12 cookies, how long will each section be?
Answer:
each section will be .7 inches long
Step-by-step explanation:
8.4/ 12
Can someone pls explain to me on how to do this and give me the answer for this .
Answer:
1360.7 feet^3
Step-by-step explanation:
radius = diameter / 2 = 9 /2 = 4.5 feet
Volume = radius^2 x pi x height = 4.5^2 x 3.14 x 10.7 = 680.3595 feet^3
the water tanks are two so
total volume = 680.3595 x 2 = 1360.719 feet^3
for round the answer to the nearest tenth, we have to look at the number after 7. If it is smaller than 5 we can leave 7, if it its higher or equal to 5, we have to change 7 in 8. In this case is 1, so it remains 7
Final answer = 1360.7 feet^3
The back of Dante's property is a creek. Dante would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 720720 feet of fencing available, what is the maximum possible area of the pasture
The correct value is 720 ft of fencing.
Answer:
Max Area = 64800 sq.ft
Step-by-step explanation:
A square will always give us the maximum area.
Thus, one side would be;
720/4 = 180 feet
So, we want a square 180 ft by 180 ft
however, from the question, we are to use the creek as one side. So, we'll take the 180 ft that we don't need because of the creek and then add it to the opposite side to get 180 + 180 = 360 ft.
Thus,we now have a rectangle with dimensions: 180 ft by 360 ft
Area is given by;
area = length × width
Maximum Area = 180 × 360
Max Area = 64800 sq.ft
What coordinates best represent the location of a point K on the coordinate plane below?
(-7, -4)
(-7, -4)
(-7, 4)
(-7, 4)
(-4, -7)
(-4, -7)
(-4, 7)
Answer:
The Correct answer is C ( -7, 4)
Step-by-step explanation:
The Correct answer is C ( -7, 4) yepppp
Lots of points + brainlyist. Pls.
The interpretation of the given compound interest expression is:
2400 is the amount of initial deposit
1.03 is the amount
12t is the number of times the account has compounded since it opened
How to Interpret Compound Interest Problems?The formula for compound interest is:
A = P(1 + (r/t))^(nt)
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
We are given the equation as:
S = 2400(1.03)^(12t)
Thus:
2400 is the amount of initial deposit
1.03 is the amount
12t is the number of times the account has compounded since it opened
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PLS HELP !!! I WILL GIVE BRAINLIEST !!! BUT ONLY ANSWER CORRECTLY OR I WILL REPORT U.
Answer:
diamond: yz = hi
Step-by-step explanation:
since its SAS the other side of the angle needs to be equal
Find the equation of the line that is perpendicular to y = 2x + 8 and passes though the point (8. -8).
-)
A)
yo žx - 4
y=-3x - 4
B)
y = 2x - 12
D)
y - 2x - 12
Answer:
y=2x-24
Step-by-step explanation:
y--8=2(x-8)
y+8=2x-16
y=2x-24
Write a cubic function in standard form that has x-intercepts at (-1,0) (2,0) (4,0) and a y intercept at (0,-24)
After answering the presented question, we can conclude that Therefore, the cubic function in standard form that has x-intercepts at (-1,0) (2,0) (4,0) and a y-intercept at (0,-24) is \(f(x) = 3x^3 - 21x^2\) \(+ 14x + 24.\)
what is function?In mathematics, a function appears to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.
To find a cubic function in standard form, we can start by using the intercept form of the cubic equation:
\(f(x) = a(x-x1)(x-x2)(x-x3)\\f(x) = a(x+1)(x-2)(x-4)\\-24 = a(0+1)(0-2)(0-4)\\-24 = a(-8)\\a = 3\\\)
So the cubic function in standard form that satisfies the given conditions is:
\(f(x) = 3(x+1)(x-2)(x-4)\\f(x) = 3x^3 - 21x^2 + 14x + 24\\\)
Therefore, the cubic function in standard form that has x-intercepts at (-1,0) (2,0) (4,0) and a y-intercept at (0,-24) is \(f(x) = 3x^3 - 21x^2\) \(+ 14x + 24.\)
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On a horizontal number line, -35 is located to the left of -22. Enter an inequality that represents this statement.
This inequality indicates that -35 is less than -22, confirming that -35 is positioned to the left of -22 on a horizontal number line.
To represent the statement "On a horizontal number line, -35 is located to the left of -22" as an inequality, we can use the less than symbol (<).
Since -35 is to the left of -22, it means that -35 is a smaller number than -22.
Therefore, the inequality that represents this statement is:
-35 < -22
This inequality indicates that -35 is less than -22, confirming that -35 is positioned to the left of -22 on a horizontal number line.
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A coordinate grid with 2 lines. The first line is labeled y equals 0.5 x plus 3.5 and passes through (negative 3, 1), (negative 2.7, 2.1), and (0, 3.5). The second line is labeled y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction and passes through the points (negative 4, 3), (negative 2.7, 2.1), and (StartFraction 1 over 3 EndFraction, 0). Which is the approximate solution to the system y = 0.5x + 3.5 and y = −A system of equations. y equals 0.5 x plus 3.5. y equals negative StartFraction 2 over 3 EndFraction x plus StartFraction 1 over 3 EndFraction.x + shown on the graph? (–2.7, 2.1) (–2.1, 2.7) (2.1, 2.7) (2.7, 2.1)
Answer:
2.1 2.7
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
edge test ;)
Find the value of x. *
(x + 15)
106
(x-10)
(2x - 35)°
Answer:
m gc
Step-by-step explanation:
chuck was chopping wood.when he was done he had 25 kg of firewood what was most likely the weight of the wood before he chopped it
Answer:
The weight of the wood before he chopped it is 245 N
Step-by-step explanation:
The law of conservation of mass states that for a given isolated system, mass (or matter) can not be created neither can it be destroyed, but it can be transformed into different forms
Therefore, whereby all the wood Chuck chops is taken as firewood, (wood which is dry is about 100% consumable as firewood) the mass of the wool before he chopped the wood = The mass of the firewood he had after chopping the wood = 25 kg
Weight = Mass × The acceleration due to gravity, g
g = Constant = 9.8 m/s²
The weight of the wood before he chopped it = 25 kg × 98 m/s² = 245 N.
Answer:
as much as it wants
Step-by-step explanation:
How many solutions are there to the inequality x1 + x2 + x3 ≤ 11, where x1, x2, and x3 are nonnegative integers? [Hint: Introduce an auxiliary variable x4 such that x1 + x2 + x3 + x4 = 11.]
The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.
We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.
We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.
We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.
We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:
| ** | * | ****
This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.
We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.
Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.
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