According to the question the standard deviation is approximately $9,400.
What is standard deviation?Standard deviation is a measure of variability or dispersion in a data set. It is a measure of how much the individual data points within a set deviate from the mean. The standard deviation is calculated by taking the square root of the variance and is expressed as the same unit of measurement as the data set.
The standard deviation of pre-tax family incomes when the head of the household has a university degree can be computed using the empirical rule. According to the empirical rule, approximately 68% of the data lies within one standard deviation of the mean, 95% of the data lies within two standard deviations of the mean, and 99.7% of the data lies within three standard deviations of the mean.
Given that 70% of the pre-tax family incomes when the head of the household has a university degree are between $76,300 and $95,100,
we can calculate that the standard deviation is approximately ($95,100 - $76,300) / 2.66 ≈ $9,400.
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Symbolize as a system in x and y but do not solve it: The sum of
one number and half another is
negative five. Twelve less than twice the second number yields the
first number.
The system of equations according to the given instructions are x + (1/2)y = -5; 2y - 12 = x
The sum of one number and half another is negative five. Twelve less than twice the second number yields the first number.
Let x represent the first number and y represent the second number.
System:
x + (1/2)y = -5
2y - 12 = x
The system of equations that represents this situation is:
x + (1/2)y = -5
2y - 12 = x
Where x represents the first number and y represents the second number.
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What is the expression written using each base only once? 48 x 43 O A 411 O B. 1211 O C. 424 O D. 6411
The expression written using each base only once is 4¹¹ , the correct option is (a).
The expression 4⁸×4³ can be simplified using the rule of exponents,
The rule of exponents states that when we multiplying two exponential expressions with the same base, the exponents gets added.
which means that, nᵃ×nᵇ = nᵃ⁺ᵇ;
In this case the expression is: 4⁸×4³ , it has common base as "4",
So, by the rule of exponents, the power(exponents) gets added up ;
The expression "4⁸×4³" can be rewritten as 4⁸⁺³, which is equal to 4¹¹,
Therefore, Option(a)4¹¹, is the expression written using each base only once.
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The given question is incomplete, the complete question is
What is the expression written using each base only once? 4⁸×4³
(a) 4¹¹
(b) 12¹¹
(c) 4²⁴
(d) 64¹¹.
the ratio 20 miunte to 1 hour can be written in the form of 1:n find the value of n
Answer:
Step-by-step explanation:
1 hour = 60 minutes, so ratio is
20:60 = 1:3
∴ n = 1
emily is saving up to buy an iphone 7 that costs $850 so far she has saved $250, she would like to buy the phone in 10 weeks from now. how much must she save every week to have enough money to purchase the phone in 10 weeks
HELPPP
Answer:
60
Step-by-step explanation:
850-250=600
600/10=60
60
Answer:
she must save $60 each week to have enought money to purchase the iPhone 10
Step-by-step explanation:
Because 850-250=600
600/10=60
What is the y-intercept?
Answer:
The y-intercept is 1
at the point (0,1)
Step-by-step explanation:
The y-intercept is the point at which a graph crosses the y-axis.
jane has a kitten named Fluff-ball. Fluff-ball usually sleeps in a cat bed 20 meters from the kitchen and hardly ever moves. But whenever Jane opens a can of cat food, the kitten comes running into the kitchen as fast as he can. If Fluff-ball takes 5 seconds to reach the kitchen, how fast can he run? Please answer in meters per second.
Fluff-ball can run at a speed of 4 meters per second.
What is speed ?Speed is a measure of how fast an object is moving. It is typically measured in units of distance per unit time, such as meters per second (m/s) or miles per hour (mph). Speed is a scalar quantity, meaning it has magnitude but no direction.
According to given information :Fluff-ball can run at a speed of 4 meters per second.
This is because speed is equal to distance divided by time, and in this case the distance is 20 meters and the time is 5 seconds:
Speed = distance/time = 20 meters/5 seconds = 4 meters per second.
Therefore, Fluff-ball can run at a speed of 4 meters per second.
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Restict the domain of the function f so that the
function is one-to-one and has an inverse function.
Then find the inverse function f-1 state the domain and range of f
and f-1.
To restrict the domain of the function f so that it is one-to-one and has an inverse function, we need to find a subset of the domain in which the function is one-to-one. This means that for every value of x in the restricted domain, there is exactly one value of f(x).
Once we have restricted the domain, we can find the inverse function f-1 by switching the x and y values in the original function and solving for y. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.
For example, consider the function f(x) = x^2. This function is not one-to-one because for every value of x, there are two values of f(x) (one positive and one negative). However, if we restrict the domain to x ≥ 0, the function becomes one-to-one and we can find the inverse function.
The restricted function is f(x) = x^2 for x ≥ 0. The inverse function is f-1(x) = √x for x ≥ 0. The domain of f is x ≥ 0 and the range is f(x) ≥ 0. The domain of f-1 is x ≥ 0 and the range is f-1(x) ≥ 0.
In general, to restrict the domain of a function so that it is one-to-one and has an inverse function, we need to find a subset of the domain in which the function is one-to-one. Once we have restricted the domain, we can find the inverse function by switching the x and y values and solving for y. The domain of the inverse function will be the range of the original function, and the range of the inverse function will be the domain of the original function.
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3. Ling is putting up a wallpaper border on three walls that are each 14 feet long and 12 feet tall. How many feet of wallpaper border will she use if she puts the border only at the top of the wall?
By answering the above question, we may infer that Ling will thus require equation 42 feet of wallpaper border to install at the top of the three walls.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
Three walls, each 14 feet long and 12 feet tall, are being wallpapered by Ling. Just the top of the wall will be covered by the border. As a result, each wall requires a 14-foot-long wallpaper border.
The length of the border on each of the three walls must be added together to determine the overall length of wallpaper border required. So:
Whole wallpaper border length is one wall's border length times the number of walls.
Overall wallpaper border length is 14 feet multiplied by 3 walls.
42 feet is the total length of the wallpaper border.
Ling will thus require 42 feet of wallpaper border to install at the top of the three walls.
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Please help quickly! Both circles have the same center. The circumference of the inner circle is 125.6 inches. What is the area of the shaded region?
Use 3.14 for pi. Write your answer as a whole number or decimal rounded to the nearest hundredth.
Answer:
The area of the shaded region can be calculated by subtracting the area of the inner circle from the area of the outer circle. The area of the inner circle is pi multiplied by the square of the radius, or 3.14 * (125.6/2)^2, which equals 19644.8. The area of the outer circle is pi multiplied by the square of the radius, or 3.14 * (125.6)^2, which equals 49766.56. Subtracting the inner circle’s area from the outer circle's area, the area of the shaded region is 30121.76, rounded to the nearest hundredth
Step-by-step explanation:
The legs of an isosceles trapezoid are 10. The bases are 9 and 21. Find the area of the trapezoid and the lengths of the diagonals
The area of the given isosceles trapezoid is 120 square units.
An isosceles trapezoid is a quadrilateral formed by a trapezium whose base angles are equal due to which the left and right sides are also equal in length.
In the given question,
Length of left/right side = 10
Length of bigger base = 21
Length of smaller base = 9
If we join the edges of the smaller base to the bigger base in such a way that we get 2 right-angled triangles formed by the legs of the trapezoid and the base,
we can say that the length of the base would be
=(bigger base-smaller base)/2
=(21-9)/2
=6
and we know that the length of the legs is 10
So to the Pythagorean theorem,
the height of the trapezoid would be
h=√(10² - 6²) = √64 = 8
Now that we know all the variables, we can easily calculate the area of the trapezoid by the formula
= height × (bigger base+smaller base)/2
= 8 ×(21+9)/2
= 4 × (30)
= 120 square units
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Please help meeeeeee
Answer:
She earns $2,560
Step-by-step explanation:
She earns 2,560 because this is 8% of 32000. How do we know?
Multiply 32000 by 0.088, which is 8% of 100.
Plugging Into Exponential Formulas
A person places $8290 in an investment account earning an annual rate of 6%, 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 12 years.
We have the following response after answering the given question: To interest the nearest penny, the balance in the account after 12 years is thus $17,821.76.
what is interest ?To calculate simple interest, divide the principal by the interest rate, the duration, and other variables. The marketing formula is simple return = capital + interest + hours. The easiest way to calculate interest is with this approach. The most popular method for calculating interest is as a percentage of the principal amount. For instance, if he borrows $100 from a friend and agrees to pay it back at 5% interest, he will only pay his portion of the 100% interest. $100 (0.05) = $5. Interest must be paid when you borrow money and must be added to any loans you make. The yearly percentage of the loan amount is frequently used to calculate interest. This percentage represents the loan's interest rate.
Continuously compounded interest is calculated as follows:
[tex]V = Pe^(rt) (rt)[/tex]
where: V = the investment's final value
P is the original investment's principle.
r equals the yearly interest rate (as a decimal)
t is the duration of the investment, in years.
P = $8290, r = 0.06 (6% as a decimal), and t = 12 years in this example.
So, [tex]V = 8290e^(0.06*12) = $17,821.76[/tex]
To the nearest penny, the balance in the account after 12 years is thus $17,821.76.
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\( \tan x \cdot \sin x+\cos x=? \) a) \( \sec x \) b) \( \csc x \) c) \( \cot x \) d) \( 1+\tan x \)
The correct answer is option d) \( 1+\tan x \), since \( \sec x=1+\tan x \).
The correct answer for the given expression \( \tan x \cdot \sin x+\cos x=? \) is option d) \( 1+\tan x \).
Step-by-step explanation:
We can start by using the identity \( \tan x = \frac{\sin x}{\cos x} \) to rewrite the expression:
\( \frac{\sin x}{\cos x} \cdot \sin x+\cos x=? \)
Next, we can simplify the expression by multiplying the numerator and denominator by \( \cos x \):
\( \frac{\sin^2 x+\cos^2 x}{\cos x}=? \)
Now, we can use the identity \( \sin^2 x+\cos^2 x=1 \) to further simplify the expression:
\( \frac{1}{\cos x}=? \)
Finally, we can use the identity \( \frac{1}{\cos x}=\sec x \) to rewrite the expression in terms of \( \sec x \):
\( \sec x=? \)
Therefore, the correct answer is option d) \( 1+\tan x \), since \( \sec x=1+\tan x \).
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23% of the people surveyed prefer country music. 2653 people said that they did not like country music. How many people said that they like country music?
793 people in the country said that they like country music if 23% of the people surveyed prefer country music.
The given data is as follows:
percentage of people prefer music = 23%
People did not like country music = 2653
Let us assume make this equation has equal properties,
0.23x = people who like country music
We know that 2,653 people did not like music. We can write this equation as:
x - 0.23x = 2653
0.77x = 2653
x = 2565 / 0.77
x = 3446.75
Taking the x value approximately, we get the x value as,
x = 3447
Now we can substitute the x value in the above equation, we get,
0.23x = 0.23(3447)
= 792.81
Therefore we can conclude that 793 people in the country said that they like country music.
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The random variable X is distributed as Bernoulli(p). Given X = x the random variable Y ~ Poisson(12) for 1> 0. (a) Derive the distribution of Y (b) Evaluate E(Y)
(a) The distribution of Y is P(Y = y) = (12^y * e^-12)/y!
(b) E(Y) = 12.
The random variable X is distributed as Bernoulli(p). Given X = x the random variable Y ~ Poisson(12) for 1> 0.
(a) The distribution of Y ~ Poisson(12) is given by:
P(Y = y) = (12^y * e^-12)/y!
(b) The expected value of a Poisson distribution is simply the mean, which in this case is 12. Therefore, E(Y) = 12.
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Find the measure of bfg
Answer:
33 degrees
Step-by-step explanation:
Angles BFG + GFC = 90
5r +68 + 8r +113 =90
1
Collect like terms
13r + 181 = 90
Subract 181 from both sides
13r = 90-181
13r = - 91
r = - 7
Now insert the value of r into BFG (5r +68)
5r + 68 = 5(-7) +68
= -35 + 68
=33
Check your answer by inserting the value of r into 8r +113
8r + 113 =8(-7) +113
-56+113= 57
The two angles 33 and 57 must add up to 90, a rt angle
Add the proper constant to the binomial so that the resulting trinomial is perfect square. Then factor the trinomial y2 _ 18y Add the proper constant to make a perfect square trinomial: y2 _ 18y (Type an integer or a simplified fraction )
To make the trinomial y2 - 18y a perfect square, we need to add a constant that is equal to (18/2)^2 = 81.
This is because a perfect square trinomial is in the form (x + a)^2 = x^2 + 2ax + a^2. In this case, x = y and 2a = -18, so a = -9 and a^2 = 81. So, the trinomial becomes y2 - 18y + 81, which is a perfect square.
To factor the trinomial, we can use the formula (x + a)^2 = x^2 + 2ax + a^2, where x = y and a = -9. So, the trinomial y2 - 18y + 81 can be factored as (y - 9)^2.
Therefore, the proper constant to add to the binomial y2 - 18y to make it a perfect square trinomial is 81, and the factored form of the trinomial is (y - 9)^2.
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Estimate by rounding
$14.49 + $68.64 + $128.05
Answer:
$211 if rounding to nearest whole number (this may be what looking for)
$211.20 if rounding to nearest tenth
Step-by-step explanation:
The answer depends on what precision of rounding is done so i am providing 2 answers
Rounding to the nearest whole number:
14,49 rounded = 14
68.64 rounded = 69
128.05 rounded = 128
$14.49 + $68.64 + $128.05 = 14 + 69 + 128
= $211
Rounding to the tenths:
14,49 rounded = 14.5
68.64 rounded = 68.6
128.05 rounded = 128.1
$14.49 + $68.64 + $128.05= 14.5 + 68.6 + 128.1 = $211.20
One auto repair shop chargers $30 for a dignosis and $25 per hour for labor. Another auto repair shop charges $35 per hour for labor. For how many hours are the total charges for both of the shops the same?
The total charges for both auto repair shops will be the same when 3 hours of labor have been performed.
Let's call the number of hours worked "h". The total charges for the first auto repair shop will be $30 (for the diagnosis) plus $25 per hour, or $30 + $25h. The total charges for the second auto repair shop will be $35 per hour, or $35h. We want to know when the total charges for both shops will be the same, so we can set the two equations equal to each other and solve for h:
$30 + $25h = $35h
$10h = $30
h = 3
So the total charges for both auto repair shops will be the same when 3 hours of labor have been performed.
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I need help with this question
you multiply x by y and then multiply 5 to the power of 67 to then come to an answer of 500000000000x
A physics class has 40 students. Of these, 10 students are physics majors and 14 students are female. Of the physics majors, three are female. Find the probability that a randomly selected student is female or a physics major.
The probability that a randomly selected student is female or a physics major would be 0.65.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring needs to be 1.
The probability that a randomly selected student is female or a physics major can be calculated:
P(PM or F) = P(PM) + P(F) - P(PMF)
Where P(PM or F) = Probability of student selected is Physics Major or Female needed to find.
P(PM) = Probability of student selected is Physics Major
P(PM) = Number of Physics Major / Total number of students in the Physics class
P(PM) = 14 / 40 = 0.35
P(F) = Probability of student selected is Female = Number of female students in the Physics class / Total number students in the Physics class = 18 / 40 = 0.45
P(PMF) = Probability of student selected is Physics Major and Female = 6 / 40 = 0.15
Substituting the values into equation (1);
P(PM or F) = 0.35 + 0.45 - 0.15
P(PM or F) = 0.65
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Math part 4 question 7
For the given function f(x) = (x - 4)² - 3, the following statements are correct -
B: relative minimum at (4,-3).
C: decreasing interval from (-∞, 4).
E: increasing interval is (4, ∞).
What is a function?
In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.
To find the relative maximum and minimum of the function, we need to find its critical points by setting the derivative of the function equal to zero -
f(x) = (x - 4)² - 3
f'(x) = 2(x - 4)
2(x - 4) = 0
x = 4
So, the only critical point of the function is x = 4.
Plug in the value of x = 4 in the equation -
(4 - 4)² - 3
0 - 3
-3
Since f''(4) is positive, the critical point at x = 4 is a relative minimum.
Therefore, the function has a relative minimum at (4, -3).
To find the increasing and decreasing intervals, we can look at the sign of the first derivative -
f'(x) = 2(x - 4)
For x < 4, f'(x) is negative, meaning that f(x) is decreasing on the interval (-∞, 4).
For x > 4, f'(x) is positive, meaning that f(x) is increasing on the interval (4, ∞).
Therefore, the decreasing interval is (-∞, 4), and the increasing interval is (4, ∞).
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Exercise 6.2: \( 3+3 \) points. Let \( A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & -1 & 1\end{array}\right] \). (a) Is \( A \) diagonalizable as an element of \( M_{3 \times 3}(\mathbb{R})
The matrix \( A \) is not diagonalizable as an element of \( M_{3 \times 3}(\mathbb{R}) \), because there does not exist a basis of \( \mathbb{R}^{3} \) consisting of eigenvectors of \( A \).
The matrix \(A=\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & 1 \\ 0 & -1 & 1\end{array}\right] \) is diagonalizable as an element of \( M_{3 \times 3}(\mathbb{R}) \) if and only if there exists a basis of \( \mathbb{R}^{3} \) consisting of eigenvectors of \( A \).
To determine if \( A \) is diagonalizable, we need to find the eigenvalues and eigenvectors of \( A \).
The characteristic polynomial of \( A \) is given by:
\(\det(A-\lambda I)=\left|\begin{array}{ccc}1-\lambda & 0 & 0 \\ 0 & 1-\lambda & 1 \\ 0 & -1 & 1-\lambda\end{array}\right|=(1-\lambda)^{3} \)
The eigenvalues of \( A \) are the roots of the characteristic polynomial, which are \( \lambda=1 \) with multiplicity 3.
To find the eigenvectors of \( A \), we need to solve the equation \( (A-\lambda I)x=0 \) for each eigenvalue.
For \( \lambda=1 \), we have:
\( (A-1I)x=0 \)
\(\left[\begin{array}{ccc}0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & -1 & 0\end{array}\right]x=0 \)
The solution to this equation is the eigenspace of \( \lambda=1 \), which is spanned by the eigenvector \( x=\left[\begin{array}{c}1 \\ 0 \\ 0\end{array}\right] \).
Since the eigenspace of \( \lambda=1 \) has dimension 1, there is only one linearly independent eigenvector for this eigenvalue. Therefore, the matrix \( A \) is not diagonalizable as an element of \( M_{3 \times 3}(\mathbb{R}) \), because there does not exist a basis of \( \mathbb{R}^{3} \) consisting of eigenvectors of \( A \).
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(Finance ) A total of k^(10),000 is to be invested. some in bonds and some in certificates of deposit (CDs ). If the amount invested in bonds is to exceed that in certificates of deposits by k^(3),000, how much will be invested in each type of investrient.
By applying Two-Variable Linear Equation it can be concluded that the amount invested in bonds is $6,500 and the amount invested in CDs is $3,500.
Two-Variable Linear Equation is a form of relation equal to the algebraic form which has two variables and both are raised to the power of one.
We will use this concept to calculate the amount of each type of investment.
The total amount invested is $10,000, with some going to bonds and some going to certificates of deposit (CDs). According to the question, the amount invested in bonds is to exceed that in CDs by $3,000. We can write this as an equation:
$10,000 = x + y , where:
x = the amount invested in bonds
y = the amount invested in CDs
We are also told that x = y + $3,000. We can substitute this into the first equation:
$10,000 = x + y
= y + $3,000 + y
= 2y + $3,000
2y = $7,000
y = $3,500
Now we can substitute this back into the equation for x:
x = y + $3,000
= $3,500 + $3,000
= $6,500
So the amount invested in bonds is $6,500 and the amount invested in CDs is $3,500.
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The diameter of a red blood cell is 0.00074 cm. Write the diameter in the expanded form and in the exponential form.
Answer: Your welcome!
Step-by-step explanation:
Expanded form: 7.4 x 10-4 cm
Exponential form: 7.4E-4 cm
Expanded form is when a number is written as the sum of its digits multiplied by their respective powers of 10. In this case, the number is 7.4 x 10-4, which means that 7.4 is multiplied by 10 to the power of -4.
Exponential form is when a number is written as a base number times a power of 10. In this case, the number is 7.4E-4, which means that 7.4 is multiplied by 10 to the power of -4.
Help :'( I really need this done 100 points if u do it pls pls help image below pls help :'(
→ the lenght = 13 square units
→ the width = 2 square units
→ the area of the rectangle = 13×2 = 26 square units
→ the area of the triangle = 26 : 2 = 13 square units
Answer:
Step-by-step explanation:
you would copy and paste another triangle on top to form a rectangle. That would make the rectangle's length 13 units and its width 2 units. the area of a rectangle is found by A=length x width which in this case is 26 units^2. A single triangle's area is 1/2 the area of the rectangle making it 26/2 which is 13.
So the area of the triangle is 13 units^2.
HELP ME YALL THIS FOR A QUIZ:(1) y-6=15 (2) g-4.8=19 write and solve the equation
For the directed line segment whose endpoints are A(-5,-2) and B(5,3), find the coordinates of the point that partitions the segment BA into a ratio of 3 to 2.
The coordinates of the point that partitions the segment BA into a ratio of 3 to 2 is (-1, 0).
What is meant by Directed Line Segment?Directed line segments are line segments which has an initial point and the terminal point along with the direction.
Given a directed line segment BA.
The coordinates of A are (-5, -2) and the coordinates of B are (5, 3).
Let P be the required point which partitions the segment BA in to 3 : 2.
P would be at a 3/5 along the line from B to A.
Write the components of the segment using the end points.
Components = < (x₂ − x₁),(y₂ − y₁) >
= < (-5 - 5) , (-2 - 3) >
= < -10, -5 >
Components of BP = < 3/5 (-10, -5) >
= < -6, -3 >
Coordinates of P = Coordinates of initial point + component of BP.
= (5 + -6, 3 + -3)
= (-1, 0)
Hence the required coordinates is (-1, 0).
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Level 2 Problems
11. Given the similar triangles at right.
Note: Be careful. You do not set up
a. The scale factor from small to big is
b. y=
54
1562-72
C. W=
72
54
162
48
W
The value of the scale factor is 3. And the value of the variables 'v' and 'w' will be 36 and 96, respectively.
What is dilation?Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.
The scale factor is given as,
SF = 162 / 54
SF = 3
Then the equation is given as,
v / (72 + v) = 1/3
Simplify the equation, then we have
3v = 72 + v
2v = 72
v = 36
Then the other equation is given as,
48 / (48 + w) = 1/3
144 = 48 + w
w = 96
The value of the scale factor is 3. And the value of the variables 'v' and 'w' will be 36 and 96, respectively.
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how many pennies would you receive if you cashed in 135 dimes
?
1 dime = 0.1 dollar
You would receive $13.50 if you cashed in 135 dimes. That's the equivalent of 1,350 pennies.
If you cashed in 135 dimes, you would receive 1,350 pennies.
This is because each dime is worth 0.1 dollars, or 10 pennies. So, to find the total number of pennies you would receive, you can simply multiply the number of dimes by the number of pennies in each dime:
135 dimes * 10 pennies/dime = 1,350 pennies
So, you would receive 1,350 pennies if you cashed in 135 dimes.
You can read more about currency at https://brainly.com/question/24373500
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