We can infer that the function y = 3 log2x - 5 has the following end behaviour:
Y gets closer to infinity as x gets closer to positive infinity.Y gets closer to negative infinity as x moves to the right and approaches zero.what is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
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.
from the question:
We may look at what happens to the function as x gets closer to positive and negative infinity to figure out the final behavior of the function y = 3 log2x - 5.
The formula 3 log2x also approaches infinity as x moves closer to positive infinity, and log2x moves closer to infinity as well. As a result, y becomes closer to infinity as x gets closer to positive infinity. The following can be written:
lim x→∞ 3 log2x - 5 = ∞
Similar to how log2x approaches negative infinity, the complete phrase 3 log2x also does as x approaches 0 from the right. Hence, when x moves towards 0 from the right, y moves towards negative infinity. The following can be written:
lim x→0+ 3 log2x - 5 = -∞
We can then infer that the final behavior of the function y = 3 log2x - 5 is as follows:
Y gets closer to infinity as x gets closer to positive infinity.Y gets closer to negative infinity as x moves to the right and approaches zero.to know more about the function visit:
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Sample A has 780 number of successes from a sample size of 820.
Sample B has 795 number of successes from a sample size of 804.
Find the 90% confidence interval for the difference between the two sample proportions.
In response to the supplied query, we may state that there is a proportionality statistically significant difference between the two population proportions because the interval comprises 0.
what is proportionality?Relationships are regarded to as proportional when they continuously have the same ratio. For instance, the number of trees in an orchard and the number of apples in a harvest of apples depend on the average number of apples produced by each tree. A linear relationship between two numbers or variables is referred to as being proportional in mathematics.
The following is the point estimate for the variance between the two sample proportions:
ME is equal to z/2 * [p1(1 - p1) / n1 + p2(1 - p2) / n2]
where:
The z-score that corresponds to the required degree of confidence, in this case 90%, is z/2, or 1.645.
The proportions of the sample are p1 and p2.
These are the sample sizes, n1 and n2.
When we enter the values, we obtain:
ME = 1.645 * √[(0.9512)(1 - 0.9512) / 820 + (0.9891)(1 - 0.9891) / 804]
ME = 0.0528
-0.0379 ± 0.0528
or
-0.0907 to 0.0149
As a result, we have 90% confidence that the actual change in population proportions is between -0.0907 and 0.0149. We cannot infer that there is a statistically significant difference between the two population proportions because the interval comprises 0.
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Can someone please help me with this math problem, ASAP?
The expression for the quadratic function can be written as:
g(x + a) - g(x) = 4ax + 2a² - 4a
How to determine the expression?Here we want to find the expression:
g(x + a) - g(x)
For the quadratic function:
g(x) = 2x² - 4x
So just let's evaluate the function in these values, we will get:
g(x + a) =2*(x + a)² - 4*(x + a)
Expanding that we will get:
= 2(x² + 2ax + a²) - 4x - 4a
= 2x² + 4ax + 2a² - 4x - 4a
Subtracting the original equation we will get:
g(x + a) - g(x) = 2x² + 4ax + 2a² - 4x - 4a - 2x² - 4x
= 4ax + 2a² - 4a
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Q.6.
Carol wants to earn at least $150 for her charity while running a race. She will earn $20 for
participating plus $7 for each mile she runs. If m represents each mile she runs, which
inequality represents the inequality?
7m+20 <150
7m+20>150
20m+7≤ 150
20m +72 >150
Answer:
7m + 20 ≥ 150
Closest option is 7m + 20 > 150 which is the second choice
Step-by-step explanation:
The words "at least" indicate a ≥ inequality.
There is a fixed earning of $20 for entering the race. So this amount will be earned on regardless of how much Carol runs
For each mile she runs she earns $7. For running m miles, she earns 7m dollars
Total amount earned for running m miles = 7m + 20
This must be at least $150
So the correct inequality is
7m + 20 ≥ 150
I don't see this exact inequality in any of the answer choices but that is the correct answer.
HELP I NEED IT VERY BADLY
power fill in the blanks below write this number with powers.
19,306 = 1 x 10 + 9 x 10 + 3 x 10 + 6 x 10
Answer:
19,306 = 10 + 90 + 30 + 60
Step-by-step explanation:
The sequence of the differences, 2, 4, 8, 16, 32, … is a geometric sequence with:
a1=
and r=
Just putting out the answers :)
The formula used to find any term of the geometric sequence is found as: an = 2(2)ⁿ⁻¹.
Explain about the geometric sequence?A series must have a constant ratio between each term and the term before it in order to be considered geometric.If they all have the same characteristics, then the value of r represents the common difference.The geometric sequence equations has the general form an=a1rⁿ⁻¹, where r denotes the common ratio, a1 denotes the first term, and n denotes the term's position in the sequence.
sequence: 2, 4, 8, 16, 32, …
a1 = 2
r = 4/2 = 2
So,
an = 2(2)ⁿ⁻¹
Thus, the formula used to find any term of the geometric sequence is found as: an = 2(2)ⁿ⁻¹.
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12 - ___ =7.32
What is the missing blank
Answer:
Your blank answer is 4.68
Step-by-step explanation:
Well lets make the missing blank into a variable.
12 - x = 7.32
This way we can solve for x. Simplify.
Add x to both side.
12 = 7.32 + x
Subtract 7.32 to both side leaving you x.
12 - 7.32 = x
x = 4.68
Answer:
12 - 4.68 = 7.32
Step-by-step explanation:
Now we have to,
→ Find the missing number in the equation.
Let us assume that,
→ Missing number = m
Forming the equation,
→ 12 - m = 7.32
Then the value of m will be,
→ 12 - m = 7.32
→ -m = 7.32 - 12
→ -m = -4.68
→ [ m = 4.68 ]
Hence, the answer is 4.68.
If a baseball is projected upward from ground level with an initial velocity of 64 feet per second, then its height is a function of time, given by s = - 16? + 64t.
What is the maximum height reached by the ball?
Therefore , the solution of the given problem of function comes out to be height is 64 feet .
What is meant by the word function?
The study of mathematics includes histology, architecture, and both actual and fictitious geographic locations, as well as arithmetic, numerals, and their divisions. A function explains the relationships between different components, each of which has a corresponding result. A function is made up of a variety of components that, when put together, produce specific outputs for each input.
Here,
The highest spot on the ball's trajectory, which is at the vertex of the parabolic path, must be identified in order to calculate the maximum height the ball has ever attained.
The following equation describes the height of the projectile as a function of time:
s = -16t² + 64t
We can apply the following method to determine the parabola's vertex:
t = -b/2a
where b = 64 and a = -16.
By replacing these numbers, we obtain:
t = -64/(2*(-16)) = 2
Thus, after two seconds, the utmost height is reached.
We can enter t = 2 into the calculation to get the height at this point:
s = -16(2)² + 64(2) = 64 feet
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Given that 224 hours of work need to be done to complete a project. (1) How long will it take 4 men, each working an 8-hour day to complete the project? (II) If each of them is paid 57-50 per hour, how much will it cost to employ them altogether? (iii) How many hours of overtime must they put in per day if the project is to be completed in 4 days? (iv) Given that the overtime rate of payment is l times as much as the regular hourly rate, find the cost of the project now.
If 4 men, each working an 8-hour day, have to complete 224 hours of work, then the number of days required to complete the work is:
Total number of hours of work / Number of hours of work done by 4 men in a day
= 224 / (4 x 8)
= 7
So, it will take 4 men, each working an 8-hour day, 7 days to complete the project.
II. Each of the 4 men will work for 7 days, and each man works 8 hours a day. So, the total number of hours worked by all the men is:
Total number of men x Total number of days x Number of hours worked by each man per day
= 4 x 7 x 8
= 224 hours
Therefore, the total cost of employing all 4 men is:
Total number of hours x Rate per hour
= 224 x $57.50
= $12,880
III. If the 4 men have to complete the project in 4 days, then the number of hours of work they have to do each day is:
Total number of hours of work / Total number of days to complete the project
= 224 / 4
= 56 hours
Each man works 8 hours a day, so the total number of hours of overtime they have to put in per day is:
Number of hours of work per day - Number of hours worked by each man per day
= 56 - 8
= 48 hours
Therefore, each man must put in 6 hours of overtime per day to complete the project in 4 days.
IV. If the overtime rate of payment is l times as much as the regular hourly rate, then the overtime rate of payment is:
l x $57.50
= $57.50l
Let the overtime rate of payment be $r per hour. Then:
r = $57.50l
The cost of the project is the sum of the cost of regular hours and the cost of overtime hours. The cost of regular hours is:
Number of regular hours x Regular hourly rate
= 4 x 8 x 7 x $57.50
= $16,240
The cost of overtime hours is:
Number of overtime hours x Overtime hourly rate
= 4 x 6 x 7 x $57.50l
= $12,180l
So, the total cost of the project is:
Total cost = Cost of regular hours + Cost of overtime hours
= $16,240 + $12,180l
Answer:
Step-by-step explanation:
(i) To complete the project, 4 men will need to work a total of 224 hours. Each man works for 8 hours per day. Therefore, the number of days it will take to complete the project is:
Number of days = 224 total hours / (4 men x 8 hours/day) = 7 days
So it will take 4 men, each working 8 hours per day, 7 days to complete the project.
(ii) Each man is paid $57.50 per hour, and they will work for a total of 7 x 8 = 56 hours altogether. Therefore, the total cost of employing them all is:
Total cost = 4 men x $57.50/hour x 56 hours = $12,320
(iii) If the project is to be completed in 4 days, each man will need to work for a total of:
224 total hours / (4 men x 4 days) = 14 hours per day
Since each man already works for 8 hours per day, they will need to put in an additional 6 hours of overtime per day to complete the project in 4 days.
(iv) The regular hourly rate is $57.50 per hour, and the overtime rate is 1.5 times the regular hourly rate (150% of the regular hourly rate). Therefore, the overtime rate is:
Overtime rate = $57.50 x 1.5 = $86.25/hour
To find the total cost of the project, we need to add the cost of the regular hours and the cost of the overtime hours. The cost of the regular hours is:
Regular hours cost = 224 regular hours x $57.50/hour = $12,880
The cost of the overtime hours is:
Overtime cost = (4 men x 6 overtime hours/man/day x 4 days) x $86.25/hour
= 96 x $86.25
Therefore, the total cost of the project is:
Total cost = Regular hours cost + Overtime cost
= $12,880 + $8,280
= $21,160
where the overtime rate is 1.5 times the regular hourly rate.
Need help asap! (For 30 points)
Answer:
11%
Step-by-step explanation:
110 divided by 10 is 11% or 11 times 10 is 110
Answer:
10% of 110 is 11
Step-by-step explanation:
Finding the fraction of a number is the same as multiplying a fraction with the number
10/100 of 110 = 10/100 x 110
so the answer is 11
this is due tomorrow
Answer: C
Step-by-step explanation:
Which expressions are polynomials?
Select each correct answer.
-7x²+ 5/3x
6x² + 5x
x^2+ 5x1/5
-x^2+5x
Answer:
The polynomials are:
-7x²+ 5/3x
6x² + 5x
-x^2+5x
The expression x^2+ 5x1/5 is not a polynomial because it contains a fraction with x in the denominator.
A salesperson receives 3% commission in sales what commission does the salesperson receive for $9500
As a result, for purchases of $9500, the salesperson gets a royalty of $285.
What does "commission" imply in business?Commission, also known as a sales bonus, is paid to employees in accordance with the amount of sales they make. Statement generation is offered without charge by SumUp Bills. Frequently, a fee is calculated as a percentage of the sale's value.
To find the commission that the salesperson receives for $9500 in sales, we can use the formula:
commission = rate x sales
where rate is the commission rate as a decimal, and sales is the amount of sales.
In this case, the rate is 3% or 0.03, and the sales is $9500.When these numbers are added to the algorithm, we obtain:
commission = 0.03 x $9500
Simplifying this expression, we get:
commission = $285
Therefore, the salesperson receives a commission of $285 for $9500 in sales.
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12 points Please help!
all of them are equivalent
question in the picture below
The two fractions' sum is therefore (a + b) / (a² × b²).
What in math is a sum?A sum, usually referred to as a summation, is the product of combining two or more quantities or numbers. A summation always has an even term count. It could be two terms simply, or it might total 100,000 or a million. Many terms can be included in some summations.
We require a common denominator in order to add these two fractions.
The first fraction's denominator is a² × b, and the second fraction's denominator is a × b².
Get the supreme strength of each component that exists in either denominator, then utilize the result of these factors to determine the least frequent multi of these two denominators:
LCM (a² × b, a × b²) = a² × b²
The two fractions can now be rewritten using the following common denominator:
1/(a² × b) + 1/(a × b²) = (1 × b + 1 × a) / (a² × b²)
If we condense this phrase, we get:
1/(a² × b) + 1/(a × b²) = (a + b) / (a² × b²)
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What is the area of this polygon?
16 cm2
24 cm2
40 cm2
18 cm2
Answer:
Where's the question...
(d.) (I + 2A)
−1 =
−1 2
4 5 !
where I is the identity matrix
We can write the addition matrix as -
(I + 2A) →
[- 1 4]
[8 11]
What is identity matrix?The identity matrix is the only idempotent matrix with non-zero determinant.
Given is the matrix relation as -
(I + 2A)
We can write the addition of matrix as -
(I + 2A) →
[1 0]
[0 1]
+
2[-1 2]
2[4 5]
(I + 2A) →
[1 0]
[0 1]
+
[-2 4]
[8 10]
(I + 2A) →
[- 1 4]
[8 11]
Therefore, we can write the addition matrix as -
(I + 2A) →
[- 1 4]
[8 11]
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If they were originally 12 apples at home, the number of apples after a 50% increase would be:
The number of apples after the increase will be 18.
How many apples would there be?Percentage is the fraction of an amount that is usually expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to change a number to a percentage, multiply by 100.
After the apples are increased, the new number of apples would be half more than the initial number of apples.
The formula that can be used to determine the new number of apples is: New number of apples = original number of apples x (1 + increase/100)
= 12 x (1 + 50/100)
= 12 x (1 + 0.5)
= 12 x 1.5 = 18
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LOOK AT THE IMAGE BLEOW TO SEE THE PROBLE:
π - This is an irrational number. 22/7 - The number is rational but not an integer. 3.3 - The number is an integer but not a whole number.
What is rational and irrational numbers?The term "rational number" refers to any number that can be stated as a fraction, as well as a positive, negative, or zero. If q is not equal to zero, it may be expressed as p/q.
Irrational numbers are those that are not logical in nature. Let's explain; irrational numbers may be expressed as decimals but not as fractions, hence they cannot be expressed as the ratio of two integers.
π - This is an irrational number.
22/7 - The number is rational but not an integer.
3.3 - The number is an integer but not a whole number.
The number is a whole number but not a natural number.
9 -This number can be written as a natural number.
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How is the total price including sales tax calculated? a. (purchase price) times (percent sales tax); then added to original amount c. (purchase price) times (percent sales tax); then divided by the original amount b. (purchase price) times (percent sales tax); then subtracted from original amount d. (purchase price) times (percent sales tax); then multiplied by the original amount
Answer: PP(Percentage) + PP or PP(1.%)
Step-by-step explanation:
Your car cost $42,000 when you purchased it in 2015. The value of the car decreases by 15% once a year.
How much will your car be worth in 7 years? Round your answer to th nearest dollar.
Step-by-step explanation:
V = P(1 - r)^t
where V is the value of the car after t years, P is the initial value of the car, r is the annual depreciation rate as a decimal, and t is the number of years.
Plugging in the values given in the problem, we get:
V = 42000(1 - 0.15)^7
V = 42000(0.85)^7
V = 42000(0.327)
V = $13734.00
Therefore, the car will be worth $13,734.00 after 7 years. Rounded to the nearest dollar, the value is $13,734.
Answer:
A) $12,800.00. B) $13,629.44. The value of a car purchased for $20,000 decreases at a rate of 12% per year. What will be the value of the car after 3 years? C) ...
Solve the system of inequalities by graphing.
y < 6
y > x + 3
The solution to the inequalities, y < 6 and y > x + 3 is the common intersecting region.
What are inequalities and it's types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, y < 6.
Now, To determine wether it inclues the origin or not we'll set, y = 0.
So, 0 < 6 is true so y < 6 includes the origin.
Now, y > x + 3.
0 > 0 + 4 is not true therefore, y > x + 3 doest not inclue the origin.
The solution to these now can be determine by the common intersecting region.
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Based on the 2009 season, the Texas Rangers have a winning percentage of .533. Use the binomial model to find the probability that the Rangers win 4 of their next 5 games.
P(x)=[n!x!(n−x)!]pxqn−x
A. 12.4%
B.18.8%
C. 23.7%
D.50%
Based on the 2009 season, the Texas Rangers have a winning percentage of .533. The probability that the Rangers win 4 of their next 5 games is 18.8%.
How to find the probability?We can use the binomial distribution formula to find the probability that the Texas Rangers win exactly 4 of their next 5 games:
P(4 wins) = (5 choose 4) * (.533)^4 * (1-.533)^1
= (5! / (4! * 1!)) * (.533)^4 * (.467)^1
= 5 * 0.533^4 * 0.467^1
= 18.8%
where "choose" is the binomial coefficient, which represents the number of ways to choose a subset of size k from a set of size n, and is given by:
(n choose k) = n! / (k! * (n-k)!)
So the probability that the Rangers win 4 of their next 5 games is 18.8%,.
Therefore, the answer is B.
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9. Define malleability and ductility
Answer:
Malleability and ductility refer to a material's ability to be shaped, bent, or stretched without breaking. Malleability is a measure of how easily a material can be hammered, pressed, or rolled into different shapes, while ductility is a measure of how much a material can be stretched before it breaks. Metals and alloys are generally highly malleable and ductile, while concrete and glass are less so
Step-by-step explanation:
Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer Methods. Each
section of Finite Math has 40 students and earns the college $40,000 in revenue. Each section of Applied Calculus has 40
students and earns the college $60,000, while each section of Computer Methods has 10 students and earns the college
$29,000. Assuming the college wishes to offer a total of seven sections, accommodate 220 students, and bring in $298,000
in revenues, how many sections of each course should it offer?
Finite Math
Applied Calculus
Computer Methods
Need Help?
Read It
section(s)
section(s)
section(s)
Watch It
The sections of each course it should offer are 3 finite maths, 2 applied calculus and 2 computer methods
How many sections of each course should it offer?Let's use the following variables to represent the unknowns:
x: number of sections of Finite Mathy: number of sections of Applied Calculusz: number of sections of Computer MethodsFrom the problem, we can write the following system of equations:
x + y + z = 7 (total number of sections)
40x + 40y + 10z = 220 (total number of students)
40000x + 60000y + 29000z = 298000 (total revenue)
Simplify
x + y + z = 7
4x + 4y + z = 220
40x + 60y + 29z = 298
We can solve this system of equations using substitution
So, we have
x = 7 - y - z
By substitution, we have
4(7 - y - z) + 4y + z = 22
This gives
28 - 4y - 4z + 4y + z = 22
So, we have
28 - 3z = 22
This gives
3z = 6
Divide
z = 2
Recall that
40x + 60y + 29z = 298
So, we have
40x + 60y + 29*2 = 298
40x + 60y + 58 = 298
This gives
40x + 60y = 240
Divide by 20
2x + 3y = 12
Also, recall that x = 7 - y - z
So, we have
2(7 - y - z) + 3y = 12
This gives
2(7 - y - 2) + 3y = 12
2(5 - y) + 3y = 12
Open brackets
10 - 2y + 3y = 12
Evaluating the like terms, we have
y = 2
Lastly. we have
x = 7 - y - z
x = 7 - 2 - 2
x = 3
Hence, the number of sections of Finite Math is 3
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how many feel long is the remaining piece ?
The remaining feet long is A. 3 7/12 feet long
How to determine this
Kelsey has a board of 6 1/3 feet long
When he uses 2.75 feet
To calculate the remaining feet
= 6 1/3 - 2.75 feet long
By converting 2.75 to fraction
2.75 = 2 3/4
= 11/4
6 1/3 = 19/3
So, 19/3 - 11/4
= 43/12
= 3 7/12
Therefore, the remaining piece is 3 7/12 feet long
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8. DEF is an equilateral triangle.
The midsegments of ADEF form AAB.
What type of triangle is AABC? Explain your reasoning.
The type of triangle AABC is an equilateral triangle, as it is formed by the midsegments of the equilateral triangle ADEF.
What are the coordinates of midpoint of the line segment AB?Since the midsegments of a triangle are parallel to its opposite sides and half the length of the opposite sides, the midsegments of an equilateral triangle are congruent to each other, and their length is half the length of the sides of the equilateral triangle.
Suppose we've two endpoints of a line segment as:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
[tex]x = \dfrac{p+m}{2} and y = \dfrac{q+n}{2}[/tex]
We are given that;
An equilateral triangle DEF
AAB is formed by the midsegments of triangle ADEF, which means that AAB is also an equilateral triangle. To see why this is true, we can use the following argument:
The midsegment of DE is parallel to AB and has half the length of AB.
The midsegment of EF is parallel to AA' and has half the length of AA'.
The midsegment of FD is parallel to BB' and has half the length of BB'.
Therefore, AB = AA' = BB', and the angles at A and B are both 60 degrees (since DEF is equilateral).
Thus, AAB is an equilateral triangle, because all its sides are equal in length and all its angles are equal to 60 degrees.
Therefore, by midpoint the answer will be equilateral triangle.
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There is a pair of parallel sides 4,9,10 in the following shape, What is the area of the shape? u
The surface area of the shape is 110 square units.
What exactly is a math area?The area of a two-dimensional figure is the area enclosed by its perimeter. The area of a closed figure is the number of unit squares that cover its surface. Area is measured in square units such as cm2 and m2. The area of a shape is measured in two dimensions.
The rectangle's surface area is:
Area = 10 × 9 = 90 unit square
The area of the triangle is:
Area = 0.5 × 10 × 4 = 20 unit square
The figure's area is as follows:
Total = 90 + 20
Total = 110 unit square
Hence, the shape's area is 110 unit square.
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b) Work out the size of angle x. Give your
answer in degrees (º).
56°
X
59°
77°
Answer:
Step-by-step explanation how do I use this appp :
Allison needs 13 inches of cloth for a sewing project, but the fabric store only sells the cloth by the centimeter. Since 1 inch is the same as 2.54 centimeters, how much cloth will Allison buy in centimeters?
Answer:
33.02 centimeters of cloth
Step-by-step explanation:
Since 1 inch is equal to 2.54 cemtimeters then all you need to do is multiply 13x2.54 and you have your answer of 33.02
Necesito estas respuestas
The scale factor for the given transformation is -
{k} = 2/3.
What is scale factor in mathematics?A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.
Given is a figure {Q} that is a transformation of figure {P}.
The base length of the figure {P} is 15 cm. The base length for figure {Q} is 10 cm. So, we can write the scale factor as -
{K} = 10/15
{K} = 2/3
Therefore, the scale factor for the given transformation is -
{k} = 2/3.
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