Paolo was asked to find the original dimension of an enlarged pentagon, His solution is shown next to the pentagons. What error did Paolo make in his solution?
Answers
The error was that; Pablo set up an incorrect proportion
Here, we want to get the error made by Pablo
Mathematically, when two shapes are similar, the ratio of their corresponding sides are equal
Thus, we have it that;
\(\begin{gathered} \frac{x}{3}=\text{ }\frac{8}{12} \\ \\ 12\times\text{ x = 8}\times3 \\ 12x\text{ = 24} \\ x\text{ = }\frac{24}{12} \\ x\text{ =2} \end{gathered}\)So, what we can see here is that he set up the wrong proportion
Related Questions
Pls hurry I need an answer!!!!!!
Answers
Answer:
133°
Step-by-step explanation:
Angles FBE and EBD add up to 180°
Answer:
133
Step-by-step explanation:
let angle EBD be x
X+47=180(being st. line )
X=133
there are 16 students working on a project if each student need 1/4 stick of clay are needed in all?
Answers
Answer:
4 sticks of clay
Step-by-step explanation:
To find the total amount of clay needed, multiply the number of students by the amount need for each one of them.
\(16\) · \(\frac{1}{4}\)
Multiply these by converting 16 into a fraction.
\(\frac{16}{1}\) · \(\frac{1}{4}\)
Multiply the numerators and denominators across.
\(\frac{16}{1}\) · \(\frac{1}{4}=\frac{16}{4}\)
Simplify this.
\(\frac{16}{4} =4\)
The total amount of clay needed is 4 sticks.
I hope this helps :) Good luck ^^
Each of the 25 students in Mr Walker's class sold 16 raffle tickets. If each ticket costs $15 how much money did Mr Walker's students raise?
Answers
Answer: $6000
Hope this helps!-xoxo
what is the solution?
x=3 and y=4
x=5 and y=4
x=4 and y=3
x=3 and y=2
Answers
Answer:
give me more instructions so i can actually help
Step-by-step explanation:
431.67 In a different number, the 4 represents a value which is one-tenth of the value of the 4 in the number above. What value is represented by the 4 in the other number?
Answers
So the different number has a 4 with a value of 40.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To solve this problem, we need to first identify the place value of the digit 4 in the given number.
The digit 4 is in the hundreds place in the number 431.67, so its value is 4 x 100 = 400.
According to the problem statement, the 4 in the different number represents a value which is one-tenth of the value of the 4 in 431.67. Therefore, the value of the 4 in the different number is:
400/10 = 40
To determine the value of the different number, we need to look at the other digits in the number. Since we don't have any information about the other digits, we cannot determine the value of the different number. The answer is that the value of the different number cannot be determined with the information given.
Therefore, So the different number has a 4 with a value of 40.
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PLS HELP ME IM RUNNING OUT OF TIME ILL MARK AS BRAINLIEST AND GIVE 30 BRAINLY POINTS
The soccer net in Peter’s back yard is
5/12
feet high, but only 4 feet wide. Jill’s soccer net is also
5/12
feet high, but is 12 feet wide. How many times larger is the area of Jill’s soccer net? Explain your solution.
Answers
Hope this helps please mark as brainliest
Answer:
Jill’s is only 8 feet wider than Peters as both of them have 5/12 feet high.
Step-by-step explanation:
How many servings can be made from 12 cups
Answers
Answer:
depands
Step-by-step explanation:
on how much ppl and yea
Give the domain and range. On a coordinate plane, points are at (negative 2, negative 1), (0, 1), (2, 3). a. domain: {2, 0, 2}, range: {1, 1, 3} b. domain: {–1, 1, 3}, range: {–2, 0, 2} c. domain: {–2, 0, 2}, range: {–1, 1, 3} d. domain: {1, 1, 3}, range: {2, 0, 2} Please select the best answer from the choices provided A B C D
Answers
Answer:
c. domain: {-2, 0, 2}, range: {-1, 1, 3}
Step-by-step explanation:
From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.
The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.
In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.
Therefore, the correct answer is:
c. domain: {-2, 0, 2}, range: {-1, 1, 3}
Can someone Explain Pythagorean theorem, Exponents, Bedmas, Mean, Median, Mode, Range, Area and Perimeter in simple words
Answers
Answer:
Pythagorean Theorem: C²= a²+b²
a²+b²=c²
C is the longest line of a right angled triangle and a and b are the other two. If you have "a" and "c", but need to find b. You need to sqaure a and then subtract that from c². Then you have b
An Exponent is any example of ². When a small number is above another number. You multiple the "original" number x amount of time. Ex. 3³ 3*3*3
Bedmas is another way of saying "order of operation". Its the order that you calculate functions. It is calculated in this order: Brackets, Exponents, Division/Multiplication, Addition/Subtraction.
I attached an example of Mean, Median, Mode, and Range.
Area: Area is the total space that a 2D object covers. And to calculate it we have to multiply the length of two sides that share a corner. For example, if we have a rectangle that the length of one side is equal to 3cm and the second side is equal to 5cm. Then we multiply them together to get the area. 3*5=15
Perimeter: The perimeter is the "outline" of a 2D shape. To calculate the perimeter we have to add all the sides together.
the sum of two consecutive multiples of 9 is 63. find these multiples
Explain step by step for me please
Answers
Answer:
27
36
Step-by-step explanation:
So if they are consecutive multiples of 9, just make the numbers you multiply by x and x + 1
9x + 9x + 9 = 63
18x = 54
x = 3
3 * 9 = 27
4 * 9 = 36
CHECK:
27 + 36 = 63
Answer:
see below
Step-by-step explanation:
We can write the first number as 9n because it is a multiple of 9, and the second number will be 9(n + 1). We can write:
9n + 9(n + 1) = 63 because they have a sum of 63.
9n + 9n + 9 = 63
18n + 9 = 63
18n = 54
n = 3
This means that the first number is 9 * 3 = 27 and the second is 9 * (3 + 1) = 9 * 4 = 36.
1. Given a right triangle the first angle is ten degrees more than three times the degree measure of the second angle and the third angle is the right angle. What is the angle measurement of the first angle? Doint)
Answers
Answer:
The first angle is \(70^{o}\).
Step-by-step explanation:
Let the measure of the second angle be represented by \(x^{o}\).
Thus, the first angle = \((3x+10)^{o}\)
Third angle = \(90^{o}\)
Sum of angles in a triangle = \(180^{o}\)
So that;
\(x^{o}\) + \((3x+10)^{o}\) + 90 = \(180^{o}\)
\(x^{o}\) + \(3x^{o}\) + \(100^{o}\) = \(180^{o}\)
\(4x^{o}\) = \(180^{o}\) - \(100^{o}\)
\(4x^{o}\) = \(80^{o}\)
divide both sides by 4 to have;
\(x^{o}\) = \(20^{o}\)
The first angle = \((3x+10)^{o}\)
= ( 3 x 20 + 10)
= 60 + 10
= \(70^{o}\)
Therefore, the first angle is \(70^{o}\).
A large insurance company maintains a central computing system that contains a variety of information about customer accounts. Insurance agents in a six-state area use telephone lines to access the customer information database. Currently, the company's central computer system allows three users to access the central computer simultaneously. Agents who attempt to use the system when it is full are denied access; no waiting is allowed. Management realizes that with its expanding business, more requests will be made to the central information system. Being denied access to the system is inefficient as well as annoying for agents. Access requests follow a Poisson probability distribution, with a mean of 40 calls per hour. The service rate per line is 18 calls per hour.
Reqiured:
a. What is the probability that 0, 1, 2, and 3 access lines will be in use?
b. What is the probability that an agent will be denied access to the system?
c. What is the average number of acess lines in use?
Answers
Answer:
Part A:
\(P_0=0.13298\\P_1=0.29547\\P_2=0.328320\\P_3=0.24321\)
Part B:
\(P_3=0.24321\)
Part C:
\(Average\ Number:=1.6817\)
Step-by-step explanation:
Given data:
Mean =μ= 40 calls
Service Rate=λ=18 calls
Solution:
Formula:
\(P_i=\frac{\frac {(\frac{\mu}{\lambda}) ^{i} }{i!} }{\sum \frac {(\frac{\mu}{\lambda}) ^{i} }{i!}}\)
Where i is access lines
Part A:
Probability of 0 access line, i=0:
\(P_0=\frac{\frac {(\frac{40}{18}) ^{0} }{0!} }{\frac {(\frac{40}{18})^{0} }{0!}+\frac {(\frac{40}{18})^{1} }{1!}+\frac {(\frac{40}{18})^{2} }{2!}+\frac {(\frac{40}{18})^{3} }{3!}}\)
\(P_0=\frac{1}{1+2.222+2.4691+1.8290}\)
\(P_0=0.13298\)
Probability of 1 access line, i=1:
\(P_1=\frac{\frac {(\frac{40}{18}) ^{1} }{1!} }{\frac {(\frac{40}{18})^{0} }{0!}+\frac {(\frac{40}{18})^{1} }{1!}+\frac {(\frac{40}{18})^{2} }{2!}+\frac {(\frac{40}{18})^{3} }{3!}}\)
\(P_1=\frac{2.222}{1+2.222+2.4691+1.8290}\\P_1=0.29547\)
Probability of 2 access line, i=2:
\(P_2=\frac{\frac {(\frac{40}{18}) ^{2} }{2!} }{\frac {(\frac{40}{18})^{0} }{0!}+\frac {(\frac{40}{18})^{1} }{1!}+\frac {(\frac{40}{18})^{2} }{2!}+\frac {(\frac{40}{18})^{3} }{3!}}\)
\(P_1=\frac{2.4691}{1+2.222+2.4691+1.8290}\\P_2=0.328320\)
Probability of 3 access line, i=3:
\(P_3=\frac{\frac {(\frac{40}{18}) ^{3} }{3!} }{\frac {(\frac{40}{18})^{0} }{0!}+\frac {(\frac{40}{18})^{1} }{1!}+\frac {(\frac{40}{18})^{2} }{2!}+\frac {(\frac{40}{18})^{3} }{3!}}\\P_3=\frac{1.8290}{1+2.222+2.4691+1.8290}\\P_3=0.24321\)
Part 2:
Only 3 users can access simultaneously, denied Probability is P_3(4th access line)
\(P_3=0.24321\)
Part 3:
Average Number:
\(Average\ Number:\frac{\mu}{\lambda} (1-P_3)\\Average\ Number:\frac{40}{18} (1-0.24321)\\\\Average\ Number:=1.6817\)
The figure shows a plane slicing through a cone. The plane is neither parallel nor perpendicular to the base of the cone, and the plane does not intersect the base of the cone.
Answers
==================================================
Explanation:
Imagine that this plane was a saw blade, or a laser, that cut the cone. We would have two pieces and each piece would have a shape of an ellipse on them. The cutting plane would also have the same ellipse shape.
Or you think of the cutting plane as a flat piece of cloth. If we cut everything around the cone, then we would have an ellipse shaped hole as a result.
The reason why we get an ellipse and not a circle is because the plane is angled like that. It needs to be perfectly parallel to the circular base in order to get a circular cross section.
What is the probability of theft occurring in a room if it is left unlocked if 0.75 of dorm rooms are left unlocked, 3% of dorm rooms are affected by theft, and 84.2% of thefts occur in unlocked rooms
Answers
The probability that a theft can happen in a room that is left unlocked based on the statistics of dorm rooms affected by theft, is 1.89%
How to find the probability?To find the probability that a room will be subjected to theft if it is left unlocked, the formula is:
= Probability that dorm room is left unlocked x Probability of dorm room being affected by theft x Probability that a theft occurs in a unlocked room
The probability of an unlocked room being robbed is therefore:
= 0.75 x 0.03 x 0.842
= 0.0225 x 0.842
= 0.018945
= 1.89%
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Convert from radians to degrees
Answers
Answer:
The answer is
105°Step-by-step explanation:
In order to convert a value from radians to degrees we multiply the value by \( \frac{180}{\pi} \)
So from the question the value is
\( \frac{7\pi}{12} \)Converting it into degrees we have
\( \frac{7\pi}{12} \times \frac{180}{\pi} \)Reduce the fraction with π
That's
\( \frac{7 \times 180}{12} = \frac{1260}{12} \)We have the final answer as
105°Hope this helps you
Find the measure of the complement of a 66° angle.
The measure of the complement of a 66° angle is.
(Simplify your answer. Type an integer or a decimal.)
Please help. Btw it’s only one number
Answers
Complementary angles add up to 90°, write an equation using this knowledge and the information provided in the question:
66°+x° = 90°
Subtract 66° from both sides:
x° = 24°
I need the answer to this problem (picture provided) please help, it's due soon!
Answers
Answer:
x=32° is the correct answer
Step-by-step explanation:
x+75°+73°=180
x+148°=180
x=180°-148°
x=32°
Which of the following is a factor of 24x^6 - 1029y^3?
Answers
The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)
Factors of Polynomials:When a polynomial is factored, its prime factorization is used to break it down into the product of two or more other polynomials. Polynomials may be easily simplified with the use of factoring.
When a polynomial is factored, its factors are expressed as the polynomial's product. Finding the zeros of the polynomial expression or the values of the variables in the supplied expression are both made possible by factoring polynomials.
Here we have
24x⁶ - 1029y³
Take 3 as common
=> 3(8x⁶ - 343y³)
As we know 8 = 2³ and 343 = 7³
=> 3[(2x²)³ - (7y)³]
From the algebraic identities
a³-b³ = (a-b)(a²+ab+b²)Take a = 2x² , b = 7y and apply above formula
=> 3[(2x² - 7x)((2x²)²+(2x²)(7y)+(7y)²)]
=> 3 [ (2x² - 7x) (4x⁴ +14x²y+49y²)]
Therefore,
(24x⁶ - 1029y³) = 3 (2x² - 7x) (4x⁴ +14x²y+49y²)
Therefore,
The factors of (24x⁶ - 1029y³) are 3, (2x² - 7x), (4x⁴ +14x²y+49y²)
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Please help me
10 points
Answers
Answer:
I think that the answer is 56
6i - 5 = 2i +27
distributive property
Answers
6i = 2i + 27 + 5
6i = 2i + 32
6i - 2i = 32
4i = 32
Divide both sides by 4.
i = 8
PLEASE HELP ME
An article claimed the state's typical price of a gallon of gasoline is $2.69. The prices from 5 gas stations surveyed were $2.79, $2.99, $2.69, $2.89, and $2.69.
According to this data, what is wrong with the article's statement?
Answers
This statement in the article is wrong because $2.69 is not the mean price ($2.81)
How to determine what is wrong with the data?The prices from 5 gas stations surveyed are given as:
$2.79, $2.99, $2.69, $2.89, and $2.69.
There are no outliers in the dataset
So, the dataset can be summarized by the mean
The mean is
Mean = Sum/Count
So, we have
Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5
Evaluate
Mean = 2.81
The article quoted $2.69 as the typical price
This statement in the article is wrong because $2.69 is not the mean price ($2.81)
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log 7 (x^2 + 11) = log 7 15
Answers
Answer:
x = ±2
Step-by-step explanation:
log 7 (x^2 + 11) = log 7 15
We know that log a ( b) = log a(c) means b =c
x^2 + 11 = 15
Subtract 11 from each side
x^2 = 15-11
x^2 =4
Take the square root of each side
sqrt(x^2) =±sqrt(4)
x = ±2
Find g(x), where g(x) is the translation 2 units left and 13 units up of f(x)=–7x+7.
Answers
Answer:
\(g(x)=-7x+6\)
Step-by-step explanation:
Translations
For a > 0
\(f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}\)
\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)
\(f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}\)
\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)
Parent function:
\(f(x)=-7x+7\)
Translation of 2 units left:
\(\implies f(x+2)=-7(x+2)+7\)
Translation of 13 units up:
\(\implies f(x+2)+13=-7(x+2)+7+13\)
Simplifying:
\(\implies g(x)=-7(x+2)+7+13\)
\(\implies g(x)=-7x-14+7+13\)
\(\implies g(x)=-7x+6\)
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The number name of 98745632 in indian system
Answers
Answer:
nine crore eighty seven lakh forty five thousand six hundred thirty two is the answer
Simplify: x^9/11 * x^4/11Give your answer in both rational exponent form and nth root notation.
rational exponent form:
nth root notation:
Answers
The value of the index form is x¹³/11
What are index forms?Index forms are simply described as mathematical forms or expressions that are used to represent numbers or variables that are too large or too small to be written conveniently.
Some rules of index forms are;
Add the exponents of the values when multiply forms of the same basesSubtract the exponents of the values when dividing forms of same basesAdd like basesFrom the information given, we have that;
x⁹/11 × x⁴/11
Since they are of the same bases, add the exponent values
x¹³/11
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what is the answer???
Answers
Answer:
The diameter is 22cm
Step-by-step explanation:
I dont know if thats what the question is asking but here
Answer:
Diameter- 22cm, circumference - 69.08cm
Step-by-step explanation:
How we find the diameter is we simply multiply the radius by 2 and get 22.
How we find the circumference is we use the diameter and multiply it by pi (3.14) and get 69.08cm.
I wasn't to sure what you were asking here but I did the circumference and the diameter.
The proportion of the memory space of a flash drive that is unused is 3/8.
There are 40 gigabytes of used memory. What is the total capacity of the drive?
Answers
Total capacity of drive is 64 gigabyte
Ratio and Proportion:
A ratio is a comparison of two amounts that is calculated by dividing the first amount by the second.
Proportion refers to the equality of two ratios.
Let, The total capacity of the drive is = X gigabytes
given,
The proportion of the memory space of a flash drive that is unused is 3/8
The proportion of the memory space of a flash drive that is used is equal to
1 - 3/8 = 5/8
used memory = 40 gigabyte
or X of 5/8 = 40
X = 40 * 8/5
X = 64 gigabyte
so, the total capacity of drive is 64 gigabyte
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A line with a slope of 1 passes through the point (5, 3). What is its equation in slope "-intercept" form?
Answers
Answer: y=x−2 y = x − 2
Step-by-step explanation:
Roxy’s new employer pays employees bimonthly, which is twice a month. She’ll earn $30 per hour with the new company. She plans to continue making extra money by dog sitting on weekends. Roxy works 40 hours per week for 52 weeks during the year. Each time she dog sits on the weekend, she earns $75. Use this information about Roxy to complete the statements. Type the correct answer in each box. Use numerals instead of words. Roxy’s annual income from her new employer before taxes will be $ . Her bimonthly pay before taxes will be $ . To reach Roxy’s yearly pretax income goal of $63,300, she will need to dog sit at least times.
Answers
Answer:
12 times
Step-by-step explanation:
first, find out how much she makes weekly.
40 (hours per week she works * 30 ($ she will earn per hour)
40 * 30 = 1200 per week
for 52 weeks so multiply that by her weekly pay
multiply her weekly pay (1200) by the weeks she works annually (52)
52 * 1200 = 62,400
she makes just $62,400 (annually, before taxes) with her new employer
subtract how much more money she needs
62,400 - 63,300 = -900
she needs 900 dollars
divide by the money she makes on weekends (for dog sitting)
900/75 = 12
she will need to dog sit at least 12 times to make approx. $63,300 annually, before taxes.
hope this helps:)
The graph below shows the solutions to which inequality?
A. x^2-3x+3 ≥0
B. x² + 3x-3 <0
C. x²-3x+3<0
D. x² + 3x-3>0
Answers
The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.
option B.
What is the solution of the inequality?The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;
The solution of the graph,
x > -4 and x < 1
The first equation with "≥" is ruled out because the graph doesn't have a thick dot.
Let's simplify the second expression;
x² + 3x - 3 < 0
solve using quadratic formula;
x > -3.79 or x < 0.79
The third expression is ruled out since its solution will be complex.
For the last expression;
x² + 3x - 3 > 0
x < -3.79 or x > 0.79
Thus, the correct inequality expression is x² + 3x - 3 < 0.
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