Answers
First part;
Following the transformation (x, y) → (3•x, 2•y), the images are;
A'(9, 10), B'(15, 6), C'(6, 4)
Second part;
The distance between points A and B is 2•√2 which is different from the distance between the image A' and B' which indicates that the transformation is a non rigid transformation.
How can the images and the type of transformation be found?First part;
The given points are;
A(3, 5), B(5, 3), C(2, 2)The given transformation is presented as follows;
(x, y) → (3•x, 2•y)
Therefore, the images are;
A(3, 5) → A'(3 × 3, 2 × 5) = A'(9, 10)
B(5, 3) → B'(3 × 5, 2 × 3) = B'(15, 6)
C(2, 2) → C'(3 × 2, 2 × 2) = C'(6, 4)
A(3, 5) → A'(9, 10)B(5, 3) → B'(15, 6)C(2, 2) → C'(6, 4)Second part;
Length of AB = √((5-3)² + (3-5)²) = 2•√2
Length of A'B' = √((15-9)² + (6-10)²) = 2•√13
2•√2 ≠ 2•√13AB ≠ A'B'Given that the length of AB ≠ the length of A'B' then we have;
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The points of the image are (9, 10), (15, 6) and (6, 4) and the resulting image is a nonrigid motion.
How to determine the image of the points?The points are given as:
A = (3, 5)
B = (5, 3)
C = (2, 2)
The transformation is given as:
(x, y) ⇒ (3x, 2y)
So, we have:
A' = (9, 10)
B' = (15, 6)
C' = (6, 4)
Hence, the image of the transformation is (9, 10), (15, 6) and (6, 4)
See attachment for the image
Also, the resulting image is a nonrigid motion.
This is so because the lengths of the image and the preimage are not equal
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Related Questions
PROBLABILITY!!!
(I added the picture needed)
1.Create a sample space and find the product of each combination. What is the probability that a person wins the game? Express your answer as a fraction in lowest terms and as a percent rounded to the nearest tenth.
(answer to this one is 9/28 and 32.1%)
2. You realize a short time into the carnival that you don’t have enough prizes to last the entire event. You call your teacher, and she suggests that you change the winning number so that a participant will win only 25% of the time. What number will that be? Support your answer.
3. Participants achieving a winning score of 36 or higher in four consecutive attempts will receive a large prize! What is the probability of this occurring?
4. After changing the game rules, participants and the crowd are disappointed when the first five games yield scores of 12, 18, 30, 28, and 24. What statement can you recommend the teacher posts to reassure everyone that the game is fair?
Answers
Based on the game rules of randomly picking a card and multiplying it by the roll from a number cube, the following are true:
Probability is 3/8 or 37.5%.To win 25% of the time, player needs to get 32 or higher. Probability of a score of 36 or higher in 4 attempts is 1/1,1296.Teacher should remind everyone that all numbers except only 24 and 30 can appear equally.How can the data be represented?There are 6 sides to dice and 4 cards. The sample space is:
Dice Card Product
1 5 5
1 6 6
1 7 7
1 8 8
2 5 10
2 6 12
2 7 14
2 8 16
3 5 15
3 6 18
3 7 21
3 8 24
4 5 20
4 6 24
4 7 28
4 8 32
5 5 25
5 6 30
5 7 35
5 8 40
6 5 30
6 6 36
6 7 42
6 8 48
Frequency table
Product Frequency
5 1
6 1
7 1
8 1
10 1
12 1
14 1
16 1
15 1
18 1
21 1
24 2
20 1
28 1
30 2
32 1
25 1
35 1
40 1
36 1
42 1
48 1
Total 24
The frequency table shows that to get 28 or more, a person will have a relative frequency of:
= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1
= 9
Probability is:
= 9 / 24
= 3/8
= 37.5%
What product does a player need to win 25% of the time?The number of products required to win 25% of the time is:
= 25% x 24
= 6
To find the winning number, count down from the highest product 6 times to get 32.
How can the larger prize be won?The probability of getting 36 or higher is:
= ∑(Probabability of picking 36 and above numbers)
= 1 / 24 + 1/24 + 1/24 + 1/24
= 1 / 6
The probability of repeating this 4 times is:
= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6
= 1 / 1,296
= 0.0007716
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The vehicle preference of police officers and firefighters is given in the table. Based on the information in the table, which or the following is an example of independent events
Answers
Answer:
Step-by-step explanation:
I had this exact question and I figured it out.
the answer is: P(police officer and chooses car)
In order to get this answer I did the P(police officer) X P(choosing car)
It ended up being 36/45 X 15/45. Which is equal to around .2666667.
Now you take the Intersection of police officer and chooses car and you divide it by 45. That value on the chart is 12.
lucky enough, the product of 36/45 and 15/45 is equal to 12/45.
So 0.8 X 0.33 = .26
.26 = .26
Answer:
answer is P(police officer and chooses car)
Step-by-step explanation:
the probability of P(policer officer) and P(choose a car) are independent probabilities ( they are not overlapping probabilities)
Need help now.
Someone please.
Answers
Answer:
$1,075
Step-by-step explanation:
Simple Intereat Formula:
A = P(1+rt)
where A is the final amount,
P is the principal(original amount invested)
r = annual interest rate
t = time in years
Given P = 1000
r = 2.5/100
t = 3 (Beginning of 4th year means the 4th year is not counted)
A = 1000(1+(0.025)(3))
= 1000(1.075)
=$1,075
What are some of the questions that you should ask when evaluating rankings or other metrics that claim to demonstrate CSR
Answers
Some of the questions that should be asked when evaluating rankings or other metrics that claim to demonstrate CSR are: option A, B, and C.
What is CSR?CSR is acronym for corporate social responsibility and it can be defined as an organization's (company's) obligation to act in a manner that benefits and adds significant value to the society and the people, usually as it conduct its business operations.
Some of the questions that should be asked when evaluating rankings or other metrics that claim to demonstrate CSR include the following:
"What was the methodology used?""Who contributed to the study and how were they qualified to do so?""Do the findings seem to match what your common sense tells you?"Read more on CSR here: https://brainly.com/question/1373962
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Complete Question:
What are some of the questions that you should ask when evaluating rankings or other metrics that claim to demonstrate CSR? (check all that apply)
A. What was the methodology used?
B. Who contributed to the study and how were they qualified to do so?
C. Do the findings seem to match what your common sense tells you?
D. Was the list published in print or online?
Explain how to use equivalent ratios to find
125% of 200.
Answers
Answer:
Step-by-step explanation So if you take that times 21 25 times two gives you X equals 250. So the answer is 2 50. And I use these equivalent fractions and then solve the proportion to come up with 2 50. Instead of doing a little aero trick you could have cross multiplied 200 times 1 25 and 100 times X.ion:
Generate a frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.
Use the ranges listed in the table below
Answers
The value should be placed in the second column for the range 11 - 15 will be 4. Then the correct option is C.
What is a frequency table?The data is given below.
3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.
Arrange the data in ascending order, then we have
2, 3, 3, 6, 12, 12, 13, 15, 17, 17, 18, 19, 20, 21, 25.
Then the frequency table will be
Range Number of values
1 - 5 3
6 - 10 1
11 - 15 4
16 - 20 5
21 - 25 2
The value should be placed in the second column for the range 11 - 15 will be 4.
Then the correct option is C.
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What is the value of x in the figure at the right?
Answers
Answer:
b 12
Step-by-step explanation:
62=5x+2(opposite angle are equal)
5x=60
x=12
(1+sinA+cosA)^2 = 2(1+sinA) (1+cosA)
Answers
Answer:
Step-by-step explanation:
[tex]L.H.S = 1^2+Sin^2A+Cos^2A+2SinA+2CosA+2SinACosA\\ \{(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca\}\\ = 1 + (Sin^2A+Cos^2A) + 2SinA+2CosA+2SinACosA \\ \{Sin^2A+Cos^2A=1\}\\ = 1 + 1 + 2SinA+2CosA+2SinACosA \\ = 2(1 + SinA+CosA+SinACosA)\\ = 2(1^2 + (SinA+CosA).1+ SinACosA )\\ \{x^2+(a+b)x + ab = (x+a)(x+b)\} \quad here \quad x=1\\ = 2(1+SinA)(1+CosA).\\[/tex]
Fawzia took a taxi from her house to the airport. The taxi company charged a pick-up
fee of $2.60 plus $1.50 per mile. The total fare was $17.60, not including the tip. How
many miles was the taxi ride?
Answers
Answer:
9.375 miles
Step-by-step explanation:
1) Let's set up an equation.
2.60 + 1.50x = 17.60
1.50x = 17.60 - 2.60
1.60x = 15
x = 15/1.60
x = 9.375
The graph of a function f(x) passes through the following points:
(0,2), (1, 0), (-1,-4)
Which of the following could be f(x)?
O f(x) = 2x - 2
O f(x) = 2x² - 2
○ f(x) = - 2x - 2
○ f(x) = 2√x-2
Answers
The function is f(x) = -2x² + 2 if the function f(x) passes through the following points:(0,2), (1, 0), (-1,0)
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have:
The graph of a function f(x) passes through the following points: (0,2), (1, 0), (-1,0)
Let
f(x) = ax² + bx + c
Plug x = 0, and y = 2
c = 2 ...(1)
Plug x = 1 and y = 0
a + b + c = 0 ..(2)
Plug x = -1 and y = 0
a - b + c = 0 ...(3)
After solving (1), (2), and (3)
a = -2
b = 0
c = 2
f(x) = -2x² + 2
Thus, the function is f(x) = -2x² + 2 if the function f(x) passes through the following points:(0,2), (1, 0), (-1,0)
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Please help with these 3 questions! Will give brainliest and 25 points.
Answers
a. I and II only true statement.
b . ∠3 = 84°
c . m∠KJM = 138° and m∠KLM = 59°
Properties of an Isosceles trapeziumOnly one pair of sides are parallelThe diagonals are equal in measure.The opposite angles are supplementaryThe base angles are equal in measure.Therefore, i and ii are true for an isosceles trapezium.
∠2 ≅ ∠3
∠1 ≅ 96°
Therefore,
∠3 = 180 - 96
∠3 = 84°
m∠KJM = 180 - x - 14
5x - 2 = 180 - x - 14
5x - 2 = 180 - x - 14
5x + x = 180 - 14 + 2
6x = 168
x = 168 /6
x = 28
m∠KJM = 5(28) - 2 = 138°
m∠KLM = 180 - 10y + 29
3y + 14 = 180 - 10y + 29
3y + 10y = 180 + 29 - 14
13y = 195
y = 195 / 13
y = 15
m∠KLM = 3(15) + 14
m∠KLM = 45 + 14
m∠KLM = 59°
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A sphere and a cylinder have the same radius and height. The volume of the cylinder is 54 meters cubed. Amie found the volume of the sphere.
A sphere with height h and radius r. A cylinder with height h and radius r.
Her work is shown below.
V = two-thirds + 54. V = two-thirds + StartFraction 162 Over 3 EndFraction. V = StartFraction 164 Over 3 EndFraction meter cubed.
What is Amie’s error?
Amie should have multiplied 54 by Two-thirds.
Amie should have multiplied 54 by Four-thirds pi.
Amie should have multiplied 54 by Four-thirds.
Amie should have multiplied 54 by Two-thirds pi.
Answers
The error in Amie's evaluation as described in the task content is; Amie should have multiplied 54 by Two-thirds.
What is Amie's error in the evaluation?Since it follows that the she needs the volume of the sphere in which case the radius of the sphere is half the height.
Hence we have;
V(sphere) = (4/3) πr² × h/2
V = (2/3) × πr²h
Where πr²h = Volume of the cylinder = 54cm
Hence, Amie should have multiplied 54 by Two-thirds.
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If a card is drawn from a deck and a coin is tossed, what is the probability the card will be a heart and the coin will be tails?
Answers
No idea
Sorryyyyy
I dont know
Which phrase best describes the translation from the graph y = (x + 2)2 to the graph of y = x2 + 3?
Answers
The parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3
What is translation?This is a way of changing the position of an object on an xy-plane.
Given the parent function expressed as y = (x + 2^)2
From the resulting image after translation, we can see that the parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3
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Problem 11-3 blair & rosen, inc. (b&r) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. a client who contacted b&r this past week has a maximum of $55,000 to invest. b&r's investment advisor decides to recommend a portfolio consisting of two investment funds: an internet fund and a blue chip fund. the internet fund has a projected annual return of 12%, while the blue chip fund has a projected annual return of 9%. the investment advisor requires that at most $25,000 of the client's funds should be invested in the internet fund. b&r services include a risk rating for each investment alternative. the internet fund, which is the more risky of the two investment alternatives, has a risk rating of 5 per thousand dollars invested. the blue chip fund has a risk rating of 4 per thousand dollars invested. for example, if $10,000 is invested in each of the two investment funds, b&r's risk rating for the portfolio would be 5(10) + 5(10) = 100. finally, b&r developed a questionnaire to measure each client's risk tolerance. based on the responses, each client is classified as a conservative, moderate, or aggressive investor. suppose that the questionnaire results classified the current client as a moderate investor. b&r recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 250.
(a) formulate a linear programming model to find the best investment strategy for this client. let i = internet fund investment in thousands b = blue chip fund investment in thousands if required, round your answers to two decimal places. i + b s.t. i + b available investment funds i + b maximum investment in the internet fund i + b maximum risk for a moderate investor i, b 0
(b) build a spreadsheet model and solve the problem using solver. what is the recommended investment portfolio for this client? internet fund = $ blue chip fund = $ what is the annual return for the portfolio? $
(c) suppose that a second client with $55,000 to invest has been classified as an aggressive investor. b&r recommends that the maximum portfolio risk rating for an aggressive investor is 310. what is the recommended investment portfolio for this aggressive investor? internet fund = $ blue chip fund = $ annual return = $
(d) suppose that a third client with $55,000 to invest has been classified as a conservative investor. b&r recommends that the maximum portfolio risk rating for a conservative investor is 150. develop the recommended investment portfolio for the conservative investor. internet fund = $ blue chip fund = $ annual return = $
Answers
Linear programming which shows the best investment strategy for the client is Max Z=0.12I +0.09B and subject to constraints are :I+ B<=25000,
0.005 I +0.004B<=250.
Given maximum investment client can make is $55000, annual return= 9%, The investment advisor requires that at most $25,000 of the client's funds should be invested in the internet fund. The internet fund, which is the more risky of the two investment alternatives, has a risk rating of 5 per thousand dollars invested. the blue chip fund has a risk rating of 4 per thousand dollars invested.
We have to make a linear programming problem.
Let
I= Internet fund investment in thousands.
B=Blue chip fund investment in thousands.
Objective function:
Max Z=0.12I+0.09B
subject to following constraints:
Investment amount: I+ B<=25000
Risk Rating: 5/100* I+4/100*B<=250 or 0.005 I +0.004B<=250
I,B>=0.
Hence the objective function is Max Z=0.12 I+ 0.09 B.
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Solve the quadratic equation 8x²-5x-4=0
Give your answer to 3 significant figures
Answers
The solution of the quadratic equation 8x² – 5x – 4 = 0 will be 1.085 and negative 0.460.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The quadratic equation is given below.
8x² – 5x – 4 = 0
Then we have
a = 8, b = -5, c = -4
Then the solutions will be
[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}\\\\\\\rm x = \dfrac{-(-5)\pm \sqrt{(-5)^2 - 4 * 8 * (-4)}}{2 * 8 }\\\\\\x = \dfrac{5 \pm 12.37}{16}\\\\\\x = \dfrac{5- 12.37}{16}, \dfrac{5 +12.37}{16}[/tex]
On further solving, we have
x = 1.085, -0.460
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19. Which of the following expressions can be used to calculate the area of a square with side length 5 inches?
O 5.5
05.4
O 5+5
O5+4
Answers
Answer:
5 × 5
Step-by-step explanation:
the area (A) of a square is calculated as
A = s² ( s is the side length ) , then
A = 5² = 5 × 5 = 25 in²
Find the area of the segment (unshaded area) of Circle G with radius 4in. Round to the nearest tenth.
Answers
Angle is 90°
The sector is 1/4 th of circle
Area of sector
πr²/4π(4)²/44πin²Triangle is right angled
Area
1/2(4)²16/28in²Area of unshaded region
4π-84(π-2)4(3.14-2)4(1.14)4.56in²Answer:
4.6 in² (nearest tenth)
Step-by-step explanation:
To find the area of the unshaded region, subtract the area of ΔAGB from the area of sector AGB.
The measure of an arc is equal to its corresponding central angle measure. Therefore, the central angle of sector AGB is 90°.
As the two sides of ΔAGB adjacent the central angle are the radii of the circle they are therefore equal in length ⇒ ∠GAB = ∠GBA.
Therefore, ΔAGB is an isosceles triangle.
Area of triangle (using the Sine Rule):
[tex]\sf A=\dfrac{1}{2}ab \sin C[/tex]
(where a and b are the side lengths and C is the included angle)
Given:
a = b = radius = 4 inC = 90°[tex]\implies \sf Area\:of\:triangle=\dfrac{1}{2}(4)(4)\sin 90^{\circ}=8\:in^2[/tex]
Area of a sector of a circle
[tex]\textsf{A}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]
[tex]\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}[/tex]
Substituting the given angle and radius:
[tex]\implies \textsf{A}=\left(\dfrac{90^{\circ}}{360^{\circ}}\right) \pi (4)^2=4\pi\:\: \sf in^2[/tex]
Area of the unshaded region:
[tex]\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\& = 4 \pi - 8\\& = 4.566370614...\\ & = 4.6\:\sf in^2\:\:(nearest\:tenth)\end{aligned}[/tex]
A carnival tent is set up using a 32-foot pole as the center. The Support wires each have an angle of elevation of 38 degrees from the ground to the top of the pole. Approximately how many feet of wire is needed for one support for the tent?
Answers
the fabric tent is: From the choices: D. 312 feet Let: X
be the length of each wire Using ..
Help me pls it is geomerty traingle proof
and here the question
Given: NQ¯¯¯¯¯¯¯¯ is the bisector of ∠MNP and ∠NMQ≅∠NPQ
Prove: △MNQ≅△PNQ
Answers
△MNQ ≅ △PNQ by SAS congruence theorem.
What is the SAS Congruence Theorem?If two triangles are congruent by the SAS congruence theorem, then they have two pairs of corresponding congruent sides and a pair of corresponding included sides that are congruent.
∠MNQ ≅ ∠PNQ [congruent angles formed by angle bisector]
Therefore, opposite sides to the angles, MQ and PQ would also be congruent.
Thus, MQ ≅ PQ
NQ ≅ NQ [reflexive property]
This means that both triangles have two pairs of corresponding congruent sides and a pair of corresponding included sides that are congruent.
Thus, △MNQ ≅ △PNQ by SAS congruence theorem.
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Find the measure of x.
X
56.76°
56.76
x = [?]
Round to the nearest hundredth.
Answers
Adjacent over hypothesis is cosine. So,
Cos(56.76) = 56.76/x
X = 56.76/cos(56.76)
X = 103.55
Billy thinks of a number that is not zero.
He multiples his number by -3
Is:
The answer is positive
The answer is negative
The answer could be
positive or negative
Answers
Hope this is helpful :)
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Billy thinks of a nonzero number. He multiplies it by 3. He gets...? 3 options given
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
This problem does not give us the information about the starting number (we can't read Billy's mind).
First, I'm going to assume that the number is positive
[tex]\bf{A\;positive\;number\;multiplied\;by\;-3;\;yields\;a\;negative}[/tex]
Next, I'll assume that Billy's number is a negative one.
[tex]\bf{The\;number\;is\;a\;positive\;one}[/tex].
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=The\;answer\;could\;be\;either\;positive\;or\;negative.\;It\;depends\;on\;the\;sign}\\of\:the\:starting\:number.[/tex]
You have to fill a can of gasoline with a capacity of 12 liters.
The gas pump indicates that gasoline is selling for $1.15/litre.
Which equation allows you to calculate the cost of gasoline C according to the quantity of gasoline in liters n ?
Please choose an answer.
C = 1,15n + 12
C= -1,15n + 12
C = 0,12n - 1,15
C = 1,15n
Answers
Answer:
C=0,12N-1,15
Step-by-step explanation:
Which inequality represents Three times a number is greater than 15. a. 3x > 15 b. 3x = 15 c. 3x + 15 d.15 + 3x
Answers
Answer:
a.
Step-by-step explanation:
> is a symbol of inequality representing greater than
The function fis given by this table of values.
-1
96
0
48
X
f(x)
Use this table to complete the statements.
1
24
2
12
3
6
The parent function of the function represented in the table is
If function fis vertically compressed by a factor of 4, the
A point in the table for the transformed function is
-values will be
Answers
Answer:
no man you should reconsider the question again
try typing again i guess its wrong
Answer: exponential, f(x), divided by 4, 1,6
Step-by-step explanation:
a(x + 1) - b(x + 1) - x - 1
Answers
Answer:
Step-by-step explanation:
Solution
I'm assuming you want this simplified. If not leave a note.
a(x + 1) - b(x + 1) - x - 1 remove the brackets
ax + a - bx - b - x - 1 gather like terms
ax - bx - x + a - b - 1
x(a - b - 1) + (a - b - 1) Use the distributive property to simplify
Answer
(x + 1)(a - b - 1)
The common factor is (a - b - 1). That can be pulled out on either side of the isolated + sign
A report of the National Center for Health Statistics says that the heights of 20-year-old men have mean 176.8 centimeters (cm) and standard deviation 7.2 cm. There are 2.54 centimeters in an inch. What are the mean and standard deviation in inches
Answers
The mean and standard deviation in inches are 69.6063 inches and 2.83465 inches respectively. Computed using unit conversions.
Unit conversion is the process of converting a magnitude of the same nature from one unit to another using fixed constants.
The constant between centimeters and inches are as follows:
1 inch = 2.54 cm,
or, 1 cm = 1/2.54 inches = 0.3937 inches.
In the question, we are informed that in a report of the National Center for Health Statistics, the heights of 20-year-old men have a mean of 176.8 (cm) and a standard deviation of 7.2 cm.
We are asked to find the mean and standard deviation in inches.
To calculate the mean in inches:-
We know that 1 cm = 1/2.54 inches.
Therefore, the mean of 176.8 cm = 176.8/2.54 inches = 69.6063 inches.
To calculate the standard deviation in inches:-
We know that 1 cm = 1/2.54 inches.
Therefore, the standard deviation of 7.2 cm = 7.2/2.54 inches = 2.83465 inches.
Thus, the mean and standard deviation in inches are 69.6063 inches and 2.83465 inches respectively. Computed using unit conversions.
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Can someone help me out on matching these angles? ASAP, gotta have answers fast pls
Answers
Answer:
8. a , c
9. b
10. c
M angle IMJ= help me thank u :)
Answers
The value of the angle ∠IMJ using angles of Intersecting Chords Theorem is; 62.5°
How to find the angle of intersecting chords?From the given image, we see that;
mIJ = 40°
mLK = 85°
Now from angles of Intersecting Chords Theorem, we know that If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle. Thus;
∠IMJ = ¹/₂(mIJ + mLK)
∠IMJ = ¹/₂(40+ 85)
∠IMJ = 62.5°
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evaluate x+2x+1/x^2-25
Answers
The evaluation of the algebraic fraction x+2x+1/x^2-25 is[tex]\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}[/tex]
What is the division of algebraic expression?The division of an algebraic expression can be carried out by using the long division method or expansion of the.
Given that:
[tex]\mathbf{\dfrac{x+2x+21}{x^2-25}}[/tex]
where:
x^2 - 25 is the divisor.By expanding the denominator, we have:
[tex]\mathbf{\dfrac{x+2x+21}{(x+5)(x-5)}}[/tex]
[tex]\mathbf{\dfrac{3x+21}{(x+5)(x-5)}}[/tex]
Creating a partial fraction from the denominator, we have:
[tex]\mathbf{\dfrac{3x+21}{(x+5)(x-5)} = \dfrac{a_o}{x+5} +\dfrac{a_1}{x-5}}[/tex]
Multiply the equation by the denominator, and we have:
[tex]\mathbf{\dfrac{(3x+21)(x+5)+(x-5)}{(x+5)(x-5)} = \dfrac{a_o(x+5)(x-5)}{x+5} +\dfrac{a_1(x+5)(x-5)}{x-5}}[/tex]
Simplifying, we have:
3x + 21 = a₀(x-5)+a₁(x+5)
Solve for the unknown parameter by plugging the real roots of the denominator: -5, 5
[tex]\mathbf{a_o =\dfrac{-3}{5}}[/tex]
[tex]\mathbf{a_1 =\dfrac{18}{5}}[/tex]
Replacing the solutions into the partial fractions parameters to obtain the final result, we have:
[tex]\mathbf{\dfrac{-(\dfrac{3}{5})}{x+5} +\dfrac{\dfrac{18}{5}}{x-5}}[/tex]
[tex]\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}[/tex]
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