Answers
Answer:
The answer is 56.33 in decimal form but in fraction form the answer is 5633/
100
Step-by-step explanation:
6.55 x 8.6
Related Questions
three line segments have measures of 4 units, 6 units, and 8 units. Will the segments form a triangle?
Answers
Given:
Three line segments have measures of 4 units, 6 units, and 8 units.
To find:
Will the segments form a triangle?
Solution:
We know that three line segments can form a triangle if the sum of two smaller sides is greater than the largest side.
Three line segments have measures of 4 units, 6 units, and 8 units. Here, the measure of the largest sides is 8 units.
The sum of two smaller sides is
[tex]4+6=10[/tex]
[tex]4+6>8[/tex]
Since the sum of two smaller sides is greater than the largest side, therefore the segments will form a triangle.
picture is shown !
Complete the remainder of the
table for the given function rule:
y = -2x + 9
please help
Answers
Answer: 17; 13; 9; 5; 1
Step-by-step explanation:
y = -2x + 9
When x = -4, y = 17
When x = -2 , y = -2x + 9 = -2(-2) + 9 = 13
When x = 0 , y = -2x + 9 = -2(0) + 9 = 9
When x = 2 , y = -2x + 9 = -2(2) + 9 = 5
When x = 4 , y = -2x + 9 = -2(4) + 9 = 1
Which 3-dimensional figure is associated with the volume formula V = 1/3 π r 2 h?
A. pyramid
B. cylinder
C. sphere
D. cone
Help ASAP!
Answers
Answer
c
Step-by-step explanation:
It is not d because of the way that it is formed
Given the points a(0, 0), B(e, f), c(0, e) and D(f, o), determine if line segments AB and CD are parallel, perpendicular or
neither
Answers
Bit confusing but that should be right
Three companies, A, B and C, make computer hard drives. The proportion of hard drives that fail within one year is 0.001 for company 0.002 for company B and 0.005 for company C. A computer manufacturer gets 50% of their hard drives from company A, 30% from company B and 20% from company C. The computer manufacturer installs one hard drive into each computer.
(a) What is the probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year? [4 marks]
(b) I buy a computer that does experience a hard drive failure within one year. What is the probability that the hard drive was manufactured by company C? [4 marks]
(c) The computer manufacturer sends me a replacement computer, whose hard drive also fails within one year. What is the probability that the hard drives in the original and replacement computers were manufactured by the same company? [You may assume that the computers are produced independently.] [6 marks]
(d) A colleague of mine buys a computer that does not experience a hard drive failure within one year. Calculate the probability that this hard drive was manufactured by company C. [6 marks]
Answers
(a) The probability of a computer failure from Company A is 0.001; from Company B is 0.002; and from Company C is 0.005.
Therefore, the probability that a computer will experience a hard drive failure within one year is:(0.50 x 0.001) + (0.30 x 0.002) + (0.20 x 0.005)= 0.0012. The probability of a randomly selected computer experiencing a hard drive failure within one year is 0.0012 or 0.12%.
(b) Bayes' theorem will be used to calculate this probability:Let A be the event that the computer's hard drive was manufactured by Company C. Let B be the event that the computer experienced a hard drive failure. P(A|B) is the probability that the hard drive was manufactured by Company C given that a hard drive failure was experienced.
P(A|B) = P(B|A) P(A) / P(B) Where: P(B|A) = 0.005 (the probability of failure if the hard drive was manufactured by Company C)P(A) = 0.20 (the proportion of hard drives that the computer manufacturer gets from Company C)P(B) = (0.50 x 0.001) + (0.30 x 0.002) + (0.20 x 0.005) = 0.0012 (as in part a)
Therefore: P(A|B) = (0.005 x 0.20) / 0.0012 = 0.0833 or 8.33%.
(c)Let A be the event that both hard drives were manufactured by Company A; B be the event that both hard drives were manufactured by Company B; and C be the event that both hard drives were manufactured by Company C. Then we need to find the probability of event A or B or C, given that a hard drive failure was experienced:P(A U B U C|F) = P(F|A U B U C) P(A U B U C) / P(F)where F is the event that the hard drive in the replacement computer fails.P(F|A U B U C) = P(F) = (0.50 x 0.001) + (0.30 x 0.002) + (0.20 x 0.005) = 0.0012P(A U B U C) = (0.50)^2 + (0.30)^2 + (0.20)^2 = 0.46P(F) = P(A U B U C) P(F|A U B U C) + P(A' n B n C) P(F|A' n B n C)= 0.46 x 0.0012 + 0.04 x 0.3 = 0.000552P(A U B U C|F) = P(F|A U B U C) P(A U B U C) / P(F)= (0.0012 x 0.46) / 0.000552 = 1.00or 100%. Therefore, the probability that the original and replacement computers were produced by the same company is 100%.
(d) Bayes' theorem will be used to calculate this probability:Let A be the event that the hard drive was manufactured by Company C. Let B be the event that the computer did not experience a hard drive failure. P(A|B) is the probability that the hard drive was manufactured by Company C given that no hard drive failure was experienced.P(A|B) = P(B|A) P(A) / P(B)Where:P(B|A) = 1 - 0.005 = 0.995 (the probability that the hard drive did not fail if it was manufactured by Company C)P(A) = 0.20 (as in part b)P(B) = 1 - (0.50 x 0.001) - (0.30 x 0.002) - (0.20 x 0.005) = 0.9988
Therefore:P(A|B) = (0.995 x 0.20) / 0.9988 = 0.1989 or 19.89%. Therefore, the probability that the hard drive was manufactured by Company C given that it did not fail is 19.89%.
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The probability that the hard drive was manufactured by company C given that a failure was not experienced by the computer within one year is approximately 0.256.
(a)Probability that a randomly chosen computer purchased from this manufacturer will experience a hard drive failure within one year = 0.5 x 0.001 + 0.3 x 0.002 + 0.2 x 0.005 = 0.0016
(b)Let's denote the event that a computer failure is experienced within one year by F and the event that the hard drive is made by company C by C.
Then we are required to calculate P(C | F), which is the probability that the hard drive was manufactured by company C given that a failure was experienced by the computer within one year. This can be found by using the Bayes' rule as follows:
[tex]$$P(C|F) = \frac{P(F|C)P(C)}{P(F|A)P(A) + P(F|B)P(B) + P(F|C)P(C)}$$[/tex]
where P(C) = 0.2, P(A) = 0.5 and P(B) = 0.3.$$P(F|A) = 0.001, P(F|B) = 0.002, P(F|C) = 0.005$$
Thus, we have:[tex]$$P(C|F) = \frac{0.005 \times 0.2}{0.001 \times 0.5 + 0.002 \times 0.3 + 0.005 \times 0.2} \approx 0.476$$[/tex]
Therefore, the probability that the hard drive was manufactured by company C given that a failure was experienced by the computer within one year is approximately 0.476.
(c)Let's denote the event that the original hard drive is manufactured by company A, B and C by A, B, and C respectively.
Similarly, let's denote the event that the replacement hard drive is manufactured by company A, B, and C by A', B', and C' respectively.
We are required to calculate P(A = A', B = B', C = C' | F), which is the probability that the hard drives in the original and replacement computers were manufactured by the same company given that a failure was experienced by both computers within one year.
This can be found by using the Bayes' rule as follows:
[tex]$$P(A = A', B = B', C = C'|F) = \frac{P(F|A = A', B = B', C = C')P(A = A')P(B = B')P(C = C')}{P(F)}$$[/tex]
where: [tex]$$P(F) = P(F|A = A', B = B', C = C')P(A = A')P(B = B')P(C = C') + P(F|A \ne A', B \ne B', C \ne C')P(A \ne A')P(B \ne B')P(C \ne C')$$[/tex]
Here, we are assuming that the probabilities of computer failure are independent of each other and the company that manufactured the hard drives of the two computers are independent of each other. Therefore, we have:
[tex]$$P(F|A = A', B = B', C = C') = P(F|A)P(F|B)P(F|C) = 0.001 \times 0.002 \times 0.005$$[/tex]
[tex]$$P(F|A \ne A', B \ne B', C \ne C') = 0$$[/tex]
Also, we have:$$P(A = A') = P(B = B') = P(C = C') = \frac{1}{3}$$
[tex]$$P(A \ne A', B \ne B', C \ne C') = \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = \frac{8}{27}$$[/tex]
Thus, we have:$$P(A = A', B = B', C = C'|F) = \frac{0.001 \times 0.002 \times 0.005 \times (\frac{1}{3})^3}{P(F)}$$
[tex]$$P(A \ne A', B \ne B', C \ne C'|F) = \frac{P(F) - 0.001 \times 0.002 \times 0.005 \times (\frac{1}{3})^3}{\frac{8}{27}}$$[/tex]
Now, we need to find P(F). This can be done as follows:
[tex]$$P(F) = P(F|A = A', B = B', C = C')P(A = A')P(B = B')P(C = C') + P(F|A \ne A', B \ne B', C \ne C')P(A \ne A')P(B \ne B')P(C \ne C')$$$$= 0.001 \times 0.002 \times 0.005 \times (\frac{1}{3})^3 + 0 = 4.6296 \times 10^{-8}$$Thus, we have:$$P(A = A', B = B', C = C'|F) = 0.0296$$[/tex]
[tex]$$P(A \ne A', B \ne B', C \ne C'|F) = 0.9704$$[/tex]
Therefore, the probability that the hard drives in the original and replacement computers were manufactured by the same company given that a failure was experienced by both computers within one year is 0.0296.(d)Let's denote the event that the hard drive is made by company C by C and the event that a computer failure is not experienced within one year by F'. We are required to calculate P(C | F'), which is the probability that the hard drive was manufactured by company C given that a failure was not experienced by the computer within one year. This can be found by using the Bayes' rule as follows:
[tex]$$P(C|F') = \frac{P(F'|C)P(C)}{P(F'|A)P(A) + P(F'|B)P(B) + P(F'|C)P(C)}$$[/tex]
where P(C) = 0.2, P(A) = 0.5 and P(B) = 0.3.$$P(F'|A) = 0.999, P(F'|B) = 0.998, P(F'|C) = 0.995$$
Thus, we have: [tex]$$P(C|F') = \frac{0.995 \times 0.2}{0.999 \times 0.5 + 0.998 \times 0.3 + 0.995 \times 0.2} \approx 0.256$$[/tex]
Therefore, the probability that the hard drive was manufactured by company C given that a failure was not experienced by the computer within one year is approximately 0.256.
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Plz help me, correct answers will get brainliest <3
Answers
Answer:
∠ B = 48°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180° for ∠ B
∠ B = 180° - (90 + 42)° = 180° - 132° = 48°
Damien receives an annual salary of $55,300; he is paid weekly, and his regular workweek is 39.5 hours. a) Calculate his regular pay per payment period. b) Calculate his hourly rate of pay. $ c) If his overtime rate is double the regular pay, calculate the overtime rate of pay. d) What is Damien's gross pay for a pay period in which he worked 8 hours overtime at double regular pay?
Answers
Damien's regular pay per payment period is $1,062.50, his hourly rate of pay is $26.87, his overtime rate of pay is $53.74, and his gross pay for a pay period in which he worked 8 hours overtime is $1,492.42.
a) Calculation of Damien's regular pay per payment period: Given, Damien receives an annual salary of $55,300.Damien is paid weekly and his regular workweek is 39.5 hours. Therefore, the regular pay per payment period = 55,300/52 = $1,062.50So, Damien's regular pay per payment period is $1,062.50.
b) Calculation of Damien's hourly rate of pay: Let's calculate the hourly rate of pay for Damien, we will divide the regular pay per payment period by the regular workweek hours. Hourly rate of pay = 1,062.50/39.5 = $26.87Thus, Damien's hourly rate of pay is $26.87.
c) Calculation of Damien's overtime rate of pay: The overtime rate of pay will be double the hourly rate of pay. Hence, Damien's overtime rate of pay will be: Double the hourly rate of pay = 2 × 26.87 = $53.74. Therefore, Damien's overtime rate of pay is $53.74.
d) Calculation of Damien's gross pay for a pay period in which he worked 8 hours overtime at double regular pay: Damien worked 8 hours overtime, so his gross pay for the pay period will be: Regular pay = 39.5 hours × $26.87 per hour = $1,062.50. Overtime pay = 8 hours × $53.74 per hour = $429.92Gross pay = Regular pay + Overtime pay= 1,062.50 + 429.92= $1,492.42Therefore, Damien's gross pay for a pay period in which he worked 8 hours overtime at double the regular pay is $1,492.42.
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utilizando as propriedades dos radicais calcule ⁵√32⁵
Answers
[tex] \purple{ \tt{ \huge{ \: ✨Answer ✨ \: }}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \red{ \boxed{ \boxed{ \tt{ \huge{{ \: 32 \: }}}}}}[/tex]
please help i don't understand.
Answers
Answer:
75.4
Step-by-step explanation:
Hello There!
We can easily solve for the volume of the cone using this formula
[tex]V=\pi r^2\frac{h}{3}[/tex]
where r = radius and h = height
we are given that the radius had a length of 3 ft and the height has a length of 8 ft
Because we know the values all we have to do is plug them into the formula
so
[tex]V=\pi 3^2\frac{8}{3}\\3^2=9\\9\pi =28.27433388\\28.27433388*\frac{8}{3} =75.39822369[/tex]
so we can conclude that the volume of the cone is 75.39822369 ft³
Finally we round to the nearest hundredth and get that the answer is 75.4
eight more than the quotient of a number and four
Answers
Answer:
hi
Step-by-step explanation:
A video game regularly costs $29.95 is on sale for 15% off. About how much is the sale price of the game is you include 8% sales tax?
Answers
Answer:
$27.50
Step-by-step explanation:
First, find the cost with the 15% off sale
29.95(0.85)
= 25.46
Find the price with the sales tax:
25.46(1.08)
= 27.5
So, the sale price of the game with tax is approximately $27.50
Evaluate each expression using the values m = 7, r = 8, and t = 2.
1. 5m – 6
2. 4m + t
3. r/t
4. mt
5. 5t + 2m
6. rm
7. 3m – 5t
8. mr/t
PEEEEASSSSEEEE HELP!!!! :(
Answers
So I'll walk through the first 2. Then please try the other ones and let me know if you run into more problems.
5m-6
If m is equal to 7, then replace m with 7.
5(7)-6
5x7=35 so the expression is now 35-6. Solve.
35-6=29
So that was the first one.
4m+t
We just do what we do with the first problem.
4(7)+(2)
4x7=28 so the expression is 28+2.
28+2=28
---
hope it helps
p.s. When there is subtraction, add. When there is division, multiply to cancel that out. When there is multiplication, divide to cancel. etc.
Answer:
1,5(7)-6=29
2,4(7)+2=30
3,8/2=4
4,7*2=14
5,5(2)+2(7)=24
6,8*7=56
7,3(7)-5(2)=11
8,7*8/2=28
just #16 and please show your work!! i will give brainliest!!
Answers
Answer:
the bottom triangle is scaled down version of above one
then
[tex] \frac{18}{6} = \frac{x}{2} [/tex]
[tex]x = 6[/tex]
and
[tex] \frac{18}{6} = \frac{y}{5} [/tex]
[tex]y = 15[/tex]
Find the coordinates of the endpoint of the image?
Answers
Given:
The end points of the line segment AB are A(-2,-3) and B(4,-1).
The rule of translation is:
[tex](x,y)\to (x+4,y-3)[/tex]
To find:
The coordinates of the end points of the line segment A'B'.
Solution:
It is given that the end points of the line segment AB are A(-2,-3) and B(4,-1).
We have,
[tex](x,y)\to (x+4,y-3)[/tex]
By using the above translation rule, we get
[tex]A(-2,-3)\to A'(-2+4,-3-3)[/tex]
[tex]A(-2,-3)\to A'(2,-6)[/tex]
And
[tex]B(4,-1)\to B'(4+4,-1-3)[/tex]
[tex]B(4,-1)\to B'(8,-4)[/tex]
Hence, the endpoint of the line segment A'B' are A'(2,-6) and B'(8,-4).
instantaneous rate of change for the function:
f(x)= 5x^lnx ; x=3
Use the formula for instantaneous rate of change, approximating the limit by using smaller and smaller values of h, to find the instantaneous rate of change for the given function at the given value. f(x) = 5x x=3 The instantaneous rate of change for the function at x=3 is (Do not round until the final answer. Then round to four decimal places as needed)
Answers
The instantaneous rate of change for the function f(x) at x = 3 is 16.9068.
To determine the instantaneous rate of change for the function; f(x) = 5x^ln(x), where x = 3, we can use the formula for the instantaneous rate of change, approximating the limit by using smaller and smaller values of h.
The instantaneous rate of change of the function f(x) at x = 3 can be found as follows:
Let h be a small increment of x that approaches zero. Then the formula for the instantaneous rate of change is given by:
f'(3) = lim[h→0] {(5(3+h)^(ln(3+h))-5(3^(ln3)))/h}
For the above formula, we have: Let f(x) = 5x^ln(x)
Then, f'(x) = 5x^ln(x) * [(d/dx) ln(x)] + 5*ln(x)*x^(ln(x) - 1)
Now, for the given problem, we can substitute 3 for x, and solve as follows: f'(3) = 5(3^ln(3)) * [(d/dx) ln(x)] + 5*ln(3)*3^(ln(3) - 1)
f'(3) = 5(3^ln(3)) * [(1/x)] + 5*ln(3)*3^(ln(3) - 1)
f'(3) = 5(3^ln(3)) * [(1/3)] + 5*ln(3)*3^(ln(3) - 1)
f'(3) = 5(3^ln(3) / 3) + 5*ln(3)*3^(ln(3) - 1)
Then, f'(3) = 5e ln(3) + 5 ln(3) / 3= (5e ln(3) + 5 ln(3) / 3)= 16.9068 (rounded to four decimal places).
Therefore, the instantaneous rate of change for the function f(x) at x = 3 is 16.9068.
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(50 POINTS) Express each sum using summation notation.
14. 3 + 3^2/2 + 3^3/3 ... + 3^n/n
15. 1 + 3 + 5 + 7 +... [2(12) - 1]
Answers
14: a
1
=
39
/2 0.25 313% 16%
15: 54
The average speed of an airplane is 550 miles per hour Create an equation to represent the distance, d, in miles, that the airplane travels after t hours at the average speed.
Answers
Answer:
Step-by-step explanation:
1
Answer:
56
Step-by-step explanation:
i just is smart
yhhhhhhhhhhh
How many roots does the equation 3x² = 1 - 7x have and what is the nature of the roots
Answers
Answer:
Step-by-step explanation:
Rewrite this quadratic in standard form: 3x^2 + 7x - 1.
The coefficients of x are {3, 7, -1}, and so the discriminant is b^2 - 4ac, or
7^2 - 4(3)(-1), or 49 + 12, or 61. Because the discriminant is positive, this quadratic has two real, unequal roots
Calculate the flux of the vector field F (x,y, z) = 6i - 7k through a sphere of radius 5 centered at the origin, oriented outward. Fhux Calculate the flux of the vector field F (x,y, z) = i - 3j + 9K through a cube of side length 5 with sides parallel to the axes: oriented outward.
Answers
To calculate the flux of a vector field through a surface, we can use the surface integral of the dot product between the vector field and the outward-pointing normal vector of the surface.
Let's first calculate the flux of the vector field F = 6i - 7k through a sphere of radius 5 centered at the origin, oriented outward.
The equation of the sphere centered at the origin is [tex]x^2 + y^2 + z^2 = 5^2.[/tex]
To find the outward-pointing normal vector at each point on the sphere's surface, we normalize the position vector (x, y, z) by dividing it by the magnitude of the vector.
The outward-pointing normal vector is given by N = (x, y, z) / [tex]\sqrt{(x^2 + y^2 + z^2).}[/tex]
Now, we calculate the flux using the surface integral:
Flux = ∬S F · dS,
where S is the surface of the sphere.
The dot product F · dS can be expanded as F · N dS, where dS represents the differential area vector.
The magnitude of the differential area vector on the sphere's surface is given by dS = [tex]r^2[/tex]sin(θ) dθ dφ, where r is the radius of the sphere, and θ and φ are the spherical coordinates.
Since the sphere is symmetric about the origin, the flux will be the same for all points on the surface, and we can simplify the integral as:
Flux = F · N ∬S dS.
To find the flux, we need to calculate the dot product F · N and evaluate the surface integral over the sphere's surface. Let's calculate it:
F = 6i - 7k
N = (x, y, z) /[tex]\sqrt{(x^2 + y^2 + z^2)}[/tex] = (x, y, z) / 5
F · N = (6i - 7k) · (x/5, y/5, z/5) = (6x/5) - (7z/5)
Now, let's evaluate the surface integral over the sphere's surface:
Flux = ∬S F · dS = ∬S (6x/5 - 7z/5) dS
To evaluate the integral, we can use spherical coordinates. The limits of integration will be:
θ: 0 to 2π (complete rotation around the z-axis)
φ: 0 to π (from the positive z-axis to the negative z-axis)
Flux = ∫(φ=0 to π) ∫(θ=0 to 2π) (6r sin(φ) cos(θ)/5 - 7r sin(φ) sin(θ)/5) [tex]r^2[/tex]sin(φ) dθ dφ
Simplifying and evaluating the integral will give you the flux of the vector field through the sphere.
Now, let's move on to calculating the flux of the vector field F = i - 3j + 9k through a cube of side length 5 with sides parallel to the axes, oriented outward.
Since the sides of the cube are parallel to the coordinate axes, the normal vector to each side will be aligned with the corresponding unit vector.
For example, the normal vector to the side with a normal vector i will be (1, 0, 0), and the normal vector to the side with a normal vector j will be (0, 1, 0), and so on.
To calculate the flux, we need to find the dot product between the vector field F and the outward-pointing normal vectors of each side, and then sum up the flux for all six sides of the cube.
Let's calculate the flux for each side of the cube and then sum them up to get the total flux.
Side 1: Outward normal vector = (1, 0, 0)
Dot product = (i - 3j + 9k) · (1, 0, 0) = 1
Side 2: Outward normal vector = (-1, 0, 0)
Dot product = (i - 3j + 9k) · (-1, 0, 0) = -1
Side 3: Outward normal vector = (0, 1, 0)
Dot product = (i - 3j + 9k) · (0, 1, 0) = -3
Side 4: Outward normal vector = (0, -1, 0)
Dot product = (i - 3j + 9k) · (0, -1, 0) = 3
Side 5: Outward normal vector = (0, 0, 1)
Dot product = (i - 3j + 9k) · (0, 0, 1) = 9
Side 6: Outward normal vector = (0, 0, -1)
Dot product = (i - 3j + 9k) · (0, 0, -1) = -9
Now, sum up all the dot products to get the total flux:
Flux = 1 + (-1) + (-3) + 3 + 9 + (-9) = 0
The total flux of the vector field through the cube is zero.
I hope this helps! Let me know if you have any further questions.
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Which of these are equivalent? NO LINKS. NEED HELP ASAP
Answers
Answer:
3 AND 6 - 2 AND 5!
Step-by-step explanation:
hope i helped!
Neil is going to a bookstore 45 miles away. The bridge was closed on the way back, so
he had to take an alternate route and had to drive 15 mph slower, which make the trip
back take 7 minutes longer. How fast was he going on the way to the bookstore?
Answers
Determine whether the polygons to the right are similar. If so, write a similarity statement and give the scale factor. If not, explain.
Answers
Answer:
(a) Similar polygons; scale factor is 2
(b) Similar polygons; scale factor is 1.5
Step-by-step explanation:
Given
See attachment for polygons
Required
Determine if they are similar or not
Solving (a): The triangle
The angles in both triangles show that the triangles are similar
To calculate the scale factor (k), we simply take corresponding sides.
i.e.
[tex]k = \frac{DF}{BA} = \frac{FE}{AC} = \frac{DE}{BC}[/tex]
[tex]k = \frac{6}{3} = \frac{8}{4} = \frac{10}{5}[/tex]
[tex]k = 2=2=2[/tex]
[tex]k = 2[/tex]
The scale factor is 2
Solving (b): The trapezium
The angles in both trapeziums show that the trapeziums are similar
To calculate the scale factor (k), we simply take corresponding sides.
i.e.
[tex]k = \frac{KN}{GJ}[/tex]
[tex]k = \frac{6}{4}[/tex]
[tex]k = 1.5[/tex]
The scale factor is 1.5
Somebody pls help
Solve the problems. What are the equations of the trend line shown here?
Answers
Answer:
1) y = -7/10x + 21
Step-by-step explanation:
1)
Points (5, 7) and (15, 0)
Slope:
m=(y2-y1)/(x2-x1)
m=(0-7)/(15-5)
m=(-7)/10
m= -7/10
Slope-intercept:
y - y1 = m(x - x1)
y - 7 = -7/10(x - 5)
y - 7 = -7/10x + 14
y = -7/10x + 21
Find the union and intersection for the following sets. Use a Venn diagram to verify your answers. A = {1, 4, 6, 8, 9) B=(2,3,4,5,7,8) a. Find AUB= b. Find An B=
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By filling in the elements accordingly and comparing the Venn diagram with the calculated results, the accuracy of the union and intersection can be confirmed i.e. AUB = {1, 2, 3, 4, 5, 6, 7, 8, 9} and An B = {4, 8}.
To find the union (AUB) and intersection (An B) of the sets A = {1, 4, 6, 8, 9} and B = {2, 3, 4, 5, 7, 8}, we compare the elements in the sets. The union (AUB) is the combination of all unique elements from both sets, while the intersection (An B) consists of the elements common to both sets.
(a) The union (AUB) is {1, 2, 3, 4, 5, 6, 7, 8, 9}, which includes all the distinct elements present in both sets.
(b) The intersection (An B) is {4, 8}, representing the elements that are common to both sets A and B.
To verify these results, you can draw a Venn diagram. Draw two overlapping circles representing sets A and B, and fill in the elements accordingly. The overlapping region represents the intersection, and the combination of all elements in both circles represents the union. Comparing the Venn diagram with the calculated results confirms the accuracy of the union and intersection.
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Which shows a correct comparison? A: 5 milliliters > 50 liters B: 2 liters < 200 milliliters C: 100 liters < 1,000 milliliteres D: 3,200 milliliters > 3 liters
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Answer:
d
Step-by-step explanation:
Note that
> means greater than
< means less than
for example : 2 < 3 means 2 is less than 3
3 >2 means 3 is greater than 2
To determine which comparison is better we have to convert litre to millimetre
1 litre = 1000mm
A 5 mm > (50 x 1000)
5 mm > 50,000
5 is not greater than 50,000
B. (2 x 1000) < 200 mm
2000 < 200
2000 is not less than 200
C. (100 x 1000) < 1,000
100,000 < 1000
100,000 is not less than 1000
D. 3200 > (3 X 1000)
3200 > 3000
3200 is greater than 3000
Given that MN = 5, NO = 12, and MO = 13, find cos O.
Answers
Answer:
12/13
Step-by-step explanation:
Given that MN = 5, NO = 12, and MO = 13, find cos O.
Since the reference angle is P, hence;
MN is the opposite = 5
MO is the hypotenuse = 13 (longest side)
NO is the adjacent = 12
Cos O = adj/hyp
Substitute the given values
Cos O = 12/13
Hence the value of Cos O is 12/13
Please please help this is overdue
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Answer
only the graph is a function. I can tell by doing the vertical line test on the graph and making sure that each x value only happens once. On the table it is not a function since the x values repeat.: Let S = {1,2,3,...,18,19). Let R be the relation on S defined by xRy means "xy is a square of an integer". For example 1R4 since (1)(4) = 4 = 22. a. Show that R is an equivalence relation (i.e. reflexive, symmetric, and transitive). b. Find the equivalence class of 1, denoted 7. c. List all equivalence classes with more than one element.
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a. The relation R defined on the set S = {1, 2, 3, ..., 18, 19} is an equivalence relation. It is reflexive, symmetric, and transitive, b. The equivalence class of 1, denoted [1], consists of the perfect squares in S: {1, 4, 9, 16}, c. The equivalence classes with more than one element are [1], [2], [3], ..., [18], and [19]. Each equivalence class represents a set of numbers that are squares of integers.
a. To show that the relation R is an equivalence relation, we need to demonstrate that it is reflexive, symmetric, and transitive.
i. Reflexive: For R to be reflexive, every element in S must be related to itself. Since the square of any integer is still an integer, xRx holds for all x in S, satisfying reflexivity.
ii. Symmetric: For R to be symmetric, if xRy holds, then yRx must also hold. Since multiplication is commutative, if xy is a square of an integer, then yx is also a square of an integer. Hence, R is symmetric.
iii. Transitive: For R to be transitive, if xRy and yRz hold, then xRz must also hold. Since the product of two squares of integers is itself a square of an integer, xz is also a square of an integer. Thus, R is transitive.
b. To find the equivalence class of 1, denoted [1], we determine all elements in S that are related to 1 under R. In this case, [1] consists of the perfect squares in S: {1, 4, 9, 16}.
c. The equivalence classes with more than one element are [1], [2], [3], ..., [18], and [19]. Each equivalence class represents a set of numbers that are squares of integers. The equivalence class [1] includes all perfect squares in S, while the other equivalence classes consist of a single element, which are non-square integers.
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do not send links or files!! i really need help lol
Answers
Answer:
x²+11x+30
Step-by-step explanation:
for this question, all we need to do is multiply (x+5) by (x+6)
we can use the distributive property.
(x+5)(x+6)
x² + 5x + 6x + 30
x² + 11x + 30
Complete the following steps to plot an image of your own choosing (a) Create a list containing a set of ordered pairs needed to create your image. Name the list mylist. Be sure to list the points in the order in which they will be connected together. The created list should begin and end with (0,0) in order to connect the last point back to the first point. (b) Use the command HGMatrix to convert your matrix into a matrix and assign this matrix the name mylistmat and then use the Plotimage command to plot the corresponding image.
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To plot an image of your own choosing, you can follow these steps. First, create a list containing a set of ordered pairs that represent the points needed to create your image.
To create the image, you need to define the set of ordered pairs that form the outline of the desired shape. The points in the list should be ordered in a way that connects them together to form the shape. Including (0,0) at the beginning and end ensures that the last point connects back to the first point.
Once you have the list of ordered pairs, you can convert it into a matrix using the "HGMatrix" command. This step is necessary for plotting the image using the "Plotimage" command. The matrix, named "mylistmat," will represent the points in a format suitable for plotting.
Finally, using the "Plotimage" command, you can plot the image based on the points in "mylistmat." The command will take the ordered pairs and connect them together to create the desired image.
By following these steps, you can plot your own image using the specified list, matrix conversion, and image plotting commands.
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