Which lines are parallel? Justify your answer.
Lines a and b are parallel because their alternate exterior angles are congruent.
Lines a and b are parallel because their same side exterior angles are supplementary.
Lines e and f are parallel because their alternate exterior angles are congruent.
Lines e and f are parallel because their same side exterior angles are congruent.
Answers
Answer:
Lines e and f are parallel because their same side exterior angles are congruent
Answer:
Your answer is in the screenshot below
Step-by-step explanation:
Related Questions
Which students ran faster than Amy?
Answers
Students that ran faster than Amy are Chris and Ethan.
Speed is the ratio between distance and time. The formula for speed
v = d ÷ t
d = distances (miles)t = time (hours)v = velocity (mph)Amy's speed
d = 2 milest = 36 minutes = 36/60 hours = 0.6 hoursv = d ÷ tv = 2 ÷ 0.6
v = 3.33 mph
Brian's speed
From the time versus distance graph from 0 miles to 2 miles it can be seen that the time required is 40 minutes.d = 2 milest = 40 min = 40/60 h = 2/3 hv = d ÷ tv = 2 ÷ 2/3
v = 2 × 3/2
v = 3 mphBrian is slower than Amy
Chris's speed
The equation y = 3/42 xy = distance
x = time (min)If d = 2 miles
y = 2y = 3/42 x
2 = 3/42 x
x = 2 × 42/3
x = 2 × 14
x = 28 mint = 28 min = 28/60 h = 7/15 hv = d ÷ t
v = 2 ÷ 7/15
v = 2 × 15/7
v = 4.3 mphChris is faster than Amy
Ethan's speed
From the table, we can use any data.Pick data #2d = 3 milest = 33 min = 33/60 h = 11/20 hv = d ÷ tv = 3 ÷ 11/20
v = 3 × 20/11
v = 5.5 mphEthan is faster than Amy
Learn more about speed here: https://brainly.com/question/24872445
#SPJ1
Rae's unpaid credit card balance was $1,603. Her APR is 28.6%. What is her new
balance after she makes one new transaction for $51? Round answer to the
hundredths place. If answer doesn't have a hundredths place then include a zero so
that it does. Use a word not a symbol for the units.
Answers
$2010.458 is her new balance after she makes one new transaction for $51.
What does a credit balance mean?
The amount that the credit card company owes you is shown as a credit balance on your billing statement. Each payment you make results in credits being added to your account.
When you return something you purchased with your credit card, you can receive an additional credit.
Credit balance = $1,603
APR = 28.6%
= 28.6% * $1,603
= 458.458
Credit balance = $1,603 + 458.458
= $2061.458
net balance = $2061.458 - 51
= $2010.458
Learn more about credit balance
brainly.com/question/14781034
#SPJ1
Find y.
I will give Brainliest to correct answer !
Answers
Since the graph was obtained by transforming the graph of the square root function, an equation for the function the graph represent is: \(g(x) = -\sqrt{9(x - 1)} + 2\)
What is a square root function?In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this context, the required square root function can be obtained by applying a set of transformations to the parent square root function as follows;
f(x) = √x
g(x) = -√9(x - 1) + 2
\(g(x) = -\sqrt{9(x - 1)} + 2\)
Read more on translation here: brainly.com/question/4521517
#SPJ1
Suppose 24% of students chose to study French their sophomore year, and that meant that there were 54 such students. How many students chose not to take French their sophomore year?
Answers
171
24 % = 54
1 % = 2.25
100 % = 171
Match each verbal description to its equivalent function rule as applied to the given function below.
f(x) = 70 + 5/(*) = 71 +5
g(
= 213 + 17
9(2)
= 14 + 79(1) = 141 +7
9(2)
73 + 149(*) = 75 + 14
9(2)
= – 7:– 169(1) = -71 – 16
9(30)
= 70
189(1) = 71 – 18
g(x)
- 720 + 169(3)
-75 + 16
The function f stretched vertically by a
factor of 2 and translated down by 3 units.
<
The function f translated
2 units down and 3 units right.
Answers
9514 1404 393
Answer:
g(x) = 14x +7g(x) = 7x -18g(x) = -7x -16g(x) = 21x +17Step-by-step explanation:
The transformations of interest here are ...
g(x) = b·f(x) . . . . vertical scaling by a factor of bg(x) = f(-x) . . . . . reflection across the y-axisg(x) = f(x -h) +k . . . translation h units right and k units up1. The transformation parameters are given as b=2, (h, k) = (0, -3). Then we have ...
f1(x) = 2f(x) = 2(7x +5) = 14x +10 . . . . . vertical stretch by 2
g(x) = f1(x -0) -3 = 14(x -0) +10 -3
g(x) = 14x +7
__
2. (h, k) = (3, -2)
g(x) = f(x -3) -2 = 7(x -3) +5 -2 = 7x -21 +3
g(x) = 7x -18
__
3. The reflection gives us ...
f1(x) = f(-x) = 7(-x) +5 = -7x +5
Then the translation 3 left is (h, k) = (-3, 0).
g(x) = f1(x -(-3)) +0 = -7(x +3) +5 = -7x -21 +5
g(x) = -7x -16
__
4. The transformation parameters are b = 3 and (h, k) = (0, 2).
f1(x) = 3f(x) = 3(7x +5) = 21x +15 . . . . . . vertical stretch by 3
g(x) = f1(x) +2 = 21x +15 +2
g(x) = 21x +17
Lisa wrote a business plan for an entrepreneurship class, and now she has to make bound copies. Lisa could use a printer who charges a setup fee of $40 and $5 for every copy printed. Another possibility is to go to the office supply store, where she could pay an up-front fee of $30 and $10 per copy. There is a certain number of copies that makes the two options equivalent in terms of cost. How many copies is that?Write a system of equations, graph them, and type the solution.
Answers
The equation for the first option would be
\(y=40+5x\)Where "x" is the number of copies and y the cost.
The second equation will be
\(y=30+10x\)If we graph both equations we have
As we can see, they will be equal in terms of cost with 2 copies. The cost will be 50.
We can see it at the intersection of the two graphs! we can also do it with algebra, if the costs are equal (same "y") we can say
\(\begin{gathered} 40+5x=30+10x \\ \\ 10=5x \\ \\ x=2 \end{gathered}\)The number of copies is 2.
1. A target is divided into 100 squares colored in dark blue, white, and light blue. Amber throws a beanbag that lands on the target.
co
9 25
dark blue
What is the probability that it will land on a dark blue square?
26
white
light blue
Answers
The probability of landing on the dark blue target is 2/5.
Finding probabilityProbability is the ratio of required to the total possible outcomes of an event.
The required outcome = dark blue= 25Total possible outcomes= entire sample Space = 100P(dark blue ) = 40/100
divide through by 20
P(dark blue ) = 2/5
Therefore, the probability of landing on target is 2/5
Learn more on probability:https://brainly.com/question/24756209
#SPJ1
g is a trigonometric function of the form � ( � ) = � cos ( � � + � ) + � g(x)=acos(bx+c)+dg, left parenthesis, x, right parenthesis, equals, a, cosine, left parenthesis, b, x, plus, c, right parenthesis, plus, d. Below is the graph of � ( � ) g(x)g, left parenthesis, x, right parenthesis. The function has a maximum point at ( 3.5 , − 4 ) (3.5,−4)left parenthesis, 3, point, 5, comma, minus, 4, right parenthesis and a minimum point at ( − 1 , − 5 ) (−1,−5)left parenthesis, minus, 1, comma, minus, 5, right parenthesis. Find a formula for � ( � ) g(x)g, left parenthesis, x, right parenthesis. Give an exact expression. � ( � ) = g(x)=g, left parenthesis, x, right parenthesis, equals A graph of a trigonometric wave on an x y coordinate plane. The x axis scales by two and the y axis scales by one. There is a point on the graph at the minimum at (negative one, negative five) and a point on the maximum next to the mentioned point at (three and one half, negative four).
Answers
The exact expression for g(x) is 2.25cos((2π/4.5)×(x-3.5)) - 4.
Describe Function?A function can be represented using a formula or an equation, and it can be graphed on a coordinate plane. The input values are typically represented on the x-axis and the output values on the y-axis.
From the given information, we know that the function g(x) has a maximum point at (3.5, -4) and a minimum point at (-1, -5).
The general form of a cosine function is f(x) = A×cos(Bx + C) + D, where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.
Since the function has a maximum point at (3.5, -4), we know that the graph has been shifted to the left by 3.5 units. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) + D.
Similarly, since the function has a minimum point at (-1, -5), we know that the graph has been shifted upwards by 1 unit. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) - 4.
To determine A and B, we can use the fact that the period of the function is 4.5 units (the distance between the maximum and minimum points). Therefore, we have B = 2*pi/4.5.
To determine A, we can use the fact that the amplitude is half the distance between the maximum and minimum points, which is 0.5*(5-(-4)) = 4.5. Therefore, we have A = 4.5/2 = 2.25.
Substituting these values into the equation for g(x), we have:
g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4
Therefore, the exact expression for g(x) is:
g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4.
To know more about equation visit:
https://brainly.com/question/22964920
#SPJ1
11. Descartes is thinking of a number that when he multiplies it by 9, he gets the number he is thinking of. What number is Descartes thinking of? brainly
Answers
Descartes must be thinking of the number 0.
Now, Let's call the number Descartes is thinking of "x".
Hence, According to the problem, if Descartes multiplies "x" by 9, he gets "x" back. In other words, 9 times "x" is equal to "x".
So we can write this as an equation:
⇒ 9x = x
Now we need to solve for "x". We can start by subtracting "x" from both sides of the equation:
⇒ 9x - x = 0
⇒ 8x = 0
divide both sides by 8 to get:
⇒ x = 0
Thus, Descartes must be thinking of the number 0.
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ1
What is 8/12=8/12= in simplest form
Answers
Answer:
The answer is 2/3
Step-by-step explanation:
8/12 = 4 × 2/4 × 3 = 3/2
Thus, The simplest form of 8/12 is 2/3
-TheUnknownScientist 72
what is the product of 2/1 and (-2/3)?
Answers
Answer: -4/3 or - 1 1/3
Step-by-step explanation: 2 times -2 = -4 and 3 times 1 is 3.
Which of the following effects of a BAC of .2 percent does NOT relate to one’s driving ability?
A. lack of coordination
B. Breathalyzer test results indicating a high BAC
C. Impaired gross motor skills such as walking or gestures
D. Impaired reactions
It is either between B or C.
Answers
The effect that does NOT relate to one's driving ability is breathalyzer test results indicating a high BAC. Option B.
Breathalyzer testWhile the breathalyzer test measures the blood alcohol concentration (BAC), it is a method used to determine the level of alcohol in a person's system and is commonly used in assessing impairment for driving under the influence.
Therefore, it directly relates to one's driving ability and is not excluded from the effects on driving ability caused by a BAC of .2 percent.
On the other hand, options, lack of coordination, impaired gross motor skills, and impaired reactions all directly relate to one's driving ability as they affect the physical and cognitive abilities necessary for safe and efficient driving.
More on breathalyzers can be found here: https://brainly.com/question/26086547
#SPJ1
HELP QUICK PLEASE!!!
Answers
Answer: p = -2/3, sum = 0
Step-by-step explanation:
Additive inverse has the name numerical value as the given number but has the opposite sign so when they are added together they equal zero. The sum of any number and its additive inverse equal 0.
EX: 1 and -1
1+ (-1) = 0
EX: -4.5 and 4.5
-4.5 + 4.5 = 0
You have a jar of marbles in front of you 2 are green, 9 are yellow, 3 are white and 7 are red. What is e probability, as a decimal, of selecting a marble that is white or yellow, followed by a marble that is green?
Answers
Sample space = 21
Pr(White or Yellow) = Pr(White) + Pr(Yellow)
Pr(White) = 3/21 = 1/7
Pr(Yellow) = 9/21 = 3/7
Therefore,
Pr(White or Yellow)= 1/7 + 3/7 = 4/7
Discussed the strength of the correlation, the slope of a line of best fit, and whether there are any clusters or outliers on the scatter plot .
Answers
10. Leo runs the 100-meter dash in 19.305
seconds. Explain and show how you can
write an expression in expanded form
for the decimal that shows more than 0
hundredths.
Answers
The expanded form of the expression is 10 + 9 + 0.3 + 0.00 + 0.005
How to write in expanded form ?He runs the 100 meters dash in 19.305 seconds.
Therefore, the seconds he runs the race can be represented in expanded form as follows:
Expanded form is a way to write a number by adding the value of its digits.
We can use a place value chart to think of the value of a number's digits.
Therefore,
19.305 in expanded form is as follows:
19.305 = 10 + 9 + 0.3 + 0.00 + 0.005
learn more on expanded form here: https://brainly.com/question/199541
#SPJ1
NO LINKS OR ELSE YOU'LL BE REPORTED! Please give me the correct answer.Only answer if you're very good at math.
Answers
Answer:
positive
Step-by-step explanation:
hope this helps :)
Answer:
positive
Step-by-step explanation:
because your adding +2 when ur at 0
3. A water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. Find this minimum length of pipe. B 6.00 mi CH P 12.0 mi A 10.0 mi D
Answers
The minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.
We are given that a water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. We need to find this minimum length of pipe.
The given figure is shown below: \(AB = 10 \ miles\)\(BC = 6 \ miles\)\(CP = 12 \ miles\). We are given that \(LAPD = LCPB\).
Now, we need to find the minimum length of pipe required for delivering the water to points A and B.The total length of the pipe, \(L_{total} = LA + AB + BP\)Since \(LAPD = LCPB\), we can say that\(AP^2 + PD^2 = BP^2 + PC^2\).
From the triangle ACP, we can say that\(AC^2 = AP^2 + PC^2\). So, we can substitute AP^2 + PC^2 with AC^2 to get\(AP^2 + PD^2 = BP^2 + AC^2\)Now, we can substitute AP = AC - PC and BP = BC + PC in the above equation to get\((AC - PC)^2 + PD^2 = (BC + PC)^2 + AC^2\).
After solving this equation, we get\(AC = \frac {37}{8}\) and \(PC = \frac {27}{8}\)Now, we can calculate the length of pipe required as follows: \(L_{total} = LA + AB + BP = 10 + 6 + \frac {27}{8} = \boxed{20.375 \ miles}\). Therefore, the minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.
For more such questions on length, click on:
https://brainly.com/question/2005046
#SPJ8
A rectangle swimming pool was 4 meters wide with a surface area of 20 square meters. What is the length of the pool?
Answers
The length of the pool is 5 meters
How to calculate the length of the pool?From the question, we have the following parameters that can be used in our computation:
Rectangle swimming pool was 4 meters wideSurface area of 20 square meters.The length of the pool is calculated as
Length = Surface area / Width
substitute the known values in the above equation, so, we have the following representation
Length = 20/ 4
EValuate
Length = 5
Hence, the length is 5 meters
Read more about area at
https://brainly.com/question/24487155
#SPJ1
F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
Write F ∩ H and F ∩ H using interval notation. If the set is empty, write ∅.
Answers
The final interval notation is F ∩ H = [7, 4] & F ∪ H = [-∞, ∞].
What is the interval notation?
A set of real numbers known as an interval in mathematics contains all real numbers falling inside any two of the set's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1.
We have,
F and H are sets of real numbers defined as follows.
F = { v l v < 4}
H = { v l v ≥ 7}
F is the set of all real numbers that are less than or equal to 4. H is the set of real numbers greater than 7.
F U H is the union (or combination) of the two sets, so it is the set of all real numbers that are less than equal to 3 or greater than 6:
F ∩ H is the set of real numbers that are in both sets; but since F is less than or equal to 4 and H is greater than 7, there are no numbers that are in both sets. Hence the answer is the empty set, Ø:
F ∩ H = Ø
F ∩ H = [7, 4]
F ∪ H = [-∞, ∞]
Hence, the final interval notation is F ∩ H = [7, 4] & F ∪ H = [-∞, ∞].
To learn more about interval notation visit,
https://brainly.com/question/26025356
#SPJ4
MISTERBRAINLYY!!
The paint in a certain container is sufficient to paint an area equal to 9.375m2. How many bricks of dimensions 22.5cm×10cm×7.5cm can be painted out of this container?
Answers
There are three area options for the number of bricks:
4165551250How many bricks can be painted out of a container?
The number of bricks that can be painted out is equal to the paint area (A), in square centimeters, divided to the area of a brick (A'), in square centimeters. That is:
n = A / A'
A' = w · h
Where:
w - Width of the brick, in centimeters.h - Height of the brick, in centimeters.There are three possible answers:
Case 1: A = 93750 cm², w = 22.5 cm, h = 10 cm
A' = 22.5 · 10
A' = 225
n = 93750 / 225
n = 416.667
n = 416
Case 2: A = 93750 cm², w = 22.5 cm, h = 7.5 cm
A' = 22.5 · 7.5
A' = 168.75
n = 93750 / 168.75
n = 555.556
n = 555
Case 3: A = 93750 cm², w = 10 cm, h = 7.5 cm
A' = 10 · 7.5
A = 75
n = 93750 / 75
n = 1250
To learn more on areas: https://brainly.com/question/16151549
#SPJ1
Pleaseee helppp!!! I’m not sure
Answers
It’s A, 8(7+8+16)
Hope this helps!
Find the exact (leave pi) and the approximate ( pi = 3.14 ) circumference for each circle
(#s A-F ONLY)
Answers
Answer/Step-by-step explanation:
a. Circumference (C) = πd
d = 12 cm
π = 3.14
Exact value of C = π*12 = 12π cm
Approximate value of C = 12*3.14 = 37.68 cm
b. Circumference (C) = πd
d = 8 m
π = 3.14
Exact value of C = π*8 = 8π m
Approximate value of C = 8*3.14 = 25.12 m
c. Circumference (C) = πd
d = 6 km
π = 3.14
Exact value of C = π*6 = 6π km
Approximate value of C = 6*3.14 = 18.84 km
d. Circumference = πd
d = 9 ft
π = 22/7
Exact value of C = π*9 = 9π ft
Approximate value of C = 9*22/7 = 28.2857143 ≈ 28.29 ft (nearest hundredth)
e. Circumference = 2πr
r = 4 mm
π = 22/7
Exact value of C = 2*π*4 = 8π mm
Approximate value of C = 2*22/7*4 = 25.1428571 ≈ 25.14 mm (nearest hundredth)
f. Circumference = 2πr
r = 7 mi
π = 22/7
Exact value of C = 2*π*7 = 14π mi
Approximate value of C = 2*22/7*7 = 44 mi (nearest hundredth)
How many miles does he run in one year
Answers
Answer Key:
1. Since the question says Mr. Smith runs 2.7 miles every day of the week, you will need to multiply it with 365, the days of the year. The total answer you would get D. 985.5 miles.
| I just want to help you with #2 anyway
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($) 2
4
6
8
10
Probability 0.45 0.3 0.1 0.1 0.05
Expected Value = [?]
Round to the nearest hundredth.
PLEASE HELP !!!
Answers
============================================================
Explanation:
Refer to the table below (attached image). I've copied your table and added a third row at the bottom. This new row is the result of multiplying each payout value with the corresponding probability.
Example: for the first entry of this row, have 2*0.45 = 0.9
Once that third row is filled out, you add up everything in that row. That will lead to the expected value.
The expected value is: 0.9+1.2+0.6+0.8+0.5 = 4
Interpretation: You expect, on average, to win $4 each time you play the game. This assumes that the cost to play the game is 0 dollars. If the cost is something else, then it will affect the expected value.
Because the expected value is not 0, this game is not mathematically fair (the bias is leaning in favor of the player).
7. By using binomial expansion show that the value of (1.01)^12 exceed the value of (1.02)^6 by 0.0007 correct to four decimal places.
Answers
Binomial expansion is used to factor expressions that can be expressed as the power of the sum of two numbers.
The proof that (1.01)^12 exceeds (1.02)^6 by 0.0007 is\(\mathbf{(1.01)^{12} - (1.02)^6 \approx 0.0007 }\)
The expressions are given as:
\(\mathbf{(1.01)^{12}\ and\ (1.02)^6}\)
A binomial expression is represented as:
\(\mathbf{(a + b)^n = \sum\limits^n_{k=0}^nC_k a^{n - k}b^k}\)
Express 1.01 as 1 + 0.01
So, we have:
\(\mathbf{(1.01)^{12} = (1 + 0.01)^{12}}\)
Apply the above formula
\(\mathbf{(1.01)^{12} = ^{12}C_0 \times 1^{12 - 0} \times 0.01^0 + ......... .......... + ^{12}C_{12} \times 1^{12 - 12} \times 0.01^{12} }}\)
\(\mathbf{(1.01)^{12} = 1 \times 1 \times 1 + ......... .......... + 1 \times 1 \times 10^{-24} }}\)
\(\mathbf{(1.01)^{12} = 1 + ......... .......... + 10^{-24} }}\)
This gives
\(\mathbf{(1.01)^{12} = 1.1268\ (approximated)}\)
Similarly,
Express 1.02 as 1 + 0.02
So, we have:
\(\mathbf{(1.02)^6 = (1 + 0.02)^6}\)
Apply \(\mathbf{(a + b)^n = \sum\limits^n_{k=0}^nC_k a^{n - k}b^k}\)
\(\mathbf{(1.02)^6 = ^6C_0 \times 1^{6 - 0} \times 0.02^0 + ^6C_1 \times 1^{6 - 1} \times 0.02^1 +.............. + ^6C_6 \times 1^{6 - 6} \times 0.02^6 }\)\(\mathbf{(1.02)^6 = 1 \times 1 \times 1 + 6 \times 1 \times 0.02 +.............. + 1 \times 1 \times 6.4 \times 10^{-11} }\)
\(\mathbf{(1.02)^6 = 1 + 0.12 +.............. + 6.4 \times 10^{-11} }\)
This gives
\(\mathbf{(1.02)^6 = 1.1261\ (approximated) }\)
Calculate the difference as follows:
\(\mathbf{(1.01)^{12} - (1.02)^6 \approx 1.1268 - 1.1261 }\)
\(\mathbf{(1.01)^{12} - (1.02)^6 \approx 0.0007 }\)
The above equation means that:
(1.01)^12 exceed the value of (1.02)^6 by 0.0007
Read more about binomial expansions at:
https://brainly.com/question/9554282
While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd. The actual number of cattle in the herd was 600.
What was the percent of error, rounded to the nearest percent?
15%
20%
25%
30%
Answers
The solution is, the percent of error, rounded to the nearest percent is 25%.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
given that,
While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd.
The actual number of cattle in the herd was 600.
now, we have to find the percent of error, rounded to the nearest percent.
so, we get,
Herbert estimated that there were 750 cattle in the herd.
The actual number of cattle in the herd was 600.
so, error = 750 - 600
= 150
so, we get,
the percent of error = 150 * 100 / 600
= 25%
Hence, The solution is, the percent of error, rounded to the nearest percent is 25%.
To learn more on percentage click:
brainly.com/question/13450942
#SPJ2
Does standard deviation means independent events
Answers
Standard deviation does not mean independent events.
Does standard deviation means independent events?No, the standard deviation is a measure of the spread or variability of a set of data. It measures how much the individual data points in a dataset deviate from the mean or average of the dataset.
Independence, on the other hand, refers to the relationship between two or more events, where the occurrence of one event does not affect the probability of the other event occurring.
Standard deviation is not directly related to the concept of independence. However, when calculating the standard deviation of a dataset, it assumes that each data point is independent and identically distributed. This means that the value of one data point does not affect the value of another data point, and that each data point is drawn from the same underlying distribution.
Learn more on standard deviation here;
https://brainly.com/question/24298037
#SPJ1
Find a vector equation for the line through the point P = (4, 2, 4) and parallel to the vector v = < -2, -5, -3 > . Assume r(0) = 4i + 2j + 4k and that v is the direction vector of the line. R(t) = Rewrite this in terms of the corresponding parametric equations for the line. x = ______y = ______z = ______
Answers
Answer:
The parametric equations are
x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4
Step-by-step explanation:
Step(i):-
Given point P = ( 4,2,4)
Given vector is -2 i - 5 j - 3 k
The vector equation of a line through the point a⁻ and parallel to b⁻ is
r⁻ = a⁻ + t b⁻
Given r⁻ = 4 i + 2 j + 4 k
r⁻ = 4 i + 2 j + 4 k + t (-2 i - 5 j - 3 k)
Step(ii):-
The Cartesian form
\(\frac{x-a_{1} }{b_{1} } = \frac{y-a_{2} }{b_{2} } = \frac{z-a_{3} }{b_{3} } = t\)
\(\frac{x-4 }{-2 } = \frac{y-2 }{-5 } = \frac{z-4 }{-3 } = t\)
\(\frac{x-4 }{-2 } = t\)
⇒ x - 4 = -2 t
⇒ x = - 2 t + 4
\(\frac{y-2 }{-5 } = t\)
⇒ y - 2 = - 5 t
⇒ y = - 5 t + 2
\(\frac{z-4 }{-3 } = t\)
z - 4 = -3 t
z = - 3 t + 4
Conclusion:-
The parametric equations are
x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4
HELPP PLSS What is the volume of the triangular prism?
A) 180 cm3
B)360 cm3
C) 720 cm3
D)1440 cm3
Answers
Answer: D. 1440cm
Step-by-step explanation:
volume=lengthxwidthxheight
8x15x12=1440