Answers
Answer:
the answer is they are congruent
Related Questions
A line segment AB has the coordinates A (2,3) AND B ( 8,11) answer the following questions (1) What is the slope of AB? (2) What is the length of AB? (3) What are the coordinates of the mid point of AB?(4) What is the slope of a line perpendicular to AB ?
Answers
Given:
Endpoints of a line segment AB are A(2,3) and B(8,11).
To find:
(1) Slope of AB.
(2) Length of AB.
(3) Midpoint of AB.
(4) Slope of a line perpendicular to AB.
Solution:
We have, endpoints of line segment AB, A(2,3) and B(8,11).
(1)
Slope of AB is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{11-3}{8-2}[/tex]
[tex]m=\dfrac{8}{6}[/tex]
[tex]m=\dfrac{4}{3}[/tex]
Therefore, the slope of AB is [tex]\dfrac{4}{3}[/tex].
(2)
Length of AB is
[tex]AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]AB=\sqrt{(8-2)^2+(11-3)^2}[/tex]
[tex]AB=\sqrt{(6)^2+(8)^2}[/tex]
[tex]AB=\sqrt{36+64}[/tex]
[tex]AB=\sqrt{100}[/tex]
[tex]AB=10[/tex]
Therefore, the length of AB is 10 units.
(3) Midpoint of AB is
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{2+8}{2},\dfrac{3+11}{2}\right)[/tex]
[tex]Midpoint=\left(\dfrac{10}{2},\dfrac{14}{2}\right)[/tex]
[tex]Midpoint=\left(5,7\right)[/tex]
Therefore, the midpoint of AB is (5,7).
(4)
Product of slopes of two perpendicular lines is -1.
Let the slope of line perpendicular to AB be m₁.
[tex]m_1\times \dfrac{4}{3}=-1[/tex]
[tex]m_1=-\dfrac{3}{4}[/tex]
So, slope of line perpendicular to AB is [tex]-\dfrac{3}{4}[/tex].
4(5 – w) = –2(2w – 3)
Answers
The probability that a vehicle will change lanes while making a turn is 45%. Suppose a random sample of 7 vehicles are observed making turns at a busy intersection. Find the probability that a least 5 vehicles will change lanes while making the turn.
Answers
Answer:
0.1529
Step-by-step explanation:
Given that:
Probability of changing lane ; p = 45% = 0.45
Sample size (number of trials) = n = 7
Probability that atleast 5 vehicles will change lane :
Using the binomial probability formula :
P(x = x) = nCx * p^x * (1 - p)^(n-x)
(1 - p) = 1 - 0.45 = 0.55
P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)
P(x = 5) = 7C5 * 0.45^5 * 0.55^2
P(x = 5) = 21 * 0.45^5 * 0.55^2 = 0.117221
P(x = 6) = 7C6 * 0.45^6 * 0.55^1
P(x = 6) = 7 * 0.45^6 * 0.55^1 = 0.031969
P(x = 7) = 7C7 * 0.45^7 * 0.55^0
P(x = 7) = 1 * 0.45^7 * 0.55^0 = 0.003736
P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)
P(x ≥ 5) = 0.117221 + 0.031969 + 0.003736
P(x ≥ 5) = 0.152926
P(x ≥ 5) = 0.1529
Using the binomial distribution, it is found that there is a 0.1529 = 15.29% probability that a least 5 vehicles will change lanes while making the turn.
For each vehicle, there are only two possible outcomes, either they change lanes while making a turn, or they do not. The probability of a vehicle changing lanes while making a turn is independent of any other vehicle, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
The probability that a vehicle will change lanes while making a turn is 45%, hence [tex]p = 0.45[/tex].A sample of 7 vehicles is taken, hence [tex]n = 7[/tex].The probability that at least 5 vehicles will change lanes while making the turn is:
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{7,5}.(0.45)^{5}.(0.55)^{2} = 0.1172[/tex]
[tex]P(X = 6) = C_{7,6}.(0.45)^{6}.(0.55)^{1} = 0.0320[/tex]
[tex]P(X = 7) = C_{7,7}.(0.45)^{7}.(0.55)^{0} = 0.0037[/tex]
Then
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) = 0.1172 + 0.0320 + 0.0037 = 0.1529[/tex]
0.1529 = 15.29% probability that a least 5 vehicles will change lanes while making the turn.
To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377
What is the length of segment DA?
Answers
Answer:
Step-by-step explanation:
The length of this line segment is the distance between its endpoints A and B. So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.
Answer: DA = 6
====================================================
Explanation:
The triangles are similar, allowing us to make the proportion below
DB/DA = DA/DC
Plug in the given values. Cross multiply and solve for x
DB/DA = DA/DC
9/DA = DA/4
9*4 = (DA)*(DA)
36 = (DA)^2
(DA)^2 = 36
DA = sqrt(36)
DA = 6
The length of DA is exactly the geometric mean of the lengths BD and DC
geometric mean of x and y = sqrt(x*y)
Identify the radius of the circle.
Help ASAP pls!!!
*its hw*!
Answers
Which diagram represents the type of solution to this system of equations?
7x − 12y + z = -1
8x − 10y = 5
21x − 36y + 3z = -3
A.
B.
C.
D.
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Answer: The answer should be A.
Step-by-step explanation: When solving the first and third equations, it becomes 0=0. I'm assuming that is one solution. Then 8x-10y=5 should be the other solution. In other words, there is 2 solutions.
The correct diagram represents the type of solution to this system of equations is shown in Option A.
We have to given that,
System of equations are,
7x - 12y + z = -1 .. (i)
8x - 10y = 5 .. (ii)
21x - 36y + 3z = -3 .. (iii)
Now, From equation (i);
Multiply by 3;
3( 7x - 12y + z) = -1 × 3
21x - 36y + 3z = - 3
Which is same as equation (iii).
Hence, Equation (i) and (ii) are parallel to each other.
And, It's a triple relationship.
Thus, Only option A has parallel planes.
So, Option A is true.
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-6 + (-3) - (-2) =
A. 11
B. 7
C. -7
D. -11
Answers
Answer:
C. -7
Step-by-step explanation:
C. -7
Step by step explanation:
-6+(-3)-(-2) When there is a in front of an expression in parentheses, the expression remains the same and when there is a in front of an expression in parentheses, change the sign of each term in the expression
-6-3+2= -7
A president, treasurer, and secretary, all di erent, are to be chosen from a club consisting of 12 people (whose names are I, J, K, L, M, N, O, P, Q, R, S, and T). How many di erent choices of ocers are possible if: (a) There are no restrictions
Answers
Answer:
There are 220 choices
Step-by-step explanation:
Given
[tex]People = 12[/tex]
[tex]Selection =3[/tex] (President, Treasurer and Secretary)
Required
Determine number of selection (if no restriction)
This is calculated using the following combination formula:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
Where
[tex]n = 12[/tex]
[tex]r= 3[/tex]
So, we have:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
[tex]^{12}C_3 = \frac{12!}{(12 - 3)!3!}[/tex]
[tex]^{12}C_3 = \frac{12!}{9!3!}[/tex]
[tex]^{12}C_3 = \frac{12*11*10*9!}{9!3!}[/tex]
[tex]^{12}C_3 = \frac{12*11*10}{3!}[/tex]
[tex]^{12}C_3 = \frac{12*11*10}{3*2*1}[/tex]
[tex]^{12}C_3 = \frac{12*11*10}{6}[/tex]
[tex]^{12}C_3 = 2*11*10[/tex]
[tex]^{12}C_3 = 220\ ways[/tex]
There are 220 choices
The monthly electric bills in a certain community are normally distributed, with a mean of $245 and a standard distribution of $55. If there are 461 households in the community, about how many of them have electric bills less than $200?
A. 45
B. 21
C. 95
D. 81
Answers
95 households have electricity bills of less than $200. Option C is correct.
Given that,
The monthly electric bills in a certain community are normally distributed, with a mean of $245 and a standard distribution of $55. There are 461 households in the community, how many of them have electric bills less than $200 is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
probability for the number of households has electric bills less than $200.
x = 200 , μ = 245 ; σ = 55
Now,
Probability,
z (p < 200) = [tex]\frac{X -\mu}{\sigma}[/tex]
z (p < 200) = (200 - 245)/55
= --45/5
= -0.818181
p < 200 = 0.206 (from z table)
Now, the number of households that has electricity bill less than $200,
= 461 * 0.206
= 94.966
≈ 95
Thus, 95 number of household have electricity bills of less than $200. Option C is correct.
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What is the volume of the following rectangular prism pls help me I’m being timed
Answers
Answer:
ummmmm I guess I could add the dimensions in the text.
Step-by-step explanation:
The picture is a black screen.
50 POINTS PLZ HELP MEEEE
Answers
Answer:
Step-by-step explanation:
It’s c
Answer:
c
Step-by-step explanation:
$40 game; 30% off; 5% tax
Answers
A 5-kilogram bag of cat food costs $18.90. What is the unit price?
$
per kilogram
Answers
Answer:
3.78
Step-by-step explanation:
3.78
Explanation:
18.80 ÷5=3.78
find the value of w(u(-4)) i need some help lol
Answers
Answer:
The functions u and w are defined as follows. u(x) =-2x+2 w(x) = 2x2 +1 Find the value of w (u (4)). w (u (4)) = 05Step-by-step explanation:
. p−20=−30 .
i need your help
Answers
Answer:
p = -10
Step-by-step explanation:
-30 + 20 = -10
Assume that last year in a particular state with 700000 children there were 1205 children out of 32600 in a random sample who were diagnosed with Autism Spectrum Disorder. Nationally, 1 out of 88 children are diagnosed with ASD. Is there sufficient data to show that the incident rate of ASD is higher in that state than nationally
Answers
Answer:
We accept Hₐ there is enough evidence to claim that the incidence of ASD is bigger in this state than it is nationally
Step-by-step explanation:
The population follows a binomial distribution, and the fact that
p₀ = 1205/32600 = 0,03696 and then q₀ = 1-0,03696 = 0,9630
And both
p₀*n = 0,03696*32600 = 1205 > 10
q₀*n = 31395 > 10
The binomial distribution can be approximate to a Normal Distribution, then we need to develop a one tail test ( to the right) to evaluate if the claim " There is sufficient data to show that the incident rate is higher in the mentioned state than the national one.
Therefore:
Hypothesis Test H₀ ⇒ p₀ = p
Alternative Hypothesis Hₐ ⇒ p₀ > p
p is the population proportion mean
p = 1/88 = 0,011
We must test having a very wide Confidence Interval since the matter we are trying is public health then we choose CI = 95 %
CI = 95 % α = 5 % α = 0,05
Critical value for 0,05 is from z-table z(c) = 1,64
We compute z(s)
z(s) =( p₀ - p )/ √ p₀*q₀/n
z(s) = 0,03696 - 0,011 / √ (0,03696*0,9630)/ 32600
z(s) = 0,02596* 180,55/ √ 0,0356
z(s) = 4,687 / 0,189
z(s) = 24,9
Comparing z(s) and z(c) 24,9 > 1, 64
z(s) is out of the acceptance region and we have to reject H₀
We accept Hₐ there is enough evidence to claim that the incidence of ASD is bigger in this state than it is nationally
Select all of the fractions that are equivalent to -2/3 ( SELECT ALL THAT APPLY)
Options
A)3/-2
B)-2/-3
C)- 2/3
D)-3/-2
E)2/-3
F)-3/2
Answers
Answer:
- 2/3, 2/-3
Step-by-step explanation:
none of the rest work 3/2 is a completely different number and having two negatives in a fraction make it a positive
I have a box of crackers that weighs 5.25 oz. if one serving of crackers is .15 ounces. How many servings are in the box?
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Answer:
0.15÷5.25 should give u the answer
solve for x (x-2)(x+1)=3x-2 what is x and x
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in the picture will explain the explanation
I need help again
I am
Sorry
Answers
Answer:
x = 171.16 - 5.8
x = 165.36
please give me brainlist
Step-by-step explanation:
Answer:
165.36 is Pete's height
Step-by-step explanation
You have to subtract 5.8 by 171.16 and that will be Pete's height.
Jkgdgdkhhgkdksytsktsykkusutskfkxh
Answers
Answer:
39% , 0.39 , 39/100
Step-by-step explanation:
I thought your randomness of letters was your question lol. Hope this helps though!
is -3/7 a rational or irrational number?
Answers
Answer:
rational
Step-by-step explanation:
it can express as a ratio of two numbers, therefore it is rational. it wouldn't be rational if it was for example 0.333333 that goes on forever.
PLEASE HELP MEE!!!!!!!!Joshua is 11 years old, and his dad is 33
years old. What is the ratio of Joshua's
age to his dad's age?
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Answer:
11:33 or in simplified terms 1:3
Step-by-step explanation:
Hope this helps!:)
what is 42/18 written as a mixed number?
Answers
Step-by-step explanation: 2 1/3
Benjamin colors 40% of total grids on his paper he colors 8 grids enter the total number of grids on Benjamin's paper
Answers
Answer:
320%
Step-by-step explanation:
Jacob has several wood dowel remnants. He needs
several pieces that are at least 2 1/4 feet long to use for
4.
a project. Select ALL of the lengths that would be
useable.
(Select all that apply.)
2
feet
16
2.3 feet
2.25 feet
2 feet
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Answer:
2 feet, 2.3 feet, 2.25 feet, and 16 feet
help
graph
i understand it but will it be to the right or left
Answers
Answer:I believe left
Step-by-step explanation:
Let f be a continuous function on the interval [a, b]. Determine if the following statement is true or false. The expression lim f(xi") ax may lead to different limits if we choose the x * to be the left endpoints instead of midpoints. ni=1 Choose the correct answer below. O A. The statement is true. Each sum will be smaller when picking a left endpoint, so the limit will be smaller. OB. The statement is false. Any sample point can be chosen within the interval without affecting the limit. O C. The statement is true. The value of the function at the left endpoint is not the same as the value at the midpoint of the interval D. The statement is false. The value of the function at the left endpoint is the same as the value at the midpoint of the interval. w Click to select your answer
Answers
Answer:
The correct answer is B.
Step-by-step explanation:
We have the expression:
[tex]\displaystyle \lim_{n\to\infty}\sum_{i=1}^{n}f(x_i\, ^\star)\Delta x[/tex]
In this case, B is the correct answer.
B states that any sample point can be chosen without affecting the limit.
This is a true statement. Regardless of which point we choose for our sample point, since n approaches infinity, we will have infinite partitions.
Hence, this will not affect the sum of our expression.
A and C are false because we have infinite partitions, so the statements cannot be true. D is not true simply because the left-hand values do not have to be the same as the midpoint-values depending on the behavior of the function for [a, b].
Could some help with this problem it is due in about 20 mins and I am really stuck I will give a brainlist to the best answer :)
Answers
Answer:
Step-by-step explanation:
29.
2x+4+x+2x-9=180
5x-5=180
5x=180
x=36
Q=76°
P=63°
R=36°
30.
C=90° (Given)
4x+7+8x-1+90=180
12x+96=180
12x=84
x=7
B=55°
A=35°
help possible branliest
Answers
Answer:
1.81
2.2^7
3. 4^5
4. 2^9
5. 1
6. 4^5
7. 6
8. 3^8
9. 15^0
10. 2^3
11. 3^2
12. 216
13. 5^3
14. 225
15. 343
16. 11^2
17. 625
18. 5^4
19. 169
20. 10^4
Step-by-step explanation: