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Answer:

2 feet, 2.3 feet, 2.25 feet, and 16 feet

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].

Answer:

3.78

Step-by-step explanation:

Answer:

This question is incomplete

Step-by-step explanation:

Answer:

C. -7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

39% , 0.39 , 39/100

Step-by-step explanation:

I thought your randomness of letters was your question lol. Hope this helps though!

Answer:

11:33 or in simplified terms 1:3

Step-by-step explanation:

Hope this helps!:)

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)

vertex at

(

−

1

,

−

4

)

Explanation:

Given:

y

=

2

x

2

+

4

x

−

2

Convert the given form into "vertex form"

y

=

m

(

x

−

a

)

2

+

b

with vertex at

(

a

,

b

)

XXX

y

=

2

(

x

2

+

2

x

)

−

2

complete the square

XXX

y

=

2

(

x

2

+

2

x

+

1

)

−

2

−

2

XXX

y

=

2

(

x

+

1

)

2

−

4

XXX

y

=

2

(

x

−

(

−

1

)

)

2

+

(

−

4

)

which is the vertex form with vertex at

(

−

1

,

−

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graph{2x^2+4x-2 [-5.455, 7.034, -5.54, 0

If xy = 1, then differentiating both sides with respect to x gives

x dy/dx + y = 0

(use the product rule)

Solve for dy/dx :

dy/dx = -y/x

Solve the starting equation for y and substitute that into the derivative.

xy = 1   →   y = 1/x

→   dy/dx = -(1/x)/x = -1/x²

Answer:

0.15÷5.25 should give u the answer

in the picture will explain the explanation

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.

Learn more about probability here:

brainly.com/question/14290572

#SPJ2

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

Answer:

p = -10

Step-by-step explanation:

-30 + 20 = -10

Answer:

Step-by-step explanation:

It’s c

Answer:

c

Step-by-step explanation:

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:

Answer:

320%

Step-by-step explanation:

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.

Answer:I believe left

Step-by-step explanation:

Answer:

ummmmm I guess I could add the dimensions in the text.

Step-by-step explanation:

The picture is a black screen.

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].  

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:

In this problem:

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

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

Answer:

I would say B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Step-by-step explanation: 2 1/3