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3 years ago

Determine the discriminant for the given equation x^2+4x+5=0. Then describe the roots(how many and what type).

1 answer:

3 0

Discriminant = b^2 - 4ac, where a, b and c come from the form of the quadratic equation as ax^2 + bx + c

Discriminant = (4)^2 - 4(1)(5)
= 16 - 20
= -4

-4 < 0, therefor there are no roots

(If the discriminant = 0, then there is one root
If the discriminant > 0, there are two roots, and if it is a perfect square (eg. 4, 9, 16, etc.) then there are two rational roots
If the discriminant < 0, there are no roots)

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In a state where license plates contain six digits, what is the probability that the license number of a randomly selected car h

andre [41]

Answer:

Step-by-step explanation:

Given : In a state where license plates contain six digits.

Probability of that a number is 9 = $\dfrac{1}{10}$ [Since total digits = 10]

We assume that each digit of the license number is randomly selected .

Since each digit in the license plate is independent from the other and there is only two possible outcomes for given case (either 9 or not), so we can use Binomial.

Binomial probability formula: $P(X=x)=^nC_xp^x(1-p)^{n-x}$

, where n= total trials , p = probability for each success.

Let x be the number of 9s in the license plate number.

$X\sim Bin(n=6, p=\dfrac{1}{10}})$

Then, the probability that the license number of a randomly selected car has exactly two 9's will be :

$P(X=2)=^6C_2(\dfrac{1}{10})^2(1-\dfrac{1}{10})^{6-2}\\\\=\dfrac{6!}{2!(6-2)!}(\dfrac{1}{100})(\dfrac{9}{10})^4=0.098415$

Hence, the required probability = 0.098415

5 0

3 years ago

The dwarf seahorse hippocampus zosterae swims at a rate of 52.68 feet per hour.convert this speed to ines per minute

DaniilM [7]

<h3>52.68 feet per hour = 10.536 inches per minutes</h3>

<h3>Further explanation</h3>

Acceleration is rate of change of velocity.

$\large {\boxed {a = \frac{v - u}{t} } }$

$\large {\boxed {d = \frac{v + u}{2}~t } }$

<em>a = acceleration ( m/s² )</em>

<em>v = final velocity ( m/s )</em>

<em>u = initial velocity ( m/s )</em>

<em>t = time taken ( s )</em>

<em>d = distance ( m )</em>

Let us now tackle the problem !

$1 ~ foot = 30.48 ~ cm$

$1 ~ inch = 2.54 ~ cm$

$1 ~ foot = 12 ~ inches$

$\boxed {52.68 ~ feet = 52.68 \times 12 ~ inches = 632.16 ~ inches}$

$1 ~ day = 24 ~ hours$

$\boxed {1 ~ hour = 60 ~ minutes}$

If the dwarf seahorse hippocampus zosterae swims at a rate of 52.68 feet per hour , then :

$52.68 ~ feet/h = \frac{52.68 ~ feet}{1 ~ hour}$

$52.68 ~ feet/h = \frac{52.68 \times 12 ~ inches}{60 ~ minutes}$

$52.68 ~ feet/h = \frac{632.16 ~ inches}{60 ~ minutes}$

$\large {\boxed {52.68 ~ feet/h = 10.536 ~ inches/min} }$

<h3>Learn more</h3>

Velocity of Runner : brainly.com/question/3813437
Kinetic Energy : brainly.com/question/692781
Acceleration : brainly.com/question/2283922
The Speed of Car : brainly.com/question/568302

<h3>Answer details</h3>

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate

3 0

3 years ago

Brainliest for the correct awnser!! A calculator was used to perform a linear regression on the values in the table. The results

marin [14]

Answer:

Option B

Step-by-step explanation:

Taking the derivative of the residual function, then applying the normal equation:

[a; b] = (X'*X)^(X'*y)

with

X = [1 1; 2 1; 3 1; 4 1; 5 1]

X' is transpose of X

y = [11; 8; 4; 1; 0]

[a; b] = [-2.9 13.5]

6 0

3 years ago

) 6. What is the volume of the composite figure

sattari [20]

1,468 sqft hope that’s right

6 0

3 years ago

Can anyone help me on this? Vocabulary for segment of a tangent that has an endpoint that has an point of u tangency

Alik [6]

Answer:

Tangent segment ? I think. I don't know for sure because of the way you wrote the question- I got a bit confused.

7 0

3 years ago