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2 years ago

Determine the number of roots, using the most efficient method possible.

Mathematics

1 answer:

Dmitry [639]2 years ago

7 0

Answer:

2 roots in every case, not all are real.

Step-by-step explanation:

All of these equations are quadratic equations (degree 2). Every quadratic has two roots. They may be identical (looks like 1 root), and they may be complex (zero real roots), but there are always 2 of them.

a) the y-value of the vertex is negative and the parabola opens downward (leading coefficient -5), so there are no real zeros and both roots are complex.

b) each binomial factor contributes a root. Both roots are real.

c) the discriminant is positive, (3²-4·2·1=1), so both roots are real.

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The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2 respectively. Let A de

antoniya [11.8K]

Answer:

a) $P(A) =P(a)+P(b) +P(c)= 0.1+0.1+0.2 = 0.4$

b) $P(B) =P(c) +P(d)+P(e)=0.2+0.4+0.2=0.8$

c) $P(A') = 1-P(A) =1-0.4=0.6$

d) $P(A \cup B) =0.4 +0.8-0.2 =1.0$

e) The intersection between the set A and B is the element c so then we have this:

$P(A \cap B) = P(c) =0.2$

Step-by-step explanation:

We have the following space provided:

$S= [a,b,c,d,e]$

With the following probabilities:

$P(a) =0.1, P(b)=0.1, P(c) =0.2, P(d)=0.4, P(e)=0.2$

And we define the following events:

A= [a,b,c], B=[c,d,e]

For this case we can find the individual probabilities for A and B like this:

$P(A) = 0.1+0.1+0.2 = 0.4$

$P(B) =0.2+0.4+0.2=0.8$

Determine:

a. P(A)

$P(A) =P(a)+P(b) +P(c)= 0.1+0.1+0.2 = 0.4$

b. P(B)

$P(B) =P(c) +P(d)+P(e)=0.2+0.4+0.2=0.8$

c. P(A’)

From definition of complement we have this:

$P(A') = 1-P(A) =1-0.4=0.6$

d. P(AUB)

Using the total law of probability we got:

$P(A \cup B) =P(A) +P(B)-P(A \cap B)$

For this case $P(A \cap B) = P(c) =0.2$ , so if we replace we got:

$P(A \cup B) =0.4 +0.8-0.2 =1.0$

e. P(AnB)

The intersection between the set A and B is the element c so then we have this:

$P(A \cap B) = P(c) =0.2$

8 0

3 years ago

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand co

Lina20 [59]

Answer: There is 162 ml of first brand and 108 ml of second brand.

Step-by-step explanation:

Since we have given that

Percentage of vinegar that the first brand contains = 7%

Percentage of vinegar that the second brand contains = 12%

Percentage of vinegar in mixture = 9%

Total amount of dressing = 270 ml

We will use "Mixture and Allegation":

First brand Second brand

7% 12%

--------------------------------------------------------

12%-9% : 9%-7%

3% : 2%

So, ratio of first brand to second brand in a mixture is 3:2.

So, Amount of first brand she should use is given by

$\dfrac{3}{5}\times 270\\\\=162\ ml$

Amount of second brand she should use is given by

$\dfrac{2}{5}\times 270\\\\=108\ ml$

Hence, there is 162 ml of first brand and 108 ml of second brand.

4 0

3 years ago

Eduardo and Paul are leaving the same airport in Florida. Eduardo’s flight to Jamaica is 273 miles long. Paul's flight to Hondur

k0ka [10]

Answer:

B. 41.8° is the correct answer

Step-by-step explanation:

We are given that,

Length of Eduardo's flight path = 273 miles

Length of Paul's flight path = 357 miles

Distance between their destinations = 238 miles.

Now, using the law of cosines, we get,

$238^2=273^2+357^2-2\times 273\times 357\times \cos \theta$

i.e. $56644=74529+127449-194922\times \cos \theta$

i.e. $56644=201978-194922\times \cos \theta$

i.e. $194922\times \cos \theta=145334$

i.e. $\cos \theta=0.7456$

i.e. $\theta=\arccos 0.7456$

i.e. θ = 41.8°

Hence, the angle between their flight paths is 41.8°.

4 0

3 years ago

CAN SOMEONE PLS HELP!!!

Soloha48 [4]

Where’s the question

8 0

2 years ago

I got the table part but can someone explain why is the function relate to the graph for me? Please and thank you! ^.^

Rufina [12.5K]

Well for each pair of x and y value of the table, you can always find the coordinates of that point on the graph.
eg. x=y=-2 you can find the point {-2,-2} on the graph

6 0

3 years ago