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BARSIC [14]
3 years ago
11

Find the real solutions of the equation. (2x-6)^2 + 4(2x -6) +3 = 0

Mathematics
1 answer:
miskamm [114]3 years ago
7 0

Answer:

(

2

x

−

6

)

2

+

4

(

2

x

−

6

)

+

3

=

0

Simplify the left side.

Tap for more steps...

(

2

x

−

6

)

2

+

8

x

−

21

=

0

Use the quadratic formula to find the solutions.

−

b

±

√

b

2

−

4

(

a

c

)

2

a

Substitute the values  

a

=

4

,  

b

=

−

16

, and  

c

=

15

into the quadratic formula and solve for  

x

.

16

±

√

(

−

16

)

2

−

4

⋅

(

4

⋅

15

)

2

⋅

4

Simplify.

Tap for more steps...

x

=

4

±

1

2

The final answer is the combination of both solutions.

x

=

5

2

,

3

2

Step-by-step explanation:

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The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first deter
VMariaS [17]

Answer:

He must survey 123 adults.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

Assume that a recent survey suggests that about 87​% of adults have heard of the brand.

This means that \pi = 0.87

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.

How many adults must he survey in order to be 90​% confident that his estimate is within five percentage points of the true population​ percentage?

This is n for which M = 0.05. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.05 = 1.645\sqrt{\frac{0.87*0.13}{n}}

0.05\sqrt{n} = 1.645\sqrt{0.87*0.13}

\sqrt{n} = \frac{1.645\sqrt{0.87*0.13}}{0.05}

(\sqrt{n})^2 = (\frac{1.645\sqrt{0.87*0.13}}{0.05})^2

n = 122.4

Rounding up:

He must survey 123 adults.

6 0
3 years ago
Can someone help me with this :(
julia-pushkina [17]

Answer:

9

Step-by-step explanation:

6+x, when x = 3

6+(3)

6+3=9

5 0
3 years ago
Read 2 more answers
Felix wants to buy some lemonade for the dinner party.
Xelga [282]

Answer:

Yes. Felix is correct.

Step-by-step explanation:

Find out how much ml does a can of lemonade have, I would assume its 330ml since I searched up the ml of a lemonade can.

Find out how much cans of lemonade there are in 2 packs of 8.

2 packs = 8 x 2 = 16 cans of lemonade

Now find out how much ml 16 lemonade cans equal to.

1 can of lemonade = 330ml

16 cans of lemonade = 330 x 16 = 5280ml

Now let's find 5 bottles of 1 litre.

1 litre x 5 = 5 litres.

5280 = 5 litres and 280ml

So Felix is correct about 2 packs of 8 cans is more than 5 bottles of 1 litre.

6 0
3 years ago
-p/4=-2<br> Solve the equation
Alex_Xolod [135]

Combine like terms in each member of an equation.

Using the addition or subtraction property, write the equation with all terms containing the unknown in one member and all terms not containing the unknown in the other.

Combine like terms in each member.

Use the multiplication property to remove fractions.

5 0
3 years ago
HELP PLEASE 10 POINTS!!!!!! A country's population in 1993 was 171 million. In 1999 it was 176 million. Estimate the population
Lilit [14]

Let 1993 = time 0 = 0.  

Let 1999 = time 6 = 6  

Let 2012 = time 19 = 19  

So, a = 171 (million). First solve for k.  

176 = 171 e^k6  

176/171 = e^(k*6)  

ln (176/171) = 6k  

k = 1/6 ln (176/171)  

So, in 2012 we have: P(19) = 171 e^(19k), where k = 1/6 ln (176/171)


Hope this helped!

3 0
3 years ago
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