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lbvjy [14]
2 years ago
13

What value of b will cause 16x ^ 2 + bx + 4 = 0 to have one real solution ?

Mathematics
1 answer:
bekas [8.4K]2 years ago
6 0

Answer:

b  =  16

Step-by-step explanation:

16*x  + b*x  + 4  =  0

Solving for x we get:

x₁,₂  =   - b  ±  √  b² - 4*a*c   ] / 2*a         (1)

If we take a look to the square root

√ b² - 4*4*16      =  √ b²  - 256

if we make √ b²  - 256    = 0

b²  =  256       ⇒      b  =  16

Then equation (1) becomes:

x₁,₂  = ( - 16  ±  0  ) / 32

x  = -  1/2

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Find the percent of increase. Original Price: $200 Retail Price: $250
Alexxandr [17]

Answer:

The percent of increase is 25%

Step-by-step explanation:

Percentage increase = increase in price/original price × 100 = ($250 - $200)/$200 × 100 = $50/$200 × 100 = 25%

6 0
3 years ago
Two opposing opinions were shown to a random sample of 1,500 buyers of a particular political news app in the United States. The
kifflom [539]

Answer:

A) 98% Confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B

= (0.51, 0.57)

This means that the true proportion of all thay would chose opinion B can take on values between the range of (0.51, 0.57)

B) For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Step-by-step explanation:

Confidence Interval for the population proportion is basically an interval of range of values where the true population proportion can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample proportion) ± (Margin of error)

Sample proportion of all US buyers of this particular app who would have chosen Opinion B = 0.54

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error)

Critical value at 98% confidence interval for sample size of 1500 is obtained from the z-tables.

Critical value = 2.33

Standard error = σₓ = √[p(1-p)/n]

p = sample proportion = 0.54

n = sample size = 1500

σₓ = √(0.54×0.46/1500) = 0.0128685664 = 0.01287

98% Confidence Interval = (Sample proportion) ± [(Critical value) × (standard Error)]

CI = 0.54 ± (2.33 × 0.01287)

CI = 0.54 ± 0.02998)

98% CI = (0.51, 0.57)

98% Confidence interval = (0.51, 0.57)

B) The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met?

For this confidence interval to be obtained using sample data, a couple of conditions are necessary to be satisfied. They include;

- The sample data must have been obtained using a random sampling technique.

- The sampling distribution must be normal or approximately normal.

- The variables of the sample data must be independent of each other.

On the second point, the condition for a binomial distribution to approximate a normal distribution is that

np ≥ 10

and n(1-p) ≥ 10

The quantity np is the actual sample mean which is the actual number of buyers that chose Opinion B while n(1-p) is the number of buyers that did not chose Opinion B.

For the confidence interval obtained to be valid, the conditions stated must be satisfied and for the sampling distribution to be approximately normal, the number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B must both be greater than 10.

Hope this Helps!!!

8 0
3 years ago
Answer the following question in complete sentences:
Olenka [21]

Answer:

it creates outliers

Step-by-step explanation:

A gap in a dot plot is a certain range where no data exists for certain values, thus, creates values more or less than the data cluster, which can be defined by the word outlier

6 0
3 years ago
True or false. If p(t) is the inverse of T(p), and P(5)=7, then T(7)=5.
yanalaym [24]

True

(: have a nice day

4 0
2 years ago
Read 2 more answers
Which set represents the same relation as the graph below?<br><br> A<br> B<br> C<br> D
eimsori [14]

Answer:

B. {( -1,-2 ), ( -3,-2 ), ( -5,4 ), ( 2,0 ), ( 3,3 ), ( 4,5 ), ( 6,-4 )}

Step-by-step explanation:

We are given the graph showing the points of a relation.

According to the graph, we see that, the given points of the relation are:

( -1,-2 ), ( -3,-2 ), ( -5,4 ), ( 2,0 ), ( 3,3 ), ( 4,5 ) and ( 6,-4 ).

As, we see that there are 7 points in the relation.

So, option C and D are not correct as they have 5 and 6 points respectively.

Also, option A is wrong as it contains different set of points.

Hence, we get that option B is correct.

That is the set representing the graphed relation is {( -1,-2 ), ( -3,-2 ), ( -5,4 ), ( 2,0 ), ( 3,3 ), ( 4,5 ), ( 6,-4 )}

8 0
3 years ago
Read 2 more answers
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