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2 years ago

(a) Use the fundamental theorem of algebra to determine the number of roots for 2x^2+4x+7 show your work

Mathematics

1 answer:

postnew [5]2 years ago

4 0

Answer:

The answer to your question is: This polynomial does not have root, it does not intercept the x-axis.

Step-by-step explanation:

2x² + 4x + 7

To determine the number of roots of this polinomial, just look at the higher power and that number will be the maximum possible number of roots.

In this exercise, the maximum power is 2, so this polynomial could have at most 2 roots.

b) Find the possible roots of the polynomial, which are multiples of 7

Possible roots: ±1, ±7

2x² + 4x + 7

Use synthetic division to find the roots

2 4 7 1

2 6

2 6 13 +1 is not a root

2 4 7 -1

-2 -2

2 2 5 -1 is not a root

2 4 7 7

14 126

2 18 133 +7 is not a root

2 4 7 -7

-14 70

2 -10 -77 -7 is not a root

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Which graph has the same end behavior as the graph of f(x) = –3x^3 – x^2 + 1?

ololo11 [35]

To find out end behavior, we always look at the largest exponent (3 in this case) and the sign of the term with the largest exponent (negative in this case). We can rule out the first two choices because since it is a cubic graph (exponent of 3) the graph will be pointing in opposite directions. Then, the negative tells us that as the x values approache infinity, the y values will approach negative infinity. So the correct answer is the last choice.

Hope this helps

4 0

2 years ago

An insurance company sells an auto insurance policy that covers losses incurred by a policyholder, subject to a deductible of 10

Marrrta [24]

Answer:

Option E - 1000

Step-by-step explanation:

Let X stand for actual losses incurred.

Given that X follows an exponential distribution with mean 300,

To find the 95-th percentile of all claims that exceed 100.

In other words,

0.95 = Pr (100 < x < p95 ) / P(X > 100)

= Fx( P95) − Fx(100 ) / 1− Fx (100)

, where Fx is the cumulative distribution function of X

since, Fx(x) = 1 - e^ (-x/300)

0.95 = 1 - e^ (-P95/300) - [ 1 - e^ ( -100/300) ] / 1 - [ 1 - e^ ( -100/300) ]

= e^ ( -1/3 ) - e^ ( - P95//300) / e^(-1/3)

= 1 - e^1/3 e^ (-P95/300)

The solution is given by , e^ ( - P95/300) = 0.05e^(-1/3)

P95 = -300 ln ( 0.05e^(-1/3) )

= 999

= 1000

8 0

2 years ago

A certain article indicates that in a sample of 1,000 dog owners, 610 said that they take more pictures of their dog than of the

lbvjy [14]

Answer:

(a) The 90% confidence interval is: (0.60, 0.63) Correct interpretation is (3).

(b) The 95% confidence interval is: (0.42, 0.46) Correct interpretation is (1).

(c) First, the confidence level in part(b) is more than the confidence level in part(a) is, so the critical value of part(b) is more than the critical value of part(a), Second the margin of error in part(b) is more than than in part(a).

Step-by-step explanation:

(a)

Let X = number of dog owners who take more pictures of their dog than of their significant others or friends.

Given:

X = 610

n = 1000

Confidence level = 90%

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The sample proportion is:

$\hat p=\frac{X}{n}=\frac{610}{1000}=0.61$

The critical value of z for a 90% confidence level is:

$z_{\alpha/2}=z_{0.10/2}=z_[0.05}=1.645$

Construct a 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends as follows:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.61\pm 1.645\sqrt{\frac{0.61(1-0.61}{1000}}\\=0.61\pm 0.015\\=(0.595, 0.625)\\\approx(0.60, 0.63)$

Thus, the 90% confidence interval for the population proportion of dog owners who take more pictures of their dog than their significant others or friends is (0.60, 0.63).

Interpretation:

There is a 90% chance that the true proportion of dog owners who take more pictures of their dog than of their significant others or friends falls within the interval (0.60, 0.63).

Correct option is (3).

(b)

Let X = number of dog owners who are more likely to complain to their dog than to a friend.

Given:

X = 440

n = 1000

Confidence level = 95%

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

The sample proportion is:

$\hat p=\frac{X}{n}=\frac{440}{1000}=0.44$

The critical value of z for a 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Construct a 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend as follows:

$CI=\hat p\pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.44\pm 1.96\sqrt{\frac{0.44(1-0.44}{1000}}\\=0.44\pm 0.016\\=(0.424, 0.456)\\\approx(0.42, 0.46)$

Thus, the 95% confidence interval for the population proportion of dog owners who are more likely to complain to their dog than to a friend is (0.42, 0.46).

Interpretation:

There is a 95% chance that the true proportion of dog owners who are more likely to complain to their dog than to a friend falls within the interval (0.42, 0.46).

Correct option is (1).

(c)

The confidence interval in part (b) is wider than the confidence interval in part (a).

The width of the interval is affected by:

The confidence level
Sample size
Standard deviation.

The confidence level in part (b) is more than that in part (a).

Because of this the critical value of z in part (b) is more than that in part (a).

Also the margin of error in part (b) is 0.016 which is more than the margin of error in part (a), 0.015.

First, the confidence level in part(b) is more than the confidence level in part(a) is, so the critical value of part(b) is more than the critical value of part(a), Second the margin of error in part(b) is more than than in part(a).

4 0

1 year ago

Jo is on the phone with a gardener who asks about the square feet of Jo's backyard. Jo counts 20 steps long and 40 steps wide (w

Sever21 [200]

Hey there!

Each step is three feet. This can be represented by 3s= feet. We can plug that in to figure out our side lengths.

20(3)=60

40(3)=120

Now we can multiply these two together to get the area.

120(60)= 7,200

Therefore, his backyard is about 7,200 square feet.

I hope this helps!

4 0

2 years ago

He temperature in Tampa, Florida is 15 degrees warmer than twice the temperature in Chicago, Illinois. The temperature in Tampa

dusya [7]

Answer:

2x+15=75

Step-by-step explanation:

Let the temperature of chicago be x

75-15=2x

Reversing the equation

2x+15=75

6 0

2 years ago

Read 2 more answers