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zhuklara [117]
3 years ago
6

What are the factors of x^2+4x+3​

Mathematics
2 answers:
lianna [129]3 years ago
5 0

Answer:

(x+3)(x+1)

Step-by-step explanation:

x^2+4x+3​

What 2 numbers multiply to 3 and add to 4

3*1 =3

3+1 = 4

(x+3)(x+1)

r-ruslan [8.4K]3 years ago
4 0

Answer:

<h2>(x + 1)(x + 3)</h2>

Step-by-step explanation:

"First notice that the function is a quadratic and so will have two factors. Since the coefficient of  

x 2  is 1, the factors will be of the form:  

( x + a ) ( x + b )

We will assume that a and b are integers.

Hence, we need to find a and b such that the product of the factors is equal to the given quadratic function .

Now consder the absoute value of constant term, 3. Since 3 is prime its only factors are 3 and 1. Since the constant term is positive, a and b can only be 3 and 1 or -3 and -1.

Finally observe that the coefficient of  x  is positive 4 and that the sum of 3 and 1 is positive 4. Thus, a and b must be 3 and 1 (or the other way around, but this makes no difference to our factorisation) "

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Answer:

(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942  

(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978  

And the 90% confidence interval would be given (0.0942;0.09978).  

We are confident at 90% that the difference between the two proportions is between 0.0942 \leq p_A -p_B \leq 0.09978

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

p_A represent the real population proportion female for Biology

\hat p_A =\frac{84199}{144796}=0.582 represent the estimated proportion female for biology

n_A=144796 is the sample size for A

p_B represent the real population proportion female for calculus AB

\hat p_B =\frac{102598}{211693}=0.485 represent the estimated proportion female for Calculus AB

n_B=211693 is the sample size required for B

z represent the critical value for the margin of error  

The population proportion have the following distribution  

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})  

The confidence interval for the difference of two proportions would be given by this formula  

(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}  

For the 90% confidence interval the value of \alpha=1-0.90=0.1 and \alpha/2=0.05, with that value we can find the quantile required for the interval in the normal standard distribution.  

z_{\alpha/2}=1.64  

And replacing into the confidence interval formula we got:  

(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942  

(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978  

And the 90% confidence interval would be given (0.0942;0.09978).  

We are confident at 90% that the difference between the two proportions is between 0.0942 \leq p_A -p_B \leq 0.09978

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