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SOVA2 [1]
3 years ago
13

Help Help Help!!! :) solve the system of equations y=2x^2-3 y=3x-1

Mathematics
1 answer:
stellarik [79]3 years ago
4 0
Solution:  
y = 2x^2 - 3 ---- equation 1
 y = 3x - 1 ------equation 2 
 Then we get, 
 2x^2 - 3 = 3x - 1 
 Now, simplifying the equation, we get 
 2x^2 - 3x - 3 + 1 = 0
 2x^2 - 3x - 2 = 0 
 After factoring the equation, we get
 (2x+1)(x-2) = 0 
 So, this means
 (2x+1) = 0 and (x-2) = 0 
 From this, we get 
 x = -1/2 and x = 2 
 Putting values of x = -1/2 in equation 2 
 y = 3(-1/2) - 1
 y = -2.5 
 Now, putting value of x = 2 in equation 2 
 y = 3(2) -1
 y = 5
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Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement
Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

p = 0.173, n = 120. So

\mu = E(X) = np = 120*0.173 = 20.76

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

Z = \frac{X - \mu}{\sigma}

Z = \frac{34 - 20.76}{4.14}

Z = 3.2

Z = 3.2 has a pvalue of 0.9993

X = 21

Z = \frac{X - \mu}{\sigma}

Z = \frac{21 - 20.76}{4.14}

Z = 0.06

Z = 0.06 has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

6 0
3 years ago
Please I need help <br> No fake answers
Dominik [7]

y=13x+5 ===(0,5) , (-2, -21)

y=-3x ===(0,0) , (-3,9)

y=x-10 ===(8,-2) , (-5, -15)

5 0
3 years ago
Which rate is the lowest price?
lubasha [3.4K]

Answer:

The correct answer is$5.50 for 5

Step-by-step explanation:

5.50/5=1.1

3 0
3 years ago
Read 2 more answers
Select the correct answer.
gtnhenbr [62]

Answer:

5 years

Step-by-step explanation:

To determine the number of years needed for the company to process a certain amount of milk, we use the given function which relates the number of years, x, and the gallons of milk, y. We simply substitute the number of gallons to y and solve for x.  

y = x^6 − 9x^4 + 70x^2

630 = x^6 − 9x^4 + 70x^2

Solving for x, we will have

x = 4.8866 years or approximately 5 years

Hope this answer helps you :)

Have a great day

Mark brainliest

7 0
2 years ago
Order from least to greatest. 7/25, 6/25, 11/50.
fenix001 [56]
7/25, 6/25, and 11/50. Looks like they are already in order, or you meant to do that... 
3 0
3 years ago
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