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ohaa [14]
2 years ago
15

Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the

solution set be identin
y < x^2 - 3
y > x^2 + 2

Mathematics
1 answer:
Norma-Jean [14]2 years ago
7 0

The graphs of f(x) and g(x) are transformed function from the function y = x^2

The set of inequalities do not have a solution

<h3>How to modify the graphs</h3>

From the graph, we have:

f(x) = x^2 -3 and g(x) = -x^2 +2

To derive y < x^2 - 3, we simply change the equality sign in the function f(x) to less than.

To derive y > x^2 + 2, we perform the following transformation on the function g(x)

  • Shift the function g(x) down by 2 units
  • Reflect across the x-axis
  • Shift the function g(x) down by 3 units
  • Change the equality sign in the function g(x) to greater than

<h3>How to identify the solution set</h3>

The inequalities of the graphs become

y < x^2 - 3 and y > x^2 + 2

From the graph of the above inequalities (see attachment), we can see that the curves of the inequalities do not intersect.

Hence, the set of inequalities do not have a solution

Read more about inequalities at:

brainly.com/question/25275758

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If the product of a number and -4 is subtracted from the number, the result is 3 more than the number. Find the number
lesya [120]

Answer: The number is 0.75 or 3/4

Step-by-step explanation:

let x = the number.

Now set up an equation: The product of a number (x) and -4 = -4x. So -4x is subtracted from the number - x.     x-(-4x)

Then, that equals 3 more than the number (x) = x+3

So the equation is x-(-4x)=x+3.

Then, solve the equation!

x-(-4x)=x+3

x+4x=x+3  (Distribute the negative to the parentheses)

5x=x+3  (Combine like terms)

4x=3  (Get the Xs on one side by subtracting x from both sides)

x=0.75 or 3/4  (divide by the coefficiant, 4, on both sides)

3 0
3 years ago
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f the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many
Oksanka [162]

Answer:

n=1849

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".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.03 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Assuming that the proportion is estimated \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.03}{2.58})^2}=1849  

And rounded up we have that n=1849

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3 years ago
Which story problem is solved using multiplication? Answer options with 5 options
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D is the answer because it says each and that’s a key word to understand that it’s multiplying
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Adult male heights have a normal probability distribution with a mean of 70 inches and a standard deviation of 4 inches. What is
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Answer: 0.5

Step-by-step explanation:

Given : Adult male heights have a normal probability distribution .

Population mean : \mu = 70 \text{ inches}

Standard deviation: \sigma= 4\text{ inches}

Let x be the random variable that represent the heights of adult male.

z-score : z=\dfrac{x-\mu}{\sigma}

For x=70, we have

z=\dfrac{70-70}{4}=0

Now, by using the standard normal distribution table, we have

The probability that a randomly selected male is more than 70 inches tall :-

P(x\geq70)=P(z\geq0)=1-P(z

Hence, the probability that a randomly selected male is more than 70 inches tall = 0.5

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