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3 years ago

What is the maximum vertical distance between the line y = x + 56 and the parabola y = x2 for −7 ≤ x ≤ 8?

1 answer:

5 0

-7 and 8 are the solutions to the given equation system.
Therefore, the maximum distance between the y values of the two equations must lie exactly between their points of intersection. That is on x value:
x = (-7 + 8)/2 = 0.5
The maximum distance is:
y = 0.5 + 56 = 56.5
y = 0.5² = 0.25
56.5 - 0.25 = 56.25 units

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A population is estimated to have a standard deviation of 9. We want to estimate the population mean within 2, with a 99% level

cupoosta [38]

Answer:

The sample required is $n = 135$

Step-by-step explanation:

From the question we are told that

The standard deviation is $\sigma = 9$

The margin of error is $E = 2$

Given that the confidence level is 99% then the level of significance is mathematically evaluated as

$\alpha = 100-99$

$\alpha = 1 \%$

$\alpha = 0.01$

Next we will obtain the critical value $\frac{\alpha }{2}$ from the normal distribution table(reference math dot armstrong dot edu) , the value is

$Z_{\frac{\alpha }{2} } = Z_{\frac{0.05 }{2} } = 2.58$

The sample size is mathematically represented as

$n = [ \frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ]^2$

substituting values

$n = [ \frac{ 2.58 * 9 }{2} ]^2$

$n = 135$

3 0

3 years ago

Select all the correct answers.

nalin [4]

Answer: B

Step-by-step explanation:

3 0

2 years ago

What is the graph of the linear function that is represented by the equation y= 1/2x-2

kondor19780726 [428]

Answer:

See picture attached.

Step-by-step explanation:

Start with the y-intercept of -2 and plot that on the graph. Then, use the slope of 1/2x to plot more points to help you draw the line. Remember rise over run. Go up one from the y-intercept and right two. If you need to, you can also go down one and left two.

Hope this makes sense.

7 0

3 years ago

Factor -24a3b3c3 - 84a4b2c.

sammy [17]

Answer:

-12a³b²c ( 2bc² + 7a)

Step-by-step explanation:

To factorize, we must separate the highest common factors between the products that make up the given expression. To get the highest common factor between the two products,

-24a3b3c3 = -2 * 2 *2 * 3 * a³ *b² *b * c² * c

- 84a4b2c = -2 * 2 *3 * 7 * a³ * a *b² * c

The common elements are -2, 2, 3, a³, b², c

The product of the common elements

= -12a³b²c

Hence, factorizing

-24a3b3c3 - 84a4b2c = -12a³b²c ( 2bc² + 7a)

4 0

3 years ago

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natima [27]

Answer:

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Step-by-step explanation:

3 0

3 years ago

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