Three times a number r plus 8 is fewer than -12

Weight gain during pregnancy. In 2004, the state of North Carolina released to the public a large data set containing informatio

Kryger [21]

Answer:

From the given data, there is not enough evidence to prove that there is a statistically significant difference between the two population means

Step-by-step explanation:

The number of younger moms, in the study = 837

The average weight gain of younger moms, $\overline x$ ₁ = 30.67 pounds

The standard deviation of the weight gain of younger moms, s₁ = 14.69 pounds

(30.67 - 28.52)/√((14.69^2)/837 + 13²/143))

The number of younger moms, in the study = 143

The average weight gain of mature moms, $\overline x$ ₂ = 28.52 pounds

The standard deviation of the weight gain of mature moms, s₂ = 13 pounds

The test statistic for the difference in two populations is given as follows;

$t=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{s_1^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}$

Therefore, we get;

$t=\dfrac{(30.67-28.52)}{\sqrt{\dfrac{14.69^{2} }{837}-\dfrac{13^{2}}{143}}} \approx 1.7919$

The test statistic ≈ (1.7919)

Using a graphing calculator, we get;

The critical-t = ±1.971379, p = 0.07459697

Therefore, given that the test statistic, (1.7919), < critical-t (0.07459697), we fail to reject the null hypothesis, therefor, the given data does not provide convincing evidence that there is a significant difference between the two population means

7 0

3 years ago

Can you guys help me on the number 2 I’m really stuck

JulsSmile [24]

Answer:

we have to see question 1 to help with number two

5 0

3 years ago

show that the curve has 3 points of inflection and they all lie on 1 straight line:\[y=\frac{1+x}{1+x^{2}}\]

ohaa [14]

Y = (1 + x) / (1 + x^2)

y'
= [(1 + x^2)(1) - (1 + x)(2x)] / (1 + x^2)^2
= [1 + x^2 - 2x - 2x^2] / (1 + x^2)^2
= [-x^2 - 2x + 1] / (1 + x^2)^2

y''
= [(1 + x^2)^2 * (-2x - 2) - (-x^2 - 2x + 1)(2)(1 + x^2)(2x)] / (1 + x^2)^4
= [(1 + x^2)(-2x - 2) - (4x)(-x^2 - 2x + 1)] / (1 + x^2)^3
= [(-2x - 2x^3 - 2 - 2x^2) - (-4x^3 - 8x^2 + 4x)] / (1 + x^2)^3
= [-2x - 2x^3 - 2 - 2x^2 + 4x^3 + 8x^2 - 4x] / (1 + x^2)^3
= [2x^3 + 6x^2 - 6x - 2] / (1 + x^2)^3

Setting y'' to zero, we have:
y'' = 0
[2x^3 + 6x^2 - 6x - 2] / (1 + x^2)^3 = 0
(2x^3 + 6x^2 - 6x - 2) = 0

Using trial and error, you will realise that x = 1 is a root.
This means (x - 1) is a factor.
Dividing 2x^3 + 6x^2 - 6x - 2 by x - 1 using long division, you will have 2x^2 + 8x + 2.

2x^2 + 8x + 2
= 2(x^2 + 4x) + 2
= 2(x + 2)^2 - 2(2^2) + 2
= 2(x + 2)^2 - 8 + 2
= 2(x + 2)^2 - 6

Setting 2x^2 + 8x + 2 to zero, we have:
2(x + 2)^2 - 6 = 0
2(x + 2)^2 = 6
(x + 2)^2 = 3
x + 2 = sqrt(3) or = -sqrt(3)
x = -2 + sqrt(3) or x = -2 - sqrt(3)

Note that -2 - sqrt(3) < -2 + sqrt(3) < 1
We will choose random values belonging to each interval and test them out.

-5 < -2 - sqrt(3) < -2 < -2 + sqrt(3)
f''(-5) = [2(-5)^3 + 6(-5)^2 - 6(-5) - 2] / (1 + (-5)^2)^3 = -9/2197 < 0
f''(-2) = [2(-2)^3 + 6(-2)^2 - 6(-2) - 2] / (1 + (-2)^2)^3 = 18/125 > 0
Note that one value is positive and the other is negative.
Thus, x = -2 - sqrt(3) is an inflection point.

-2 - sqrt(3) < -2 < -2 + sqrt(3) < 0 < 1
f''(-2) = [2(-2)^3 + 6(-2)^2 - 6(-2) - 2] / (1 + (-2)^2)^3 = 18/125 > 0
f''(0) = [2(0)^3 + 6(0)^2 - 6(0) - 2] / (1 + (0)^2)^3 = -2 < 0
Note that one value is positive and the other is negative.
Thus, x = -2 + sqrt(3) is also an inflection point.

-2 + sqrt(3) < 0 < 1 < 2
f''(0) = [2(0)^3 + 6(0)^2 - 6(0) - 2] / (1 + (0)^2)^3 = -2 < 0
f''(2) = [2(2)^3 + 6(2)^2 - 6(2) - 2] / (1 + (2)^2)^3 = 26/125 > 0
Note that one value is positive and the other is negative.
Thus, x = 1 is an inflection point.

Hence, we have three inflection points in total.

When x = -2 - sqrt(3), we have:
y
= (1 - 2 - sqrt(3)) / (1 + (-2 - sqrt(3))^2)
= (-1 - sqrt(3)) / (1 + 4 + 4sqrt(3) + 3)
= (-1 - sqrt(3)) / (8 + 4sqrt(3))

When x = -2 + sqrt(3), we have:
y
= (1 - 2 + sqrt(3)) / (1 + (-2 + sqrt(3))^2)
= (-1 + sqrt(3)) / (1 + 4 - 4sqrt(3) + 3)
= (-1 + sqrt(3)) / (8 - 4sqrt(3))

When x = 1, we have:
y
= (1 + 1) / (1 + 1^2)
= 2 / 2
= 1

Using the slope formula, we have:
(y - 1) / (x - 1) = [[(-1 + sqrt(3)) / (8 - 4sqrt(3))] - 1] / ( -2 + sqrt(3) - 1)
(y - 1) / (x - 1) = 1/4, which is the equation of the line which the inflection points at x = 1 and x = -2 + sqrt(3) lies on.

Note that I am skipping the intermediate steps for simplifying here, but the trick is to rationalise the denominator by multiplying a conjugate on both numerator and denominator.

Now, we just need to check that the inflection point at x = -2 - sqrt(3) lies on the same line as well.
L.H.S.
= [[(-1 - sqrt(3)) / (8 + 4sqrt(3))] - 1] / (-2 - sqrt(3) - 1)
= 1/4
= R.H.S.

Once again, I am skipping simplifying steps here.

Anyway, this proves all three points of inflection lies on the same straight line.

4 0

3 years ago

What is 12c - c____ in simplest form?

bagirrra123 [75]

Imagine that the variable c represents something tangible, like an orange. So what this equation is asking is subtract 1 orange from 12 oranges. So you are left with 11 oranges.

Another way to think about this problem is if you rewrite the equation slightly to:

12c - c =
12c - 1c =
11c

6 0

3 years ago

Find the area for the following figure. O 124. 86 cm2 62.93 cm2 26.5 cm2 137.45 cm2

Semmy [17]

The answer is 62.93

8 0

3 years ago