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3 years ago

HHHHHHHHHHHHHHHHHHHHHHHHHHHHEEEEEEEEEEEEEEEEEEEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPP 30 POINTS

Mathematics

1 answer:

Vinvika [58]3 years ago

7 0

Answer:

7.28 units

Step-by-step explanation:

Using the Pythagorean theorem, $a^{2} + b^{2} = c^{2}$ , we get:

$2^{2}+7^{2}=c^{2}\\4+49=c^{2}\\53=c^2\\\sqrt{53}=c\\c=\sqrt{53}$

$\sqrt{53}$ ≈ 7.28

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A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a ne

Evgen [1.6K]

Answer:

a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between 0.6290 and 0.6948.

b. If the sample size is changed, the confidence interval changes as the standard error depends on sample size.

About 90% percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about 10% percent will not contain the true population proportion.

Step-by-step explanation:

We have to calculate a 90% confidence interval for the proportion.

The sample proportion is p=0.6619.

$p=X/n=370/559=0.6619$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.6619*0.3381}{559}}\\\\\\ \sigma_p=\sqrt{0.0004}=0.02$

The critical z-value for a 90% confidence interval is z=1.6449.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.6449 \cdot 0.02=0.0329$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.6619-0.0329=0.6290\\\\UL=p+z \cdot \sigma_p = 0.6619+0.0329=0.6948$

The 90% confidence interval for the population proportion is (0.6290, 0.6948).

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3 years ago

The coordinates of an ordered pair have opposite signs. In which quadrant(s) must the ordered pair lie?

Virty [35]

If they have opposite signs the point can be in either the second or fourth quadrants.

-x and +y is in the second quadrant

+x and -y is in the fourth quadrant.

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4 years ago

Read 2 more answers

Finding an Equation of a Tangent Line In Exercise, use implicit differentiation to find an equation of the tangent line to the g

timofeeve [1]

Answer:

Equation of tangent line at point (1,0) to given function is

y=x-1

Step-by-step explanation:

Equation of tangent line is

y-y₁=m(x-x₁)-----(1)

where m is slope of line and can be found by implicitly differentiating the given function w.r.to x

$x+y-1=ln(x^{2}+y^{2})\\\\\frac{d}{dx}(x+y-1)=\frac{d}{dx}(ln(x^{2}+y^{2})\\\\1+\frac{dy}{dx}=\frac{2x}{x^{2}+y^{2}}+\frac{2y}{x^{2}+y^{2}}\frac{dy}{dx}\\\\\frac{dy}{dx}=\frac{2x-x^{2}-y^{2}}{x^{2}+y^{2}-2y}\\\\at \,(1,0)\\\\\frac{dy}{dx}=\frac{2(1)-1-0}{1+0-0}\\\\\frac{dy}{dx}=1\\\\$