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3 years ago

Mrs.Kunkleman asks her students to write the Pythagorean theorem in their own words

Mathematics

1 answer:

masha68 [24]3 years ago

5 0

Step-by-step explanation:

The Pythagorean theorem can be understood as a mathematical relationship between the sides of a right triangle that helps to understand geometric problems in real situations, such as finding measurements, calculating areas, etc.

The theorem says that the square of the hypotenuse is equal to the sum of the squares on the other sides.

In a right triangle the hypotenuse is the longest side of the triangle, on the side opposite to its longest angle, and the other two sides will be the sides. So the Pythagorean theorem formula is:

a² = b² + c²

where a represents the hypotenuse and b and c the other sides.

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The authors of a paper describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked

Serggg [28]

Answer:

a) The 99% confidence interval would be given by (24.409;24.979)

b) n=464

Step-by-step explanation:

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".

Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=47-1=46$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,46)".And we see that $t_{\alpha/2}=2.01$

Now we have everything in order to replace into formula (1):

$525-2.01\frac{75}{\sqrt{47}}=503.01$

$525+2.01\frac{75}{\sqrt{47}}=546.99$

So on this case the 95% confidence interval would be given by (503.01;546.99)

Part b

The margin of error is given by this formula:

$ME=t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And on this case we have that ME =7 msec, we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{t_{\alpha/2} s}{ME})^2$ (2)

The critical value for 95% of confidence interval is provided, $t_{\alpha/2}=2.01$ from part a, replacing into formula (2) we got:

$n=(\frac{2.01(75)}{7})^2 =463.79 \approx 464$

So the answer for this case would be n=464 rounded up to the nearest integer

8 0

3 years ago

Graph by using the slope and the y intercept.

Mashutka [201]

1. a) equation of the line :

$y = \dfrac{2}{5}x - 7$

y - intercept = -7

so, it will pass through point (0, -7)

and if we plug the value of x as 5, we get

$y = (\dfrac{2}{5} \times 5) - 7$

$y = 2 - 7$

$= - 5$

so, it will pass through point (5, -5) too

now, just plot the points (0 , -7) and (5 , -5) and join them.

2. b) equation of line is :

$y = - 3x + 5$

here, y - intercept = 5

so the line passes through point (0 , 5)

now, Plugging the value of x = 1 we get :

$y =( - 3 \times 1) + 5$

$y = - 3 + 5$

$y = 2$

so, the given line passes through point (1 , 2)

plotting the points, we can get our required line.

6 0

3 years ago

given y>0 and dy/dx=(3x^2+4x)/yif the point (1,√10) is on the graph relating x and y, then what is y when x=0

jonny [76]

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{3x^2+4x}y\iff y\,\mathrm dy=(3x^2+4x)\,\mathrm dx$
$\implies\displaystyle\int y\,\mathrm dy=\int(3x^2+4x)\,\mathrm dx$
$\implies \dfrac12y^2=x^3+2x^2+C$

When $x=1$ you have $y=\sqrt{10}$ , so

$\dfrac12(\sqrt{10})^2=1^3+2(1)^2+C\implies 5=1+2+C\implies C=2$

and so the particular solution to the ODE is

$\dfrac12y^2=x^3+2x^2+2$

Then when $x=0$ , you get

$\dfrac12y^2=0^3+2(0)^2+2=2$
$\implies y^2=4$
$\implies y=2$

where we omitted the negative root because it's given that $y>0$ .