Which of the following points satisfies the inequality y>1/3x-2 which side should be shaded

Sergio [31]

$\dfrac{e^x-e^{-x}}{e^x+e^{-x}}=t\\\\
\dfrac{e^{2x}-1}{e^{2x}+1}=t\\\\
e^{2x}-1=t(e^{2x}+1)\\\\
e^{2x}-1=e^{2x}t+t\\\\
e^{2x}-e^{2x}t=t+1\\\\
e^{2x}(1-t)=t+1\\\\
e^{2x}=\dfrac{t+1}{1-t}\\\\
e^{2x}=-\dfrac{t+1}{t-1}\\\\
2x=\ln\left(-\dfrac{t+1}{t-1}\right)\\\\
x=\dfrac{\ln\left(-\dfrac{t+1}{t-1}\right)}{2}\qquad t\in(-1,1)



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8 0

3 years ago

Read 2 more answers

In Mohammad’s class, 80% of the students are boys. There are 24 boys in the class. What is the total number of students in Moham

irina1246 [14]

Answer:

30 students

Step-by-step explanation:

80% of N = 24 where N is the total number of students

So

.80 N = 24

N = 24 / .80 = 30

sorry this was a late response

6 0

3 years ago

A grinding wheel manufacturer designed a new grinding wheel. Repeated tests were conducted on wheels of approximately the same w

sergejj [24]

Answer:

a) $a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

b) $P(X \geq 3) = 1-P(X$

c) $P(\bar X \geq 225)=1- P(\bar X$

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Part a

Let X the random variable that represent the cuts of a population, and for this case we know the distribution for X is given by:

$X \sim N(225,16.5)$

Where $\mu=225$ and $\sigma=16.5$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.25$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=0.674=\frac{a-225}{16.5}$

And if we solve for a we got

$a=225 +0.674*16.5=236.121$

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

$X\sim Bin(n=10, p=0.25)$

And we want this probability:

$P(X \geq 3) = 1-P(X$

We can find the individual probabilities like this:

$P(X=0)=(10C0)(0.25)^0 (1-0.25)^{10-0}=0.0563$

$P(X=1)=(10C1)(0.25)^1 (1-0.25)^{10-1}=0.1877$

$P(X=2)=(10C2)(0.25)^2 (1-0.25)^{10-2}=0.2816$

$P(X \geq 3) = 1-P(X$

Part c

For this case we know that the distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And we want this probability:

$P(\bar X \geq 225)$

And for this case we can use the complement rule and the z score given by:

$z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we replace we got:

$P(\bar X \geq 225)=1- P(\bar X$

4 0

3 years ago

If the equation is translated left 1 unit and down 5 units , what is the new equation

STatiana [176]

6 I believe I’m not sure

6 0

3 years ago

) Evaluating a polynomial limit analytically You should have learned by now the process for finding the derivative of a polynomi

wolverine [178]

Answer:

This code or is program to find a given value of derivative of a polynomial.

Step-by-step explanation:

We know already how to apply or make the procedures mathematically talking so this short program will eventually help you how to find logic.

// libraries

#include <stdio.h>

#include <conio.h>

//use to control floating elements

float poly(float a[], int, float);

//main

int main()

{

// Enter the degree of polynomial equation

float x, a[10], y1;

int deg, i;

printf("Enter the degree of polynomial equation: ");

scanf("%d", &deg);

printf("Ehter the value of x for which the equation is to be evaluated: ");

// Enter the coefficient of x to the power

scanf("%f", &x);

for(i=0; i<=deg; i++)

{

printf("Enter the coefficient of x to the power %d: ",i);

scanf("%f",&a[i]);

}

// The value of polynomial equation for the value of x

y1 = poly(a, deg, x);

printf("The value of polynomial equation for the value of x = %.2f is: %.2f",x,y1);

return 0;

}

/* function for finding the value of polynomial at some value of x */

float poly(float a[], int deg, float x)

{

float p;

int i;

p = a[deg];

for(i=deg;i>=1;i--)

{

p = (a[i-1] + x*p);

}

return p;

}

8 0

2 years ago