What are the integers of 171

Answers

Answer 1

Answer:

Answer:

56, 57, and 58.

Step-by-step explanation:

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Given C=n+15, determine the value of C when n=4

Answers

Answer:

Step-by-step explanation:

If N=4 and the problem is C= N+15 that means you add 4 to 15 and then get 19 which will be your answer for C. You can also check this by subtracting 19-15 or 19-4!!! I hope this helps!!! Have a great day whom ever you are

Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 64x2 + 81y2 = 1. $ L=\iint_{R} {\color{red}9} \sin ({\color{red}384} x^{2} + {\color{red}486} y^{2})\,dA $.

Answers

$\displaystyle\iint_R\sin(384x^2+486y^2)\,\mathrm dA$

Notice that Given that $R$ is an ellipse, consider a conversion to polar coordinates:

$\begin{cases}x(r,\theta)=\frac r8\cos\theta\ny(r,\theta)=\frac r9\sin\theta\end{cases}$

The Jacobian for this transformation is

$J=\begin{bmatrix}\frac18\cos\theta&-\frac r8\sin\theta\n\frac19\sin\theta&\frac r9\cos t\end{bmatrix}$

with determinant $\det J=\frac r{72}$

Then the integral in polar coordinates is

$\displaystyle\frac1{72}\int_0^(\pi/2)\int_0^1\sin(6r^2\cos^2t+6r^2\sin^2t)r\,\mathrm dr\,\mathrm d\theta=\int_0^(\pi/2)\int_0^1r\sin(6r^2)\,\mathrm dr\,\mathrm d\theta=\boxed{(\pi\sin^23)/(864)}$

where you can evaluate the remaining integral by substituting $s=6r^2$ and $\mathrm ds=12r\,\mathrm dr$ .

Final answer:

To evaluate the integral, we make a change of variables using the transformation x=u/8 and y=v/9 to transform the region into a unit circle. Then we convert the integral to polar coordinates and evaluate it.

Explanation:

To evaluate the given integral, we can make the appropriate change of variables by using the transformation x = u/8 and y = v/9. This will transform the region R into a unit circle. The determinant of the Jacobian of the transformation is 1/72, which we will use to change the differential area element from dA to du dv. Substituting the new variables and limits of integration, the integral becomes:

L = \iint_{R} 9 \sin (612 u^{2} + 768 v^{2}) \cdot (1/72) \,du \,dv

Next, we can convert the integral from Cartesian coordinates(u, v) to polar coordinates (r, \theta). The integral can be rewritten as:

L = \int_{0}^{2\pi} \int_{0}^{1} 9 \sin (612 r^{2} \cos^{2}(\theta) + 768 r^{2} \sin^{2}(\theta)) \cdot (1/72) \cdot r \,dr \,d\theta

We can then evaluate this integral to find the value of L.

Learn more about Evaluation of Integrals here:

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A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the student guesses the whole test, the expected number of correct answers is 20 with a standard error of .Compute the z-test statistic for the observed value 13.Find the observed significance level or P-value of the statistic.

Answers

Answer:

$z=(13-20)/(4)=-1.75$

Assuming:

H0: $\mu \geq 20$

H1: $\mu <20$

$p_v = P(Z<-1.75) = 0.0401$

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

$X \sim Binom(n=100, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^(n-x)$

Where (nCx) means combinatory and it's given by this formula:

$nCx=(n!)/((n-x)! x!)$

We need to check the conditions in order to use the normal approximation.

$np=100*0.2=20 \geq 10$

$n(1-p)=20*(1-0.2)=16 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=100*0.2=20$

$\sigma=√(np(1-p))=√(100*0.2(1-0.2))=4$

So we can approximate the random variable X like this:

$X\sim N(\mu =20, \sigma=4)$

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". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z<b)$

The z score is given by this formula:

$z=(x-\mu)/(\sigma)$

If we replace we got:

$z=(13-20)/(4)=-1.75$

Let's assume that we conduct the following test:

H0: $\mu \geq 20$

H1: $\mu <20$

We want to check is the score for the student is significantly less than the expected value using random guessing.

So on this case since we have the statistic we can calculate the p value on this way:

$p_v = P(Z<-1.75) = 0.0401$

1+1+2+2+8+19+1234385993 hehe i will brainlest

Answers

Answer: 1234386026

Step-by-step explanation:

Answer:

1,234,386,030

Step-by-step explanation:

A truck averages 20 miles per gallon. The equation m = 20g represents the relationshi, where m is the yotal miles a trick can go and g is the gallons of gas in the tank. How far can the truck go on 6, 8, or 10 gallons of gas?

Answers

Answer:
6 gallons = 120 miles
8 gallons = 160 miles
10 gallons = 200 miles

Multiply 20, the number of miles you get per gallon by the number of gallons of has you put into the truck.

Example:
10gallons x 20miles per gallon = 200 miles

Find an equation of the circle that satisfies the given conditions. (Give your answer in terms of x and y.)Center

(4, −5)

and passes through

(7, 4)

Answers

Answer:

$(x-4)^2+(y+5)^2=90$

Step-by-step explanation:

The equation of a circle of radius r, centered at the point (a,b) is

$(x-a)^2+(y-b)^2=r^2$

We already know the center is at $(4,-5)$ , we are just missing the radius. To find the radius, we can use the fact that the circle passes through the point (7,4), and so the radius is just the distance from the center to this point (see attached image). So we find the distance by using distance formula between the points (7,4) and (4,-5):

radius $=√((7-4)^2+(4-(-5))^2)=√(3^2+9^2)=√(90)$

And now that we know the radius, we can write the equation of the circle:

$(x-4)^2+(y-(-5))^2=√(90)^2$

$(x-4)^2+(y+5)^2=90$

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