MATHEMATICS COLLEGE

There are 24 boys for every 36 girls

Answers

Answer 1

Answer:

Answer:

2 boys for every 3 girls

Step-by-step explanation:

24/36 = 6/9 = 2/3, 2 boys for every 3 girls,

Answer 2

Answer:

Answer:

I think this is what the question is looking for. I hope this helps.

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Renya plans to make a down payment plus monthlypayments in order to buy a motorcycle. At one dealer
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Answers

Answer:

For the first, it would take 6 months to reach $3,500. For the second dealer, it would take 3 months to reach $3,500.

Explanation:

I hope this helps!

Compute the area of the region D bounded by xy=1, xy=16, xy2=1, xy2=36 in the first quadrant of the xy-plane. Using the non-linear change of variables u=xy and v=xy2, find x and y as functions of u and v.x=x(u,v)= ?

y=y(u,v)=?

Find the determinant of the Jacobian for this change of variables.

∣∣∣∂(x,y)/∂(u,v)∣∣∣=det=?

Using the change of variables, set up a double integral for calculating the area of the region D.

∫∫Ddxdy=?

Evaluate the double integral and compute the area of the region D.

Area =

Answers

Answer:

53.7528

Step-by-step explanation:

Notice that when

$xy = 1 ,\,\,\, xy = 16 , \,\,\, xy^2 = 1 \,\,\,, xy^2 = 36 \n\n$

If you set

$u = xy , v = xy^2$

as they suggest, then

$y = (v)/(u)} \,\,\,\, \text{and} \,\,\,\, \n\n{\displaystyle x = (u)/(y) = (u)/(v/u) = (u^2)/(v)$

Then

${\diplaystyle (\partial(x,y))/(\partial(u,v))} =\det \begin{pmatrix} 2u/v && -u^2/v^2 \n -v/u^2 && 1/u \end{pmatrix} = (1)/(v) }$

Therefore

$\iint\limits_(D) dx\,dy = \int\limits_(1)^(36)\int\limits_(1)^(16) (1)/(v) \, du \, dv = 15 \ln(36) = 53.7528$

A Jacobian matrix is formed by the first partial derivatives of a multivariate function that utilizes a training algorithm, and further calculation as follows:

Jacobian:

To evaluate the integral, cover the bounds, the integrand, and the differential area dA.

Transform the four equations in terms of u and v, notice that $u= xy \ \ and \ \ xy = 1, xy = 16$

implies that $1\leq u \leq 16.$

Similarly, $v= xy^2\ \ and\ \ xy^2= 1 , xy^2= 25$ implies that $1 \leq v \leq 25$

so write this integration region as $S= {(u,v) |1 \leq u \leq 18, 1 \leq v \leq 25}.$

Translate the equations from uv - plane to xy- plane. It is obtained by solving,

$u= xy, y= xy^2 \n\n\left.\begin{matrix}u=xy & \n v=xy^2& \end{matrix}\right\} \to \left.\begin{matrix}u^2=x^2y^2 & \n v=xy^2& \end{matrix}\right\} \n\n\to x=(u^2)/(v), y=(v)/(u)$

Convert dA part of the integral , using is $dA= |(\partial (x,y))/(\partial(u,v))| dudv.$

That is, $dA= \begin{vmatrix}(\partial x)/(\partial u) & (\partial x)/(\partial v)\n (\partial y)/(\partial u) & (\partial y)/(\partial v) \end{vmatrix} \ du dv \n\n$

Sampule the partial derivatives to find the Jacobian.

$dA=\begin{vmatrix}(2u)/(v) &-(u^2)/(v^2) \n -(v)/(u^2) &(1)/(u) \end{vmatrix} \ dudv\n\n=[((2u)/(v)) ((1)/(u)) -(- (u^2)/(v^2))(-(v)/(u^2))]\ du dv\n\n=((2)/(v)- (1)/(v)) \ dudv\n\n=(1)/(v)\ du dv\n\n$

The Jacobian the transformation is $dA= (1)/(v)dudv$

The region is $S={(u,v) |1\leq u \leq 16, 1\leq v\leq 25}.$

Rewrite the integral, using the transformation: $S,\ x=(u^2)/(v) =, y=(v)/(u) \ \ and\ \ dA=(1)/(v) dudv\n\n\int\int_R 1dA =\int \int_S (1)/(v)\ dudv= \int^(25)_(1) \int^(16)_(1) \ (1)/(v) \ dudv\n\n$

Evaluate the inner integral with respect to u.

$\to \int\int_R 1dA = \int^(25)_(1) \int^(16)_(1) \ (1)/(v) \ dudv\n\n$

by solving the value we get

$= 30 \ ln (5) \approx 48.28$

Find out more about the Jacobians here:

brainly.com/question/9381576

People tend to evaluate the quality of their lives relative to others around them (Frieswijk et al., 2004). In one study, researchers conducted interviews with n = 9 frail elderly people. During the interview, each person was compared with a fictitious person who was worse off than the elderly person. The scores below are the measures from a life-satisfaction scale for the elderly sample. Assume that the average score on this scale in the population is u = 20. Are the data sufficient to conclude that the elderly people in this sample are either significantly more or less satisfied than others in the general population? The life-satisfaction scores for the sample are 18, 23, 24, 22, 19, 27, 23, 26, 25. a. Which kind of t-test should you use? b. How many tails should the test have? Circle a word or phrase in the problem that told you this. c. State the null and alternative hypotheses in statistical notation: d. Determine the critical t using an alpha = .05. Sketch the null distribution, note the location of the critical t, and shade the critical region. e. Calculate the t-statistic and plot it on the sketch you drew above. f. Make a decision (either reject the null or fail to reject it)

Answers

Answer:

Step-by-step explanation:

Hello!

Research.

n=9 frail elderly were interview and compared to a fictitious person who was worse off then the interviewee, a life-satisfaction score was determined for each person.

18, 23, 24, 22, 19, 27, 23, 26, 25

Assuming that the population average score is μ= 20, the researchers think that the elderly in the sample are more or less satisfied than others in the general population.

a. You have the information of one sample, assuming this sample has a normal distribution and each elderly interviewed is independent, then the t-test of choice is a one-sample t-test.

b. and c. If you say that the elderly are "more or less" satisfied than the others, this means that they are either as satisfied as to the general population or not satisfied as to the general population. Symbolically:

H₀: μ = 20

H₁: μ ≠ 20

This is a two-tailed test, meaning, you will have two critical regions.

α: 0.05

Left critical value: $t_(n-1;/\alpha 2) = t_(8; 0.025)= -2.306$

Right critical value: $t_(n-1;1-\alpha /2) = t_(8;0.975) = 2.306$

$t_(H_0)= (X[bar]-Mu)/((S)/(√(n) ) ) ~t_(n-1)$

X[bar]= 23

S= 3

$t_(H_0)= (23-20)/((3)/(√(9) ) )= 3$

Considering that the calculated t-value is greater than the right critical value, the decision is to reject the null hypothesis, so using a significance level of 5% you can conclude that the average life-satisfaction score of the elderly is different than 20.

I hope it helps!

Verify the identity Cotx/tanx+cotx = 1-sin^2x

Answers

$\bf sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \n\n\n tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}\n\n -------------------------------\n\n \cfrac{cot(x)}{tan(x)+cot(x)}=1-sin^2(x) \n\n\n \textit{doing the left-side}\implies \cfrac{(cos(x))/(sin(x))}{(sin(x))/(cos(x))+(cos(x))/(sin(x))}\implies \cfrac{(cos(x))/(sin(x))}{(sin^2(x)+cos^2(x))/(cos(x)sin(x))}$

$\bf \cfrac{(cos(x))/(sin(x))}{(1)/(cos(x)sin(x))}\implies \cfrac{cos(x)}{\underline{sin(x)}}\cdot \cfrac{cos(x)\underline{sin(x)}}{1}\implies cos^2(x)\implies 1-sin^2(x)$

Help plsss it’s timed i need to passss plsss

Answers

Answer:

65°

Step-by-step explanation:

To obtain Angle A, we use the cosine rule ;

Cos A = (b² + c² - a²) / 2bc

Cos A = (12² + 14² - 14²) / 2(12)(14)

Cos A = 144 / 336

A = Cos^-1(144/336)

A = 64.62°

A = 65°

PLEASE HELP !!!!! 1) Find the equation of the trend line (line of best fit). SHOW WORK

2) Predict the number of tips that would be collected if 100 costumers were served at the restaurant on a given day. Explain your reasoning.

3)EXPLAIN how to use the regression calculator to make a reasonable prediction given a data table

(I don't know how to attach more than 1 picture by the way )

Answers

Answer:

1) y = 1.8741176487x + 3.655964863

2) About $191 using the equation, about $180 or more using the data you are given.

3) I can use the regression calculator by using the largest number of customers you have in the data set and lowest number of customers and compare them to see if the numbers are in ascending or descending order.

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