Evaluate variable expressions involving integers

A number, y, is equal to the difference of a larger number and 3. The same number is one-third of the sum of the large number an

Aleonysh [2.5K]

<span>Let the larger number be x.

</span><span>A number, y, is equal to the difference of a larger number and 3.

y = x - 3

x - y = 3

</span>The same number is one-third of the sum of the large number and 9.

y = (1/3)(x + 9)

3y = x + 9

x - 3y = -9

The equations are:
x - y = 3
x - 3y = -9

5 0

2 years ago

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Using the power series methods solve the 1st order Lane-Emden Equation:

nikklg [1K]

Answer:

Step-by-step explanation:

xy = 2y + xy = 0

Hence, 2y + xy = 0 ---------(1)

Differentiating equation (1) n times by Leibnitz theorem, gives:

2y(n) + xy(n) + ny(n - 1) = 0

Let x = 0: 2y(n) + ny(n - 1) = 0

2y(n) = -ny(n - 1)

∴ y(n) = -ny(n - 1)/2 for n ≥ 1

For n = 1: y = 0

For n = 2: y(1) = -y

For n = 3: -3y(2)/2

For n = 4: -2y(3)

5 0

2 years ago

A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that yo

aev [14]

Answer:

1. M=108

2. μ=110

3. In the explanation.

4. Test statistic t = -1.05

5. P-value = 0.1597

Step-by-step explanation:

The question is incomplete: to solve this problem, we need the sample information: size, mean and standard deviation.

We will assume a sample size of 10 matches, a sample mean of 108 points and a sample standard deviation of 6 points.

1. The mean points is the sample points and has a value of 108 points.

2. The null hypothesis is H0: μ=110, meaning that the mean score is not significantly less from 110 points.

3. This is a hypothesis test for the population mean.

The claim is that the mean score is significantly less than 110.

Then, the null and alternative hypothesis are:

$H_0: \mu=110\\\\H_a:\mu< 110$

The significance level is 0.05.

The sample has a size n=10.

The sample mean is M=108.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6}{\sqrt{10}}=1.9$

4. Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{108-110}{1.9}=\dfrac{-2}{1.9}=-1.05$

The degrees of freedom for this sample size are:

$df=n-1=10-1=9$

5. This test is a left-tailed test, with 9 degrees of freedom and t=-1.05, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.1597) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean score is significantly less than 110.

7 0

2 years ago

The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents th

Novay_Z [31]

Answer:

Step-by-step explanation:

I use 84+ CE

stat edit, then fill in the #s

then

vars 5

then

2'nd stat plot, on

then, click stat

Click arrow 1 time to the left to get to Calc

then click (4)(LinReg(ax+b))

then click enter 5 times

(y=-25.31428571x+1000.285714

y=-25.3x+1000.3

now, lets use computer:

y=-25.31(543)+1000.3

y=-12743.03

round to the biggest whole number )

this doesn't really work, so I will put 1999, 2000, 2001, 2002, 2003, 2004 instead of 0, 1, 2, 3, 4, 5 and do the same thing

now I get

y=-25.31428571x+51603.54286

y=-25.3x+51603.5

now, lets use computer:

y=-25.3(543)+51603.5

y=37865.6

round to the biggest whole number:

y=37866

so, year 37866

7 0

2 years ago

7. Tamara goes on a spring break trip with her school to visit historical sites in Italy. She purchases $200 of souvenirs while

fgiga [73]

Answer:

b

Step-by-step explanation:

6 0

2 years ago

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