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3 years ago

Y=x+4 y=3x solve by substitution

2 answers:

4 0

Y=x+4 becomes 3x=x+4 by substitution then you subtract x to get 4 by itself then you will have 2x =4. So your answer is x=2.

VikaD [51]3 years ago

4 0

So what i did was i wrote down the problem Y=x+4

i plug in 3x where the y is so you would have the problem rewritten as 3x=x+4.

Now the first thing I did was to take x and change it to -x: 3x=x+4
-x -x
Then i cross out the two x's and then take 3x and subtract it to x cause there's an understood 1 next to it which gave me 2x.: 2x=4

After that i put the 2 under 2x and 4 because this is where I divide. Cross out the two 2's. then take 4 divide it by 2 which he answer is x=2. Hope this helped! :D

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Data were collected over a 10-year timespan from a sample of penguins that were randomly given either metal or electronic tags.

taurus [48]

Question:

Data were collected over a 10-year timespan from a sample of 100 penguins that were randomly given either metal or electronic tags. One variable examined is the length of foraging trips. Longer foraging trips can jeopardize both breeding success and survival of chicks waiting for food. Mean length of 344 foraging trips was 12.70 days for metal-tagged penguins. Mean length of 512 foraging trips was 11.60 days for electronic-tagged penguins. An estimate of the standard error for this difference of means is SE=0.283.

a) We will address the question of whether foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins. State hypotheses in terms of two means.

b. Calculate the sample statistic xM - xE

c. Calculate a t-test statistic, using the given estimate of SE.

d. What are the correct (conservative) degrees of freedom for a t-distribution for this test?

e. Use t-distribution methods to find the p-value and draw a rough curve with appropriate shaded region. You may give either a precise p-value from software or bounds on a p-value from Table A.

f. State the conclusion of the test in context, using nontechnical language.

Answer:

See explanation below

Step-by-step explanation:

a) The null and alternative hypotheses are:

H0 : uM - uE = 0

H1 : uM - uE > 0

b) Calculating the sample statistic,

xM-xE, we have:

Given xM = 12.70 days

xE = 11.60 days

xM - xE = 12.70 - 11.60 = 1.10 days

Therefore sample statistic = 1.10

c) Calculating the test statistic, using the given estimate of SE, we have:

Given standard error, SE = 0.283

$\frac{xM - xE}{SE} = \frac{12.70 - 11.60}{0.283} = 3.89$

Therefore, t test = 3.89

d) The correct degrees of freedom.

We have:

$Min(n_M-1, n_E-1 ) = Min(344-1, 512-1) = Min(343, 511)$

df = 343

e) p-value:

Pvalue = P(Z > 3.89) = 0.00000602

Since p value is less than significance level of 0.05, we reject null hypothesis H0.

f) Conclusion:

There is enough evidence to conclude that foraging trips are longer on average among metal-tagged penguins than among electronic-tagged penguins.

7 0

3 years ago

10. Sketch the graph of -5x^2- 16xy +7y^2-198 0. Show the steps used in rotating the axes

stiv31 [10]

So sorry i don’t know the answer but get an app called desmond, it helps a lot

5 0

4 years ago

A particle moves along the curve below. y = √ 8 + x 3 As it reaches the point ( 1 , 3 ) , the y -coordinate is increasing at a r

Dmitry [639]

Answer:

<em>The x-coordinate is changing at 10 cm/s</em>

Step-by-step explanation:

<u>Rate of Change</u>

Suppose two variables x and y are related by a given function y=f(x). If they both change with respect to a third variable (time, for instance), the rate of change of them is computed as the derivative using the chain rule:

$\displaystyle \frac{dy}{dt}=\frac{dy}{dx}\cdot \frac{dx}{dt}$