On a farm there are 50 sheep and a farmer how many feet are there in total

Answers

Answer 1

Answer:

Answer:

200 sheep legs and 2 farmer legs, or 202 legs in total.

Step-by-step explanation:

One sheep has 4 legs. and there are 50 sheep. So, we have to multiply 50*4 to get 200. Then, we have to add the two legs the farmer has. 200 + 2 = 202. Therefore, there are 202 legs on the farm.

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Don completes the square for the function y = x2 + 6x + 3. Which of the following functions reveals the vertex of the parabola?A. y = (x + 3)2 – 3 B. y = (x + 3)2 – 6 C. y = (x + 2)2 – 6 D. y = (x + 2)2 – 3
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Which of the following statements about the image below is true?

Answers

Answer:

d. Line UR and Line VW are parallel

Step-by-step explanation:

If they were to continue going straight, they would not touch, making them parallel.

I hope this helps!

What is the greatest common factor of 5x^6+35x^4+15x^3

Answers

5 will go into everything. That is one of the factors.

x^3 is in everything as well.

The highest common factor is 5x^3

$(5x^6)/(5x^3) = x^(6-3) = x^3$

$(35x^4)/(5x^3) = 7x^(4-3) = 7x$

$(15x^3)/(5x^3) = 3*x^(3-3) = 3*1 = 3$

So the greatest common factor (determined by the last term) is 5x^3

And the left over polynomial is x^3 + 7x + 3

A rock falls off a balcony. It's height (in feet) is given by the formula f(x)=-16t^2+13.4t+120, where t is measured in seconds. How long will it take the rock to hit the ground? Round your answers to the nearest three decimal places.

Answers

Answer:

3.189 seconds

Step-by-step explanation:

You want f(t) = 0, so ...

0 = -16t^2 +13.4t +120

0 = t^2 -0.8375t -7.5 . . . . divide by -16

0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*

0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square

√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root

t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875

It will take the rock about 3.189 seconds to hit the ground.

_____

* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...

(t^2 -2at +a^2) = (t -a)^2

Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.

_____

Comment on the question

We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...

The white "Spirit" black bear (or Kermode) Ursus americanus kermodei, differs from the ordinary black bear by a single amino acid change in the melanocortin 1 receptor gene (MC1R). In this population, the gene has two forms (or alleles): the "white" allele b and the "black" allele B. The trait is recessive: white bears have two copies of the white allele of this gene (bb), whereas a bear is black if it has one or two copies of the black allele (Bb or BB). Both color morphs and all three genotypes are found together in the bear population of the northwest coast of British Columbia. If possessing the white allele has no effect on growth, survival, reproductive success, or mating patterns of individual bears, then the frequency of individuals with 0, 1, or 2 copies of the white allele (b) in the population will follow a binomial distribution. To investigate, Hedrick and Ritland (2011) sampled and genotype 87 bears from the northwest coast:42 were BB
24 were Bb
21 were bb
Assume that this is a random sample.
A formal hypothesis test was carried out to compare the observed and expected frequencies of genotypes. The procedure obtained P = 0.0001.
1. "The frequency distribution of genotypes has a binomial distribution in the population" is the________ hypothesis, whereas "The frequency distribution of genotypes does not have a binomial distribution" is the _________ hypothesis.
2. The degrees of freedom for the test statistic are __________.
Say whether the each of the following statements is true or false solely on the basis of these results:
3. The difference between the observed and expected frequencies is statistically significant.________
4. The test statistic exceeds the critical value corresponding to α = 0.05. ___________
5. The test statistic exceeds the critical value corresponding to α = 0.01. ____________

Answers

Answer:

1) i ) Null hypothesis, ii) Alternate hypothesis

2) Degree of Freedom = 14.9011

3) True

4) True

5) True

Step-by-step explanation:

1) "The frequency distribution of genotypes has a binomial distribution in the population" is the NULL hypothesis, whereas "The frequency distribution of genotypes does not have a binomial distribution" is the ALTERNATE hypothesis.

2) Degrees of freedom: see attached calculation for

3) True, the difference between the observed and expected frequencies is statistically significant since p-value < ∝alpha(0.05)

4) True

when, 14.9011 > 3.8415 where ∝ = 0.05

when, p-value < alpha,TS > critical value

here p-value < 0.0001 < 0.05

5) True

when, 14.9011 > 6.635 where ∝ = 0.01

when, p-value < alpha,TS > critical value

here p-value < 0.0001 < 0.01

Final answer:

The null hypothesis states that the genotype frequency distribution follows a binomial distribution, with the alternative hypothesis stating the contrary. The degrees of freedom for the test statistic are two. The P value of 0.0001 is statistically significant, thus the test statistic exceeds the critical values corresponding to both α = 0.05 and α = 0.01.

Explanation:

1. The frequency distribution of genotypes has a binomial distribution in the population is the null hypothesis, whereas The frequency distribution of genotypes does not have a binomial distribution is the alternative hypothesis.

2. For this chi-square test, since there are 3 possible outcomes (BB, Bb, bb) the degrees of freedom are 3-1 = 2.

3. The difference between the observed and expected frequencies is statistically significant, that is true. A P value of 0.0001 is highly significant, clearly less than 0.05, and denotes a significant difference.

4. The test statistic exceeds the critical value corresponding to α = 0.05. This is true, as the statistically significant low P value indicates the test statistic is in the critical region.

5. The test statistic exceeds the critical value corresponding to α = 0.01. This is also true.

Learn more about Statistics in Biology here:

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For which value of k does the system has no solutions?Equation:
3x + y = 4
kx + y = −2
Answers:
A: -3
B: -2
C: 3
D: 4

Answers

Answer:

The answer to this question is 4

Step-by-step explanation:

[10 points] Let v1, v2 and v3 be three linearly independent vectors in R 3 . (a) Find the rank of the matrix A = (v1 − v2) (v2 − v3) (v3 − v1) . (b) Find the rank of the matrix B = (v1 + v2) (v2 + v3) (v3 + v1) .

Answers

Answer:

The solution and complete explanation for the above question and mentioned conditions is given below in the attached document.I hope my explanation will help you in understanding this particular question.

Step-by-step explanation:

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