3/7 of the coins in a box are nickels. The rest are pennies . If there are 48 pennies how many coins are there altogether?

An evolutionary biologist examined the relative fitness of Escherichia coli bacteria grown for 2000 generations, about 300 days,

Varvara68 [4.7K]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is:

X: fitness of a line of E. coli grown on an acidic environment.

n= 6 E. coli lines

Recorded fitness for each line: 1.24, 1.22, 1.23, 1.24, 1.18, 1.09

The relative fitness of 1 indicates that both bacteria types are equally fit.

A relative fitness larger than 1 indicates that the acid-evolved line is more fit than the parental line kept at neutral pH when both are grown in acidic conditions.

Meaning that if the average fitness of the E. coli lines grown on an acidic environment is greater than 1 then they are better adjusted to live in acidic conditions, symbolically: μ > 1

The statistic hypotheses are:

H₀: μ ≤ 1

H₁: μ > 1

α: 0.05

Assuming that the variable has a normal distribution you have to apply a one-sample t-test:

$t= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~~t_{n-1}$

X[bar]= 1.20

S= 0.06

$t_{H_0}= \frac{1.20-1}{\frac{0.06}{\sqrt{6} } } = 8.40$

The p-value for this test is 0.0002

Since the p-value= 0.0002 is less than α:0.05 the decision is to reject the null hypothesis.

Then at a 5% significance level, there is significant evidence to conclude that the bacteria evolved in acidic pH are better adapted to acidic conditions.

I hope you have a SUPER day!

7 0

2 years ago

What is the area of the rectangle

soldi70 [24.7K]

In order to answer the question we need a picture of some kind

6 0

2 years ago

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Help me please thanks

kow [346]

Correct answer:
First reflect across the y-axis, then rotate 90 degrees clockwise about point K, then shift 3 units down.

6 0

2 years ago

Gabby and Sydney bought some pens and pencils. Gabby bought 4 pens and 5 pencils for $6.71. Sydney bought 5 pens and 3 pencils f

denpristay [2]

Answer:

The cost of each pens is $1.19

The cost of each pencils is $0.39

Step-by-step explanation:

Given as :

The number of pens bought by Gabby = 4

The number of pencils bought by Gabby = 5

The number of pens bought by Sydney = 5

The number of pencils bought by Sydney = 3

The total cost of Gabby items = $6.71

The total cost of Sydney items =$7.12

Let The cost of each pens = x

And The cost of each pencils = y

Now, According to question

For Gabby

4 x + 5 y = $6.71 .............1

For Sydney

5 x + 3 y = $7.12 .............2

Now, Solving both equations

5 × (4 x + 5 y) - 4 × (5 x + 3 y) = 5 × 6.71 - 4 × 7.12

Or, 20 x + 25 y - 20 x - 12 y = 33.55 - 28.48

Or, (20 x - 20 x) + (25 y - 12 y) = 5.07

or, 0 + 13 y = 5.07

∴ y = $\frac{5.07}{13}$

I.e y = $0.39

So, The cost of each pencils = y = $0.39

Again , put The value of y in eq 1

I,e 4 x + 5 y = $6.71

Or, 4 x + 5 × 0.39 = 6.71

or, 4 x + 1.95 = 6.71

or, 4 x = 6.71 - 1.95

or , 4 x = 4.76

∴ x = $\frac{4.76}{4}$

I.e x = $1.19

The cost of each pens = x = $1.19

Hence The cost of each pens is $1.19

And The cost of each pencils is $0.39 Answer

6 0

2 years ago

What is greater 1/3 or 1/8

Ludmilka [50]

1/3 is greater. Picture a pie with nothing cut into it. Then, you cut 3 equal pieces out of it, leaving no pie remaining. So, if you take 1 piece, you have 2 pieces that you didn't take. So if you do the exact same thing, but you cut <em>8 </em>pieces out of the pie and you take 1 piece, there are still 7 pieces remaining. So 1/8 is a smaller part of the pie than the 1/3, since you are cutting the pie into 8 identical pieces while with 1/3 you are cutting the same sized pie into 3 pieces. Sorry if I was confusing, just ask me if you want an easier-to-understand explanation. Also, if you pick a "brainliest" answer, it actually <em>gives </em>you points.

8 0

2 years ago

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