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dlinn [17]
3 years ago
13

For the graph shown, select the statement that best represents the given system of equations.

Mathematics
2 answers:
Step2247 [10]3 years ago
8 0

Answer: The statement 'C. Consistent and independent' best represents the given system of equation.

Step-by-step explanation:

If a system of equations has at least one solution then it is called consistent while if it does not have any solution then it is called inconsistent.

The consistent system further divides into two types,

Independent : If a consistent system has exactly one solution.

Dependent : If a consistent system has infinitely many solutions.

Here, the given system of equations,

5y - 7x = 10,

3y + 4x = 6,

Since, by solving these equations,

We get, x = 0 and y = 2,

Hence, the solution of the given system of equations is (0,2) ( also shown in the graph )

By the above definition,

⇒ It is an independent consistent system.

⇒ Option C is correct.

Marina86 [1]3 years ago
4 0
The answer is C.<span>consistent and independent</span>
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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
3 years ago
A $400 suit is marked down to $260. Find the percent of markdown.
notka56 [123]
The answer is B. -$140
4 0
2 years ago
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Question 23 on this pictured math sheet please. Have a great day!
Alex_Xolod [135]

Answer:

+2x+15

Step-by-step explanation:

-3x+5x=+2x

(+2x-7) × (+8)

(+2x)(+15)

I THINK

3 0
3 years ago
What number should be added to 51 to get a sum -21
Anastaziya [24]
We can write out a formula in order to solve this. Since sum represents addition, if x represents the unknown number, we can write the formula: x+51=-21. Then, to solve for x, you would subtract 51 from both sides to get x=-72 which is the final answer. 
3 0
3 years ago
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Use the identity (x+y)(x2−xy+y2)=x3+y3 to find the sum of two numbers if the product of the numbers is 28, the sum of the square
fgiga [73]

Answer:

Step-by-step explanation:

1) f(x) = x+y , xy = 49 --> f(x) = x+49/x

f '(x) = 1-49/x2 , x = ±√49 , choose x = +7

y = 49/x = 7

smaller = 7

larger = 7

2) Vertical Distance is difference between the two functions

V(x) = x+56 - x2, V '(x) = 1 -2x --> x = 1/2 --> V(1/2) = 56.25 <---Max Vertical distance

Boundary at -7 and 8 are less

3) I googled the equation, it is really y(n) = kn/(49+n2)

y '(n) = (k(49+n2) - 2kn2)/(49+n2) , Setting to zero, k(49+n2) -2kn2 = 0 , n = 7

4) Let x and y be the sides of the rectangle. A = xy = 37.5 Million or y = 37.5/x

The length of the fences is f(x) = 2x + 3y = 2x+112.5/x

f '(x) = 2-112.5/x2 --> x = √56.5 = 7.5 and y = 37.5/7.5 = 5 then scale by √Million

smaller = 5000 ft and larger = 7500 ft

this took me ages to work out so hopefully it helped

4 0
2 years ago
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