02.06)If 1 pint is equal to 2 cups, then 5 pints would equal __

Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. Whe

Rama09 [41]

You can see how this works by thinking through what's going on.

In the first year the population declines by 3%. So the population at the end of the first year is the starting population (1200) minus the decline: 1200 minus 3% of 1200. 3% of 1200 is the same as .03 * 1200. So the population at the end of the first year is 1200 - .03 * 1200. That can be written as 1200 * (1 - .03), or 1200 * 0.97

What about the second year? The population starts at 1200 * 0.97. It declines by 3% again. But 3% of what??? The decline is based on the population at the beginning of the year, NOT based no the original population. So the decline in the second year is 0.03 * (1200 * 0.97). And just as in the first year, the population at the end of the second year is the population at the beginning of the second year minus the decline in the second year. So that's 1200 * 0.97 - 0.03 * (1200 * 0.97), which is equal to 1200 * 0.97 (1 - 0.03) = 1200 * 0.97 * 0.97 = 1200 * 0.972.

So there's a pattern. If you worked out the third year, you'd see that the population ends up as 1200 * 0.973, and it would keep going like that.

So the population after x years is 1200 * 0.97x

5 0

3 years ago

Hey can you please help me posted picture of question

marta [7]

Two transformations occur on F(x) to obtain G(x).

a) Multiplication by -1
This means, the function is reflected across x-axis

b) Multiplication by 5.
This means vertical stretch by a factor of 5.

So, G(x) can be obtained by reflecting F(x) across x-axis and stretching it vertically be a factor of 5.

So, the correct answer is option B

7 0

3 years ago

Read 2 more answers

Helpppppppppppppppppppppppppppppppppppp

Alexxandr [17]

To take out terms outside the radical we need to divide the power of the term by the index of the radical; the quotient will be the power of the term outside the radical, and the remainder will be the power of the term inside the radical.
First, lets factor 8:
$8=2 ^{3}$
Now we can divide the power of the term, 3, by the index of the radical 2:
$\frac{3}{2}$ = 1 with a remainder of 1
Next, lets do the same for our second term $x^{7}$ :
$\frac{7}{2}$ = 3 with a remainder of 1
Again, lets do the same for our third term $y^{8}$ :
$\frac{8}{2} =4$ with no remainder, so this term will come out completely.

Finally, lets take our terms out of the radical:
$\sqrt{8x^{7} y^{8} }= \sqrt{ 2^{3} x^{7} y^{8} } =2 x^{3} y^{4} \sqrt{2x}$

We can conclude that the correct answer is the third one.

4 0

3 years ago

Read 2 more answers

Write the point-slope equation of the line that passes through(3,5) and (7,1)

Liono4ka [1.6K]

Answer: y - 1 = –(x –7)

or y –5 = –1(x –3)

The attachment shows the graph of these equations (identical)

Step-by-step explanation:

The basic form for a point-slope equation is

y - b = m(x - a)

a is the x-value from the given coordinate, b is the y-value form the given coordinate, m is the slope. x and y are the variables in the function.

To find the slope, m, use the given coordinates. Get the difference in the y-values and divide by the difference in the x-values. This is "rise over run."

Subtract the first coordinate from the second coordinate.

Given coordinate points: (3,5) and (7,1) substitute values:

m= 1 –5 / 7 –3 becomes m= –4/4 so the slope, m = –4/4

That is –1 The "1" is "understood," so only the negative sign represents the slope in the equation

To write the equation: Take the basic form, substitute b and a values from either given coordinate. And use the value of m we just calculated.

y - b = m(x - a) Using the second coordinate: (7,1)

y - 1 = –(x –7)

or using the first coordinate:

y –5 = –(x –3)

5 0

3 years ago

the lines graphed below are parallel. the slope of the red line is -4/3. what is the slope of the green line

ch4aika [34]

Answer:

-4/3

Step-by-step explanation:

If the lines are parallel, they have the same slope.

Since the red line has a slope of -4/3, the green line will have a slope of -4/3

5 0

3 years ago

02.06)If 1 pint is equal to 2 cups, then 5 pints would equal ___ cups.