Amelia has 22 1/2 cm of ribbon. She cuts it into pieces that are 1 7/8 cm long. How many pieces does she have?

The population of rabbits on an island is growing exponentially. In the year 1990, the population of rabbits was 1200, and by 19

kobusy [5.1K]

Answer:

2023 rabbits

Step-by-step explanation:

The exponential model consists of the following expression:

$y = A \cdot r^{t}$

Where:

$A$ - Initial population.

$r$ - Increase rate.

$t$ - Time

$y$ - Current population.

The initial population and increase rate are, respectively:

$1200 = A \cdot r^{0}$

$A = 1200$

$1700 = 1200 \cdot r^{4}$

$r^{4} = \frac{1700}{1200}$

$r^{4} = \frac{17}{12}$

$r = \sqrt[4]{\frac{17}{12} }$

$r \approx 1.091$

The exponential model that predicts the population of rabbits is:

$y = 1200\cdot 1.091^{t}$

Lastly, the expected population for the year 1996 is:

$y = 1200\cdot 1.091^{6}$

$y\approx 2023.624\,rabbits$

5 0

3 years ago

1.) Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth .x squared minus 21 x equals n

Andrew [12]

Part 1
We are given $x^2-21x=-4x$ . This can be rewritten as $x^2-18x=0$ .
Therefore, a=1, b=-18, c=0.
Using the quadratic formula
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-\left(-18\right)\pm \sqrt{\left(-18\right)^2-4\left(1\right)\left(0\right)}}{2\left(1\right)}$
$x=\frac{18\pm 18}{2}$

The values of x are
$x_1=\frac{18-18}{2}=0$
$x_2=\frac{18+18}{2}=18$

Part 2
Since the values of y change drastically for every equal interval of x, the function cannot be linear. Therefore, the kind of function that best suits the given pairs is a quadratic function.

Part 3.
The first equation is $y=x^2+2$ .
The second equation is $y=3x+20$ .

We have
$x^2+2=3x+20$
$x^2-3x-18=0$
Factoring, we have
$\left(x-6\right)\left(x+3\right)=0$
Equating both factors to zero.
$x_1-6=0\rightarrow x_1=6$
$x_2+3=0\rightarrow x_2=-3$

When the value of x is 6, the value of y is
$y=3\left(6\right)+20=38$

When the value of x is -3, the value of y is
$y=3\left(-3\right)+20=11$

Therefore, the solutions are (6,38) or (-3,11)

7 0

2 years ago

I will mark brainlist for this science question please. I need to figure out where to put where. And what percentages. Your choi

ozzi

Answer:

Long wings: 0

Short wings: 100

Step-by-step explanation:

Genotype of the flies: ww

The cross will yield the genotype ww and the flies will express the recessive phenotype which is short wings.

The probability for long wings will be 0 as there is no dominant allele present. The probability for short wings will be 100 as all the flies will have short wings.

Hope that helps.

3 0

2 years ago

Harry works for a major sporting goods distributor. He earns a base salary of $30,000 per year and 5% commission on his sales. H

FrozenT [24]

Harry made $10,000 that the end of the year.

3 0

3 years ago

Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car on

elena55 [62]

9514 1404 393

Answer:

f(x) = 0.15x +25

Step-by-step explanation:

We are given two points:

(x, y) = (180, 52) or (350, 77.50)

The slope is given by ...

m = (y2 -y1)/(x2 -x1)

m = (77.50 -52)/(350 -180) = 25.50/170 = 0.15

The y-intercept is given by ...

b = y -mx

b = 52 -0.15×180 = 25

Then the equation for the linear function is ...

f(x) = mx +b

f(x) = 0.15x +25

8 0

3 years ago