The square root of 279 lies between what two whole nunbers

A bag contains 8 green marbles, 12 red marbles, and 16 blue marbles. What is the probability that a person reaches into the bag

kolezko [41]

8/36 because:
8+16+12=36
and if you simplify it the answer will be 4/18 2/9

3 0

3 years ago

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What is the equation of the line that passes through (4, 2) and is parallel to 3x – 2y = -6?

Dmitrij [34]

Answer:

y = $\frac{3}{2}$ x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x - 2y = - 6 into this form

Subtract 3x from both sides

- 2y = - 3x - 6 ( divide all terms by - 2 )

y = $\frac{3}{2}$ x + 3 ← in slope- intercept form

with slope m = $\frac{3}{2}$

• Parallel lines have equal slopes, hence

y = $\frac{3}{2}$ x + c ← partial equation of parallel line

To find c substitute (4, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = $\frac{3}{2}$ x - 4 ← equation of parallel line

3 0

3 years ago

PLEASE HELP QUICK, I need to know the answer.

Marysya12 [62]

The equivalent expression is $7^{2}$ .

We have the following expression -

$\frac{7^{-3} }{7^{-5} }$

We have to find its equivalent value.

<h3>What is the equivalent expression of the following expression-</h3>

$f(x, y) =\frac{A^{x} }{A^{y} }$

In order to divide two exponents with same base, we use the 'Quotient property of exponents.

The equivalent expression can be written as -

f(x, y) = $A^{x} A^{-y} = A^{x-y}$

In the question given we have -

$\frac{7^{-3} }{7^{-5} }$

Using the property discussed above -

$7^{-3}\;7^{5}$ = $7^{-3+5}$ = $7^{2}$

Hence, the equivalent expression is $7^{2}$ .

To solve more questions on exponents, visit the link below -

brainly.com/question/17173276

#SPJ5

3 0

2 years ago

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The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,

uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

$\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right)$ .

We need to solve it and obtain an expression for $P(t)$ in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

$\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right)$ .

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that $k=0.04$ and $K=500$ and the initial condition $P(0)=100$ .

Notice that this equation is separable, then

$\frac{dP}{P(1-P/K)} = kdt$ .

Now, intagrating in both sides of the equation

$\int\frac{dP}{P(1-P/K)} = \int kdt = kt +C$ .

In order to calculate the integral in the left hand side we make a partial fraction decomposition:

$\frac{1}{P(1-P/K)} = \frac{1}{P} - \frac{1}{K-P}$ .

So,

$\int\frac{dP}{P(1-P/K)} = \ln|P| - \ln|K-P| = \ln\left| \frac{P}{K-P} \right| = -\ln\left| \frac{K-P}{P} \right|$ .

We have obtained that:

$-\ln\left| \frac{K-P}{P}\right| = kt +C$

which is equivalent to

$\ln\left| \frac{K-P}{P}\right|= -kt -C$

Taking exponentials in both hands:

$\left| \frac{K-P}{P}\right| = e^{-kt -C}$

Hence,

$\frac{K-P(t)}{P(t)} = Ae^{-kt}$ .

The next step is to substitute the given values in the statement of the problem:

$\frac{500-P(t)}{P(t)} = Ae^{-0.04t}$ .

We calculate the value of $A$ using the initial condition $P(0)=100$ , substituting $t=0$ :

$\frac{500-100}{100} = A}$ and $A=4$ .

So,

$\frac{500-P(t)}{P(t)} = 4e^{-0.04t}$ .

Finally, as we want the value of $t$ such that $P(t)=200$ , we substitute this last value into the above equation. Thus,

$\frac{500-200}{200} = 4e^{-0.04t}$ .

This is equivalent to $\frac{3}{8} = e^{-0.04t}$ . Taking logarithms we get $\ln\frac{3}{8} = -0.04t$ . Then,

$t = \frac{\ln\frac{3}{8}}{-0.04} \approx 24.520731325$ .

So, the population of rats will be 200 after 25 months.

6 0

3 years ago

The radius of a circle is 1 centimeter. What is the circle's circumference?

igomit [66]

Answer:

6.28 cm

Step-by-step explanation:

The formula for the circumference of a circle with radius r is C = 2*pi*r.

If we let pi = 3.14 and r = 1 cm, then the circumference of this circle is

C = 2(3.14)(1 cm) = 6.28 cm

6 0

3 years ago