You randomly draw a marble from a bag. You then put it back before drawing a second marble.

A scientist counts 25 bacteria present in a culture and finds that the number of bacteria tripled each hour. the function y=25•3

LUCKY_DIMON [66]

Answer: The answer is 3.5

Step-by-step explanation:

5 0

3 years ago

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The drama club sold $779 worth of tickets to the school play. Student tickets cost $3 a piece and tickets for everyone else cost

svetlana [45]

Answer:

The equation will be: $3s+5t=779$

Step-by-step explanation:

The number of student tickets that were sold $=s$

and the number of other tickets that were sold $=t$

Student tickets cost $3 a piece and tickets for everyone else cost $5 each.

So, the total cost of $s$ student tickets $=\$3s$ and the total cost of $t$ other tickets $=\$5t$

Given that, the drama club sold total $779 worth of tickets.

So, the equation will be: $3s+5t=779$

3 0

3 years ago

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Expression written using exponents

Scilla [17]

Since there are no specific requirements given other than expression written using exponents, I am just going to give some examples.

1. 5x^2 - 3

2. 8^5 - 15x + 7

3. 15x^10 - 8x^7 + 16x^5 + 17^3 - 4^2 +13x - 2

5 0

3 years ago

The following integral requires a preliminary step such as long division or a change of variables before using the method of par

shtirl [24]

Division yields

$\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}$

Now for partial fractions: you're looking for constants a, b, and c such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

$\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a$

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

$\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}$

7 0

3 years ago

Please solve this geo problem

Sunny_sXe [5.5K]

Step-by-step answer:

The first step in solving a problem of geometry and trigonometry is to draw a diagram, with all the given information in it. The attached image does just that.

Here, we have (horizontal) distance of building to the tower is 400'.

We see two right triangles, each with a leg of 400' (horizontal).

The vertical distances are denoted h1 and h2 for the angles of elevation 24 and 20 degrees respectively.

Using the definition of tangent, we have

h1= 400tan24=178.1

h2=400tan20=145.6

The height of the tower is therefore h1+h2=178.1+145.6=323.7 feet

4 0

3 years ago