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3 years ago

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For the experiment of drawing a single card from a standard 52-card deck, find (a) the probability of the following event, an

d (b) the odds in favor of the following event. -Neither a red card nor an ace

1 answer:

BlackZzzverrR [31]3 years ago

6 0

I am so happy and my

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Consider the circle of radius 5 centered at (0, 0). Find an equation of the line tangent to the circle at the point (3, 4) in sl

Wittaler [7]

Answer:

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

Step-by-step explanation:

The equation of a circle of radius $5$ centered at $(0,0)$ is:

$x^{2} + y^{2} = 5^{2}$ .

$x^{2} + y^{2} = 25$ .

Differentiate implicitly with respect to $x$ to find the slope of tangents to this circle.

$\displaystyle \frac{d}{dx}[x^{2} + y^{2}] = \frac{d}{dx}[25]$

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(y^{2}) = 0$ .

Apply the power rule and the chain rule. Treat $y$ as a function of $x$ , $f(x)$ .

$\displaystyle \frac{d}{dx}(x^{2}) + \frac{d}{dx}(f(x))^{2} = 0$ .

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}(2f(x)\cdot f^{\prime}(x)) = 0$ .

That is:

$\displaystyle \frac{d}{dx}(2x) + \frac{d}{dx}\left(2y \cdot \frac{dy}{dx}\right) = 0$ .

Solve this equation for $\displaystyle \frac{dy}{dx}$ :

$\displaystyle \frac{dy}{dx} = -\frac{x}{y}$ .

The slope of the tangent to this circle at point $(3, 4)$ will thus equal

$\displaystyle \frac{dy}{dx} = -\frac{3}{4}$ .

Apply the slope-point of a line in a cartesian plane:

$y - y_0 = m(x - x_0)$ , where

$m$ is the gradient of this line, and
$(x_0, y_0)$ are the coordinates of a point on that line.

For the tangent line in this question:

$\displaystyle m = -\frac{3}{4}$ ,
$(x_0, y_0) = (3, 4)$ .

The equation of this tangent line will thus be:

$\displaystyle y - 4 = -\frac{3}{4} (x - 3)$ .

That simplifies to

$\displaystyle y= -\frac{3}{4} x + \frac{25}{4}$ .

3 0

3 years ago

Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil.

Anna [14]

In this case you the probabilities can be multiplied similarly to if you flipped a coin twice. .45 * .80 = .36

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3 years ago

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A car is traveling 150 feet per second. Convert this to miles per hour.

Nana76 [90]

There are 3600 seconds in 1 hour.

Multiply feet per second by 3600 to get feet in 1 hour:

150 x 3600 = 540,000 feet in 1 hour.

1 mile = 5280 feet.

Divide feet per hour by 5280 to get miles per hour:

540,000 / 5280 = 102.27 miles per hour.

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3 years ago

One number is bigger than other number by 3 and the sum of these two number is 43

Zepler [3.9K]

$x-first\ number\\x+3-second\ number\\x+(x+3)=x+x+3=2x+3-the\ sum\ of\ these\ numbers\\43-the\ sum\ of\ these\ numbers\\\\therefore\\\\2x+3=43\ \ \ \ |subtract\ 3\ from\ both\ sides\\2x=40\ \ \ \ \ |divide\ both\ sides\ by\ 2\\x=20-first\ number\\x+3=20+3=23-second\ number\\\\Answer:\boxed{20\ and\ 23}$

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3 years ago

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In Chemistry class, Samantha finds that she can make a certain solution by mixing 0.04 liters of chemical A with 0.02 liters of

Jet001 [13]

Answer:

0.16 liters of water

Step-by-step explanation:

Samantha's recipe makes 0.06 liters of solution. She wants 0.48 liters of solution, an amount 0.48/0.06 = 8 times as great as made by one recipe.

The recipe calls for 0.02 liters of water. To make 8 times the amount of solution, Samantha will use 8 times as much water: 0.16 liters.

Samantha will use 0.16 liters of water to make 0.48 liters of solution.

__

Alternate solution

The fraction of solution that is water is (0.02 L)/(0.06 L) = 1/3. For 0.48 L of solution, the water needed is 1/3×0.48 L = 0.16 liters.

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2 years ago

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