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mrs_skeptik [129]

3 years ago

8

A farmer created a corn maze. He charged $5 to run through the maze. Some of the trails led to winning a cash prize of $30. Make

a tree diagram to show for your own reference......make sure it has: all the "group possible" paths customers might take, entering the maze on the upper, middle, or lower path and proceeding to an exit with or without a pumpkin (at each fork in the maze a person is equally likely to take any path. Finally, find the EXPECTED VALUE of playing this game.
A) $.50
B) $1.50
C) $2.50
D) $3.50

1 answer:

Pachacha [2.7K]3 years ago

8 0

I think the answer is A

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Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

The triangle in consideration has height $\frac{2}{x_0}$ and base $2x_0$ . So the area is

$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

6 0

3 years ago

PLEASE HELP!!<br><br> what is the explicit formula for this sequence -7, -4, -1, 2, 5

trasher [3.6K]

Answer:

The explicit formula for the given expression is $a_n=-10+3n$ .

Step-by-step explanation:

The given sequence is

-7, -4, -1, 2, 5

The difference between two consecutive terms is same, therefore the given sequence is an arithmetic sequence.

The first term of the given AP is -7 and the common difference is

$-4-(-7)=-4+7=3$

The explicit formula for an AP is

$a_n=a+(n-1)d$

Where, a is first term, d is common difference and n is number of terms.

Substitute a=-7 and d=3 in the above equation.

$a_n=-7+(n-1)3$

$a_n=-7+3n-3$

$a_n=-10+3n$

Therefore the explicit formula for the given expression is $a_n=-10+3n$ .

6 0

3 years ago

Maria deposits $1,950 into a savings account that earns simple interest at a rate of 3%. She makes no withdrawals. How much inte

Elenna [48]

Answer:

x = .06418

Step-by-step explanation:

2 + (9.2)−8x = 2.32

(9.2)−8x = 2.32 − 2

log (9.2)−8x = log .32

−8x log 9.2 = log .32

−8x log 9.2

−8 log 9.2

=

log .32

−8 log 9.2

x = .06418

6 0

3 years ago

A market buys watermelons for $1.25 they want to make a 20% profit what should they charge for the watermelons

Serhud [2]

Answer: $1.50

Step-by-step explanation:

Cost price of watermelon = $1.25

Profit percent = 20%

Profit = Profit percent × Cost price

= 20% × $1.25

= 20/100 × $1.25

= 0.2 × $1.25

= $0.25

Selling price = Cost price + Profit

Selling price = $1.25 + $0.25

Selling price = $1.50

They should charge $1.50 for the watermelons

6 0

3 years ago

If 25% of a number is 12. What is 75% of the number

KIM [24]

Answer:

=900

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers