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3 years ago

Student identification codes at a high school are 4-digit randomly generated codes beginning with 1 letter and ending with 3 num

bers. there are 26,000 possible codes. what is the probability that you will be assigned the code a123?

Mathematics

1 answer:

irinina [24]3 years ago

4 0

$\dfrac{1}{26,000}\approx3.8\%$

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What is 8 hundredths?

soldi70 [24.7K]

Answer:

Step-by-step explanation:

Well 8 hundredths is also know as 0.08 if we put in in the decimal form.

I hope this helps :D

8 0

2 years ago

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A gardener has 27 pansies and 36 daisies. He plants an equal number of each type of flower in each row. What is the greatest pos

Sergio [31]

Answer:

Step-by-step explanation:

36 can go into 3

27 can go into 3

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3 years ago

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I am having trouble with this relative minimum of this equation.<br>

Norma-Jean [14]

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach. You have to let me know if you want this done another way.

Here are some rules I'm going to use:

$(f+g)'=f'+g'$ (Sum rule)

$(cf)'=c(f)'$ (Constant multiple rule)

$(x^n)'=nx^{n-1}$ (Power rule)

$(c)'=0$ (Constant rule)

$(x)'=1$ (Slope of y=x is 1)

$y=4x^3+13x^2-12x-56$

$y'=(4x^3+13x^2-12x-56)'$

$y'=(4x^3)'+(13x^2)'-(12x)'-(56)'$

$y'=4(x^3)'+13(x^2)'-12(x)'-0$

$y'=4(3x^2)+13(2x^1)-12(1)$

$y'=12x^2+26x-12$

Now we set y' equal to 0 and solve for the critical numbers.

$12x^2+26x-12=0$

Divide both sides by 2:

$6x^2+13x-6=0$

Compaer $6x^2+13x-6=0$ to $ax^2+bx+c=0$ to determine the values for $a=6,b=13,c=-6$ .

$a=6$

$b=13$

$c=-6$

We are going to use the quadratic formula to solve for our critical numbers, x.

$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}$

$x=\frac{-13 \pm \sqrt{169+144}}{12}$

$x=\frac{-13 \pm \sqrt{313}}{12}$

Let's separate the choices:

$x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}$

Let's approximate both of these:

$x=0.3909838 \text{ or } -2.5576505$ .

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

$f(x)=4x^3+13x^2-12x-56$

$f'(x)=12x^2+26x-12$

$f''(x)=24x+26$

So if f''(a) is positive then we have a minimum at x=a.

If f''(a) is negative then we have a maximum at x=a.

Rounding to nearest tenths here: x=-2.6 and x=.4

Let's see what f'' gives us at both of these x's.

$24(-2.6)+25$

$-37.5$

So we have a maximum at x=-2.6.

$24(.4)+25$

$9.6+25$

$34.6$

So we have a minimum at x=.4.

Now let's find the corresponding y-value for our relative minimum point since that would complete your question.

We are going to use the equation that relates x and y.

I'm going to use 0.3909838 instead of .4 just so we can be closer to the correct y value.

$y=4(0.3909838)^3+13(0.3909838)^2-12(0.3909838)-56$

I'm shoving this into a calculator:

$y=-58.4654411$

So the approximate relative minimum is (0.4,-58.5).

If you graph $y=4x^3+13x^2-12x-56$ you should see the graph taking a dip at this point.

3 0

3 years ago

The width of a rectangle is 8 cm less than its length. The perimeter of the rectangle is 52 cm. What is the width of the rectang

ozzi

L = X
w = X - 8
P = 52 cm

P = 2l + 2w
52 = 2(X) + 2(X - 8)
52 = 2x + 2x - 16
52 + 16 = 4x
68 = 4x
68/4 = 4x/4
17 = X.

The length of the rectangle is 17 cm.

W = X - 8
W = 17 - 8
W = 9 cm.

The width of the rectangle is 9 cm.

6 0

3 years ago

The water in a reservoir decreased by 47% during a drought. Before the drought, the reservoir held 44,580 acre ft (AF) of water.

yawa3891 [41]

Multiply 44580 by .47
that gives you 20952.6 which equals 47% of the water
take the 44580, and subtract the 20952.6
giving you the remainder as your answer
23627.4

6 0

2 years ago