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(5 nPr 1) + (5 nPr 2) + (5 nPr 3) + (5 npr 4) =5 + 20 + 60 + 120 =205 integers.

FV=1600; P=0; N=25; R=0.05/4;a=FV/(1 + R)^N; print"PV =$",a

PV = 1,172.85  dollars- this amount will grow to 1,600 dollars in 25 quarters @ 5% compounded quarterly.

For cross products we have the following
 

a x a = 0  (simiarly for b x b etc)

a x b = - b x a   etc.

(b + c) x a = b x a  +  c x a   =   -a x b  -  a x c    etc.

Can you take it from here?

A, B, C, D, E. Normally, 5 letters taken 4 at a time, you would have:5P4 =120 permutations. But, because each letter can be repeated up to 4 times and each of the 4 letters has 5 options, then the total number of permutations is simply: 5^4 =625  four-letter "words".

However, since you want each 4-letter word to have at least one vowel in it(A, or E), then we have to figure out those permutations that don't have at least one vowel in them. You have 3 consonants, B, C, and D and since each can be repeated up to 4 times, we therefore have: 3^4 =81 permutations which will have NO vowels in them. We, therefore, have to subtract them from the above total of 625 permutations:

So, 625 - 81 =544 four-letter "words" which have at least one vowel in them.

Find the area of triangle ABC if AB = BC = 12 and angle ABC = 150 degrees.    

Since AB = BC triangle ABC is isoceles and angles BAC and BCA are equal 

Since ABC = 150^o and the sum of the interior angles of a triangle is 180^o  

then angles A and C total 30^o and therefore each of them is 15^o  

Draw a perpendicular from the apex B down to a point on side AC - call the point P  

                                                          BP  

Using the sine function:    sin(15) = ———  

                                                          12 

                                                BP = (12)(0.65029) = 7.80        this is the height of the triangle

                                                            AP

Using the cosine function:  cos(15) = ———  

                                                            12 

                                                 AP = (12)(0.96593) = 11.59       this is half the base of the triangle  

So the whole base of the triangle is (2)(11.59) = 23.18              (We could have skipped this step.  Do you know why?)  

                                                                1

The formula for the area of a triangle is  — • base • height  

                                                                 2  

So, the area of this triangle is 0.5 • 23.18 • 7.80 = 90.40 units²  

The answer in the back of the book might be slightly different, because of the rounding that happened here.  

_.

Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (3,4), vertical axis of symmetry, and contains the point (1,0).
What is (a , b, c)?

Hello Guest!

\( y = ax^2 + bx + c\\ V(3,4)\\ P_1(1,0)\\ \color{blue}P_2(5,0)\)

\( y = ax^2 + bx + c\\ 4 = 9a + 3b + c\\ 0 = a + b + c\\ 0 = 25a + 5b + c\)

\(4 = 9a + 3b + c\\ \underline{0=9a+9b+9c}\\ 4=-6b-8c\\ \color{blue}2=-3b-4c\)

\(0=25a+25b+25c\\ \underline{0=25a+\ 5b\ +\ c}\\ \color{blue}0=20b+24c\)

\(12=-18b-24c\\ \underline{\ 0\ =\ 20b\ +\ 24c}\\ 12=2b\)

\(\ b\ =\ 6\)

  \(0=20b+24c\\ c=-20b/24\\ c=-120/24\)

  \(b=\ 6\)

  \(c =\ -5\\ a=\ -1\)

\(y = ax^2 + bx + c\\ \color{blue}y=-x^2+6x-5\)

  !

\(\)

You are right!  If a circumference is 16, the area of a circle is 20.372 units squared; the area of a square with a perimeter of 16 is only 16 units squared. 

How would I find the maximum if the graph is opening upwards?

When the minute hand of a clock points exactly at a full minute, the hour hand is exactly three minutes away. Give all possible times in a 12-hour period that satisfy condition.

Hello Guest!

\(Z_{hour}=\frac{t}{12min}\\ t=12min\cdot Z_{hour}\\ t=1min\cdot Z_{minut}\\ t\in \{60\cdot 1\ minute\}\)

t [min] =              0   12    24    36    48    60          648  660  672  684  696 720

\(Z_{hour[min]}\)          0     2      4     6     8       5             50   52     54   56    58   60 

\(Z_{minut}\)               0    12    24   36    48      0             0    12     24   36    48   60

The hour hand and the minute hand are never exactly three minutes apart when the minute hand points exactly to the minute on the dial.

  !

I think it is the opposite guest... IDK the best way to explain it, but look at this graph:

Hint: the area of the square should be as large as possible.

How did you get the answers?

For A), I got x is [1, 2)

For b), I got x has no solution.

For c), I got that x is [2.5, 3).

Mainly just confused on d) :).

Thank you so so much!

(a) The solution is 1 <= x <= 2.

(b) The solution is 2 <= x <= sqrt(5).

(c) The solution is sqrt(5) < = x <= 3,

(d) There are 204 solutions.

I gave the wrong link.

The ratio of the area of the trapezoid FGIH to the area of trapezoid DEGF is 7/5

hmm.. I don't know who you are

the hours 09 and 19 both display a 9 for 60 minutes each

the other 22 hours have a 9 for   09   19   29 39 49 59       6 minutes per hour

24 hours = 1440 minutes

(60+ 60 + 6* 22) / 1440 = 252/1440 = 0.175      17.5 % of the time

link:::https://web2.0calc.com/questions/the-display-of-a-24-hour-digital-clock-shows-hours-and-minutes_1

There're three answers; 2nd and 3rd answers are correct!

Hello, E Pavlov!   The smallest quarter-circles overlap each other. So, you must subtract the area of overlapping from the whole area.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            

There are 5!*3 = 360 ways of assigning the pets.

The minimum value occurs when x = y = 0, so the minimum value is 1.

482_total  - 138_Friday  - 225_Saturday =   .......... miles_Sunday

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