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First, determine what 1 out of twelve people is for this group. 280/7=40. Then multiply by 12 to get 12 * 40 = 480.

Good solution. Here's a quicker way. Once we separate the sequences, notice that 4(1+2+3+...+24+25) = 4(1)+4(2)+4(3)+...+4(24)+4(25)=4+8+12+...+96+199. So the second sequence is 4 times the first. So the answer is

5(1+2+3+4+...+23+24+25)=

5((25)(26))/2=

1625

Though what was shown previously leads to a contradiction, I will try to figure out a possible solution anyway. First, take p=3+2q.

Substitute into the third equation: 3+2q+r=12+2q. Nothing we can get here can avoid r=9. Then, using the second equation, we find that 18=2, which is not true. I don't think a solution can be found. Check carefully to make sure you didn't have a typo in typing the system.

Seven years ago, Grogg's dad was 6 times as old as Grogg, and 4 years ago, his dad was 4 times as old as Grogg. How old is Grogg's dad currently?  

Call Grogg's age now "G" and his dad's age now "D"  

Seven years ago                           (D – 7)  =  6 * (G – 7)  

Four years ago                              (D – 4)  =  4 * (G – 4)  

Multiply them out                            D – 7  =  6G – 42          (eq 1)  

                                                       D – 4  =  4G – 16          (eq 2)  

Subtract (eq 2) from (eq 1)                – 3  =  2G – 26  

                                                           23  =  2G  

                                                             G  =  11.5  

Find D by

plugging G back into (eq 1)               D – 7  =  (6)(11.5) – 42 

                                                        D – 7  =  69 – 42  

                                                              D  =  27 + 7  

                                                              D  =  34  

Check answer by

plugging G back into (eq 2)                D – 4  =  (4)(11.5) – 16  

                                                         D – 4  =  46 – 16 

                                                               D  =  30 + 4  

                                                               D  =  34 

_.

Yes - just right-click, and select "download".

Find the ordered triple (p,q,r) that satisfies the following system:  

p - 2q = 3  

q - 2r = -2 + q  

p + r = 9 + p  

Let's identify the three equations as equations 1, 2, and 3.  

p - 2q = 3           (eq 1)  

q - 2r = -2 + q     (eq 2)  

p + r = 9 + p        (eq 3)  

by (eq 3)                                              p + r  =  9 + p  

subtract p from both sides                         r  =  9  

by (eq 2)                                            q – 2r  =  –2 + q  

subtract q from both sides                      –2r  =  –2  

divide both sides by –2                               r  =  1  

If the system is to be actual, then  

r can not be equal to both 9 and 1,  

so there must be something wrong  

with the problem as stated.                      no solution  

_.

ABC is a right-angled triangle, the right angle being at C.

The altitude from C onto AB meets AB at H.

AH = x, HB = y, and CH = h.

 the length of XY

The angle bisector from P bisects QR in X.

\(sin\ 60 ^{\circ}=\dfrac{\overline{XY}}{0.5\cdot \overline{QR}}\\ \overline{XY}=0.5\cdot \overline{QR}\cdot sin\ 60^{\circ}=0.5\cdot 9\cdot sin\ 60^{\circ}\\ \color{blue}\overline{XY}=3.897 \)

  !

Nevermind, it's because they both intercept the same arc CD. Thanks!

Sorry, the question seemed to have been cut off - it was "Explain why angles A and B are congruent"

https://imgur.com/a/QFFEfQG

Hello! What is your question? I will start off by giving the definition of an inscribed angle: an angle formed by two cords intersecting each other.

What "spiral below", lazy ?

You have 9 digits to start with. I assume you can repeat the digits. if that is the case, then:

You should have: 9 x 9 x 9 x 9 ==9^4 ==6,561 4-digit integers which include 3 in them.

If we remove the 3, then we have only 8 digits left, since we cannot start an integer with "0".

Therefore, we have: 8 x 8 x 8 x 8 ==8^4 ==4,096 - 4-digit integers which DO NOT include 3.

The difference: 6,561  -  4,096 ==2,465 4-digit integers that include at least one 3 in them.

No picture is needed though.

Hello! Let me know if you have any questions about my explanation and if you find any typos or math mistakes.

The answer to your question is 1625.

The pattern may look complicated at first so lets break things down; break this series into two series. This will be: 1+2+3+4+...+24+25 and 4+8+12+16+...+96+100. What do you notice about these patterns? Well, the first pattern is consecutive integers from 1 to 25 (inlcusive) and the second pattern are all the multiples of 4 from 4 to 100 (inclusive).

Now let's find the value of both the series. First let's sum the numbers from 1 to 25 inclusive; this should be straight foward. So 1+2+3+4+...+24+25 = 325 and for our second series: 4+8+12+16+...+96+100 = 1300. And when you add 325+1300, you get 1625 as our final answer.

Here's some explanation on how I added the two smaller series (Source: https://brainly.in/question/12430191#:~:text=Answer,-10%20people%20found&text=The%20final%20answer%20is%2020200.): 

sum = (n/2)(a+b)

n = number of multiples

a = value of first multiple

b = value of last multiple

Where is the pic?

To calculate the execution time of the program, we need to determine the number of cycles required and divide it by the processor's clock rate. Given that the processor spends 2 cycles on each instruction and the program executes 3 billion instructions, the total number of cycles required would be:

Total Cycles = 2 cycles/instruction * 3 billion instructions = 6 billion cycles

Real numbers a and b satisfy  

a + ab = 250  

a - ab = -240  

If you add the two equations together                a + ab  =   250  

                                                                           a – ab  = –240  

                                                                          ————————  

you get                                                              2a         =  10  

from which                                                                  a  =  5  

The problem doesn't ask for b,  

but ... find b by substituting  

a back into a + ab = 250                                    5 + 5b  =  250  

                                                                                5b  =  245  

                                                                                  b  =  49  

check b by substituting  

a back into a – ab = –240                                  5 – 5b  =  –240  

                                                                              –5b  =  –245  

                                                                                  b  =  49  

_.

The relationship should be 

\((x+h)^{2}+(y+h)^{2}=(a+b)^{2}\)

The spinner has 14 sides, so the probability is 1/14.  

That is equal to \(\frac{11}{28000000}\).

2/5 * 150 = 60.

The only multiple of 6 and 4 on this spinner is 12, so the probability is 1/12.

The fractional form of 0.8 is \(\frac{4}{5}\) because \(\frac{4}{5}=0.8\).