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SpyIntel [72]
3 years ago
5

Which of the following equations will have a negative solution?​

Mathematics
1 answer:
DedPeter [7]3 years ago
3 0

Answer:

The third equation, 7\frac{1}{2} +m = 4\frac{2}{3}.

Step-by-step explanation:

In this question, we have to solve the equation for each of the options and after doing so we will see that the only option that will have m equal a positive number is the third option. Here is how we solve that equation:

7\frac{1}{2} +m = 4\frac{2}{3} \\m = 4\frac{2}{3} - 7\frac{1}{2}\\m = -2\frac{5}{6}  

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There are eight different jobs in a printer queue. Each job has a distinct tag which is a string of three upper case letters. Th
N76 [4]

Answer:

a. 40320 ways

b. 10080 ways

c. 25200 ways

d. 10080 ways

e. 10080 ways

Step-by-step explanation:

There are 8 different jobs in a printer queue.

a. They can be arranged in the queue in 8! ways.

No. of ways to arrange the 8 jobs = 8!

                                                        = 8*7*6*5*4*3*2*1

No. of ways to arrange the 8 jobs = 40320 ways

b. USU comes immediately before CDP. This means that these two jobs must be one after the other. They can be arranged in 2! ways. Consider both of them as one unit. The remaining 6 together with both these jobs can be arranged in 7! ways. So,

No. of ways to arrange the 8 jobs if USU comes immediately before CDP

= 2! * 7!

= 2*1 * 7*6*5*4*3*2*1

= 10080 ways

c. First consider a gap of 1 space between the two jobs USU and CDP. One case can be that USU comes at the first place and CDP at the third place. The remaining 6 jobs can be arranged in 6! ways. Another case can be when USU comes at the second place and CDP at the fourth. This will go on until CDP is at the last place. So, we will have 5 such cases.

The no. of ways USU and CDP can be arranged with a gap of one space is:

6! * 6 = 4320

Then, with a gap of two spaces, USU can come at the first place and CDP at the fourth.  This will go on until CDP is at the last place and USU at the sixth. So there will be 5 cases. No. of ways the rest of the jobs can be arranged is 6! and the total no. of ways in which USU and CDP can be arranged with a space of two is: 5 * 6! = 3600

Then, with a gap of three spaces, USU will come at the first place and CDP at the fifth. We will have four such cases until CDP comes last. So, total no of ways to arrange the jobs with USU and CDP three spaces apart = 4 * 6!

Then, with a gap of four spaces, USU will come at the first place and CDP at the sixth. We will have three such cases until CDP comes last. So, total no of ways to arrange the jobs with USU and CDP three spaces apart = 3 * 6!

Then, with a gap of five spaces, USU will come at the first place and CDP at the seventh. We will have two such cases until CDP comes last. So, total no of ways to arrange the jobs with USU and CDP three spaces apart = 2 * 6!

Finally, with a gap of 6 spaces, USU at first place and CDP at the last, we can arrange the rest of the jobs in 6! ways.

So, total no. of different ways to arrange the jobs such that USU comes before CDP = 10080 + 6*6! + 5*6! + 4*6! + 3*6! + 2*6! + 1*6!

                    = 10080 + 4320 + 3600 + 2880 + 2160 + 1440 + 720

                    = 25200 ways

d. If QKJ comes last then, the remaining 7 jobs can be arranged in 7! ways. Similarly, if LPW comes last, the remaining 7 jobs can be arranged in 7! ways. so, total no. of different ways in which the eight jobs can be arranged is 7! + 7! = 10080 ways

e. If QKJ comes last then, the remaining 7 jobs can be arranged in 7! ways in the queue. Similarly, if QKJ comes second-to-last then also the jobs can be arranged in the queue in 7! ways. So, total no. of ways to arrange the jobs in the queue is 7! + 7! = 10080 ways

3 0
3 years ago
Prove that if two lines intersect each other then the vertically opposite angles are equal.
Svetradugi [14.3K]

If two lines intersect each other then the vertically opposite angles are equal.

<h3>What is a line?</h3>

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

To prove, two lines intersect each other then the vertically opposite angles are equal.

Suppose there are two lines AB and CD intersecting at a point O.

So, the angles a and c ; b and d are vertically opposite.

Now taking line AB,

Since sum of angles made on a straight line is 180°.

Thus ∠a + ∠b = 180°    ...(i)

Similarly taking line CD,

∠b + ∠c = 180°            ....(ii)

Comparing eq (i)  and (ii) we get,

∠a + ∠b = ∠b + ∠c

Therefore, we get

∠a = ∠c

which are vertically opposite angles.

Taking line CD,

Since sum of angles made on a straight line is 180°.

Thus ∠c + ∠b = 180°    ...(iii)

Similarly taking line CD,

∠c + ∠d = 180°            ....(iv)

Comparing eq (iii)  and (iv) we get,

∠c + ∠b = ∠c + ∠d

Therefore, we get

∠b = ∠d

which are vertically opposite angles.

Thus, if two lines intersect each other then the vertically opposite angles are equal.

To learn more about angles:

brainly.com/question/11337367

#SPJ4

7 0
2 years ago
Mr. Rijo bought 49 bags of soil one week and 28 bags of soil the next week. Which expression correctly applies the
earnstyle [38]

Answer:

49 + 28 = 7(7 + 4)

Step-by-step explanation:

49 bags of soil one week

28 bags of soil the next week

49 + 28 bags of soil purchased in total

Find the GCF (Greatest Common Factor) of 49 and 28.

49/7 = 7

28/7 = 4 (GCF is 7 since it is the largest number that can divide both 49 and 28 equally)

Factor out the GCF + rewrite division above (optional for visualization)

49/7 = 7 -> 49 = 7 * 7

28/7 = 4 -> 28 = 7 * 4

49 + 28 = 7(7 + 4)

Let me know if you have any questions!

8 0
2 years ago
I need help I'm confused again need help asap ​
san4es73 [151]

Answer:

1/8th chance of spinning yellow

or as a decimal 0.125

Step-by-step explanation:

Hope this helps

7 0
3 years ago
Help me on this one NOW!!! please
neonofarm [45]
What is the task for this formula
8 0
3 years ago
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