Exercise 8.3.4: Selecting coders for 3 different projects. About (a) A manager must select three coders from her group to write three different software projects. There are 7 junior and 3 senior coders in her group. The first project can be written by any of the coders. The second project must be written by a senior person and the third project must be written by a junior person. How many ways are there for her to assign the three coders to the projects if no person can be assigned to more than one project

Answer:

[tex]S_{25}=555[/tex]

Step-by-step explanation:

Given that,

In an AP, the 6th term is 39 i.e.

[tex]a_6=a+5d\\\\39=a+5d\ ....(1)[/tex]

In the same AP, the 19th term is 7.8 i.e.

[tex]a_{19}=a+18d\\\\7.8=a+18d\ ......(2)[/tex]

Subtract equation (1) from (2).

7.8 - 39 = a+18d - (a+5d)

-31.2 = a +18d-a-5d

-31.2 = 13d

d = -2.4

Put the value of d in equation (!).

39 = a+5(-2.4)

39 = a- 12

a = 39+12

a = 51

The sum of n terms of an AP is given by :

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

Put n = 25 and respected values,

[tex]S_{25}=\dfrac{25}{2}[2(51)+24(-2.4)]\\\\=555[/tex]

Hence, the sum of first 25 terms of the AP is equal to 555.

Answer:

0.875?

Step-by-step explanation:

I just did 7 divided by 8

Answer:

14/16

49/56

Step-by-step explanation:

I looked it up for you!!!

Answer:

6x+8

Step-by-step explanation:

Brainliest?

Answer:

0 = 0

Step-by-step explanation:

Subtract 4 from both sides of the equation

3 + 4 − 4 = 3 + 4 − 4

Simplify

Subtract the numbers

3 = 3 + 4 − 4

3 = 3

Subtract 3x from both sides of the equation

3 − 3 = 3 − 3

Combine like terms

0 = 3 − 3

Result

0 = 0

Answer:

47.12

Step-by-step explanation:

Answer:

1/3 x 3/4

Step-by-step explanation:

he took 1/3 of 3/4 means that he did 1/3 x 3/4

Answer:

A: X(t)=37cos(70)t and y(t)=-16t^2+37sin(70)t

Step-by-step explanation:

Answer:

A on edge

Step-by-step explanation:

Answer:

8y+5

Step-by-step explanation:

Answer:

∠1 = 148°

Step-by-step explanation:

the triangle interior angles = 180°

the unknown interior angle = 180° - 82° - 66° = 32°

∠1 = 180° - 32° = 148°  because it is supplementary to 32°  (adds together to total 180°)

For adding variables we use the coefficient as 1 if there is no number infront of variable.

An expression is combination of variables, numbers and operators.

A coefficient is a multiplicative factor in some term of a polynomial, a series, or an expression; it is usually a number, but may be any expression.

Let us consider a algebraic expression

ax+by+z=0

In the given expression a, b are coefficients of x and y respectively.

We use coefficient as one when there is no number before a variable because when we add variables there should be some number before varibales. So we consider 1 as coefficient for those variables which does not have any coefficient.

Hence, for adding variables we use the coefficient as 1 if there is no number infront of variable.

To learn more on Expressions click:

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Answer:

1/2 of

4/3 x

3 x

1 unit of

Step-by-step explanation:

have a nice day!

Answer:

1/2 of

4/3 x

3 x

1 unit of

half of, twice, greater than

Step-by-step explanation:

Hope this helps!

If not, I am sorry.

Answer:

F = (-2,4); E = (-2,0); D = (2,0)

Step-by-step explanation:

F = 4 points from A, so by a scale factor of 2, it would be 2 times father away from A. The same thing applies for all of the other points; just find how much father A is from a point, then dilate that point by multiplying it by the scale factor, and settling the point closer or father from A.

Answer:

x=-4

Step-by-step explanation:

The angles have to equal eachother, so:

130=134+x

subract 134 from both sides

-4=x

Answer:

5000 pounds

Step-by-step explanation:

Hello There!

There are 2000 pounds in 1 ton

So to convert tons to pounds we multiply by 2000

2.5x2000=5000

So 2.5 tons is the equivalent if 5000 pounds

Answer:

Let me know if there is anything you don't get

∠3 = 102 because ∠1 and ∠3 are supplementary and 102 + 78 = 180

∠4 = 102 because ∠1 and ∠4 are consecutive interior angles

∠5 = 78 because ∠1 and ∠5 are corresponding angles

∠6 = 133 because ∠2 and ∠6 are supplementary angles

∠7 = 47 because ∠2 and ∠7 are vertical angles

∠8 = 47 because ∠2 and ∠8 are opposite interior angles

∠9 = 133 because ∠8 and ∠9 are supplementary, and we just saw ∠2=∠8

∠10 = 102 because ∠1 and ∠10 are supplementary

You could have used a whole bunch of different relations, but I wanted to focus on ∠1 and ∠2 since those were told to us

Step-by-step explanation:

For this question you need to know several parts of geometry.  Let me know if anything doesn't make sense.

First, parallel lines are two or more lines which are angles in such a way that no matter how long they are they will not cross.  In other words they are slanted at the same angle.  you can see this with lines a and b in this picture.

Second, a transversal is a line that crosses through two or more parallel lines.  A transversal creates a number of angles that have special properties.  I would like you to look specifically at line c as I describe these angles.  line c is a transversal to Ines a and b.  Also line d is also a transversal.

There are seven special angles to know.

The easiest is supplementary angles.  This you don't need parallel lines, but if any two lines ever cross this creates 4 angles.  you can actually look at where lines c and b intersect in your problem.  Angles 2. 6 and 7 are labeled but there is one more unlabeled one.  Now, 180 degrees is a straight line.  With angles you can see angles 6 and 7 add together to be a straight line.  Similarly 2 and 6 do as well.  These are two sets of supplementary angles.  

To list off the supplementary angles here 9 and 8 are supplementary, as are  2 and 6, 6 and 7, 1 and 3, 1 and 10, and finally 4 and 5.

From supplementary angles comes vertical angles.  Again, if you look at angles 2, 6 and 7 we already know ∠2 + ∠6 = 180 and ∠6 + ∠7 = 180.  Well lets say ∠6 = 133.  Well then, we could use algebra to see that both ∠2 AND ∠7 are 47 degrees.  This is the property of vertical angles.  if you have two lines intersecting, any two angles that have a third in between the are called vertical angles, and are equal.

some examples of vertical angles are ∠2 and ∠7as well as ∠3 and ∠10,  

Finally we go into parallel line specific angles.  If you have two or more parallel lines with a transversal, so in particular look at a and b as the parallel lines and c as the transversal.  The transversal creates some special angles.  in particular, the transversal crosses a and b at the same angle, so angles 8 and 7 have the same value.  These are known as corresponding angles, since they correspond tot he same position with a transversal crossing through parallel lines.  

the corresponding angles in the picture are ∠8 and ∠7, ∠3 and ∠4 and finally ∠1 and ∠5.  the last two using line d as a transversal.

After corresponding angles opposite interior angles I think are the next logically to look at.  Opposite means they are on two different parallel lines and on different sides of the transversal, while interior means they are between the parallel lines.  so if you look at the parallel lines a and b there are angles 8 and 2 that are interior angles.  Since 8 is against line a and 2 is against line b, and ∠8 is above transversal c while ∠2 is below it, they are opposite angles.  so 8 and 2 are opposite interior angles.  Now, if you look at ∠8 and ∠7 you know these are corresponding angles, then ∠7 and ∠2 are vertical angles.  This means opposite interior angles are equal.

A list of opposite interior angles are ∠8 and ∠2, and ∠10 and ∠4.

Alongside opposite interior, there are opposite exterior angles.  opposite means on different parallel Ines and on opposite sides of the transversal, while this time exterior means not between the parallel lines.  Now just like we figured with opposite interior angles

The only labeled pair of opposite exterior angles are ∠9 and ∠6.  Now just like we figured with opposite interior angles, let's start with ∠8 and ∠9, which are supplementary.  then ∠8 and ∠7 are corresponding angles so ∠9 and ∠7 are supplementary.  We can also see ∠7 and ∠6 are supplementary.  well, since ∠9 + ∠7 = 180 = ∠6 + ∠7 then ∠9 = 180 - ∠7 = ∠6 so ∠9 = ∠6.  This shows opposite exterior angles are  equal.

So we did two kinds of opposite angles, it might make sense there are non opposite angles.  And there are.  these are called consecutive angles.  There are consecutive exterior and consecutive interior angles.  An example of each are ∠1 and ∠4 for consecutive interior, consecutive because they are on the same side of the transversal, and interior because they are between the two parallel lines.  ∠3 and ∠5 are consecutive exterior angles.

You can use similar reasoning we have been so far to conclude all consecutive angles are supplementary

Answer:

12

Step-by-step explanation:

bc I added 7+5 equals 12

Answer:

Large: 17,125

Small: 78,100

Step-by-step explanation:

Answer:

52 or 28

Step-by-step explanation:

An isosceles has 2 congruent angles.

There are 2 possibilities:

A) There are two 76-deg angles and one angle of a different measure.

76 + 76 + x = 180

x = 28

B) There are two congruent angles, and 76 is the non-congruent angle.

x + x + 76 = 180

2x = 104

x = 52

Answer: 52 or 28

Answer:

x2 - 9x +20

Step-by-step explanation:

Answer:

4y + 4x - 4

4(y + x - 1)

Step-by-step explanation:

Brainliest plz

Answer:

4x+4y-4

Step-by-step explanation:

Lets simplify step by step:

5y - 8x - 7- y + 12 x + 3 = 5y +-8x +-7 + -y + 12x + 3

Now let’s combine the like terms:

5y +-8x +-7 + -y + 12x + 3

(-8x + 12x) + (5y + -y) + (-7 + 3)

So the answer would be 4x+4y-4

Hope this helps :)

Answer:

log150=2.1716091259

Step-by-step explanation:

Press it on your calculator

Answer:

i dont know im just doing this for the points

Answer:

7.10 I think its 7.10

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 11.52

Explanation:

1.28 x 9 = 11.52

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Given:

The inequality is:

[tex]-20t>-80[/tex]

To find:

The solution for the given inequality and graph of it.

Solution:

We have,

[tex]-20t>-80[/tex]

Divide both sides by -20 and change the sign of inequality because inequality is divided by a negative number.

[tex]\dfrac{-20t}{-20}<\dfrac{-80}{-20}[/tex]

[tex]t<4[/tex]

Therefore, the solution for the given inequality is [tex]t<4[/tex].

All the value less than 4 are in the solution set. It means all the values on the left side of 4 are in the solution set.

Since 4 is not included in the solution set, therefore there is an open circle at 4.

The graph for the given inequality is shown below:

Answer:

student randomly selected from a list of all students at the school

Answer:

c = 31.5

Step-by-step explanation:

Given c varies directly as [tex]\sqrt{d}[/tex] then the equation relating them is

c = k[tex]\sqrt{d}[/tex] ← k is the constant of variation

To find k use the condition c = 14 when d = 64, then

14 = k ×[tex]\sqrt{64}[/tex] = 8k ( divide both sides by 8 )

1.75 = k

c = 1.75[tex]\sqrt{d}[/tex] ← equation of variation

When d = 324 , then

c = 1.75 × [tex]\sqrt{324}[/tex] = 1.75 × 18 = 31.5

Answer:

$575

Step-by-step explanation

1150/2 = 575

Answer:

$1150

Step-by-step explanation:

because it is a buy one (for sale price), get one free

Answer:

Mean: 10

Median: 10.5

Mode: none

Step-by-step explanation:

there is no mode, mean is 10 and median is 10.5

Answer:

Stratified sampling

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this question:

Population divided into groups, and random samples are drawn from the groups. This is a mark of stratified sampling.