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motikmotik
3 years ago
5

In a group of 120 recruits at the police academy 80 are college graduates and 25 are army veterans. If 15 of the recruits are bo

th college graduate and army veterans as shown above, how many are neither college graduate nor army veterans?
Mathematics
1 answer:
Gre4nikov [31]3 years ago
4 0

Answer:

the number of recruits neither be college graduate and nor army veterans is 30

Step-by-step explanation:

The computation of the number of recruits neither be college graduate and nor army veterans is as follows;

= Total recruits - (college students + army veterans - both college graduates & army veterans)

= 120 recruits - (80 + 25 - 15)

= 120 recruits - 90  

= 30

hence, the number of recruits neither be college graduate and nor army veterans is 30

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A triangle has an angle that measures 10°. The other two angles are in a ratio of 3:14. What
ivann1987 [24]

Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the measures of other two angles of triangle.

\red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}

We know that,

  • The other two angles of triangle are in the ratio of 3 : 14. So, let us consider the other two angles of the triangle be 3x and 14x.

Angle sum property,

  • The angle sum property of triangle states that the sum of interior angles of triangle is 180°. By using this property, we'll find the other two angles of the triangle.

\rule{200}{3}

\sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}}

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

\rule{200}{3}

Second AnglE :

  • 3x
  • 3 × 10
  • 30°

∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

\rule{200}{3}

Third AnglE :

  • 14x
  • 14 × 10
  • 140°

∴ Hence, the measure of the third angle of the triangle is 140°.

5 0
2 years ago
Select the property of equality used to arrive at the conclusion. If x = 4, then 5x = 20 the addition property of equality the m
shtirl [24]

Answer:

The Division Property of Equality

Step-by-step explanation:

<u>The Addition Property of Equality:</u> When you add something to one side of the equation, you must add the same thing to the other side.

<u>The Subtraction Property of Equality:</u> When you subtract something from one side of the equation, you must subtract the same thing from the other side.

<u>The Multiplication Property of Equality:</u> When you multiply something to one side of the equation, you must multiply the same thing to the other side.

<u>The Division Property of Equality:</u> When you divide something from one side of the equation, you must divide the same thing from the other side.

In this case, you have to divide both sides of the equation by 5 to get x = 4. That means that the division property of equality was used.

I hope this helps! Have a great day!

8 0
3 years ago
Read 2 more answers
10 points! I will thanks, rate, and give best answer!!
vfiekz [6]
Answer: The fourth term is -102

----------------------------------------------

Explanation:

The term after the nth term is generated by this rule  a_{n+1} = -4(a_n) + 2 which means that we first
Step 1) multiply the nth term ( a_n ) by -4
Step 2) Add the result of step 1 to the value 2 to get the next term in the sequence

Let's follow those steps above to generate the first four terms

The first term is a_1 = 2. In short, the first term is 2

The second term is...
a_{n+1} = -4(a_n) + 2
a_{1+1} = -4(a_1) + 2
a_{2} = -4(2) + 2
a_{2} = -8 + 2
a_{2} = -6
So the second term is -6

The third term is...
a_{n+1} = -4(a_n) + 2
a_{2+1} = -4(a_2) + 2
a_{3} = -4(-6) + 2
a_{3} = 24 + 2
a_{3} = 26
The third term is 26

Finally, the fourth term is...
a_{n+1} = -4(a_n) + 2
a_{3+1} = -4(a_3) + 2
a_{4} = -4(26) + 2
a_{4} = -104 + 2
a_{4} = -102
The fourth term is -102.
4 0
3 years ago
Refer to the Newsela article "A Step-by-Step Guide to the Scientific Method."
iVinArrow [24]

Answer:

Controlled Observation

Step-by-step explanation:

Answer..

6 0
3 years ago
Read 2 more answers
8x+11=14-1x how does it work
Alenkinab [10]

Answer:

x = 1/3

Step-by-step explanation:

Step 1: Write equation

8x + 11 = 14 - 1x

Step 2: Solve for <em>x</em>

  1. Simplify: 8x + 11 = 14 - x
  2. Add x to both sides: 9x + 11 = 14
  3. Subtract 11 on both sides: 9x = 3
  4. Divide both sides by 9: x = 3/9
  5. Simplify: x = 1/3

Step 3: Check

<em>Plug in x to verify it's a solution.</em>

8(1/3) + 11 = 14 - 1(1/3)

8/3 + 11 = 14 - 1/3

41/3 = 41/3

3 0
2 years ago
Read 2 more answers
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