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klio [65]
3 years ago
6

Choose the pair of events that is mutually exclusive. (a). Even integers and multiples of 3 (b). Odd integers and multiples of 4

(c). Integers greater then 40 and integers less then 50. (d). Prime numbers and even integers
Mathematics
2 answers:
Grace [21]3 years ago
8 0

Answer: <em>odd integers and multiples of  4 is correct on gradpoint/ connexus</em>

notka56 [123]3 years ago
7 0
(b). Odd integers and multiples of 4. Both events are mutually exclusive: Not any odd number is divisible by an even number

(c). Integers greater then 40 and integers less then 50. Mutually exclusive since we can't have greater & smaller at the same time

(d). Prime numbers and even integers .Mutually exclusive. Not a sigle prime number is even

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The half-life of a certain radioactive material is 78 hours. An initial amount of the material has a mass of 790 kg.. Write an e
adoni [48]
<span> half life i= 78 hours 
 amount after 78 hours is 395 kg: 
395 = 790e^(k*78) 

Dividing by 790 and taking natural log
ln (395/790) = (k*78) 
-0.6931 = 78k 
-0.00888 = k  

lets calculate  how much is left after 18 hours: 
Amount(18)
= 790e^(-0.00888*18) 
Amount = 673.301 kg
hope this helps</span>
4 0
2 years ago
Read 2 more answers
Find the volume of the sphere
madam [21]

Answer:

sphere volume = 3052.1 in³

Step-by-step explanation:

sphere volume = 4/3πr³ = 4/3(3.14)(9³) = 3052.1 in³

6 0
3 years ago
Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5​
Bond [772]

Answer:

The solution to the equation system given is:

  • <u>x = 2</u>
  • <u>y = -1</u>

Step-by-step explanation:

First, we must know the equations given:

  1. 2x + 3y = 1
  2. 3x + y = 5​

Following Crammer's Rule, we have the matrix form:

\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]

Now we solve using the determinants:

x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2

y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

  • 2x + 3y = 1
  • 2(2) + 3(-1)= 1
  • 4 - 3 = 1
  • 1 = 1

And, with the second equation:

  • 3x + y = 5​
  • 3(2) + (-1) = 5
  • 6 - 1 = 5
  • 5 = 5

 

4 0
2 years ago
Which of the following best describes the relationship between (x+2) and the polynomial 3x^2-x-14
Flauer [41]
One is a linear and the other is a quadratic polynomial.
And (x+2) is indeed a factor.

You can rewrite it as (x+2)(3x-7)
8 0
2 years ago
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Solve for the missing sides 30-60-90 triangle show work please and thank you
Alex_Xolod [135]

Answer:

4.

x=8\sqrt{3}

y=16

5.

x=3

y=3\sqrt{3}

Step-by-step explanation:

The sides of a (30 - 60 - 90) triangle follow the following proportion,

a-a\sqrt{3}-2a

Where (a) is the side opposite the (30) degree angle, (a\sqrt{3}) is the side opposite the (60) degree angle, and (2a) is the side opposite the (90) degree angle. Apply this property for the sides to solve the two given problems,

4.

It is given that the side opposite the (30) degree angle has a measure of (8) units. One is asked to find the measure of the other two sides.

The measure of the side opposite the (60) degree side is equal to the measure of the side opposite the (30) degree angle times (\sqrt{3}). Thus the following statement can be made,

x=8\sqrt{3}

The measure of the side opposite the (90) degree angle is equal to twice the measure of the side opposite the (30) degree angle. Therefore, one can say the following,

y=16

5.

In this situation, the side opposite the (90) degree angle has a measure of (6) units. The problem asks one to find the measure of the other two sides,

The measure of the side opposite the (60) degree angle in a (30-60-90) triangle is half the hypotenuse times the square root of (3). Therefore one can state the following,

y=3\sqrt{3}

The measure of the side opposite the (30) degree angle is half the hypotenuse (the side opposite the (90) degree angle). Hence, the following conclusion can be made,

x=3

6 0
3 years ago
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