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Rasek [7]
3 years ago
14

Samantha must include 1 English class, 1 Algebra class, and 1 Biology class in a schedule. There 3 English teachers, 4 Algebra t

eachers, and 2 Biology teachers. How many different schedules are possible?
Mathematics
1 answer:
astra-53 [7]3 years ago
4 0

To solve this problem, we make use of the formula of combination.

nCr = n! / r! (n – r)!

where n is the total number of subject teachers and r is the number of subjects r = 1

 

For the English class n = 3

3C1 = 3! / 1! (3 – 1)! = 3

 

For the Algebra class n = 4

4C1 = 4! / 1! (4 – 1)! = 4

 

 

For the Biology class n = 2

2C1 = 2! / 1! (2 – 1)! = 2

 

The total number of different schedules would be the product of the three combinations:

total combinations possible = 3 * 4 * 2

total combinations possible = 24

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A car is driving at 65 kilometers per hour. How far, in meters, does it travel in 3 seconds?
kati45 [8]

Step-by-step explanation:

65 km / h = 65,000 m / 3600 s

what do we need to multiply 3600 with to get 3 ?

3600 × f = 3

f = 3/3600 = 1/1200

now, we need to multiply 65,000 by the same factor to get how many meters the car is driving in these 3 seconds :

65000 × 1/1200 = 65000/1200 = 54.16666666...

so, rounded, it travels 54 meters in 3 seconds.

3 0
2 years ago
A carnival game has the possibility of scoring 50 points, 75 points, or 150 points per turn. The probability of scoring 50 point
MariettaO [177]

Answer:

The game’s expected value of points earned for a turn is 71.

Step-by-step explanation:

Here we know that:

Points     Frequency

50           55

75            32

150          13

Here points earned is a random variable.

We need to find its expected value,

Finding Expected value:

Expected value of a random variable is its mean value. So we will first find the mean value of points earned per turn from the table we are given.

Total number of turns = sum of frequencies

= 55 + 32 + 14 = 100

Total points earned = 50(55) + 75(32) + 150(13)

= 7100

Expected value of points earned for a turn = Mean value of points

= Total points/no. of turns

= 7100/100

= 71

8 0
3 years ago
Sandra you sir debit card to buy lunch for $8.74 on monday on tuesday she deposit 8 and 74 since back until accounts was the ove
blsea [12.9K]
I think its increase
3 0
3 years ago
Find the size of each of the angles marked with letter​
lilavasa [31]

Answer:

f = 78 , g = 32 , h = 74

Step-by-step explanation:

f and 78° are alternate angles and are congruent , then

f = 78

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

h and 74° are alternate angles and are congruent , so

h = 74

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

the sum of the 3 angles in the triangle = 180°

sum the 3 angles and equate to 180

78 + g + h = 180

78 + g + 74 = 180

152 + g = 180 ( subtract 152 from both sides )

g = 28

4 0
2 years ago
What is the product of (-4x2-5x-1)(4x2-6x-2)
Stells [14]
(-4x2-5x-1)(4x2-6x-2)

Final result :

-2 • (13x + 1) • (2x2 - 3x - 1)
Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2".

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(-13x - 1) • ((22x2 - 6x) - 2)
Step 2 :

Pulling out like terms :

3.1 Pull out like factors :

-13x - 1 = -1 • (13x + 1)

Step 3 :

Pulling out like terms :

4.1 Pull out like factors :

(4x2 - 6x - 2) = 2 • (2x2 - 3x - 1)

Trying to factor by splitting the middle term

4.2 Factoring 2x2 - 3x - 1

The first term is, 2x2 its coefficient is 2 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -1

Step-1 : Multiply the coefficient of the first term by the constant 2 • -1 = -2

Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is -3 .

-2 + 1 = -1
-1 + 2 = 1

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Step 4 :

Pulling out like terms :

5.1 Pull out like factors :

-26x - 2 = -2 • (13x + 1)

Final result :

-2 • (13x + 1) • (2x2 - 3x - 1)
7 0
3 years ago
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