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victus00 [196]
3 years ago
14

A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in

which at least one member of the group is a senior partner?
Mathematics
1 answer:
lina2011 [118]3 years ago
8 0

Answer:100

Step-by-step explanation:

There are ten total people:

10C3

10!/(7!×3!) = 120

Note: but that includes all the cases where there are no senior partners

So firstly let figure out the number of cases where there are no senior partners

because there are 6 junior partners

6C3

= 6!/(3!×3!) = 20

120 - 20 = 100 or the number of possible groups where there is at least 1 senior partner.

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Answer:

39 or 1/39

Step-by-step explanation:

You need to divide these but it depends on how you divide them

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Use synthetic substitution to evaluate the polynomial P(x) = x^3-3x^2+4x-7 for x=3
Zina [86]

Answer:

\frac{x^3-3x^2+4x-7}{x-3} =(x^2+4)+\frac{5}{x-3}

Step-by-step explanation:

We are given polynomial as

P(x)=x^3-3x^2+4x-7

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we can use synthetic division

so, we got

Remainder =5

Quotient is

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=x^2+4

we can write as

\frac{x^3-3x^2+4x-7}{x-3} =(x^2+4)+\frac{5}{x-3}


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3 years ago
Using your knowledge of exponential and logarithmic functions and properties, what is the intensity of a fire alarm that has a s
Ierofanga [76]

Option B:

I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}

Solution:

Given sound level = 120 decibel

To find the intensity of a fire alarm:

$\beta=10\log\left(\frac{I}{I_0} \right)

where I_0=1\times10^{-12}\ \text {watts}/ \text m^2}

Step 1: First divide the decibel level by 10.

120 ÷ 10 = 12

Step 2: Use that value in the exponent of the ratio with base 10.

10^{12}

Step 3: Use that power of twelve to find the intensity in Watts per square meter.

$10^{12}=\left(\frac{I}{I_0} \right)

$10^{12}=\left(\frac{I}{1\times10^{-12}\ \text {watts}/ \text m^2} \right)

Now, do the cross multiplication,

I=10^{12}\times1\times\ 10^{-12} \ \text {watts}/ \text m^2}

I=1\times\ 10^{12-12} \ \text {watts}/ \text m^2}

I=1\times\ 10^{0} \ \text {watts}/ \text m^2}

I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}

Option B is the correct answer.

Hence I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}.

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