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Rufina [12.5K]
2 years ago
13

Can someone help me solve this please, I'm stuck.

Mathematics
1 answer:
salantis [7]2 years ago
8 0

The expression (3a + 2b)^7 is a binomial expression;

The coefficient of the fourth term is 15120

<h3>How to determine the coefficient fourth term?</h3>

The equation is given as:

(3a + 2b)^7

The above expression is a binomial expression;

Assume the expression is:

(x + y)^n

The equation of the expansion is:

(x + y)^n = ^nC_r * x^{n-k} * y^k

When the expression is expanded, the parameters of the fourth term are

n = 7

r = 4

x = 3a

y = 2b

So, we have:

(3a + 2b)^7 = 7C4 * (3a)^(7-4) * (2b)^4

Evaluate each factor

(3a + 2b)^7 = 35 * (3a)^3 * (2b)^4

Evaluate the powers

(3a + 2b)^7 = 35 * 27a^3 * 16b^4

Evaluate the product

(3a + 2b)^7 = 15120a^3b^4

The coefficient of the above expression is 15120

Hence, the coefficient of the fourth term is 15120

Read more about binomial expressions at:

brainly.com/question/13602562

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Katarina [22]

Answer:

<em>The Washington High School won the meet by scoring 162 points </em>

<em>The Johnson High School came in second place by scoring 159 points, 3 points less than the winner.</em>

Step-by-step explanation:

<u>Arithmetics </u>

We need to perform a number of basic arithmetics operations and derive conclusions out of the results.

We know that

  • 10 points are awarded for each first-place finish
  • 8  points are awarded for each second-place finish
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* Washington High School had 10 first-place finishes, 6 second-place finishes, and 2 third-place finishes.  

Total points: 10*10+6*8+2*7=162 total points

* Johnson High School had 8 first-place finishes, 9 second-place finishes, and 1 third-place finish.

Total points: 8*10+9*8+1*7=159 total points

* Roosevelt High School had 4 first-place finishes, 5 second-place finishes, and 4 third-place finishes.

Total points: 4*10+5*8+4*7=108 total points

* Lewis High School had 3 first-place finishes, 3 second-place finishes, and 6 third-place finishes.

Total points: 3*10+3*8+6*7=96 total points

The Washington High School won the meet by scoring 162 points

The Johnson High School came in second place by scoring 159 points, 3 points less than the winner.

8 0
3 years ago
How much should you invest at 4% simple interest in order to earn $50 interest in 6 months
LenaWriter [7]
Simple interest formula
Interest = Pit = $50
P=principal (initial investment)
i=annual interest rate = 0.04
t=time in years = 6 months = 0.5 years

Substitute values,
$50 = P*0.04*0.5 
Solve for P
P=$50/(0.04*0.5)=$2500


4 0
3 years ago
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649,420
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3 years ago
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The sand pit for the long jump has a width of 2.7 meters and a length of 9.54 meters. Just in case it rains, the principal wants
sveta [45]

Answer:

A = 25.758 m²

Step-by-step explanation:

Width of the sand pit, b = 2.7 m

Length of the sand pit, l = 9.54 m

We want to cover the sand pit with a piece of plastic. We need to find how many square meters of plastic will be needed to cover the sand pit. It is equal to the area of sand pit. It is in the shape of rectangle. Its area is given by :

A = l × b

A = 2.7 × 9.54

A = 25.758 m²

So, 25.758 m² of plastic will be needed to cover the sand pit.

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