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3 years ago

Combine like terms to simplify the expression: 2a+3b-4c-b+2a+2c

Mathematics

1 answer:

Ulleksa [173]3 years ago

8 0

Hey there! I'm happy to help!

First let's combine all of the terms with a.

2a+2a=4a

Now the ones with b.

3b-b=2b

And the ones with c.

-4c+2c=-2c

So, our simplified expression is 4a+2b-2c.

Have a wonderful day! :D

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A true-false quiz with 10 questions was given to a statistics class. Following is the probability distribution for the score of

disa [49]

Answer:

$E(X)=\sum_{i=1}^n X_i P(X_i)$

And if we use the values obtained we got:

$E(X)=5*0.05 +6*0.15 +7*0.33 +8*0.28+ 9*0.12 +10*0.07=7.48$

For this case this value means that the expected score is about 7.48

Step-by-step explanation:

For this case we assume the following probability distribution:

X 5 6 7 8 9 10

P(X) 0.05 0.15 0.33 0.28 0.12 0.07

First we need to find the expected value (first moment) and the second moment in order to find the variance and then the standard deviation.

In order to calculate the expected value we can use the following formula:

$E(X)=\sum_{i=1}^n X_i P(X_i)$

And if we use the values obtained we got:

$E(X)=5*0.05 +6*0.15 +7*0.33 +8*0.28+ 9*0.12 +10*0.07=7.48$

For this case this value means that the expected score is about 7.48

In order to find the standard deviation we need to find first the second moment, given by :

$E(X^2)=\sum_{i=1}^n X^2_i P(X_i)$

And using the formula we got:

$E(X^2)=(5^2 *0.05)+(6^2 *0.15)+(7^2 *0.33)+(8^2 *0.28)+ (9^2 *0.12 +(10^2 *0.07))=57.46$

Then we can find the variance with the following formula:

$Var(X)=E(X^2)-[E(X)]^2 =57.46-(7.48)^2 =1.5096$

And then the standard deviation would be given by:

$Sd(X)=\sqrt{Var(X)}=\sqrt{1.5096}=1.229$

5 0

3 years ago

Read 2 more answers

You purchased a vehicle for 32,000. It's value will depreciate at a rate of 18.62%. What will it's value be in 5 years, when you

Len [333]

Answer:

F = $11,421.90

Final value after 5 years F = $11,421.90

Complete question;

You purchased a vehicle for $32,000. It's value will depreciate at a rate of 18.62%. What will it's value be in 5 years, when you finally have it paid off

Step-by-step explanation:

Given;

Initial value P = $32,000

Depreciation rate r = 18.62% = 0.1862

Time t = 5

Final value = F

Using the compound depreciation formula;

F = P(1 - r)^t

Substituting the values;

F = $32,000(1 - 0.1862)^5

F = $11,421.90

Final value F = $11,421.90

8 0

3 years ago

Read 2 more answers

Mona wrote 7 tests, and her test average is 93. There will be one more test before the end of the year. What is the lowest grade

olga55 [171]

For this case, the first thing we are going to do is assume that all the tests are worth the same.
Then, we define a variable:
x: score of Mona's last test
We write now the inequality that models the problem:
$\frac{93 + x}{2} \geq 90$
From here, we clear the value of x: $93 + x \geq 90*(2) 

93 + x \geq 180

 x \geq 180 - 93

 x \geq 87$
Answer:
the lowest grade that Mona can get for her last test so that her test average is 90 or more is:
x = 87

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3 years ago

The repayment schedule is for a $1,300 loan at 7.5% for 6 months. What is the amount for interest at payment 5?

max2010maxim [7]

Answer: The answer is $2.77.

Step-by-step explanation: Given that we have to pay the loan of $1300 at interest rate of 7.5% in 6 months. According to the table,

Amount for interest in payment 1 = $8.13,

Amount of interest in payment 2 = $6.79

and

Amount of interest in payment 3 = $5.45.

We can see here that the difference in the amounts to be paid in consecutive months will be same, i.e., the payments will form an arithmetic progression (A.P.).

The common difference = 8.13-6.79=6.79-5.45=1.34.

Therefore, amount of interest in payment 4 = $(5.45-1.34) = $4.11

and amount of interest in payment 5 = $(4.11-1.34) = $2.77.

Please see the attached modified table.

Thus, the answer is $2.77.