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2 years ago

(1/2) (10t) = 50,000

Mathematics

1 answer:

vekshin12 years ago

3 0

Answer: The value of t become 10000.

Step-by-step explanation:

Since we have given that

$\dfrac{1}{2}\times 10t=50000$

We need to find the value of t from the above expression:

first we divide 10t by 2 to get 50000.

$\dfrac{10t}{2}=50000\\\\5t=50000\\\\t=\dfrac{50000}{5}\\\\t=10000$

Hence, the value of t become 10000.

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Which expressions are equivalent to 2 ln a 2 ln b - ln a? Check all that apply. Ln ab2 - ln a ln a 2 ln b ln a2 ln b2 - ln a 2 l

marysya [2.9K]

Equivalent expressions are expressions with same simplified form. Equivalent expressions for the given expression are;

Expression 2: $\ln(a) + 2\ln(b) = \ln(a) + \ln(b^2) = \ln(ab^2)$
Expression 3: $\ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)$
Expression 5: $\ln(ab^2)$

<h3>What are equivalent expressions?</h3>

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

<h3>What is logarithm and some of its useful properties?</h3>

When you raise a number with an exponent, there comes a result.

Lets say you get

$a^b = c$

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

$b = log_a(c)$

Some properties of logarithm are:

$log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(b^c) = c \times log_a(b)\\\\log_b(b) = 1\\\\ log_a(b) + log_b(c) = log_a(c)$

Log with base e = 2.71828.... is written as $\ln(x)$ simply.

The expression given is $2\ln(a) + 2\ln(b) - \ln(a)$

We get its simplified form as

$2\ln(a) + 2\ln(b) - \ln(a) = \ln(a) + \ln(b^2) = \ln(ab^2)$

Simplifying given expressions:

Expression 1: $\ln(ab^2) - \ln(a) = \ln(ab^2/a) = \ln(b^2)$

This isn't same as simplified form of original

. Thus , this expression is not equivalent to the given expression.

Expression 2: $\ln(a) + 2\ln(b) = \ln(a) + \ln(b^2) = \ln(ab^2)$

This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.

Expression 3: $\ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)$

This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.

Expression 4: $2\ln(ab) = \ln((ab)^2) = \ln(a^2b^2)$

This isn't same as simplified form of original expression. Thus , this expression is not equivalent to the given expression.

Expression 5: $\ln(ab^2)$

This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.

Thus, equivalent expressions for the given expression are;

Expression 2: $\ln(a) + 2\ln(b) = \ln(a) + \ln(b^2) = \ln(ab^2)$
Expression 3: $\ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)$
Expression 5: $\ln(ab^2)$

Learn more about equivalent expressions here:

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1 year ago

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Answer: hypothesis testing with a null hypothesis that the number of customers is less than or equal to the usual number.

Step-by-step explanation:

Your question isn't complete as you didn't provide the options. These are given above.

Based on the options, the calculation that would help them determine the most likely range of customers arriving for that meal is a hypothesis testing with a null hypothesis that the number of customers is less than or equal to the usual number.

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2 years ago

What are the first 5 terms of <br>n+ 3

andrezito [222]

Answer:

The sequence of first five terms

4 , 5, 6, 7, 8

Step-by-step explanation:

Given $n^{th}$ of the sequence

aₙ = n + 3 ..(i)

put n =1

a₁ = 1 +3

a₁ = 4

The first term of the sequence = 4

Put n =2 in equation (i)

a₂ = 2+3

a₂ = 5

The second term of the sequence = 5

put n=3 in equation (i)

a₃ = 3+3 = 6

The third term of the sequence = 6

Put n=4 in equation (i)

a₄ = 4 +3

a₄ = 7

The fourth term of the sequence = 7

Put n = 5 in equation (i)

a₅ = 5+3

a₅ = 8

The fifth term of the sequence = 8

The sequence of first five terms

4 , 5, 6, 7, 8

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2 years ago

100 points

Pavlova-9 [17]

STEP
1
:

y
Simplify —
3
Equation at the end of step
1
:

y
(((18•(x5))•(y3))+((6•(x2))•(y4)))+((((24•(x6))•—)•x)•y)
3
STEP
2
:

Equation at the end of step
2
:

y
(((18•(x5))•(y3))+((6•(x2))•(y4)))+((((23•3x6)•—)•x)•y)
3
STEP
3
:

Canceling Out:

3.1 Canceling out 3 as it appears on both sides of the fraction line

Equation at the end of step
3
:

(((18•(x5))•(y3))+((6•(x2))•(y4)))+((8x6y•x)•y)
STEP
4
:

Equation at the end of step
4
:

(((18•(x5))•(y3))+((2•3x2)•y4))+8x7y2
STEP
5
:

Equation at the end of step
5
:

(((2•32x5) • y3) + (2•3x2y4)) + 8x7y2
STEP
6
:

STEP
7
:
Pulling out like terms

7.1 Pull out like factors :

8x7y2 + 18x5y3 + 6x2y4 = 2x2y2 • (4x5 + 9x3y + 3y2)

Trying to factor a multi variable polynomial :

7.2 Factoring 4x5 + 9x3y + 3y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :
2x2y2 • (4x5 + 9x3y + 3y2)

3 0

1 year ago