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The intensity level of the earthquake in New Madrid, Missouri in 1812 was about 1.6 times less than the intensity level of the earthquake Valdivia, Chile, in 1960.

We use the following formula for comparing the intensity level of earthquakes-

Log (i1 / i2) = M1 - M2

where i = intensity level determined by a seismograph

M = magnitude on a Richter scale.

Now, from the given information-

magnitude of earthquake in New Madrid = 7.9

Thus, M1 = 7.9

Then intensity of the earthquake in New Madrid = i1

magnitude of earthquake in Chile = 9.5

Thus, M2 = 9.5

Then intensity of the earthquake in Chile = i2

⇒ log (i1 / i2) = 7.9 - 9.5

log (i1 / i2) = -1.6

This means that the intensity level of the earthquake in New Madrid, Missouri in 1812 was about 1.6 times less than the intensity level of the earthquake Valdivia, Chile, in 1960.

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According to the given  the given  logarithm log₃ 1/9 the value is = -2

Logarithmic functions are significant due of their link to exponential functions. Logarithms are useful for solving exponential equations and investigating the properties underlying exponential functions.

log₃ 1/9

Can be written as:

log₃ (1/9) = x

using the log definition in exponential form. if x and b are positive real number and b dose not equal 1 then  log_b (x) = y is equivalent to b^y = x.

3^x = 1/9

creating equivalent expression in the equation that all have equal base.

3^x = 3^-2

if the base are the same, two expression are only equal if the exponential are also equal

x = -2

the variable x is equal to -2

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Answer:

You know a table is a function when each element inside the domain matches with only one element within the range.

Answer: You know a table is a function when each element inside the domain matches with only one element within the range.

Step-by-step explanation:  hope this helps

If a² = b² , then a = b is not true for all real numbers.

We know that ' if a = b, then  a² = b²'.

We need to prove that the converse of this statement is not always true.

i.e., we need to show that if a² = b² , then a = b is not true for all real numbers.

To show that a statement is wrong we just need to find a counter example for the statement.

For this, let a = -5 and b = 5.

Clearly, a ≠ b

But -5² = 25 and 5² = 25

That is, a² = b² but a ≠ b.

Hence we proved that 'If a² = b² , then a = b is not true for all real numbers'.

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The answer to the expression -160=6x-8(5x+3)  is x = 4.

An expression is written in the form of variables and constants combined with arithmetic operations. There are many types of expressions in mathematics they are algebraic expressions, logarithmic expressions, trigonometric expressions, and many more.

The given expression - 160 = 6x - 8(5x+3) can be writen as,

6x - 8(5x+3) = -160.

First, we will distribute what is inside the brackets.

∴ 6x - 40x - 24 = -160.

-34x = -160 + 24.

-34x = -136.

34x = 136.

x = 136/34.

x = 4.

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Answer:

The answer I think is

Step-by-step explanation:

The offer that will make her more money and how much more will she make is

This is further explained below.

Generally, the equation for the total made is  mathematically given as

T= flat rate +(hours worked*hourly pay)

Therefore, for the first family

T= 40 + (6+5)

T=$51

For the 2nd family

T'= 20 + (6+10)

T'=$36

In conclusion, the offer that will make her more money and how much more will she make is

T'=51-36

T'=$15

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CQ

Simone wants to babysit this weekend to make some extra money she changes a flat fee then changes per hour or part thereof that she babysits Saturday afternoon she will babysit for 6 hours she had to choose between two families to babysit for. the first family offers her 40 plus $5 per hour. The second family offers her $20 and $10 per hour. Which offer will make her more money and how much more will she make

Answer:

7 vans

Step-by-step explanation:

62 ÷ 9 = 6.86.8 is not a whole number, so when you round it to the nearest whole number you get 7.[Also, 9 × 7 = 63, which is close to 62]∴ 7 vans will be needed.

Answer:

7 vans

Step-by-step explanation:

Each van can take 62 people so you share the 62 among the vans, and each van is 9,therefore 62÷9=6.888889 and people cannot be in decimals so you round the figure to a whole number which is equal to 9.

Answer:

5.611 or 5 11/18

Step-by-step explanation:

hope this is helpful!

Answer:5/3

Step-by-step explanation:

Answer:

The ray extends infinitely in one direction.

Step-by-step explanation:

It starts at the point and the arrow at the ends mean it extends in that direction away from the point infinitely.

Simplifying the problem, 4 - 9 + 5 - 1 - 6 + 11 would give the result of 4.

In order to simplify the problem given of 4 - 9 + 5 - 1 - 6 + 11, you can put the numbers into brackets and then carry out math operation:
= (4 - 9) + (5 - 1) - (6 + 11)

Solving the numbers in the brackets gives:

= -5 + 5 - 1 - 6 + 11

= 4

In conclusion, the simplified form would be 4.

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Using it's concept, the range of the function is given as follows:

0 ≤ m ≤ 1200.

The range of a function is the set that contains all possible output values for the function.

For this problem, we have to consider these two bullet points next, considering the mass is the output value of the function.

Considering these masses, the range of the function is given as follows:

0 ≤ m ≤ 1200.

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Answer: 254

Step-by-step explanation:

89 + 38 x 2

89 + 38 = 127

127 x 2 = 254

Answer:

11:50 AM

Step-by-step explanation:

We should first find the sum of the times it would take her to clean each room, along with the break time.

Kitchen = 80 minutes
Lounge = 40 minutes
Bedroom = 90 minutes
Bathroom = 35 minutes
Break = 45 minutes

[tex]\text{Total time (in minutes) } = 80 + 40 + 90 + 35 + 45 = 290.[/tex]
We should then divide this amount of minutes by 60 to find how many hours it took her.

[tex]\text{Total time (in hours) } = \frac{290}{60} = 4\frac56[/tex]
This means it took her 4 hours and 50 minutes to finish cleaning.

Therefore, if she started working at 7 AM and worked for 4 hours and 50 minutes, she was done by 11:50 AM.

Answer:

are there options?

Step-by-step explanation:

No extraneous solution to the equation

The equation is

2[tex](x - 1)^{4/1}[/tex] + 4 = 36

We have to find the extraneous solution of the equation and for this first, we need to find the value of x.

2[tex](x - 1)^{4}[/tex] + 4 = 36

2[tex](x - 1)^{4}[/tex] = 32

[tex](x - 1)^{4}[/tex] = 16

x - 1= 2

x = 3

Now we will put the value of x in the equation.

2[tex](3 - 1)^{4}[/tex] + 4 = 36

2 [tex]2^{4}[/tex] + 4 = 36

2 × 16 + 4 = 36

32 + 4 = 36

36 = 36

Therefore we get that there is no extraneous solution to the equation, x = 3 is the solution of the equation.

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The value of the expression 0.036m³/₄ is determined by algebraically substituting the value of m=46 x 10⁴ and solving the radical expression.

In the given radical expression, 0.036 is a constant and m is a variable with a power of ¾.

We will solve for the variable term first which will be written as a radical and multiply it with the constant.

Substituting m=46x10⁴ in the expression 0.036m³/₄.

0.036m³/₄=0.036(46x10⁴)³/₄

Now rewrite the expression as a radical,

0.036(46x10⁴)³/₄= 0.036∜(46*104)3

Multiply the exponents within radicand term,

= 0.036∜(463*1012)

Now simplify the expression,

= 0.036∜(463*(103)4

= 0.036*103 *∜463

= 0.036*103 *∜97,336

= 36 ∜97,336

= 36*17.66≈636

Hence, the correct answer is option A.

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The logarithmic equation log₁₂ 144 = 2

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  is an exponential function is  [tex]a^N=x[/tex] then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex]

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

According to statement,

log₁₂ 144

this can be written as ,

log₁₂ (12²)

= 2 log₁₂ (12)

= 2 . 1                   (as, log a with base a = 1 )

= 2

Thus , log₁₂ 144 = 2

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The domain of the function h(x) = x² - x - 12 when the function operation f(x) = g(x) is performed is ( - ∞ , ∞ ).

A domain is a collection of potential input values. All input values visible on the x-axis make up the graph's domain. The collection of potential output values represented on the y-axis is known as the range.

Consider the two functions,

f(x) = x - 4 and g(x) = x² - 16

The function operation f(x) = g(x).

g(x) - f(x) = h(x)

x² - 16 - ( x + 4 ) = h(x)

h(x) = x² - x - 16 + 4

h(x) = x² - x - 12

The collection of input or argument values for which a function is actual and defined is known as its domain.

So, the domain of the function h(x) is ( - ∞ , ∞ ) or - ∞ < x < ∞.

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The system of inequalities fits in this scenario are x + y & lt; = 2815x + 10Y & lt;= 300.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including: The symbol a b indicates that an is smaller than b. When a & gt; b is used, it indicates that an is bigger than b. A is not equivalent to b in any scenario. Since an is strictly less than or strictly greater than b, these relationships are known as stringent inequalities. Equivalence is not considered. In the given questions the inequalities are x + y & lt;= 2815x + 10y & lt;= 300

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Answer:

33%

Step-by-step explanation:

moving the decimal two places to the right

The system of equations which is as represented in the task content above when solved by elimination, substitution or matrices has no solution.

This goes to say that the above given system of equations ultimately has no solution using matrices

It follows from the task content that the solution pair of the system of equation as given in the task content is to be determined.

Given system of equation;

4x-6y=9

-10x+15y = 8

By multiplying the first equation by 5 and the second equation by -2; we have;

20x - 30y = 45

20x - 30y = -16

Hence, it is evident that the system of equations above has equal slope but different intercept equations.

Consequently, subtract equation 2 from 1 so that we have;

0 = 61....an equality which doesn't hold true.

Ultimately, the system of equations has no solution.

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The first term and common difference of the arithmetic series are -11 and 3.

In the arithmetic series, S₄₀ = 1900 and U₄₀ = 106

Hence,

Sₙ = n / 2 (2a + (n - 1)d)

S₄₀ = 20(2a + 39d)

S₄₀ = 40a + 780d

1900 =  40a + 780d

Uₙ = a + (n - 1)d

U₄₀ = a + 39d

106 = a + 39d

Combine the equation

a + 39d = 106

40a + 780d = 1900

20a + 780d = 2120

40a + 780d = 1900

20a = - 220

a = -220 / 20

a = -11

Hence,

106 = a + 39d

106 = -11 + 39d

106 + 11 = 39d

117 = 39d

divide both sides by 39d

d = 117 / 39

d = 3

Therefore, the first term and common difference of the arithmetic series are -11 and 3.

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the answer to the given logarithm expression is log₃ 125 = 3

Another technique to explain exponents in mathematics is through logarithms. A base number's logarithm equals another number.

The power's inverse function is the logarithm. For instance, log10 100 = 2 if 102 = 100. A power to which a number must be increased in order to achieve another value is referred to as a logarithm.

This is the most practical method for displaying enormous numbers. Logarithms have several important properties that prove that multiplication and division of logarithms can  be written in terms of addition and subtraction logarithms. A second name for the common logarithm is the base 10 logarithm.. This is represented as log10 or simply log. The base 10 logarithm is another name for the common logarithm. The common logarithm specifies the number of times the number 10 must be multiplied in order to produce the desired result.. We need to evaluate log₃ 125

Using the property

logₐ (mⁿ) = n logₐ m

125 = 5³log₃ 125 can be written as log₃ 125= 3 log₅ 5

We know that logₐ a = 13 log₅ 5= 3

Therefore, we calculated the logarithm, which is log₃ 125 = 3

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The measures of the angles are <1 = 38, <2 = 142, <3 = 38 and <4 = 142

The diagram that completes the question is added as an attachment

From the diagram, we have

<1 + <2 = 180 degrees --- supplementary angles

Given that

<1 = 38 degrees

We have

38 + <2 = 180

Evaluate

<2 = 142

Also, we have

<3 = <1

<4 = <2

This means that

<3 = 38

<4 = 142

Hence, the measures of the angles are <1 = 38, <2 = 142, <3 = 38 and <4 = 142

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Answer:

Step-by-step explanation:cevaplandıında banada haber verin rez kardeşlerim

After thoroughly calculating the simplifying the expression 164[3+2+ (9-7)] is   1148

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence.

The following are some examples of expressions and word phrases that they relate to:

Formula: 3 + 7

Expressions and equations are different from one another because an expression consists of a combination of numbers, variables, and operation symbols, whereas an equation consists of two different expressions joined together by an equals sign. This shows that the expression's two sides have the same value.

Simplification of the expression 164[3+2+ (9-7)]

⇒ 164[3+2+ (9-7)] =

⇒ 164[5+(2)] =

⇒ 164[5+(2)]

⇒ 164(7)

⇒ 1148

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