Write log 150 as a sum or difference of two logarithms. Simplify if possible.

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 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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The change in position from the shaded figure to the unshaded figure is best described as a translation.

A translation transformation is such that the entire shape is copied and then this copy is moved to another part of the graph.

In a translation, the size of the shape does not change. Other things that don't change include the orientation of the shape. It remains the exact same, but in a new location.

The shape, size and orientation of the shaded figure is the same as the unshaded figure so this is a translation.

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Answer:

y = x - 3.

Step-by-step explanation:

We use the point-slope form of the straight line:

y - y1 = m(x - x1) where m = slope and (x1, y1) is a point on the line.

So, for this line we have:

y - (-1) = 1(x - 2)

y + 1 = x - 2

y = x - 2 - 1

y = x - 3.

The side AC is 8.5 cm.

We know that a triangle is a polygon that has three sides. There are so many kinds of triangle such as;

In this case what we have is a right angled triangle ABC. Having seen this, we now have to find the side that has been marked AC in the triangle shown.

In this case, we are required to obtain the side that has been marked as AC and we have to use the given side AB and the angle that is given as angle BAC.

Now;

AB = 11 cm

Angle BAC = 39 degrees

AC = unknown

Thus we now have to make use of the trigonometric ratios;

Cos θ = opposite/ adjacent

opposite = AC

Adjacent = 11 cm

AC= 11 cm cos 39 degrees

AC = 8.5 cm

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Answer:

37.5

Step-by-step explanation:

    37.5

4 | 150.0

  - 12 ↓

---------------

      30.0

    - 28 ↓

-----------------

         20

       - 20

--------------------

            0

I hope this helps!

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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Answer:

33%

Step-by-step explanation:

moving the decimal two places to the right

Answer:

Bro Im not gonna give u answer but im gonna give hint. I think u should make a chart with all possibilties and see how many of them can add upt o 11.

No, when finding the difference in elevations we should not consider only the absolute value of the difference because elevation differences can give a negative value as well.

Absolute value describes the distance from zero that a number is on the number line, without considering direction.

We know that while measuring elevation there can be a positive value which means that the distance measured is above sea level and there can also be a negative value elevation which means that the distance measured is below sea level.

For example:

If we are measuring the difference in distance of two points below sea level.

One point is at -6 feet

Another point is at -14 feet

The difference between these points is:

= -14 - (-6)

= -14 + 6

= -8

We can have a negative difference in elevation but the absolute value will always give a positive value.

Therefore,

No, when finding the difference in elevations we should not consider only the absolute value of the difference because elevation differences can give a negative value as well.

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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.

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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Y = x*-0.25

Hope this helps.

Answer:

a

Step-by-step explanation:

Answer:

x = 28.75

Step-by-step explanation:

RZ and RT will have the same length since Z is a midpoint

8x - 10 = 220

Add 10 to both sides

8x = 230

Divide both sides by 8

x = 28.75

Answer: 254

Step-by-step explanation:

89 + 38 x 2

89 + 38 = 127

127 x 2 = 254

The average elevation of Louisiana denoted as an integer is -8 feet.

An integer is a real number which is not a fraction. Examples of integers are -4,0,7,26.

The elevation above sea-level of a place is represented by a number and it is calculated by length above or below the average water level of all water bodies on earth.

Places above sea level are denoted by a positive numbers while places below the average sea-level are denoted by negative numbers.

Here the height of Louisiana is 8 feet below the sea-level , so to denote the height of Louisiana we us the negative integer -8 feet.

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Answer:

3/11

Step-by-step explanation:

divide each side by 2

Answer:

3/11

Step-by-step explanation:

Let's simplify the value,

→ 6/22

→(6 ÷ 2)/(22 ÷ 2)

→ 3/11

Thus, the value is 3/11.

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

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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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.

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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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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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 option B , which says that the mean of the two data sets are equal is the correct statement.

To answer the question we need to understand the meaning of a boxplot

A boxplot is a standardized way of showing the distribution of data based on a five number summary minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

According to the problem showed in question ,

As we can see from the two box plots that the mean for both the box plots is less than 80 but greater than 75.

Hence we can say that the mean of the two given data sets are equal

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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

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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Answer:

are there options?

Step-by-step explanation: