Select the correct answer.What is the solution to this equation?loge + + log 3 = log (+ + 1)OA1 =IO HICOB.1 =O C.सेNICOOD. r = 1

3x-2y=24

3x - 2y + 2y = 24 +2y Adding 2y to both sides of the equation

3x - 24 = 2y + 24 - 24 Subtracting 24 from both sides of the equation

(3x - 24)/2= 2/2y Dividing by 2 on both sides of the equation

3/2x - 12 = y

From this form of the equation we deduce the slope (coefficient of x) is 3/2 and the y-intercept is equal to -12.

To find the x-intercept, we replace y= 0 in the equation and isolate x

3/2x - 12 = 0

3/2x - 12+12 = 0+12 Adding 12 to both sides of the equation

x= 12/(3/2) Isolating x

x= 8

The x-intercept is 8

Answer: 57

Given:

We are asked to find the 15th term, meaning n = 15

Therefore, the 15th term is 57.

EXPLANATION

Since we have the expression:

Removing the parentheses:

Rearranging terms:

Adding like terms:

The final expression is as follows:

The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.

The true statement based on the information is that D. There were fewer attendees than purchased tickets.

A box and whisker plot is a graphical representation of variance in a set of data. A histogram analysis is sufficient in most circumstances, but a box and whisker plot can provide more detail while allowing different sets of data to be displayed in the same graph.

The box and whisker figure highlights data on the number of Broadway tickets sold and actual attendance at the performances. In this case, the graph shows that the number of tickets are more.

Therefore, the correct option is D.

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Using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.

So, in September, Lucky weighed = 3.07 pounds

The equation form is:

So, now solve this linear equation and find 'x' as follows:

Therefore, using linear equations, the amount of weight Lucky gained between September and today is 7.74 pounds.

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The solution for the inequality is 11.746 ≤ x ≤ 24.44

Kali earns a 15.75 plus a flat fee of 50 from her job.

She wants to earn between 200 and 400.

Let 'x' denote her earning potential.

Then the inequality for her earning potential is given by,

200 ≤ 15.75x + 50 ≤ 400

We solve this inequality for x.

Subtract 50 from the inequality,

⇒ 200 -15 ≤ 15.75x ≤ 400 -15

⇒ 185 ≤ 15.75x ≤ 385

Divide by 15.75,

⇒ 11.746 ≤ x ≤ 24.44

is the solution for the inequality.

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Given

Notice that the right side of the equation consists of like terms (they do not depend on m). Therefore, Step 1 goes with Combine like terms.

Then,

Step 2 applies the distributive property.

As for the properties of the equality,

Thus, steps 3 through 5 are:

Step 3 - Addition property

Step 4 - Division property

Step 5 - Multiplication property

Answer:  Table A has a proportional relationship

See the diagram below

==================================================

Explanation:

Table A has a proportional relationship because all the points are on the same straight line. That line in this case is y = 2x

Whatever x is, multiply it by 2 and you'll get the y value

Example: If x = 4, then y = 2*x = 2*4 = 8 which gives the point (4,8)

Another phrase for "proportional relationship" is "direct variation".

Using linear algebra, we concluded, the Mathew spent $50 and lan spent $80

Vectors, matrices, vector spaces, and linear transformations are all topics covered in the mathematical field of linear algebra. Linear algebra is much better understood than other areas of mathematics, which are regularly stimulated by novel concepts and unresolved issues.

According to the question,

Let Mathew spent $x

lan spent = 2x - 20

Total money spent = $130

⇒ 2x - 20 + x = 130

⇒ 3x - 20 = 130

⇒ 3x = 150

⇒ x = 50

2x - 20 = 2(50) - 20

= 80

So, Mathew spent $50 and lan spent $80

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Let:

x = Cost of one plain pizza

y = Cost of one soda

two friends went to a restaurant and ordered one plain pizza and two sodas. the bill totaled $15.95. so:

later that day, five friends went to the same restaurant. they ordered 3 plain pizzas and 5 sodas. their bill totaled $45.90. so:

Let:

From (1) solve for x:

Replace (3) into (2):

Replace the value of y into (3):

Therefore, the price of one plain pizza is $12.05

The complete statement is:

This can be rewritten as _f(x)_ = 3x - 2, since y can be replaced with _f(x)__.

A general relation is written as:

y = something that depends of x.

This is a relation that relates the variable y with the variable x, where we define x as the input and y as the output.

If this is a function, we can use the notation:

y = f(x).

(or any letter of x, f(x) is the most common notation used)

in this case, we have:

y = 3x - 2

And in function notation, this will be writen as:

f(x) = 3x - 2

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Answer:

30 percent of 120 is 36

Answer:

18

Step-by-Step Explanation:

[tex]\frac{dy}{dx}=9x^2 + 4x-5 \\ \\ \frac{d^2 y}{dx^2}=18x+4 \\ \\ \frac{d^3 y}{dx^3}=18[/tex]

Hence, the minimum number of sets of knives kaj should buy is 48  sets.

Given this, a restaurant must have at least 736 knives.

At the moment, it possesses 155 knives.

Every set includes 12 knives.

Let the number of knife sets be.

Reason: Minimum number of sets indicates ≥

This means ≤ the maximum amount of sets

Step: 2

In light of the inquiries,

[tex]155+s*12\geq 736[/tex]

[tex]12s\geq 736-155[/tex]

[tex]12s\geq 581[/tex]

[tex]s\geq \frac{581}{12}[/tex]

[tex]s\geq 48.42[/tex]

Step 3: Count the number of knife sets [tex]s\geq 48.42[/tex]

that is greater than or equal to 48

Therefore, the required minimum is 48 sets of knives.

What are sets?

In mathematics, a set is a well-defined collection of objects. Sets are named and represented using capital letters. In the set theory, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc.

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The number of rankings that are possible when the company has 40 salespeople is 78960960.

Based on the information given, permutations will be used. The formula is illustrated thus:

Permutations = n! / (n – r)!

N is the number of things you are choosing from,

r is the number of items.

“!” is a factorial of a number

The company has 40 salespeople and the board member at the company asks for a list of the top 5. This will be;

= 50! / (40 - 5)!

= 40! / 35!

= 40 × 39 × 38 × 37 × 36

= 78960960

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(1, 42)

1) Since we have an equation of the line y = 2 + 5(x + 7) let's find one point that ∈ to this line.

2) Let's plug into that for x, the value of x=1

y= 2+ 5(1+7)

y= 2 +5(8)

y= 2 +40

y= 42

3) So one of the points that lie on this line is (1, 42) i.e. belong to that line.



Answer:

1/5

Step-by-step explanation:

a reciprocal is the multiplicative inverse

Answer:

The reciprocal of 5 is 1/5

Step-by-step explanation:

The reciprocal of a number is the fraction flipped upside down

6/1    =  1/6

⇒ 5/1 =    1/5

The most appropriate unit for Nathan to use instead of centimeters per minute is centimeters per year.

An earthquake simply means a rapid motion of the solid layer of the Earth.

In this case, Nathan told his brother that up until a 7.8-magnitude earthquake hit Nepal in 2015, Mount Everest had been moving northeast at a rate of 7.7×10^-6 centimeters per minute.

Since the year is being discussed, the unit should be based on the year.

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The number of pounds and ounces that we have in 134 ounces is; 8 pounds 6 ounces

We know that in units conversion, there are different units and their conversion rates. For example;

1 meters = 100 cm

1000 meters = 1 kilometer

1000 grams = 1 kilograms

100 cents = 1 dollar

Now, we want to convert ounces to pounds.

The conversion rate for ounces to pounds is;

1 ounce = 0.0625 pounds

We are given 134 ounces of cold cuts for a party. Converting that to pounds gives us;

134 * 0.0625/1 = 8.375 pounds

Now, we want it in pounds and ounces and so we convert the decimal part to ounces

1 pound = 16 ounces

0.375 pounds = 0.375 * 16/1 = 6 ounces

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For this type of probability question, there are different ways to solve the same question but let's analyze the situation and calculate as simple as possible.

For our question, there are two parts, the first one first is the probability to pick someone who is a woman. Once there are 60 people of which 30 are women, it means this probability is 30/60. Let's keep this probability.

Now let's move on to the second part. The situation where we pick someone who is without a date. once there are 60 people and all 30 women have a date and 16 men also have a date it means 30 + 16 - 60 = 14 people does not have a date. So the probability to pick someone without a date is 14/60.

Now once we have analyzed the two parts of the question, and we have two probabilities all we need is to sum our probabilities, as follows:

But why do we sum and do not multiply? Because we use the proposition OR at "Find the probability of picking someone at random and getting a person who is a woman OR without a date" If the proposition was AND we would have multiplied both probabilities.

Answer:

C. -68

Step-by-step explanation:

Using absolute value symbols, it makes any negative number a positive. But, the negative sign is outside the absolute value signs, making the number -58. -68 is the only number less than -58.

Given function is

Now,

Being a perfect square,

Therefore,

So,

Theerfore, the maximum value of the given function is -6.

Given:

The triangle having two similar angles.

This is the isosceles traingle.

Draw the altitude to the given traingle,

D divides the side BC into two equal side having length,

Now, use the tan ratio for right triangle ABD,

Using the pythagorean theorem,

The length of the sloping side of the roof is 23.3 feet.

No. of girls = 14

No. of Boys =16

Therefore the ratio, from girls to boys is,

Which can also be written as,

Therefore, the wrong ratio is option D.

That is,

So, the answer is option D.

{3,8} give the values of set that implies the set has two elements 3 and 8. [3,8] give the range of values that can be used in any functions with values from 3, 4, 5, 6, 7, 8 both 3 and 8 included.

Sets are collections of well-defined objects or elements in mathematics. A set is denoted by a capital letter symbol, and the number of elements in a finite set is denoted by the cardinal number of a set enclosed in a curly bracket{...}.

A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output. Every function has a domain and a codomain, as well as a range.

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Answer:

a.

Fee of whole band = Fee of writer + guitarist + singer

Fraction of fee of whole band = 4/12 + 1/12 + 1/12

= 4+1+1/12

=6/12

=1/2

b.

Fee of writer= 4/12 of £3000

=3000 × 4/12

= £1000

Fee of singer= 1/12 of £3000

= 3000 × 1/12

= £250

Fee of guitarist= Fee of singer

= £250

Rational numbers can be formed by dividing 2 integers. It can be represented in this format x/y where y is not 0. Rational numbers, in decimal form are not repetitive and unending.

Therefore,