Water flows into a tank according to the rate F(t) = t+6/1+t, and at the same time empties out at the rate E(t) = ln(t+2)/t+1, with both F(t) and E(t) measured in gallons per minute. How much water, to the nearest gallon, is in the tank at time t = 10 minutes. You must show your setup but can use your calculator for all evaluations.

Similar to one-step and two-step equations, the basic objective of multi-step problems is to isolate the unknown variable on one side of the equation while maintaining the constant or number on the other side.

Solving a 3-step problem typically involves the following steps:

It can be helpful to break the problem down into smaller parts and solve each part separately. This can make the problem feel more manageable and help you avoid making mistakes.

If you get stuck at any point, it can be helpful to take a break and come back to the problem later, or to ask someone for help.

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The correct statement regarding the together rate is given as follows:

A. The total time, in hours, it would take Jenna to address the 1800 envelopes alone is given by 1800/(x + 10).

The together rate is given by the sum of each separate rate, thus the sum given in the problem on the image represents the total time it takes for them to address all the envelopes.

Jenna can address 10 more envelopes per hour than Kyle, hence:

The number 1800 represents the total number of cards, hence from this and from the bullet points, statement A is correct.

The problem is given by the image shown at the end of the answer.

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Answer: x=2, y=-8

Step-by-step explanation: there are a couple of different methods you can use, my favourite is substitution

to do this, find a value of x or y from one equation and plug it into the other. let's use x in this case

so we have 13x-6y=22 and x=y+6

for the x value of the first equation, plug in x=y+6 from the second equation to get:

13(y+6)-6y=22

then you solve for y,

13y+78-6y=22

7y=-56

y=-8

then to solve for x, plug in your y value to either of the first 2 equations. lets use x=y+6

so you'd have x=(-8)+6 to give you x=2

hope this helps!

There is no input mapped into two or more outputs in the given relation:

(-3,4) (6,0),(-3,4),(-8,-2)

Thus, the relation is a function.

A relation maps elements of a set (inputs, usually defined by the variable x) into elements of another set (outputs, usually defined by the variable y).

So, for example, the coordinate pair (x, y) means that a relation is mapping the input x into the output y.

A relation is also a function if there is no input being mapped into two or more outputs.

For the case of the given relation:

(-3,4) (6,0),(-3,4),(-8,-2)

The mappings are:

-3  → 4   (this one appears twice)

6  → 0

-8  → -2

So no input is mapped into two or more outputs, then the relation is a function.

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The process to calculate slope of  line is explained below.

The Slope of line passing through two points (a,b) and (c,d) can be calculated by using  formula ;

slope = (d - b)/(c - a) ;

The slope of a line is denoted by letter "m" .

For Example : If the line is passing through the points (0,2) and (3,8)  .

on comparing we get the values as a = 0 , b = 2 , c = 3 and d = 8 .

On substituting values in the slope formula that is mentioned above  ,

we get ;

Slope(m) = (8 - 2)/(3 - 0)

On Simplifying further ,

we get ;

= 6/3

= 2 .

So , the slope of line will be = 2 .

The given question is incomplete , the complete question is

How do you calculate slope of a line quickly ?

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Answer:

D

Step-by-step explanation:

( g-h)(n).

n+5 - (n^2-5n)

-n^2+5n+n+5

-n^2+6n+5

The income of whales star after 3 years and getting 19% rise every year will be  $1685159 .

Given, The whales' star cornerback is paid $1 million and is guaranteed a 19% pay raise for the next three years .

To get the salary of whale star after 3 years of increment with 19%.

Salary =  $1 million

Salary after 1st increment =  $1 million +  $1 million of 19%

Salary after 1st increment = $1190000

Salary after 2nd increment =  $1190000 + $1190000 of 19%

Salary after 2nd increment = $1416100

Salary after 3rd increment =  $1416100 + $1416100 of 19%

Salary after 3rd increment = $1685159

Final salary after 3 years will be  $1685159.

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Answer:

315

Step-by-step explanation:

multiply (3.78x10^6) first to get 3780000 then divide 3,780,000 by 12,000 to get 315

Answer:

6 1/2 hours     12-hour clock

18 1/2 hours   24- hour clock

Step-by-step explanation:

I attached a picture of how I solved it!

The clock just crossed the 9th hour.

Given is that a clock that strikes only the hours has just finished striking a total of 9 times in the last 24 hours.

Since, the clock strikes only on hours, the clock just crossed the 9th hour.

Therefore, the clock just crossed the 9th hour.

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The measure of the length r (SQ) of the triangle ΔQRS will be 2.40 inches.

The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.

The sine law in the triangle ΔQRS is given as,

QR / sin S = SQ / sin R = SR / sin Q

The third angle of the triangle ΔQRS is given as,

∠Q + ∠R + ∠S = 180°

∠R + 30° + 129° = 180°

∠R = 21°

Then the measure of the length r (SQ) will be calculated as,

5.2 / sin 129° = SQ / sin 21°

SQ = 2.40 inches

The measure of the length r (SQ) of the triangle ΔQRS will be 2.40 inches.

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Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility for three.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

add all number

9+9+0 = 18

and 18/3 = 6

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The value of a continuous function is that it produces a single output for any given input, no matter how small the change in the input. This makes it reliable and predictable, allowing for precise calculations and predictions.

Continuous functions are a type of mathematical function that produces a single output value for any given input. This means that no matter how small the change in the input is, the output value remains the same. This makes continuous functions reliable and predictable, allowing for precise calculations and predictions. As an example, a continuous function can be used to calculate how far an object will travel over a certain amount of time if provided with the initial velocity and acceleration. This is because the function will not change its output value when the input is altered, no matter how small the change is. Continuous functions are therefore an essential tool for many applications in mathematics and science.

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The exponential function that goes through the points (0, 14) and (3, 896) is y = 14·3ˣ. This function has a base of 3 and a coefficient of 14.

An exponential function in the form y =abˣ is a function

where y is equal to a multiplied by b raised to the power of x.

To find the function that goes through the points (0, 14) and (3, 896),

We can write the following equation to find the base of the exponential function that goes through the points (0, 14) and (3, 896):

b³ = 896/14

We can then solve for b by taking the cube root of both sides of the equation to get:

b = 3

Now that we know the base of the function, we can use the point (0, 14) to find the value of the coefficient a.

Since the x-value of this point is 0, we can plug 0 in for x in the exponential function y=abˣ to get:

y = ab⁰ = a

Since the y-value of the point (0, 14) is 14, we can set this equal to a to solve for the value of a:

a = 14

So, the exponential function is y = 14·3ˣ

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The resultant answer after solving the given inequality by taking the subject x is x < (12 + 2y)/3.

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 digits on the number line are made.

So, we have the inequality:

3x - 2y < 12

Now, solve the inequality by taking x as the subject as follows:

3x - 2y < 12

3x < 12 + 2y

3x/3 < 12/3 + 2y/3

x < (12 + 2y)/3

Therefore, the resultant answer after solving the given inequality by taking the subject x is x < (12 + 2y)/3.

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Correct question:

What is the solution to the inequality 3x - 2y < 12?

Answer: f(x)= 2x+ 1

Step-by-step explanation:

Let's set up an equation

f(x)=mx+b

We know it's 3 inches tall and grows 2 inches weekly.

Our equation is

f(x)= 2x + 1

Now let's test the week is 1

f(1) = 2(1) +1

f(1) = 3

Let test the week is 2

f(2) = 2(2)+1

f(2) = 5

So we know this equation work

Each juice bottle costs $9.44.

What is a juice bottle?

Liquids that are flavoured with concentrate or other biological food sources, such meat or seafood, such as clam juice, are referred to by this term. It is added to foods or other drinks, like smoothies, as an ingredient or flavor.

To determine the cost of each bottle of juice, you can set up the following equation:

j + 2.25 = 11.69

Where j is the cost of each bottle of juice.

To solve for j, you can subtract 2.25 from both sides of the equation:

j = 11.69 - 2.25

This simplifies to:

j = 9.44

So, each bottle of juice costs $9.44.

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The compound inequality x > 3 or x < 5 is 4 , that set of all real numbers.

What is inequality ?

If an inequality has no real solution, this means that there are no numbers that can be substituted into the inequality to make the statement true. If an inequality has all real numbers as the solution, this means that every real number can be substituted into the inequality to make a true statement.

Have given,

x > 3 and x < 5

Since this compound inequality is an or statement , it includes all of the integral numbers in each of the solutions, which in this case is all the numbers on the number line .

The region of the line greater than 3 and less than 5 that number is 4.

Hence,

The compound inequality x > 3 or x < 5 is 4 , that set of all real numbers .

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Have given,

x > 3 and x < 5

Since this compound inequality is an or statement , it includes all of the integral numbers in each of the solutions, which in this case is all the numbers on the number line .

The region of the line greater than 3 and less than 5 that number is 4.

The compound inequality x > 3 or x < 5 is 4 , that set of all real numbers.

After one half-life, 50% remain in the initial parent nuclei, 25% after two, and so on. The amount of radiation emitted by a radioactive source depends on both its half-life and the initial number of radioactive atoms present.

Atoms strive for stability, thus they release energy from their nucleus in the form of a particle or ray to achieve a more stable state.

The unstable atom is referred to as a radioactive atom, the process is known as radioactivity, and the energy emitted is radiation.

If these forces are out of balance or if the nucleus has an excessive amount of internal energy, an atom is unstable (radioactive).

An overabundance of neutrons or protons can make the nucleus of an atom unstable.

The initial parent nuclei still contain 50% of them after one half-life, 25% after two, and so on.

The half-life and the initial quantity of radioactive atoms present both affect how much radiation is produced by a radioactive source.

Therefore, after one half-life, 50% remain in the initial parent nuclei, 25% after two, and so on. The amount of radiation emitted by a radioactive source depends on both its half-life and the initial number of radioactive atoms present.

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Answer:

6.25%

Step-by-step explanation:

One factor of equation x³ + 6x² + 12x + 8 is (x + 2).

Describe equation.

Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

According to the given question:

Here,

The Expression is

=>  x³ + 6x² + 12x + 8

=> (x³ +8) + 6x (x+2)

= > (x + 2) ( − 2x + 4) + 6x(x + 2)

= >(x + 2) {  − 2x + 4 + 6x}

= > (x + 2) ( + 4x + 4)

=> (x + 2) { x² + 2(2)(x) +2²}

=> (x+2) is a factor

Therefore, one factor of equation x³ + 6x² + 12x + 8 is (x + 2).

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a) The slope of the main portion of the slide is of: 5/6 = 0.8333.

b) If the bottom of the slide was only 12 inches above the ground, then the slope would be of 1/3 = 0.3333.

The slope of an inclined object is obtained as the division of the height of the object by the length of the object.

From the text, the parameters for the slide are given as follows:

Then the slope of the slide is of:

Slope = 10/12 = 5/6 = 0.8333.

After the change in the bottom, the parameters would be of:

Then the new slope of the slide is given as follows:

Slope = 4/12 = 1/3 = 0.3333.

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The number of terms that the expression 5xy 9yz 3zx 5x 4y has is 5 terms.

What is an algebraic expression?

An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

How to determine terms?

To determine the number of terms in an algebraic expression, we only have to count the spaces (addition and/or subtraction symbols) and add the unit, in this way we will have the number of terms.

5xy 9yz 3zx 5x 4y has 4 spaces

4 + 1 = 5 terms.

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We know that,

Greatest common factor= the greatest common factor is the greatest factor that divides both numbers.

According to question.

Given data,

Factor of a= a

Factor of b=b× b× b× b

Factor of c=c× c× c× c× c× c× c

Therefore,

Factor of a=a× a× a× a× a ×a ×a

Factor of b4=b ×b ×b× b

Factor of c=c

Greatest common factor=ab4c

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DMAS is four type of arithmetic we deal everyday in our mathematical problem

What are four basic property of arithmetic?

Commutative, associative, distributive and identity are the four basic properties of arithmetic.

Addition and multiplication ate two arithmetic which is commutative.

Division, addition, subtraction and multiplication are the four type of arithmetic

Examples:

1+1=2 is addition

4-2=2 is subtraction

3*2=6 is multiplication

4/2=2 is division

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To express a mathematical operation symbolically, we employ a mathematical expression.

In mathematics, an expression is a sentence that has at least two terms and an operator in the middle. Expressions may be divided into two categories: numerical expressions, which include simply numbers, and algebraic expressions, which contain both numbers and variables. A mathematical expression consists of two parts: terms and operator, where terms refer to variables and integers. It is referred to as a constant term if an expression just contains numbers, and it is known as a coefficient if it also contains numbers and a variable.

We utilize expressions to symbolically represent any mathematical activity as well as mathematical models. The specifics of our computation, for instance, can be succinctly represented in terms of two or more mathematical terms. We can identify unknown numbers with the equal sign, allowing us to resolve difficult issues. In real life, we utilize expressions to figure out how much we make and spend, how quickly things change, how long it will take to go a certain distance, and other things. When calculating the rate of change, we use the differentiated term dy/dx. When calculating speed, time, and distance, as well as time and speed, we employ equations with variables.

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Answer:

To try and relate or understand our feelings and try and give an example. For example the expression “it’s raining cat’s and dog’s” well that means it’s raining heavily!

Hope I helped

Step-by-step explanation:

The geometric sequence 2, −6, 18, −54, ... to represent the 9th term is

d. f(9)=f(8)+3(8)

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous one by a fixed, non-zero number, called the common ratio. In the given sequence, the common ratio is -3, so the nth term of the sequence can be found by multiplying the previous term by -3.

Using the recursive formula for a geometric sequence, the nth term can be found by multiplying the first term, f(1), by the common ratio raised to the (n-1) power, or f(n) = f(1)•(-3)^(n-1). In the given sequence, f(1) is 2, so the 9th term can be found by multiplying 2 by -3 raised to the 8th power, or f(9)=f(1)•(-3)^8.

Alternatively, the nth term can also be found by multiplying the previous term, f(n-1), by the common ratio, or f(n) = f(n-1)•(-3). Since the 8th term in the given sequence is -54, the 9th term can be found by multiplying -54 by -3, or f(9)=f(8)•(-3).

Therefore, the 9th term in the given sequence is -486 and the correct answer is d. f(9)=f(8)+3(8).

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Answer: C: pay the complete balance each month

The question uses 6 mathematical phrases. The coefficient is made up of two integers, and the other variables are x, y, z, and A.

A mathematical expression is a sentence that describes the relationship between two or more concepts and one or more symbols. There are many distinct words, including numbers, variables, and variables with coefficients. Different mathematical operators can be used to denote an equation, including the signs for addition and subtraction, plus and minus, multiplication and division, equal and inequal signs, and so on.

Using the formula above, 5xyA2 = 3xyz

There are six words and one equal sign, as we can see.

A, B, C, and There are six words and one equal sign, as we can see.

Five, three, and A are numerals and four variables, respectively. The coefficient of the variables is represented by the numbers.

A, y, and x are all used twice, as well. A2 or the square of A is how you write the product of A and A.

When we multiply 5 by x, y, and A2, we get the formula 3xyz, where 3 is multiplied by x, y, and z.

hence, we determine 6 terms in the question

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Answer:

f(x) = 6 * sin(2x) - 10

Step-by-step explanation:

We can use the given information to write the general formula of a sinusoidal function as follows:

f(x) = A * sin(B(x - C)) + D

The amplitude of the function, A, is equal to the difference between the maximum and minimum values of the function, which in this case is -10 - (-4) = 6.

The period of the function, B, is equal to the distance between consecutive maximum or minimum points, which in this case is 2 - 0 = 2.

The phase shift of the function, C, is equal to the horizontal shift of the entire function, which in this case is 0 since the minimum point is at x = 0.

The vertical shift of the function, D, is equal to the y-coordinate of the minimum point, which in this case is -10.

Therefore, the formula of the given function is:

f(x) = 6 * sin(2(x - 0)) - 10

We can simplify this formula by removing the unnecessary parentheses and constants:

f(x) = 6 * sin(2x) - 10

This is the final formula for the given sinusoidal function, where x is entered in radians.