f(x) = x 0 (9 − t2) et2 dt, on what interval is f increasing? (enter your answer using interval notation.)

As per the given volume, it take 223 minutes to fill the pool.

The term volume in math is defined as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface and it measured as cubic units.

Here we have given that a 9,000-gallon pool is being filled at a rate of 40 gallon per minute.

Here we need to find the time taken to fill the pool.

While we looking into the given question, we have identified the following values,

Total volume of pool = 9000 gallon.

Amount of water filled in one minute = 40 gallon,

then the time take by the pool to fill is calculated by dividing the total amount by the amount of water per minute then we get,

=> 9000/40

When we simplify this one then we get,

=> 225

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Answer:

6x - 9

Step-by-step explanation:

18x -11 - (12x - 2)   Can be written

18x -11 -1(12x -2)  Distribute the -1

18x - 11 -1(12x) + (-1)(-2)

18x - 11 -12x +2  Combine like terms

6x -9

Graph 1 has n<14 inequalities, and graph 2 has n>14 inequalities.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to one another.

The two rules of inequality :

Rule 1: Adding or subtracting the same amount from both sides of an inequality does not change the inequality symbol. Rule 2: Multiplying or dividing both sides by a positive number does not change the inequality symbol.

Here graph 1 depicts

The line is extending to the left of the number 14, excluding 14.

So, the inequality will be;

n < 14.

The graph 2 depicts

The line, which includes the number 14, is moving to the right.

So, the inequality will be ;

n≥14

As a result, the inequalities are n14 and n14 of graphs 1 and 2, respectively.

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In the function f(x) = a(b^x), the initial value is always a because a is independent on x. So, when x changes, b^x will change as well but a will remain the same.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. A function is an equation with a single solution for y for each value of x. A function pairs each input of a particular type with exactly one output.

For example, let a = 2, b = 3, and x = 0: f(0) = 2 3^0 = 2 1. If x = 1, then f(1) = 2 3^1 = 2 3. If x = 2, then f(2) = 2 3^2 = 2 9, etc. As you can notice a = 2 remain unchanged as the initial value, because a is independent on x change.

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Answer:

47,174,400 possible number plates

See important note at the bottom of the explanation

Step-by-step explanation:

The easiest way to handle a problem of this type is to note the following

There are 9 digits 1-9 that we can use for the first four characters of the license plate

So the number of ways to arrange the first 4 digits without repetition is
9  x 8 x 7 x 6 = 3024 possible ways

For the letters, assuming that we are using the English alphabet, the 5th spot where the first letter after the numbers is can be done in 26 possible ways since there are 26 alphabets.

For the second letter that will leave us with 25 possibilities

For the third and final spot there are 24 possibilities

This means that, without repetition, the letters can be arranged in 26 x 25 x 24 ways = 15,600 ways

Together we can arrange the digits and letters in 3024 x 15600 ways which works out to
3024 x 15600 = 47,174,400 ways or possible number  plates

Or we could simply write this in one step as

9 x 8 x 7 x 6 x 26 x 25 x 24 = 47,174,400 ways or possible number  plates

Note

Even though there are 10 digits 0 - 9, the question clearly states that we should choose from digits 1 through 9 only.

If we are allowed to use all 10 digits the first 4 digits can be put together in 10 x 9 x 8 x 7 = 78,624,000 ways

You should clarify this with your teacher.

The value of 3/x-1 - 4/x+3 is (13-x)/(x-1)(x+3)

Algebraic fractions are fractions using a variable in the numerator or denominator, such as . Because division by 0 is impossible, variables in the denominator have certain restrictions. The denominator can never equal 0.

The numerator and denominator are called the terms of the algebraic fraction.

We simplify the expression by finding the LCM of the denominator.

therefore 3( x+3) - 4(x-1))/(x-1)(x+3)

opening the parentheses

(3x+9-4x+4)/(x-1)(x+3)

= (13-x)/(x-1)(x+3)

Therefore the value of 3/x-1 - 4/x+3 is (13-x)/(x-1)(x+3)

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When the inequality is solved, we have r-2. Each side can be multiplied or divided by the identical positive value, added to or subtracted from by the same amount, and more.

Using inequality characters like "," ">," "," or "," expressions using linear inequalities compare exactly two values. Such values could be algebraic, numerical, or both.

Here,

Linear inequalities: How are they solved

In the first step, solve the equality for y.

Step 2: Sketch the boundaries of the inequality on a graph.

The region that addresses the inequality should be shaded. Step 3. Step four requires you to solve the third inequality for y. In step 5, the boundary line of the second inequality must be graphed. Cover the region that fulfills the second condition.

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Our Pythagorean triplets will be (6,8,10), (5,12,13), and (3,4,5).

So what is the Pythagorean triplet?

The square of the greatest number in a Pythagorean triplet equals the sum of the squares of the other two numbers.

The greatest side in a right-angled triangle is called the hypotenuse.

So, in our first triplet A(6,8,10) the greatest side is 10. So, hypotenuse = 10.

= [tex]hypotenuse^{2}[/tex] = [tex]10^{2}[/tex] = 100.

Now, [tex]6^{2}[/tex] + [tex]8^{2}[/tex] = 36 + 64 = 100.

[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]8^{2}[/tex]

Thus A(6,8,10) is a Pythagorean triplet.

In the second case B(5,12,13) hypotenuse = 13.

= [tex]hypotenuse^{2}[/tex] = [tex]13^{2}[/tex] = 169.

Now, [tex]12^{2}[/tex] + [tex]5^{2}[/tex] = 144 + 25 = 169.

[tex]13^{2}[/tex] = [tex]12^{2}[/tex] + [tex]5^{2}[/tex]

Thus B(5,12,13) is a Pythagorean triplet.

In the Third case C(7,13,15) Hypotenuse = 15.

= [tex]hypotenuse^{2}[/tex] = [tex]15^{2}[/tex] = 225.

Now, [tex]7^{2}[/tex] + [tex]13^{2}[/tex] = 49 + 169 = 218.

[tex]15^{2}[/tex] [tex]\neq[/tex] [tex]7^{2}[/tex] + [tex]13^{2}[/tex]

Thus C(7,13,15) is not a Pythagorean Triplet.

In the last case D(3,4,5) Hypotenuse = 5.

= [tex]hypotenuse^{2}[/tex] = [tex]5^{2}[/tex] = 25.

Now, [tex]3^{2}[/tex] + [tex]4^{2}[/tex] = 9 + 16 = 25.

[tex]5^{2}[/tex] = [tex]3^{2}[/tex] + [tex]4^{2}[/tex]

Thus D(3,4,5) is a Pythagorean triplet.

Therefore our three results A(6,8,10) B(5,12,13) and D(3,4,5) are Pythagorean triplets.

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Answer:

Undefined

Step-by-step explanation:

[tex]f(x)=2+|x-3|\\f'(x)=\frac{x-3}{|x-3|}\\f'(3)=\frac{3-3}{|3-3|}=\frac{0}{0}[/tex]

Therefore, the function is not differentiable at x=3

The distance from Point B to Point C of the triangle will be 45 feet.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Triangle ABC is similar to Triangle ADE. Then the equation is given as,

x / 15 = (40 + 20) / 20

x / 15 = 60 / 20

x / 15 = 3

x = 45 feet

The distance from Point B to Point C of the triangle will be 45 feet.

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The complete question is given below.

No, 1234 is not an arithmetic sequence. A sequence is a list of numbers, arranged in a specific order.

An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is always the same. It is also known as an arithmetic progression.

The sequence 1234 does not have a common difference between its terms. It's just a set of numbers arranged in a specific order, but the difference between the terms is not always the same.

Arithmetic sequence has the general formula of a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the number of the term. The sequence 1234 doesn't follow this formula.

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Answer:

This is a simple algebraic equation, it can be solved by isolating the variable on one side of the equation.

-2.75x + 7 = -26

Add 26 to both sides of the equation:

-2.75x + 33 = 0

Divide both sides by -2.75:

x = -12

So the solution of the equation is x = -12.

Note that x = -12 is the value of x that makes the equation true

Answer:

x = 12

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

x = 12

The inverse additive of 2 3 is -2 3.. This means that when you add the two numbers together, the result is 0.

2 3 + (-2 3)

= (2 x -1) + (3 x -1)

= -2 + (-3)

= -5

= 0

The additive inverse of 2 3 is -2 3. In mathematics, an additive inverse is a number that when added to another number will produce a result of zero. This means that when you add 2 3 and -2 3 together, the result will be 0. To calculate this, we first start by multiplying each number by its opposite sign. So,

2 x -1 = -2 and

3 x -1 = -3.

Then, we add the two numbers together

: -2 + (-3) = -5.

Finally, we simplify the equation to 0. The additive inverse of 2 3 is -2 3, meaning that when added together, the result will be 0.

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$93.60

Simple interest shows the amount of money an account earns based on the initial deposit.

Interest Formula

The formula to find the amount of interest earned is I = Prt. In this equation, I is the total interest earned, P is the principal or the initial deposit, r is the interest rate as a decimal, and t is the time in years.

To find the total balance of the account just add the interest amount to the principal. So, A = I + P, where A is the total balance.

Solving for Simple Interest

For this question, the variables are:

Now, we can plug these values into our formula.

After 4 years, the account will earn $93.60 in simple interest.

Answer:

Step-by-step explanation:

2590

The rate of change of f on the interval [2, 4] is 6.

The rate of change of a function f on the interval [a,x] is the slope of the corresponding secant line m(sec), which is given by the following formula:

m(sec)=(f(x)-f(a))/(x-a)

To calculate the rate of change, we can take an example function f(x) = x^2. Let's say we want to find the rate of change of f on the interval [2, 4]. Using the formula from above, we get:

m(sec)=(f(4)-f(2))/(4-2)

= (4^2 - 2^2)/(4-2)

= (16 - 4)/2

= 12/2

= 6

Therefore, the rate of change of f on the interval [2, 4] is 6.

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The categories are usually "felony," "misdemeanor," and "infraction." Decisions on crime classification are made by state legislators; the determination focuses on the seriousness of the crime.

8.33% probability that Michael will be chosen first and Susan will be chosen second.

Initially, there are 4 people(Susan, John, Lisa, and Michael). The probability of Michael being chosen first is 1/4.

Now, suppose Michael was chosen.

There are 3 people(Susan, John and Lisa). The probability of Susan being chosen is 1/3.

What is the probability that Michael will be chosen first and Susan will be chosen second.

Multiplying these probabilities

8.33% probability that Michael will be chosen first and Susan will be chosen second.

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Answer: 23

Step-by-step explanation:

Answer:23

Step-by-step explanation:

The amount that her clothes weigh more than her books would be

= 57kg

The amount for the shipping cost for her school would be

= 5600+25400 = $31000

Postal Service:

The Postal Service is an American indie pop supergroup from Seattle, Washington, consisting of singer Ben Gibber, producer Jimmy Tamborello, and backing vocalist Jenny Lewis.

The band released her only album Give Up in 2003 on her Sub Pop Records to mostly positive reviews. The album reached his number 114 spot on the US Billboard 200 album chart and was certified platinum by the Recording Industry Association of America.  Laura Bergen joined the line-up for the entire tour, providing additional vocals and instruments, while Jen Wood and Jenny Lewis filled in for some shows.

According to the Question:

The mass of Moya's books = 70 kilograms

The mass of Moya's clothing = 127 kg

The difference between the both masses = 127 - 70 = 57kg

The cost per kg for books = $80 per kg

The cost per kg of clothing = $200

Therefore, the amount for the shipping cost for her school would be = (70×80) + (127 ×200)

= 5600+25400 = $31,000.

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The thermometer functions because of temperature-related expansion and contraction. Conduction is the process by which heat moves from one item to another.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

given

The thermometer will display a greater temperature as the liquid expands and rises as it gets hotter.

The thermometer functions because of temperature-related expansion and contraction.

Conduction is the process by which heat moves from one item to another.

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The selling price of the washer/dryer is $1,137.86. Thus, the correct answer is option b.

To find the cost of the washer/dryer, we need to reverse the markup percentage. We can do this by dividing the markup by 100 and then multiplying by the selling price.

Markup = (Markup Percentage) x (Cost)

So, if we rearrange this equation and solve for cost:

Cost = (Markup) / (Markup Percentage)

Plugging in the given information:

Cost = $295.00 / 0.35

Cost = $842.86

To find the selling price, we add the markup to the cost:

Selling Price = Cost + Markup

Selling Price = $842.86 + $295.00

Selling Price = $1,137.86

The selling price of the washer/dryer is $1,137.86.

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The complete question- Appliance World places a markup on a washer/dryer combination of $295.00, which is 35%based on cost. Find the cost, then the selling price. What is the selling price of the washer/dryer? a)$1,098.74. b) $1,137.86 c)$1,032.19. d)$1,059.43

On solving the question, the answer of given trigonometric question  is tanx-sinx.

This is due to the fact that trigonometry is still regarded as a very challenging and abstract branch of mathematics in comparison to other branches. When learning trigonometry, students frequently run into mistakes, misunderstandings, and barriers. A subfield of mathematics known as trigonometry studies how angles and length ratios relate to one another. Applications of geometry to astronomical research led to the field's emergence in the Hellenistic civilization during the third century BC.

cosecx(secx−1)−cotx(1−cosx)

= 1/sinx*1(1-cosx)/sinxcosx−cosx(1−cosx)/sinx

=((1−cosx)−sinxcosx(1−cosx))/sinxcosx

=sinxcosx(1−cosx)−cos^2x(1−cosx)​

=(1−cosx)(1−cos2x)/sinxcosx

=(1−cosx)×sin2^x/sinxcosx

=tanx(1−cosx)

=tanx−tanxcosx

=tanx−sinx/cosx×cosx

=tanx−sinx

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One can use either the slope formula m = (y2 – y1)/(x2 – x1) or the standard line equation, y = mx + b to solve for the slope, m.

You can find the slope of the line by determining the rise and run of two locations on the line. The rise is the vertical change between two places, while the run is the horizontal change. The slope is calculated by dividing the climb by the run: Riserun = Slope Slope = rise and run.

Depending on the form of the equation in front of you, the procedure for calculating the slope will differ. If the equation is written as y = mx + c, the slope (or gradient) is simply m. If the equation is not in this form, attempt rearrangement. You will need to do the following to determine the gradient of additional polynomials:

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The value of the ratio OC'' : OC' is given as follows:

OC'' : OC' = 1 : 4.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

For point C', the scale factor is given as follows:

k = 2.

For point C'', the scale factor is given as follows:

k = 1/2.

The ratio between two amounts a and b is given by the division of a and b, as follows:

a : b.

Hence the ratio between the distances OC'' and OC' is given as follows:

(1/2)/2 = 1/2 x 1/2 = 1/4.

(division of fractions, we multiply the first fraction, of 1/2, by the inverse of the second fraction 2/1, which is of 1/2).

In ratio notation, we have that:

OC'' : OC' = 1 : 4.

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A sentence must have a singular or plural subject and verb in order to be grammatically correct. To put it another way, the tenses of the subject and verb must match.

According to their structure and function, sentences can be divided into eight categories: declarative, interrogative, exclamatory, imperative, simple, compound, complex, and compound-complex sentences.

You must look at what a grammatical name accomplishes in an English sentence in order to recognise it. Consider: At this morning's assembly, Susan performed a song. You must take into account the work each unit performs in the sentence in order to identify the various units' grammatical names.

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Answer:

216.7 m/min

Step-by-step explanation:

1 km = 1000 m

1 hour = 60 min

13km/h = 13 (1000 m) / (60 min) = 216.7 m/min

Answer:216.6667

Step-by-step explanation:

kph × 16.66667

m/min =13 × 16.66667

m/min =216.6667

So, 30 and 5 are the values that are missing is calculated by ratio and proportion.

An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

If both the antecedent and the consequent are multiplied or divided by the same non-zero number, the ratio remains the same.

i.e.,

We can see from the provided table that:

In the second column,

Since, 6x0.5=3

Thus, multiply 10 by the same number.

10x0.5=5

For the third column,

since,

50=10x5

multiply by the same number, then

6x5=30

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Answer:

180 cm

Step-by-step explanation:

I had to look up some of these equations

Central angle  'a' = 2 arcsin ( c/(2R) = 2 arcsin (120/(2*100) ) = 73.74°

d= R cos ( a/2) = 100 cos ( 73.74/2) = 80 cm

So from the cutout to the bottom will be   80 + 100 = 180 cm

a) To determine the distance covered by a bus in a given number of minutes, we can use the formula: distance = speed x time. Since the speed of the bus is given in miles per hour (mph) and we want to know the distance covered in minutes, we need to convert the time to minutes. Therefore, distance = speed x (time in minutes / 60).

b) To determine the distance covered by a bus traveling at sodi mph for 3 hours, we can use the formula: distance = speed x time.

distance = sodi x 3

c) To determine the distance covered by a bus traveling at sodi mph for 30 minutes, we need to convert 30 minutes to hours. Therefore, time = 30/60 = 0.5 hours.

distance = sodi x 0.5

It's important to note that I'm not able to understand the value of "sodi" as it is not a valid unit for speed or distance. Please provide the correct value for sodi.