A glass aquarium is in the form of a rectangular parallelepiped with dimensions 50cm by 100cm, and its depth is 30cm.How many liters of water will it hold?

The number of 3 digit combinations possible for the six digit wheel combination lock is; 216 combinations.

It follows from the task content that the number of possible 3 digit combinations for the six digit wheel as required is to be determined.

The number of possible selections in a given sample space is defined by the combination which defines the situation.

On this note, each digit from the 3 digit combinations could be any of the six digits on the wheel.

Therefore, the number of possible combinations is; 6 × 6 × 6 = 216 combinations.

Ultimately, the number of possible combinations is; 216 combinations.

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Answer:

f(-1) = 7

Step-by-step explanation:

Hello!

You can evaluate for f(-1) by substituting -1 for x in the equation.

f(-1) is 7.

Answer:

f(-1) = 7

Step-by-step explanation:

Hello!

You can evaluate for f(-1) by substituting -1 for x in the equation.

f(-1) is 7.

Mr Manet need 5 guitars for his 4 grandsons and 1 granddaughter.

Each guitar costs $88,

So the total cost of guitars is $88 x 5 = $440

The best estimate among the choices is Choice B. $450

The estimate should always be higher than the actual cost.

Solution:

There is 2 possibility for the first letter from the left.

Then there are 2 possibilities for the second letter. Then and so on till the 5-th letter.

In this way, you will get

Each is unique, and each is achievable in this way.

There are no other arrangements. So that, we can conclude that the correct answer is:

Explanation:

The rate of increase yearly is

The number of lionfish in the first year is given beow as

Part A:

To figure out the explicit formula of the number of fish after n years will be represented using the formula below

By substituting the formula, we will have

Hence,

The final answer is

Part B:

to figure out the amoutn of lionfish after 6 years, we wwill substitute the value of n=6

Hence,

The final answer is

Part C:

To figure out the recursive equation of f(n), we will use the formula below

From the question the common difference is

Hence,

The recursive formula will be

We remember that two interior angles are those inside the are of the lines, Thus, the angles in the area:

Are interior. Now, we identify two sides, the right side, and the left side, which have been separated by the transversal line.

Thus, the angle that is is the same side as ∡3, and also that is interior is ∡5.

As per given by the question,

There are given that a graph.

Now,

1. The given graph is cosine graph.

2. The aplitute of the given graph is,

From the graph, it is lie between -2 to 2.

So,

The amplitude of the given graph is 2.

Now,

3. The equation of the midline is,

Now,

4.The period of the fumction is,

Now,

The equation of the function.

First the general form of cosine graph function is,

Then,

Now,

Where, D is vertical shift.

Hence, the equation of the function is,

We have the next given information:

China has a population of approximately 1,382,323,332 people.

The United States has a population of about 324,118,787 people.

a) We need to use scientific notation which is given by the next form:

Where a is the coefficient rounded to the nearest tenth.

and a is the terms moved to the decimal point.

For China:

1382323332.0, we moved the decimal point nine spaces to the right.

then

1.382323332

Expressed in scientific notation and rounded to the nearest tenth:

For the United States:

324,118,787 with the decimal point 324,118,787.0

then

324118787.0

Move the decimal point 8 spaces to the right, then:

3.24118787

Expressed in scientific notation and rounded to the nearest tenth:

Part b:

To find how many more people live in China than in the United States, we need to subtract between China and the United States:

Then:

1,382,323,332 - 324,118,787 = 1,058,204,545

Now

1,058,204,545 equal to 1058204545.0

We need to move the decimal point 9 spaces:

1.058204545

Expressed as scientific notation and rounded to the nearest hundredth:

EXPLANATION

x + y = 8 ----------------------------------------(1)

5x - 3y = 24 ------------------------------------------(2)

If we are to eliminate y in the equations, we first need to multiply through equation (1) by 3.

3x + 3y = 24 ----------------------------------------(3)

Add equation (2) and equation (3).

If we add equation(1) and equation(3) together, -3y will cancel-out 3y.

(5x + 3x) = (24 + 24)

8x = 48

Therefore, the correct option is D. 8x = 48

We have to calculate the height of the stack of hay bales.

We can start by calculating the volume as the number of bales times the volume of one hay:

Now, we know that this volume will be the area of the base times the height.

The area of the base can be calculated as the product of the length and the width:

We then can calculate the height as the volume divided by the base area:

Answer the height is 16 feet.

The common difference between each term is -3.

19 - 22 = -3

16 - 19 = -3

13 - 16 = -3

The recursive formula of an arithmetic sequence follows the pattern below:

where d = common difference and number of terms "n" must be more than or equal to two.

To be able to get the recursive formula, we will plug in the common difference assuming that first term a₁ = 22. Therefore, the recursive formula is:

In order to find f(2) we just have to replace x by 2 in its equation:

f(x) = 3x - 1

↓

f(2) = 3 · 2 - 1

f(2) = 6 - 1

f(2) = 5

Since g(x) = f(2) is

g(x) = 5

using the equation of g, we have that

2x - 3 = 5

In order to find x we just solve the previous equation

2x - 3 = 5

↓ adding 3 both sides of the equation

2x - 3 + 3 = 5 + 3

2x = 8

↓ dividing by 2 both sides of the equation

2x/2 = 8/2

x = 4

Answer- D: x = 4

a) To determine which category represents approximately one-fifth of the publisher's revenue, you can compare the given pie chart with a pie chart divided into 5 parts.

The category that is approximately one-fifth of the revenue, that is, 20% of the total revenue, is textbooks.

To solve parts b and c you can use the following pie chart to compare with the given chart for the publisher's revenue:

b) Looking at the pie charts, the categories "paperback" and "poetry" are approximately 20% of the total revenue.

c) The category "Nonfiction" is 10% of the total revenue, the category "poetry" is approximately half of the size of the category "nonfiction" so you can say that it corresponds to 5% of the total revenue.

done

Answer:

3/4

Step-by-step explanation:

As y is changing by 3, x is changing by 4

The next step to constructing a tangent line from Q to circle P is to construct the perpendicular bisector of the segment PQ.

For this, Leo can construct arcs from point P and from point Q that are greater than half the length of segment PQ.

The next step is to construct arcs from point P that are greater than half the length of segment PQ.

This lines are 2 lines that cross over the same intercept in the y-axis.

they both have the y-intercept: -4

they also have the same slope but one on them is negative which makes the line cross each other at the y-intercept.

The graph should be:

total number of balls = 5 + 3 = 8

The possibilities are:

RR (two red) and RB (one red and one blue)

RR and RB are mutually exclusive

P(RR) =

Answer:

perimeter: add p + m + n

area: use (p × m)/2

find missing side: use p^2 + m^2 = n^2

The triangle has sides

a=8

b=14

c=19

You need to determine the measure of x

To determine the value of x you have to use the Law of Cosines that states that:

Where a, b, and c are the sides of the triangle, and theta represents the angle we are looking for.

So first step is to replace the formula with the given data and solve the exponents

Next solve for the cosine of theta:

And calculate the inverse cosine to determine the measure of the angle

Answer:

The correct option is option a.

$18.08 for 9 bottles is the better buy.

Explanation:

The best buy is the item with the lesser price tag.

Let us chech which of the given items has the lesser price tag.

a. $18.08 for 9 bottles of juice

Let us find how much one bottle costs.

1 bottle = 18.08/9

= 2.01

1 bottle of juice costs $2.01 approximately

b. $22.23 for 11 bottles of juice

1 bottle = 22.23/11

= 2.03

1 bottle of juice costs $2.03 approximately.

Comparing these prices per bottle of juice, we realise that the one with $18.08 for 9 bottles is the better buy.

Answer:

Table A represents a function

Step-by-step explanation:

Table A represents function because it is the only table that doesn't repeat an output or input number.

A geometric sequence is defined as:

Where r ≠ 0 is the common ratio and a ≠ 0 is the first term of the sequence.

From the statement, we know that r = 2/3 and the first term is a = 5.

Replacing these numbers in the expression of the 7th term, we get:

320/729

Problem

Solution

We have the following sequence of terms 34,25,16,7,....

Part a

The common difference for this case would be:

25-34= -9

16-25=-9

7-16= -9

Then the answer for part a would be -9

Part b

We want to write the following form:

an = a1 + (n-1) d

For this case d=-9, a1= 34

And then we can write the genral expression like this:

an = 34 + (n-1 ) (-9)

With n = 1,2,3,4....

Part c

In order to find the 20 th term we can replace n =20 and we got:

a20= 34 + (20-1) (-9) = 34-171= -137

Answer

Option B is correct.

9.56556555... is an irrational number.

Step-by-step Explanation

Rational numbers are numbers that can be expressed as a clear fraction consisting of the numerator and the denominator both being integers.

The decimal form or decimal expansion of a rational number terminates after a particular/finite number of digits (e.g., 0.25, 0.762 etc.) or begins to repeat/recur the same sequence over and over again (e.g., 0.333..., 0.267267... etc)

Anything other than these two rules, the number is regarded as an irrational number.

The number given is 9.56556555...

The dots indicate thst the numbers after the decimal point conbtinue till eternity.

Observing the numbers after the decimal point for the given number, one can see that 565 repeats once and then the number after the second 565 is 55, indicating that the 565 doesn't recur till infinity.

Since the numbers after the decimal point doesnt contain a finite number of digits and the numbers don't recur till infinity, we can conclude that 9.56556555... isn't a rational number.

Hope this Helps!!!

The resultant matrix for the given expressions are as follows -

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

Matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. A matrix has [n] rows and [m] columns. The order of a matrix is given by - [m] x [n].

Given are the three different matrices as -

A = [tex]\left[\begin{array}{ccc}9&-6\\7&5\\\end{array}\right][/tex]

B = [tex]\left[\begin{array}{ccc}4&3\\-7&-6\\\end{array}\right][/tex]

C = [tex]\left[\begin{array}{ccc}0.5&3.6\\2.4&-3.2\\\end{array}\right][/tex]

We can solve the given expressions as follows.

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

Therefore, the resultant matrix for the given expressions are as follows -

[A]  → 2B - C = [tex]\begin{pmatrix}7.5&2.4\\ -16.4&-8.8\end{pmatrix}[/tex]

[B] → C + 2A = [tex]\begin{pmatrix}18.5&-8.4\\ 16.4&6.8\end{pmatrix}[/tex]

[C] → 2B - 10C + A = [tex]\begin{pmatrix}12&-36\\ -31&25\end{pmatrix}[/tex]

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The solution of the equation e^(x/4) = |4x| for the x by graphical approach is 0.27 and -0.24.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A formula known as an equation uses the same sign to denote the equality of two expressions.

As per the given expression,

e^(x/4) = |4x|

The function e^(x/4) is an exponential function and the plot of this function has been plotted below.

The mode function |4x| has also been plotted below.

The point of intersection is the point where both will be the same or the solution meets.

The first point of intersection is (0.267,1.0691) so x = 0.267 ≈ 0.27

The second point of intersection (-0.2357,0.9428) so x = -0.2357 ≈ -0.24

Hence " The solution of the equation e^(x/4) = |4x| for the x by graphical approach is 0.27 and -0.24.".

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We know that angles a and b are in the first quadrant. We also know this values:

We have to find sin(a+b).

We can use the following identity:

For the second term, we can replace the factors with another identity:

Now we know all the terms from the right side of the equation and we can calculate:

Answer: sin(a+b) = 63/65

Given a straight line angle = 180

So, the angles (9x-100) and (40-x) are supplementary angles

So,

Solve for x:

So, the answer will be x = 30

Given the following equation:

You can solve for the variable "x" as following:

1. You need to apply the Division property of equality by dividing both sides of the equation by "p":

2. Remember that:

Then:

3. Now you have to apply the Subtraction property of equality by subtracting "q" from both sides of the equation:

The answer is: