Logarithms and natural logarithms are fundamentally different math structures and rely on totally different sets of properties to worth with.

True or False

The domain of the linear function that models the volume is:

D: 0 ≤x ≤640

The correct option is the fourth one, counting from the top.

Here we have the following linear function:

V(x) = 640 - x

V(x) represents the volume of water left in the bucket, while x represents the amount of water that has leaked from the bucket.

The domain will represent the possible values of x.

first, the smaller value of x.

It is x = 0, and it represents the moment before the leak started, when the bucket was completely full and had a volume of:

V(0)=  640 ounces.

The largest possible value of x is x = 640, which is the case where all the water in the bucket has come out.

Then the domain is:

D: 0  ≤x ≤640

Finally, the correct option is the last one.

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Answer:

Step-by-step explanation:

You'd multiply them by setting them correctly. When you multiply them you'd get 1.12 (don't know if you wanted the answer or just wanted to know how to multiply them)

Answer: 1.12 is the answer

Step-by-step explanation:

for an example here !

Answer:

A

Step-by-step explanation:

In an ordered pair, the coordinates are (x,y)

The only answer that describes a coordinate with an (x,y) that matches the table is A

There are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.

What is a combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Here, we

Consider lining up all the blue marbles and placing one red marble in between them. Let that arrangement be fixed. The remaining red marbles will be 5 red marbles. Note that the arrangement will be:

x BR x BR x BR x BR x BR x BR x BR x B x

Note that this is the same even if our arrangement is

x B x RB x  RB x RB x RB x RB x RB x RB x

There is a total of 13 places to arrange 8 blue marbles among 12 red marbles.

8 marbles can be placed in ¹³C₈ ways

Total possible arrangements = ¹³C₈ = 1287

Hence, there are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.

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The mentioned data 100 kilometres in an hour is the speed of rate of object.

The 100 kilometres represents distance and an hour indicates the time. The complete data in the sentence is indicative of coverage of 100 kilometres in an hour by whatever the object is, which is not mentioned in the question.

However, writing distance with respect to time indicates the rate or speed. Widely applicable, it can anything. Few examples of its indication are rate of descending or ascending of plane, kite, lift or any other object. It can refer to the speed of person, car, train or other such objects or animals holding capacity to travel.

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The required probability that 2 or fewer students are left-handed in a random sample of 65 students from the school is 0.0360.

Let X be a random variable which denotes the number of students who are left handed out of a sample of 65 students.

Here we have 65 students, therefore the number of trials would be 65. It would be reasonable to assume that the probability of one student being left handed is independent of any other student.

Therefore, the trials are independent.

There are only two possible outcomes for each trial i.e, either success or failure. The probability of success for each trial is 0.1

Hence we can say that X follows a binomial distribution with n = 65 and p = 0.1

X ~ Bin(65,0.1)

We need the probability that 2 or fewer students are left handed. This is given as :

P(X≤2)

we shall use the BINOM.DIST() function to find this

The syntax is given as:

= BINOM.DIST(number_s,trials,probability_s,cumulative)

Here,

number_s denotes the number of success required (2 in this case)

trials is the number of trials(65 in this case)

Probability_s is the probability of success in each trial (0.1 in this case)

cumulative, if true indicates the CDF or false if the PDF of X(TRUE in this case)

Hence the function which we use is

= BINOM.DIST(2,64,0.1,TRUE)

on running this code in any cell of excel, we get the probability as 0.035973

The required probability is 0.0360

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Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations that represent algebraic operations on complex numbers.

Using letters or alphabets to represent numbers without giving their exact quantities is the idea behind algebraic expressions. The principles of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables. Constants and variables can both be used in an algebraic expression.

Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.

4x + 3y - 8 , x - 4, and so forth.

These expressions are represented by variables, constants, and coefficients that are unknown. The combination of these three words is referred to as an expression. It should be noted that, in contrast to an algebraic equation, an algebraic expression lacks sides and the equal sign.

In mathematics, addition, subtraction, multiplication, and division are the four fundamental arithmetic operations that represent algebraic operations on complex numbers.

According to the given information

Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations that represent algebraic operations on complex numbers.

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The price for the monthly fee will be;

⇒ x = $9.99  

And, The price per movie rental will be;

⇒ y = $2.99

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Yolanda is charged $21.95 for her monthly fee and 4 movie rentals.

And, Jeffrey is charged $30.92 for the same monthly fee and 7 movie rentals.

Now,

Let the price for the monthly fee = x

And, The price for the movie rental = y

Hence, We can formulate the expression for Yolanda;

⇒ x + 4y = $21.95

And,  We can formulate the expression for Jeffrey;

⇒ x + 7y = $30.92

Subtract equation (ii) from (i), we get;

⇒ 7y - 4y = $30.92 - $21.95

⇒ 3y = $8.97

⇒ y = $2.99

And, x + 4y = $21.95

x + 4 × 2.99 = 21.95

x + $11.96 = $21.95

x = $21.95 - $11.96

x = $9.99

Thus, The price for the monthly fee = $9.99  

And, The price per movie rental = $2.99

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The amount of money invested at the rate [tex]2\frac{1}{4}[/tex]% is $8500 and the amount of money invested at the rate 2% is $3000.

Given that, Phyllis invested $11,500, a portion earning a simple interest rate of [tex]2\frac{1}{4}[/tex] % per year and the rest earning a rate of 2% per year.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

Let x be the amount invested at [tex]2\frac{1}{4}[/tex] =2.25% per year

Now, S.I= (x×2.25×1)/100

= 0.0225x

Then, (11,500-x) be the amount invested at 2% per year

S.I =((11,500-x)×2×1)/100

=(11,500-x)×0.02

= 230-0.02x

After one year the total interest earned on these investments was $251.25.

Now, 0.0225x+230-0.02x=251.25

⇒ 0.0025x+230=251.25

⇒ 0.0025x=21.25

⇒ x=21.25/0.0025

⇒ x=$8500

So, 11,500-x=$3000

Therefore, the amount of money invested at the rate [tex]2\frac{1}{4}[/tex]% is $8500 and the amount of money invested at the rate 2% is $3000.

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Using the slope formula, we know that the relationship between AB and CD is that they are (C) parallel.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.

A line's steepness can be determined by looking at its slope.

The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

So, formula: m = y2 - y1/x2 - x2

For AB:

m = y2 - y1/x2 - x2

m = -5+2/3-1

m = -3/2

For CD:

m = y2 - y1/x2 - x2

m = 5-2/5-7

m = -3/2

The two lines have equal slopes, and when slopes are equal, lines are said to be parallel.

Therefore, using the slope formula, we know that the relationship between AB and CD is that they are (C) parallel.

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Correct question:
Determine the relationship of AB and CD gave the following points: A (1, -2), B (3, -5), C (7, 2), and D (5, 5).

a. Neither

b. Perpendicular

c. Parallel

The supplied regular polygon's solitary outside angle measures 32.5 degrees.

additionally, we must determine the size of a single external angle.

As a result, the polygon that is presented has 11 sides.

What does the term "exterior angle" mean?

In a rectilinear figure, the angle between a side and its neighboring side stretched outward.

360 degrees is the sum of all outside angles.

By dividing 360 by the total number of sides, we must determine the size of a single outside angle.

As a result, the supplied regular polygon's solitary exterior angle has a measure of 32.5 degrees.

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The equation of the line is y = 0.4x - 793.65 and the minimum wage is $18.35

The equation of a line can be formed with the help of the slope of the line and a point on the line. Let us understand more about the slope of the line and the needed point on the line, to better understand the formation of the equation of a line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.

a)

Taking two points from the table;

Using 1996 and 1997

The data are; (1996, 4.75), (1997, 5.15)

m = y₂ - y₁ / x₂ - x₁

m = 5.15 - 4.75 / 1997 - 1996

m = 0.4

The slope of the line is 0.4

Using the line equation;

y = mx + c

Taking one point, we can find y-intercept here

5.15 = 0.4(1997) + c

5.15 = 798.8 + c

c = 5.15 - 798.8

c = -793.65

The equation of the line is y = 0.4x - 793.65

b) The minimum wage in 2030

y = 0.4x - 793.65

y = 0.4(2030) - 793.65

y = 18.35

The minimum wage is $18.35

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The empirical probability that George will get back on his feet the next time Angie knocks him down is 5/114.

Event probabilities are closely related to empirical probabilities, also called empirical probabilities.

Empirical probability is an estimate of the probability of a particular outcome occurring again, based on the number of instances of that outcome in the sample set.

In the given question.

Also includes George the Turtle, who flipped Angie the Tortoise 114 times.

Three times George got back on his feet with help. Empirical probabilities are exactly what we are looking for.

Based on our observations, we will now empirically calculate whether George will be able to stand again.

Therefore,

The Empirical probability = 5/114

So, the next time Angie knocks George down, the empirical probability that George will be able to get back up on his own will be his 5/114.

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The probability that A will have more heads than B is 1/2, when A and B are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.

Given, a and b are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.

we have to find the probability that a will have more heads than b.

Now, p1  = "probability that A obtains more heads than B.".

p2 = "probability that B obtains more heads than A.".

p3 = "probability that A obtains as many heads as B.".

Such that p1 + p2 + p3 = 1.

Since, both flips n coins, A wins with the same probability as B.

p1 = p2

Now, A flips and extra coin.

½ of the time it gives tails and doesn't contribute, but ½ of the time is gives heads meaning that A now wins if they before had equal number of heads.

p1+1/2(1 − p1 − p2)=1/2.

Hence, the probability that A will have more heads than B is 1/2, when A and B are playing a game where a has n + 1 coins, b has n coins, and they each flip all of their coins.

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The solution is

Angle 1 and Angle 5 = Corresponding Angles

Angle 1 and Angle 8 = Co-Interior Angles

Angle 2 and Angle 8 = Alternate Interior Angles

Angle 3 and Angle 5 = Alternate Exterior Angles

What are Parallel Lines Cut by Transversal?

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

From the figure , we can see that

The angles 5 , 6 , 7 and 8 are all on the straight line t

The angles 1 , 2 , 3 and 4 are all on the straight line n

The line m is the transversal line

Now ,

From the theorem of angles on a parallel lines , we get

Alternate angles are equal

So , 2 = 8 and 3 = 5

Now ,

Angle 2 and Angle 8 = Alternate Interior Angles

Angle 3 and Angle 5 = Alternate Exterior Angles

Corresponding angles are equal

So , 1 = 5 and 2 = 6

Now ,

Angle 1 and Angle 5 = Corresponding Angles

Co-Interior angles are supplementary

So , 1 + 8 = 180°

Now , Angle 1 and Angle 8 = Co-Interior Angles

Hence ,

Angle 1 and Angle 5 = Corresponding Angles

Angle 1 and Angle 8 = Co-Interior Angles

Angle 2 and Angle 8 = Alternate Interior Angles

Angle 3 and Angle 5 = Alternate Exterior Angles

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As per the double integral, the flux of the vector is 2√11(6z + 1) + 176

What is double integral small definition?

In math, Double integrals are used to find the flux of a vector field through a given surface S and find the normal to the given surface and equations of the surface to find the limits of integration.

And it is calculate by the formula as Flux= ∫∫F⋅ndS

Here we have given that S be the part of the plane 2x + 1y + z = 2 which lies in the first octant, oriented upward.

And we need to find the the flux of the vector field F = 1i + 1j + 3k across the surface S.

As per the formula of flux of vector, it can be written as,

=>Flux =  ∫∫(1i + 1j + 3k) . 2 dS

When we integrate this one the we get,

=> Flux = 2√11(6z + 1) + 176

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Step-by-step explanation:meow

Answer:

100

Step-by-step explanation:

Use Pemdas or Order of Operations:

First in the brackets:

3+2=5
next in the brackets:

45 - 5 = 40

Now you get the equation:

3 x 20 + 40

First solve 20 x 3:

60; +40 = 100

Thus 100 is your total.

Answer:

Step-by-step explanation:

This is not a valid proof, as it simply repeats the given statement without providing any justification or reasoning. To prove that AB CD, we need to use logical reasoning and the properties of lines and angles to show that the statement is true.

One way to prove this statement is to consider the angles of the quadrilateral ZBZD. Since ZBZD is a quadrilateral, it has four angles. We are given that ZB is parallel to AD and that BC is parallel to AD. This means that the angles formed by these lines must be equal.

Additionally, since ZBZD is a quadrilateral, the sum of its angles must be 360 degrees. Therefore, if the angles formed by ZB and AD are equal, and the angles formed by BC and AD are equal, then the angles formed by ZB and BC must also be equal.

Therefore, we can conclude that ZB and BC are parallel, which means that AB CD. This completes the proof.

True, parabola consists of all the set of points that are equidistant from the fixed point and the fixed line.

As given in the question,

Given statement is: Parabola consist of set of all the points which are equidistant from fixed point and fixed line.

Therefore, parabola consists of all the set of points that are equidistant from the fixed point and the fixed line is a true statement.

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Answer:

There are 6 large blue marbles, so there are 8 + 6 - 6 = 8 ways to choose a large blue marble or a large marble.

There are 10 blue marbles (6 large blue marbles and 4 small blue marbles), so there are 10 + 8 - 6 = 12 ways to choose a blue marble or a large marble.

Therefore, there are 8 + 12 = <<8+12=20>>20 ways to choose a blue marble or a large marble.

Step-by-step explanation:

Answer: 24 different ways.

Step-by-step explanation: Hope it helps, please pick brainliest!

The value of x for the given right-angle triangle using the trigonometric function will be 1.0.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

As per the given right angle triangle,

sin 16° = x/3.5

x = 1.0

Hence "Using the trigonometric function, the value of x for the given right-angle triangle will be 1.0.".

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a)  The average score on the original exam is 76

b) The average score after 2 months = 67.41

c) The average score after 11 months = 56.574

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

For this case we know that the average scores for the class are given by the following model:

[tex]f(t) =76 - 18 log_{10} (t+1)[/tex] , 0≤ t ≤ 12

Where t is in months. The graph attached illustrate the function for this case

And for this case we can answer the questions like this:

Part a

We just need to replace t =0 into the model and we got:

[tex]f(t) =76 - 18 log_{10} (0+1)[/tex] = 76

Part b

We just need to replace t =2 into the model and we got:

[tex]f(t) =76 - 18 log_{10} (2+1)[/tex] = 67.41

Part c

We just need to replace t =11 into the model and we got:

[tex]f(t) =76 - 18 log_{10} (11+1)[/tex] = 56.574

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Question:

Students in a mathematics class were given an exam and then tested monthly with an equivalent exam. The average scores for the class are given by the human memory model f(t) = 76 − 18 log10(t + 1), 0 ≤ t ≤ 12 where t is the time in months. Verify your answers in parts (a), (b), and (c) using a graphing utility.

(a) What was the average score on the original exam (t = 0)? f(0) =

(b) What was the average score after 2 months? (Round your answer to one decimal place.) f(2) =

(c) What was the average score after 11 months? (Round your answer to one decimal place.) f(11) =

The slope of the line in the table given is 11

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.

The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by

m = y₂ - y₁ / x₂ - x₁

Taking two points from the table

m = 1172 - 864 / 72 - 44

m = 11

The slope of the line is 11

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Answer:

48°

Step-by-step explanation:

this is because no if you take any two points in along line AB and CB it will always be 48°.

The slope of the line passing through the two points [tex](1,2)[/tex] and [tex](3,8)[/tex] is [tex]\frac{3}{1}[/tex] i.e. [tex]3[/tex]

The formula for finding the slope when two points are given

[tex]y=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\y=\frac{8-2}{3-1} \\y=\frac{6}{2} \\y=\frac{3}{1}\\y=3[/tex]

The slope of the line is [tex]3[/tex]

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The lines with the equations 10x+5y =-5 and y=-2x+6 are parallel

From the question, we have the following parameters that can be used in our computation:

10x+5y =-5 and y=-2x+6

Make y the subject in both equations

So, we have the following representation

y = -2x - 1 and y = -2x + 6

As a general rule of linear equations

Parallel lines have equal slope

A linear equation is represented as

y = mx + c

Where

slope = m

Using the above as a guide, we have the following:

The slope of y = -2x - 1 and y = -2x + 6 is -2

Hence, the lines are parallel

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Answer:2x^2+23

Step-by-step explanation:

7x^2+3-5x^2+20    (distribute (-5) to x^2 and (-4))

2x^2+3+20              (combine like terms)

2x^2+23

Types of  built in functions are;

Standard library functions and User-defined functions.

Given,

Built in functions;

A built-in function is one that is pre-installed in a programing language, software program, or other user-accessible tool. For instance, the SUM function is a built-in feature of most spreadsheet programs that sums up all the cells in a row or column.

There are two types of function in C programming: Standard library functions and User-defined functions.

Standard library function;-

These are defined in header lines.

Eg; A standard library function called printf() is used to display formatted output on a screen (display output on the screen). The header file stdio.h has a definition for this function.

Therefore, we must use #include stdio.h> to include the stdio.h header file in order to use the printf() method.

User- defined functions;

As needed, you can also build functions. User-defined functions are those that the user has created.

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Answer:

w + 18 = 22

Step-by-step explanation:

HC = 18 lb

HC + GD = 22 lb

GD + HC = 22

GD + 18 = 22

w + 18 = 22

a) The earnings of Portfolio 1 are given as follows: $679.5.

b) The Portfolio with the greatest earnings is: Portfolio 1.

The earnings are found by the sum of the multiplication of the equivalent decimal of the return by the investment.

The equivalent decimals are given as follows:

Then the earnings of the Portfolio 1 are given as follows:

0.028 x 1425 - 0.0155 x 1380 + 0.117 x 3400 + 0.0849 x 3100 = $679.5.

The earnings of the Portfolio 2 are given as follows:

0.028 x 4500 - 0.0155 x 3600 + 0.117 x 2150 + 0.0849 x 1980 = $489.86.

Hence Portfolio 1 earned the most, as 679.5 > 489.86.

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