Describe the discontinuity of the graphed function. Be sure to indicate the location of each discontinuity and identify the type of discontinuity.

i)The amount of petrol sold by the petrol station on a particular day is 21,600 L

II) Number of customers who would expect to buy 44 L of petrol is 2.28

i)The amount of petrol sold by the petrol station on a particular day can be estimated using the following equation:

Total petrol sold = Mean amount of petrol per customer x Number of customers

= 36 L x 600 customers

= 21,600 L

ii) To find the number of customers who would expect to buy 44 L of petrol, we need to find the probability of a customer buying that amount. We can use the standard normal table and the z-score formula (z = (x - mean) / std dev) to calculate the probability of a customer buying 44 liters of petrol.

z = (44 - 36) / 7 = 2.57

Using the standard normal table, we can find that the probability of a customer buying 44 liters of petrol is about 0.0038 or 0.38%.

Therefore, we can estimate that about 2.28 customers would expect to buy 44 liters of petrol on that day by multiplying the probability of buying 44 liters of petrol by the total number of customers.

Number of customers who would expect to buy 44 L of petrol = 0.38% * 600 = 2.28

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The complete question is:

The amount of petrol bought by a customer at a petrol station is normally distributed with mean 36 L and standard deviation 7 L.                                                                                                              on a particular day, the petrol station has 600 customers. i) how much petrol would you expect the petrol station to sell on this day? ii) how many customers would you expect to buy 44 l of petrol?          

2.21 × 10^20 is expressed in scientific notation.

What does scientific notation consist of?

Writing extremely large or extremely small numbers is done using scientific notation. When a number in the range of 1 to 10 is multiplied by a power of 10, the result is represented in scientific notation.

                         For instance, 650,000,000 can be expressed using scientific notation as 6.5 108. In scientific notation, a number is expressed in the form n10ab, where an is an integer such that 1|a|10 and b is also an integer.

The decimal point has to go 20 places to the left to give the number 2.21; that means the exponent on the 10 is 20.

= 2.21E20

= 2.21 × 10^20

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Bori will run 10.5 miles in 75 minutes, using the concepts of unitary method.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method. We typically utilise this technique for math calculations. This approach will be helpful to you while tackling problems involving ratio and proportion, algebra, geometry, etc.

Let us use the unitary method to solve this sum as well.

Bori can run 7 miles in 50 minutes.

This implies that, in 50 mins, Bori will run 7 miles.

Therefore, in 1 minute, Bori will run [tex]\frac{7}{50}[/tex] miles.

We have to find the number of miles Bori will run in 75 minutes.

Thus, in 75 mins, Bori will run [tex]\frac{7}{50} * 75[/tex] miles.

= 10.5 miles

Therefore, Bori will run 10.5 miles in 75 minutes.

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Answer:

I don't see all the answer choices, but it should be a graph with the slope of -1/2 and intersects y at -2.

Step-by-step explanation:

This equation will help you figure out what a graphed line will look like --> y=mx+b
In this equation, m represents the slope of the line, while b represents the y intercept. Since "m" is negative in the given equation, the line's slope is decreasing. Since "b" is also negative, the point the line intercepts at y will be (0,-2). I hoped this helped.

Answer:

r = 5

Step-by-step explanation:

calculate the slope m of the 2 given points and equate to - 2

using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (r, - 2 )

m = [tex]\frac{-2-2}{r-3}[/tex] = [tex]\frac{-4}{r-3}[/tex]

equating to - 2 gives

[tex]\frac{-4}{r-3}[/tex] = - 2 ( multiply both sides by r - 3 to clear the fraction )

- 4 = - 2(r - 3) ← divide both sides by - 2 )

2 = r - 3 ( add 3 to both sides )

5 = r

The emails would you expect the principal to receive each day is 2.45.

X = 0; P(X) = 0.05

X = 1; P(X) = 0.15

X = 2; P(X) = 0.35

X = 3; P(X) = 0.25

X = 4; P(X) = 0.15

X = 5; P(X) = 0.05

Now the number of emails should be

= 0 × 0.05 + 1 × 0.15 + 2 × 0.35 + 3 × 0.25 + 4 × 0.15 + 5 × 0.05

= 0 + 0.15 + 0.70 + 0.75 + 0.60 + 0.25

= 2.45.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

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The equation that has 2 as its root is 2x² - 7x + 6 = 0 (option c)

Suppose we are given a quadratic function f(x) = ax² + bx + c, then x = q is a root if f(q) = 0.

Let's check for the given functions:

a.  x² - 4x + 5 = 0

f(2) =  2² - 4(2) + 5

f(2) = 4 - 8 + 5 = 1

Since f(2) ≠ 0, hence 2 is not its root.

b. x² + 3x - 12 = 0

f(2) = 2² + 3(2) - 12

f(2) = 4 + 6 - 12 = -2

Since f(2) ≠ 0, hence 2 is not its root.

c. 2x² - 7x + 6 = 0

f(2) = 2(2)² - 7(2)+ 6

f(2) = 2(4) - 14 + 6 = 0

Hence, x = 2 is its root.

d. 3x² - 6x - 2 = 0

f(2) = 3(2)² - 6(2) - 2

f(2) = 12 - 12 - 2 = -2

Since f(2) ≠ 0, hence 2 is not its root.

Hence, the correct option is   2x² - 7x + 6 = 0 (option c)

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To implement string matching algorithm, we can use naive algorithm and write the program in C.

To conduct the string matching we can use naive algorithm. Among the pattern finding algorithms, naive pattern searching is the most basic. It looks for all characters in the main string that match the pattern.

The program in C:

---------------------------------------

#include <stdio.h>

#include <string.h>

int match(char [ ], char [ ]);

int main() {

 char x[200], y[200];

 int po;

 printf("Write your text\n");

 gets(x);

 printf("Write thepattern you want to find\n");

 gets(y);

 pos = match(x, y);

 if (pos != -1) {

   printf("Found at location: %d\n", pos + 1);

 }

 else {

   printf("No match.\n");

 }

 return 0;

}

int match(char text[], char pattern[]) {

 int p, q, r, text_long, pattern_long, pos = -1;

 text_long    = strlen(text);

 pattern_long = strlen(pattern);

 if (pattern_long > text_long) {

   return -1;

 }

 for (p = 0; p <= text_long - pattern_long; p++) {

   pos = r = p;

   for (q = 0; q < pattern_long; q++) {

     if (pattern[q] == text[r]) {

       r++;

     }

     else {

       break;

     }

   }

   if (q == pattern_long) {

     return pos;

   }

 }

 return -1;

}

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Equation for a line given a slope of 2/3 through the pt (-6,10) is y =  [tex]\frac{2}{3}[/tex] x + 16.

Given data :

The equation of a line in point slope form is

y - y1 = m ( x - x1 )

where m represents the slope and ( x1, y1 ) a point on the line here

m = 2 / 3 and  ( x1, y1 ) = ( -6, 10)

y - 10 = [tex]\frac{2}{3}[/tex] ( x - - 6 )

y - 10 = [tex]\frac{2}{3}[/tex] ( x + 6 )

y =  [tex]\frac{2}{3}[/tex] ( x + 6 ) + 10

y =  [tex]\frac{2}{3}[/tex] x + 16

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The values of x, y, and z are 25,15 and, 7 respectively.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. 

Given that,

x=y+10................(i)

y=z+8..................(ii)

x+y+z=47............(iii)

Solving these equations to find the values of x,y, and z.

Putting The value of x from the first equation in the third equation:

we get,

y+10+y+z=47

Solving this equation further, we get,

=>2y+z=47 -10=37

=>2(z+8)+z=37

=>2z+16+z=37

=>3z=37-16=21

=>z=21/3=7

=>y=z+8=7+8=15

=>x=y+10=15+10=25

Thus, The values of x, y, and z are 25,15 and, 7 respectively.

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The expression is a multiplication of five times the quantity one minus two times the quantity g times the quantity h. The expression can be rewritten as (1-2g)5h, which is the same expression but with fewer symbols.

1. Simplify the expression inside the parentheses: (1-2g)

2. Multiply what is inside the parentheses by 5: (1-2g)5

3. Multiply the result by h: (1-2g)5h

This expression is a multiplication of five times the quantity one minus two times the quantity g times the quantity h. To simplify it, first we need to simplify the expression inside the parentheses. To do this, we subtract two times g from one, which gives us the result of 1-2g. We then multiply the result by 5, which gives us the result of (1-2g)5. Finally, we multiply the result by h, which gives us the final result of (1-2g)5h. This is the same expression as the original, but with fewer symbols. The result of the expression is the product of the five, the difference of one and two times g, and h.

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Answer:

1/2 = 3/6 and 1/3 = 2/6

Step-by-step explanation:

we need to make the denominators the same to be able to compare

The solution of the inequality is x < -15/2x.

What is the linear equation?

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. An example of a linear equation is y=mx + b.

We can start solving the inequality by first isolating x on one side of the inequality.

x(2x-1)>15

Divide both sides by x(2x-1)

1>15/(x(2x-1))

To get rid of the fraction, we can invert the inequality and multiply both sides by x(2x-1)

x(2x-1)<15

Now we can simplify the inequality by factoring the left side:

x(2x-1)<15

2x-1 < 15/x

2x < 15/x + 1

2x < (15 + x) / x

Now we can multiply both sides by x

2x*x < 15 + x

2x^2 < 15 + x

Now we can subtract x from both sides

2x^2 - x < 15

Now we can factor the left side

(x-5)(2x+3) < 0

Now we can find the solution of the inequality by finding the values of x that make the inequality true

x = 5, 2x +3 < 0

x < -15/2x

Hence, the solution of the inequality is x < -15/2x.

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Answer:

Step-by-step explanation:

yes I can help ok ok ok

Chad used the scale of 1 scale inch which is equal to 9 feet.

In the conventional system of measuring, an inch is a unit of length. Either in or " can be used to denote length in inches. For instance, 16 in or 16" can be used to write 5 inches.

Given that,

The length of the gym in real life = 81 feet

The length of the gym in scale drawing = 9 inches

1 scale inch = length of the gym in real life/length of the gym in the scale drawing

1 scale inch = 81/9 = 9

Thus, Chad used the scale of 1 scale inch which is equal to 9 feet.

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well, the better bargain for Rita is the bigger savings so, we know "B" gives $14 flat right off the 75 bucks, how about "A"? is the 15% more than 14 bucks?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 75}}{\left( \cfrac{15}{100} \right)75}\implies 11.25[/tex]

woopsie, no dice, so she's better off taking the $14 rebate.

(a) On writing 299790000 in scientific notation , the value of a is 2.9979 and value of k is 8  .

(b) On writing 0.51 in scientific notation , the value of a is 5.1 and value of k is -1 .

What is Scientific Notation ?

The general form of writing a number in scientific notation is ⇒ [tex]a\times 10^{k}[/tex] ;

Part (a) ;

the number is given to be : 299790000 ;

For writing it in scientific notation, decimal point will be placed after 2 ;

So , the scientific notation of the number is ⇒ [tex]2.9979 \times 10^{8}[/tex] ,

On comparing it with the general form of scientific notation,

we get , a = 2.9979 and k = 8 .

Part (b) ;

the number is given to be : 0.51 ;

For writing it in scientific notation, decimal point will be placed after 5 ;

So , the scientific notation of the number is ⇒ [tex]5.1 \times 10^{-1}[/tex] ,

On comparing it with general form of scientific notation,

we get , a = 5.1 and k = -1 .

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Answer:

The difference between constant and variable is that, while the first, as we have already said, remains fixed within a formula, the variable can assume different values.

Step-by-step explanation:

A constant term in an expression is a term that has a fixed value and does not change, while a variable term is a term that can take on different values. For example, in the expression 5x + 2, the 2 is a constant term because it is always 2, while x is a variable term that can take on different values.

In a real-world situation, a constant term represents a quantity that does not change. For example, if we were to write an expression to represent the cost of a product, the constant term would be the fixed cost of the product that does not change. On the other hand, a variable term represents a quantity that is subject to change. For example, in the same scenario, the variable term would represent the quantity of the product being bought, which can change.

In summary, a constant term represents a fixed value that does not change, while a variable term represents a value that is subject to change in a real-world situation.

The vertices of the dilated figure is S'(-20, 4), T'(-12, 20), U'(-4, 4), V'(-12, -4)

Transformation is the movement of a point in the coordinate plane. Types of transformation are reflection, rotation, translation and dilation.

Dilation is the enlargement or reduction in the size of a figure by a scale factor.

Given the coordinates of polygon S(-5, 2), T(-3, 5), U(-1, 1), V(-3, -1). For a dilation with a scale factor of 4, the new coordinates are:

S'(-20, 4), T'(-12, 20), U'(-4, 4), V'(-12, -4)

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Answer: (My view) 6.

Step-by-step explanation: Letting "n" be the number of pictures taken. The probability of no one look at the camera for n photos is of (3/4)^n.

Hence, the probability of at least one photo be the picture craven is of:

(1 - (3/4)^n), and since the likelihood of that being equal to 4/5, it's feasible to assume that (1 - (3/4)^n) = 4/5, solving for that would give:

(3/4)^n = 1/5. Notice that the proposal can also be interpreted as "The number of pictures needed such that the probability of a picture NOT including one with everyone looking at the camera is at most 1/5",

Therefore, (3/4)^n < 1/5;

To solve for that:

n = 1:

3/4 > 1/5,

n = 2:

9/16 > 1/5

n = 3

27/64 > 1/5

n = 4

81/256 > 1/5

n = 5

243/1024 > 1/5

But finally:

n = 6

729/4096 < 1/5

For at least 6 pictures she must take to have at least a 4/5 chance of having a picture in which everyone is looking at the camera.

Let p define the probability of success in a Bernoulli trial, and P define the probability Sara wants to reach "at least" and n be defined as the number of trials. Then,

= 1 - (1 - p)ⁿ ≥ P

= (1 - p)ⁿ ≤ 1 - P

= n ≥ ln(1-P)/ln(1-p)

= n ≥ ln (0.2) / ln (0.75)

=5.6

Hence for at least n=6 photos, there is at least a chance of 4/5 that everyone is looking at the camera.

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if D is the incenter of ABC, DF=6, and DB=10 then EB is 8.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that D is the incenter of ABC, DF=6, and DB=10

We need to find EB

As D is the incenter then DF=DG=DE

so DE is 6

We know DB and DE

DBE is a right triangle and we can find EB by pythagoras theorem

EB²+DE²=DB²

EB²+36=100

EB²=100-36

EB²=64

Take square root on both sides

EB=8

Hence, if D is the incenter of ABC, DF=6, and DB=10 then EB is 8.

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The mixed number would be [tex]10\frac{31}{100}[/tex].

What is a mixed number?

A mixed number is a number that is made up of a whole number and a fraction. It is a combination of a whole number and a fraction that represents a value between two whole numbers. For example, 3 1/2 is a mixed number, with 3 as the whole number and 1/2 as the fraction.

To express 10.31 as a mixed number:

The whole number part is 10.

To find the fractional part, subtract the whole number from the decimal: 0.31

To express the fractional part as a fraction, we will have to divide it by 1 and write the decimal as a fraction, in this case 0.31= 31/100

Now we can express 10.31 as a mixed number, that is 10 31/100

Hence, the mixed number would be [tex]10\frac{31}{100}[/tex].

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According to the information, it can be inferred that the fraction that is equivalent to the height that differentiates silver A and silver B is 1/2.

To calculate the difference in height between the two floors, we must identify the height of each of the floors. According to the above, we must solve the fractions, that is, do the division as shown below:

Plant A:

Plant B:

Subsequently, we need to identify the difference between these two results as shown below:

Finally, we must identify which fractional is equal to 0.5, in this case it would be 1/2 (option D).

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Step-by-step explanation:

a. To find dy/dx when y = 2xlog e (2x), we can use the chain rule. First, we rewrite the function as y = 2x(ln(2x) + 1) where ln is the natural logarithm. Then, we can take the derivative of y with respect to x:

dy/dx = 2(ln(2x) + 1) + 2x(1/2x) = 2ln(2x) + 2 + 2/x

b. To find f′(0) when f(x) = e^x^2/e^x+1, we can take the derivative of the function with respect to x:

f′(x) = (2xe^x^2(e^x+1) - e^x^2(e^x+1)) / (e^x+1)^2

Setting x = 0, we get:

f′(0) = 2e^0(e^0 + 1) - e^0(e^0 + 1) / (e^0 + 1)^2 = 1 / (e^0 + 1)^2 = 1 / 2^2 = 1/4

Categorical variables are grouped into categories, ordinal variables can be ordered, continuous variables have infinite values, and discrete variables have a finite number of values.

Categorical or nominal variables are variables that can be grouped into categories. These categories can represent anything that is not quantitative, such as gender, race, or religion. Ordinal variables are variables that can be ordered or ranked. These variables are typically used to measure preferences or attitude, such as ratings or rankings. Continuous variables are variables with an infinite number of possible values, such as height, weight, or temperature. These variables can have any value within a given range. Discrete variables are variables with a finite number of possible values, such as integers or counts. These variables are typically used to count the number of occurrences of a particular event or outcome. All four of these types of variables are important for understanding data and making predictions or decisions based on that data.

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On solving the provided question we can say that the equation h(x) = 3x / x^2 +5x +7 => [tex]h(x^2) =[/tex] [tex]3x^2 / x^4 + 5x^2 + 7[/tex]

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

here,

given h(x) = 3x / x^2 +5x +7

[tex]h(x^2) =[/tex] [tex]3x^2 / x^4 + 5x^2 + 7[/tex]

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A correlation is a statistical measure of the relationship between two variables and is expressed as a numerical value between -1 and 1.

A correlation is a measure of the relationship between two variables that is expressed as a numerical value between -1 and 1. To calculate a correlation, start by collecting data on the two variables. Then, calculate the covariance, which is the sum of the product of the differences between the two variables, divided by the number of data points. Finally, calculate the correlation by dividing the covariance by the product of the standard deviations of the two variables. The correlation can range from -1, which signifies a perfect negative correlation, to 1, which signifies a perfect positive correlation. A correlation of 0 indicates that there is no correlation between the two variables.

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The equation has B. No solution.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

here, given that,

1/4*(-16r-28)= - 4r - 7

-16r - 28 = -16r-28

this statement is not true.

so, The equation has B. No solution.

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The linearization of the function at a is L(x) = 1/2 + √3/2(x - π/6).

Linearization is a method of taking the gradient of a nonlinear function with respect to all variables. It is used to approximate the output of a function based on the value and slope of the function, at a given point.

The Linearization of function f(x,y) at (a,b) is L(x,y) = f(a,b) + (x−a)fx(a,b) +(y−b)fy(a,b)

Now we take a look at the given function, and the value of point a:

f(x) = sin (x)

a = π/6

Then we differentiate the function, with respect to x:

f(x) = sin (x)

f’(x) = cos (x)

We input the value of a = π/6 into the function:

y = f(π/6)

  = sin (π/6)

  = 1/2

f’(π/6) = cos (π/6)

          = √3/2

Now we input the value of f(a) and f'(a) into the linearization formulas:

L(x) = f(a) + f'(a)(x - a)

      = 1/2 + √3/2 (x - π/6)

Thus the linearization of the function at a is L(x) = 1/2 + √3/2(x - π/6).

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