Which of the following is a Simplification law?
a) M.(~M+N) = M.N
b) M+(N.O) = (M+N)(M+O)
c) ~(M+N) = ~M.~N
d) M.(N.O) = (M.N).O

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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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: 5 chairs and 2 extra chairs

Step-by-step explanation:

Note that [tex]\frac{27}{5}=5.4[/tex]. This means we can place up to 5 chairs at each table.

However, this means that there will be [tex]27-5(5)=2[/tex] chairs left over.

Using the formula of length of an arc, the radius of the circle is 3 units

The length of an arc is a measure of the distance along the curved path of the arc. It is a portion of the circumference of the circle of which the arc is a part.

It can be calculated using the following formula:

Length of arc = (Arc angle / 360) * Circumference of the circle

Where:

Arc angle is the measure of the angle formed by two radii at the center of the circle. It is measured in degrees.

Circumference of the circle is the distance around the circle. It is calculated using the formula C = 2πr, where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14.

Alternatively, the length of an arc can also be calculated using the formula :

Length of arc = (Arc angle/360) * 2πr

Also, the formula of length of an arc is given as

s = rθ

s = length of arc

r = radius of arc

θ = angle in radians

In the question given, we can substitute the values and solve for the radius.

s = rθ

3π / 2 = r * π/2

r = (3π / 2) / (π / 2)

r = 3

The radius of circle is 3 units

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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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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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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 product of three numbers is 12,295.

We are given that the sum of three numbers x, y, and z is 165, so we can write:

x + y + z = 165

We are also told that when the smallest number x is multiplied by 7, the result is n. So we can write:

x * 7 = n

It is also given that the value n is obtained by subtracting 9 from the largest number y, so we can write:

y - 9 = n

And that this number n also results by adding 9 to the third number z, so we can write:

z + 9 = n

We have 3 equations with 3 unknowns, we can use these equations to solve the problem.

From the equation x * 7 = n, we can substitute n = y-9, and we get:

x * 7 = y - 9

From the equation z + 9 = n, we can substitute n = y-9, and we get:

z + 9 = y - 9

Now we have 2 equations with 3 unknowns x,y,z.

To solve for the third unknown, we can use the equation x + y + z = 165 and substitute the values that we know from the previous equations:

x + (y - 9) + (z + 9) = 165

Solving for x we get:

x = (165 - (y-9) - (z+9)) = (165 - y + 9 - z - 9) = (165 - y - z + 18) = (183 - (y+z))

Now we can substitute this value into one of the previous equations:

(183 - (y+z)) * 7 = y - 9

Solving for y and z we get:

y = 95 and z = 71

And the product of the three numbers is:

x * y * z = (183 - (y+z)) * y * z = (183 - (95 +71)) * 95 * 71 = (183 - 166) * 95 * 71 = 17 * 95 * 71 = 12,295

So the product of three numbers is 12,295.

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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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Answer:

8x

Step-by-step explanation:

The correct option to represents downloads and rentals this person purchases is, (6, 14) and (8, 12).

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

We have to given that;

A digital download, x, costs $3 and a digital rental, y, costs $2 for a song. a person has $48 maximum to spend in a month.

Now, Let (x, y) represent number of downloads and rentals this person purchases.

Hence, We can formulate;

⇒ 3x + 2y ≤ $48

So, We can check all the options which satisfy the above equation.

By option C; (x, y) = (6, 14)

⇒ 3x + 2y ≤ $48

⇒ 3×6+ 2×14 ≤ $48

⇒ 18 + 28 ≤ 48

⇒ 46 ≤ 48

Hence, This option satisfy the equation.

By option D; (x, y) = (8, 12)

⇒ $3x + $2y ≤ $48

⇒ 3×8 + 2×12 ≤ 48

⇒ 24 + 24 ≤ 48

⇒ 48 = 48

Thus, It satisfy the equation.

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Answer:

Step-by-step explanation:

yes I can help ok ok ok

The length of segment PM would be 12 units

I won't proceed based on your circle's association with any specific segments; instead, I'll use the illustration below.

We can determine QM = 15, SM = 10, and RM = 18 from the image. We apply the formula for determining segment lengths when there are two chords in a circle to determine the length of segment PM.

Our equation QM = (SM)(RM) (PM)

We now enter the information and resolve: (10)(18) = (15)(x) (x)

(10)(18) = 180

(15)(x) = 15x

180 = 15x → 180 ÷ 15 = 12 & 15x ÷ 15 = x

x = 12

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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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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

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.

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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By solving a simple linear equation, we will see that there are 1666667 grains of salt on 100 grams

We want to see how many grains of salt would be in 100 grams, only by knowing that the mass of a salt grain is 0.06 mg

Where:

1mg = 0.001g

Then the mass of x grains of salt, is given by the function below:

m(x) = x*0.06 mg

m(x) = x*0.00006 g

Now we want to find the value of x such that the mass is 100 grams, then we can write the equation:

x*0.00006 g = 100g

Solving that equation for x, we will get:

x = 100g/0.00006 g

x = 1666667

So there are about 1666667 grains of salt on 100 grams of salt.

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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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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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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

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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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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(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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Considering the information about trees, The value of a is 5500

The value of r is calculated to be 0.92

In 1 October 2030 the number is 2022

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem,  N = ar^t

the starting, a = 5500

the base, r =

the exponents = t

Solving for the base

N = ar^t

5500 = ar^t in 2018 t = 0

a = 5500

in 2019, t = 1

N = ar^t

5060 = 5500 * r

r = 5060/5500

r = 0.92

From 2018 to 2030 = 12 years, hence t = 12

N = 5500 * 0.92^12

N = 2,022.165132

N = 2022

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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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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?          

Answer:

Step-by-step explanation:

a) The probability that the point selected at random lies in ∆ADM is 1/4. This is because ∆ADM is one of the four equal parts of the square ABCD.

b) The probability that the point selected at random lies in ∆ADM but not in ∆ADN is 1/8. This is because ∆ADM and ∆ADN are two of the four equal parts of the square ABCD, and the union of these two parts forms one quarter of the square. Hence, the probability of the point lying in one of these parts but not in the other is 1/8.

c) The probability that the point selected at random lies neither in ∆ADM nor in ∆ADN is 3/4. This is because the union of ∆ADM and ∆ADN forms one quarter of the square ABCD, while the remaining three quarters of the square lie outside of both ∆ADM and ∆ADN. Hence, the probability that the point lies outside of both these parts is 3/4.

Check the picture below.