What is the domain and range

By applying permutation theory, it can be concluded that there are 6840 different orders of 1st, 2nd, and 3rd place winners

Permutation is rearranging a collection of objects in a different order from the original order. In permutations, order matters.

If an object can be selected more than once then the number of permutations is:

P = [tex]n^{r}[/tex]

Otherwise, If an object can only be selected once, then the number of permutations is:

P = n! / (n-r)!

where n is the number of total objects and r is the number of the selected objects to arrange. Hence. n cannot be less than r.

We are given information that there are 20 runners competing in a marathon.

We are asked to find how many different orders could the 1st, 2nd, and 3rd place medals are received. It means that the order matters and they can only be selected once, so we use the second permutation formula, where n = 20 and r = 3.

P = n! / (n-r)!

  = 20! / (20-3)!

  = 20! / 17!

  = 10 * 19 * 18

  = 6840

Thus, there are 6840 different orders of 1st, 2nd, and 3rd place winners.

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Using BODMAS, the answer of the given question is  13232 / 15.

The brackets must be solved first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction, according to BODMAS rule. Any expression can only be solved correctly if the BODMAS rule or the PEDMAS rule are applied.

The other operations must be solved in the same order. Brackets (B) are followed by the order of powers or roots, which is then followed by multiplication, addition, subtraction, and finally division.

According to the question,

[tex]27 \frac{2}{3} \times 32 - \frac{2}{5} \div 64^{\frac{5}{6} }[/tex]

Using BODMAS,

⇒ 83/3 × 32 - [tex]\frac{2}{5}[/tex] ÷ [tex]64^{\frac{5}{6} }[/tex]

⇒ 83/3 × 32 - 2/5 ÷ [tex](2^{6})^{\frac{5}{6} }[/tex]

⇒ 83/3 × 32 - 2/5 ÷ 2⁵

⇒  83/3 × 32 - 2/5 × 1/2⁵

⇒  83/3 × 32 - 2⁴/5

⇒ 2656 / 3 - 2⁴/5

⇒ 2656 / 3 - 16/5

⇒ 13280 -  48 / 15

⇒ 13232 / 15

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To find the pay/hour that makes traveling on the plane and bus travel equally attractive, we can use the concept of "opportunity cost" by comparing the cost of the plane ticket with the cost of the bus ticket plus the pay/hour.

One way to do this is to use the concept of "opportunity cost," which is the cost of foregone opportunities. In this case, the opportunity cost of traveling by plane is the cost of the plane ticket, while the opportunity cost of traveling by bus is the cost of the bus ticket.

To find the pay/hour that would make traveling by plane and bus equally attractive, we can set up an equation where the opportunity cost of the plane ticket equals the opportunity cost of the bus ticket plus the pay/hour. This equation can be written as:

Plane ticket cost = Bus ticket cost + Pay/hour

To find the pay/hour, we will have to know the costs of the plane and bus tickets and solve the equation for Pay/hour.

Pay/hour = Plane ticket cost - Bus ticket cost

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Answer:

8.3 miles

Step-by-step explanation:

1 2/3 times 5= 8.3. He rode 8.3 miles

Answer:

0.115

Step-by-step explanation:

The required equations are y = 3x + 2, y = 3x + 5 which have no solution.

The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.

For no solution of equation,

equation of line must be parallel and for parallel line, Slope should be same.

Or we can say There won't be a solution if (a1/a2) = (b1/b2) (c1/c2). An inconsistent pair of linear equations is the name given to this kind of equation.

y = 3x + 2

y = 3x + 5

Thus, required two equation are y = 3x + 2, y = 3x + 5 which have no solution.

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The angle, in degrees, of the compass direction of a line connecting will be 53.9 degrees

Your entire distance from the beginning location is your hypotenuse.

We employ the hypotenuse formula because...

The Pythagoras theorem can be used to determine the length of the hypotenuse in a right triangle. According to the theory, the hypotenuse's square is equal to the sum of its two other sides' squares.

R2=A2+B2

R2=17.52+242R2

=306.25+576

R=√882.25

=29.7 meters

However, the assertion that R=A + B is incorrect (the assertion on the figure is FALSE!).

Your direction is northwest.

Now use trigonometry:

sinθ=B/R

sinθ=24/29.70

=0.808

θ=53.9 degrees. This is your angle.

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It is a good idea to scale the number line when making a dot plot when the range of data values is large.

Scaling the number line allows you to fit all the data points on the plot, making it easier to read and interpret. When the range of data values is small, you do not need to scale the number line, but if the range is large, you may need to compress or expand the scale of the number line to fit all the data points.

Additionally, when dealing with large numbers or decimal numbers, scaling the number line can make the dot plot more readable and easy to compare. It can also be useful when you want to compare different data sets that have different ranges, you can use the same scale on both dot plots, which makes it easier to compare the data.

Finally, you may also need to scale the number line when the data contains outliers, this will help to see the distribution of the data better.

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plot the frequency distribution with frequency 11, 8, 7, 5, 2, 2,2 and box numbers on X axis

It will show a graph which is Positively skewed.

Answer:

21 dollars is the change.

Step-by-step explanation:

If u do division 25/4 its equals to 5.25 which could be the answer too.

Answer: 0

Also could you mark my answer as brainliest? It helps and doesnt hurt a bit

Answer:

3.1

Step-by-step explanation:

Answer:

4.2 has a greater value

since 4.2 is greater than 3.6

Step-by-step explanation:

Since neither numbers are negative, the absolute value around the numbers do not change the values. So nothing changes and we know 4.2 is greater than 3.6

If in a survey of women in a certain country (ages 20 - 29), the mean height was 63.2 inches with a standard deviation of 2.67 inches.

a. The height that represents the 95th percentile is 67.61.

b. The height that represents the first quartile is  61.4.

Mean (μ) = 63.2

Standard deviation  (σ) =  2.67

a. The value of the 95th percentile

Value of the 95th percentile = 63.2 + 1.65(2.67)

Value of the 95th percentile = 63.2 + 4.4055

Value of the 95th percentile = 67.61

b.  value of the first quartile (25th percentile)

Value of the  first quartile = 63.2 + (-0.67) (2.67)

Value of the  first quartile = 63.2 + (-1.7889)

Value of the  first quartile = 61.4

Therefore the height that represents the 95th percentile is 67.61 and the height that represents the first quartile is  61.4.

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The store manager can use f∘g function to find the final price of a bicycle.

Let the buying price be Y,

Store is offering sale on the item given by function,

f(x) = x - 30

And offering an additional discount given by function,

g(x) = x - 0.1x = 0.9x

So final price be written as;

0.9x - 30    [ 10% off and 30$ discount ]

Then 0.9x - 30 = f∘g ( operations of functions of functions ).

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

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The measure of angle ABE is 40 degrees.

When two lines intersect each other, the vertically opposite angles are equal.

Therefore, angle ABE = angle CBD

angle ABE = 40 degrees.

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There are 136 solutions to the equation:

X1 + X2 + X3 = 15

where X1, X2, and X3 are non-negative integers. I'm not gonna list them all, but, it starts off with:

01. 0, 0, 15.

02. 0, 1, 14.

03. 0, 2, 13.

134.14, 0, 1.

135.14, 1, 0.

136.15, 0, 0.

The constraint of:

1<X1<6

implies X1 either equals 1, or is greater than 1.

So, there are 65 solutions where X1 equals 1, or is greater than 1, and less than 6!

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Lola is correct because each expression has a value of 1. Option A is correct.

The expression is the relationship between variables and represented as y = ax + b is an example of a polynomial expression.

here,
Given expression
A = [tex][[a /b]^{-4}]^0[/tex]
B = [tex][[a /b]^{0}]^{-4}[/tex]

Since we know that,
a⁰ = 1

So,
A = [1]
B = 1⁻⁴ = 1

Thus, Lola is correct because each expression has a value of 1. Option A is correct.

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Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value(s) for the variable are entered, two algebraic expressions that are equivalent will have the same value (s).

An algebraic expression is a mathematical expression made up of variables, coefficients, constants, and operations including addition, subtraction, multiplication, and division. In most cases, something is said to be equivalent if two of them are the same.

Similar to this, analogous expressions in mathematics are those that, despite their differences in appearance, have the same meaning.

The two expressions, however, produce the identical outcome when the values are inserted into them.

Example

If the provided expression has an equivalent, write it down: 3x+9

Solution:

expressed in this way: 3x+9

The analogous equation is equal to the expression when 3 is removed from it, which is = 3(x+3).

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A system of linear equations can be classified into 3 different ways based on their nature of roots and their graphical representation.

Step 1: Examine the given graph.

Step 2: Determine if the lines cross exactly once, are exactly the same, or are parallel to each other.

Step 3: Classify the system of linear equations as consistent dependent, consistent independent, or inconsistent based on your findings in step 2.

A system of linear equations is consistent dependent if it has an infinite number of solutions i.e the graphs of the lines in the system are the same, it is consistent independent when it has exactly one solution i.e the graphs of the lines in the system cross exactly once and a system is inconsistent if it has no solutions i.e the graphs of the lines do not intersect and they are parallel.

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Answer:  k = 5/2 = 2.500

Step-by-step explanation: k=25​=221​=2.5

Stocks will be worth $1180 in 2024 due to a 10% percent annual decline in value.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Steve bought $2,000 worth of stocks in 2019. The value of the stocks has been decreasing by 10 percent each year

thus the value of stocks becomes 90 percent or 0.9 times each year

After 5 years Value of stocks = 2000 * (0.9)⁵

After 5 years Value of stocks = 1180.98

Therefore the value of stocks in 2024 will be $1180 as stock decreases by 10% every year.

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There will be approximately around 5000× 2¹⁸ = 262,144,000 bacteria.

Similar to the function of protonophores, bacterial populations have natural defences against antibiotics. These mechanisms interfere with the membrane electrochemical gradients that allow bacterial populations to develop persister subpopulations that are drug-tolerant.

Every four hours, the population will double, making a total of 18 times in a 72-hour period.

In the beginning there are 5000 bacteria and There are 24 hours in a day, hence there will be 72 hours in 3 days (3× 24).

There will be around 5000 × 2¹⁸ = 262,144,000 bacteria.

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For each quadratic equation, the value of a, b and c are mentioned below. Also maximum or minimum points are mentioned here.

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

a. y = 3x²-3x + 5, comparing this with general quadratic equation ax² + bx + c and get a = 3 and b = -3 and c = 5

thus x = - (b/2a)

x = - (-3/6)

x = -1/2

as a > 0 thus the equation has the minimum value and that is:

y = 3(-1/2)² -3(-1/2) + 5

y = 3/4 + 3/2 + 5

y = 13/2

b. y = -2x² + x  comparing this with general quadratic equation ax² + bx + c and get a = -2 and b = 1 and c = 0

thus x = - (b/2a)

x = - (1/-4)

x = 1/4

as a < 0 thus the equation has the maximum value and that is:

y = -2(1/4)² + (1/2)

y = -1/8 + 1/2

y = 3/8

c. y = 1/2x² + 6 comparing this with general quadratic equation ax² + bx + c and get a = 1/2, b = 0 and c = 6

thus x = - (b/2a)

x = - (1/2×0)

x = 0

as a > 0 thus the equation has the minimum value and that is:

y = 1/2(0)² + 6

y = 6

d. y=-3x² + 1/2x - 2 comparing this with general quadratic equation ax² + bx + c and get a = -3, b = 1/2 and c = -2

thus x = - (b/2a)

x = - [(1/2)/-6]

x = 1/12

as a < 0 thus the equation has the maximum value and that is:

y=-3(1/12)² + 1/2 (1/12) - 2

y = - 1/48 + 1/24 - 2

y = -45/48

e. y=x²-2x+6 comparing this with general quadratic equation ax² + bx + c and get a = 1, b = -2 and c = 6

thus x = - (b/2a)

x = - (-2/2)

x = 1

as a > 0 thus the equation has the minimum value and that is:

y=(1)²-2(1)+6

y = 5

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Let's consider what the question asks for:

 --> domain and range, x-intercept, y-intercept of the equation

Let's find the domain:

 --> the only range of x-values that will make this equation 'untrue'

      --> is when the function inside the square root becomes negative

         --> as a square root cannot have a negative value inside it

                [tex]x+8\geq 0\\x\geq -8\\\\\text{Our domain is therefore [-8}[/tex],∞)

Let's find our range:

 --> the function doesn't have any limitations vertically

               [tex]\text{Our range is therefore}[/tex]  (-∞,∞)

Our x-intercept

 --> is when the y-value is zero

      [tex]0=-2\sqrt{x+8} \\\sqrt{x+8} =0\\x+8=0\\x=-8[/tex]

                [tex]\text{Our x-intercept is therefore -8}[/tex]

Our y-intercept:

 --> is when the x-value is zero

    [tex]y=-2\sqrt{x+8} \\y=-2\sqrt{0+8} \\y=-2\sqrt{8} \\y=-2*2\sqrt{2} \\y=-4\sqrt{2}[/tex]

                [tex]\text{Our y-intercept is therefore }-4\sqrt{2}[/tex]

Answer:

  Domain: [-8, ∞)

  Range: {-∞,∞)

  X-intercept is -8

  Y-intercept is [tex]-4\sqrt{2}[/tex]

Total Surface area of the inner cube = 6 * 2 = 12 m²

Take a vertical cross-section through the center of the arrangement as shown in the following figure —

The surface area of the outer cube is 24 m²

Therefore, each face of this cube equals  4 m²

=> Each edge of the larger cube is two meters

The inner sphere's diameter is 2 meters since it meets the surface of the outer cube.

Thus, the sphere's radius (Viz OR) is equal to 1 m.

Taking into account Right Triangle OQR, QR  = √ [ 1² + 1² ] = √2 m

=> The smaller cube's face area is equal to 2 m².

The inner cube's total surface area is equal to 6 * 2 = 12 m²

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The full question:

A sphere is inscribed in a cube that has a surface area of 24 m2. A second cube is then inscribed within the sphere. What is the surface area of the inner cube?

If the rank of matrix A is equal to the number of columns of A, and the rank of matrix A is equal to the rank of the augmented matrix [A|b], then the system Ax = b will have a unique solution for all choices of b. Otherwise, the system Ax = b will not have a unique solution for all choices of b.

To determine if the system ax = b has a solution for all choices of b, we need to look at the rank of the matrix A and the rank of the matrix formed by appending the vector b to the matrix A.

The rank of a matrix is the number of linearly independent rows or columns in the matrix. If the rank of matrix A is equal to the number of columns in A, then matrix A is full rank and the system Ax = b will have a unique solution for all choices of b. If the rank of matrix A is less than the number of columns in A, then matrix A is not full rank, and the system Ax = b will not have a unique solution for all choices of b.

If the rank of matrix A is equal to the rank of the matrix formed by appending the vector b to matrix A, the system Ax = b will have a unique solution for all choices of b. If the rank of matrix A is less than the rank of the matrix formed by appending the vector b to matrix A, the system Ax = b will not have a unique solution for all choices of b.

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To evaluate an algebraic expression is to determine its value when a certain number is used in place of the variable. Therefore the correct option is 25/49

To evaluate the expression of 5/7 to the power of 2 we will-

[tex]5/7² = 5/7 X 5/7 = 25/49[/tex]

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The percentage of students are boys = 51.5% and The percentage of students always wear glasses = 21.3%

What is percentage ?

percentage can be defined as the product of ratio of given value , total value and hundred.

Given ,

A principal of a school with 484 students collected information about how many of the students wear glasses complete the two way frequency table

So, the number of boys always wears glasses are 40

the number of boys sometimes wears glasses are 48

the number of boys never wear glasses are 161 .

Total number of boys = 249

the number of girls always wears glasses are 36

the number of girls sometimes wears glasses are 55

the number of girls never wear glasses are 144.

Total number of girls = 235

Total number of students always wears glasses = 76

Total number of students sometimes wears glasses = 103

Total number of students never wear glasses = 305 .

Total number of students = 484 .

The percentage of students are boys = 51.5%

The percentage of students always wear glasses = 21.3%

Hence, The percentage of students are boys = 51.5% and The percentage of students always wear glasses = 21.3%

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