Given f(x) = 4x -17 and g(x)=5/2x+7;x≠0 solve the equation f^-1(x)=g^-1(x)

The study of statistics rests on two major​ concepts probability which  is the branch of mathematics that deals with the likelihood of events occurring and Data Analysis is the process of examining and interpreting data in order to gain insights and make better decisions

Probability theory is based on the idea that, given enough data, the frequency of an event can be predicted and allows for the formulation of mathematical models that can quantify the likelihood of particular outcomes. Probability is the foundation of statistics and helps to explain the behavior of chance events.It involves the collection, organization, and analysis of data from a variety of sources, such as survey responses, observations, experiments, or existing databases.

Data analysis is used to identify patterns and relationships in data, draw conclusions, and make decisions. It is an important part of statistics, as it helps to uncover insights that would otherwise remain hidden. Data analysis tools, such as statistical models, can be used to gain greater insight into the data.

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Answer:32.9

Step-by-step explanation:

Hope this helps! :)

Answer:

Diameter = 103.35 cm

Step-by-step explanation:

Pizza = circle

Area of a Circle = π * r²

π = 3.1416

r = radius

Area of a pizza = 850cm²

850 = 3.1416 * r²

850/3.1416 = r²

270.56 = r²

√270.56 = √r²

16.45 = r

radius = 16.45  (aprox)

diameter of a pizza = 2π r

diameter of a pizza = 2*3.1416*16.45

diameter of a pizza = 103.35 cm

In Exercises 1 through 4, we are given the coefficients and centers to find the Newton polynomials P₁(x), P₂(x), P₃(x), and P₄(x), and evaluate them at the value x = c. We can use the divided difference formula to calculate the coefficients of the Newton polynomials.

Given:

a₀ = 4, x₀ = 1

a₁ = -1, x₁ = 3

a₂ = 0.4, x₂ = 4

a₃ = 0.01, x₃ = 4.5

a₄ = -0.002

c = 2.5

Using the divided difference formula:

f[x₀] = a₀ = 4

f[x₀, x₁] = (a₁ - a₀) / (x₁ - x₀) = (-1 - 4) / (3 - 1) = -2.5

f[x₀, x₁, x₂] = [(a₂ - a₁) / (x₂ - x₁) - (a₁ - a₀) / (x₁ - x₀)] / (x₂ - x₀) = [(0.4 - (-1)) / (4 - 3) - (-1 - 4) / (3 - 1)] / (4 - 1) = 1.35

f[x₀, x₁, x₂, x₃] = [(a₃ - a₂) / (x₃ - x₂) - (a₂ - a₁) / (x₂ - x₁) + (a₁ - a₀) / (x₁ - x₀)] / (x₃ - x₀) = [(0.01 - 0.4) / (4.5 - 4) - (0.4 - (-1)) / (4 - 3) + (-1 - 4) / (3 - 1)] / (4.5 - 1) = -0.022

The Newton polynomials are:

P₁(x) = a₀ + f[x₀, x₁](x - x₀) = 4 - 2.5(x - 1)

P₂(x) = P₁(x) + f[x₀, x₁, x₂](x - x₀)(x - x₁) = 4 - 2.5(x - 1) + 1.35(x - 1)(x - 3)

P₃(x) = P₂(x) + f[x₀, x₁, x₂, x₃](x - x₀)(x - x₁)(x - x₂) = 4 - 2.5(x - 1) + 1.35(x - 1)(x - 3) - 0.022(x - 1)(x - 3)(x - 4)

P₄(x) = P₃(x) + a₄(x - x₀)(x - x₁)(x - x₂)(x - x₃) = 4 - 2.5(x - 1) + 1.35(x - 1)(x - 3) - 0.022(x - 1)(x - 3)(x - 4) - 0.002(x - 1)(x - 3)(x - 4)(x - 4.5)

To evaluate the polynomials at x = c = 2.5:

P₁(2.5) = 4 - 2.5(2.5 - 1)

P₂(2.5) = 4 - 2.5(2.5 - 1) + 1.35(2.5 - 1)(2.5 - 3)

P₃(2.5) = 4 - 2.5(2.5 - 1) + 1.35(2.5 - 1)(2.5 - 3) - 0.022(2.5 - 1)(2.5 - 3)(2.5 - 4)

P₄(2.5) = 4 - 2.5(2.5 - 1) + 1.35(2.5 - 1)(2.5 - 3) - 0.022(2.5 - 1)(2.5 - 3)(2.5 - 4) - 0.002(2.5 - 1)(2.5 - 3)(2.5 - 4)(2.5 - 4.5)

Given:

a₀ = 5, x₀ = 0

a₁ = -2, x₁ = 1

a₂ = 0.5, x₂ = 2

a₃ = -0.1, x₃ = 3

a₄ = 0.003

c = 2.5

Using the divided difference formula, we can calculate the coefficients of the Newton polynomials.

Given:

a₀ = 7, x₀ = -1

a₁ = 3, x₁ = 0

a₂ = 0.1, x₂ = 1

a₃ = 0.05, x₃ = 4

a₄ = -0.04

c = 3

Using the divided difference formula, we can calculate the coefficients of the Newton polynomials.

Given:

a₀ = -2, x₀ = -3

a₁ = 4, x₁ = -1

a₂ = -0.04, x₂ = 1

a₃ = 0.06, x₃ = 4

a₄ = 0.005

c = 2

Using the divided difference formula, we can calculate the coefficients of the Newton polynomials.

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B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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The exact value of y is \(\sqrt{3}\)

The correct answer is an option (c)

Let us assume that in the attached diagram of right triangle the angle A measures 45 degrees.

Here, the hypotenuse measures \(\sqrt{6}\)

We know that in right triangle, the sine of angle θ is nothing but the ratio of opposite side of angle θ to the hypotenuse.

Consider the sine of angle A

sin(A) = opposite side of angle A / hypotenuse

sin(45°) = y / ( \(\sqrt{6}\))

We know that from the standard trigonometric table the value of sin(45°) is \(\frac{1}{\sqrt{2} }\)

Substitute this value in above equation we get,

\(\frac{1}{\sqrt{2} }\) =  y / ( \(\sqrt{6}\))

We solve this equation to find the value of y.

y =  \(\sqrt{6}\) ×  \(\frac{1}{\sqrt{2} }\)

y = \(\frac{\sqrt{3}\sqrt{2} }{\sqrt{2} }\)

y = \(\sqrt{3}\)

Therefore, the correct answer is an option (c)

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Answer:

One to many

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Answer:

2hrs 24 mins

Step-by-step explanation:

Ok so let's make this problem a bit simpler by splitting it up.

Tim paints a room in 6 hours.

So, we can also say that she paints 1/6 of that room in 1 hour

Bella paints it in 4 hours

So, we can also say that she paints 1/4 of that room in 1 hour

Now, lets see what we have:

Bella: 1/4 every hour

Tim: 1/6 every hour

The problem states that they are working together, so we need to add the values we have:

1/4 + 1/6

We cannot just add them, we must make them have the same common denominator.

LCD is 12, you can find that by just doing the times tables for 4 and 6 and seeing what number they match on first.

3/12 + 2/12 = 5/12

So, tim and bella working together paint 5/12 of a room in 1 hour.

They paint 5/12 of a room in 60 minutes

They paint 1/12 of the room in 12 minutes(divide both values by 5)

So if they paint 1/12 of the room in 12 minutes, we can multiply both values by 12 to get our answer.

They paint the full room in 144 minutes(12*12).

144 minutes is 2 hours and 24 minutes

We know that n^2 is a multiple of both 24 and 108, which means it must be a multiple of their least common multiple (LCM). The LCM of 24 and 108 is 216.

So, n^2 must be a multiple of 216. This means that n must be a multiple of the square root of 216, which is 6√6.

Therefore, every integer n in s must be of form 6√6 * k, where k is a positive integer.

To find the divisors of every integer n in s, we need to find the common factors of all such expressions.

We can express 6√6 as 2√6 * 3. So, every integer n in s can be written as 2√6 * 3 * k.

The divisors of every integer n in s must be factors of 2√6 and 3.

The factors of 2√6 are 1, 2, √6, and 2√6.

The factors of 3 are 1 and 3.

Therefore, the integers that are divisors of every integer n in s are 2 and 3, which are both positive integers.

So, the correct answer is none of the given options (a, b, c, d).

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To indicate that one value is greater than, less than, or equal to another, an inequality in a word problem is written using mathematical symbols like, >, or.

Determine the values that the inequality will compare before using the correct mathematical symbol to express the relationship between them in a word problem. Once the values have been determined, represent the relationship between them using the proper mathematical symbol. For instance, the inequality would be phrased as "x > 5" if the problem stated that "x is greater than 5". Other possible symbols for inequalities are (less than), (less than or equal to), and (more than) (greater than or equal to). It is crucial to always use the appropriate mathematical symbols when creating an inequality since they are needed to indicate the direction of the comparison. Moreover, make sure to incorporate all essential components, including the values being compared, the mathematical symbol, and the equals sign, if required. These procedures can be used to effectively write an inequality in a word problem.

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If  circumference of a circle is 7π cm then area of circle is 38.465 square centimeter

The circumference of a circle is 7π cm

We have to find the area of the circle

To find area we have to know the radius

Circumference = 2πr

7π= 2πr

r=7/2

= 3.5 cm

Area of circle = πr²

=3.14×(3.5)²

=3.14×3.5×3.5

=38.465 square centimeter

Hence, if  circumference of a circle is 7π cm then area of circle is 38.465 square centimeter

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Answer:

10y° = 130°

(4x - 22)° = 50°

(7x + 4)° = 130°

(3y + 11)° = 50°

Step-by-step explanation:

From the picture attached,

Two lines are intersecting each other at a pint making two pairs of vertical angles.

By definition, pair of vertical angles are equal in measure.

10y° = (7x + 4)° [Vertical angles]

-7x + 10y = 4 -----(1)

(3y + 11)° = (4x - 22)° [Vertical angles]

-4x + 3y = -33 ------(2)

[Equation (1) × 3] - [Equation (2) × 10]

(-21x + 30y) - (-40x + 30y) = 12 + 330

-21x + 40x = 342

19x = 342

x = \(\frac{342}{19}=18\)

From equation (1),

-7(18) + 10y = 4

-126 + 10y = 4

10y = 130

y = 13

Therefore, 10y° = 130°

(4x - 22)° = 50°

(7x + 4)° = 130°

(3y + 11)° = 50°

Answer:

SAS

Step-by-step explanation:

As per the given diagram, the following facts are evident.

(BR) = (CR), Both sides have two small orange lines on them. This shows that these sides are congruent.

(<B) = (<C), this is shown by the box around both angles, indicating that both angles have a measure of (90) degrees.

(AB) = (AC), Both sides have one small orange line on them. This indicates that these sides are congruent to each other.

Therefore, the sides are congruent by the theorem (SAS); side-angle-side, congruence.

Answer:

Let's take a look at the lengths of the sides: 90, 120, 150. What do we notice here?

It's a 3:4:5 triangle.

90/30 = 3, 120/30 = 4, 150/30 = 5.

That the 2 triangles formed by line running diagonally through the base creates AT LEAST 2 right angles.

Since the total amount of degrees in a quadliateral is 360,

180(s-2)

And we know that there are 2 right angles which equals to 180 and the sides are all parallel to each other,

That must mean that the 2 remaining angles of the box add up to 180,

Therefore all angles are 90 degrees.

Answer:

Step-by-step explanation:

The area of a rectangle = length × width

Since we are finding the width

We have

\(width = \frac{area}{length} \\ \)

From the question

area = 6216 cm²

length = 84 cm

The width is

\(width = \frac{6216}{84} \\ \)

We have the final answer as

Hope this helps you

Answer:

R(x, y) = (x, -y)

Step-by-step explanation:

When we have a reflection across some line, the distance between the original point and the reflected point to the line is invariant.

For a reflection around the x-axis, the x-value is invariant, then the only value that can change is the y-value.

So if we have a point like (4, 7)

Which is at a distance of 7 units to the x-axis, the only other point that is also at a distance of 7 units to the x-axis that has the same x-value is (4, -7)

Here we already can see the rule.

If we have a point (x, y), the reflection across the x-axis gives us the point (x. -y)

Then we can write this reflection as a function in the next way:

R(x, y) = (x, -y)

This means that if the input is the point (x, y), the output is the point (x, -y)

Answer:

54

Step-by-step explanation:

\(\dfrac{(14+42-6)}{10}+7^2\)

Parentheses (14 + 42 - 6) = 50:

⇒ 50/10 + 7²

Exponents 7² = 49:

⇒ 50/10 + 49

Multiplication/division  50/10 = 5:

⇒ 5 + 49

Addition/subtraction:  5 + 49 = 54

⇒ 54

Answer:

the answer for the question is 8x2000

which is 16000 pounds

In this problem the total number of students are: 260 students

so the probablility is:

Answer:

-G + 15 = - 2G + 23

    - 15             -15

-G     = -2G + 8

+2G      +2G

S0, G = 8 is the answer

Step-by-step explanation:

Answer:

7.D

8.A

Step-by-step explanation:

7.

r=√((0-6)²+(0+8)²)=√(36+64)=√100=10

eq. of circle is (x-6)²+(y+8)²=10²

(x-6)²+(y+8)²=100

8.

CM=1/2CD=1/2×60=30

OM=18

OC=√(30²+18²)=√(900+324)=√(1224)=√(4×306)=√(4×9×34)=2×3√34=6√34

radius r=OC=6√34

OF=r=6√34

ON=15

FN=√((6√34)²-15²)=√(1224-225)=√999=√(9×111)=3√111

Answer:

Dude

Step-by-step explanation:

You forhot to put the question in :p

Answer:

Step-by-step explanation:

To increase the difference between 456.674 and 234.458 by 345.856, we follow the following steps :

Step 1: Subtract 456.674 from 234.458 and,

Step 2:  Add 345.856 to the result.

so,  456.674 - 234.458 = 222.216

222.216 + 345.856 = 568.072

Therefore, the increased difference between 456.674 and 234.458 by 345.856 is 568.072

Answer:

»»»»»

ZBDC = ( 180 - x - y )°

:-))

»»»»»

Answer:

If there are 4 boys and they ate 3 pizzas, and each boy ate the same amount, then each boy ate 3/4 of a pizza. If you want to express this as a fraction, it would be 3/4 of a pizza per boy. If you want to express it as a decimal, it would be 0.75 pizzas per boy. If you want to express it as a percentage, it would be 75% of a pizza per boy.