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3 years ago

Help me with this please!

Mathematics

2 answers:

DedPeter [7]3 years ago

8 0

Answer:

Area of triangle = 20√2

Step-by-step explanation:

Formula:

Area of triangle = bh/2

b - base of triangle

h - height of triangle

<u>Distance formula</u>

d = √(x₂ - x₁)² +(y₂ - y₁)²

From the figure we can see that, the given triangle is right angled triangle.

Base = AC and Height = AB

A(1,3), B(4,7) and C(9, -5)

AB = √(4 - 1)² +(7 - 3)² = √(3² + 4²) = 5

AC = √(9 - 1)² +(-5 - 3)² = √(8² + -8²) = 8√2

<u>To find the are of triangle</u>

Area = bh/2 = (5* 8√2)/2 = 20√2

Therefore the area of triangle = 20√2 square units

svetoff [14.1K]3 years ago

8 0

Answer:

Area = 20√2 is the area of triangle.

Step-by-step explanation:

We have given the triangle in the graph.

We have to find the area of the triangle.

The formula for the area of triangle is :

Area = 1/2(base×height)

In the graph, the base is represented by AC, and height is represented

by AB.

First, we use distance formula to find AC and AB.

Base = AC =√(9-1)² + (-5-3)² = 8√2

Height = AB=√(4-1)² +(7-3)² = 5

Put this values of height and base in the formula we get,

Area = 1/2 (8√2 ×5)

Area = 20√2 is the area of triangle.

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A statistics textbook chapter contains 60 exercises, 6 of which are essay questions. A student is assigned 10 problems. (a) What

Scilla [17]

Answer:

a) P=0.3174

b) P=0.4232

c) P=0.2594

d) The shape of the hypergeometric, in this case, is like a binomial with mean np=1.

Step-by-step explanation:

The appropiate distribution to model this is the hypergeometric distribution:

$P(X=x)=\frac{\binom{s}{x}\binom{N-s}{M-x}}{\binom{N}{M}}=\frac{\binom{6}{x}\binom{54}{10-x}}{\binom{60}{10}}$

a) What is the probability that none of the questions are essay?

$P(X=0)=\frac{\binom{6}{0}\binom{54}{10-0}}{\binom{60}{10}}\\\\P(X=0)=\frac{1*(54!/(10!*44!)}{60!/(10!*50!)} =\frac{2.3931*10^{10}}{7.5394*10^{10}} = 0.3174$

b) What is the probability that at least one is essay?

$P(X=1)=\frac{\binom{6}{1}\binom{54}{9}}{\binom{60}{10}}\\\\P(X=1)=\frac{6*(54!/(9!*43!)}{60!/(10!*50!)} =\frac{3.1908*10^{10}}{7.5394*10^{10}} =0.4232$

c) What is the probability that two or more are essay?

$P(X\geq2)=1-(P(0)+P(1))=1-(0.3174+0.4232)=1-0.7406=0.2594$

8 0

3 years ago

The plan for the Thorne’s backyard play area, shaped like a trapezoid, is shown. The area of the play area is 286.56 square feet

lorasvet [3.4K]

The length of material needed for the border is the perimeter of the backyard play area

<h3>How to calculate the length of material needed </h3>

The area of the play area is given as:

$Area = 286.56$

The area of a trapezoid is calculated using:

$Area = 0.5 * (L1 + L2) * H$

Where L1 and L2, are the parallel sides of the trapezoid and H represents the height.

The given parameter is not enough to solve the length of material needed.

So, we make use of the following assumed values.

Assume that the parallel sides are: 25 feet and 31 feet long, respectively.

While the other sides are 10.2 feet and 8.2 feet

The length of material needed would be the sum of the above lengths.

So, we have:

$Length = 25 + 31 + 10.2 + 8.2$

$Length = 74.4$

Using the assumed values, the length of material needed for the border is 74.4 feet

Read more about perimeters at:

brainly.com/question/17297081

6 0

2 years ago

Solve the system of equations. x+y=4 y=x^2 - 8x + 16 a) {(-3,7).(-4, 8)} b) [(4,0)} c) {(3,1),(4,0) d) {(3,7). (4.0)} e) none

Marysya12 [62]

Answer: The required solution of the given system is

(x, y) = (3, 1) and (4, 0).

Step-by-step explanation: We are given to solve the following system of equations :

$x+y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x^2-8x+16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

From equation (i), we have

$x+y=4\\\\\Rightarrow y=4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of y from equation (iii) in equation (ii), we get

$y=x^2-8x+16\\\\\Rightarrow 4-x=x^2-8x+16\\\\\Rightarrow x^2-8x+16-4+x=0\\\\\Rightarrow x^2-7x+12=0\\\\\Rightarrow x^2-4x-3x+12=0\\\\\Rightarrow x(x-4)-3(x-4)=0\\\\\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x-3=0,~~~~~~~x-4=0\\\\\Rightarrow x=3,~4.$

When, x = 3, then from (iii), we get

$y=4-3=1.$

And, when x = 4, then from (iii), we get

$y=4-4=0.$

Thus, the required solution of the given system is

(x, y) = (3, 1) and (4, 0).

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3 years ago

Let I (x) be the statement "x has an Internet connection" and C(x, y) be the statement "x and y have chatted over the Internet,"

FrozenT [24]

Answer:

Step-by-step explanation:

L(x) means that Student X has an internet connection

C(x,y) means that students X and Y have chatted over the internet

The domain for variables X and Y comprise all students in your class. We now use quantifiers or algebraic functions to express each of the statements:

(A) Jerry does not have an internet connection

L(x) = 0

Where X represents Jerry

(B) Rachel has not chatted over the internet with Chelsea

C(x,y) = 0

Where X and Y represent Rachel and Chelsea

L(x) + L(y) = 0

Where X and Y represent Jan and Sharon. If they have NEVER chatted over (the question didn't say they have never "with each other", it says they have never chatted at all) the internet, then they've probably never had an internet connection!

(D) No one in the class has chatted with Bob

Let Y represent Bob and X1, X2, ..., Xn represent everyone else in the class.

The value of Y is not significant here (because it is raised to the power of zero and that makes it equal to 1 and when 1 is multiplied by any X value, the X value or student remains the same) but we have to put it, to represent Bob.

The quantifier here is C (X1Y°, X2Y°, X3Y°, ..., XnY°)

5 0

4 years ago

What is the inverse of the function f(x) = 2x + 1?

Luda [366]

Answer:

$f^{-1}(x)=\frac{1}{2}x-\frac{1}{2}$ ⇒ answer 1

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- To find the inverse of a function :

# Write y = f(x)

# Switch the x and y

# Solve to find the new y

# The new y is $f^{-1}$

* Lets solve the problem

∵ f(x) = 2x + 1

- Put y = f(x)

∴ y = 2x + 1

- Switch x and y

∴ x = 2y + 1

- Solve to find the new y

∵ x = 2y + 1

- Subtract 1 from both sides

∴ x - 1 = 2y

- Divide both sides by 2

∴ (x - 1)/2 = y

- Divide each term in the left hand side by 2

∴ y = 1/2 x - 1/2

- Replace y by $f^{-1}$

∴ $f^{-1}(x)=\frac{1}{2}x-\frac{1}{2}$

* The inverse of the function is $f^{-1}(x)=\frac{1}{2}x-\frac{1}{2}$

7 0

3 years ago

Read 2 more answers