In triangle ABC, AC = 13 cm, angle A = 4y - 71°, angle B = y + 7°, and angle C = 106 - 2y°. In triangle RST,
RT = 2x + 5 cm and angle R = 113°. Angle B is congruent to Angle S
and segment AB is congruent to segment RS.

Answer:

B, F

Step-by-step explanation:

[tex]2x^2(x-4)^2=0 \\ \\ \implies x^2=0, (x-4)^2=0 \\ \\ \implies x=0,4[/tex]

According to Trigonometric Identity , tan(theta) = -5 / 13

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. The relationship between a triangle's side length and angle is expressed by a variety of specific trigonometric identities.

Sin, cos, and tan are the three fundamental trigonometric ratios. The reciprocals of sin, cos, and tan are represented by the three additional trigonometric ratios sec, cosec, and cot in trigonometry, respectively.

According to the given information

We know that

tan(theta) = 1/cot(theta)

                = 1 / -2.6

                = -1 / 2.6

                = -10 / 26

                = -5 / 13

According to Trigonometric Identity , tan(theta) = -5 / 13

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Answer:

See below and attached graph

Step-by-step explanation:

If you are using a graphing calculator it is a breeze. You write down the equation as it is and it should plot it, depending on what calculator you use.

If you are doing this manually here are the steps
We are given y - 2 = 3(x-2)

Expand the brackets on the right hand side
3(x - 2) = 3x - 6

So the original equation becomes
y - 2 = 3x - 6

Adding 2 to both sides
y - 2 + 2 = 3x -6 + 2

y = 3x - 4   [1]

This form of equation is known as a slope-intercept form of the line

We need two points to plot a line. This can be done by choosing a value for x, finding the y value which gives one point. Then repeat for another value of x to get y for that value giving another point. Draw a straight line through both points

Point 1
Let's choose x = 2 and plug this into the equation [1]
y = 3·2 - 4 = 6- 4 = 2.
So (2, 2) is one point on the graph

Point 2

Choose another value for x, say x = 4

y = 3·4 - 4

y = 12-4

y = 8

So (4, 8) is another point

Draw a line through these two points

The equation that result if you square both sides of the equation  √x+2 = 12 is x + 2 = 144.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, the equation √x+2= 12 can be solved as follows;

The first step to solve the equation is by squaring both sides of the equation as follows:

√x+2 = 12

square both sides of the equation

Hence,

(√x+2)² = 12²

The square root will cancel the square on the left side of the equation. Therefore,

(√x+2)² = 12²

x + 2 = 12 × 12

Hence,

x + 2 = 144

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The statement that best describes the type of triangle is;

The triangle is a scalene triangle and also an acute triangle.

Triangles could be classified based on their interior angles or even the number of equal sides of the triangle. Thus;

A triangle is called an acute triangle if all three angles are less than 90°

A triangle is called a right triangle if one angle is 90°

A triangle is called an obtuse triangle if one angle is greater than 90°

A triangle is called an Equilateral triangle if all three sides are the same length

A triangle is called an Isosceles triangle if two sides are the same length

A triangle is called a Scalene triangle if all three sides are of different lengths.

We are given the three angles of the triangle as; 40 °, 60°, and 80°.

Likewise we are given the length of the three sides as 8 cm, 10 cm, and 20 cm.

Since none of the angles nor sides are equal nor 90 degrees, then we can call this a scalene triangle. It can also be classified as an acute angle as all three angles are less than 90 degrees.

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Answer: 1

Step-by-step explanation:

I'll go over problem 9 part (a) to get you started.

The sine rule, aka law of sines, is this

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c}[/tex]

where the uppercase letters A,B,C are the angles and the lowercase letters a,b,c are the sides opposite those respective angles. Eg: angle B is opposite side b.

Some textbooks may have the lowercase letters up top, but it doesn't matter since it's the same ratio. All that matters is things stay consistent. The lowercase letters must be together on the same level, and same goes for the uppercase letters on their own separate level.

We can then break up that equation into these 3 separate equations, to make things more bite-sized so to speak.

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\\\\frac{\sin(B)}{b} = \frac{\sin(C)}{c}\\\\\frac{\sin(A)}{a} = \frac{\sin(C)}{c}\\\\[/tex]

Let's focus on the 3rd equation and do a bit of algebraic manipulation like so

[tex]\frac{\sin(A)}{a} = \frac{\sin(C)}{c}\\\\\sin(A) = \frac{a\sin(C)}{c}\\\\\frac{\sin(A)}{\sin(C)} = \frac{a}{c}\\\\[/tex]

Through similar steps, we can say:

[tex]\frac{\sin(B)}{b} = \frac{\sin(C)}{c}\\\\\sin(B) = \frac{b\sin(C)}{c}\\\\\frac{\sin(B)}{\sin(C)} = \frac{b}{c}\\\\[/tex]

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

To summarize the previous section, we found that:

[tex]\frac{\sin(A)}{\sin(C)} = \frac{a}{c}\\\\\frac{\sin(B)}{\sin(C)} = \frac{b}{c}\\\\[/tex]

It then allows us to do the following steps for problem 9, part (a)

[tex]\frac{a+b}{c} = \frac{\sin(A)+\sin(B)}{\sin(C)}\\\\\frac{a+b}{c} = \frac{\sin(A)}{\sin(C)}+\frac{\sin(B)}{\sin(C)}\\\\\frac{a+b}{c} = \frac{a}{c}+\frac{b}{c}\\\\\frac{a+b}{c} = \frac{a+b}{c}\\\\[/tex]

We have confirmed that the equation in problem 9 part (a) is indeed an identity. Take note how I kept the left hand side the same the entire time while the right hand side transformed into the left side.

Similar steps will be taken for problem 9, part (b). I'll let you do that part.

Answer:

-41.328

Step-by-step explanation:

Answer:

-41.328

Step-by-step explanation:

Addition multiplied by subtraction gets you subtraction. +-=-

so now, ()= multiplication

so now all you have to do is 17.22 times 2.4 which gets us 41.328

then, add the negative sign which gives you -41.328

yw :)

When tiles are drawn, with replacement, from a bag of lettered tiles, X is the number of vowels in 5 draws variable has binomial distribution

The possibility that a value would take one of two independent values given a particular combination of factors or assumptions is summarised by the statistical distribution known as the binomial distribution.

The basic presumptions of the binomial distribution are:

As opposed to a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution used in statistics.

The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.

The result is then multiplied by the sum of the number of attempts and the number of successes.

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Variance  of customers who pay by card = 16

Mean number of customers = 20

Given that,

Customers at a gas station pay with a credit card (A), debit card (B), or cash (C). Assume that successive customers make independent choices with

P(A)=0.4,

P(B)=0.2,

and

P(C)=0.4

Because we are interested in whether or not a debit card was used, we can use the binomial distribution.

Let X= the number of customers who use a debit card.

Here, probability of customers who pay with debit card (or success) is

p=0.2

(a) Mean and variance of the number of customers who pay with a debit card:

The mean number of customers who pay with a debit card can be calculated as given below:

μ=np =100×0.2

=20

The variance of the number of customers who pay with a debit card can be calculated as given below:

σ²=np(1−p) =100×0.2(1−0.2)

=16

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Answer:

listed below

Step-by-step explanation:

5.) x=77 and y=63

6.)y=60 and x= 1230

7.)y=65 and x=92

8.)y=69 and x=175

The area of the land is 3600 + 60n.

What is area?

Area is a mathematical concept that expresses the size of a region on a plane or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

Given: A contractor is building a new subdivision.

A rectangular piece of land for a new house and yard is 60 feet wide.

The length of the land is longer than the width by a distance of n feet.

So, width = 60 feet

and length = 60 + n feet

Since, the area of rectangular piece of land (A)

Area = length x width

Area = (60 + n) x 60

Area = 3600 + 60n

Hence, the area of the land is 3600 + 60n.

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the measure of ∠LPM is 90°

the measure of ∠PMN is 102°

the length of LN is 10 units.

Define Rhombus.

A rhombus is a special case of a parallelogram, and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and the opposite angles are equal.

For a Rhombus, LMNO

∠LON = 102°

NP = 5 units

By the properties of Rhombus, we know that

All sides of a rhombus are congruent (equal)

So, LM = MN = NO = OL

and

Opposite angles are equal and the opposite sides are parallel.

So, ∠LON = 102° = ∠LMN

Since Adjacent angles add up to 180°.

Therefore ∠L + ∠M = 180°

                 ∠M + ∠N = 180°

                 ∠N + ∠O = 180°

                 ∠O + ∠L = 180°

So, ∠N = 180° - ∠O = 180° - 102° =78°

      ∠L = 180° - ∠O = 180° - 102° =78°

      ∠M = 180° - ∠L = 180° - 78° =102°

Diagonals bisect each other at 90° or we can also say that each of the two diagonals in a rhombus is the perpendicular bisector of the other.

So, ∠LPM = ∠NP0 = ∠MPN = ∠LPO =90°

Thus, the measure of ∠LPM is 90°

         the measure of ∠PMN is 102°

         the length of LN is 10 units.

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Answer:

Lpm= 90

PMN=51

LN= 10

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

3.4^0 = 1

9^1 = 9

1 * 9 = 9

A 99% confidence interval for the true proportion of college students believing in ghosts is Option(c)  (0.4901, 0.6699)

According to the question,

A professor wanted to know what proportion of college students believe in ghosts.

For that he drawn a sample from the college.

Sample size : n = 200

Proportion of students that believed in ghosts in sample = 58%

=> p = 0.58

Proportion of students who does not believe in ghost : q = 1 - p

=> q = 0.42

We have to create a 99% confidence interval for a true proportion of college students believing in the ghosts

Formula of C.I = [tex]p \pm ( z_{\alpha} \sqrt{\frac{pq}{n}})[/tex]

Where p and q is sample proportion , z is value of CI at given α level of significance and n is sample size

C.I at 99% = 0.58 ± 2.576 √0.58×0.42/200

=> 0.58 ± 2.576 √0.001218

=>  0.58 ± 2.576 × 0.035

=> 0.58 ± 0.08958

C.I = ( 0.58 - 0.08958 , 0.58 + 0.08958)
=> C.I = (0.4901, 0.6699)

Hence, Option (c) is correct

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Answer:

41%

Step-by-step explanation:

Answer:

2.8

Step-by-step explanation:

x-1.2=1.6

x=1.2+1.6

x=2.8

The end behavior of the graph of the polynomial function:

As x approaches ∞, y approaches -∞

As x approaches -∞, y approaches ∞

What is an end behavior?

The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f.

Here, we have

f(x) = –x⁵ + 9x⁴ – 18x³

F(x) is a fifth-degree (odd function ) with a negative leading coefficient

If the exponent is odd and the leading coefficient is negative then the end behavior is

As x approaches ∞, y approaches -∞

As you go on the right, f(x) goes down

As x approaches -∞, y approaches ∞

As you go on the left, f(x) goes up.

Hence, the end behavior of the graph of the polynomial function: As x approaches ∞, y approaches -∞

As x approaches -∞, y approaches ∞

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As per the linear equation, the x-intercept of the graph of the equation will be (-8, 0).

It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.

As per the information given in the question,

The given equation is,

y= -1/4 x + 2

Now, let's take y = 0 for x- intercept,

So, the equation will be,

0 = 1/4x + 2

1/4x = -2

x= -8

The x-intercept is (-8, 0).

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The question sees incomplete, your question may be:

Here is a linear equation: y = 1/4x + 2 What is the x-intercept of the graph of the equation?

Answer:

Y=6x-12

Step-by-step explanation:

whenever the X is at zero the number across from it is the Y-intercept. and to find the slope just count how much they are increasing or decreasing by.

Answer:

  7.2 cm

Step-by-step explanation:

You want the value of C to the nearest tenth centimeter, given that 4^2 + 6^2 = C^2.

Simplifying gives ...

  4^2 + 6^2 = C^2

  16 +36 = C^2 = 52

  C = √52 ≈ 7.2

The length of the missing side is about 7.2 cm.

Sister's age will be equal to 12 and Kim's age is 24.

An equation is an expression that shows the relationship between two or more numbers and variables. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Consider that x is sister's age, Kim's age is twice that of her sister

Thus Kim's age = 2x

Kim’s age + Sister’s age = 36

The equation:

x + 2x = 36

Now solve the equation;

x + 2x = 36

3x = 36

 x = 36 / 3

 x = 12

Therefore, Kim's age = 2x = 2(12) = 24

Hence, Sister's age is 12 and Kim's age is 24.

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Answer:

0.1904

Step-by-step explanation:

4/7 ÷ 3 is = 0.1904

Answer: I hope this helps

Step-by-step explanation:

4/7 divided by 3

Dividing is equivalent to multiplying by the reciprocal
4/7 times 1/3 or 4/7•1/3

Multiply the fractions

And you get

4/21 or 0.190476

A. Model is fitted using training dataset and E. Validation dataset is used to minimize model overfitting are true about machine learning algorithms

The process by which an AI system completes its task—generally, forecasting output values from provided input data—is known as a machine learning algorithm. Classification and regression are the two key operations of machine learning algorithms.

Simple linear regression, decision trees, logistic regression, the KNN algorithm, and other well-known supervised learning techniques are some examples.

Machine learning is crucial because it helps businesses identify trends in customer behaviour and operational patterns and facilitates the creation of new goods.

According to the question,

Option A and option E are correct about the machine learning algorithms

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It has been (mathematically) proven that there is no polynomial time algorithm for any np-complete problem. the given statement is false.

In order to solve previously unsolvable issues, Leonid Khachiyan developed a polynomial-time method, in which the number of processing steps increases as a power of the number of variables rather than exponentially.

Determining whether NP-complete problems are tractable or intractable remains one of the most crucial concerns in theoretical computer science since it is unknown if any polynomial-time algorithms will ever be developed for them.

So, it is unknown if any polynomial-time algorithms will ever be developed for them.

By applying different constraints, a linear function is maximized or reduced in linear programming, a mathematical modelling approach. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

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The solution in inequality notation and in interval notation is (-∞ . -√5]∪[√5,36)

The term inequality refers the a relationship between two expressions or values that are not equal to each other is called 'inequality.

Here we have given the inequality (x² - 5)/ (x - 36) < 0

And we need to find the solution in inequality notation and in interval notation.

In order to find the inequality notation, we have to solve the given inequality, then we get.

(x² - 5)/ (x - 36) < 0

(x² - 5) < 0

x² < 5

x < √5

While we looking into the inequality we must know that the denominator must not be 0.

So, the interval notation can be written as,

=>  (-∞ . -√5]∪[√5,36)

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Answer: A or D

Step-by-step explanation: It can be A. But it can also be D.  I would try D tho because with D, your combining 3 people together.

The matrix resulting from the multiplication of matrices B and C is given as follows:

[-92, -730; 3350, 19648]

The matrices in this problem are defined as follows:

For the product of the matrices, the row of matrix B multiplies the column of matrix C.

Then the element at the first row and the first column of the product matrix is given as follows:

2 x 4 - 10 x 10 = -92

The element at the first row and the second column of the product matrix is given as follows:

2 x -25 - 10 x 68 =  -730.

The element at the second row and the first column of the product matrix is given as follows:

60 x 4 + 311 x 10 = 3350.

The element at the second row and the second column of the product matrix is given as follows:

60 x -25 + 311 x 68 =  19648.

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The distance between Wet Creek and Soggy will be 894.03 miles.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The distances between Dry Ravine, Wet Rivulet, and Saturated Waterway can be addressed by a triangle.

The distance between Dry Ravine and Wet Rivulet is 530 miles and the distance between Dry Gorge and Saturated Waterway is 721 miles.

The distance between Wet Creek and Soggy will be given as,

d² = 530² + 721²

d² = 280,900 + 518,400

d² = 799,300

d = 894.03 miles

The distance between Wet River and Soaked will be 894.03 miles.

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