Write 3 expressions that can be used to find angle C.

Answer:

14

Step-by-step explanation:

Follow DMAS formula:

DMAS rule is followed when multiple arithmetic operations are there in a given problem like addition, subtraction, multiplication and division. It tells they should be performed in order of Division, Multiplication, Addition and Subtraction.

=50+6*3 -82

=50+18-82

=68-82

=14

Answer:

64

Step-by-step explanation:

PEMDAS

6(12+4) distribute the 6 to the numbers inside

96

50+96-82

50+96= 146

146-82 = 64

Therefore, the Taylor polynomials T2(x) and T3(x) centered at a=0 for the function f(x) = 25ln(1+x) are:

T2(x) = 25 + 25x - 12.5x^2

T3(x) = 25 + 25x - 12.5x^2 + 16.67x^3

To calculate the Taylor polynomials T2(x) and T3(x) centered at a=0 for the function f(x) = 25ln(1+x), we need to find the derivatives of f(x) and evaluate them at x=0.

First, let's find the derivatives of f(x):

f'(x) = 25/(1+x)

f''(x) = -25/(1+x)^2

f'''(x) = 50/(1+x)^3

Now, let's evaluate these derivatives at x=0:

f'(0) = 25/(1+0) = 25

f''(0) = -25/(1+0)^2 = -25

f'''(0) = 50/(1+0)^3 = 50

Using these values, we can now write the Taylor polynomials:

T2(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 = 25 + 25x - 12.5x^2

T3(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 = 25 + 25x - 12.5x^2 + (16.67)x^3

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Answer:

1/2 * 5 * 5

4

1/3, 7

79 in³

Step-by-step explanation:

The area of the base : base is shaped like a triangle ;

Area of triangle = 1/2 base * height :

Base and height = 5

Area of base = 1/2 * 5 * 5 = 12.5 in²

Volume of triangular prism = Area of base * height

Volume of triangular prism = 12.5 * 4 = 50 in³

For the triangular pyramid :

Area of base * height of pyramid *1/3

12.5 * 7 * (1/3) = 29.17

The volume of the paperweight :

Volume of triangular pyramid + volume of triangular prism

29.17 + 50

79.17 = 79 in³

Answer:

True

That is the formula to solve an inequality

The solution of the inequality x + 3 < 7 is x < 4.

Consider the inequality,

x + 3 < 7

Subtracting 3 from each side of the equation,

x + 3 - 3 < 7 - 3

x < 4

In order to represent x < 4 on a number line, we will follow the steps given below.

Step 1: Mark zero on a number line, then mark equal distances to the right and left.

Step 2: In the given inequality x < 4, the value of x is less than 4. So, we need to move to the left of 4.

Step 3: Mark a black empty circle on 4 and shade the line from 4 towards the left side until the arrow. The circle at point 4 will be left empty because a blank circle shows that 4 is not included. This means that x is less than 5 and not equal to 4.

Hence we get the required number line.

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Answer:

3 + 7 =10

Step-by-step explanation:

i have three cookies the tree cookies are choclate chip cookies and i have 7 more cookies they are oreos  i add all the cookies and i get 10                                       7 oreos + 3 choclate = 10 cookies

Answer:

97

Step-by-step explanation:

exterior angle property of triangle

64+33 equals 97

in other ways

By Angle sum property of triangle, the measure of 3rd angle is 83 and

angle 1 and 3rd angle are supplementary

so,

180 - 83 = 97

Answer:

\( 365.97\: cm^2\)

Step-by-step explanation:

Area of the shape = Area of triangle with base 22 cm and height 16 cm + Area of semicircle with radius (22/2 = 11) 11 cm

\( = \frac{1}{2}bh + \frac{1}{2} \pi {r}^{2} \\ \\ = \frac{1}{2} \times 22 \times 16 + \frac{1}{2} \times \times 3.14 {(11)}^{2} \\ \\ = 11 \times 16 + 3.14 \times 60.5 \\ \\ = 176 + 189.97 \\ \\ = 365.97 \: {cm}^{2} \)

Step-by-step explanation:

The radius would be 11 which is half of the width and the height is 16.

A= πr(r+√h²+r²)

A= π•11•(11+√16²+11²)

A≈ 1051.11836

The correct statement regarding the transformations is given as follows:

The linear function moves down 1 unit and stretches, which is the 2nd option.

Transformations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y.

Examples of transformations are as follows:

For this problem, we have the parent function g(x) = x and the transformed function f(x) = 2x - 1. Then:

Hence the second option is correct, the one which states that:

The linear function moves down 1 unit and stretches.

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Answer:

0.0233 or about 2.33%

Step-by-step explanation:

On a TI-84, you can use the cumulative distribution function (2nd->DISTR->normalcdf) to determine the probability that in a normal distribution, a randomly selected variable will fall into a certain interval that you supply.

normalcdf(132.7, 1e99, 95.1, 18.9) = 0.0233274727 ≈ 2.33%

Therefore, the probability that a randomly selected adult has an IQ greater than 132.7 is 0.0233 or about 2.33%

The probability of getting an ace from a well-shuffled deck of 52 cards is  1/13 and the probability of not getting an ace is 12/13

We can calculate the probability by the following method:

Total number of cards in a pack of cards= 52

Number of ace cards in a pack of cards= 4

Probability of an event= Number of possibilities of that event / Total number of possibilities

(i) If drawing an ace card is considered an event, suppose E, then:

P(E)= Number of ace cards/ Total number of cards

= 4/52

(ii) Probability of any event other than E= 1- Probability of the event E=

If the drawing of a non-ace card is considered an event, suppose E', then

P(E')= 1- the probability of drawing an ace card

= 1- P(E)

= 1-1/13

= (13-1)/ 13

= 12/13

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The number of possible groups or combination of three men can be formed from 10 is 120.

According to the given question.

Total number of men in a company, n = 10.

Number of men to be selected, r = 3

As we know that, What is a combination in math?

Image result for what is combination

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Therefore, the number of possible groups or combination of three men can be formed from 10

= \(^{10} C_{3}\)

= 10!/ 3!7!

= 10(9)(8)/3(2)

= 5 × 3 × 8

= 120

The number of possible groups or combination of three men can be formed from 10 is 120.

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Answer:

3x-6+1

Step-by-step explanation:

I know algebraaaaaa

Answer:

x=20,10

Step-by-step explanation:

Answer:

Answer: The missing number is 3.2

Step-by-step explanation:

• let the missing number be x

\({ \tt{ \frac{4}{25} = \frac{x}{20} }} \\ \\ { \tt{x = \frac{4 \times 20}{25} }} \\ \\ { \tt{x = \frac{80}{25} }} \\ \\ { \tt{x = 3.2}}\)

it A

Step-by-step explanation:

Equation employing the slope-intercept method for two points

The slope-intercept version of the equation may be used to calculate the two-point Y-intercept.

The shape of a point-slope is\(\mathbf{Y-Y_{1} = m(X-X_{1})}.\)

Steps to find the y-intercept with two ordered pairs?

Determine the slope using two points.

\(Slope = \frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{Rise}{Run} = \frac{\bigtriangleup Y}{\bigtriangleup X}\)

As an illustration, two points are (3, 5) and (6, 11)

Slope = \(\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{11 - 5}{6 - 3} = \frac{6}{3} = 2\)

In the slope-intercept form of the equation, substitute the slope(m).

\(\\y = mx+b \\y = 2x+b\)

Either point may be substituted in the equation. You may either use (3,5) or (6,11).

\(\\y = 2x+b \\5 = 2(3)+b\)

Find the answer to the equation for b, the line's y-intercept.

\(\\5 \ \ \ = 2(3) + b \\5 \ \ \ = 6 + b \\\underline{-6\ = -6 \ \ \ \ \ \ \ } \\-1 = b\)

Substitute b,  into the equation.

\(\\y = 2x + b \\y = 2x - 1\)

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Answer:

In this section we will discuss the method of graphing an equation in two variables. In other words, we will sketch a picture of an equation in two variables.

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

The center line in a box plot represents the median

The purpose of this test is to evaluate the effects of rotational acceleration on the semicircular ducts and dynamic equilibrium. This test is called Rotational Acceleration Test.

The purpose of the rotational acceleration test is to assess how the semicircular ducts and the body's dynamic equilibrium respond to rotational movements. The semicircular ducts are part of the vestibular system, which is responsible for detecting changes in head position and rotational movements.

During the test, the individual is subjected to controlled rotational acceleration, usually in a specially designed chair or device. The rotational acceleration induces a sense of spinning or movement, stimulating the semicircular ducts.

By observing the individual's responses, such as eye movements or changes in body posture, healthcare professionals can gather information about the functioning of the vestibular system and the body's ability to maintain balance.

This test is particularly useful in diagnosing disorders of the vestibular system, such as vestibular dysfunction, vertigo, or balance disorders. It helps healthcare providers determine the extent of the impairment and develop appropriate treatment plans or interventions to improve balance and reduce symptoms.

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Answer: To solve the inequality, we start by isolating the variable n:

-6(n-1) < 3

-6n + 6 < 3

-6n < -3

n > 1/2

And for the other inequality:

2(n+1) > 0

2n + 2 > 0

2n > -2

n > -1

Now, we can plot these solutions on a number line:

[-----1/2-----][-------------n > 1/2----------------]

[-----n > -1-----][-------------]

So, the solution set for the inequality is n > -1 and n > 1/2, which means that n belongs to the interval (1/2, +∞).

Step-by-step explanation:

Answer:

1%

Step-by-step explanation:

out of 52 cards, there are 4 jacks, 4 queens and 4 kings; these are the 'face cards'

P(3 face cards, no replacement):  12/52 × 11/51 × 10/50

P = .00995 which is, rounded to nearest tenth, 1%

The solution is 0.009954

The probability of selecting three face card from a deck of cards without replacement is 0.9954 %

What is Probability?

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

The value of probability lies between 0 and 1

Given data ,

Let the probability of selecting three face cards be represented as P

Now , the value of P is given by

The total number of cards = 52 cards

The number of face cards in the deck = 4 Jacks + 4 Kings + 4 Queens

So ,

The number of face cards in the deck = 12 cards

The probability of selecting a face card =
number of face cards in the deck / total number of cards

Substituting the values in the equation , we get

The probability of selecting a face card = 12/52

Since the selected card is not replaced ,

Now , the number of cards in the deck = 52 -1 = 51 cards

Number of face cards in the deck = 12 - 1 = 11

The probability of selecting the second face card = Number of face cards in the deck / number of cards in the deck

Substituting the values in the equation , we get

The probability of selecting second face card = 11/51

Since the selected card is not replaced ,

Now , the number of cards in the deck = 51 -1 = 50 cards

Number of face cards in the deck = 11 - 1 = 10

The probability of selecting the third face card = Number of face cards in the deck / number of cards in the deck

Substituting the values in the equation , we get

The probability of selecting third face card = 10/50

Now , the probability P = probability of selecting a face card x probability of selecting second face card x probability of selecting third face card

Substituting the values in the equation , we get

The probability P = ( 12/52 ) x ( 11/51 ) x ( 10/50 )

The probability P = 0.00995

Hence , The probability of selecting three face card from a deck of cards without replacement is 0.0.00995

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The system of equations represented by this matrix has only one unique solution (x=2, y=-3). Thus, even though there is a free variable, there are no other solutions for the system.

An augmented matrix is a representation of a system of linear equations. To have a free variable means that there is at least one column in the augmented matrix that does not have a leading 1. However, having a free variable does not necessarily mean that the system has infinitely many solutions.
An example of an augmented matrix with a free variable but not infinitely many solutions is:
[ 1  0  2 | 4 ]
[ 0  1 -3 | 6 ]
[ 0  0  0 | 0 ]
In this matrix, the first and second columns have leading 1's, indicating that they are pivot columns. The third column, however, does not have a leading 1 and therefore represents a free variable.

Despite this, the system of equations represented by this matrix has only one unique solution (x=2, y=-3). Thus, even though there is a free variable, there are no other solutions for the system.
This example satisfies the criteria of having a free variable but not infinitely many solutions.

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An augmented matrix can have a free variable but still have a unique solution if it is not over-determined or inconsistent.

An example of an augmented matrix that has a free variable but does not have infinitely many solutions can be represented by the following:

\(\left[\begin{array}{cccc}1&0&|&2\\0&1&|&3\\0&0&|&0\end{array}\right]\)

In this augmented matrix, the last row consists of all zeros, indicating a linearly dependent equation. The presence of a free variable can be observed in the fact that the matrix does not have a unique solution.

To understand why this matrix does not have infinitely many solutions, we can interpret it as a system of linear equations. The first row represents the equation x = 2, while the second row represents y = 3. The last row, with all zeros, implies 0 = 0, which is always true.

Since the system has a free variable, it means there are infinitely many possible values for the variables x and y that satisfy the system. However, despite the presence of a free variable, the system does not have infinitely many solutions. Instead, it has a unique solution (x = 2, y = 3). This is because the last row of zeros indicates that the system is not over-determined or inconsistent.

In conclusion, an augmented matrix can have a free variable but still have a unique solution if it is not over-determined or inconsistent.

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Answer:

$5.70

Step-by-step explanation:

1. 25.00 - 2.20 = $22.80

2. 22.80 divided by 4 = $5.70

Answer:

$5.70

Step-by-step explanation:

let the price for each canvas be $x

hence the price of 4 canvases will be $4x

It is given that after she paid for 4 canvases, she had a balance of $2.20 on her orginally $25 gift card.

Hence we can assemble an equation:

$4x + $2.20 = $25

4x + 2.2 = 25   (subtract 2.2 from both sides)

4x = 25 - 2.2

4x =22.8  (divide both sides by 4)

x = 22.8 / 4

x = 5.7

Hence each canvas cost $5.70

Answer:

You have D which is correct but E is also correct because 4 is 1/4 of 16

Step-by-step explanation:

So D and E are your answers

Two ounces of liquid is equivalent to four tablespoons. both are unit of measurement of volume

This can be useful when converting recipes or measuring ingredients. A tablespoon is a unit of measurement that is typically used to measure small amounts of ingredients such as spices, butter, oil, and other liquids. It typically holds three teaspoons of liquid or dry ingredients.

One tablespoon is equivalent to 15 milliliters, which is equal to 0.51 fluid ounces in the United States. Therefore, two ounces is equal to four tablespoons. When measuring ingredients, be sure to use the appropriate measurements for accuracy and to avoid over- or under-measuring.

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Answer:

x=3

Step-by-step explanation:

An equation's omitted factors are the values of x for which the result is unknown. This indicates that if the denominator or x(x-3) equals 0, your solution is undefined.

Set up this equation and solve for the potential possibilities of x to find these numbers: x(x-3)=0

Divide both sides by (x-3) to find one of the values:

x(x-3)/(x-3)=0(x-3)

Because (x-3) cancels on the left side of the equation and everything divided by 0 is zero on the right, you should get: x=0.

Now that you've determined one of the excluded values, work out the other:

To begin, split both sides by x:

x(x-3)=0

x-3=0

Finally, multiply both sides by -3 to get: x=3

The other solution in the given range is x = 130°

We know that tone of the solutions of the given equatio is x = -230, now, remember the definition of coterminal angles, if A and B are coterminal angles, then:

Sin(A) = Sin(B).

And the family of coterminal angles is defined as:

B = A + n*360°

Where n is integer.

So here we just need to find the next coterminal angle to -230°, so the next solution is:

x' = -230° + 360° = 130°

That is the other solution in the range -360°, 360°

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