Assemble the statements and reasons

The radius of a circle with the same vertex as a center, if the arc inside the triangle divides it into two regions of equal area is (18 × ✓π) / π

From the information, the triangle has a 60 degree angle, and the two adjacent sides are 12 and 12 square root 3.

The area of a triangle will be;

A = 1/2 × a × b × sin C

= 1/2 × 12 × 12✓3 × sin 60

= 108

Area of sector = πr² / 360 × 60.

r² = (108/2) × 6 ) π

r² = 324 / π

r = 18✓π / π

The radius is 18✓π / π.

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Marta's rope is 10 inches shorter than three times the length of David's rope and they measure 120 inches long together , then Marta's rope is 77.5 inches long and David's rope is 32.5 inches long.

Let's call the length of David's rope x.

According to the problem, Marta's rope is 10 inches shorter than three times the length of David's rope, so we can write an equation for Marta's rope:

length of Marta's rope = 3 * x - 10

And the combined length of both of their ropes is 120 inches, so we can write another equation:

x + (3 * x - 10) = 120

Expanding the second equation and solving for x, we get:

4x - 10 = 120

Adding 10 to both sides:

4x = 130

Dividing both sides by 4:

x = 32.5

So, David's rope is 32.5 inches long.

We can use the first equation to find the length of Marta's rope:

length of Marta's rope = 3 * x - 10 = 3 * 32.5 - 10 = 87.5 - 10 = 77.5 inches

So, Marta's rope is 77.5 inches long.

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CP of 100 pencils = Rs.250

CP of 1 pencil = 250/100 = 2.5

SP of 1 dozen pencils = Rs.33

SP of 12 pencils = Rs.33

SP of 1 pencil = \frac{33}{12}=2.75

SP>CP

So, Profit% = SP - CP/ CP × 100 = 2.75 - 2.5/2.5 × 100 = 10 %

Hence The profit % is 10%

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[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{1}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 1 } \implies 6[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ 6}(x-\stackrel{x_1}{1}) \\\\\\ y-1=6x-6\implies {\Large \begin{array}{llll} y=6x-5 \end{array}}[/tex]

A mathematical theorem is a statement that contains hypotheses, conclusions, and proofs.

Mathematics revolves around the theorems. A thorough proof is a specific kind of logical reasoning that has been used to demonstrate the truth of a claim, which is what a theorem is.

"When n is higher than 2, there are no pretty much the entire number answers to the problem xn + yn = zn." This equation, also referred to as "Fermat's Last Theorem," was presented for the first time by French scientist Pierre de Fick in 1637 and had baffled the world's greatest minds for further than three centuries.

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Answer:

Step-by-step explanation:

-183

Answer:

Any negative minus a positive is a negative:

-183

Step-by-step explanation:

Hope it helps! =D

Answer:

  4

Step-by-step explanation:

You want to know how many more questions Brian needed to answer correctly to get a passing grade of 60% on his 85-question test, given that he answered correctly 70% of the 20 arithmetic problems, 40% of the 30 algebra problems, and 60% of the 35 geometry problems.

The number of correct answers Brian supplied was ...

  0.70·20 +0.40·30 +0.60·35 = 14 +12 +21 = 47

The number of correct answers Brian needed for a passing grace was ...

  0.60·85 = 51

Brian needed to answer 51 -47 = 4 more questions correctly to earn a passing grade.

The value of the x-coordinate of the solution will be -2. Then the correct option is C.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equations are given below.

y = (5/2)x + 2         ...1

y = - x - 5              ...2

From equations 1 and 2, then we have

(5/2)x + 2 = - x - 5

(7/2)x = -7

x = -2

The value of the x-coordinate of the solution will be -2. Then the correct option is C.

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Answer:

31.4 in^2

Step-by-step explanation:

Circumference formula: pi times 2 times radius

so equation would be 3.14 (pi value) times 2 times 5 and you get your answer

Answer: e = 1/18

Step-by-step explanation:

e = 18/320

e = 1/18

Answer: 0.05625

Step-by-step explanation: So, you divide 18 by 320, and that gives you 0.05625, and you can double check by multiplying 0.05625 by 320, which gives you 18.

Answer:

Step-by-step explanation:

Rephrase it.

3(5) + 9² + (27 x 1/3) - (-10)

15 + 9x9 + 9 - (-10)

15 + 81 + 9 - (-10)

96 + 9 - (-10)

115

The longest line segment that can be drawn in a right rectangular prism with dimensions of 14 cm long, 13 cm wide, and 9 cm high is about 21.2 cm.

The right triangular face's hypotenuse is another name for this diagonal, which is also referred to as the space diagonal.

In this instance, the right triangle face with sides of 14, 13, and 9 cm can be taken into consideration. With the Pythagorean theorem in use,

we have:

14² + 13² + 9² = c²

196 + 169 + 81 = c²

446 = c²

c = [tex]\sqrt(446)[/tex]

c = 21.2 cm (rounded to the nearest tenth)

So the longest line segment that can be drawn in a right rectangular prism with dimensions of 14 cm long, 13 cm wide, and 9 cm high is about 21.2 cm.

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There are 6 cars that hold 3 people and 9 cars that hold 5 people.

Let's call the number of 3-passenger cars "x" and the number of 5-passenger cars "y".

We know the total number of cars is 15, so:

x + y = 15

We also know that the total number of passengers is 63, so:

3x + 5y = 63

Now we can use the first equation to solve for one of the variables in terms of the other:

y = 15 - x

Substitute this expression for y into the second equation:

3x + 5(15 - x) = 63

Expand

3x + 75 - 5x = 63

Evaluate like terms:

2x = 12

Divide both sides by 2:

x = 6

Recall that

y = 15 - x

So, we have

y = 15 - 9

y = 6

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Los múltiplos de 5 son 5,10,15,20,25,30,35,40,45,50,..........

Los múltiplos son números que se multiplican por un número con un entero positivo (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, etc.). En términos simples, un múltiplo es el producto de un número con otro número (enteros enteros, no fracciones ni decimales).

Los números múltiples son mayores o iguales que el número en sí. Esto se debe a que el primer múltiplo se multiplica por 1. Entonces, el primer múltiplo es el número mismo. Un número o números pueden tener múltiplos de una lista ilimitada de múltiplos. Porque los números se pueden multiplicar continuamente por otros enteros más grandes.

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The total area of the composite figure is 484 square feet.

The area is the amount of area occupied by an object's flat (2-D) surface or shape.

Given:

A composite figure is shown.

To find the complete area:

Here, we have dissected three figures separately.

So, the complete area,

= The area of the triangle with a height 22 feet and base 8 feet +

the area of the rectangle with a length 16 feet and width 22 feet +

the area of the triangle with a height 4 feet and base 22 feet

=  (1/2 x 22 x 8) + (16 x 22) + (1/2 x 4 x 22)

= 88 + 44 + 352

= 484 square feet.

Hence, the area is 484 square feet.

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Answer:

Median

Step-by-step explanation:

I took the test myself.

600 élèves :

On sait que 7/30+1/6 ne font pas partie des 400 élèves qui possèdent téléphone portable et ordinateur . 7/30+1/6=12/30=2/5 mais parmi ces élèves figurent ceux qui n'ont ni l'un, ni l'autre. Ils font donc partie des 2/5 qui viennent d'être dénombrés

Il faut donc les retrancher, sinon ils seraient comptés deux fois

donc le nombre n'ayant ni l'un ni l'autre est : 2/5-1/15=5/15=1/3

Par conséquent 2/3 ont unt téléphone et un ordinateur

Comme ces 2/3 correspondent à 400 élèves, le nombre total d'élèves interrogés sera donc de 400*3/2=600 élèves.

The percent markup of a department, if they sell 300 shirts at a cost of $9 each is 50%

According to the question, we learn that a department store buys 300 shirts at a cost of $1,800 and sells them for $9 each. This means :

The selling price of 300 shirts = 300 × $9

The selling price of 300 shirts = $2700

Selling price > cost price i.e., 2700 > 1800

when selling price is greater than cost price it means department store made a profit.

Profit = selling price - cost price

Profit = 2700 - 1800 = $900

Profit percentage = profit/ cost price × 100

Profit % =[tex]\frac{900}{1800} \times 100[/tex]

Profit % = 50%

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Option 234 cm is the correct option.

The measurement equivalent to 2.34 meters is: 234 cm

To convert meters to centimeters,

you multiply the number of meters by

100.

So, 2.34 meters multiplied by 100 is equal to 234 centimeters.

An object is only identified or classified using numbers on a nominal scale, which is a measuring scale. Only non-numeric (quantitative) factors or situations where numbers have no meaning are often addressed by this assessment.

By increasing the number of metres by 100, one may convert measurements from metres to centimetres. One metre equals one hundred centimetres, or 1 m = 100 cm, as is common knowledge.

Cm is used to represent it in writing. It may also be described as the unit of length in the current metric system, the International System of Units (SI). It is equal to one hundredth of a metre.

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Answer:

No, it is not.

Step-by-step explanation:

remember PEMDAS (parenthesis, exponents, mult., etc)

use distributive property, but solve parenthesis first

3x(x+4)²

(x+4)(x+4) = x² + 8x + 16

3x(x² + 8x + 16) >>> 3x³ + 24x² + 48x

so the equation is not equal

(a) The sample size for the above sample is 15.

(b) The sample mean for these data is 3.8.

(c) The sample median is 3.6.

(d) To compute the 20% trimmed mean for the above data set is 3.7.

(e) The sample mean is less descriptive as the location's center (median) than the trimmed mean.

The following measurements were recorded for the drying time, in hours

3.4      2.5      4.8      2.9      3.6 is:

2.8      3.3      5.6      3.7      2.8

4.4      4.0      5.2      3.0      4.8

(a) We have to determine the sample size for the above sample.

The number of participants or observations included in a study is referred to as the sample size. This number is commonly represented by the symbol n.

Sample Size (n) = 15

(b) We have to calculate the sample mean for these data.

Sample Mean = Total Sum of data/Total Number

Sample Mean = (3.4 + 2.5 + 4.8 + 2.9 + 3.6 + 2.8 + 3.3 + 5.6 + 3.7 + 2.8 + 4.4 + 4.0 + 5.2 + 3.0 + 4.8)/15

Sample Mean = 56.8/15

Sample Mean = 3.8

(c) We have to calculate the sample median.

To define the sample median we first represent the data in ascending order.

2.5, 2.8, 2.8, 2.9, 3.0, 3.3, 3.4, 3.6, 3.7, 4.0, 4.4, 4.8, 4.8, 5.2, 5.6

Sample Size(n) = 15

So Median = (n+1)/2th term

Median = (15 + 1)/2th term

Median = 16/2th term

Median = 8th term

So the 8th term in the given data is 3.6. So,

Median = 3.6

(d) We have to compute the 20% trimmed mean for the above data set.

To compute the 20% termed mean, remove 20% of the largest and 20% of the smallest elements from the sample and compute the mean of the new sample.

New sample: 2.9 3.0 3.3 3.4 3.6 3.7 4.0 4.4 4.8

New Mean = 33.3/9

New Mean = 3.7

(e) We have to check is the sample mean for these data more or less descriptive as a center of location than the trimmed mean.

The mean value is 3.8, the median value is 3.6, and the trimmed mean value is 3.7. As a result, the sample mean is less descriptive as the location's center (median) than the trimmed mean.

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The complete question is:

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint.

3.4      2.5      4.8      2.9      3.6

2.8      3.3      5.6      3.7      2.8

4.4      4.0      5.2      3.0      4.8

Assume that the measurements are a simple random

sample.

(a) What is the sample size for the above sample?

(b) Calculate the sample mean for these data.

(c) Calculate the sample median.

(d) Compute the 20% trimmed mean for the above data set.

(e) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?

Answer:

6.3×10^6

Step-by-step explanation:

6.3×10^6

in standard form

The number of table in the form of mixed number will be 4 ¹/₂ tables.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

27 children sit at table of 6, fillling where possible. Then the number of table is given as,

⇒ 27 / 6

⇒ 4 ³/₆

⇒ 4 ¹/₂ tables

The number of table in the form of mixed number will be 4 ¹/₂ tables.

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The equation of the line with a slope of -2/5 and passing through the point (5, -8) in standard, slope-intercept, form is; y = -0.4·x - 6

An equation consists of expressions and or numbers, expressed to be equivalent, by joining them with an '=' sign.

A standard form of the equation of a straight line is the slope-intercept form, which can be presented as follows; y = m·x + c

Where;

m = The slope of the graph of the equation

c = The y-intercept

The equation in the slope-intercept form can be obtained from the point-slope form, using the details of the slope of the graph of the equation (-2/5), and the point through which the graph of the equation passes (5, -8)

The point-slope of the equation is therefore;

y - (-8) = (-2/5)×(x - 5)

y + 8 = -2·x/5 + 2

y = -2·x/5 + 2 - 8 = -2·x/5 - 6 = -0.4·x - 6

The equation with a slope of -2/5 and passing through the point (5, -8), therefore is; y = -0.4·x - 6

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Answer:

-9

Step-by-step explanation:

3(5)-3(4)•y

3(5)-3(4)•2

15 - 12 · 2

15 - 24

-9

Answer:

To solve the equation 3(5) - 3(4)•2, we need to simplify each term and then substitute the value of 2 for y.

Starting with the first term:

3(5) = 15

Next, the second term:

-3(4)•2 = -24

So, putting it all together:

15 - 24 = -9

So when y is 2, the equation simplifies to -9.

Step-by-step explanation:

Answer:

So the inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x - 3) / 2.

Step-by-step explanation:

To find the inverse of a function, we switch the x and y variables and solve for y. So, we start with:

y = 2x + 3

Switching x and y, we get:

x = 2y + 3

Now, we solve for y:

x - 3 = 2y

y = (x - 3) / 2

So the inverse function of f(x) = 2x + 3 is f⁻¹(x) = (x - 3) / 2.

Answer & Step-by-step explanation:

To determine f's inverse function (x)= 2x + 3, we can follow these steps:

Step 1: Replace f(x) with y: y = 2x + 3

Step 2: Solve for x in terms of y:

y = 2x + 3

y - 3 = 2x

x = (y - 3) / 2

Step 3: Replace x with f^(-1)(x):

f^(-1)(x) = (x - 3) / 2

Therefore, the inverse function of f(x) = 2x + 3 is f^(-1)(x) = (x - 3) / 2.