If x - 2/3 = 1/2 then

The centroid of the given triangle is [tex]( 2\frac{2}{3} , -3\frac{1}{3} )[/tex], which is option B.

What is a centroid of a triangle?

A place where a triangle's medians coincide is the centroid of the triangle. The line segments that are drawn from a vertex to the midpoint of the vertex's opposite side are known as medians.

A triangle is divided into two smaller triangles with equal areas by each of its medians. The centroid of a triangle is where the medians of the triangle cross. Unlike other points of concurrency in a triangle, the centroid always lies inside one.

The formula of the centroid of a triangle when the coordinates of the vertices are known is:

Centroid = [tex](\frac{x_1 +x_2+x_3}{3} , \frac{y_1 +y_2+y_3}{3})[/tex]

From the graph, we can find the vertices of the triangle

A = (x₁, y₁) = (-3,-7)

B = (x₂,y₂) = (5,1)

C = (x₃,y₃) = (6,-4)

Centroid = [tex](\frac{x_1 +x_2+x_3}{3} , \frac{y_1 +y_2+y_3}{3}) = (\frac{-3+5+6}{3} ,\frac{-7+1-4}{3}) = (\frac{8}{3} ,\frac{-10}{3} ) = ( 2\frac{2}{3} , -3\frac{1}{3} )[/tex]

Therefore the centroid of the given triangle is [tex]( 2\frac{2}{3} , -3\frac{1}{3} )[/tex].

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If we generate the multiple datasets from a distribution with a given mean and variance , then mean and variance of from generated data will not be same .

The sample mean and the variance are random variables that vary from sample to sample, even if the samples are drawn from the same population.

When we generate a sample from a distribution with a known mean and variance, the sample mean and variance will be estimates of the population mean and variance ;

So , because of sampling variability, the estimates obtained from different samples may differ from one another and from the true population parameters.

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If you multiply the left side of an equation by 4, what must you multiply the right side of the equation by 4

Here you you multiply the left side of an equation by 4.

According to the solving for unknow rule you must perform same function to both side of the equation. If you multiply the left side of an equation by any integer then you must multiply the same integer on right hand side of the equation

To maintain equality, you must multiply the right side of the equation by 4 as well.

This is because the left side of the equation represents the same quantity as the right side, so any operation that is performed on one side must also be performed on the other side to preserve the equality.

Therefore, you must multiply the right side of the equation by 4

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The value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is indicated here by the symbol "."

The two triangles are similar thus the measure of its angle are also equal.

Using the similar triangle we have:

Angle D = Angle A = 82 degrees.

Angle F = 67 degrees

Using the sum of interior angles of triangle we have:

∠D + ∠F + ∠E = 180

82 + 67 + ∠E = 180

∠E = 31

From the figure we observe that,

∠E + ∠G = 180 (straight line)

31 + ∠G = 180

∠G = 149

Hence, the value of ∠E = 31 degrees and the value of ∠G = 149 degrees for the given triangle.

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Answer:

0.15 repeating

Step-by-step explanation:

Answer:

None

Step-by-step explanation:

Let's clarify that a radical symbol beside a number means what number squared (or to the power of 2) can give me the number in the symbol.

In this case it would be 4 because

[tex]4*4=16[/tex]

A method I use is to find the square root is dividing the number in the radical symbol 2 times

First by the original number, and then by the product of the last equation. It will not always work, but it works in some cases like this one.

[tex]\frac{16}{2} = 8\\ \\\frac{8}{2}=4\\ \\\sqrt{16}=4[/tex]

Second step, multiply 4 by 4, which equals 16.

Since the square root of 16 is 4, you can substitute 4 in the rest of the equations instead of the radical expression.

None of the following equations equal 16, which means none of the following equations if equal to [tex]\sqrt{16} *4[/tex]

Answer:

b) octogon

c) irregular pentagon

d) irregular hexagon

Step-by-step explanation:

After solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.

A fraction in mathematics is a number that is stated as a percentage, such as 1/2 or 2/3.

The number on top denotes the component of the unit under consideration, while the number at the bottom indicates the total number of parts that make up one unit.

An element of a whole is a fraction.

The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.

A fraction appears in the numerator or denominator of a complex fraction.

So, we have the operations:

7/3a - 8/5 + 4/15a

Now, solve as follows:

7/3a - 8/5 + 4/15a

7/3a + 4/15a - 8/5

7*5 + 4 /15a - 8/5

39/15a - 8/5

Therefore, after solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.

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Answer:

7x

Step-by-step explanation:

That would be   ( -2x )(-5) + -3x(1) = 10x - 3x = 7x

Answer:

Step-by-step explanation:

A square has 4 equal sides therefore to find the side of one we would divide the perimeter by 4. Doing that we get 7 inches.

Now seeing as it has four equal sides in order for us to find the area we would do:

Area = side x side = 7x7 = 49 squared inches

The solutions to the equation x³ - x² - 18 = 0 are given as follows:

x = 3, x = -1 ± 2.236i.

The equation for this problem is defined as follows:

x³ - x² - 18 = 0

x - 3 is a factor, hence one solution is given as follows:

x - 3 = 0

x = 3.

Also considering that x - 3 is a factor, and x - 3 is of the first degree while the equation is of the third degree, we have that:

(x - 3)(ax² + bx + c) = x³ - x² - 18

ax³ + (b - 3a)x² + (c - 3b)x - 3c = x³ - x² - 18

Hence the coefficients are given as follows:

Hence the remaining solutions are given as follows:

x² + 2x + 6 = 0.

Using a quadratic function calculator:

x = -1 ± 2.236i.

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Answer: $25.59

Step-by-step explanation: you can multiply 3 times 8.53 which comes too $25.59 but we can add as well.

8.53 + 8.53= 17.06 Now we have to add it 1 more time soo

17.06 + 8.53= $25.59..    

Hope this helps :)

Answer:

why and why not why .I have no idea wish I did

Answer: that would be 5^4 = 625

Step-by-step explanation:

Answer:

544

Step-by-step explanation:

How many 4 letter words can be constructed from ABCDE  that would be 5^4 = 625

How many 4 letter words can be constructed using BCD      that would be 3^4 = 81

So the number of words that use at least one vowel would be  5^4 - 3^4  =  625-81 = 544

240

Step-by-step explanation:

12-8+4+[(6+2)-3]2×3

= 4+4[(6+2)-3]2×3

= 8[(6+2)-3]2×3

= 8[(8)-3]2×3

= 8[5]2×3

= 8[5]6

= 40(6)

= 240

Answer:

20 boxes

Step-by-step explanation:

Each box ca hold 12 eggs

There are 230 eggs

So you will need 230/12 = 19 1/6 boxes =  19.167 boxes

Since you cannot get less than 1 box, round up to 20 boxes. There will be some empty spaces in one of the boxes

Answer:

Option 1 and 5 will be your answer :)

Step-by-step explanation:

Let the equation representing number of sold is,

y - y' = m(x - x')

Where m = number of condo sold per month  

(x', y') is a point from the given table,

Slope of line passing through two points  and  =

Slope of the passing through (1, 8) and (0, 11) will be,

m =  = -3

Therefore, equation of the line passing through (3, 2) and slope (-3),

y - 2 = (-3)(x - 3)

y - 2 = -3(x - 3)

Similarly, equation of the line passing through (0, 1) and slope (-3),

y - 11 = -3(x - 0)

Therefore, Option (1) and (5) will be the answer.

The answer is (b) The margin of error will be about 2 times larger.

The margin of error in a confidence interval is affected by the sample size, so decreasing the sample size will generally increase the margin of error. Specifically, the margin of error is inversely proportional to the square root of the sample size.

That is, if we reduce the sample size by a factor of k, then the margin of error will increase by a factor of sqrt(k).

In this case, the original sample size was 1000, and the proposed sample size is 250, which is 1/4 of the original size. Therefore, the margin of error for the smaller sample will be:

sqrt(1000/250) times the original margin of error.

Simplifying this expression, we get:

sqrt(4) times the original margin of error.

So the margin of error for the smaller sample will be about 2 times the original margin of error.

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Function 1 and Function 2 have y-intercepts that are equal. The solution has been obtained by using slope-intercept form.

What is slope-intercept form?

The line that represents the graph of the equation y = mx + b has a slope of m and a y-intercept of b. The m and b values are real integers, and the slope-intercept form of the linear equation is used.

We are given two functions.

Now, we will represent the functions in the slope-intercept form to find the y-intercept.

Function 1

⇒4x - 2y = -2

⇒2x - y = -1               (Dividing both sides by 2)

⇒ -y = -1 - 2x

⇒y = 2x + 1

So, the y-intercept is 1.

Function 2

We are given two points as (-1,3) and (0,1)

The slope comes out to be = -2

So, b = 3 - (-2)(-1) = 1

So, the y-intercept is 1.

Hence, function 1 and function 2 have y-intercepts that are equal.

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it's A and D good luck

Answer:

A., D.

Step-by-step explanation:

Let t = number of two-point questions.

Let f = number of four-point question.

First we deal with the number of questions.

There are 42 questions. All the questions are either 2-point questions or 4-point questions.

t + f = 42

Now we deal with the number of points.

t two-point questions are worth 2t points.

f four-point questions are worth 4f points.

Altogether, they are worth 2t + 4f points.

The total number of points is 100, so

2t + 4f = 100

The system of equations has the equations:

t + f = 42

2t + 4f = 100

Answer: A., D.

Answer:

Mari bought 6 packages of tomato seeds and each package contains 24 seeds then

Seeds = (6) * (24) = 144.

Mari has a total of 144 seeds.

Mari planted a pack of seeds and has 15 germinated seeds.

144-24-15 = 105

Mari then has 105 seeds left.

Answer

C At least 100 but no more than 120 seeds will sprout

The  statement about the seeds in the remaining packets is best supported by this information is option C:  At least 100 but no more than 120 seeds will sprout

Mari bought 6 packages of tomato seeds and each package contains 24 seeds so:

Seeds = 6 x 24  = 144.

Note that Mari has a total of 144 seeds. In the question, Mari planted a pack of seeds and has 15 germinated seeds.

Hence:

144-24-15 = 105

Mari then has 105 seeds left.

Hence option c: At least 100 but no more than 120 seeds will sprout, is correct.

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See full text below

Mari bought 6 packets of tomato seeds. Each

packet contained 24 seeds. She planted 1 packet

of the seeds, and 15 seeds sprouted.

Which statement about the seeds in the remaining

packets is best supported by this information?

A No more than 50 sees will sprout

B Between 50 and 100 seeds will sprout

C At least 100 but no more than 120 seeds will

sprout

D All 120 seeds will sprout

Answer: Let's call Sarah's original amount of money as x. Then, Christine had 0.8x.

After they spent $684 altogether, Christine had 0.8x - 0.25(0.8x) = 0.8x - 0.2x = 0.6x left.

Sarah had x - 684.

Since Christine had thrice as much money left as Sarah, we can write an equation:

0.6x = 3(x - 684)

Expanding the right side of the equation:

0.6x = 3x - 2052

Solving for x:

2.6x = 2052

x = 787.69

So Sarah originally had 787.69 dollars and spent 787.69 - 684 = 103.69 dollars.

Step-by-step explanation:

a.) The equation for g(x) is g(x) = 6((x+5)/2)³and output is 384.

b.) The inverse machine, g¹(a), we need to undo each of the four steps in reverse order is g¹(a) = [tex]((a/6)^{(1/3)})*[/tex]2 - 5

c.) To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result is  3.

What is Function?

A function is a mathematical rule that takes one or more inputs (also called independent variables or arguments) and produces a single output (also called a dependent variable or function value). In other words, a function is a relationship between the inputs and the output, where each input produces a unique output.

Functions can take many different forms and can be used to describe a wide variety of mathematical and real-world phenomena.

a. The equation for g(x) is:

g(x) = 6((x+5)/2)³

When 3 is put in for x, the output is:

g(3) = 6((3+5)/2)³= 6(4)³ = 384

b. To find the inverse machine, g¹(a), we need to undo each of the four steps in reverse order:

Putting this in equation form, we get:

g¹(a) = [tex]((a/6)^{(1/3)})[/tex]*2 - 5

c. To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result:

g¹(384) =[tex]((384/6)^{(1/3)})[/tex]*2 - 5 =[tex](64^{(1/3)})[/tex]2 - 5 = 42 - 5 = 3

Since the output of g¹(a) is 3 when we input the output of g(x), we can conclude that g¹(a) correctly undoes the output of g(x).

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The equation of the linear function is y = x - 5

From the question, we have the following parameters that can be used in our computation:

The ordered pairs (0,-5) and (-2,-3)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

y = mx - 5

Using the other point (-2, -3), we have

-2m - 5 = -3

Evaluate the like terms

-2m = 2

Divide by 2

m = 1

Substitute the known values in the above equation, so, we have the following representation

y = x - 5

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Complete question

Find the equation of the linear function represented by the line that goes through: (0,-5) and (-2,-3) in slope-intercept form.

y = ___?___

The height of the cylinder is 18 cm and its volume is 450π cubic centimeters, given that the radius of its base is 5 cm and its total surface area is 165πcm².

A right circular cylinder is a three-dimensional geometric shape with a circular base and a curved surface that extends upward in a cylindrical fashion.

Let's begin by identifying the formula for the total surface area of a cylinder. It is given by:

Total surface area = 2πr(h + r)

Where r is the radius of the base, h is the height, and π is a mathematical constant (approximately 3.14). We are given that the total surface area of the cylinder is 165πcm², and the radius of its base is 5 cm. Substituting these values in the formula, we get:

165π = 2π(5 + h)5 + 2π(5)²

Simplifying this equation, we get:

165π = 10πh + 150π

Dividing both sides by 10π, we get:

h + 15 = 33

Therefore, the height of the cylinder is 18 cm (33 - 15).

Now, let's find the volume of the cylinder. The volume of a cylinder is given by:

Volume = πr²h

Substituting the values of r and h, we get:

Volume = π(5)²(18)

Simplifying this equation, we get:

Volume = 450π

Therefore, the volume of the cylinder is 450π cubic centimeters.

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Complete Question:

The total surface area of a right circular cylinder is 165πcm². If the radius of its base is 5 cm; find its height and volume.

a. It is not specified in the given information what the total number of seniors at Lewis High is, so it is not possible to directly compare the number of seniors who apply for college to the number of seniors at Lewis High.

b. The same issue applies to this question as well. It is not specified what the total number of seniors at Lewis High is, so it is not possible to directly compare the number of seniors who apply for college with those who don't.

c. If two out of every three seniors at Lewis High apply for college, then one out of every three seniors does not. Therefore, the fraction of graduating seniors at Lewis High who do not apply to college is 1/3.

d. If three out of every five seniors at Lewis High who apply for college are female students, then two out of every five are male students. Therefore, the fraction of seniors who are males who apply for college is 2/5. Again, without knowing the total number of graduating seniors at Lewis High, it is not possible to directly compare the number of males who apply for college with the number of graduating seniors.

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Two of every 3 seniors at Lewis High apply for college. Three of every 5 seniors at Lewis High who apply for college are female students.yout

a. How does the number of seniors who apply for college compare to the number of seniors at Lewis High?

b. How does the number of seniors who apply for college compare to those who don't?

c. What fraction of the graduating seniors at Lewis High do not apply to college?

d. What fraction of the seniors are males who apply for college? How does the number of males who apply for college compare with the number of graduating seniors?

The probability of getting both the marbles to be red will be 4/25.

Probability is a number that indicates the likelihood of an event occurring. Probability is defined as the ratio of favorable outcomes to all outcomes.

Probability = Number of favorable outcomes / Number of samples

Given that two red and three black marbles are in a bag. If Abby takes a marble out of the bag without looking, puts it back, and then draws another marble.

The probability of getting red in the first draw,

P = 2 / 5

Now the marble is returned and again the probability of getting the red marble is,

P = 2 / 5

The probability of getting both the marbles red will be,

Pb = ( 2/ 5 ) x ( 2 / 5 )

Pb = 4 / 25

Therefore, there is a 4/25 chance that both marbles will be red.

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Answer:

C 11

Step-by-step explanation:

you have 1 less penny than dimes which is 10 pennies

you have 2 less nickels than dimes which is 9

11+10+9=30

well, let's first off get the whole area of the circular garden, and then from it subtract the area of the squarish sculpture, thus what's leftover is simply the shaded area, or just the garden minus the sculpture.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{whole~circle}{\pi (6x)^2}~~ - ~~\stackrel{square}{(4x)(6x)}}\implies 36\pi x^2-24x^2\implies {\Large \begin{array}{llll} 12x^2(3\pi -2) \end{array}}[/tex]