Simplify the expression:
6(2x+4)
————-
3

Answer:

see below

Step-by-step explanation:

The absolute value means take the non negative value

l-9l  = 9

l64l =64

l-22l=22

Answer:

1. 9   2. 64   3. 22

Step-by-step explanation:

The obsolute value is how far away the number is from zero

For example:

I-94I is 94

but

-I94I is -94

if the negative is outside the equation then its a negative

The answer  is that there are 165 ways to distribute eight identical bottles of water to three friends.

We can use the formula for distributing identical objects to distinct groups, which is (n+r-1) choose (r-1), where n is the number of objects and r is the number of groups. In this case, n=8 and r=3.

So the formula becomes (8+3-1) choose (3-1), which simplifies to 10 choose 2. Using the combination formula, 10 choose 2 equals 45. However, this only accounts for cases where all three friends receive at least one bottle of water.

To account for cases where some friends may receive no water, we need to add the number of ways where two friends receive water and one friend receives no water, and the number of ways where one friend receives water and two friends receive no water.

There are three ways to choose which friend receives no water, and then we need to distribute the remaining eight bottles of water among the remaining two friends. Using the formula from earlier, this gives us (8+2-1) choose (2-1) = 9.

So for the case where two friends receive water and one friend receives no water, there are 3 * 9 = 27 ways. Similarly, for the case where one friend receives water and two friends receive no water, there are 3 * 9 = 27 ways.

Adding these cases to the initial case where all three friends receive at least one bottle of water, we get a total of 45 + 27 + 27 = 99 ways. However, we still need to account for cases where all eight bottles of water go to a single friend, which is just 3 ways.

So the final answer is 99 + 3 = 102 ways to distribute eight identical bottles of water to three friends, where some friends may receive no water.

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For the given triangle abc, g is the centroid of  and the length of line segment d g is 9 x 2 so the length of line segment gf is 133 units.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. The specified object is a triangle having vertices A, B, and C. triangle with equal sides.

There are three sides and three angles in every triangle, some of which may be the same. In the case of a right triangle, the three sides are given unique names: the hypotenuse, which is the side that faces the right angle, and the legs, which are the other two sides.

from given information;

2x = 19 * 14

Solving for value of x,

x = 19 * 14 / 2

x = 19 * 7

x = 133.

as both lines are same,

now we found that the length of line segment gf is 133 units.

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Using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.

The square of a side of a plane triangle is equal to the sum of the squares of the other sides minus twice the product of those sides and the cosine of the angle between them, according to a trigonometry rule.

So, it is a given that the distance between the home plate and the pitcher's mound on a softball field is 43 feet.

27° east of the pitcher's mound is the angle at which a ball is struck.

Before an outfielder catches the ball, it travels 162 feet.

Using the law of cosines, we may now:

a² = b² + c² - 2bcosA

When b=43, c=162, and A=27° are entered, we get:

a² = 43² + 162² - 2(43)(162)cos27°

a² = 1849 + 26244 - 12413.4

a² = 15679.6

a = 125.21

a = 125ft

Therefore, using the laws of cosines we know that to get the ball back to the pitcher, the outfielder must throw it 125 feet.

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Complete question;
On a softball field, home plate is 43 feet from the pitcher’s mound. A ball is hit at an angle of 27° east of the pitcher’s mound. The ball travels 162 feet before it is caught by an outfielder. Law of cosines: a2 = b2 + c2 – 2bccos(A) Rounded to the nearest foot, the outfielder must throw the ball feet to return it to the pitcher.

The total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

The area is the total area occupied by a flat (2-D) surface or the form of an object.

Create a square on paper by using a pencil.

Two dimensions make it up.

A form's area on paper is the space it takes up.

So, given, a square metal frame encircles a circular mirror.

The mirror has a 4x radius.

The metal frame's side length is 12x.

According to the basic formula for the area of a circle and a square:

area of a circle = pi * radius * radius

Square Area = Side * Side

In the given situation:

Mirror's Area = pi * 4x * 4x = pi * 16x² = 50.24x

Squared mirror's Area = 12x * 12x = 144x²

The area of the metal frame is the sum of the areas of the squared and round mirrors.

Metal frame area =   144x² -  50.24x²

Metal frame size = 93.76x²

Therefore, the total area filled by a flat (2-D) surface or an object's form is referred to as the area and the required area of the metal frame is 93.76x² unit square.

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Correct question:

A circular mirror is surrounded by a square metal frame. The radius of the mirror is 4x. The side length of the metal frame is 12x. What is the area of the metal​ frame?

Taking a difference, we can see that the trip to city C is 482.6 mi longer.

Here we know that the distance from city a to city b is 256.8 miles, and the distance from city a to city c is 739.4 miles

To find how much farther is the trip to city c than the trip to city b, we just need to take the difference between the two distances above.

That means that we need to take the distance to city c and subtract the distance to city b.

We will get:

739.4 mi -  256.8 mi = 482.6 mi

The trip to city C is 482.6 mi more than the trip to city B.

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sin(43) × hypotenuse of 19 gives you oppo

= 13

Answer:

is this math

Step-by-step explanation:

Answer:

3x!

Step-by-step explanation:

Since the sides are the same (marked with the lines on the side) the 2 angles are also the same! :D

sum area = -3x - 6y + 12 and product area = -36x - 72y.

what is rectangle?

A rectangle is a geometric shape that is defined as a four-sided flat shape with four right angles (90-degree angles) and opposite sides that are parallel and equal in length.

The area of a rectangle is given by the product of its length and width. Assuming that the length of the rectangle is given by -3x - 6y and its width is 12, we can express the area in terms of a sum and a product as follows:

Sum:

Area = length x width

Area = (-3x - 6y) + 12

Area = -3x - 6y + 12

Product:

Area = length x width

Area = (-3x - 6y) x 12

Area = -36x - 72y

Note that the product expression is not equal to the sum expression. This is because we used different assumptions for the length of the rectangle in each case.

Therefore, sum area = -3x - 6y + 12 and product area = -36x - 72y.

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Answer:

The Richter scale and how it measures earthquake magnitude. The Richter scale calculates an earthquake's magnitude (size) from the amplitude of the earthquake's largest seismic wave recorded by a seismograph. ... (That is, an earthquake measuring 5.0 releases 31 times more energy than an earthquake measuring 4.0.)

Answer:

20 kg

Step-by-step explanation:

12/3 = 4

4 x 2 = 8

12 + 8 = 20

Answer:

20 kg of dough

Step-by-step explanation:

Step 1:

12 : 3 = x : 5

Step 2:

3x = 60

Answer:

x = 20

Hope This Helps :)

Answer:

D

Step-by-step explanation:

The correct relationship of the three principles is: The well-ordering principle for the integers is equivalent to strong mathematical induction, and neither is equivalent to weak mathematical induction.

The well-ordering principle for the integers states that every non-empty set of non-negative integers has a least element. Strong mathematical induction is a proof technique that involves proving that a statement is true for a base case, and then assuming that it is true for all cases up to a certain value, and then proving that it must also be true for the next case.

This requires assuming the truth of all cases up to a certain value, which is where the well-ordering principle comes in. Weak mathematical induction is a proof technique that involves proving that a statement is true for a base case, and then assuming that it is true for a particular case, and then proving that it must also be true for the next case.

Weak mathematical induction does not require assuming the truth of all cases up to a certain value, and is therefore weaker than strong mathematical induction.

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Answer:

\(\huge\boxed{\sf 30\ marbles}\)

Step-by-step explanation:

Total marbles = 48

Ratio of red marbles to black marbles = 5 : 3

Total ratio = 5+3 = 8

Red Marbles:

= \(\sf \frac{5}{8} * 48\)

= 5 * 6

= 30 marbles

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

In Sin(90) the answer is 1

In sin(-90) the answer is -1

The only difference is that the negative degrees has a negative sign before the one.

Answer:

B) sin(90°) > sin(−90°)

Step-by-step explanation:

Edge

Answer: I say a dictionary.

Step-by-step explanation:

Answer:

9 inches

Step-by-step explanation:

4 x 3 = 12

so 3 x 3 = 9

The solution to the system of equations f(x) = g(x) is:

x = -2, y = 3.

A system of equations is a set of equations that is related, and the solution of the system is found when the equations are equal, that is, when the equations all intersect.

In the context of this problem, the equations are given as follows:

The solution to the given system of equations is at the value of x for which f(x) = g(x), hence it is obtained as follows:

f(x) = g(x)

2x + 7 = -x + 1 (solve just line any equality, isolating the desired variable).

2x + x = 1 - 7

3x = -6

x = -6/3

x = -2.

The y-coordinate of the solution of the system is given as follows:

y = -(-2) + 1 = 2 + 1 = 3.

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Answer:

The answer is 24.

Answer:

24

Step-by-step explanation:

Seeing that triangle ACD is a 5-12-13 right triangle, AD=12. Then using Pythagorean Theorem, we can calculate BD to be BD=\(\sqrt{15^2-12^2}=\sqrt{3^2(5^2-4^2)}=3\sqrt{25-16}=3\sqrt{9}=3 \cdot 3 = 9$\). Thus, the area of triangle ABD is \($\frac{1}{2} \cdot 12 \cdot 9=6 \cdot 9=54 \text{ sq units}$\) and the area of triangle ACD is \($\frac{1}{2} \cdot 12 \cdot 5=6 \cdot 5=30 \text{ sq units}$\). The area of triangle ABC is the difference between the two areas: \($54 \text{sq units} - 30 \text{sq units} = \boxed{24} \text{sq units}$.\)

Answer:

-8

Step-by-step explanation:

First multiple the x by -4 giving -4x then multiply the same -4 by 2 giving -8

The MLE is a Minimum Variance Unbiased Estimator (MVUE) for theta if it is unbiased and achieves the smallest variance among all unbiased estimators. In this case, we have already established that the MLE is biased. Therefore, it cannot be the MVUE for theta.

MLE (Maximum Likelihood Estimator) of theta:

To find the MLE of theta, we need to maximize the likelihood function. In this case, the likelihood function is given by:

L(theta) = (ye^(-y/theta))/(theta^6)

To maximize the likelihood, we take the logarithm of the likelihood function:

ln L(theta) = -y/theta + 6 ln(y) - 6 ln(theta)

To find the maximum, we differentiate ln L(theta) with respect to theta and set it equal to zero:

d/dtheta ln L(theta) = y/theta^2 - 6/theta = 0

Simplifying the equation:

y = 6 theta

Therefore, the MLE of theta is theta_hat = y/6 = Y/6.

Unbiasedness of MLE:

To verify if the MLE is an unbiased estimator for theta, we need to calculate the expected value of theta_hat and check if it equals the true value of theta.

E(theta_hat) = E(Y/6) = (1/6) * E(Y)

Given that E(Y) = 40 (as stated in the problem), we have:

E(theta_hat) = (1/6) * 40 = 40/6 = 20/3

Since E(theta_hat) does not equal the true value of theta (which is unknown in this case), the MLE is not an unbiased estimator for theta.

Method of Moments Estimator (MOME) and MLE:

The Method of Moments Estimator (MOME) estimates the parameter by equating the sample moments to their corresponding population moments. In this case, the MOME estimates theta by setting the sample mean equal to the population mean.

E(Y) = theta

So, the MOME of theta is theta_hat_MOME = Y.

Comparing this with the MLE, we can see that the MOME and MLE are different estimators.

Sufficiency and MVUE:

To show that n Y_i; i=1 is a sufficient statistic for theta, we can use the factorization theorem. The joint probability density function (pdf) of the random variables Y1, Y2, ..., Yn is given by:

f(y1, y2, ..., yn; theta) = (ye^(-y1/theta))/(theta^6) * (ye^(-y2/theta))/(theta^6) * ... * (ye^(-yn/theta))/(theta^6)

This can be factored as:

f(y1, y2, ..., yn; theta) = (ye^(-sum(yi)/theta))/(theta^6)^n

The factorization shows that the joint pdf can be written as the product of two functions: g(Y1, Y2, ..., Yn) = ye^(-sum(yi)/theta) and h(T; theta) = (1/(theta^6)^n).

Since the factorization does not depend on the parameter theta, we can conclude that n Y_i; i=1 is a sufficient statistic for theta.

The MLE is a Minimum Variance Unbiased Estimator (MVUE) for theta if it is unbiased and achieves the smallest variance among all unbiased estimators. In this case, we have already established that the MLE is biased. Therefore, it cannot be the MVUE for theta.

Note: In this particular scenario, the MLE is biased and not the MVUE for theta.

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Since you didn't specify the desired range, you can choose the appropriate number of standard deviations based on your needs or conventions.

To determine within how many standard deviations from the mean all the values fit, you need to follow these step-by-step instructions:

Calculate the mean (average) of the given values by adding all the numbers together and dividing by the total count.

Mean = (85 + 89 + 152 + 119 + 157 + 71 + 163 + 144 + 161 + 141 + 150 + 60) / 12 = 126.58 (rounded to two decimal places)

Calculate the variance by finding the squared difference between each value and the mean, summing up all the squared differences, and dividing by the total count.

Variance = [(85 - 126.58)^2 + (89 - 126.58)^2 + ... + (150 - 126.58)^2 + (60 - 126.58)^2] / 12

Take the square root of the variance to obtain the standard deviation.

Standard Deviation = √Variance

Once you have the standard deviation, you can determine within how many standard deviations from the mean all the values fit. Generally, if a value falls within one standard deviation of the mean, it is considered close to the mean.

Remember, standard deviations are a measure of dispersion, so the range within which the values fall depends on the specific criteria or rule you want to apply (e.g., one, two, or three standard deviations).

Since you didn't specify the desired range, you can choose the appropriate number of standard deviations based on your needs or conventions.

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Each angle inside the square ABCD is equal to 90 degrees.

We can make use of the properties of a square to demonstrate that the measure of each angle within the square is equivalent to 90 degrees.

Given the contrary vertices of the square as A(2, - 4) and C(10, 4), we can track down the other two vertices B and D utilizing the properties of a square.

How about we track down the length of one side of the square first. The formula for the distance between two points (x1, y1) and (x2, y2) is as follows:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Utilizing this recipe, we can track down the length of AC:

AC = ((10 - 2)2 + (4 - (-4))2) = (82 + 82) = (64 + 64) = (128 + 82) Since a square has all sides that are the same length, we can say that AB = BC = CD = DA = 802.

Let's now locate AC's midpoint, M. The formula for the midpoint between two points (x1, y1) and (x2, y2) is as follows:

We can determine M's coordinates using this formula: M = ((x1 + x2)/2, (y1 + y2)/2).

M = ((2 + 10)/2, (-4 + 4)/2) = (6, 0) Now that we know the coordinates of B and D, we can see that BM and DM are AC's perpendicular bisectors and that M is AC's midpoint.

The incline of AC can be determined as:

m1 = (y2 - y1)/(x2 - x1) = (4 - (-4))/(10 - 2) = 8/8 = 1 The negative reciprocal of the slope of a line that is perpendicular to AC is its slope. Therefore, BM and DM have a slope of -1.

With a slope of -1, the equation for the line passing through M can be written as follows:

y - 0 = - 1(x - 6)

y = - x + 6

Presently, we should track down the focuses B and D by subbing the x-coordinate qualities:

For B:

B = (10, -4) for D: y = -x + 6 -4 = -x + 6 x = 10

The coordinates of each of the four vertices are as follows: y = -x + 6; 4 = -x + 6; D = (2, 4) A (-2, -4), B (-10, -4), C (-4), and D (-2, 4)

The slopes of the sides of the square can be calculated to demonstrate that each angle within the square is 90 degrees. The angles formed by those sides are 90 degrees if the slopes are perpendicular.

AB's slope is:

m₂ = (y₂ - y₁)/(x₂ - x₁)

= (-4 - (- 4))/(10 - 2)

= 0/8

= 0

Slant of BC:

Slope of CD: m3 = (y2 - y1)/(x2 - x1) = (4 - (-4))/(10 - 10) = 8/0 (undefined).

Slope of DA: m4 = (y2 - y1)/(x2 - x1) = (4 - 4)/(2 - 10) = 0/(-8) = 0

As can be seen, the slopes of AB, BC, CD, and DA are either 0 or undefined. m5 = (y2 - y1)/(x2 - x1) = (-4 - 4)/(2 - 2) = (-8)/0 (undefined). A line that has a slope of zero is horizontal, while a line that has no slope at all is vertical. Since horizontal and vertical lines are perpendicular to one another, we can deduce that the sides of the square form angles of 90 degrees.

In this manner, we have shown that each point inside the square ABCD is equivalent to 90 degrees.

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Answer:

88.8888888889% or 88% rounded

plz Brainliest?!?!?

The width of the shelf is 10 inches. The correct option is D.

A right-angled triangle is a triangle that has one angle measuring 90 degrees, which is known as the right angle. The sides adjacent to the right angle are known as the legs of the triangle, while the side opposite the right angle is known as the hypotenuse.

The Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, is one of the fundamental theorems of mathematics and is used extensively in various fields.

Let's call the width of the shelf "x". According to the given diagram, we have a right triangle where the base is x, the perpendicular is 10 inches, and the angle between the hypotenuse and the perpendicular is 45 degrees.

Using trigonometric ratios, we know that:

tan(45) = perpendicular/hypotenuse

tan(45) = 10/x

Since tan(45) is equal to 1, we can simplify the equation to:

1 = 10/x

Solving for x, we get:

x = 10

Therefore, the width of the shelf is 10 inches.

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Answer:

-1

Step-by-step explanation:

they gave you the value to x so all you have to do is plug it in

h(-2) = -2 (-2) - 5

h(-2) = 4 - 5

h(-2) = -1

Substituting the value, x = - 2 into the function, the value of the function h(-2) is - 1

Given the function :

At h(-2) :

h(-2) = - 2(-2) - 5

h(-2) = 4 - 5

h(-2) = - 1

Therefore, the value of h(-2) is - 1

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We need to make 28 pairwise comparisons among the eight means to compare the mean SAT scores for each ethnic group.

To make all pairwise comparisons among the eight means, we need to calculate the number of unique pairs of means. The formula for calculating the number of unique pairs is n(n-1)/2, where n is the number of items.

The SAT is a standardized test widely used for college admissions in the United States. The test measures knowledge and skills in reading, writing, and mathematics. The test is scored on a scale of 400-1600, with separate scores for the reading/writing and math sections, each ranging from 200-800. The College Board publishes mean SAT scores for various groups, including ethnic groups, genders, and geographic regions.

In this case, we have 8 ethnic groups, so the number of unique pairs of means is:

8(8-1)/2 = 28

Therefore, we need to make 28 pairwise comparisons among the eight means to compare the mean for each ethnic group.

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The College Board publishes mean SAT scores for eight ethnic groups. How many tests are required to make all pairwise comparisons among the eight means?

Consider the experiment of picking one digit first from the initial set (digits from 1 t) 6, and then pgrabbing a second digit without eplace,ment.

As for the first part of the experiment, there are 6 digits to choose from; however, during the second round, there are only 5 digits available. Therefore, according to the counting principle, the sample space has

30 elements. he answer is 30 elements in the sampele space.