What does FG mean mass?

The GCF of the given expressions is 4x⁷⁶

The greatest common factor, abbreviated as GCF, of two numbers is the largest number that is a factor of, or divides evenly into, both of the numbers. When two numbers are relatively small, we have a quick and simple way to calculate their greatest common factor. We do this by listing all of the factors of each number, and then identifying the largest number that is in both lists.

Given here, The expressions 20x⁷⁶ and 8x⁹² and GCF(20,8)=4

and x⁷⁶ is a factor of  8x⁹²

∴ GCF(20x⁷⁶ , 8x⁹²) =4x⁷⁶

Hence, The GCF of the given expressions is 4x⁷⁶

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Answer: The answer is 10x2

Step-by-step explanation:

The population of the city grew from 2010 to 2020 by 13.37%.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

We have to given that;

In 2010, the population of a city was 237,000.

And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.

We know that;

Where, A = P (1+r)ⁿ

A = final population.

P = Initial population.

r = rate

n = time

Hence, The population in 2015 is, =

A = 237,000(1 + 0.076)⁵

A = 341829.629

And, The population in 2020 =

A = P (1 - r)ⁿ

A = 341829.629 (1 - 0.047)⁵

A = 268704.047

So, Percent grow = (268704.047 - 237,000) / 237,000 × 100

                           = 31704.047 / 237,000 × 100

                            = 13.37 %

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Answer:

17.3 miles / gallon

Step-by-step explanation:

Rates can be represented in different forms, such as speed (meters per second) or water flow rate (liters per minute or second)

Given information from the question,

2 gallons = 34.6 miles

1 gallon = 34.6 ÷ 2 = 17.3 miles / gallon

Answer:

Jared's groceries = 495

Step-by-step explanation:

We calculate 11% from Jared monthly income:
11% x 4500 = 495

Jared's groceries = 495

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Answer:218

explanation: 162 divided by 9 = 18 and 18 multiplied by 12 =218

Coordinate (-a , b ) belongs to second quadrant.

The axes (x-axis and y-axis) of a two-dimensional Cartesian plane system divide the plane into four infinite regions called quadrants. The horizontal line or x-axis and vertical line or y-axis intersect each other at the right angle.  The intersection of two lines is known to be the reference point. All the measurement is done by taking this point as the reference (or starting point) in the coordinate system.

"A quadrant is simply defined as the region of a cartesian plane formed when the x-axis and y-axis intersect each other."

Given, Coordinate ≡ (-a , b)

1st Quadrant: The upper right-hand corner of the graph is the first quadrant. In this quadrant the values of x and y both are positive.

2nd Quadrant: The upper left-hand corner of the graph is the second quadrant. In this quadrant, the value of x is negative whereas the value of y is positive.

3rd Quadrant: The lower left-hand corner of the graph is the third quadrant. It contains the negative values of both x and y.

4th Quadrant: Finally, the fourth quarter is at the lower right-hand corner, which has a positive value of x and a negative value of y.

Hence, by the above observation, given coordinate (-a, b) belongs to the 2nd quadrant.

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Number of students that do two subjects are 12.

Number of students that do only exactly one subject are;

For Art;

⇒ 14

For Chemistry;

⇒ 11

For Bio;

⇒ 8

Number of students that do at least two of the subjects are 15.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology.

All the students do at least one of the three subjects.

3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only.

Here,

Total students = 48

So, Number of students that do two subjects are = 4 + 3 + 5

                                                                            = 12

And, Number of students that do only exactly one subject are;

For Art;

⇒ 24 - (3 + 4 + 3)

⇒ 14

For Chemistry;

⇒ 22 - (3 + 5 + 3)

⇒ 11

For Bio;

⇒ 20 - (3 + 4 + 5)

⇒ 8

Number of students that do at least two of the subjects are;

⇒ 3 + 3 + 4 + 5

⇒ 15

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The fourth point is (-6.5, -14)

Vertices of a parallelogram?

The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.

The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.

One way to find the fourth vertex is to use the vector that connects one vertex to another. The vector from (-7,-6) to (6,3) is (13,9), and from (6,3) to (4,-4) is (-2,-7)

If we use the vector which is opposite of (-2,-7) that is (2,7) and add it to the third point (4,-4) , we will get the fourth point.

(2,7) + (4,-4) = (6,3)

so the fourth point is (6,3)

Another way is to find the midpoint of the diagonal of the parallelogram which are (-7,-6) and (4,-4) and then add the vector which is opposite of (6,3) to (4,-4) that is (-6,-9) which is also the vector from (6,3) to (4,-4)

Midpoint of (-7,-6) and (4,-4) = (-0.5,-5)

(-0.5,-5) + (-6,-9) = (-6.5, -14)

Hence, the fourth point is (-6.5, -14)

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The total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Cost of a binder = 2.25

Cost of a pencil = 0.75

We have to find the total cost for Ben to buy 1 binder and P pencils.

Cost of 1 binder = 2.25

Cost of P pencils = 0.75 × P = 0.75 P

Total cost of 1 binder and P pencils = 2.25 + 0.75 P

Hence the total cost for Ben to buy 1 binder and P pencils is 2.25 + 0.75 P.

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mean of the sampling distribution of the difference in sample proportions is 0.36.

The best method for the random sampling will be to write the students' names on paper and pick them out of a hat, as each student will have an equal chance of being chosen.

22% of the population of eastern grey squirrels weigh more than 0.5 kg.

36% of the population of western grey squirrels weigh more than 0.5 kg.

Eastern grey squirrel sample size is 60.

There were 120 western grey squirrels in the sample.

Required:

The difference in sample proportions' mean of the sampling distribution (eastern minus western)

The difference of the mean yields the mean of the difference.

Mean = p1 - p2 is the sampling distribution's average for the difference in the sampling proportion from two populations.

Where;

p1 = 22% of the eastern grey squirrel, which equals 0.22.

p2 = 36% of the western grey squirrel, which equals 0.36.

Therefore;

p1 - p2 = 0.22 - 0.36 is the mean.

The right answer is (E) 0.22 - 0.36.

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The perimeter of the rectangle is  4y + 6 (cm).

All four side lengths must be added up in order to get the perimeter, or the distance around the rectangle. Since there are two of each side length, it is simple to multiply the total of the length and the breadth by two in order to do this task effectively. The formula for perimeter is perimeter=(length Plus width)2.

The diagram shows a rectangle. All measurements are in centimetres  an expression in terms of y, for the perimeter of the rectangle.

The perimeter of the rectangle is

2(y+3)+24

=2y + 6 + 2y = 4y + 6 (cm)

{ the perimeter:

2 *  width + 2 * Length}

The perimeter of the rectangle is  4y + 6 (cm).

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Answer:

912 cm²

Step-by-step explanation:

Formula for area of triangle: 1/2bh

So you'll first multiply the base by the height of the triangle

48 x 38 = 1,824

Then you'll multiply 1,824 by 1/2(which is the same as dividing it by 2)

1,824 ÷ 2 = 912

Salesman C have a larger paycheck than both of the other salesmen in

None of the weeks.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, we have,

Salesman A works  earns $65 per sale, with a maximum weekly commission of $1,300

Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale.

Salesman C does not earn any commission. His weekly salary is $900.  Now we have that, A is getting $1300 commission,

and, salary of C is $900, he has no commission.

i.e. C can't earn more than A

Hence, Salesman C have a larger paycheck than both of the other salesmen in None of the weeks.

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The solution is Option D.

The week 1 is when Salesman C have a larger paycheck than both of the other salesmen and is given by the equation C = $ 900

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of sales be represented as x

Let the maximum weekly salary of Salesman C be = $ 900

Now , the weekly salary of Salesman A = $ 65x

where x is the number of sales

And , the weekly salary of Salesman B = $ 300 + $ 40x

Now , on week 1,

Salesman A made 11 sales

Substitute the value of x = 11 in the equation , we get

So , the salary of Salesman A on week 1 = 65 ( 11 )

On simplifying the equation , we get

The salary of Salesman A on week 1 = $ 715

And , Salesman B made 14 sales

Substitute the value of x = 14 in the equation , we get

The salary of Salesman B on week 1 = 300 + 40 ( 14 )

On simplifying the equation , we get

The salary of Salesman B on week 1 = 300 + 560

The salary of Salesman B on week 1 = $ 860

So , Salary of Salesman C on week 1 > salary of Salesman B on week 1 > salary of Salesman A on week 1

And , $ 900 > $ 860 > $ 715

Hence , the solution to the equation is week 1

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The length of the median = 6[tex]\sqrt{3}[/tex]

If we call the longer base "a" and the shorter base "b", then we know that:

a:b = 2:1

Since the ratio of the four sides is 1:1:1:1, we know that the height, median and the longer base are all equal.

We can use that information to determine the area of the trapezoid. The formula for the area of a trapezoid is:

Area = (a + b) * h / 2

We know that the area is  27[tex]\sqrt{3}[/tex] and the height and median are equal, so we can set up the equation:

(a + b) * h / 2 = 27[tex]\sqrt{3}[/tex]

We also know that a:b = 2:1, so we can substitute that in:

(2b + b) * b / 2 = 27[tex]\sqrt{3}[/tex]

Simplifying, we get:

3b^2 = 54 * [tex]\sqrt{3}[/tex]

So the length of the median (h) is b

= [tex]\sqrt{(54 * \sqrt{3} / 3) }[/tex]

= 6[tex]\sqrt{3}[/tex]

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You had a better score relative to the rest of your class.

To compare the scores of you and your friend relative to the rest of their classes, we need to calculate the standard deviation of your score and your friend's score from the average of their respective classes.

A standard deviation of 2 means that 68% of the scores in the class fall within 1 standard deviation of the mean, or between 84 and 88 in the case of Mrs. Wilson's class. Since 88 is greater than 86 (the mean) and less than 2 standard deviations away (88-86 < 2*2=4) , so your score of 88 is better than the average score in your class.

On the other hand, 85 is less than 82 (the mean) and more than 1 standard deviation away (85-82 > 2) so your friend's score of 85 is less than the average score in their class.

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The common difference is 0.42. The comparison of each ratio's successive values over time for a single firm.

Now, According to the question:

What is meant by ratio?

Therefore, simplifying the equation then we get,

if you take the ranges (y) and subtract one from the other you get 0.42.

(22.84 - 22.42)/(2 - 1) = 0.42/1 = 0.42

(23.26 - 22.84)/(3 - 2) = 0.42

(23.68 - 23.26)/(4 - 3) = 0.42

Hence, The common difference is 0.42

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Answer:

Step-by-step explanation:

These are the tests for similar triangles:

AA - if 2 pairs of corresponding angles are equal.  

SSS - if corresponding sides have the same ratio.

SAS - if 2 pairs of corresponding sides have the same ratio and the included angles are equal.

This diagram does not indicate any of these relationships exist.

Therefore the triangles are not similar.

Answer:

R = 144400000/59 [this is a fraction]

Answer:

x = 11

Step-by-step explanation:

The two angles are consecutive interior angles so they add up to 180

13x -26 + 5x + 8 = 180

13x + 5x -26 + 8 = 180

18x - 18 = 180
18x = 180 + 18

18x = 198

x = 11

Answer: 4

Step-by-step explanation:

1. Question: 2x+1=9

2. Subtract 1 from the 9

Answer to step 2: 2x=8

3. Divide 8/2 (4x2)

4. Answer: x=4

Answer: X= 4; look below for the explanation of algebra tiles

Step-by-step explanation: First, we need to determine the value of x. We can use the rule of inverse operations. So, the opposite of addition is subtraction, and the opposite of multiplication is division. Now, using that, we start with the inverse operations of 1 + 9. That'd be 9 - 1. So, that's 8. Now, according to the order of inverse operations, we divide the 2 by 8. So, 8 divided by 2 is 4. Therefore x = 4.

Now, using the tiles, we need to get 8 tiles, + 1 tile, which should get you your answer. I hope this helped!

The value of the expression is -44 and thus does not depend on the value of x

An algebraic expression can be described as a mathematical expression made up of variables, terms, factors, coefficients and constants.

They are also made up of mathematical or arithmetic operations, which includes;

From the information given, we have that;

(x-5)(x+8)-(x+4)(x-1)

expand the bracket

x² + 8x - 5x - 40 - (x² -x + 4x - 4)

x² + 8x - 5x - 40 - x² + x - 4x + 4

collect like terms

3x - 3x - 40 - 4

add or subtract like terms

0 - 44

Hence, the expression does not depend o x

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Answer:

[tex]\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}[/tex]

Rewrite the third fraction:

[tex]\implies \dfrac{a^2}{36-a^2}=\dfrac{-a^2}{-(36-a^2)}=\dfrac{-a^2}{a^2-36}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Difference of two squares }\\\\$x^2-y^2=(x-y)(x+y)$\\\end{minipage}}[/tex]

Apply the difference of two squares to the denominator of the third fraction:

[tex]\implies a^2-36=a^2-6^2=(a-6)(a+6)[/tex]

Therefore the expression can be written as:

[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{-a^2}{(a-6)(a+6)}[/tex]

[tex]\implies \dfrac{a}{a-6}-\dfrac{3}{a+6}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

The least common multiplier (LCM) of the denominator is (a - 6)(a + 6).

Adjust the fractions based on the LCM:

[tex]\implies \dfrac{a(a+6)}{(a-6)(a+6)}-\dfrac{3(a-6)}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

Simplify:

[tex]\implies \dfrac{a^2+6a}{(a-6)(a+6)}-\dfrac{3a-18}{(a-6)(a+6)}-\dfrac{a^2}{(a-6)(a+6)}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}-\dfrac{d}{c}=\dfrac{a-b-d}{c}:[/tex]

[tex]\implies \dfrac{a^2+6a-(3a-18)-a^2}{(a-6)(a+6)}[/tex]

Simplify:

[tex]\implies \dfrac{3a+18}{(a-6)(a+6)}[/tex]

Factor out 3 from the numerator:

[tex]\implies \dfrac{3(a+6)}{(a-6)(a+6)}[/tex]

Cancel the common factor (a + 6):

[tex]\implies \dfrac{3}{a-6}[/tex]

Therefore:

[tex]\dfrac{a}{a-6}-\dfrac{3}{a+6}+\dfrac{a^2}{36-a^2}=\dfrac{3}{a-6}\quad \textsf{if}\;\;a \neq -6,a \neq 6[/tex]

The area of rectangle with side whole number = ab sq. units,

and area of rectangle with fraction side = ac/bd sq. units.

A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with four equally long sides.

Given  to find the area of rectangle,

Area of rectangle is given by product of length and width.

A = l x b

Let the dimensions of a rectangle are all whole numbers, a by b

Area = a x b

A = ab sq. units

another rectangle with dimensions all fractions say, a/b by c/d .

Area = a/b x c/d

A = ac/bd sq. units

In all situations, the area of the rectangle must be calculated by multiplying its length and breadth.

Hence the area of rectangle is product of length to width in both cases.

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The two side lengths are congruent, and their opposite angles are congruent, and the hypotenuse is the length of either leg times the square root of two, √2.

A 45° 45° 90° triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.

A 45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2.

properties of 45°-45°-90°:

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The ^ operator in logical mathematics means the OR operation . Therefore , the statement ∧ and ∠means that a or the negation of a is joined by the or operation .

These are known as logical operations as they are based upon logic.The meaning of the term logic is reasoning which means to resonate. The reasoning may be a legal opinion or mathematical confirmation.

We apply logic on expression to check whether they are true of false . Some of the mathematical logics are a negation, conjunction, and disjunction logical operations. The symbols used for them in mathematical logic is, ‘~’ for negation ‘^’ for conjunction and ‘ v ‘ for disjunction.

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Answer:

12?

Step-by-step explanation:

Lowkey don't understand the last part of your q but if it's 4 times then if the original was 12 48 is four times bigger

Answer:

4

Step-by-step explanation:

-28 = ±2^2 x ±7
60 = ±2^2 x ±3 x±5
72 = ±2^3 x ±3^2
=> Gcf of -28, 60, 72: 2^2 = 4

Answer: 12

Step-by-step explanation:

Therefore, the highest common factor of 60 and 72 is 12.

:) I know somebody already answered but like..im answering some stuff today, hope this helped by the way!

Answer:

All real numbers for both Range and Domain

R

or

(−∞,∞)