If one-third of the girls and one-half of the boys attend the Senior Dance, there will be a total of 205 students. If half the girls and all the boys attend, there will be 370 students.

How many students are in the Senior class?

The expected value with a sample size of 20 and a probability of 0.25 will be 5.

The anticipated value is an extension of the weighting factor in statistical inference. Informally, the anticipated value is the simple average of a significant number of outcomes of a randomly selected variable that was separately chosen.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

If x is a binomial random variable with n = 20 and p = 0.25. Then the expected value is given below.

E(x) = 20 x 0.25

E(x) = 5

The expected value with n = 20 and p = 0.25 will be 5.

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The gradient of line B is (-1).

The gradient of a line is used to calculate the steepness of a line and determines how much it is inclined with reference to the x-axis. To calculate the gradient of any line, the x and y coordinates of a line are used. In other words, it is the ratio of the change in the y-axis to the change in the x-axis.

The gradient is the measure of the steepness of a straight line.

Given:

coordinates taken from line B is (5, 0) and (-2, 7)

we have [tex]y_2[/tex]= 7, [tex]y_1[/tex]= 0, [tex]x_1[/tex]= 5, [tex]x_2[/tex] =-2

now, substituting the values then,

The gradient is

=[tex]( y_2- y_1)/ (x_2 - x_1)[/tex]

=(7-0) / (-2 - 5)

=7 /(-7)

=-1

Hence, the gradient is -1

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Answer:

3

Step-by-step explanation:

The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b (Wikipedia)

To find out which is the GCD of 72 and 159, keep factoring both until they cannot be factored any more

Then take the factors common to both list of factors; the greatest among them is the GCD

The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The factors of 159 are: 1, 3, 53, 159

The common factors are 1, 3

So GCD is 3

A composite function exists as a function that depends on another function. The value of f(g(x)) = x-8 and g(f(x)) = x-2.

In mathematics, function composition exists as an operation ∘ that takes two functions f and g, and has a function h = g ∘ f such that h(x) = g. In this operation, the function g exists used to the result of applying the function f to x.

Function composition is a mathematical procedure where two functions, f, and g, are taken and a function, h = g ∘ f, is produced such that h(x) = g(f(x)). The function g exists used in this operation on the outcome of applying the function f to x.

Let the two functions be f(x) = x+3  and g(x) = x-5

f(g(x)) = f(x-5)

simplifying the above equation, we get

f(x-5) = x-5+3

f(g(x)) = x-8

g(f(x))  = g(x+3)

simplifying th above equation, we get

g(x+3) = x+3-5

g(x+3) = x-2

Therefore, the value of f(g(x)) = x-8 and g(f(x)) = x-2.

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Answer:

10m + 100 = 15m

20 movies

Step-by-step explanation:

Hello!

Let the number of movies watched be m.

The equation for the first movie club would be 10m + 100, as you pay 10 dollars per movie (10*m) and you add the original membership fee (100).

The equation for the second movie club is 15m, 15 dollars per movie. Set the equations equal to each other and solve for m, the number of movies, so the price would be equal.

Therefore, you would need to watch 20 movies in each movie club for the total price to be equal.

Step-by-step explanation:

ED || AB

E is the midpoint of AC.

therefore, D is the midpoint of BC, and AB is 2×ED.

but also the height of ABC is 2×height of EDC.

now, we know, the area of a triangle is

baseline × height / 2

area EDC = baseline × height / 2 = 18 cm²

area ABC = 2×baseline × 2×height /2 =

= 4 × (baseline × height / 2) =

= 4 × area EDC = 4 × 18 = 72 cm²

the area of ABDE = area ABC - area EDC =

= 72 - 18 = 54 cm²

The simplest form of the expression [tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex] is [tex]13+7\sqrt{3}[/tex].

The simplest form of a fraction is one with a reasonably prime denominator and numerator. It indicates that, except for 1, there is no common factor between the fraction's numerator (upper portion or top) and denominator (lower part or bottom).

In elementary algebra, the procedure of rationalization is performed to get rid of the irrational number in the denominator. There are several methods for rationalizing the denominator.

An expression comprises a variable, a number, or a combination of a number, a variable, and operation symbols. An equation is created by joining two expressions with an equal sign.

Consider the expression,

[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} }[/tex]

Rationalizing the denominator,

[tex]\frac{5+\sqrt{3} }{2-\sqrt{3} } = \frac{5+\sqrt{3} }{2-\sqrt{3} } \times \frac{2+\sqrt{3} }{2+\sqrt{3}}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{(5+\sqrt{3})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}[/tex]

Using the identity,

( a + b )( a - b ) = a² - b²

Therefore,

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} =\frac{5 \times 2 + 5 \times \sqrt{3} + \sqrt{3} \times 2 + (\sqrt{3} )^{2}}{(2)^{2}-(\sqrt{3} )^{2}}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{10+7\sqrt{3}+3}{4-3}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = \frac{13+7\sqrt{3}}{1}[/tex]

[tex]\frac{5+\sqrt{3}}{2-\sqrt{3}} = 13+7\sqrt{3}[/tex]

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The expressions that can be used to find the total profit in tokens that Marcelo made is (7 × 6) - (3 × 7) and 42 - 21.

From the information, Marcelo plays a carnival game six times he spent three tokens to play each game and he won 7 tokens each game.

The appropriate expression will be:

= (7 × 6) - (3 × 7)

= 42 - 21

= 21

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It should be noted that the quotient of y and 27 will be y ÷ 27. The correct option is A.

It should be noted that quotient simply means the quantity that's produced when two numbers are divided. A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio. The quotient is the result of dividing two numbers by each other. As in the case of 8 4 = 2, when the division produced the number 2, the outcome is the quotient. The dividend is 8, while the divisor is 4.

When we divide a number, the result we ultimately get is the quotient. The mathematical symbol (÷ ) denotes division, a technique for allocating items equally among groups.

In their case, the quotient of y and 27 simply means the division of the numbers. This will be y ÷ 27.

Therefore, the correct option is A.

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Answer:

-3.625 < -3.62

Step-by-step explanation:

Solution :

the coordinates for W′ = (-1,3)

Trapezoid :

A trapezoid is necessarily a convex quadrilateral in Euclidean geometry. The parallel sides are called the bases of the trapezoid. The other two sides are called the legs (or the lateral sides) if they are not parallel; otherwise, the trapezoid is a parallelogram, and there are two pairs of bases). A scalene trapezoid is a trapezoid with no sides of equal measure

Y = (-2,1)

Y' = (0,3)

Unit shift for Y to Y'

By distance formula :

yy' = [tex]\sqrt{{(x2-x1})^{2} +( y2-y1)^{2} }\\[/tex]

= root of (2)^2 +(2^2)

= root of 4+4

Root of 16

= root of 4

Unit shift for Y to Y' = 4

then

w = (-5,-1)

shift by adding 4

W' = (-5+4, -1+4)

W' = (-1,3)

the coordinates for W′ = (-1,3)

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The trinomial form of the given expression (2x-2)(2x+8) is 4x² + 12x - 16.

Given the expression in the question;

(2x-2)(2x+8)

Expand using FOIL Method.

Apply distributive property

(2x-2)(2x+8)

2x( 2x + 8 ) -2( 2x + 8 )

Apply distributive property

2x(2x) + 8(2x) -2(2x) + 8(-2)

Perform the operation

2x(2x) + 8(2x) -2(2x) + 8(-2)

4x² + 16x - 4x - 16

Combine like terms

4x² + 16x - 4x - 16

4x² + 12x - 16

Therefore, the trinomial form of the given expression (2x-2)(2x+8) is 4x² + 12x - 16.

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Answer: (10, 8)

Step-by-step explanation:

To solve a substitution question, you have to make sure either x or y is alone on the other side of equal sign.

-x + y = -2

^^^this becomes y = -2 + x

Now, since you know what "y" is, you simply replace "y" with our new equation in the other equation.

-x - 2(-2+x) = -26

Then, you do order of operations to get the answer.

First, do distributive property.

-x + 4 - 2x = -26

Next, solve the equation.

-3x + 4 = -26

-3x = -30

x = 10

Since you found what "x" is, you substitute "x" and in one of your equations to find "y", it doesn't matter which one.

-(10) + y = -2

-10 + y = -2

y = 8

Finally, after you got "x" which is 10, and "y" which is 8, you put them in an ordered pair (x, y) which is (10, 8).

P.S. I use Sora and Deltamath too!

The expression of the length of one of the sides of the window is √114

The area of a shape is the amount of space on the shape

The area of the window is given as

Area = 114 square feet

The shape of the window is a square

The area of a square is calculated as

Area = Length^2

So, we have

114 = Length^2

Take the square root of both sides

Length = √114

Hence, the expression of the length of one of the sides of the window is √114

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The rational numbers ordered from smallest to largest are given as follows:

-3², -3, sqrt(3), 4, 5, 2³.

Rational numbers are numbers that can be represented by fractions, such as integers and terminating or repeating decimals.

They are ordered as follows:

negative infinity, ..., -5, ..., -3, ..., 0, ..., 3, ..., 5, ..., positive infinity.

That is, large negative are the smallest, and large positives are the greatest.

For this problem, the numbers are given as follows:

Hence the ordering, from least to greatest, of the numbers is given as follows:

-3², -3, sqrt(3), 4, 5, 2³.

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A) The percentage represented in each picture is as follows:

A-1) 80%

A-2) 12.5%

A-3) 10%

B) The portion represented in each picture is written as a fraction as follows:

B-1) 80% = 8/10 or 4/5

B-2) 12.5% = 1.25/10 or 1/8

B-3) 10 = 1/10 or 2/20

A percentage is a fraction of 100.

A percentage is also a ratio, showing how much of the whole is contained by the portion.

Percentages are written with the percentage sign (%).

A-1) 80% for A 10 by 10 block of 100 where 8 columns of 10 are shaded.

A-2) 12.5% for A 10 by 10 block of 100 where the first row, and 2 and a half squares of the second row are shaded.

A-3) 10% for A 10 by 10 block of 100 where 1 row of 10 is shaded.

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Answer:6

Step-by-step explanation:

when x is -1 y is 6. input -1 as x in the equation and solve, otherwise graph.

According to the empirical​ rule,  95% will be within two standard deviations of the mean.

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).

Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean. Three-sigma limits that follow the empirical rule are used to set the upper and lower control limits in statistical quality control charts and in risk analysis such as VaR.

The empirical rule is used often in statistics for forecasting final outcomes. After calculating the standard deviation and before collecting exact data, this rule can be used as a rough estimate of the outcome of the impending data to be collected and analyzed.

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The greatest number of groups Evelyn can place her stuffed animals into

= 6 Groups.

We have been given that

Evelyn should donate her collection of stuffed animals in which

No. of stuffed cats = 18

No. of stuffed dogs = 12.

We have to find out  number of groups with no stuffed animals left over.

for solving this question we can use GCF

What is GCF (Greatest Common Factor)?

The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share.

How can we find GCF?

The greatest common factor is the greatest factor that divides both numbers. To find the greatest common factor, first list the prime factors of each number.

18 and 12 share one 2 and one 3 in common. We multiply them to get the GCF, so 2 * 3 = 6 is the GCF of 18 and 12.

The common factors of 12 and 18 are 1, 2, 3 and 6. The greatest common factor of them is 6.

In each groups no. of cats and dogs are (3cats , 2 dogs)

Hence , 6 is the greatest number of groups Evelyn can place her stuffed animals into.

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a) The approximate sum of the numbers by first rounding each number is 74,600

b) The exact sum of the numbers rounded to the nearest hundred is 74,500

From the question, we are determine the approximate sum of the given numbers

The given numbers are

34,856 and 39,670

a) Round 34,856 to the nearest hundred

34,856 to the nearest hundred is 34,900

Also,

Round 39,670 to the nearest hundred

39,670 to the nearest hundred is 39,700

Now,

Add the rounded numbers

34,900 + 39,700 = 74,600

b) The exact sum of the numbers is

34,856 + 39,670 = 74,526

Rounding the result to the nearest hundred

74,526 rounded to the nearest hundred is 74,500

Hence, the exact sum of the numbers rounded to the nearest hundred is 74,500

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If the equation 8x+7y=6 is a true equation, then  the value of the equation 5+8x+7y is 11

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The equation is given as

8x + 7y = 6

The above equation is said to be true

The next step is to add 5 to both sides of the equation 8x + 7y = 6

So, we have

5 + 8x + 7y = 6 + 5

Evaluate the sum of the like terms

So, we have

5 + 8x + 7y = 11

Hence, if the equation 8x+7y=6 is a true equation, then  the value of the equation 5+8x+7y is 11

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Answer:

Points A B D

Step-by-step explanation:

I am assuming in the plane, all the points are inside. For it to be non- collinear, I am pretty sure there has to be points not on the line. In this Case, only A C D are actually on a line. Since B is to the right of C, I don't think that will make a good line. So that is the answer I am going with.

Answer:

d)a ,b,d

Step-by-step explanation:

Answer:

can you add a photo of the questions? So it's easier to see

The best there terms of the sequence will be:

a. 10, 16

b. 211, 311

c. 10 , 12.5

d. -13, -22

It should be noted that in an arithmetic sequence, there is a constant difference, which is the difference between a term and the previous term.

We find the constant difference for each sequence, and we add it to the second term to find the third term. Then we add the constant difference to the third term to find the fourth term.

a. 4 - (-2) = 6

3rd term: 4 + 6 = 10

4th term: 10 + 6 = 16

b. 111 - 11 = 100

3rd term: 111 + 100 = 211

4th term: 211 + 100 = 311

c. 7.5 - 5 = 2.5

3rd term: 7.5 + 2.5 = 10

4th term: 10 + 2.5 = 12.5

d. -4 - 5 = -9

3rd term: -4 + (-9) = -13

4th term: -13 + (-9) = -22

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Here are the first two terms of some different arithmetic sequences:

a. -2,4

b. 11, 111

C. 5, 7.5

d. 5,-4

What are the next three terms of each sequence?

Step-by-step explanation:

domain = (0,2)

range=(4,-4)

funcion =quadratic

The result of simplifying the number 32¹.² using the exponent rules is 1024

To solve this exercise we have to resolve algebraic operations following the exponent rules.

Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:

(32¹)²

32⁽¹*²⁾ =

32² =

32 * 32 =

1024

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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2nm = 2e-7 cm or written out 0.0000002 cm

To convert nm to cm, you have to divide the value by 1e+7 (10000000).

The sum of its integer and fractional parts is 5 + (-7) + 1/3 + 2/3. Option D

Fractions are defined as part of a whole.

The types of fractions include:

Given the expression;

5 1/3 + -7 2/3

The integers are:

5 and -7

The fractions are;

1/3 and 2/3

The sum of the integers and fractional parts are;

5 + (-7) + 1/3 + 2/3

Thus, the sum of its integer and fractional parts is 5 + (-7) + 1/3 + 2/3. Option D

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In linear equation , the car y's price changes the most.

What are a definition and an example of a linear equation?

According to the question

a)  Car x : £ 10320  ≈  £ 10300        10320 - 10300 = 20

    Car y  : £ 15430 ≈ £ 15400          15430 - 15400 = 30

    Car z   :  £ 17490 ≈  £ 17500        17490 - 17500  = 10

                   10 < 20 < 30

so the car y's price changes the most.

b) this car's price change £ 30

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The composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

In mathematics, function composition is an operation in which two functions, f and g, generate a new function, h, in such a way that h(x) = g(f(x)). This means that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Define fog, the composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

In math, the domain (the x-values) of one function becomes the range (the y-value answers) of the next function. Composition notation is as follows: (f o g)(x) = f(g(x)) and exists read “f composed with g of x” or “f of g of x”.

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