Students in two classrooms were given a mathematics test. The first classroom had 25 students and their average score was 86%. The second classroom had 15 students and their average score was 94%. If the teacher combined the test scores of students in both classes, what is the average score for both classes?​

The arithmetic mean of the numbers is -6 11/15

Arithmetic mean is often referred to as the mean or arithmetic average. It is calculated by adding all the numbers in a given data set and then dividing it by the total number of items in that set.

therefore, arithmetic mean= sum of items/ no of items

The average of numbers,7, 17, 1/3 ,-2/5, -12 ,7, - 121, 49,-16,-9and 4 is obtained by adding the numbers to together and dividing the result by the total frequency.

The sum of the numbers is 7 +17 +1/3-2/5 -12+7 - 121+ 49-16-9+ 4= -1111/15

the total number of items in the set is 11

therefore arithmetic mean = -1111/15÷ 11

= -1111/15×1/11

=-101/15

= -6 11/15

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The triangle proof that shows that angle Q and angle S are congruent to each other is explained below.

The side-angle-side congruence theorem (SAS) states that if the two sides and an included angle in one triangle is congruent to two corresponding sides and an included angle in the other triangle, then both triangles are congruent to each other.

If two triangles are congruent to each other, the CPCTC theorem states that all their corresponding parts are also equal or congruent to each other.

The triangle proof is given as:

Statements                                     Reasons                                                      

1. PR bisects ∠PQS                        1. Given

2. ∠1 ≅ ∠2                                      2. Definition of bisection

3. PQ ≅ PS                                     3. Given

4. RP ≅ PR                                     4. Reflexive property

5. ΔQPR ≅ ΔSPR                           5. SAS theorem

6. ∠Q ≅ ∠S                                    6. CPCTC

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The markup price on the table would be $32.

So, we have:

Now, calculate the makeup price:

Mark-up price = Discount * Selling Price

Mark-up price = (28/100) * 114

Mark-up price  = 31.92

Mark-up price ≈ 32.

Hence, the markup price on the table would be $32.

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a) The amount of money in the account at the beginning is $222,222.222.

b) The total amount of money withdrawn from the account is $400,000.

c) The amount of interest earned is $177,777.778.

It is given that we want to be able to withdraw $20,000 per year for 20 years. The account earns 9% interest annually. Let the total amount of money withdrawn in the twenty years be represented by the variable "A".

A = $20,000*20 = $400,000

Let the amount of money in the account at the beginning be represented by the variable "P".

A = P*R*T

400,000 = P*0.09*20

400,000 = P*1.8

P = 222,222.222

The interest earned is the difference between the initial and the final amount in the bank. Let the interest earned be represented by the variable "I".

I = A - P = $400,000 - $222,222.222 = $177,777.778

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Answer:

10 inches

Step-by-step explanation:

What this question is asking you to do is set up a ratio. So all you do is 14/70 = x/50 and solve for x.

Answer:

14inches = 70cents

X inches = 50cents

70x = 50×14

70x = 700

X = 10inches

The equation of the parabola which passes through the point (-3, -8) as described and has x-intercepts -7 and -4 as described is; y = -2 (x + 4) (x + 7).

It follows from the task content that the equation of the parabola whose x-intercepts are -7 and -4 and has the point, (-3, -8) on it be determined.

Since the equation of a parabola in the factored form usually takes the form;

y = a (x - f) (x - g) in which case when f and g are x-intercepts of the parabola.

Therefore, we have; y = a (x - (-4)) (x - (-7))

y = a (x + 4) (x + 7)

Hence, to find the value of a, we set y = -8 and x = -3 so that we have;

-8 = a (-3 + 4) (-3 + 7)

-8 = 4a

a = -2.

Therefore, the equation of the parabola is; y = -2 (x + 4) (x + 7).

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Periods are the rows that span the periodic table. Families or groups are the columns that go from Page 2 up.

The maximal energy level of the electrons serves as a marker for the period (or row) in the periodic table that an atom belongs to (1 through 7). The table has 7 periods, hence there are 7 energy levels. The first period's atoms have electrons in the first energy level. The second period's atoms have electrons in two different energy states. The third period's atoms have electrons in three different energy levels. The fourth period's atoms have electrons in four different energy levels. Typically, the number of the period itself is the same as the number of energy levels in each period. The first period's atoms have electrons in the first energy level.

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Answer:

------------------------------

The exact value of the sine of angle 78° sin(78°) is presented as follows;

[tex]sin(78^{\circ}) = \dfrac{\sqrt{5}-1+\sqrt{\sqrt{5}\cdot \left(6+6\cdot \sqrt{5} \right) } }{8}[/tex]

The sine of an angle is found by taking the ratio of the opposite side to the hypotenuse side of a right triangle that has the specified angle.

The sine of angle 78° is found from the sine of the sum of two angles (60° + 18°)  as follows;

sin(78°) = sin(60° + 18°)

sin(A + B) = sin(A)·cos(B) + cos(A)·sin(B)

Therefore, sin(78°) = sin(60° + 18°)  = sin(60)·cos(18°) + cos(60°)·sin(18°)

Where, 18° = A, we have;

5·A = 90°

2·A = 90° - 3·A

sin(2·A) = sin(90° - 3·A) = cos(3·A)

2·sin(A)·cos(A) = 4·cos³(A) - 3·cos(A)

2·sin(A)·cos(A) - (4·cos³(A) - 3·cos(A)) = 0

2·sin(A) - (4·cos²(A) - 3) = 0

2·sin(A) - (4·(1 - sin²(A)) - 3) = 0

4·sin²(A) - 2·sin(A) - 1 = 0

Which gives;

[tex]sin(A) = \dfrac{-1\pm \sqrt{5} }{4}[/tex]

cos²(18°) = 1 - sin²(18°)

cos(18°) = √(1 - sin²(18°))

[tex]cos(18^{\circ}) =\sqrt{1 - \left( \dfrac{\sqrt{5} -1 }{4}\right)^2} = \dfrac{1}{4} \cdot \sqrt{10+2\cdot \sqrt{5} }[/tex]

[tex]cos(18^{\circ}) = \dfrac{1}{4} \cdot \sqrt{10+2\cdot \sqrt{5} }[/tex]

Therefore;

[tex]sin(78^{\circ})=\dfrac{\sqrt{3} }{2} \cdot \left( \dfrac{1}{4} \cdot \sqrt{10+2\cdot \sqrt{5} }\right) +\dfrac{1}{2} \cdot \left( \dfrac{\sqrt{5} -1 }{4}\right)= \dfrac{\sqrt{5}-1+\sqrt{\sqrt{5}\cdot \left(6+6\cdot \sqrt{5} \right) } }{8}[/tex]

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The value of g(x) is √2x.

What is a composite function?

A function whose values are obtained from two given functions by first applying one to an independent variable and then using the result to apply the second, and whose domain is made up of those independent variable values for which the first function's result falls within the second function's domain.

Here, we have

g(f(x)) =x√6.

f(x) = 3x²

By applying a composite function

g(f(x)) =√6x

g(3x²) = x√6

g(x) must be √(2x)

because if we  substitute  x = 3x² in this we get

= (√2(3x^2))

= √2√3√(x²)

= √6 x

Hence, the value of g(x) is √2x.

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The phrase that represents the algebraic expression n - 4 is option b four less than a number.

Given,

The algebraic expression; n - 4

We have to find the phrase that represents the given algebraic expression.

Algebraic expression;

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

An algebraic expression can be categorized into different categories depending on how many terms it contains: polynomial, quadrinomial, trinomial, monomial, and binomial.

So,

n - 4

That is,

4 is less than from a number

Therefore,

The phrase that represents the algebraic expression n - 4 is option b four less than a number.

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Answer:

the answer is b

Step-by-step explanation:

The value of c for the expression, -0.65(c-7) = 1.95, is 4.

According to the question,

We have the following expression:

-0.65(c-7) = 1.95

Now, 0.65 is in multiplication on the left hand side. So, it will be in the division on the right hand side. Note that the negative sign can also be moved to the right hand side.

c-7 = -1.95/0.65

c-7 = -3

Moving 7 from the left hand side will result in the change of the sign from minus to plus:

c = -3+7

c = 4

Hence, the value of c is 4 for the given expression.

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Line AD and line EG are parallel line, Transversal CH < ABC and EFH  are same side exterior angles

The presence of two parallel lines and a transversal line leads to some important theorem used in geometry

Some of the theorems include

The exterior angles refers to angles above line AD and below line EG, which are the parallel lines. These angles according to the figure are 4 and they include

The exterior angles to the left of the transversal line forms a pair of same side exterior, similarly, to the right of the transversal line forms another pair of same side exterior angles.

The question is asking  of same side exterior angles to < ABC, which is to the left of the transversal line. The pair that are same side exterior angles to the left of the transversal line are

Hence < EFH and < ABC are same side exterior angles

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Answer:

If you let 'n' to represent a number then '-9 times a number' can be written as -9n

'less then' means subtraction:  12 less then -9 times a number  becomes -9n - 12 (the subtraction in the equation is written in the opposite way as written in words)

'8 minus 4 times the number ' becomes 8 - 4n

So, the equation is:  -9n - 12  =  8 - 4n

Get all the variables to one side. If you add  9n  to both sides:

   -9n + 9n - 12  =  8 - 4n + 9n

   -12  =  8 + 5n

Subtract 8 from both sides:

   -12 - 8  =  8 - 8 + 5n

   -20  =  5n

Divide both sides by 5:

   -20 ÷ 5  =  5n ÷ 5

   -4  =  n

Now, check the answer:   -9n - 12  =  8 - 4n

              -9(-4) - 12  =  36 - 12  = 24                 8 - 4(-4)  =  8 + 16  = 24        They check!

Step-by-step explanation:

Hope this helps! :)

The percentage increase for each of the given figures are;

a) 6%

b) 6%

c) 12%

Percentage increase is simply defined as the percentage by which a figure increases. The formula to calculate percentage increase is;

Percentage increase = (Final value - Initial Value)/initial value) * 100%

a) We are given;

Original quantity = 100

New quantity = 106

Thus;

Percentage increase = (106 - 100)/100 * 100%

Percentage increase = (6/100) * 100%

Percentage increase = 6%

b) We are given;

Original quantity = 10

New quantity = 16

Thus;

Percentage increase = (16 - 10)/10 * 100%

Percentage increase = (6/10) * 100%

Percentage increase = 60%

c) We are given;

Original quantity = 50

New quantity = 56

Thus;

Percentage increase = (56 - 50)/50 * 100%

Percentage increase = (6/50) * 100%

Percentage increase = 12%

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Complete question is;

Find the percent increase for the given original and new quantities in parts a through c.

a) Original quantity:100 New quantity:106

b) Original quantity:10 New quantity:16

c) Original quantity:50 New quantity:56

Answer:

1.7 gallons

Step-by-step explanation:

You would chand the 1/2 and 4/5 into tenths by multiplying 1/2 by 5 getting 5/10 then multiplying 4/5 by 2 to get 8/10 so you would have 13 5/10- 11 8/10 to get 1.7 gallons left.

Answer:

- 18

Step-by-step explanation:

let the number be n then double the number is 2n and

2n + 32 = [tex]\frac{2}{9}[/tex] n

multiply through by 9 to clear the fraction

18n + 288 = 2n ( subtract 2n from both sides )

16n + 288 = 0 ( subtract 188 from both sides )

16n = - 288 ( divide both sides by 16 )

n = - 18

the original number is - 18

The ratio of the volume of the triangular prism to the volume of

 the cuboid is 3: 20

What do you mean by prism?

The base of the triangular prime is a right triangle with legs 5 cm, 4 cm

∴ b = 5 cm and h = 4 cm

∵ Its height is 9 cm

∴ H = 9 cm

→ Substitute them in the rule of the prism above

∵ V =  1/2 * (5)(4) × 9

∴ V = 90 cm³

∵ The dimensions of the base of the cuboid are 6 cm and 5 cm

∴ L = 6 cm and W = 5 cm

∵ Its height is 20 cm

∴ H = 20 cm

→ Substitute them in the rule of the cuboid above

∵ V = 6 × 5 × 20

∴ V = 600 cm³

→ Find the ratio between them

∵ V: V = 90: 600

→ Divide each term of the ratio by 30 to simplify them

∴ V: V = 3: 20

∴ The ratio of the volume of the triangular prism to the volume of

 the cuboid is 3: 20

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Trignometric equation can be used to answer this:

acc to our question-

5. cos(75)= 2-√3

6. tan(22/7)= 1+√2

7. sin 3π/6= √2-√√2/2

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The fraction that represents the percentage of 57% is presented as follows:

57/100.

A fraction is represented by the division of a term x by a term y, according to the equation presented as follows:

Fraction = x/y.

The terms are know as numerator and denominator, respectively, as follows:

For a percentage of a%, the equivalent fraction is obtained as follows:

Hence, for a percentage of 57%, as is the case in this problem:

Hence the fraction is:

57/100.

The problem asks to represent the percentage as a fraction.

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Answer:

[tex]r=\frac{21}{20}[/tex]

Step-by-step explanation:

Given the following question:

[tex]\frac{1}{4} =r-\frac{4}{5}[/tex]
Add 4/5s on both sides:
[tex]-\frac{4}{5} +\frac{4}{5} =0[/tex]
[tex]\frac{1}{4} +\frac{4}{5}[/tex]
Find the LCM:
[tex]\frac{5}{20}+\frac{16}{20}[/tex]
[tex]\frac{5+16}{20}[/tex]
[tex]\frac{21}{20}[/tex]
[tex]r=\frac{21}{20}[/tex]

Hope this helps.

let's firstly convert the mixed fraction to improper fraction, now keeping in mind that the LCD of the denominators 4 and 5 is 20, let's use that LCD to do away with the denominators.

[tex]\stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{9}{4}=r-\cfrac{4}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( -\cfrac{9}{4} \right)=20\left( r-\cfrac{4}{5} \right)}\implies -45=20r-16 \\\\\\ -29=20r\implies -\cfrac{29}{20}=r\implies -1\frac{9}{20}=r[/tex]

The linear function with values of f(-1)=8 and f(5)=6 is  f(x) = [tex]\frac{-x+23}{3}[/tex].

What is linear function?

 A straight line on the graph has the equation or formula y = f(x) = px + q is linear function .One independent and one dependent variables are present. X and Y are the independent and dependent variables, respectively. P is the y-intercept or constant term, and it also represents the value of the dependent variable. A straight line on the coordinate plane is represented by a linear function.

Here the given  values are f(-1)=8 and f(5)=6.

We know that f(x)=y , Then the points are (-1,8) and (5,6).

Using slope formula ,

=> slope m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = -2/6=-1/3

Now using slope formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=>y-8=-1/3(x+1)

=>3y-24=-x-1

=> 3y=-x+23

=> y = [tex]\frac{-x+23}{3}[/tex]

Hence the linear function is f(x) = [tex]\frac{-x+23}{3}[/tex].

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If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.

What is a combination?

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

Here,

There are 4 numbers needed for the combination and one can pick between 0 and 32.

This means that there are 33 numbers that can be used for the lock including 0.

The number of possible combinations is:

= Number that can be used with no restrictions on the number combination lock limit

= 33 ⁴

= 1,185,921 combinations

Hence, If there are no restrictions on the numbers then the possible number of combinations is 1,185,921.

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The value of cos 2A/cos A-sin A = cos A + sin A is proved

cos 2A =  2cos²A - 1

= 2cos²A - (sin²A + cos²A)

= 2cos²A - sin²A - cos²A

= cos²A - sin²A

We need to prove that

cos 2A/cos A-sin A = cos A + sin A

L.H.S

cos 2A/cos A-sin A

= cos²A - sin²A/ cos A-sin A

= (cos A + sin A)(cos A-sin A)/ cos A-sin A

= cos A + sin A

R.H.S

LHS = RHS proved

Therefore, cos 2A/cos A-sin A = cos A + sin A is proved

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Graph for the modulus function is as follows.

What is modulus function?

A modulus function is a function that determines a number or variable's absolute value.

Main body:

Given that,

Which graph represents the function f(x) = 4⌈x⌉?

Now,

to represent the graph of Y =  IxI-4 .

So,

Taking x = 0, we get

Y =  IxI -4

Y =  I0I -4

Y = -4

Taking x = 1, we get

Y =  IxI - 4

Y =  I1I -4

Y = -3

Taking x = 2, we get

Y =  IxI - 4

Y =  I2I - 4

Y = -2.

Taking x = -1, we get

Y =  IxI - 4

Y =  I-1I - 4

Y = 1 -4

Y = -3

Taking x = -2, we get

Y =  IxI - 4

Y =  I-2I - 4

Y = -2

Hence the graph for the function is as follows.

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The unit rate of cups of lemonade per lemon is in the ratio of 6:1.

The unit rate is the ratio of two or more quantities or values that are compared to one another.

Unit rates are also known as the constants of proportionality, constant rate, rate of change, or slope.

The number of lemons required to make 18 cups of lemonade = 3 lemons

Rate of lemonade per lemon = 18/3 = 6/1

Ratio = 6:1 or 1:6

Conversely, the rate of lemon per cup of lemonade = 1/6

Thus, we can conclude that for Zendaya to make 6 cups of lemonade, she requires 1 lemon, or alternatively, the ratio of lemon to a cup of lemonade is 1:6.

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Answer:

  (d)  24/49

Step-by-step explanation:

You want to know P(A|B) when P(AB) = 3/7 and P(B) = 7/8.

The general equation for conditional probability tells you ...

  P(A|B) = P(AB)/P(B)

  P(A|B) = (3/7)/(7/8) = (3/7)·(8/7)

  P(A|B) = 24/49

Answer:

0.6

Step-by-step explanation:

3/4 of 4/5 is the same as asking: If you take 3/4 of 4/5, what do you get? Furthermore, 3/4 is 75 percent. Therefore, we are solving 75 percent of 4/5 when we are solving 3/4 of 4/5. To solve the problem, we start by labeling 3/4 of 4/5 like this: N1/D1 of N2/D2

Then we use this fraction of a fraction formula to solve the problem:

(N1 x N2) / (D1 x D2)

When we enter 3/4 of 4/5 into the formula, we get:

(3 x 4) / (4 x 5) = 12/20

Therefore, the answer to 3/4 of 4/5 in its lowest form is:

3/4 of 4/5 = 3/5

The answer above is 3/4 of 4/5 in fraction form. Below we have converted the response to a decimal form for you: 3/4 of 4/5 = 0.6

Hint: If you need to figure out a Fraction of Fraction problem like 3/4 of 4/5 in the future, remember that you get the answer by multiplying the numerator to and the denominator this is the same as multiplying the fractions together.

The value of f after solving the expression, 2-f/4 = f-3f/4+3, is -2.

According to the question,

We have the following expression:

2-f/4 = f-3f/4+3

We know that to find the value of f we will have to move the terms with the same variable on one side. Now, moving f and 3f/4 from the right hand side to the left hand side will result in the change of their signs.

3f/4-f/4-f +2 = 3

Moving 2 from the left hand side to the right hand side:

3f/4-f/4-f = 3-2

Taking the least common factor as 4:

(3f-f-4f)/4 = 1

(-2f)/4 = 1

Using the cross multiplication method:

-2f = 4

f = -4/2

f = -2

Hence, the value of f for the given expression is -2.

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