At the north campus of a performing arts school, 30% of the students are music majors. At the south campus, 80% of the students are music majors. The campuses are merged into one east
campus. If 65% of the 1000 students at the east campus are music majors, how many students did each of the north and south campuses have before the merger?

Check the picture below.

notice, the function namely f(x) or "y", has a hole at (-3 , 2), that means that the values for the range are anything less than 2, but never 2, so 1.1 is ok, 1.99 is also good, 1.999999999999999 is also ok, but never 2, thus y < 2.

Let's also notice, the arrowhead means the graph keeps on going to the left as well as to the bottom.

Answer:

(36^7+6^13) is divisible by 7.

Step-by-step explanation:

(36^7+6^13)

First, solve the parentheses and exponents within it.

36^7=36*36*36*36*36*36*36=78364164096

6^13=6*6*6*6*6*6*6*6*6*6*6*6*6=13060694016

Add 78364164096 and 13060694016.

It equals 91424858112.

Divide 91424858112 by 7.

It results in 13060694016.

Hence, yes.

Hope this helps.

In equation (1) the value of y = 3/5 and In equation (2) the value of y = 5/4

In the given statement is

Solve 2x + 5y = -1 for y.

To find the value of y when x= -2

Now, Equation is 2x + 5y = -1 …..(1)

Put the value of x = -2 in eq. 1

2 (-2) + 5y = -1

-4 + 5y = -1

5y = -1 + 4

y = 3/5

Again,  Solve 2xy - x = 3 for y

To find the value of y when x = 2

Now, Equation is : 2xy - x = 3 ….(2)

Put the value of x = 2 in eq. (2)

2(2)y - 2 = 3

4y - 2 = 3

4y = 5

y = 5/4

Hence, In equation (1) the value of y = 3/5 and In equation (2) the value of y = 5/4

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Answer: 8 dollars and 10 cents

Step-by-step explanation:

5.40 divided by 12 = .45

This means that each juice costs 45 cents

.45x18=8.10

Answer:

$8.10

Step-by-step explanation:

$5.40/12=$0.45 $0.45*18=$8.10

The expression given by (1/2)⁻¹ is equivalent to 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

(1/2)⁻¹

Taking the negative one exponent gives:

= 2 / 1

Simplifying the equation gives:

= 2

The expression given by (1/2)⁻¹ is equivalent to 2

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The average temperature decrease of -6.5 degrees/km Celsius is known as Normal lapse rate.

Normal lapse rate is defined as the decrease in the temperature while moving upwards in the atmosphere. Normally, the rate of decrease is 1 degree Celsius for every 165 meter rise in altitude or we can say that it is 6.5 degree Celsius for every 1 km rise in altitude.

This lapse rate is known as normal lapse rate or environmental lapse rate.

This is why when we move higher in the atmosphere, we experience low temperatures. On average this decrease is equal to the amount of temperature as discussed in the normal lapse rate.

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(5 , -2)

Step-by-step explanation:

mid point = ( (X1 + X2)/2 , (Y1 + Y2)/2 )

= ( (8 + 2)/2 , (-7 + 3)/2 )

= (5 , -2)

The investor should expect $1716.24375 at the end of 15 years .

Formula for calculation of Simple Interest :

Simple Interest = ( Rate * Principal * no . of years ) / 100 , when no additional investment is made .

Here , principal = $1760.25 , rate = 6.5 , no . of years = 15 .

Substituting values in formula above ,

SI = ( 6.5 * 1760.25 * 15 ) / 100

     = 1716.24375

Hence , the investor should expect $1716.24375 at the end

of 15 years .

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Answer:

Step-by-step explanation:

93959453

Answer:

(4/3)

Step-by-step explanation:

  1                5

---------  +  --------

  2              6

  1 (3)          5

---------  +  --------

  2(3)          6

  3            5            8

-------  +  -------  =  -------

  6           6             6

  8  ÷  2            4

-------        =     -------

  6  ÷  2             3

I hope this helps!

Step-by-step explanation:

or, 55° = (4x - 1)° [ vertically opposite angle ]

or, 55° + 1° = (4x)°

or, 56° = (4x)°

or, 56°/4° = x

or, x = 14°

Therefore the value of x is 14° .

The consecutive page no. are 126 and 127.

An example of a run of consecutive integers is 1, 2, 3, 4. Another illustration is 7, 8, and 9. An integer sequence is a set of numbers where each term is one more than the term before it.

Continually following one another, from smallest to greatest, are consecutive numerals. For instance, the sequence of the numerals 1, 2, 3, 4, 5, and so forth.

The next two numbers are (n + 1) and (n + 2) if n is an integer. Take 1 for n as an example. Its subsequent numbers can be read as (2 and 3), or as (1 + 1) and (1 + 2).

let the consecutive page numbers be x and x+1

according to question ,

          x + x + 1 = 253

          2x = 252

            x = 126

so the consecutive page numbers are 126 and 127.

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Answer:

Step-by-step explanation:

[tex]\displaystyle\\\frac{10px^2}{3c^2d} \div\frac{5px}{6c^2d^2} =\\\\\frac{10px^2}{3c^2d}*\frac{6c^2d^2}{5px} =\\\\\frac{60c^2d^2px^2}{15c^2dpx^2} =\\\\4d\\\\\\\frac{3}{x+7} \div\frac{8x^2-8x}{x^2+6x-7} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{x^2-x+7x-7} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{x(x-1)+7(x-1)} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{(x-1)(x+7)} =\\\\\frac{3}{x+7} \div\frac{8x}{x+7} =\\\\\frac{3}{x+7} *\frac{x+7}{8x} \\\\\frac{3(x+7)}{8x(x+7)}=\\\\\frac{3}{8x}[/tex]

The total cost of the shirts that the foreign student buy will be 48.71 Krona.

From the information, the person finds a special deal, 7 t-shirts for $07.93, that she would like to purchase for her family.

Therefore, the total cost will be:

= $7.93 / 7 × 5

= $5.66

Therefore, the amount when converted to Krona will be:

= $5.66 × 8.6064

= $48.7

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Answer:

The answer is C "608.313 Krona"

Step-by-step explanation:

Got it right on my quiz.

The value of the expression (7 - 1/4 × ✓16)² + (2 - 5)² is 45.

Based on the information given, the expression will be:

(7 - 1/4 × ✓16)² + (2 - 5)²

= (7 - 1)² + (-3)²

= 6² + 3²

= 36 + 9

= 45

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Answer:

x = 100, y = 80

Step-by-step explanation:

100° and x° are alternate interior angles and are congruent , so

x = 100

x° and y° are a linear pair and sum to 180° , that is

100 + y = 180 ( subtract 100 from both sides )

y = 80

The total amount that you need to pay for the lunch after the sales tax and the tip will be $ 42.85.

We are given that:

The cost of lunch = $ 32

Sales tax = $ 4.45

Tip = 20 %

So, the tip will be calculated by finding the percentage of cost that you are planning to pay has a tip.

Tip = 20 % of $ 32

Tip = 20 / 100 × $ 32

Tip = 0.2 × $ 32

Tip = $ 6.4

Total amount needed to be paid for the lunch = $ 32.00 + $ 4.45 + $ 6.40

Total amount = $ 42.85

Therefore, we get that, the total amount that you need to pay for the lunch after the sales tax and the tip will be $ 42.85.

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The sum of the given finite series is 2140

Sum notation is used to express long summation into a single formula.

Properties of sum operator:

[tex]\sum\limits^{40}_{n=1} {(3n-8)}=\sum\limits^{40}_{n=1} {3n}-\sum\limits^{40}_{n=1} {8}[/tex]

[tex]=3\sum\limits^{40}_{n=1} {n}-\sum\limits^{40}_{n=1} {8}[/tex]

[tex]=3\sum\limits^{40}_{n=1} {n}-8\times40[/tex]

[tex]=3(1+2+...+40)-8\times40[/tex]

[tex]=3.\frac{40}{2}. (1+40)-320[/tex]

= 2140

Hence, the sum of the given finite series is 2140

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Answer:

C=r-p

Step-by-step explanation:

r-c=p

We need to solve the equation for Variable C

To get c alone we need to remove r from the left hand side

Subtract R from both sides

r-c=p

r-r-c=-r+P

-c=-r+P

Now divide both sides by -1 to get c alone

c=r-p

C is alone, it is solved for C

According to the given data young's modulus for this material = 5.73 *(10^8 ) pa

Young's modulus (E) of material seems to be the ratio of compressive loading () to tensile strain (). Where stress is defined as the amount of normal force per unit area ( = F/A) and strain is defined as extension per unit length ( = dl/l).

Youngs modulus Y of a material is given Y = FL/ADL

where

A = area

DL = change of length

L = original length

F = force

so here we apply

Y = 65*9.8* 45/(3.14* 3.5*3.5* 10^-6 * 1.3)

Y = 5.73 *(10^8 ) pa

According to the given data young's modulus for this material = 5.73 *(10^8 ) pa

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I understand that the question you are looking for is:

A nylon rope used by mountaineers elongates 1.30 m under the weight of a 65.0-kg climber. If the rope is 45.0 m in length and 7.0 mm in diameter, what is Young's modulus for this material?

Answer:

4[tex]x^{2}[/tex]

Step-by-step explanation:

1st seperate the equation

[tex]\sqrt{16}[/tex] and [tex]x^{2}[/tex]

square root of 16 is 4, and x squared stays the same, so the equation becomes

4[tex]x^{2}[/tex]

To make a line perpendicular, flip the denominator and numerator of the slope and make it positive if it was negative or negative if it was positive.

In this case, our slope is 3, so to make a perpendicular line, it would become: [tex]-\frac{1}{3}[/tex]

Now to make it pass through -6, 3 we need to plug in those numbers, and we'll be removing the 3 added at the end.

x = -6

y = 3

y = x

3 = [tex]-\frac{1}{3}[/tex](-6)

3 = 2

In order to make this true, we need to add 1 to the right side.

3 = 2 + 1

3 = 3

So, the equation would be  [tex]y=-\frac{1}{3}x+1[/tex]

Answer:

Solution on screen

Step-by-step explanation:

I hope it's clear

Probability that either his partner or the pile have the joker from the deck of 43 cards including one joker ,four players each have 10 cards and 3 cards in a pile is 13/33.

As given,

Total number of cards=43

Number of cards with each players =10

Number of cards in a pile =3

Greg doesn't have joker

Total cards left = 43-10

                       = 33

Probability either his or the pile have the joker = (10 +3)/33

                                                                         = 13/33

Therefore, probability that either his partner or the pile have the joker is 13/33.

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The categorization of each variable according to the group of numbers that best captures its values is shown below:

Any integer from 0 to n.

Any number from 0 to h.

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