Each of 36 students at a school play bought either a cup of orange juice or a sandwich. A cup of orange juice costs $1 and a sandwich costs $3. The total amount collected was $76. How many students bought orange juice, and how many bought a sandwich?

Let represent the number of students who bought a cup of orange juice and represent the number of students who bought a sandwich. Then the problem can be represented by this system of equations:

+ 3 = 76
+ = 36

Answer the questions to solve the problem.

1. Explain what you should do with the two equations to eliminate one of the variables.

The value of t is 6.65

An exponential function is a mathematical function of the following form: f ( x ) = a^x. where x is a variable, and a is a constant called the base of the function.

Given:

A= 210 million

P= A e^(kt)

225 = 210 * e ^ (0.0069t)

225/210=  e ^ (0.0069t)

1.07 =  e ^ (0.0069t)

Taking log on both side

log  1.047 = 0.0069 t log e

[tex]\frac{0.0069t\ln \left(e\right)}{0.0069\ln \left(e\right)}=\frac{\ln \left(1.047\right)}{0.0069\ln \left(e\right)}[/tex]

t= log ( 1.047) / 0.0069

t= 6.65

Hence, value of t is 6.65.

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Answer:

Step-by-step explanation:

Answer:

Jim:  2/9

Step-by-step explanation:

8/9-4/6

48/54-36/54          [Convert each fraction to a common denominator:  54

                              Multiply (8/9)*(6/6)=48/54;  Multiply (4/6)*(9/9) = 36/54]

 48/54-36/54 = 12/54

12/54 can be reduced to 2/9

Jim also has 2/9

Sue- 8/9-4/6=4/3 or 1 1/3:  Sue subtracted both the numerator and denominator.  This is not correct.

Jim- 8/6 - 4/6 = 48/54 - 36/54= 12/54 or 2/9:  Good Job Jim

Bob- 8/9- 4/6 = 8/54-4/54= 4/54 = 2/27:  Bob converted both denominators to 54, but did not multiply the numerators by the same numbers.  Bad Bob.

Answer:

15cm

Step-by-step explanation:

PC = 15

BR = 15

.

............................................

Answer:

The rectangular table

Step-by-step explanation:

Square table: 36*36=1296

Rectangular table: 20*42=1460 [tex]in^{2}[/tex]

Circular table: [tex]\pi * 21^{2}[/tex]≅1384

Answer:

s. p = 270 Rs

discount = 10%

mp.= ?

Mp = s. p + discount

= 270 + 10/100*270

= 270 + 27

= 297 Rs

Answer:

[tex]\huge\boxed{\sf Rs.\ 297}[/tex]

Step-by-step explanation:

Selling Price = Rs. 270

Discount = 10%

= 10% of 250

[tex]\displaystyle =\frac{10}{100} \times 270[/tex]

= 1 × 27

= Rs. 27

= Selling Price + Discount

= 270 + 27

= Rs. 297

[tex]\rule[225]{225}{2}[/tex]

Answer:

Ok ya sure I would love to. :)

Step-by-step explanation:

Oh wait….

*Crickets chirping*

Sin3A=Cos3A

Cos(90-3A)=Cos3A

90-3A=3A

90=3A+3A

90=6A

90/6=A

^•^

The answer is A=15

Answer:

32 km/hr

Step-by-step explanation:

Firstly, you need to find the speed of both trains in km/hr.

Paolo's train= (70km x 60hr)/35= 120 km/hr

Monika's train= 684km/4.5hr= 152 km/hr

Then find the difference in speed:

152-120=32 km/hr

Volume is a three-dimensional scalar quantity. The volume of the triangular prism is 66cm².

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

Given the length of the triangle is 4cm, while the width of the triangle is 11cm, therefore, the area of the base of the triangle will be,

Area of triangle = 0.5 × 4cm × 11cm

Area of triangle = 22 cm²

Now, the volume of the prism with a base area of 22cm² and a height of 3 cm is,

Volume of the triangular prism = 22cm² × 3cm = 66cm³

Hence, the volume of the triangular prism is 66cm².

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Answer:

minimum value is 3, maximum value is 4.459

Step-by-step explanation:

[tex] log_{2}(8) = \frac{ log(8) }{ log(2) } = 3[/tex]

[tex] log_{2}(22) = \frac{ log(22) }{ log(2) } = 4.459[/tex]

Answer:

No solution

Step-by-step explanation:

 7x + 2y = 16 ----------------(I)

-21x - 6y = 24 -----------------(II)

[tex]\sf \dfrac{a_1}{a_2}=\dfrac{7}{-21}=\dfrac{-1}{3}\\[/tex]

[tex]\sf \dfrac{b_1}{b_2}=\dfrac{2}{-6}=\dfrac{-1}{3}[/tex]

[tex]\sf \dfrac{c_1}{c_2} =\dfrac{16}{24}=\dfrac{2}{3}\\\\ \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}[/tex]

So, the lines are parallel and has no solution

Answer:

(−∞,1)

Step-by-step explanation:

The adjustment of thicker fur will be selected over thinner fur, and the population will develop. Then the correct option is D.

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur.

The climate in which these mice live has slowly gotten colder.

The change in the environment most likely affect the mouse population will be

The adjustment of thicker fur will be selected over thinner fur, and the population will develop.

Then the correct option is D.

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Answer:

0 represents the ground level

The complete question is

"Which is the graph of the system x + 3y > –3 and y < One-halfx + 1?"

The solution is the intersection region of all the solutions in the system of inequalities.

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

We know that the lines are given as;

x + 3y = -3

y = 1/2 x + 1

Solving for "y" from the first line;

3y = -3 - x

y = -1 - x/3

For the line x + 3y = -3  the x-intercepts;

y = 0

y = -1 - x/3

0 = -1 - x/3

x/3 = -1

x = -3

And the y-intercept;

y = -1

For the line y = 1/2 x + 1 the x-intercepts;

y = 0

0= 1/2 x + 1

1/2x = -1

x = -2

And the y-intercept

x = 0

y = 1

Now we can graph both lines,

The solution is the intersection region of all the solutions in the system of inequalities.

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6.0000000001

Ans right

Using translation concepts, it is found that this transformation can be described as a reflection across the x-axis.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, considering the vertices of quadrilateral 1 and quadrilateral 2, the transformation from quadrilateral 1 to quadrilateral 2 has the following format:

(x,y) -> (x, -y).

Which means that it can be described as a reflection across the x-axis.

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Answer:

Step-by-step explanation:

Answer:

11.2 km/hr

Step-by-step explanation:

Shea's speed: 48km/1.25hr=38.4 km/hr

Chris's speed: 62km/1.25hr= 49.6 km/hr

Vav= 49.6-38.4= 11.2 km/hr

Answer:

6/6

Step-by-step explanation:

6/6 not equal -1/1 so these lines intersect each other at only one point hence these have only one solution.

Answer:

I can give you the answer if you can answer a question

Step-by-step explanation:

Answer:

Son's Age: 11

Mary's Age: 33

Step-by-step explanation:

Let set Mary and her son as variables,

M = Mary's age

S  = Mary's son age

Breakdown:

"Mary is three times as old as her son"

M = 3S

"In 12 years, Mary's age will be one less than twice her son's age"

M + 12 = 2(S + 12) - 1

we add 12 to both sides as it will be in 12 years for both

We know that M = 3S, so we plug this in

3S + 12 = 2(S + 12) - 1

Now solve for S (son's age),

3S + 12 - 12 = 2(S + 12) - 1 - 12

3S = 2(S + 12) - 13

3S = 2S + 24 - 13

3S - 2S = 2S - 2S + 24 - 13

S = 24 - 13

S = 11

To find Mary age, plug in her son age ,

M = 3S

M = 3(11)

M = 33

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Pythagoras' theorem is a basic relationship between the three sides of a right triangle in Euclidean geometry. The correct option is D.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

A triangle has points to monkeys, giraffes, and lions. The distance between lions and monkeys is 11 feet and between monkeys and giraffes is 16 feet. The distance between lions and giraffes is the hypotenuse of x feet. The equation that will find the distance between the lions and giraffes is,

c² = 11² + 16²

c² = 121 + 256

c² = 377

Hence, the correct option is D.

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Answer:

D on edge) 121+ 256...

Answer:

Step-by-step explanation:

Remark

An altitude is a very special line. It must start from one of the angles and connect with the side opposite that angle. The connection must form a right angle.

It cannot start anywhere else -- certainly not in the middle of a line which would make the altitude of random importance. It could not be accurately reproduced.

The proof will be given as:- [tex]\dfrac{tanx+Cotx}{Coscx Cosx} = Sec^2x[/tex].

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The proof will be given as:-

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = \dfrac{tanx}{coscxCosx}+\dfrac{Cosx}{CoscxCosx}\\\\[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} =\dfrac{\dfrac{Sinx}{Cosx}}{\dfrac{Cosx}{Sinx}}+\dfrac{\dfrac{Cosx}{Sinx}}{\dfrac{Cosx}{Sinx}}[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = \dfrac{Sin^2x}{Cos^2x}+1[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} = tan^2x+1}[/tex]

[tex]\dfrac{tanx+Cotx}{Coscx Cosx} =Sec^2x[/tex]

Therefore the proof will be given as:- [tex]\dfrac{tanx+Cotx}{Coscx Cosx} = Sec^2x[/tex].

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Answer:

  B. II  (6, 8, 10)

Step-by-step explanation:

A set of triangle side lengths will form a right triangle if they satisfy the Pythagorean theorem. The sum of squares of the shortest two sides must equal the square of the longest side.

__

Sets of integers that satisfy the Pythagorean theorem are called "Pythagorean triples." Some of these for smaller integers are ...

  (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17)

If small integer side lengths are not one of these triples, or a multiple of one of these triples, they will not form a right triangle.

I. not a match to any triple

II. matches (3, 4, 5) multiplied by 2 -- a right triangle

III. not a match to any triple

IV. not a match to any triple

_____

Of course, you can actually compute the squares to see if they satisfy the Pythagorean theorem:

I. 4² +5² = 41 ≠ 6² (acute triangle)

II. 6² +8² = 100 = 10² -- right triangle

III. 5² +13² = 194 ≠ 14² (obtuse triangle)

IV. 7² +11² = 170 ≠ 13² (acute triangle)

__

The sum f = a² +b² -c² (where c is the longest side) can be considered to be a "form factor" for the triangle. For ...

This "form factor" is related to the largest angle (C) by ...

  cos(C) = f/(2ab)

Answer:

parameter

Step-by-step explanation:

OC represents vector a and b drawn using the head-to-tail method.

A vector is an object that has both magnitude and direction.

The given vectors are

a =<5, −1> and b =<2,−2>

Representing vector a +b using the head and tail method

Here in the image attached with the answer ,

The vector a is represented by OA and the vector b is represented by OB

By head and tail method , the OC is drawn by extending the vector a towards b and b towards a

Vector OC = Vector OA + Vector OB

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