5x + y = 2
2x-3y = 62

Answer:

110

Step-by-step explanation:

There are 200 people in a cinema- This is our total amount.

25 % of the people are men.

.25 times 200= 50

There are 50 men.

1/5 (20%) of the people are women.

.2 times 200 = 40

There are 40 women.

50+40 = 90

There are 90 adults in the cinema.

If there are 200 total people in the cinema, and 90 of them are adult, then 110 of them are children.

The percentage is 55%.

The simplified fraction is 11/20.

The decimal is .55  

A) Relative frequency is number of times an event happened over total number of events:

Answer is 21/50 = 0.42

B) On a 6 sides die, there are 3 even numbers and 3 odd numbers, so the theoretical probability of landing on odd would be 3/6 = 0.50

C) Because the die has an equal amount of chance landing on even or odd, both are 3/6, then the dice is not biased.

Answer:

factor: 5(2x'y'+3xy)

Step-by-step explanation:

thats for factoring, i didnt know what you needed

Answer:

25xy

Step-by-step explanation:

collect like terms

Answer: C) 5

Step-by-step explanation:

First let's distribute the left side of the equation.

2/3a - 9 1/3 = -3(a-3)

Then let's distribute the right side of the equation.

2/3a - 9 1/3 = -3a + 9

Then let's move all the a's to one side, and all the constants to the other.

3 2/3a = 18 1/3

Then divide both sides of the equation by 3 2/3.

a = 5

Hope it helps <3

Answer:

143.81

Step-by-step explanation:

Trapezoid Area

A = 2b/2 * h

A = 9 + 23/2 * 7

A = 32/2 * 7

A = 16 * 7

A = 112

Semi-circle Area

A = πr²/2

A = π4.5²/2

A = π20.25/2

A = 63.62/2

A = 38.81

Total Area

112 + 38.81

143.81

Answer:

(x + 2)

Step-by-step explanation:

When we factor the expression x² - 8x - 20, we should get (x + 2)(x - 10).

Alternatively, we can use synthetic division or long division to get our answer.

Answer:

x + 2

Step-by-step explanation:

got it right edg '22

Answer:

 I think its D?

         Hope this helped!

Answer:

(2)They are perpendicular.

Step-by-step explanation:

The temperature (t) needs to be greater than 60

So you would have t > 60

Answer:

t > 60

Explanation:

In order to answer this question we must determine two things: what two terms will be compared in the inequality and what symbol we will use to compare them. Let's start by finding, 'what two terms will be compared.'

Read the following quote from the problem...

"Forest fires are most likely to occur when the air temperature (t) is greater than 60°F."

Since the temperature (t) must be greater than sixty degrees to start a forest fire, these are the two terms that we will be comparing in the inequality.

Now, let's find out what symbol we will use to compare the terms.

Because the problem uses the phrase "greater than" to represent the comparison between the temperature of the air and an average of sixty degrees, the symbol we will be using in the inequality is the greater than sign, >.

Finally, use all the facts we have established to write the inequality.

· t = air temperature

· > = greater than

· 60 = max temp. before forest fire occurs

Therefore, the inequality for the solution is t > 60.

Answer:

Step-by-step explanation: so you calculate how many people ate chicken, beef, fish or are vegetarian then you will add it all together

chicken=128

beef= 80

fish=32

vegetarian=112

128+80+32+112= 352 people ate at the restaurant

Answer:

Altogether, 88 people went to the restaurant.

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Answer:

  x = 20%

Step-by-step explanation:

The area is the product of side lengths. If the original side is "a", then the one increased by 25% is ...

  a + 0.25·a = 1.25a

The one decreased by x is ...

  a -x·a = a(1 -x)

We want the area of the square to be the same as that of the rectangle, so we write an equation that says that, then solve for x.

  square area = rectangle area

  a^2 = (1.25a)(a)(1-x)

  1 = 1.25 -1.25x . . . . divide by a^2, eliminate parentheses

  1.25x = 0.25 . . . . . add 1.25x -1

  x = 0.25/1.25 = 0.20

  x = 20% . . . . . . expressed as a percentage

Answer:

[tex]a = 3[/tex]

Step-by-step explanation:

[tex]3 {a}^{2} = 27 \\ \frac{3 {a}^{2} }{3} = \frac{27}{3} \\ {a}^{2} = 9 \\ a = \sqrt{9} \\ a = 3[/tex]

Answer: 9

Step-by-step explanation:

First divide both sides by 3

[tex]a^2=9[/tex]

Then root both sides([tex]\sqrt{a^2}=\sqrt{9}[/tex])

a = 9

Hope it helps <3

Edit: :o this is my 250th answer

Answer:

y = 2x - 1

Step-by-step explanation:

(3, 5) (5, 9)

slope = (9-5)/(5-3) = 4/2 = 2

y = mx + b

5 = 2(3) + b

-1 = b

y = 2x -1

Answer:

f(x)=2x-1; y=2x-1

Step-by-step explanation:

First we need to find the slope and to do so you use the equation [tex]\frac{y_{1} -y_{2}}{x_{1}-x_{2}}[/tex] .

Plugging in for the values we get (9-5)/(5-3)=4/2=2, which means we have a slope of 2.

Now we just have to find the y-intercept, and to do this we multiply the x-value by the slope (2) and see what we have to add to that to get the y-value.

For example, 5*2=10, 10-1=9, so -1 is our y-intercept.

This means our equation in slope-intercept form is y=2x-1 and in function form is f(x)=2x-1

Answer:

900L per minute

Step-by-step explanation:

1- 70 - 20 = 50

2- in this 50 min the 45000L has been drawned

3- 45000L / 50 = 900L

.. ..

Answer:

About $3.28

Step-by-step explanation:

Divide 24.33 by 7.4

Answer:

3.28783783784...

Step-by-step explanation:

You're description could turn into 24.33 : 7.4.

You turn 7.4 into 1, and divide 7.4 / 1.

(It is 7.4)

Then, you divide 24.33 / 7.4.

It is 3.28783783784.......

or, If you want you're answer close to an natural number, It is 3.

Answer:

[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]

Step-by-step explanation:

[tex]$\left(\frac{1}{2}x+3y \right)^4=\left(\frac{x}{2}+3y \right)^4\\$[/tex]

Binomial Expansion Formula:

[tex]$(a+b)^n=\sum_{k=0}^n \binom{n}{k} a^{n-k} b^k$[/tex], also [tex]$\binom{n}{k}=\frac{n!}{(n-k)!k!}$[/tex]

We have to solve [tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\sum_{k=0}^{4} \binom{4}{k} \left(3 y\right)^{4-k} \left(\frac{x}{2}\right)^k$[/tex]

Now we should calculate for [tex]k=0, k=1, k=2, k=3 \text{ and } k =4;[/tex]

First, for [tex]k=0[/tex]

[tex]$\binom{4}{0} \left(3 y\right)^{4-0} \left(\frac{x}{2}\right)^{0}=\frac{4!}{(4-0)! 0!}\left(3 y\right)^{4} \left(\frac{x}{2}\right)^{0}=\frac{4!}{4!}(81y^4)\cdot 1 =81 y^{4}$[/tex]

It is the same procedure for the other:

For [tex]k=1[/tex]

[tex]$\binom{4}{1} \left(3 y\right)^{4-1} \left(\frac{x}{2}\right)^{1}=54 x y^{3}$[/tex]

For [tex]k=2[/tex]

[tex]$\binom{4}{2} \left(3 y\right)^{4-2} \left(\frac{x}{2}\right)^{2}=\frac{27}{2} x^{2} y^{2}$[/tex]

For [tex]k=3[/tex]

[tex]$\binom{4}{3} \left(3 y\right)^{4-3} \left(\frac{x}{2}\right)^{3}=\frac{3}{2} x^{3} y$[/tex]

For [tex]k=4[/tex]

[tex]$\binom{4}{4} \left(3 y\right)^{4-4} \left(\frac{x}{2}\right)^{4}=\frac{x^{4}}{16}$[/tex]

You can perform the calculations, I will not type everything.

The answer is the sum of elements calculated.

Just organizing:

[tex]$\left(\frac{x}{2} + 3 y\right)^{4}=\frac{x^{4}}{16} + \frac{3}{2} x^{3} y + \frac{27}{2} x^{2} y^{2} + 54 x y^{3} + 81 y^{4}$[/tex]

Answer:  [tex]\bold{\dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4}[/tex]

Step-by-step explanation:

                     Binomial Tree

n=0                         1

n=1                      1      1

n=2                  1    2     1

n=3               1    3    3     1

n=4            1    4    6    4    1

Using the Binomial Theorem

[tex]\bigg(\dfrac{1}{2}x+3y\bigg)^4\\\\\\=1\bigg(\dfrac{1}{2}x\bigg)^4(3y)^0\quad \rightarrow \quad \dfrac{1}{16}x^4\\\\+4\bigg(\dfrac{1}{2}x\bigg)^3(3y)^1\quad \rightarrow \quad \dfrac{3}{2}x^3y\\\\+6\bigg(\dfrac{1}{2}x\bigg)^2(3y)^2\quad \rightarrow \quad \dfrac{27}{2}x^2y^2\\\\+4\bigg(\dfrac{1}{2}x\bigg)^1(3y)^3\quad \rightarrow \quad 54xy^3\\\\+1\bigg(\dfrac{1}{2}x\bigg)^0(3y)^4\quad \rightarrow \quad 81y^4[/tex]

______________________

[tex]= \dfrac{1}{16}x^4 + \dfrac{3}{2}x^3y + \dfrac{27}{2}x^2y^2 +54xy^3+81y^4[/tex]

Answer:

cD /100

Step-by-step explanation:

Change the percent to a fraction

c% = c/100

Multiply by the sale

D * c/100

cD /100

Answer:a

Step-by-step explanation:

Answer: 343 cm³

Step-by-step explanation:

The surface area of a cube is 6s^2, where s is the side length of a square.  Thus, first do 294/6 to get 49.  Then take the square root of 49 to get that each side of the cube is 7.  The volume of a cube is s^2, so simply do 7*7*7 to get that the volume of the cube is 343cm^3

Hope it helps <3

Answer:

V =343 cm^3

Step-by-step explanation:

The surface area of a cube is given by

SA = 6s^2 where s is the side length

294 = 6s^2

Divide by 6

294 / 6 = s^2

49 = s^2

Take the square root of each side

sqrt(49) = sqrt(s^2)

7 =s

The volume of a cube is

V = s^3

V = 7^3

V =343 cm^3

Answer:

C: 38 units

hope this helps!!

Answer:

The given relation R is equivalence relation.

Step-by-step explanation:

Given that:

[tex]((a, b), (c, d))\in R[/tex]

Where [tex]R[/tex] is the relation on the set of ordered pairs of positive integers.

To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.

1. First of all, let us check reflexive property:

Reflexive property means:

[tex]\forall a \in A \Rightarrow (a,a) \in R[/tex]

Here we need to prove:

[tex]\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R[/tex]

As per the given relation:

[tex]((a,b), (a,b) ) \Rightarrow ab =ab[/tex] which is true.

[tex]\therefore[/tex] R is reflexive.

2. Now, let us check symmetric property:

Symmetric property means:

[tex]\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R[/tex]

Here we need to prove:

[tex]\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R[/tex]

As per the given relation:

[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = bc[/tex]

[tex]((c,d),(a,b)) \in R[/tex] means [tex]cb = da\ or\ ad =bc[/tex]

Hence true.

[tex]\therefore[/tex] R is symmetric.

3. R to be transitive, we need to prove:

[tex]if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R[/tex]

[tex]((a,b),(c,d)) \in R[/tex] means [tex]ad = cb[/tex].... (1)

[tex]((c,d), (e,f)) \in R[/tex] means [tex]fc = ed[/tex] ...... (2)

To prove:

To be [tex]((a,b), (e,f)) \in R[/tex] we need to prove: [tex]fa = be[/tex]

Multiply (1) with (2):

[tex]adcf = bcde\\\Rightarrow fa = be[/tex]

So, R is transitive as well.

Hence proved that R is an equivalence relation.

The relation R is an equivalence if it is reflexive, symmetric and transitive.

The order to options required to show that R is an equivalence relation are;

Reasons:

Prove that the relation R is reflexive

Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)

The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c

By multiplication property of equality; a·b = b·a

Therefore;

((a, b), (a, b)) ∈ R

Prove that the relation, R, is symmetric

Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c

Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R

((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.

Prove that R is transitive

Symbolically, transitive property is as follows; If x = y, and y = z, then x = z

From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c

Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e

By multiplication, a·d × c·f = b·c × d·e

a·d·c·f = b·c·d·e

Therefore;

a·f·c·d = b·e·c·d

a·f = b·e

Which gives;

Therefore;

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.

Learn more about equivalent relations here:

https://brainly.com/question/1503196

Answer:

150  cans

Step-by-step explanation:

Answer:

it is 13093 i got it correct

Answer:

30 people

Step-by-step explanation:

If you start off with 1/2 a lemon for 6 people, then 1 whole would be 12. 1 1/2 would be 18 people and 2 whole lemons would be 24. so 2 1/2 is 30 people.

Answer:

Rational.

Step-by-step explanation:

Irrational numbers are real numbers that can't be written as fractions.

One clue is that the decimal goes on forever (doesn't terminate) without repeating. (pi)

.14 can be written as a fraction: 14/100

Answer:

It's rational

Step-by-step explanation:

Because irrational numbers cannot be written s a fraction and rational numbers can

Answer: option 4) 15°, 30°, 135°

Step-by-step explanation: because the triangle angle rule says that all the intererior angles of the triangle sum upto 180° always

Answer:

4) 15°,30°,135°

Step-by-step explanation:

The interior angles of a triangle will add up to 180°, so we have to choose an answer choice with angles that all add up to 180.

Answer #4 is correct because 15 + 30 + 135 = 180.

Answer:

c

Step-by-step explanation:

Answer:

Equation: f(x) = -x² + 3

Step-by-step explanation:

If we want to find the roots/solve for x, we can either graph the problem or use quadratic formula to find when f(x) = 0:

To get the equation of the graph, our parent function is: f(x) = a(x - h)² + k, or f(x) = x². Since we are reflecting over the x-axis with a vertical stretch and vertically moving up to (0, 3), we are modifying a and k only.