A total of 392 were sold for the school play. They were either adult tickets or student tickets. The number of students sold was three times the number of adult tickets sold. How many adult tickets were sold?

well, let's see it this way, we know that 3000 is the 100%, and we also know that 3K is x% of 3000, so then

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 3000 & 100\\ 3K& x \end{array} \implies \cfrac{3000}{3K}=\cfrac{100}{x} \\\\\\ 3000x=300K\implies x=\cfrac{300K}{3000}\implies x=\cfrac{K}{10}[/tex]

Apply combine gas law

[tex]\\ \rm\dashrightarrow \dfrac{P1V1}{T1}=\dfrac{P2V2}{T2}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{10(341)}{310}=\dfrac{15V2}{120}[/tex]

[tex]\\ \rm\dashrightarrow 11=\dfrac{V2}{8}[/tex]

[tex]\\ \rm\dashrightarrow V2=88in^3[/tex]

Answer:

88 in³

Step-by-step explanation:

we are given that the volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P.

Condition-1:

The volume V of a given mass of gas varies directly as the temperature T , thus

[tex]V\propto T\\\implies V=kT[/tex]

Condition-1:

The volume V of a given mass of gas varies inversely as the pressure P, therefore,

[tex]V\propto 1/P\\\implies V=k\cdot 1/P[/tex]

combining 1 and 2 yields

[tex]V\propto k\cdot T/P[/tex]

Case-1:

To find:

Finding the constant of proportionality

[tex]341= k\cdot 310/10\\\implies k=341\times 10/310 \\ \implies \boxed{k=11}[/tex]

Case-1:

To find:

when:

Finding the volume:

[tex]V= 11\times 120/15\\\implies V=11\times 8 \\ \implies \boxed{V=88}[/tex]

Using the arrangements formula, it is found that there are 240 ways for the students to sit.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex].

In this problem:

Hence:

T = 5 x 2! x 4! = 240.

There are 240 ways for the students to sit.

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Answer:

You can have almost all of these qualities and still not have a parallelogram.

Explanation:

The four shapes that meet the requirements of a parallelogram are square, rectangle, rhombus, and rhomboid.

Answer:

b=8.5cm

Step-by-step explanation:

tanx (this represents tan theta, it's just easier to type) is equal to 0.6 and since the tanx ratio is opp/adj, we know that opp/adj = 0.6

To find what b is (adjacent as it is adjacent to the angle being used and it is not the hypotenuse), we just have to rearrange.

0.6=5.1/adj

to solve for adj, we can switch 0.6 and adj. (This works because to get adj by itself on one side you would multiply it to the other side and then divide 0.6 from both sides --> simple algebra)

so then you have

adj=5.1/0.6

adj=8.5cm

(if you want to check your solution you can use pythagoeran theorem, a^2+b^2=c^2) and sub everything in and make sure all the numbers equal the right thing!

Answer:

Step-by-step explanation:

4(4/3) DIVIDED INTO     2(2/3)    (mixed numbers)

16/3    DIVIDED INTO   8/3  

     16/8=2

16/3 divided into 8/3

  is the same as

16/3 multiplied be  3/8

     48/24 =2          

Answer:

[tex]21yx^{2}-128xy+51y[/tex]

Step-by-step explanation:

Answer: 49x^14

Step-by-step explanation:

Answer: x > 38

Step-by-step explanation:

Answer: -7/3

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals of each other.

The amount needed in the account is 182,713.25 dollars then the correct option is B.

The term loan refers to a sort of credit vehicle in which a sum of money is lent to another party in exchange for the value or principal amount being repaid in the future.

Then the formula of monthly payment (MP) will be

[tex]\rm MP = P \times \dfrac{r(1+r)^n}{(1+r)^n - 1}\\[/tex]

The formula can be written as

[tex]\rm P = MP \times \dfrac{(1+r)^n-1}{r(1+r)^n}\\[/tex]

You plan on supplementing your income. you would like to withdraw a semiannual salary of $6,951.20 from an account paying 1.75% interest, compounded semiannually.

The amount needed in the account is such that you can withdraw the needed amount at the end of each period for 15 years will be

MP = $6951.20

r = 0.00875

n = 30

Then we have

[tex]\rm P = 6951.20 \times \dfrac{(1+0.00875)^{30}-1}{0.00875(1+0.00875)^{30}}\\\\P = \$182713.25[/tex]

More about the monthly payment link is given below.

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The cost of 1 shirt would be 10

you would need to multiply the cost of one shirt by the number of shirts bought (x)

Answer:

Step-by-step explanation:

perimeter = 2 (l + b)

                   = 2 {(2/3x+ 10) + (1/3x + 5)}

                   = (4/3x + 10) + (2/3 + 10)

                    = 4/3x + 20 +2/3 + 10

                     = 6/3x + 30

                     = 3x + 30

Answer:

(25 ÷ 5 ) ÷ 4

Step-by-step explanation:

solve the equation for the variable. Then plug that variable value into the expression and simplify to get the answer.

Answer:

C

Step-by-step explanation:

the quotient of 25 and 5 is 25 ÷ 4 , then multiply this by 4 , so

4 × (25 ÷ 5 ) → C

Answer:

I think the volume is 18

Step-by-step explanation:

6×3 = 18

The ladder will be safe at this height .

There are six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

According to question

Sandy has a ladder whose length = 16.5 feet

He wants to lean the ladder against a vertical wall  15.9 feet above the ground.

And he wants the angle the ladder makes with the

ground to be < 76°.

As Perpendicular = 15.9 feet

and Hypotenuse = 16.5

Sin Ф = [tex]\frac{Perpendicular }{Hypotenuse}[/tex]

Sin Ф = [tex]\frac{15.9}{16.5}[/tex]  

Sin Ф = 0.9636

Therefore,  Ф  ≈ 74.49 (approx.)

That means it is safe .

Hence, The ladder will be safe at this height as it is not greater than 76° .

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# SPJ2

Answer:im pretty sure its 20

Step-by-step explanation: because 4x5=20 and theres 24

The expression that can be used to determine the number of years that it would take to have a balance of $600 is In2 ÷ In[tex]e^{0.005}[/tex].

When an amount is compounded continously, it means that both the amount deposited and the interest already accrued increases in value continously over a period of time.

Time = In(FV/PV) ÷ In([tex]e^{0.005}[/tex]

In2 ÷ In[tex]e^{0.005}[/tex]

Answer:

16 pi  cm^2

Step-by-step explanation:

Area = pi r^2      r = 1/2 d

        = pi (4^2) = 16 pi cm^2

The system of equations can be used to find the roots of the considered  equation is y = 4+x^2 and y= x^3 + 2 + x

We do same operations on both the sides so that equality of both expressions doesn't get disturbed. Solving equations generally means finding the values of the variables used in it for which the considered equation is true.

Sometimes we can find such value, and sometimes it is not possible at all, or sometimes, there are infinite number of solutions.

For the given case, we are given with the equation [tex]4+x^2 = x^3 + 2 + x[/tex]

We can take two equations as:

[tex]y = 4+x^2 \\y= x^3 + 2 + x[/tex]

And when we will try to solve this system of equation, we will end up substituting the value of y in terms of x, and therefore, ending up on the same equation [tex]4+x^2 = x^3 + 2 + x[/tex]

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Answer:

D

y=4x^2

y=x^3+2x

Step-by-step explanation:

im trying to pass just like yall, Good luck to all

Answer:

I beleive the fist one is.

Step-by-step explanation:

The first one is a possibility, the second has a correlaition, and the third, I believe is a correlation.

Answer:

Let me know if this is not what you meant by rays, I can change it if needed.

Quadrilateral KLMN has vertices K(-2,-2), L(1,1), M(0,4), and N(-3,5)

It is first translated by (x + 2,y - 1)

then

K(-2,-2) ---> K'(-2 + 2,-2 - 1) = (0,-3)

L(1,1), ---> L'(1 + 2,1 - 1) = (3,0)

M(0,4), ---> M' (0 + 2,4 - 1) = (2,3)

and

N(-3,5) ---> N' (-3 + 2,5 - 1) = (-1,4)

and then translated by (x - 3,y + 4)

K'(0,-3) ---> K''(0 - 3,-3 + 4) = (-3,1)

L'(3,0) ---> L''(3 - 3,0 + 4)= (0,4)

M'(2,3)  ---> M'' (2 - 3, 3 + 4)= (-1,7)

and

N'(-1,4) ---> N'' (-1 - 3,4 + 4) = (-4,8)

the coordinates of K" L" M" N" after both translations are

K''= (-3,1)

L''= (0,4)

M''= (-1,7)

and

N'' = (-4,8)

hope im right if not im sorry but it going to be right cuz im good at this stuff for you

To represent the linear function in order for the data the value of a=18.

In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

It is given that for a linear function the value is changing at the rate of 5 so we can see in the table as the function independent value is changing then the value of the dependent linear function increases by 5.

So the value of a will be equal to 18.To represent the linear function in order for the data the value of a=18.

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Answer:

x=-14

Step-by-step explanation:

-x-11^2+1

-x-11^3

-x^14

x=-14

x mL of the 35% saline solution contains 0.35x mL of salt.

10 mL of the 75% solution contains 0.75 • 10 mL = 7.5 mL of salt.

After mixing, the scientist would have a total volume of (x + 10) mL. We know its concentration is 40%, so it contains 0.40 (x + 10) mL of salt.

The total amount of salt before and after mixing must be the same, so

0.35x + 7.5 = 0.40 (x + 10)

Solve for x :

0.35x + 7.5 = 0.40x + 4.0

0.10x = 3.5

x = 35

The scientist used 35 mL of the 35% solution.

Answer:

neither law can be used

Step-by-step explanation:

to solve the given triangle the given measurements are not enough (one more value should be known).