Out of 136 students in a school, 60 take French, 100 take Chemistry and 48 take Physics. If 28 take French and Chemistry, 44 take Chemistry and Physics and 20 take French and Physics, how many take all three subjects?

Answer:

B. 2

Step-by-step explanation:

Assuming the term is meant to look like this: -3x², then the answer is B.2. An exponent is a superscript (super means above, script means writing) that tells you to multiply something by itself.

In this case, -3x² means -3·x·x

If it was written as (-3x)², it would mean (-3x)·(-3x)

Answer:

2

Step-by-step explanation:

The exponent is raised to the power of any variable [smaller number].

I am joyous to assist you anytime.

Answer:

4.25 yards

Step-by-step explanation:

Area of rectangle = Base x Height

or

Height = Area of Rectangle ÷ Base

In this case, Area =38.25 sq yards and Base = 9 yards

Height = 38.25 ÷ 9 = 4.25 yards

Using the continuous compounding formula A = Pe^rt, Katie's account balance after 10 years will be approximately $103,204, with her initial investment of $33,750 at an annual interest rate of 11.17%.

To calculate what Katie's account balance will be in 10 years, with an investment of $33,750 at 11.17% compounded continuously, we use the formula for continuous compounding:

A = Pert

Where:

Plugging in the values we get:

A = $33,750 * e(0.1117 * 10)

Calculating the exponent:

A = $33,750 * e1.117

Calculating the future value:

A = $33,750 * 3.0579 (approximate value of e1.117)

A = $103,204

Katie's account balance after 10 years will be approximately $103,204.

Answer:

  64 cm²

Step-by-step explanation:

Suppose the original paper was x cm on a side. Then the original perimeter was 4x.

When the square is folded in half, two of the sides are now x/2, so the perimeter is ...

  x + x/2 + x + x/2 = 3x

If 3x = 24 cm, then x = 8 cm.

The area of the original paper is ...

  A = x² = (8 cm)² = 64 cm²

Answer:

  D.  -|0.35t -14| +14

Step-by-step explanation:

The problem statement is asking for an expression for distance in miles, so the constants in the expression will be miles. In the time it takes to get to point B (40 minutes), the ferry has gone (0.35 mi/min)×(40 min) = 14 mi. Hence the maximum value of the function must be 14. The only function with that characteristic is the one of selection D.

[tex]|\Omega|=20\\|A|=2\\\\P(A)=\dfrac{2}{20}=\dfrac{1}{10}=10\%[/tex]

Answer:

1/10.

Step-by-step explanation:

The length of each cycle is 2 + 18 = 20 minutes.

During this time  the train in stationary for 2 minutes.

So the probability of the train being at the station when you arrive is 2/20 = 1/10.

Answer:

10

Step-by-step explanation:

Each dot represents 1 rock.

There are 10 dots in the plot, so there are 10 rocks in the collection.

Answer:

No of real solutions =1

No of  extraneous solution =2

Real solution: x =3

Step-by-step explanation:

[tex]\frac{3}{x}-\frac{x}{x+6}=\frac{18}{x^2+6x}[/tex]

solving:

Taking LCM of x, x+6 and x^2+6 we get x(x+6)

Multiply the equation with LCM

[tex]\frac{3}{x}*x(x+6)-\frac{x}{x+6}*x(x+6)=\frac{18}{x^2+6x}*x(x+6)\\3(x+6)-x*x=\frac{18}{x(x+6)}*x(x+6)\\3(x+6)-x*x=18\\3x+18-x^2=18\\-x^2+3x+18-18=0\\-x^2+3x=0\\x^2-3x=0\\x(x-3)=0\\x=0 \,\,and\,\, x =3\\[/tex]

Checking for extraneous solution

for extraneous solution we check the points where the solution is undefined

The solution will be undefined. if, x=0 or x=-6 so both are extraneous solutions

Putting x =3

[tex]\frac{3}{3}-\frac{3}{3+6}=\frac{18}{(3)^2+6(0)}[/tex]

[tex]\frac{3}{3}-\frac{3}{3+6}=\frac{18}{(3)^2+6(3)}\\1-\frac{3}{9}=\frac{18}{9+18}\\1-\frac{1}{3}=\frac{18}{27}\\\frac{3-1}{3}=\frac{2}{3}\\\frac{2}{3}=\frac{2}{3}[/tex]

So, x=3 is real solution.

Now, Selecting answers from tables

No of real solutions =1

No of  extraneous solution =2

Real solution: x =3

Number of                Number of                         Real solutions

real solution            Extraneous solution

     1                                        1                                     x=3

Extraneous solution--

It is a solution which is obtained on solving the equation but it does not satisfies the equation i.e. after it is put back to the equation it does not occur as a valid solution.

True solution or real solution--

It is the solution which is obtained on solving the equation and is also a valid solution to the equation.

The equation is:

[tex]\dfrac{3}{x}-\dfrac{x}{x+6}=\dfrac{18}{x^2+6x}[/tex]

On taking lcm in the left hand side of the equation we get:

[tex]\dfrac{3\times (x+6)-x\times x}{x(x+6)}=\dfrac{18}{x^2+6x}\\\\i.e.\\\\\dfrac{3x+18-x^2}{x(x+6)}=\dfrac{18}{x(x+6)}\\\\i.e.\\\\\dfrac{3x+18-x^2}{x(x+6)}-\dfrac{18}{x(x+6)}=0\\\\i.e.\\\\\dfrac{3x+18-x^2-18}{x(x+6)}=0\\\\i.e.\\\\\dfrac{3x-x^2}{x(x+6)}=0\\\\i.e.\\\\3x-x^2=0\\\\i.e.\\\\x(3-x)=0\\\\i.e.\\\\x=0\ or\ x=3[/tex]

When we put x=0 back to the equation we observe that the first term of the left hand side of the equation becomes undefined.

Hence, x=0 is the extraneous solution.

whereas x=3 is a valid solution to the equation.

Answer:

190000 is the best answer in my opinion because by 2006 it is more then 160000 but it is less then 200000

Step-by-step explanation:

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \\\\ ~~~~~~\textit{in meters} \\\\ h(t) = -4.9t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{48}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{3.4}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf h(t)=-16t^2+48t+3.4\implies \stackrel{\textit{when it hits the ground}}{\stackrel{h(t)}{0}=-16t^2+48t+3.4}[/tex]

Check the picture below.

Answer:

The maximum number of days is 5

Step-by-step explanation:

Let

x ----> the number of days

y ---> the total cost to rent a car in dollars

we know that

The fixed rental fee plus the daily fee multiplied by the number of days must be less than or equal to Pasion's budget

so

The inequality that represent this situation is

[tex]25+10x\leq 75[/tex]

Solve the inequality  for x    

Subtract 25 both sides      

[tex]10x\leq 75-25[/tex]                  

[tex]10x\leq 50[/tex]        

Divide by 10 both sides          

[tex]x\leq 5\ days[/tex]

therefore

The maximum number of days is 5

Answer:

A)  x + 2y = 4

3x + 4y -9z = 2

-x + 7z = 1

Step-by-step explanation:

The matrix form is

x y z  

1 2 0    4

3 4 -9   2

-1 0 7    1

Here 0 represents no term in system.

So, the following system represents the above matrix.

x + 2y + 0z = 4  => x + 2y = 4

3x + 4y -9z = 2

-x + 0y + 7z = 1  => -x + 7z = 1

Therefore, the answer is A.

First of all, for a point to be the solution to the system of equations, it must be located on both lines, since we are calculating the point at which the lines cross. Therefor, we can automatically discount B and D as the answers, which state that the point does not lie on either line. To see whether it is A or C we will have to solve the equations.

1. There are quite a few ways to approach solving the system of equations, however I will show the substitution method as it requires less modification of equations.

What we need to do is to isolate either x or y in one of the equations so that we can then substitute this value into the other equation. So for example if we take the first equation and isolate x:

3y + x = 6

x = 6 - 3y (Subtract 6 from both sides)

2. Now we can substitute this into the second equation (2y - x = 9).

when x = 6 - 3y:

2y - (6 - 3y) = 9

2y - 6 + 3y = 9

5y - 6 = 9 (Add 2y and 3y)

5y = 15 (Add 6 to both sides)

y = 3 (Divide both sides by 5)

From here, we can already see that the answer is C, since A has a y-value of 4, however if we were to completely solve the question we would do the following:

3. Now that we know the value of y, we can substitute this back into our equation of x = 6 - 3y to find x:

x = 6 - 3(3)

x = 6 - 9

x = -3

So, our solution is the point (-3, 3). It also has to lie on both lines to be a solution. Therefor C. It is (-3, 3) and lies on both lines, is the correct answer.

Answer:

The answer is C

(It is (−3, 3) and lies on both lines.)

Step-by-step explanation:

Answer:

  None

Step-by-step explanation:

It simplifies to -12 = 12, which cannot be made true by any value of m.

Answer:

none

Step-by-step explanation:

Answer:

Step-by-step explanation:

x ≥ 0 means x is non-negative, but it does not mean x is an integer. An additional restriction would need to be applied for x to be a non-negative integer.

Answer:

Option A is correct.

Step-by-step explanation:

No of white cars: 25

No of blue cars : 17

Total number of white and blue cars = 25 + 17 = 42

No of silvers cars: 21

No of red cars: 9

Total number of silver and red cars = 21+9 = 30

No of white and blue cars more than silver and red cars

=Total number of white and blue cars - Total number of silver and red cars

=42 - 30

= 12 cars

So, Option A is correct.

Answer:

[7, 13/3]

Step-by-step explanation:

Answer: A. The molten mixture of rock-forming substances, gases, and water from the mantle

Magma is a mass of molten rock that is found in the deepest layers of the Earth at high temperature and pressure, and that can flow out through a volcano.

The composition of this mass is a mixture of liquids, volatile and solids that when they reach the surface in an eruption becomes lava, which when cooled crystallizes and gives rise to the formation of igneous rocks.

Answer:

  {-1/2, 1}

Step-by-step explanation:

You can divide the given polynomial by the factor (x +2) to find the remaining quadratic. That can be factored in the usual way to find the remaining zeros, or other means can be used. Such "other means" include graphing and the use of the quadratic formula.

The first attachment shows the synthetic division of f(x) by (x+2). The quotient is 2x^2 -x -1, which factors as ...

  2x^2 -x -1 = (2x +1)(x -1)

The zeros are the values of x that make these factors zero: -1/2, +1.

_____

My favorite way to find the roots of any higher degree polynomial is to use a graphing calculator. The second attachment shows that method.

We can find other zeros for the given polynomial by polynomial factoring or polynomial division. Upon dividing the given polynomial by (x+2), we get another polynomial. The zeros of this second polynomial can be found using the quadratic formula; getting the two zeros as x = 1 and x = -0.5.

Given a polynomial  [tex]f(x) = 2x^3 + 3x^2 - 3x - 2[/tex]and one of its zeros is -2; we can find the other zeros by polynomial factoring or polynomial division. First, divide the entire polynomial by (x+2) because -2 is one of the zeros. So we end up with 2x^2 - x - 1 = 0.

Now use the quadratic formula to find the remaining zeros: [tex]x = [-b\±\sqrt(b^2 - 4ac)] / (2a).[/tex]By substituting the constants from the factored polynomial equation, we will get [tex]x = [-(-1)\±\sqrt((-1)^2 - 4*2*(-1))] / (2*2) = [1\±\sqrt(1 + 8)] / 4.[/tex]This simplifies to  [tex]x = [1\±\sqrt(9)] / 4 = [1\±3] /4.[/tex] Hence our two more zeros are x = 1 and x = -0.5.

https://brainly.com/question/29775881

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1.)

   =(x-8i)(x+8i)

x^2+8ix-8ix-64i^2

x^2-64i^2

x^2-64(-1)

x^2+64

2.)

    =(4x-7i)(4x+7i)

16x^2+28ix-28ix-49i^2

16x^2-49i^2

16x^2-49(-1)

16x^2+49

3.)

    =(x+9i)(x+9i)

x^2+9ix+9ix+81i^2

x^2+18ix+81(-1)

x^2+18ix-81

4.)

    =(x-2i)(x-2i)

x^2-2ix-2ix+4i^2

x^2-4ix+4(-1)

x^2-4ix-4

5.)

    =[x+(3+5i)]^2

(x+5i+3)^2

(x+5i+3)(x+5i+3)

x^2+5ix+3x+5ix+25i^2+15i+3x+15i+9

x^2+6x+10ix+30i+25i^2+9

x^2+6x+10ix+30i+25(-1)+9

x^2+6x+10ix+30i-25+9

x^2+6x+10ix+30i-16

Hope this helps :)

The correct equivalent expression is D. [tex]\log_2{256}[/tex].

The given expression is:
[tex]\log_2{16} + \log_2{16}[/tex]

First, we need to simplify the given expression using properties of logarithms.

Using the property:
[tex]\log_b{m} + \log_b{n} = \log_b(m \times n)[/tex]

We can rewrite the given expression as:
[tex]\log_2{16} + \log_2{16} = \log_2{(16 \times 16)} = \log_2{256}[/tex]

Now we can analyze the options given:

A. [tex]\log_2{28}[/tex]: This is not equivalent because 28 is not the same as 256.

B. 8: This is not in logarithmic form and not equivalent to the simplified expression.

C. [tex]\log{256}[/tex]: This is not equivalent because the base here is 10 (common logarithm), while the given expression has a base of 2.

D. [tex]\log_2{256}[/tex]: This is correct because our simplified form is exactly [tex]\log_2{256}[/tex].

Answer:

it would take 5 seconds for the object to hit the ground after launched.

////////////////////////////////////////////////////////////////////////////////

1st step: (turn the quadratic function to a quadratic equation by setting the equal to zero): 0 = -16t2 + 80t + 0

2nd step: t = 0 & t = 5

(t = 0 is the time of launch. t = 5 represents the 5 seconds it took to hit the ground after the object was launched.)

Answer:

The object will hit the ground after 5 seconds. You can rewrite the quadratic function as a quadratic equation set equal to zero to find the zeros of the function 0 = –16t2 + 80t + 0. You can factor or use the quadratic formula to get t = 0 and t = 5. Therefore, it is on the ground at t = 0 (time of launch) and then hits the ground at t = 5 seconds

Answer:

[tex]1^2[/tex]

Step-by-step explanation:

The number 1 is called the base.  When we multiply like bases, we add the exponents.  So in order to get 1^9, we will multiply 1^7 by 1^2 because 7+2=9.

Answer:

The answer is [tex]1^{2}[/tex]

Step-by-step explanation:

Using the formula: [tex]a^{m}+a^{n}= a^{m+n}[/tex]

[tex]1^{9}=1^{7}*1^{2}=1^{7+2=9} =1^{9}[/tex]

Answer:

I think 8 hours maybe if I wrong sorry

The time taken for  tap to leak a total of 300mL is 2.4 hours.

A tap is leaking water at a rage of 1L every 8 hours.

Since 1L = 1000 mL and it takes 8 hours

So for 300 mL it takes

[tex]= 300 \times 8 \div 1000[/tex]

= 2.4 hours

Learn more about the tap here: https://brainly.com/question/24489593

Answer:

1/12

Step-by-step explanation:

There are two dices being rolled. A dice has six faces numbered from one to six. A fair dice means that the probability of each number to appear is equal. Thus the probability of any number showing up is:

P(a number appears on the dice) = how much times the number has been displayed on the dice/number of faces of the dice.

Since all numbers appear once, and there are six sides of a dice. therefore:

P(a number appears on the dice) = 1/6. Thus, P(6 appears on a dice) = 1/6.

As far as the odd numbers are concerned, there are three even numbers and three odd numbers on the dice. So P(odd number appears on the dice) = 3/6 = 1/2.

Assuming that the probabilities of both the dices are independent, we can safely multiply both the probabilities. Thus:

P(first dice lands on a 6 and second dice lands on an odd number) = 1/6 * 1/2 = 1/12.

Thus, the final probability is 1/12!!!

Answer:

a) Yes the events Chocolate and Adults are independent

b) Yes the events Children and Chocolate are independent

c) Yes the events Vanilla and Children are independent

Step-by-step explanation:

* Lets study the meaning independent and dependent probability  

- Two events are independent if the result of the second event is not

  affected by the result of the first event

- If A and B are independent events, the probability of both events  

 is the product of the probabilities of the both events

- P (A and B) = P(A) · P(B)

* Lets solve the question

# From the table:  

- The probability of chocolate is 0.35

- The probability of vanilla is 0.65

- The probability of adults is 0.60

- The probability of children is 0.40

- The probability of chocolate and adults is 0.21

- The probability of chocolate and children is 0.14

- The probability of vanilla and adult is 0.39

- The probability of vanilla and children is 0.26

a.

∵ P(chocolate) = 0.35

∵ P(Adults) = 0.60

∵ Two events are independent if P (A and B) = P(A) · P(B)  

∵ P(chocolate) · P(adults) = (0.35)(0.60) = 0.21

∵ P(chocolate and adults) = 0.21

∴ P(chocolate and adults) = P(chocolate) · P(adults)

∴ The events chocolate and adults are independent

b.

∵ P(chocolate) = 0.35

∵ P(children) = 0.40

∵ Two events are independent if P (A and B) = P(A) · P(B)  

∵ P(chocolate) · P(children) = (0.35)(0.40) = 0.14

∵ P(children and chocolate) = 0.14

∴ P(chocolate and children) = P(chocolate) · P(children)

∴ The events chocolate and children are independent

c.

∵ P(vanilla) = 0.65

∵ P(children) = 0.40

∵ Two events are independent if P (A and B) = P(A) · P(B)  

∵ P(vanilla) · P(children) = (0.65)(0.40) = 0.26

∵ P(vanilla and children) = 0.26

∴ P(vanilla and children) = P(vanilla) · P(children)

∴ The events vanilla and children are independent

The answer is:

[tex]t_1=3.60s\\t_2=7.94s[/tex]

Time equal to 3.30 seconds when the arrow was going up.

Time time equal to 7.94 seconds when the arrow was going down.

To solve the problem, we need to solve the quadratic equation and find the value of values of time where the height of the arrow is 420 feet.

Also, we are given some information, we need to substitute it and then use the quadratic equation.

The equation is:

[tex]h=-16t^{2}+vot\\\\-16t^{2}+vot-h=0[/tex]

Substituting the given information we have:

[tex]-16t^{2}+vot-h=0[/tex]

[tex]-16t^{2}+180\frac{ft}{s} t-420=0[/tex]

We have a quadratic equation where:

[tex]a=-16\\b=180\\c=-420[/tex]

Now, using the quadratic equation to find the value or values of "t", we have:

[tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]

[tex]\frac{-180+-\sqrt{180^{2}-4*-16*-420 } }{2*-16}=\frac{-180+-\sqrt{32400-26880 } }{-32}\\\\\frac{-180+-\sqrt{32400-26880}}{-32}=\frac{-180+-\sqrt{5520}}{-32} \\\\\frac{-180+-\sqrt{5520}}{-32}=\frac{-180+-(74.29)}{-32}\\\\t_1=\frac{-180+(74.29)}{-32}=3.30\\\\t_2=\frac{-180-(74.29)}{-32}=7.94[/tex]

Hence, we have two positive values of time, it means that there are two moments of time where the height of the arrow is equal to 420 feet, those times are:

[tex]t_1=3.60s\\t_2=7.94s[/tex]

Time equal to 3.30 seconds when the arrow was going up.

Time equal to 7.94 seconds when the arrow was going down.

Have a nice day!

Answer:

3.3secs, 7.9secs

Step-by-step explanation:

We are looking for the number of seconds it takes the arrow to reach a height of 420ft. We are given the projectile formula h=−16t2+v0t, where h is the height, in feet, and t is the time, in seconds. We can substitute the initial velocity v0=180 and desired height h=420 to find

420=−16t2+180t

Rewriting this quadratic equation in standard form, we have

16t2−180t+420=0

Now that the equation is in standard form, at2+bt+c=0, we can identify the coefficients a=16, b=−180, and c=420. Substituting these into the quadratic formula, we have

t=−b±b2−4ac‾‾‾‾‾‾‾‾√2a=−(−180)±(−180)2−4(16)(420)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(16)=180±5520‾‾‾‾‾√32

The approximate values for t are

t=≈180+5520‾‾‾‾‾√327.9andt=≈180−5520‾‾‾‾‾√323.3

The arrow will go up and then fall down. As the arrow goes up, it will reach 420ft after approximately 3.3s. It will also pass that height on the way down at approximately 7.9s.

Step-by-step explanation:

f(x) = (3/2)ˣ

g(x) = (2/3)ˣ

These are examples of exponential equations:

y = a bˣ

If b > 1, the equation is exponential growth.

If 0 < b < 1, the equation is exponential decay.

So f(x) is an example of exponential growth, and g(x) is an example of exponential decay.

Also, 2/3 is the inverse of 3/2, so:

g(x) = (3/2)^(-x)

So more specifically, f(x) and g(x) are reflections of each other across the y-axis.