Two passenger trains traveling in opposite directions meet and pass each other. Each train is 1/12 mi long and is traveling 50 mph. How many seconds after the front cars of the trains meet will their rear cars pass each other?

The probability of getting a particular four letter sequence is  [tex]\frac{1}{7920}[/tex].

A permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

[tex]P(n, k) =\frac{n!}{(n-k)!}[/tex]

Where:

n – the total number of elements in a set

k – the number of selected elements arranged in a specific order

! – factorial

Probability is the measure of the likelihood of an event to occur.

P(E) = number of favorable outcomes/ total number of outcomes

According to given question

We have

Total number of tiles = 11

And we have to form distinct four letter sequences by picking 4 letter tiles a bag containing 11 different alphabet.

⇒ n = 11 and k = 4

So, the total number of distinct four letter sequences formed by picking 4 tiles from a bag = [tex]11P_{4}[/tex]

⇒ total number of distinct four letters = [tex]\frac{11!}{(11-4)!} = 7920[/tex]

Since, we have to get only one particular sequence.

⇒ Total number of favorable outcomes = 1

And there are total number of four teller sequence = 7920

⇒ Total number of outcomes = 7920

Therefore, the probability of getting a particular four letter sequence = [tex]\frac{1}{7920}[/tex]

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Answer:

x = -3 is not a function because, for one thing, its graph does not pass the vertical line test.

Step-by-step explanation:

Answer:

Andy

Step-by-step explanation:

Let's say that x is Andy's speed, and d is the distance he traveled.

The time it takes Andy to reach his friend is d/x.

The time it takes Ashley to travel the first half is (d/2)/(x/2) = d/x.

The time it takes Ashley to travel the second half is (d/2)/(5x) = d/(10x).

The total time is d/x + d/(10x) = 1.1 d/x.

It takes Ashley 1.1 times longer to reach the friend.  Andy gets there first.

Answer:

15

Step-by-step explanation:

f(5) = (5)^2 - 2(5) = 25 - 10 = 15

Answer:

Multiply value in mm by 1000

Step-by-step explanation:

For example, 3m = (3 * 1000)mm

                            = 3000mm

Answer:

multiply by 1000

Step-by-step explanation:

1m = 1000mm

If i need convert meter en mikimeters

i multiply meter by 1000, example:

7 meters:

7 * 1000 = 7000 milimeters

another example:

4.75m = 4.75*1000 = 4750  milimeters

Answer:

i think u r correct

Step-by-step explanation:

good job

Answer:

B, C, and E ([tex]x\leq -7,[/tex] The graph has a closed circle, and -7 is part of the solution.)

Step-by-step explanation:

Let's first solve the inequality of [tex]15\geq 22+x[/tex].

[tex]15\geq x+22[/tex]

[tex](15)-22\geq( x+22)-22[/tex]

[tex]-7\geq x[/tex]

[tex]x\leq -7[/tex]

So the final equation comes out to be [tex]x\leq -7[/tex].

This graph has a closed circle as it is a greater than OR equal to.

And -7 is a part of this solution as it is the number x is being compared to.

Let me know if I got anything wrong.

your work for the first one is perfect!!

the second one gives you the side lengths of x+2 and x-5. the formula for the area of a rectangle is l×w so you have to multiply (x+2)(x-5) and im sure you can figure that out but the answer to that is x^2-3x-10

you set up number 3 right, you just need to continue with the distribute property which would give you 4x^2-20x+25

number 4 is the same as the other ones and the answer is 36x^2-1

number 5 is just distributing the -z^3 into everything in the parenthesis giving you -5z^3-z^4+4z^5

I cant see all your work for number 6, but I can see that your term for c is 5, when it is actually -5. it looks like you didnt subtract it to make the quadratic equal to zero and to do that you would have to subtract 5.

tbh I cant read number 7

hope that helped :)

Answer:

The answer is 51

Step-by-step explanation:

f(x) = 5x + 4

g(x) = −2x + 1

To find f(6)+g(-8) first find f(6) and g(-8) and add them

For f(6) we have

f(6) = 5(6) + 4

= 30 + 4

= 34

For g(-8)

g(-8) = - 2(-8) + 1

= 16 + 1

= 17

So we have

f(6)+g(-8) is

34 + 17

= 51

Hope this helps you

=======================================================

Explanation:

This is a piecewise function as it is composed of two pieces.

The equation for f(x) depends on what x is. Specifically whether it is even or odd.

If x is even, then f(x) = x^2-4. If x is odd, then f(x) = 3x-2

------------

f(4) means f(x) when x = 4. We have an even number input for x, so we'll go with f(x) = x^2-4

f(x) = x^2 - 4

f(4) = 4^2 - 4

f(4) = 16 - 4

f(4) = 12

------------

When x = 5, x is now odd, so use f(x) = 3x-2

f(x) = 3x-2

f(5) = 3(5) - 2

f(5) = 15 - 2

f(5) = 13

Answer:

The smallest four digit number divisible by 18, 24, and 32 is 1152.

Step-by-step explanation:

The LCM of the 3 numbers are 288

Then, the smallest four-digit number would equal 1152 (288*4)

Take L.C.M. of 18,24,32= 288

Resulting in 1152 :)

Answer:

58 Cards

Step-by-step explanation:

Answer:

A) QRST ∼ GFED

Step-by-step explanation:

We have to compare the ratios of all the sides one by one. Once I divided each side length by the equivalent side length on all four sides of both quadrilateral, make sure they are all equal.

Answer:

A) QRST is similar to GFED

Step-by-step explanation:

quadrilateral GFED is 1.25 times larger than quadrilateral QRST not to be confused with QRST is similar to DEFG because then the sides would not correspond to each other

Answer:

C.

Step-by-step explanation:

You can memorize the patterns of fractions of ninths.

0/9 = 0

1/9 = 0.1111111111111111111111

2/9 = 0.222222222222

3/9 = 0.3333333333333

4/9 = 0.4444444444444

5/9 = 0.5555555555556

6/9 = 0.6666666666667

7/9 = 0.777777777777778

8/9 = 0.88888888888889

9/9 = 1

Hope this helps!

Answer:

C. 8/9

Step-by-step explanation:

Well .8 repeating is not 8/10.

Though many would choose that.

If you do 8 ÷ 10 you get .8 not .8 repeating meaning 8/10 is not correct.

To get .8 repeating we would divide 8 by 9.

Because all natural numbers below 9 can be divided by 9 to create a .repeating itself.

For example 8 ÷ 9 = .8 repeating,

4÷9 = .4 repeating.

Thus,

C. is the correct answer.

Hope this helps :)

Answer:

<

Step-by-step explanation:

Since it is a negative value, whatever fraction is closer to 0 will be greater.

I hope this helped! Good luck with the rest of your class :)

Answer: Tossing two coins at once

Step-by-step explanation:

As during flipping two coins we have possibilities one is HH,HT,TH,TT

Answer:

Tossing two coins at once

Step-by-step explanation:

Answer y=x

Step-by-step explanation:

y=x when x equal one y equals one

The algebraic equation to match each graph will be y = | x |.

The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given graph shows that for every value of y the value of x will always be positive. Then the algebraic equation will be written as below:-

y = | x |.

Therefore, the algebraic equation to match each graph will be y = | x |.

The graph of the equation is attached with the answer below.

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Answer:

x² (x^n + 1)

Step-by-step explanation:

factor x^(n+2) + x²

= x^(n+2) + x²

= x^n • x² + x² (using law of indices)

= x²(x^n + 1)

Answer:

The correct option is:

y - x = -4

Step-by-step explanation:

The graphed equation is:

y = x - 4

The equation which will have infinite number of solution should overlap the graphed equation at infinity points.

It is only possible when both the equations are exactly same.

Consider the line given:

y - x = -4

Rearrange the equation:

y = x - 4

Thus, it is the same as the first equation.

Verify for point (0,-4)

y - x = -4

-4 - 0 = -4

-4 = -4

Proved.

Verify for point (4,0)

y - x = -4

0 - 4 = -4

0 = -4+4

0 = 0

Proved

The correct option is (1). [tex]y-x= -4[/tex]

Given equation,

[tex]y = x - 4[/tex]

the line, [tex]y = x - 4[/tex] passes through the points (0, -4) and (4, 0).

Comparing with the general equation of a straight line,

[tex]y = mx + c[/tex] , where [tex]m[/tex] is the slope and [tex]c[/tex] is the y-intercept.

The slope of the equation [tex]y = x - 4[/tex] is 1 and its The y-intercept is -4.

We know that,

Two equations will have an infinite number of solutions when they are on the same line, that is having the same slope and intercept.

Now we check for the slope and the intercept of the given options.

Option (1)  [tex]y - x = -4[/tex]

 [tex]y = x - 4[/tex]

Here the slope is 1 and y intercept is -4, which is the same as the given equation and both equations will have an infinite number of solutions.

Now option (2).

[tex]y - x = -2[/tex]

[tex]y=x-2[/tex]

The slope is 1 and y intercept is -2  

The slope is the same as the given equation but the intercept is different giving no solution.

Hence the correct option is (1). [tex]y-x= -4[/tex]

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Step-by-step explanation:

Answer:

the radius of the pool is 50.025 feet

Step-by-step explanation:

From the information given:

We can have a schematic view of a diagrammatic illustration in our mind where the distance of the pool to Lincy is (20 + r ) and the distance to the tangent is 49.

So; by using pythagoras theorem, since the radius meets the tangent at a right angle; we have:

[tex]r^2 + 49^2 = ( r + 20 )^2[/tex]

[tex]r^2 +2401 = r^2 + 40r + 400[/tex]

[tex]2401 = 40r + 400[/tex]

[tex]2401- 400 = 40r[/tex]

2001 = 40 r

r = 2001/40

r = 50.025 feet

Answer:

x = 6 + 16 sqrt(3) / 3  or equivalently 6 + 16/sqrt(3)

Step-by-step explanation:

Have enough data to solve only for x in the diagram.

The lengths that make up the base are respectively from left to right

x1 = 4 cot(60) = 4 (3/sqrt(3)) = 4sqrt(3)  m

x2 = 6 m

x3 = 4 cot(30) = 4 ( sqrt(3) / 3 ) = 4/ sqrt(3) = (4/3)sqrt(3) m

Altogether

Base, x = 4sqrt(3)/3 + 6 + 2 sqrt(3)

= 6 + 16 sqrt(3) / 3  or equivalently 6 + 16/sqrt(3)

Answer:

Step-by-step explanation:

First triangle: angles are in the ratio = 30 : 60 : 90

So, the ratio of sides = a : a√3 : 2a

a√3 = 4 m

a  * 1.732 = 4

a = 4/1.732

a = 2.31

Now, in the second triangle, angles are in the ratio = 30 : 60 : 90

So, the ratio of sides = b : b√3 : 2b

b = 4 m

b√3 = 4 * 1.732 = 6.928 m

x = a + 6 + b

x = 2.31 + 6 + 6.928

x = 15.23 m

Answer:

[tex]\boxed{\mathrm{Option \ A}}[/tex]

Step-by-step explanation:

=> [tex](x+y)+(2(x+y)+3)=9[/tex]

Solving the bracket

=> [tex]x+y+2x+2y+3 = 9[/tex]

=> [tex]3x+3y = 9-3[/tex]

=> [tex]3(x+y) = 6[/tex]

Dividing both sides by 3

=> [tex]x+y = 2[/tex]

A) 3 - 1 = 2     ←  (Correct Answer)

B) -3+1 = -2

C) -3-1 = -4

D) 3+1 = 4

E) 9-31 = -22

Answer:

41x/35y

Step-by-step explanation:

combine like terms

Answer:

10² + 24²

Step-by-step explanation:

The diagram illustrates Pythagoras' identity.

The square on the hypotenuse of a right triangle is equal t o the sum of the squares on the other 2 sides.

A is the square on the hypotenuse, thus

A² = 10² + 24²

Answer:

Step-by-step explanation:

Let side of the square be a

Now, let's find:

Hypotenuse ( h ) = a

Perpendicular ( p ) = 10

Base ( b ) = 24

Applying Pythagoras theorem in the right triangle formed by the square:

[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]

plug the values

[tex] {a}^{2} = {10}^{2} + {24}^{2} [/tex]

Hope this helps..

Best regards!!

Answer:

d

Step-by-step explanation:

2/5÷ 1/10 = [tex]\frac{2}{5}*\frac{10}{1}[/tex]

               = 2 * 2

               = 4

Answer:

b

Step-by-step explanation:

LCD of (5, 10): 10

2/5=4/10(multiply top and bottom by 2)

(4/10)/(1/10)= 4

Therefore, 1/10 is 1/4th of 2/5

Answer: 3060

Step-by-step explanation:

Formula : (r+1)th term of [tex](a+b)^n[/tex] : [tex]T_{r+1}=\ ^nC_r(a)^{n-r}(b)^r[/tex]

To find: Coefficient of [tex]x^{14}y^4[/tex] in the expansion of [tex](x + y)^{18}[/tex].

Let the term in the expansion of [tex](x + y)^{18}[/tex] be [tex]^{18}C_r x^{18-r}y^r=x^{14}y^4[/tex]

[tex]\Rightarrow\ r=4[/tex]

Now, Coefficient = [tex]^{18}C_r=^{18}C_4=\dfrac{18!}{4!14!}[/tex]     [[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]

[tex]=\dfrac{18\times17\times16\times15\times14!}{14!(24)}\\\\=3060[/tex]

Hence, the coefficient of [tex]x^{14}y^4[/tex] in the expansion of [tex](x + y)^{18}[/tex] is 3060 .

Answer:

$1.92

Step-by-step explanation:

The equation would be 6/3.12

that equals 1.92.

Answer:

54

Step-by-step explanation: