Points A, B, C, and D lie on a line in that order. If AD/AC = 2/1 and AD/AB = 3/1, what is the value of AC/BD?

Answer:

the temperature drops 2 degrees F

Step-by-step explanation:

Answer:

The problem states that the temperature drops 2 degrees F.  The word drops signifies that I should subtract 2 1/5 degrees F from 63 1/4 F.

Step-by-step explanation:

Answer:

You could save $20

Step-by-step explanation:

For buying them separately for $30 each for 5 people it would be $150 but if you buy the first option you would get 5 admission tickets for only $130

Answer:

20 dollars

Step-by-step explanation:

for the first deal is 5 for $130

and the second is for $30

$30 times 5 (the number of people) = $150

$150-$130= is 20

answer: $20

To prove that: (2cosA+1) (2cosA-1) = 2cos2A+1

We try to solve one side of the equation to get the other side of the equation.

In this case, we'll solve the right hand side (2cos2A + 1) of the equation with the aim of getting the left hand side of the equation  (2cosA + 1)(2cosA - 1)

Solving the right hand side: 2cos2A + 1

i. We know that cos2A = cos(A+A) = cosAcosA - sinAsinA

Therefore;

cos2A = cos²A - sin²A

ii. We also know that: cos²A + sin²A = 1

Therefore;

sin²A = 1 - cos²A

iii. Now re-write the right hand side by substituting the value of cos2A as follows;

2cos2A + 1 = 2(cos²A - sin²A) + 1

iv. Expand the result in (iii)

2cos2A + 1 = 2cos²A - 2sin²A + 1

v. Now substitute the value of sin²A in (ii) into the result in (iv)

2cos2A + 1 = 2cos²A - 2(1 - cos²A) + 1

vi. Solve the result in (v)

2cos2A + 1 = 2cos²A - 2 + 2cos²A + 1

2cos2A + 1 = 4cos²A - 2 + 1

2cos2A + 1 = 4cos²A - 1

2cos2A + 1 = (2cosA)² - 1²

vii. Remember that the difference of the square of two numbers is the product of the sum and difference of the two numbers. i.e

a² - b² = (a+b)(a-b)

This means that if we put a = 2cosA and b = 1, the result from (vi) can be re-written as;

2cos2A + 1 = (2cosA)² - 1²

2cos2A + 1 = (2cosA + 1)(2cosA - 1)

Since, we have been able to arrive at the left hand side of the given equation, then we can conclude that;

(2cosA + 1)(2cosA - 1) = 2cos2A + 1

Answer:

[tex]\boxed{\sf LHS = RHS }[/tex]

Step-by-step explanation:

We need to prove that ,

[tex]\sf\implies (2 cosA +1)(2cosA-1) = 2cos2A+1[/tex]

We can start by taking RHS and will try to obtain the LHS . The RHS is ,

[tex]\sf\implies RHS= 2cos2A + 1 [/tex]

We know that , cos2A = 2cos²A - 1 ,

[tex]\sf\implies RHS= 2(2cos^2-1)-1 [/tex]

Simplify the bracket ,

[tex]\sf\implies RHS= 4cos^2A - 2 +1 [/tex]

Add the constants ,

[tex]\sf\implies RHS= 4cos^2-1 [/tex]

Write each term in form of square of a number ,

[tex]\sf\implies RHS= (2cos^2A)^2-1^2 [/tex]

Using (a+b)(a-b) = a² - b² , we have ,

[tex]\sf\implies RHS= (2cosA+1)(2cosA-1) [/tex]

This equals to LHS , therefore ,

[tex]\sf\implies \boxed{\pink{\textsf{\textbf{ RHS= LHS }}}} [/tex]

Hence Proved !

Answer:

reflection

Step-by-step explanation:

B is the mirror image of A across a line between the two images

Answer:

1/6 < 2/11

Step-by-step explanation:

1/6 = 2/12

2/11 >2/12

So that means 1/6 < 2/11

Answer:  1/6 < 2/11

This is the same as saying 11/66 < 12/66

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

Explanation:

1/6 is the same as 11/66 when multiplying top and bottom by 11.

2/11 is the same as 12/66 when multiplying top and bottom by 6.

The 6 and 11 multipliers are from the original denominators (just swapped).

We can see that 11/66 is smaller than 12/66, simply because 11 < 12, so that means 1/6 is smaller than 2/11

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

Here's one way you could list out the steps

11 < 12

11/66 < 12/66

1/6 < 2/11

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

Here's another way to list out the steps. First assume that 1/6 and 2/11 are equal. Cross multiplication then leads to

1/6 = 2/11

1*11 = 6*2

11 = 12

Which is false. But we can fix this by replacing every equal sign with a less than sign

1/6 < 2/11

1*11 < 6*2

11 < 12

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

Yet another way to see which is smaller is to use your calculator or long division to find the decimal form of each value

1/6 = 0.1667 approximately

2/11 = 0.1818 approximately

We see that 0.1667 is smaller than 0.1818, which must mean 1/6 is smaller than 2/11.

Answer:

x = -4   or   x = 5

Step-by-step explanation:

To solve the absolute value equation

|X| = k

where X is an expression in x, and k is a non-negative number,

solve the compound equation

X = k or X = -k

Here we have |2 - 4x| = 18

In this problem, the expression, X, is 2 - 4x, and the number, k, is 18.

We set the expression equal to the number, 2 - 4x = 18, and we set the expression equal to the negative of the number, 2 - 4x = -18. Then we solve both equations.

2 - 4x = 18  or  2 - 4x = -18

-4x = 16   or   -4x = -20

x = -4   or   x = 5

Answer:

x = -5 . x= 4

Step-by-step explanation:

because |4| = 4 and |-4| = 4

you can see that TWO inputs can get an output of (lets say) 4

The absolute value function can be seen as a function that ignores negative signs

so to get an OUTPUT of "18" using the absolute value function

there are really two ways of getting there

"2-4x = 18"  AND "2-4x = -18"

if you solve both of those you will find that -5 and 4 will

produce the 18 and -18

Answer:

19. 3x+5/2x+7 =5

or, 3x+5=5×(2x + 7)

or, 3x + 5 = 10x + 35

or, 5 - 35 = 10x - 3x

or, -30 = 7x

or, -30/7 = x

21. let x be the other number

we know,

or, x × 1/7 =2

or, x/7 =2

or, x = 14

therefore, the other number is 14.

Answer:

you simply have to do ide the coefficients and subtract the power

Hello!

25 wooden ..... 5.5 hours

x wooden ..... 9.9 hours

_____________________

25/x = 5.5/9.9

25 × 9.9 = x × 5.5

247.5 = x × 5.5

x × 5.5 = 247.5

x = 247.5 : 5.5

x = 45 wooden

Good luck! :)

Answer:

45

Step-by-step explanation:

In questions such as these it is implied Anita can and does work at a constant rate. Therefore, we can set up the following proportion:

[tex]\frac{25}{5.5}=\frac{x}{9.9}[/tex], where [tex]x[/tex] represents the number of wooden slats she can paint in 9.9 hours.

Multiplying both sides by 9, we get:

[tex]x=\frac{9.9\cdot 25}{5.5},\\x=\boxed{45}[/tex]

Answer:

1) 6m+8n

4) 21x+14y

7) 14c+16d

10) d+3e

Step-by-step explanation:

Answer:

922.868

Step-by-step explanation:

[tex]942.600-19.732=922.868[/tex]

Answer:

c

Step-by-step explanation:

non terminating recurring. i think option c must be the answer

Answer:

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they pass, or they do not. The probability of an student passing is independent of other students, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Probability that all students pass in a class:

Class of 8 students, which means that [tex]n = 8[/tex]

Each student has a 95% chance of passing their class independent of the other students, which means that [tex]p = 0.95[/tex]

This probability is P(X = 8). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 8) = C_{8,8}.(0.95)^{8}.(0.05)^{0} = 0.6634[/tex]

Find the probability that, in exactly one of the two classes, all 8 students pass.

Two classes means that [tex]n = 2[/tex]

0.6634 probability all students pass in a class, which means that [tex]p = 0.6634[/tex].

This probability is P(X = 1). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{2,1}.(0.6634)^{1}.(0.3366)^{1} = 0.4466[/tex]

0.4466 = 44.66% probability that, in exactly one of the two classes, all 8 students pass.

Question is incomplete ; The questions solved were picked from similar questions but different parameters. However, the solution pattern are exactly the same.

Answer:

- 0.0943

- 0.386

30.185

Step-by-step explanation:

Given :

ACT:

Mean score, m = 22.5

Standard deviation, σ = 5.3

SAT :

Mean score, m = 526

Standard deviation, σ = 101

1.)

Zscore for ACT score of 22:

Since the distribution is normal ; we use the relation ;

Zscore = (score - mean) / standard deviation

Score = 22

Zscore = (22 - 22.5) / 5.3 = - 0.0943

B.)

Zscore for SAT of 487

Zscore = (score - mean) / standard deviation

Score = 487

Zscore = (487 - 526) / 101 = - 0.386

C.)

ACT score, for ACT Zscore of 1.45

Zscore = (score - mean) / standard deviation

ZScore = 1.45

1.45 = (score - 22.5) / 5.3

1.45 * 5.3 = (score - 22.5)

7.685 = score - 22.5

Score = 7.685 + 22.5

Score = 30.185

Answer:

11 hours is right answer i hope it will help you

Step-by-step explanation:

k=8.6

i think it is the right answer

Answer:

13.4 cubic feet and 23040 inches

Step-by-step explanation:

Answer:

In cubic feet =  13.3 ft^3 ...........or 13.33ft^3

In cubic inches = 23040in^3

Step-by-step explanation:

In cubic feet it becomes

4(5) = 20 feet ^2   ................but we need volume in feet

so 8 inches = .............2/3 of a foot = 0.666667

Answer therefore is   (4) x (5) x (0.666667) = 13.32ft^3

In cubic inches it becomes

4 x 12 = 48 inches

5  x 12  = 60 inches

and 8 inches

48 x 60 x 8 = 23040 in^3

We check by squaring the divider

23040/12^3 = 13.333

We only square and square again to find a cube but to square once we do this with area too.

Area 1. =  4 x 5 = 20 feet^2

Area 2. =  48 x 60 = 2880 in ^2  / 12^2 = 20

Answer:

Amazon

Step-by-step explanation:

Answer:

39°

Step-by-step explanation:

A radius of a circle (segment CD) drawn to the point of tangency (D) intersects the tangent (line DE) at a 90-deg angle.

That makes m<D = 90.

m<D + m<C + m<E = 180

90 + 51 + m<E = 180

m<E = 39

Answer:

i^−3 = i

i^−2 = −1

i^−1 = −i

i^0 = 1

i^1 = i

i^2 = −1

i^3 = −i

i^4 = 1

i^5 = i

i^ 6 = −1

See the pattern

Answer/Step-by-step explanation:

Recall: an angle can be named in three different ways:

i. Using one letter which is the vertex of the angle. i.e. if the vertex of the angle is A we can name the angle as <A.

ii. Using the number of the labelled angle. i.e. is the angle is labelled 2, we can name it <2

iii. Using the three letters of the angles with the vertex angle in the middle. i.e. if the three points that form an angle are A, B, C and the vertex is B, we can name the angle as <ABC.

✔️Let's name the each angle given according:

1. <G, <3, and <FGH

2. <D, <4, and <CDE

3. <S and <TSR (the number seems blur and difficult to read. Whatever number is used to label the angle is what you'd use in naming the angle)

Answer:

DL/dt = 529 miles/h

Step-by-step explanation:

The radio station (point A) the point just up the radio station ( point B), and the variable position of the plane ( at specif t  point C) shape a right triangle wich hypothenuse L is:

L²  =  d² + x²

d is the constant distance between the plane and the ground

Then differentiation with respect to time on both sides of the equation

2*L*dL/dt  = 2*d* Dd/dt  + 2*x*dx/dt

But   Dd/dt  =  0

L*dL/dt  =  x*dx/dt

x =  5 miles       dx/dt  =  570 m/h        L  = √ d² + x²    L  √ (5)² + (2)²

L = √29      L  = 5.39 m

5.39 *DL/dt  =  5*570 m/h

DL/dt  =   5*570/5.39   miles/h

DL/dt  =  528.76  miles/h

DL/dt = 529 miles/h

Answer:

0.1667

Step-by-step explanation:

We are given;

Arrival rate, λ = 10 requests per hour

Service rate, μ = 12 requests per hour

From queuing theory, we know that;

ρ = λ/μ

Where ρ is the average proportion of time which the server is occupied.

Thus;

ρ = 10/12

ρ = 0.8333

Now, the probability that no requests for assistance are in the system is same as the probability that the system is idle.

This is given by the Formula;

1 - ρ

probability that no requests for assistance are in the system = 1 - 0.8333 = 0.1667

Answer:

Step-by-step explanation:

A- 417 × 1002

  =  417 × (1000+2)

  =  417× 1000+ 417×2

  = 417000+ 834

  = 417834

B- 4× 573×25

    = 4× 25+ 573

    = 100+ 573

   = 57300

C- 8312+284+788+716

   = (8312+284) + (788+716)

   = 8596+ 1504

  = 10,100

D- 125×44+56×125

   = 125× (44+56)

  = 125× 100

  = 12500

Please mark me as brainlist

It took me alot of time to type sorry for that...

Answer:

2.113

Step-by-step explanation:

               [tex]3.600\\1.487 \ -\\\overline{2.113}[/tex]

Answer:

The answer is

[tex]y = 3[/tex]

[tex]y = - 4[/tex]

Step-by-step explanation:

We must find a solution where

[tex] \frac{6}{y + 1} + \frac{y}{y - 2} = \frac{6}{y + 1} \times \frac{y}{y - 2} [/tex]

Consider the Left Side:

First, to add fraction multiply each fraction on the left by it corresponding denomiator and we should get

[tex] \frac{6}{y + 1} \times \frac{y - 2}{y - 2} + \frac{y}{y - 2} \times \frac{y + 1}{y + 1} [/tex]

Which equals

[tex] \frac{6y - 12}{(y -2) (y + 1)} + \frac{ {y}^{2} + y }{(y - 2)(y + 1)} [/tex]

Add the fractions

[tex] \frac{y {}^{2} + 7y - 12 }{(y - 2)(y + 1)} = \frac{6}{y + 1} \times \frac{y}{y - 2} [/tex]

Simplify the right side by multiplying the fraction

[tex] \frac{6y}{(y + 1)(y + 2)} [/tex]

Set both fractions equal to each other

[tex] \frac{6y}{(y + 1)(y - 2)} = \frac{ {y}^{2} + 7y - 12}{(y + 1)(y - 2)} [/tex]

Since the denomiator are equal, we must set the numerator equal to each other

[tex]6y = {y}^{2} + 7y - 12[/tex]

[tex] = {y}^{2} + y - 12[/tex]

[tex](y + 4)(y - 3)[/tex]

[tex]y = - 4[/tex]

[tex]y = 3[/tex]

Answer:

Step-by-step explanation:

[tex]\frac{6}{y+1}+\frac{y}{y-2}=\frac{6}{y+1} \times \frac{y}{y-2} \\multiply ~by~(y+1)(y-2)\\6(y-2)+y(y+1)=6y\\6y-12+y^2+y=6y\\y^2+y-12=0\\y^2+4y-3y-12=0\\y(y+4)-3(y+4)=0\\(y+4)(y-3)=0\\y=-4,3[/tex]

Answer:

The probability of randomly selecting one employee who earned less than or equal to $45,000=0.00621

Step-by-step explanation:

We are given that

Mean,[tex]\mu=50000[/tex]

Standard deviation,[tex]\sigma=2000[/tex]

We have to find the probability of randomly selecting one employee who earned less than or equal to $45,000.

[tex]P(x\leq 45000)=P(\frac{x-\mu}{\sigma}\leq \frac{45000-50000}{2000})[/tex]

[tex]P(x\leq 45000)=P(Z\leq-\frac{5000}{2000})[/tex]

[tex]P(x\leq 45000)=P(Z\leq -2.5)[/tex]

[tex]P(x\leq 45000)=0.00621[/tex]

Hence,  the probability of randomly selecting one employee who earned less than or equal to $45,000=0.00621

Answer:

36

Step-by-step explanation:

2x is an exterior angle

Exterior angles = the sum of the two remote (unconnected - non supplementary interior angles).

Put symbolically

<LEG = <EGF + <EFG

<EFG = 180 - 4x           In this case you need to find the supplemtnt

<LEG = x + 180 - 4x

2x = 180 - 3x                Add 3x to both sides

5x = 180                       Divide by 5

x = 36

Answer:

The solution to the equation  log3(x+2)=1 is given by x=1

Step-by-step explanation:

We are given that

[tex]log_3(x+2)=1[/tex]

We have to find the graph which shows the  solution to the equation log3(x+2)=1.

[tex]log_3(x+2)=1[/tex]

[tex]x+2=3^1[/tex]

Using the formula

[tex]lnx=y\implies x=e^y[/tex]

[tex]x+2=3[/tex]

[tex]x=3-2[/tex]

[tex]x=1[/tex]