M drives past two traffic lights. Probability that both are red is .35 and probability that firest is red is .48. wht is probability that second light is red, given that first light is red?

Answer:

Step-by-step explanation:

Cos(A + B) = Cos(A)*Cos(B) - Sin(A)*Sin(B)

Find The Hypotenuse of A

Tan(A) = Opposite / Adjacent

Tan(A) = 15/8

Opposite = 15

Adjacent = 8

Hypotenuse = c

c^2 = opposite^2 + Adjacent^2

c^2 = 15^2 + 8^2

c^2 = 225 + 64

c^2 = 289

sqrt(c^2) = sqrt(289)

c = 17

Find the opposite of B

Adjacent = 12

Hypotenuse = 37

Opposite = b

adjacent^2 + opposite^2 = hypotenuse^2

12^2 + b^2 = 37^2

144 + b^2 = 1369

b^2 = 1369 - 144

b^2 = 1335

b = 35

Definitions

Sin(A) = Opposite / hypotenuse = 15/17

Sin(B) = opposite / hypotenuse =  35/37

Cos(A) = 8/17

Cos(B) = 12/37

Answer

Cos(A + B) = Cos(A)*Cos(B) - Sin(A)*Sin(B)

Cos(A + B) = 8/17 * 12/37 - 15/17*35/37

Cos(A + B) = 96/629 - 525/629

Cos(A + B) = -429/629

Answer:

45.584

;)

Have a nice day

Answer:

D

Step-by-step explanation:

It is D because there are only 3 sides given. I understand where you were going with B, but there is no angle given, (and you cannot prove one either), so the answer is simply D.

A - There is no angle, triangle does not matter

B - There is no angle, triangle is correct

C - It is similar, they have the same scale factor

D - There are 3 sides, and the triangle is correct

Answer:

63%.

Step-by-step explanation:

There are 12 scores below 45 and total number of scores = 19.

So percentile rank= (12/19) * 100

=  63%.

9514 1404 393

Answer:

  4. (d) 4.38 in³

  5. (b) 19 gallons

  6. (a) 6.4 yd³

Step-by-step explanation:

4. The equation can be rearranged to find the compressed volume.

Multiply both sides by the compressed volume:

  (compression ratio)×(compressed volume) = (expanded volume)

Divide both sides by the compression ratio:

  (compressed volume) = (expanded volume)/(compression ratio)

Fill in the numbers and do the arithmetic.

  compressed volume = 46.0 in³/(10.5/1) = 4.38 in³

The compressed volume is about 4.38 in³.

__

5. The area to be covered is 3170 ft². We want to cover it twice, so the total area we want to cover is 2×3170 ft² = 6340 ft². One gallon of paint covers 350 ft². We want to find the smallest integer number of gallons n such that ...

  n×(350 ft²) ≥ 6340 ft²

Dividing by the coefficient of n, we have ...

  n ≥ 6340/350 ≈ 18.11

The smallest integer value of n is 19. 19 gallons of paint will be needed.

__

6. The quantity of sand needed (q) is proportional to the area to be covered, so we have ...

  q/(400 yd²) = (1.6 yd³)/(100 yd²)

Multiplying both sides of this equation by 400 yd² gives ...

  q = (1.6 yd³)(400/100) = 6.4 yd³

6.4 yd³ of sand will be needed.

the answer is 35 I did a lot of work I can't show you here

Answer:

Can you insert a picture?  and then I could help you.

Step-by-step explanation:

Answer:

Brianne would earn 5 dollars an hour so the graph should look something like this.

Answer:

BC = 6.9

Step--step explanation:

Reference angle = 30°

Adjacent = BC

Hypotenuse = 8

Apply trigonometric function, CAH:

Cos 30° = Adj/Hypotenuse

Cos 30° = BC/8

8*Cos 30° = BC

6.92820323 = BC

BC = 6.9 (to the nearest tenth)

Let u = (1, 0) and v = (0, 1). Then

T (u) = (2*1 - 3*0, 1 + 4, 5*0) = (2, 5, 0)

T (v) = (2*0 - 3*1, 0 + 4, 5*1) = (-3, 4, 5)

=>   T (u) + T (v) = (-1, 9, 5)

but

T (u + v) = T (1, 1) = (2*1 - 3*1, 1 + 4, 5*1) = (-1, 5, 5)

=>   T (u + v) ≠ T (u) + T (v)

which means T does not preserve addition, so it is not linear.

Answer: The answer would be y = x + 8

Step-by-step explanation:

Answer:

Hello! answer: x = 40

Step-by-step explanation:

These are vertical angles meaning they will have the same measure.

40 × 3 = 120 120 - 16 = 104 therefore x = 40 hope that helps!

Answer:

#2. 6x3.14=1080 which is more than 18

Answer:

[tex]f(x) = \frac{10}{x} - 4 \\ \delta \: f(x) = \frac{f(8) - f(2)}{2} \\ = \frac{(\frac{10}{8} - 4) - ( \frac{10}{2} - 4)}{2} \\ = \frac{ \frac{ - 11}{4} - 1}{2} \\ = \frac{ \frac{ - 15}{4} }{2} \\ = - \frac{15}{8} [/tex]

Answer:

104 softballs

Step-by-step explanation:

26 x 4 = 104

Answer:

Step-by-step explanation:

I dont know how to do the box thing, but I added all the things and boys read more.

girls:1870

boys:1952

The diffrence (when subracting) is 82

Answer:

C. 13 gallons

Step-by-step explanation:

150 divided by 6 is 25. 325 divided by 25 is 13.

To travel 325 miles the van needs C. 13 gallons of gas.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, A van travels 150 miles on 6 gallons of gas.

So, In one gallon the van travels (150/6) = 25 miles.

∴ To travel 325 miles the van needs (325/25) = 13 gallons of gas.

learn more about the unitary method here :

https://brainly.com/question/28276953

#SPJ2

Answer:

third

Step-by-step explanation:

arctan of ( opp/adj) = arctan( 10/15 )

the shadow is 15 so 10 must be the height of the streetlight and

arctan (10/15) is the angle between the ground and the line from the edge of the shadow to the top of the streetlight

Answer:

B) positive x-axis.

Step-by-step explanation:

angle to be in standard position, its vertex is at the origin and the initial side lies along the positive x axis

Answer:

Positive x axis

Step-by-step explanation:

The angle lies in standard position means it begins from Q1

The first side must be x axis

Then in Q1 x>0 so it's positive x axis

Hello there I hope you are having a great day :) Cindy has a chocolate box whose length is 12 cm, height of 8 cm, and width of 6 cm. Find the volume of the box?

V = L x W x H

Volume = length x Width x Height.

12cm x 6cm x 8cm = V = 576cm^3

so the answer is 576cm^3

Hopefully that helps you :)

Step-by-step explanation:

VOLUME : is the quality of three deamination place enclosed by a closed surface it is the space that substance or shape or keep use or contains it is measured in cubic units

A RACTANGULAR :is a three dimensional figure it has length wind and height

let us analysis the problem above

length =12 cm

height = 8 cm

width=6 cm

v=1 x w x h

=(12 CM) x (8 CM) x (6 CM)

the value of the box is 576 CM ³

Answer:

A) 9/2x3/8

Step-by-step explanation:

Answer: k = 8

Step-by-step explanation:

-3k + 30 = 6

-3k = -24

k = 8

Answer:

k = 8

Step-by-step explanation:

6 = -3(k - 10)

Divide each side by -3

6/-3 = -3/-3 *(k - 10)

-2 = k-10

Add 10 to each side

-2+10 = k-10+10

8 = k

Answer:

M(x)  =  452,56 in

Step-by-step explanation:

The volume of the open box is  500 in³

V = Area of the base times height

V(b) =  x² * h               where x is the side of the square and h the heigh

Then     500 =  x²*h

Total material to use is: material of the base + material of 4 sides

material of the base is  x²

material of one side is x*h  we have 4 sides then  4*x*h

Total material M(b)

M(b)  =  x²  +  4*x*h

And    as    h  =  500/ x²

M(x)  =  x²  +  4* x* 500/x²

M(x)  =  x²  +  2000/x

Tacking derivatives on both sides of the equation

M´(x)  =  2*x   - 200/x²

M´(x)  =  0         2*x  -  200/x²  = 0

x³ -  100  =  0

x³   =  100

x   =  4,64 in

And By substitution     h  =  500/x²

h  =  500/(4,64)²           h  =  23,22  in

How do we know that x = 4,64 make V(x) minimum

we get the second derivative

M´´(x)  =  2  +  200*2x/ x⁴    =  2  +  400/x³

M´´(x) is always positive

M´´(x) > 0     then M(x) has a minimum for  x= 4,64 in

The least amount of material is:

M(x)  =  x²    +    2000/x

M(x)  =  (4,64)²  *  2000/4,64

M(x)  = 21,53  +  431,03

M(x)  =  452,56 in

Answer:

27.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

110/4 is 27.5

Given:

Consider the rule of a sequence is:

[tex]T_n=\dfrac{n^2-n}{2}[/tex]

To find:

The 6th term generated by the given rule.

Solution:

We have,

[tex]T_n=\dfrac{n^2-n}{2}[/tex]

Substituting [tex]n=6[/tex] in the above rule, we get

[tex]T_6=\dfrac{6^2-6}{2}[/tex]

[tex]T_6=\dfrac{36-6}{2}[/tex]

[tex]T_6=\dfrac{30}{2}[/tex]

[tex]T_6=15[/tex]

Therefore, the 6th term generated by the given rule is 15.

Answer:

A. A triangle can be equilateral and obtuse at the same time

Step-by-step explanation:

All angles in an equilateral triangle are 60° therefore they cannot be above 90° and less than 180°

Answer:

[tex]y = \frac{2}{z} - \frac{x}{z}[/tex]

Step-by-step explanation:

Given

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

Required

Rewrite to show y-intercept

We have: [tex]x + zy = 2[/tex]

Subtract x from both sides

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

Divide both sides by z

[tex]y = \frac{2}{z} - \frac{x}{z}[/tex]

The y intercet is: [tex]\frac{2}{z}[/tex]