The ratio of caretakers to childeren is _:_. If 24 more children are added, they should hire _ more caretakers to maintain the ratio of caretakers to children.

Answer:

dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)

dy/dt = 0 + 1.6

dy/dt = 1.6 mi/min

Step-by-step explanation:

We need to find out values for all of the variables:

The observer is not moving, therefore dx/dt = 0.

The observer is standing 4 miles away from the lift-off point, so x = 4.

The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.

The rate of change for the angle, dθ/dt, is 0.1.

Let θ be the angle of elevation of the line of sight from the horizontal. Since the hot air balloon is rising at a speed of 100 m/min, its vertical distance in time, t is d = vt = 100t.

Since the point of the observer is 200 m away( the horizontal distance), then tanθ = vertical rise/horizontal distance = 100t/200 = t/2

tanθ = t/2

To find the rate of change of the angle of elevation, we differentiate with respect to t.

So, dtanθ/dt = d(t/2)/dt

sec²θdθ/dt = 1/2

dθ/dt = 1/(2sec²θ)

At 600 m high, tanθ = vertical rise/horizontal distance = 600 m/200 m = 3

Given that tan²θ + 1 = sec²θ

dθ/dt = 1/(2sec²θ)

dθ/dt = 1/(2[tan²θ + 1])

Since tanθ = 3

dθ/dt = 1/(2[tan²θ + 1])

dθ/dt = 1/(2[3² + 1])

dθ/dt = 1/(2[9 + 1])

dθ/dt = 1/(2[10])

dθ/dt = 1/20

dθ/dt = 0.05 rad/min

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Answer:

x = 132

Step-by-step explanation:

180 - 48 = 132

Answer:

b

Step-by-step explanation:

because

Answer:

-45

Step-by-step explanation:

9x5=45, and since there is a negative, you put it before 45.

Hope I helped!

Please mark Brainliest!!!

Answer:

4.66 billion

Step-by-step explanation:

Answer:

275 miles

Step-by-step explanation:

Answer:

The new line will be parallel to the line represented by y =2x +2

The equation y = 2x + 2 is written in slope- intercept form (i.e. y=mx + b) where m represents the slope.  So the slope of this line is 2.   A line parallel to y = 2x + 2 will have the same slope.  This means the slope of the new line will also be 2.  

To determine the equation of the new line, we can use the given point  to find the y intercept of the new line:

y = 2x + b

Use x = -1 and y =3 to find b (or the y intercept ) of the new line:

3 = 2 * (-1) + b

3= -2 + b

b=5

Therefore, the equation of the line passing thru (-1,3) with the same slope as that of y = 2x + 2 will be:  y = 2x + 5

(Hope it can help)

Answer:

y=2x+5

Step-by-step explanation:

hope you understood

Answer:

$72,000

Step-by-step explanation:

6000-5000=1000

1000x6 =6000

6000x12=72,000

Answer:

you can get some fries and chickent aint enough for me keep it going people

Step-by-step explanation:

Answer:

Each hotdog is $3 and each drink is $4.

Step-by-step explanation:

Let h be the number of hotdogs and d the number of drinks,

7h + 5d = 41

4h + 8d = 44

Let's eliminate h.  Multiply the first by 4 and the second by 7.

28h + 20d = 164

28h + 56d = 308

Subtrat the first from the second.

36d = 144

d = 4

Substitute back into one of the equations.

7h + 5(4) = 41

7h + 20 = 41

7h = 21

h = 3

Answer:

b because it takes 1 hour to complete 3/4 of a page so 3/3 = 1 hour 1 1/3 =1 and a third of an hour

Step-by-step explanation:

Answer:

[tex]\sf {\dfrac {f}{3}}+22=17 [/tex]

[tex]\sf {\dfrac {f}{3}}[/tex]

[tex]{:}\dashrightarrow[/tex][tex]\sf {\dfrac {f}{3}}+22=17 [/tex]

[tex]{:}\dashrightarrow[/tex][tex]\sf {\dfrac {f}{3}}=17-22 [/tex]

[tex]{:}\dashrightarrow[/tex][tex]\sf {\dfrac {f}{3}}=-5 [/tex]

[tex]\therefore[/tex][tex]{\underline{\boxed{\bf {\dfrac {f}{3}}=(-5)}}}[/tex]

Answer: Subtract 22 from both sides.

Step-by-step explanation:

f/3 +22 = 17

f/3 +22 -22 = 17 -22  Subtracting the same value from both sides keeps the equation equal.  

Then simplify. The +22 and -22= 0 They "cancel"   17-22 = -5

f/3 = -17  f/3 is now isolated-- by itself-- in the equation.

If you had to solve for f, the next step would be to multiply both sides by  3.

Answer:

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent

Step-by-step explanation:

I'm not sure the answer

Answer: 3.65

Step-by-step explanation:

This question is asking basically what is 50% or 1/2 of 7.3.

Let's expand the number 7.3

Then, we end up getting 7.30.

We have to find 1/2 of 7.30.

[tex]\frac{1}{2}[/tex] of 7.30 = [tex]3.65[/tex]

Hope this helps you!

Answer:

20r + 310

Step-by-step explanation

For the first part.

The required expression is 20x + 310 which represents the area of the park as the sum of the areas of the sports field and the playground.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Let x represent the length in meters of the sports field.

Here, the area of the sports field = 20 × x = 20x units

And, the area of the playground = 15.5 × 20 = 310 units

Now, the required expression to represent the area of the park will be :

⇒ area of the sports field + area of the playground

⇒ 20x + 310

Thus, the required expression is 20x + 310.

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Answer:

X = 4 because 20 times 16 is 320 than if you add 4 to the 20 you will get 24. 24 times 16 is 384. BOom thats your answer and i know because i just answered it.

Step-by-step explanation:

Answer:

A = 7

B = 4

Step-by-step explanation:

If u wanna know how i got this answer plz look at the comments below since it will delete my answer U-U

Answer:

61=x ( vertical opposite angle)

61=y (corresponding angle)

Step-by-step explanation:

y = 61°( corresponding angles)

x = y = 61°(vertically opposite angles)

Answer:

i think the answer is

[tex] \frac{1}{ {x}^{ \frac{4}{3} }} [/tex]

Answer:

-2 or -5

Step-by-step explanation:

( shown in photo below )

Answer:

You have to draw we cant draw 4 you sorry i cant help

Step-by-step explanation:

Answer:

696

Step-by-step explanation:

Answer:

one thousandth is greater than 0.061

Step-by-step explanation:

Answer:

a

[tex]P(N_g) = 0.5155[/tex]

b

 [tex]P(K ) = 0.36364[/tex]

c

[tex]P(U1 | N_y ) = 0.7223[/tex]  

Step-by-step explanation:

From the question we are told that

  The number of green marbles in Urn 1 is  [tex]N_g = 4[/tex]

   The number of yellow marbles in Urn 1 is [tex]N_y = 5[/tex]

   The number of green marbles in Urn 2 is  [tex]n_g = 7[/tex]

   The number of yellow marbles in Urn 1 is [tex]n_y = 4[/tex]

    The probability of choosing Urn 1 is  [tex]P(U1) = 0.63[/tex]

    The probability of choosing Urn 2 is [tex]P(U2) = 1- 0.63 =0.37[/tex]

Generally the total marble in Urn 1 is  

     [tex]N_t = N_g +N_y[/tex]

=>  [tex]N_t = 4 + 5[/tex]

=>  [tex]N_t = 9[/tex]

Generally the total marble in Urn 2 is  

     [tex]n_t = n_g +n_y[/tex]

=>  [tex]n_t = 7+4[/tex]

=>  [tex]n_t = 11[/tex]

Generally the probability of choosing green marble is

     [tex]P(N_g) = P(U1 ) * \frac{N_g}{N_t} + [P(U2 ) * \frac{n_g}{n_t} ][/tex]

=>   [tex]P(N_g) = 0.63 * \frac{4}{9} + [0.37 * \frac{7}{11} ][/tex]

=>   [tex]P(N_g) = 0.5155[/tex]

Generally  the probability that a yellow marble was chosen, if it is known that Urn 2 was chosen is mathematically represented as

     [tex]P(K ) = \frac{n_y}{n_t}[/tex]

=>   [tex]P(K ) = \frac{4}{11}[/tex]

=>   [tex]P(K ) = 0.36364[/tex]

Generally the probability of choosing yellow marble is

     [tex]P(N_y) = P(U1 ) * \frac{N_y}{N_t} + [P(U2 ) * \frac{n_y}{n_t} ][/tex]

=>   [tex]P(N_y) = 0.63 * \frac{5}{9} + [0.37 * \frac{4}{11} ][/tex]

=>   [tex]P(N_y) = 0.4845[/tex]

Generally  the  probability that Urn 1 was chosen, if it is known that a yellow marble was drawn is mathematically represented as

     [tex]P(U1 | N_y ) = \frac{ P( U1 \ n N_y)}{P(N_y)}[/tex]

=>   [tex]P(U1 | N_y ) = \frac{0.63 * [\frac{5}{9} ] }{0.4845 }[/tex]

=>   [tex]P(U1 | N_y ) = 0.7223[/tex]      

Answer:

total number of beads :-

5+3+4=12

probability is :-

number of times a specific outcome has occurred

total number of possible outcomes

red beads - 5/12

blue beads - 3/12

green beads - 4/12

the above given fractions are the probabilities of each color bead.

Step-by-step explanation:

hope this helps, if yes please can u give me a brainly?

i would really apreciate it...

have a great day ahead :)