a
4) The function P= 95 - 30 log 2 x models
the percentage, P, of students who could
recall important features of a classroom
lecture as a function of time, where x
represents the number of days that has
elapsed since the lecture was given.
a) After how many days do only half of
the students recall important features of
the classroom lecture? (P=50)
b) After how many days have ALL
students forgotten the important features
of a classroom lecture? (P = 0)

Answer: (a) 64°

(b) Yes, it is safe

Step-by-step explanation:

A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.

We solve the above question using the trigonometric function of Sine

sin θ = Opposite side/Hypotenuse sides

θ = Angle formed with the ground = ?

Opposite side = 27 ft

Hypotenuse side = 30 ft

Hence,

sin θ = 27 ft/30 ft

sin θ = 9/10 = 0.9

θ = arc sin (0.9)

θ = 64.158067237°

Approximately to the nearest whole number = 64°

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?

From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°

Hence:

64° < 70°

Therefore, the ladder will be safe the way it is positioned.

Answer:

a) -2 and 4

b) function 2

Step-by-step explanation:

a)

rate of change is rise over run: change in y / change in x.

function 1:

- i will use first 2 pairs of data

- change in y: 5 - 3 = 2

- change in x: -2 - (-1) = -1

-rate of change = 2/-1 = -2

function 2:

- same idea, but find two points on the graph!

- (0,4) and (-1,0) for example! pick easy points

- change in y is 4. chabge in x is 1

- rate of change is 4

b)

function b has greatest rate of change. 4 > -2

Answer:

B

Step-by-step explanation:

We must find the reciprocal of 12, which is 1/12. This means 1/9 divided by 12 is 1/9 times 1/12.

Answer:

(0,-3)

Step-by-step explanation:

Rotating a point 90° from the second quadrant to the third on a (x,y) graph follows the transformation,

(x,y) → (-x,y)

Answer:

A proportion is the name we give to a statement in which 2 ratios are equal. Proportions are built off of ratios. It is usually written in one of 2 ways

Step-by-step explanation:

Answer:

there are two different ways it can go up but it will be a ratio amount of air in the

Answer:

x = -9/2

Step-by-step explanation:

1. Divide 9 by -1/3:

[tex]\frac{9}{1}[/tex] ÷ [tex]-\frac{1}{3}[/tex] = [tex]\frac{9}{1}[/tex] · [tex]-\frac{3}{1}[/tex]

= -27

2. Divide both sides by 2:

2(x - 9) = -27

[tex]\frac{2(x-9)}{2} = \frac{-27}{2}[/tex]

(x - 9) = [tex]-\frac{27}{2}[/tex]

3. Add 9 to both sides:

x = [tex]-\frac{9}{2}[/tex]

(or 4.5 if you need it in decimal form)

hope this helps!

Step-by-step explanation:-

The given line is 3x + 4y - 12 = 0

=> 4y = -3x + 12 ....(i)

=> y = -3x/4 + 3,

therefore, the slope of the line (i) = -3/4.

From P(-1,-2), draw PN perpendicular to the given line. (see attachment)

As we know,, m2 = -1/m1

So, the slope of the line PN = 4/3

the equation of the line through P(-1,-2) and having a slope 4/3 is :-

= > y - (-2) = 4/3 * (x - (-1))

= > 3y + 6 = 4x + 4

= > 4x - 3y - 2 = 0....(ii)

which is the required equation of the perpendicular from P to the given line. To find the coordinates of N (the foot of perpendicular), solve (i) and (ii) simultaneously. Multiplying (i) by 3 and

(ii) by 4, and on adding, we get

= > 25x - 44 = 0

= > x = 44/25

Multiplying (i) by 4 and (ii) by 3, and on subtracting, we get :-

= > 25y - 42 = 0

= > y = 42/25

Hence, the coordinates of the foot of the perpendicular are (44/25 , 42/25)

(44/25 , 42/25)

these are the points

Answer:

Step-by-step explanation:

17. Domain is all real numbers because the equation has a y-value for all x-values as far as we can see with the information given.

18. Range is 3< y <8, because the equation only has values for x where y is between those numbers.

19. Range is 3> y >-∞ (negative infinity) because the parabola's vertex has a y-coordinate of 3 and the parabola goes on forever in the negative direction (as seen by the arrows).

20. Domain is -∞ < x < 4 because the parabola's vertex has an x-coordinate of 4 and goes on forever in the negative x direction.

Hope this helps! :)

Answer:

The mean for Family A=78.585 , ≈78.59

Step-by-step explanation:

I solved this with a TI-84 CE calculator. To do this you press stat-edit-put in the numbers-2nd+mode-stat-right arrow key-calc-1_Var_Stats-Calculate. Then X with the _ over it would be your mean.

Translating the triangle DEF involves moving the triangle along the coordinate plane

The y-coordinate of point D after the translation (x, y) → (x + 6, y – 4) is 1

From the figure the coordinate of D is:

D = (-2.5,5)

The rule of translation is given as:

(x, y) → (x + 6, y – 4)

So, we have:

(x, y) → (-2.5 + 6, 5 – 4)

Evaluate the sum and the difference

(x, y) → (3.5, 1)

Remove the x-coordinate

y → 1

Hence, the y-coordinate of point D after the translation is 1

Read more about translation at:

https://brainly.com/question/11468584

Answer: A

Step-by-step explanation:

Hi!

Your answer is [tex]x^2+x+6[/tex]

We are asked to find the floor space it covers, which we can solve for by finding the area of the rectangular rug, given its dimensions.

Dimensions:

(x - 2) x (x + 3)

Area of a rectangle:

Length x Width = Area

Plug dimensions into the formula:

[tex](x - 2)(x +3)[/tex]

Use the Distributive Property and FOIL method to solve (if you are not familiar with the FOIL method, see the image attached below):

[tex]x^2+3x-2x-6[/tex]

Combine like terms:

[tex]x^2+x-6[/tex]

Now, this isn't a numerical value, but as we do not know the value of x, this is the simplest answer we can get.

Answer:

No se

Step-by-step explanation

Espero Averte Ayudado:

A circle with two chords is given with length X, 8, x-12, 12. Thus, The value of x is 24.

If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.

Or

|AC| = |CB|

Using the theorem of intersecting chords

[tex]12x =8(x-12)\\\\12x = 8x - 96\\\\12x - 8x = 96\\\\4x = 96\\\\x = 24[/tex]

The value of x is 24.

Learn more about chord of a circle here:

https://brainly.com/question/27455535

#SPJ1

[tex]c = 15d[/tex]

Step-by-step explanation:

find the value of the constant of proportionality k

[tex]k = \frac{v}{d} [/tex]

c =total cost

d =days

Answer: observational study

Step-by-step explanation:

i think its a observational study because they are learning about somthing and to learn about it you have to study and they are given a specemin to observe to that they can study it as it grows therfore why i think the answer  is C. Observational study.

Answer:

Step-by-step explanation:

Each card is sold by $3, the number of cards is c.

The total is 3c and it needs to be at most $50:

Is the correct inequality for this case

Let the no of cards be c

Now

The inequality is

Or

Given the fraction of each colored chalk, Andrea is right that less than 1/2 the chalk in the bucket is blue.

Total = 2/6 + 5/12 + 3/12

= (4+5+3) / 12

= 12/12

= 1

Fraction of blue : Total chalk

= 5/12 : 1

Blue = 5/12 ÷ 1

= 5/12 × 1/1

= 5/12

= 0.42

So,

1/2 = 0.5

Therefore, Andrea is right that less than 1/2 the chalk in the bucket is blue.

Learn more about fraction:

https://brainly.com/question/11562149

Answer: No

Step-by-step explanation:

Answer: It's 6.28319 feet

Step-by-step explanation:

Answer:

56ft

Step-by-step explanation:

first you need to break the shape u so 1 rectangle and 2 triangles so first we need to find the area of the rectangle

Area of rectangle= w x h so 5* 8= 40

Area of triangle = .5 x b x h so 4 x 4 x .5 = 8 and since we have 2 double that and you get 16 so then you need to add it all up and u get the answer 56

Answer:

70

Step-by-step explanation:

20% is the same thing as 1/5

350 times 1/5 is 70.

Answer:

70

Step-by-step explanation:

.2 * 350 = 70

Answer:

2. Linear Pair Prostulate
6. Transitive Property

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The mode is the number that appears the most!!!!

Now lets solve :)

2, 2, 3, 3, 4, 4, 4, 4,

There are 2 2s.

There are 2 3s.

There are 4 4s.

The mode is 4!!! :)

Have an amazing day!!

Plese rate and mark brainliest!!

The mode of the data set is 4

The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average of a set, and the median, the middle value in a set.

Therefore, the mode of the data set is 4

https://brainly.com/question/12516571

https://brainly.com/question/22739213

Step-by-step explanation:

y=(-x^2)+12x-20

=(-(3)^2)+12(3)-20

=(-9)+36-20

=16-9=7

y=7

I hope it helped you

Answer:

y = 72.49x0.50

Step-by-step explanation:

Answer: 768

Step-by-step explanation:

24 times 20 =480 dollars

16 x18=288

480+288= 768

so yea D IS THE ANSWER!!!

hope thats helps :)

∆ F/ ∆e = K

(5.4-2.1)/(1.8-0.7)= K

3.3/1.1 = K

K = 3