Mathematics High School

The relationship between the sound level in a room and the rate at
which people wake up can be modeled by a linear function as shown.
Which of these best describes the
rate of change of the frequency of
people waking up with respect to
the sound level?
Frequency of People Waking Up
vs. Sound Level
100
8% per 9 decibels
90
80
B
3% per 4 decibels
70
60
9% per 8 decibels
Frequency of People Waking Up (%)
50
40
4% per 3 decibels
30
20
10
0 145
55 65 75 85 95 105 115
Sound Level (decibels)

Answers

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The change of the frequency of people waking up with respect to the sound level, 9% per 8 decibels.

What is linear function?

Linear function is the function in which the highest power of the unknown variable is one. Linear functions used to model the real life problem in the mathematical expressions.

The linear function with dependent variable y and independent variable x can be written as,

[tex]y=mx +c[/tex]

Here, (m) is the slope of the function and (c) is the y intercept.

The slope can be found out as,

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The sound level is plotted on x-axis and frequency of people walking up (%) is plotted on y-axis. The slope of the line given the rate of change of y values with respect to x value.

In the graph given, the frequency of people walking up is 10 at 55 decibels and 55 at 95 decibels. The point, we get for this line are (55, 10) and (95, 55). Therefore the slope or the change of rate is,

[tex]\dfrac{dy}{dx}=\dfrac{55-10}{95-55}\\\dfrac{dy}{dx}=\dfrac{45}{40}\\\dfrac{dy}{dx}=\dfrac{9}{8}[/tex]

Hence, the change of the frequency of people waking up with respect to the sound level, 9% per 8 decibels.

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Related Questions

Find the slope of the line passing through the points (-3, 7) and (2, -6).

Answers

Answer:

-13/5

Step-by-step explanation:

=y2-y1/x2-x1

= -6-7/2--3

= -13/5

The equation below represents how much money Addy makes delivering papers. In the equation p represents the number of papers delivered and d represents the money per paper delivered. D = .45p Create a context, a unit rate, and an equation for someone who delivers papers and makes more than both Addy and Rachel.

Answers

Step-by-step explanation:

Step one:

we are given the equation for Addy And Rachel's earning as

[tex]D =0.45p[/tex]-------------1

Step two:

Context creation

Say john earns $0.9 per paper he delivers, estimate how much he would earn to deliver 10 papers

let the amount earn be y and the number of papers delivered be x

the equation is

y=0.9x

for x=10

Answer:

(7x-3)(x+4)

Step-by-step explanation:

hope this helps:)

Simplify the expression by adding or subtracting the linear expressions. 10x + 5 + 5x + 10 *
15x + 15
10x + 15
5x + 10
20x + 5

Answers

The answer would be 15x+15 because you would need to combine like terms. 10x+5x=15x and 10+5=15.

Complete the synthetic division problem below.
-1/ 2 8 6
What is the quotient in polynomial form?
O A. X-6
O B. X+6
C. 2x + 6
D. 2x-6

Answers

Answer:

c bc of -1/ 2 8 6 of you divide and then u multiple

The quotient of the synthetic division problem -1 | 2 8 6 in polynomial form is 2x + 6.

How to determine the quotient?

The synthetic division problem is given;

-1 | 2 8 6

Remove the number before the | sign

2 8 6

Remove the middle number;

2 6

Introduce a variable starting from an exponent of 0 (let the variable be x);

2x¹ 6x⁰

Evaluate the exponents;

2x 6

2x + 6

Hence, the quotient of -1 | 2 8 6 in polynomial form is 2x + 6.

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Can someone help me solve this triangle (geometry) question?

Answers

Answer:

I hope it will help you...

Please Help Me, Answer The Questions and I give you 100 Brainly Points

Answers

lol what’s the question

Answer:

Whats the question??? and then i can help you>>

Step-by-step explanation:

Help me and I will give Ten CuPcAkEs
For YoUr TuMmY to DeVoUr
( But be Fast Before I eat them ALL)

Answers

Answer: 51

Step-by-step explanation: plug 24 into where X is. 1.5 times 24 is 36 then add the 15 and u get 51.

What is the solution of w – 4 = 18 + 3w?

Answers

Answer:

w=-11

Step-by-step explanation:

Move the w on to the right side:

-4=18+2w

Move the 18 to the left side:

-22=2w

Divide by 2

w=-11

Hope this helps!

And Brainlists plz!

HELPP!! BRAINLIEST AND 10 POINTS !!

Answers

Answer:

y = ax^2 + bx + c

Which number is greater . 60 or 7.5

Answers

Answer:

60 is greater than 7.5.

step by step

please help due in 3 minutes

Answers

Answer:

k = $0.50

Step-by-step explanation:

The data that we have is:

Rocko paid: $12.50 for 25 tickets.

Louisa paid: $17.50 for 35 tickets.

Now, the question asks to find the constant of proportionality.

A proportional relation can be written as:

y = k*x

where k is the constant, and in this case, y is the price and x the number of tickets bought.

Then replacing with the values above, we have:

$12.50 = k*25

then:

k = $12.50/25 = $0.50

And the other data:

$17.50 = k*35

K = $17.50/35 = $0.50

So we have the same k in both cases, this means that the constant of proportionality is k = $0.50

i'm not all too familiar with the constant of proportionality, but both of the situations have a ratio of 0.5/1..

12.50/25 = 0.5/1

17.50/35 = 0.5/1

hopefully this can help you in some way! sorry if it doesn't

A circle divided into 4 parts. 2 parts are shaded.
Which fraction is equivalent to One-half? Use the diagram to help answer the question.

One-fourth
Two-fourths
Three-fourths
Four-fourths

Answers

it would have to be two-fourths

A circle is divided into 4 parts out of which 2 parts are shaded. The diagram is attached for a better understanding. The fraction equivalent to 'Half' is 'Two-fourths'.

A fraction is part of the whole. It consists of two parts, that are:

1. Numerator: The number at the top of a fraction is called Numerator.

2. Denominator: The number at the bottom of a fraction is called Denominator.

The 'Half' is written in the number system as [tex]\dfrac{1}{2}[/tex].

Let's multiply the numerator and denominator by 2,

[tex]\dfrac{1}{2}= \dfrac{1 \times 2}{2 \times 2} = \dfrac{2}{4}[/tex]

Hence, the factor 'Two-fourths' is equivalent to 'Half'.

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Solve the equation 3x = 2x +5.
What can you do to isolate the variable on one side of
the equation?
What is the solution?

Answers

Subtract 2x from both side
X = 5
The solution is 5

Answer:

1. C

2. D

Step-by-step explanation:

In that order

5) Which is the better deal for mechanical
pencils?
(Hint: better deal means CHEAPER!)
Target: 4 pencils for $1.25
Staples: 25 pencils for $5.69

Answers

Answer:

Staples

Step-by-step explanation:

5.69/25<1.25/4

Answer:

Target

Step-by-step explanation:

Buying let's say you buy 4 packs close to the amount of Staples you'd get 16 pencils.

(ps sorry if I'm wrong lol)

You have eight more dogs than cats. You have 2 fewer chickens than dogs. You have three fewer guinea pigs than cats. If you have a total of 59 pets, write an equation that would help you find how many of each pet you have. Describe what the variable represents (Let __ represent...).

Answers

Answer:

read the answers below.

Step-by-step explanation:

d = dog

d = c + 8

ch = chickens

ch = d -2

gp = guinia pigs

gp = c - 3

d + c + ch + gp = 59

gp = c- 3

gp = d -8 - 3

gp = d - 11

d + d-8 + d - 2 + d-11 = 59

4d -8 - 2 - 11 = 59

4d - 21 = 59

4d - 21 + 21 = 59 + 21

4d = 80

4d/4 = 80/4

d = 20

========

c = d - 8

c = 20 - 8

c = 12

========

ch = d - 2

ch = 20 - 2

ch = 18

=========

gp = d - 11

gp = 20 - 11

gp = 9

Find the value of x so that the function has the given value.

m(x) = 4x + 15; m(x) = 7
x = ___

Can you also explain how you solved it please. I might have some other problems using the same format. Thank you!

Answers

Answer:

-2

Step-by-step explanation:

A stadium charges $75 for each seat in section A, $50 for each seat in section B, and $40 for section C. There are three times as many seats in section B as in section A. The revenue from selling odd 20,000 seats is 897,500. Write a system to represent the situation.

A. b=3×c
a+b+c=20,000
75a+50b+40c=897,500

B. b=3×a
a+b+c=20,000
75a+50b+40c=897,500

C. a=3×b
a+b+c=20,000
40a+50b+75c=897,500

D. a=3×b
a+b+c=20,000
75a+50b+40c=897,500

Answers

Answer:

B. b=3×a

a+b+c=20,000

75a+50b+40c=897,500

Step-by-step explanation:

A stadium charges

$75 for each seat in section A

$50 for each seat in section B

$40 for section C.

There are three times as many seats in section B as in section A.

a = 3× b

The revenue from selling odd 20,000 seats is 897,500.

a + b + c = 20,000 seats

Hence,

$75 × a + $50 × b + $40 × c = 897,500

75a + 50b + 40c = 897,500

Hence, the system of equations is :

B. b=3×a

a+b+c=20,000

75a+50b+40c=897,500

It takes John 54 minutes to paint a fence with a length of 12 meters. On average, how long did he take to paint 1 meter of the fence? *
25 points
3.5 minutes
4.5 minutes
4.8 minutes
5.4 minutes
Other:

Answers

Answer:

4.5

Step-by-step explanation:

I think it will work if you Divide 54 over 12 = 4.5

change the following number into fraction 1.57 recurring

Answers

Answer:

Step-by-step explanation:

1.57

=157/100 answer

How do you solve this?

Answers

Answer:

[tex] x = 18 [/tex]

[tex] y = 7.5 [/tex]

[tex] z = 7 [/tex]

Step-by-step explanation:

✍️[tex] (8x - 7) + (3x - 11) = 180 [/tex] (consecutive interior angles are supplementary)

Solve for x

[tex] 8x - 7 + 3x - 11 = 180 [/tex]

Add like terms

[tex] 11x - 18 = 180 [/tex]

Add 18 to both sides

[tex] 11x = 180 + 18 [/tex]

[tex] 11x = 198 [/tex]

Divide both sides by 11

✅[tex] x = 18 [/tex]

✍️[tex] (2y + 23) = (4y + 8) [/tex] (alternate interior angles are congruent)

Solve for y

[tex] 2y + 23 = 4y + 8 [/tex]

Collect like terms

[tex] 23 - 8 = 4y - 2y [/tex]

[tex] 15 = 2y [/tex]

Divide both sides by 2

✅y = 7.5

✍️[tex] (2y + 23) + (3z^2 - 5) = 180 [/tex] (linear pair angles)

Plug in the value of y

[tex] (2(7.5) + 23) + (3z^2 - 5) = 180 [/tex]

[tex] (15 + 23) + (3z^2 - 5) = 180 [/tex]

[tex] 38 + 3z^2 - 5 = 180 [/tex]

Add like terms

[tex] 3z^2 + 33 = 180 [/tex]

Subtract 33 from each side

[tex] 3z^2 = 180 - 33 [/tex]

[tex] 3z^2 = 147 [/tex]

Divide both sides by 3

[tex] z^2 = \frac{147}{3} [/tex]

[tex] z^2 = 49 [/tex]

Square both sides

[tex] \sqrt{z^2} = \sqrt{49} [/tex]

[tex] z = 7 [/tex]

Write an expression that represents the area in square feet of each room in the house shown. Then
write an expression that represents the area of the whole house.
• Bedroom =
• Closet =
• Bathroom =
• Total Area =

Answers

Answer:

Bedroom = x^2 ft^2

Closet = 25 ft^2

Bathroom = 6x ft^2

Total Area = x^2 + 6x + 25 ft^2

Please answer correctly !!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

I think it's 169

Step-by-step explanation:

since a straight line is 180⁰ I subtracted 11

A large male giraffe needs to eat at least 75 pounds of food each day. At each feeding, the giraffe is fed 3 pounds of food. The giraffe has already consumed 24 pounds of food. How many more times x does the giraffe need to be fed? Write your answer as an inequality.

Answers

Answer:

Step-by-step explanation:

number 10 pleaseeee
:) tysm this is due tmmrw

Answers

The y-intercept is (0,11)

The y intercept is 11

The y intercept is defined as the value of y when x is equal to 0. When x = 0 in the chart, y = 11

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