We are given:
Initial sound Intensity: 110 dB
Rate of decreasing sound level: 16% every second
Constructing the equation:
Since the Intensity decreases by 16% of it's current value every second.
Intensity(t) = [tex]110 * (\frac{84}{100})^{t}[/tex] [where t is the time elapsed]
In this equation, we multiply the initial sound intensity by 84% (since 16% was diminished).
because we are multiplying the same value by 84%, it will keep taking that percentage of the new value, which is what we need here because the music's intensity keeps becoming 84% of the previous value.
Time at which sound level falls to 30 dB:
replacing intensity by 30 in the equation we made.
[tex]30 = 110 * (\frac{84}{100})^{t}[/tex]
[tex]\frac{3}{11} = (\frac{84}{100})^t[/tex]
taking log of both sides.
[tex]log(\frac{3}{11}) = t*log(\frac{84}{100})[/tex]
[tex]\displaystyle \frac{log(\frac{3}{11})}{log(\frac{84}{100})} = t[/tex]
t = 7.452 seconds
Answer:
Equation: [tex]y=110(0.84)^x[/tex]
(where x is the time in seconds, and y is the sound level in decibels)
Answer: The sound level falls below 30 decibels after 7.452 seconds (3 dp)
Step-by-step explanation:
We can model this as an exponential equation.
General form of an exponential equation: [tex]y=ab^x[/tex]
where:
a is the initial valueb is growth factorx is the independent variabley is the dependent variableIf b > 1 then it is an increasing function
If 0 < b < 1 then it is a decreasing function
If the sound decreases by 16% each second, then the growth (decay) factor will be 100% - 16% = 84% → 0.84
Given:
a = 110 decibelsb = decreases by 16% each second = 0.84x = time (in seconds)y = sound level (in decibels)Substituting these values into the equation:
[tex]\implies y=110(0.84)^x[/tex]
To find how long until the sound level falls below 30 decibels, set y < 30 and solve for x:
[tex]\begin{aligned}110(0.84)^x & < 30\\\\(0.84)^x & < \dfrac{3}{11}\\\\\ln (0.84)^x & < \ln \left(\dfrac{3}{11}\right)\\\\x \ln (0.84) & < \ln \left(\dfrac{3}{11}\right)\\\\x & > \dfrac{\ln \left(\dfrac{3}{11}\right)}{\ln (0.84)}\\\\x & > 7.452008851\end{aligned}[/tex]
Therefore, the sound level falls below 30 decibels after 7.452 seconds (3 dp)
Зу - 10 < 11
How to solve
Answer:
y<7
Step-by-step explanation:
3y-10 < 11 add 10 to both sides of the equation
3y < 21 divide by 3
y < 7
Help please! Again this is the last question
Use the point-slope formula to write an equation of the line that passes through 4, 5 and −6, −4 . Write the answer in slope-intercept form (if possible).
The equation of the line is _________ .
Answer:
y-5=9/10⋅(x−4)
Step-by-step explanation:
A right angle is divided into 3 equal angles. What is the measure of
each smaller angle in degrees?
Answer: 30 degrees
Step-by-step explanation:
90 degrees / 3 angles = 30 degrees
What’s life about and why are we here on this earth
Many out there got different opinions on this especially with the influence of religion and science.
LIFE is about learning the best in you and others. Its about loving, being kind and to be someone of great worth who at the the end of the day makes a mark of positivity in every life encountered. Its about living a life of meaning and that's all that matters. Every religion holds it's own perspectives and it's most important that you choose to believe in a religion that helps better Express your faith.
remember that there'll be a day you sit back and look at the life you "lived"
make sure that the choices you make now don't bring ANY regrets.
Help help help help math math
Equation of the graph: x = 3
Since the graph is a vertical line, the equation must be 'x ='
You will get the 3 by seeing its horizontal position on the x-axis
Hope that helps!
I NEED HELP WITH NUMBER 7
Answer:
c po
because that is the answer in the bakc of my module hope its help
what is the perimeter of a rectangular playground 30 m long and 24 m wide
Answer:
108m
Step-by-step explanation:
2 sides are 30m long and 2 sides are 24m long.
Add all 4 sides of the playground to find the perimeter.
30m + 24m + 30m + 24m = 108 m
A store is having a sale to celebrate President's Day. Every item in the store is advertised as one-fifth
off the original price. If an item is marked with a sale price of $140.00, what is the original price?
A cylinder and its dimensions are shown in the diagram. Which equation can be used to find V, the volume of the cylinder in cubic centimeter? I think A. is the answer :)
Answer: it’s simply a
Step-by-step explanation: X =bsquare
Help! please last question
Step-by-step explanation:
The centroid O cuts every median in the ratio 2:1. The distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side.
Therefore: |OD| = 2|OCI
3x-2=2(5x)
3x-2=10x
7x=-2
x=(-2/7)
Someone help pls tysmmm
Answer:
29
Step-by-step explanation:
Substitute v = 15 into 14 + v
14 + 15 = 29
Hope this helps :)
FIND THE RADIUS OF THE SHPERE WITH THE GIVEN VOLUME?
562.5π in.³
Answer:
Radius = 7.5 inStep-by-step explanation:
In the question we have given volume of Sphere that is 562.5 π in³ and we have asked to find the radius of given sphere. We know that the volume of sphere ,
[tex] \blue{ \boxed{ \rm{Volume \: of \: Sphere = \frac{4}{3} \pi r {}^{3} }}}[/tex]
So equating it with given volume for finding the radius of sphere :
[tex] \longmapsto \: \frac{4}{3} \pi r{}^{3} = 562.5\pi[/tex]
Step 1 : Cancelling π as it was present in both side :
[tex]\longmapsto\:\frac{4}{3} \cancel{\pi }r{}^{3} = 562.5 \cancel{\pi}[/tex]
Step 2 : Transposing 4/3 to right hand side :
[tex]\longmapsto \: r {}^{3} = 562.5 \times \frac{3}{4} [/tex]
Step 3 : Multiplying 562.5 with 3 :
[tex]\longmapsto \:r {}^{3} = \frac{1687.5}{4} [/tex]
Step 4 : Dividing 1687.5 by 4 :
[tex]\longmapsto \:r {}^{3} = 421.875[/tex]
Step 5 : Finding cube root of 421.875
[tex]\longmapsto \:r = \sqrt[3]{421.875} [/tex]
Step 6 : We get :
[tex]\longmapsto \: \red{ \boxed{r = 7.5}}[/tex]
Therefore , radius of sphere is 7.5 inches .#Keep LearningNO LINKS!!!
Three statements were made about each problem. Two are true and one is false. Mark each statement as true or false and rewrite the false statement to make it true.
Answer:
Step-by-step explanation:
Answer:
1) True, True, False
Rewritten statement: 46,013.86 cm³ of water was used to fill 40 balloons
2) False, True, True
Rewritten statement: The formula [tex]\sf V= \sf \dfrac43 \pi (2.4)^3[/tex] can be used to find the volume of the model of Earth.
3) True, False, True
Rewritten statement: The volume of all the basketballs is 13,467.62 in³
Step-by-step explanation:
Question 1[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]
Given:
r = 6.5 cmSubstituting the given radius into the formula:
[tex]\begin{aligned}\implies \sf V & = \sf \dfrac43 \pi (6.5)^3\\\\& =\sf \dfrac{2197}{6} \pi \\\\& = \sf 1150.35\: cm^3 \:(nearest\:hundredth)\end{aligned}[/tex]
[tex]\textsf{Volume of 40 balloons}=\sf 40 \times \dfrac{2197}{6} \pi=46013.86\:cm^3\:(nearest\:hundredth)[/tex]
Rewritten statement: 46,013.86 cm³ of water was used to fill 40 balloons
-------------------------------------------------------------------------------------------------------
Question 2[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]
Earth
Given:
diameter = 4.8 cm ⇒ r = 2.4 cmSubstituting the given radius into the formula:
[tex]\implies \sf V= \sf \dfrac43 \pi (2.4)^3[/tex]
[tex]\implies \sf V=57.91\:cm^3\:(nearest\:hundredth)[/tex]
Rewritten statement:
The formula [tex]\sf V= \sf \dfrac43 \pi (2.4)^3[/tex] can be used to find the volume of the model of Earth.
Saturn
Given:
diameter = 45.6 cm ⇒ r = 22.8 cmSubstituting the given radius into the formula:
[tex]\implies \sf V= \sf \dfrac43 \pi (22.8)^3[/tex]
[tex]\implies \sf V=49647.02\:cm^3\:(nearest\:hundredth)[/tex]
Difference between models= 49,647.02 - 57.91 = 49,589.11 cm³
-------------------------------------------------------------------------------------------------------
Question 3[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
Given:
r = 21 inh = 54 inSubstituting the given values into the formula:
[tex]\implies \sf V=\pi (21)^2(54)[/tex]
[tex]\implies \sf V=23814\pi[/tex]
[tex]\implies \sf V=74813.89\:in^3\:(nearest\:hundredth)[/tex]
[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3 \quad \textsf{(where r is the radius)}[/tex]
Given:
diameter = 9.5 in ⇒ r = 4.75 in30 basketballs[tex]\begin{aligned}\textsf{Volume of all 30 basketballs} &=\sf 30 \times \dfrac{4}{3}\pi (4.75)^3\\ & =\sf 13467.62\:in^3\:(nearest\:hundredth)\end{aligned}[/tex]
Rewritten statement: The volume of all the basketballs is 13,467.62 in³
Empty space in the container = volume of container - volume of basketballs
⇒ 74813.89 - 13467.62 = 61,346.27 in³
What integer best represents
a withdrawal of $85?
Answer:
the answer is -85 good luck on your test or honework :)
There are people fishing at Lake Connor: 4 have fishing licenses, and 4 do not. An inspector chooses two of the people at random. What is the probability that
the first person chosen does not have a license and the second one does? Write your answer as a fraction in simplest form
every other person has one
A teacher asks her class of 22 students, "What is your age?" Their responses are shown below.
19, 19, 14, 14, 16, 19, 19, 16, 16, 15, 17, 16, 17, 16, 15, 14, 15, 15, 17, 14, 16, 15
Find the mean, median, and mode for the data. If necessary, round to the nearest tenth.
O A 16.5; 17; 17
OB. 16.1: 16; 16
C. 16.1; 17; 16
o
D. 16.5; 16; 17
Answer:
B.
Mean: 16.1
Median: 16
Mode: 16
Step-by-step explanation:
First, order the numbers in the data set from least to greatest:
[tex]14 , 14 , 14 , 14 , 15 , 15 , 15 , 15 , 15 , 16 , 16 , 16 , 16 , 16 , 16 , 17 , 17 , 17 , 19 , 19 , 19 , 19[/tex]
First, find the mean. The mean of a data set can be found by adding all the numbers together and dividing by the amount of numbers in the set:
[tex]\frac{14 + 14 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 16 + 16 + 16 + 16 + 17 + 17 + 17 + 19 + 19 + 19 + 19}{22} = \frac{354}{22}[/tex]
Next, simplify by dividing:
[tex]\frac{354}{22} = \frac{177}{11} = 16 \frac{1}{11} or ~16.1[/tex]
Mean: 16.1
Next, find the median. The median is the number(s) directly in the middle. If there is a even amount of number in the data set, find the mean of the two median numbers:
Median: 16 , 16
Median = [tex]\frac{16 + 16}{2} = \frac{32}{2} = 16[/tex]
Median = 16
Next, find the mode. The median is the number that shows up the most. In this case, it is 16, which appears 6 times, 1 more time then the next number that appears the most 15, which appears 5 times.
Mode: 16
~
If you are asked about range, range would be the greatest digit value subtracted by the least digit value. In this case, it would be 14 & 19:
19 - 14 = 5
Range: 5
~
Question #2
Allison simplifies the expression correctly.
What is Allison's result?
pic committee for qualifying
A
ва
B
0
ol
D
}
82
Answer:
First, the student performed what was inside of the parentheses and was exponential, which is correct. We know this because of the rules called order of operations, outlined by PEMDAS, which tells us to perform mathematical operations in the following order: parentheses, exponents, multiplication, division, addition, subtraction.
So by the rules I just outlined, next the student should have performed the multiplication, but instead performed subtraction, which is incorrect.
The following is the correct simplification of the expression:
23 - 8 times 2 + 3 by the power of 2
So first we should perform parentheses, but there are none. So we move to the next option in the list, which is exponents, which we do have (3^2).
23 - 8 * 2 + 3^2
23 - 8 * 2 + 9
Next in PEMDAS comes multiplication and division. This means the next step in simplifying the expression is to evaluate 8*2.
23 - 16 + 9
Next in PEMDAS is addition, so we should perform the operation -16 + 9.
23 - 7
Finally, the last step in PEMDAS is to simplify the remaining operation (subtraction).
16
Therefore, the student did the first step correctly but performed the second step incorrectly. The final answer should be 16 after simplification.
Hope this helps!
Please I need Brainliest.
Solve This Quadratic:
7x²-26x-45
Answer:
(7x+9)(x-5)
Hope this helps!
Find the slope of the line that passes through 4, −6 and −3, 1 . Write your answer in simplest form. Select "Undefined" if applicable.
The slope is ______ .
To find the slope between two points:
⇒ must know the slope's formula
[tex]\frac{y2-y1}{x2-x1}[/tex]
(x1, y1) --> any point on the line (x2, y2) --> any point on the line but (x1, y1)Let's consider the information given
⇒ given two points ⇒ (4, -6) and (-3,1)
Let's set: (you can interchange the two values of (x1,y1) and (x2,y2), it doesn't change the answer in any way)(x1, y) --> (4, -6)
(x2, y2) --> (-3, 1)
Let's calculate the slope:
[tex]slope = \frac{1--6}{-3-4} =\frac{7}{-7} =-1[/tex]
Thus the slope is -1
Hope that helps!
Please help me understand the question
Answer:
180 units^2
Step-by-step explanation:
The formula to find the area of a sphere is:
A=4(pi)(r)^2
A sphere with radius 2r has an area = 4π(2r)² = 4π.4r² = 16πr²
The ratio of the larger sphere to the smaller = 16πr² : 4πr² = 4 : 1
If the area of the smaller sphere is 45 units then the area of the larger sphere is 45 x 4 = 180 units^2.
hope this helps :)
HHHHEEEELLLLPPPPP
PPPPLLLLLLSSSSS
10 points
Answer:
Step-by-step explanation:
1Bothlineparrell
The The 80-(A
When building a house, the number of days required to build varies inversely with with the number of workers. One house was built in 10 days by 40 workers. How many days would it take to build a similar house with 25 workers?
Answer:
16 days
Step-by-step explanation:
The table shows the relative frequencies of the results for a netball team after a
number of games.
Result of game
won
lost draw
Relative frequency
0.55
0.35
0.1
[2]
a) Complete the table.
b) The team won 15 more games than they lost.
How many games did the team play altogether?
Using proportions, it is found that:
a) The table is completed with 0.1.b) The team played 75 games.What is a proportion?A proportion is a fraction of a total amount.
Item a:
The sum of the frequencies is of 1, hence, the table is completed with 1 - (0.55 + 0.35) = 0.1.
Item b:
Considering that there were n games, we have that:
The team won 0.55n games.The team lost 0.35n games.The difference was of 15, hence:
0.55n - 0.35n = 15
0.2n = 15
n = 15/0.2
n = 75
The team played 75 games.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Answer:
ahello
Step-by-step explanation:
cameo homeo romeo can you be my juliet
Distance between athe and moon written in scientific notation
Answer:
here
Step-by-step explanation:
The distance between the earth and the moon is approximately 384000 km. To Do: Express the distance in meters in exponential notation. Therefore the answer is 3.84 × 10 8 m.
which of the following is an algebraic equation. a. 10+5=15. b. 10x+5=15. c. 10x+5. d. 10+5
Mr. Smith has 847 gallons of paint. If he uses 1/3 of his paint to paint his fence, how much paint did use to paint his fence?
Answer:
282.3 gallons
Step-by-step explanation:
if needed you can round to 282
Find the product of the following by writing one of numbers as the sum or difference of two numbers -
785*105
1006*95
3096*91
Answer:
Step-by-step explanation:
Use distributive property: a*(b+c) =a*b +a*c
1) 785 * 105 = 785 * (100 + 5)
= 785*100 + 785*5
= 78500 + 3925
= 82425
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2) 1006 * 95 = (1000 + 6) *95
= 1000*95 + 6*95
= 95000 + 570
= 95570
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3) 3096*91 = 3096 * (100 - 9)
= 3096*100 - 3096*9
= 309600 - 27864
= 281736
What is the greatest common factor of 21 and 64?
Answer:
1
Step-by-step explanation:
Factors of 21: 1, 3, 7, and 21
Factors of 64: 1, 2, 4, 8, 16, 32, and 64
These numbers do not share any other factors other than 1
please help me this
Answer:
Question 1:
So you have 80 gummies and take 2 a day for 40 days
2(40) = 80
So at the end of 80p days, 0 gummies will be left
Question 2:
Now you have 90 and take 3 a day for 40 days
3(40) = 120
You will not have enough to cover the entire 40 days if you take 3 a day.
Hope this helps :)
Answer:
See below ~
Step-by-step explanation:
Question #1
80 vitamin gummiesUsage rate = 2 per day for 40 daysRemaining = 80 - 2(40) = 80 - 80 = 0Question #2
90 jelly bean vitaminsUsage rate = 3 per day for 40 daysRemaining = 90 - 3(40) = 90 - 120 = -30But negative is not a possible answer ⇒ lowest possible is 0