Answer:
97.5% decrease
Step-by-step explanation:
You want the percentage change in noise intensity when it is reduced from 88 to 72 dB.
Intensity ratioThe intensity can be found by solving the given equation for I:
[tex]\beta_1=10\log\left(\dfrac{I_1}{I_0}\right)\\\\10^{\beta_1/10}=\dfrac{I_1}{I_0}\\\\I_1=I_0\cdot10^{\beta_1/10}[/tex]
Similarly, the reduced intensity is ...
[tex]I_2=I_0\cdot10^{\beta_2/10}[/tex]
Percent changeThe percentage change is found from ...
percentage change = (I₂/I₁ -1) × 100%
Using the above expressions for I₁ and I₂, this becomes ...
[tex]\text{\% change}=\left(\dfrac{I_0\cdot10^{\beta_2/10}}{I_0\cdot10^{\beta_1/10}}-1\right)\times100\%\\\\=(10^{(\beta_2-\beta_1)/10}-1)\times100\%=(10^{(72-88)/10}-1)\times100\%\\\\=(10^{-1.6}-1)\times100\% \approx -0.975\times100\% =\boxed{ -97.5\%}[/tex]
The noise intensity decreased by about 97.5%.
__
Additional comment
It can be useful to remember that log(2) ≈ 0.30103. That is, a reduction of 3 dB is a reduction by a factor of 2. Hence 16 db is a factor of about 40.
Answer:
97.49% (2 d.p.)
Step-by-step explanation:
Given equation:
[tex]\beta=10 \log\left(\dfrac{I}{I_0}\right)[/tex]
Divide both sides by 10:
[tex]\implies \dfrac{\beta}{10}= \log\left(\dfrac{I}{I_0}\right)[/tex]
Switch sides:
[tex]\implies \log\left(\dfrac{I}{I_0}\right)=\dfrac{\beta}{10}[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 10^{\frac{\beta}{10}}=\dfrac{I}{I_0}[/tex]
Multiply both sides by I₀:
[tex]\implies I=I_010^{\frac{\beta}{10}}\\[/tex]
Substitute the given value of I₀:
[tex]\implies I=10^{-12} \cdot 10^{\frac{\beta}{10}}\\[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies I=10^{\left(\frac{\beta}{10}-12\right)}\\[/tex]
Therefore, the value of I when β = 88 dB is:
[tex]\implies I=10^{\left(\frac{88}{10}-12\right)}\\[/tex]
[tex]\implies I=10^{-3.2}[/tex]
And the value of I when β = 72 dB is:
[tex]\implies I=10^{\left(\frac{72}{10}-12\right)}\\[/tex]
[tex]\implies I=10^{-4.8}[/tex]
Percent Decrease formula
[tex]\sf Percent\:decrease=\dfrac{original\:value-new\:value}{original\:value} \times 100[/tex]
Therefore, the percent decrease is:
[tex]\implies \dfrac{10^{-3.2}-10^{-4.8}}{10^{-3.2}} \times 100[/tex]
[tex]\implies 97.4881135...\%[/tex]
[tex]\implies 97.49\%\; \sf (2\; d.p.)[/tex]
one of the five quadratics below has a repeated root. (the other four have distinct roots.) what is the repeated root? \begin{align*}
Form the given five quadratics , the one representing the repeated roots is equal to option d. 25x² - 30x + 9 and repeated roots are 3/5 or 3/5.
Quadratics representing repeated roots has discriminant equals to zero.
Standard quadratic equation is:
ax² + bx + c = 0
Discriminant 'D' = b² - 4ac
option a. -x²+ 18x + 81
Discriminant
'D' = 18² - 4(-1)(81)
= 324 + 324
= 648
D>0 has distinct roots.
option b. 3x²- 3x - 168
Discriminant
'D' = (-3)² - 4(-3)(-168)
= 9 - 2016
= -2007
D< 0 has distinct roots.
option c. x²- 4x - 4
Discriminant
'D' = (-4)² - 4(1)(-4)
= 16 + 16
= 32
D>0 has distinct roots.
option d. 25x²- 30x + 9
Discriminant
'D' = (-30)² - 4(25)(9)
= 900 - 900
= 0
D = 0 has repeated roots.
Repeated roots are:
x = ( -b ±√D ) / 2a
= [-(-30)±√0 ]/ 2(25)
= 30/ 50
= 3/5.
option e. x² - 14x + 24
Discriminant
'D' = (-14)² - 4(1)(24)
= 196 - 96
= 100
D>0 has distinct roots.
Therefore, the quadratics which represents the repeated roots are given by option d. 25x² - 30x + 9 and its repeated roots are 3/5 or 3/5.
The above question is incomplete, the complete question is:
One of the five quadratics below has a repeated root. (There other four have distinct roots.) What is the repeated root?
a. -x²+ 18x + 81
b. 3x² - 3x - 168
c. x² - 4x - 4
d. 25x² - 30x + 9
e. x² - 14x + 24
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How do you write 90% as a fraction
Answer:
9/10
Step-by-step explanation:
90/100
is 9/10 simplified
Answer:
it 9/10 becuse nvm
Step-by-step explanation:
11. Is the triangle a right triangle? Explain. 6 8 12
Answer:
Step-by-step explanation:
35368
Could someone help me on this problem please thank you if you do!
Answer:
the third graph
Step-by-step explanation:
1. increase - then you know the line has to go upwards. so only first &3rd lines are potentially correct answer
2. look at the Y axis markings, first one goes from 5 to 11, it increased by 6. so it's not right.
answer is the 3rd one.
We placed a 2 kg textbook and a 4kg textbook at least 2cm away from each other. After a while we moved the two textbooks so now they are 8 cm away from each other. Explain which textbook has a larger gravitational pull and how do the different distances affect it?
Book 2 with 4 kg weight has the higher gravitational pull and the pull decreases with increase in distance.
What is Meant by Gravitational Force?In Physics, the gravitational force is one of the types of forces. It is a force that attracts any two objects with mass. The gravitational force is also known as the attractive force, as it always pulls the masses of two objects together. Newton’s gravitational law states that every object in the universe is pulled by other objects. The other types of forces are electromagnetic force, strong force, weak force, and so on. The formula to calculate the gravitational force is given by Gravitational Force = (Gravitational Constant × Mass of first object × Mass of the second object) / (Distance between the centre of two bodies)².
Given here:
Book 1 has 2 kg textbook and Book 2 weighs 4 kg.
In the first case The gravitational pull when they were 2 cm apart is
F₁= Gm₁m₂ / 2cm
=0.00000133486 N
While if the two books are 8 cm apart we have
F₂= Gm₁m₂ / 8
=0.0000000834288 N
clearly the gravitational pull decreases with the increase in distance.
And owing to Book 2's higher weight it has the superior gravitational pull.
Hence, Book 2 with 4 kg weight has the higher gravitational pull and the pull decreases with increase in distance.
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A rectangle has an area of 15 square millimeters. The width of the rectangle is 3 millimeters.
Answer:
5 millimeters
Step-by-step explanation:
15 = 3x
5 = x
g) 25+ [14 - {8+ (13-4)}]
Answer: 22
Step-by-step explanation:
25+ [14 - {8+ (13-4)}]
= 25 + [14 - {8 + 9 }]
= 25 + [14 - 17]
= 25 - 3
= 22
Simplify the radical expression completely:
Square root of 48x^2y^5z
The radical expression completely:
Square root of [tex]48x^2y^5z[/tex] is 4[tex]xy^2[/tex] × sqrt(3y)
Now, According to the question:
Factor 48 into its prime factors
48 = 24 × 3
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
Factors which will be extracted are :
16 = [tex]2^4[/tex]
Factors which will remain inside the root are :
3 = 3
To complete this part of the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by 2 :
4 = [tex]2^2[/tex]
At the end of this step the partly simplified SQRT looks like this:
4 × sqrt[tex](3x^2y^5)[/tex]z
Rules for simplifying variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt[tex](x^8)=x^4[/tex]
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or < (-2) , examples:
(4.1)[tex]sqrt(x^5)=x^2sqrt(x)[/tex]
(4.2) sqrt(x-7)=x-3sqrt(x-1)
Applying these rules to our case we find out that
SQRT[tex](x^2y^5) = xy^2[/tex]SQRT(y)
Simplified root:
4[tex]xy^2[/tex] × sqrt(3y)
Hence, the radical expression completely:
Square root of [tex]48x^2y^5z[/tex] is 4[tex]xy^2[/tex] × sqrt(3y)
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One bank account pays 6% interest and another pays 12%. If $6,000 was invested for a year and the interest earned was $540, how much was invested at 6%?
Answer:
360
Step-by-step explanation:
0.06x6000=360 also that 6% equal 6/100 wich is 0.06
below are two diagrams, one represents 2+5=7 the other represents 5x2=, determind the equation that matches up with each diagram then label the length of each diagram
The first diagram is the equation represented by 5 . 2 = 10 and the second diagram is the one with the equation represented by 2 + 5 = 7.
What are Tape Diagrams?Tape diagrams are diagrams which are used to understand about the relationship between quantities and also they describe how those relationships has been described by operations.
Given are two tape diagrams.
First take the equation 2 + 5 = 7.
This means that 2 is just added to 5 to get 7.
One part contains 2 and the other part contains 5.
Length of it is 7.
Consider the second equation 5 × 2 = 10.
5 × 2 actually means that 5 is added to itself two times or 2 is added to itself five times.
Either 5 + 5 = 10 or 2 + 2 + 2 + 2 + 2 = 10
We have a diagram with 5 equal parts of 2.
Length is 10.
Hence the length of the first diagram is 10 and the length of second diagram is 7.
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a bowl contains 7 blue chips and 3 white chips. two chips are to be drawn successively at random and without replacement. what is the probability of the first chip is white and the second chip is blue?
The probability of drawing a white chip first and a blue chip second is 1/5.
To find the probability of drawing a white chip first and a blue chip second, we can use the formula for conditional probability.
Conditional probability is the probability of an event occurring given that another event has already occurred. It is represented by the notation P(A|B), where A is the event of interest and B is the event that has already occurred.
The formula for conditional probability is:
P(A|B) = P(A and B) / P(B)
This formula expresses the probability of event A occurring given that event B has occurred, as a ratio of the probability of the two events occurring together and the probability of event B occurring alone.
Where A is the event of drawing a white chip first and B is the event of drawing a blue chip second.
We know that the probability of drawing a white chip first is 3/10 (since there are 3 white chips out of a total of 10 chips in the bowl), so P(A) = 3/10.
Once a white chip has been drawn, there are 9 chips left in the bowl, with 6 of them being blue. This means that the probability of drawing a blue chip second given that a white chip has already been drawn is 6/9, so P(B|A) = 6/9.
By multiplying these two probabilities together, we get:
P(A and B) = (3/10) * (6/9) = (3/10) * (2/3) = 6/30 = 1/5
Therefore, the probability of drawing a white chip first and a blue chip second is 1/5.
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the garden clud at central middle school is planting a flower bed. a scale drawing of the flower is shown. the scale 1 in. :2 ft
If the plant is n inches then,
the actual plant = 2n feet.
What is a scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).
Given:
The garden club at central middle school is planting a flower bed.
A scale drawing of the flower is shown.
The scale 1 in:2 ft
The scale factor,
the model = 1 inch
Then the actual plant = 2 feet.
If the plant is n inches then,
the actual plant = 2n feet.
Therefore, If the plant is n inches then, the actual plant = 2n feet.
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which set represents a Pythagorean triple
A. 1,2,3
B.9,12,16
C. 30,40,50
D.38,44,49
The set that represents a Pythagorean Triple is given as follows:
C. 30,40,50
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
For item c, we have that:
30² + 40² = 50²
900 + 1600 = 2500
2500 = 2500.
Which is a true statement, hence item c represents the Pythagorean Triple in the context of this problem.
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HELP PLEASE!!!!
What happens if you graph y=f(f^-1(x))? Explain.
Long division ? ?????
Answer: 37.5
Step-by-step explanation: To find this, we must move the decimal place one spot over. It would now look like this:
300. ÷ 8
Now for the division look at the attachment. In the end, you've should've got 37.5. To check if that's right, you'd multiply 0.8 and 37.5. Then again, you should get 30. I hope this helped!
Suppose Randy has 1/4 of a round cake and 1/4 of a square cake. Are the wholes the same? Does the sum 1/4 + 1/4= 2/4 make sense in this situation? Explain
Randy's cake situation will be better solved in the following manner:
a) If the area of a round cake and a square cake are different then the quarter portion will be different.
b) Though as a concept 1/4 + 1/4 = 2/4, it is not actually true in this case. If the area of different cakes are different then the quarters will also be different.
Measuring a particular region or patch of a figure is its area. Area is significant in contemporary mathematics. Area is crucial in geometry and calculus, but it also plays a role in the definition of determinants in linear algebra and is a fundamental characteristic of surfaces in differential geometry.
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James has 20$ to pay for a movie ticket and candy. Each box of candy cost 2$, the movie ticket cost 12$. Write and equation that can be used to determine how many boxes of candy, c, James can buy
Answer:
4 candy boxes
Step-by-step explanation:
2$ one candy box
then 20-12=8 then
left 8$ now,2$=1 candy box 8$=8÷2
Ans will be 4
Answer:
2c + 12 = 20. Simplified to 2c = 8
Step-by-step explanation:
We can start with a Template
Y = Xc + C
Y being the total
X being candy price
c bring candy boxes, as stated
C being ticket price
Plugging those in we get
20 = 2c + 12
Since you bought the ticket with your $20, we can subtract the ticket price from both sides, giving you
8 = 2c or 2c = 8
Solve for x. Write the equation and show ALL STEPS to solve.
(3x - 3)"
AP
(2x+13)"
Answer:
x = 16
Step-by-step explanation:
(2x+13)° = (3x-3)° [vertically opposite angles]
2x + 13 = 3x - 3
2x - 3x = -3 - 13
-x = -16
∴ x = 16
A pizza company charges $60 for 12 pizzas.
v) Create a table from 60=12m
The required table would be:
Quantity (x) Price (y)
12 $60
What is the slope-intercept form?
The slope-intercept form of a linear equation is y = mx + b, where x and y are variables, m is the slope of the line (also known as the "rate of change" or "rise over run"), and b is the y-intercept (the point where the line crosses the y-axis). The slope-intercept form is so called because it gives the slope of the line and the y-intercept in one equation
Here is the table you requested:
Quantity (x) Price (y)
12 $60
This table shows the relationship between the quantity of pizzas ordered (x) and the price (y) for a pizza company that charges $60 for 12 pizzas. The equation y = mx + b can be used to represent the relationship, where m is the unit price and b is the y-intercept. In this case, m = 5 and b = 0.
Hence, the required table would be:
Quantity (x) Price (y)
12 $60
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A ship is on its maiden voyage to the mystery island. According to the map, it has to travel
99 miles to the north and then, 20 miles to the west to reach the island. Find the shortest
route that leads to the mystery island.
Answer:
I also need help
Step-by-step explanation:
A ship is on its maiden voyage to the mystery island. According to the map, it has to travel
99 miles to the north and then, 20 miles to the west to reach the island. Find the shortest
route that leads to the mystery island.
Answer:
20 miles
Step-by-step explanation:
would you rather go 99 miles or 20 miles
HELP!! ASAP! 60 POINTS
This diagram shows right triangular prism UVWXYZ.
What is the volume of UVWXYZ? If necessary, round your answer to the nearest tenth.
In the diagram which shows right triangular prism UVWXYZ, the volume of UVWXYZ can be expressed in nearest tenth as 750 cm^3.
How can the the volume of UVWXYZbe calculated?The concept that will be used here is volume. In mathematics, 'Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3
√ (12.5^2 -7.5^2) =10 cm
The volume can be calculated as : (1/2 * 7.5 * 10 *20
=750 cm^3
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what term is used to describe this type of survey in which the people surveyed consist of those who decided to respond? what is wrong with this type of sampling method
Part A: The respondents in the population are a voluntary response sample.
Part B: The responses may not reflect the opinions of the general population
The total number of internet users in those is 1072 people.
The percentage of the total number of people that chose to respond is 38%
We can note that this survey does not compel the population to respond to the survey. These responses are given by the voluntary respondents.
Another point is that a voluntary response sample is a sample that consists of participants who are interested to participate in a sample group voluntarily.
In this type of survey, the people who are supposed to decide to provide voluntary responses to the survey are called voluntary response samples.
The percentage of those that chose to respond to this survey which is 38% is less than half of the total population. This result shows that the responses may not reflect the opinions of the general population.
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assume your favorite football team has two games left to finish the season. the outcome of each game can be win, lose, or tie. the number of possible outcomes is
The possible outcomes are the sample space of the game
The number of possible outcomes in the game is 3
Now, According to the question:
In the domain of Statistics, the number of possible outcomes for a given event help in determining the overall size of the universe of outcomes. From such a universe, one can ascertain the probability or likelihood of desirable outcomes in terms of percentage or fraction.
How to determine the possible outcomes
The number of games is given as:
n = 2 i.e. 2 games to finish the season
In each game, the soccer team can either win, lose or tie.
So, we have the outcome of each game to be:
Outcome = {Win, Lose, Tie}
Count the outcomes
Count = 3
Hence, the number of possible outcomes in the game is 3.
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The given question is incomplete , complete question is:
Assume your favorite football team has two games left to finish the season. the outcome of each game can be win, lose, or tie. the number of possible outcomes is in the game ____
PLEASE ANSWER QUICK,
Answer:
C=5Q
Step-by-step explanation:
you can answer any 12 questions from a total of 14 questions on an exam. in how many different ways can you select the question?
In 420 ways different ways can you select the question.
you can answer any 12 questions from a total of 14 questions on an exam
At least 8 questions, including 3 from the last section, must be attempted out of the 5 questions in part and the 7 questions in part 2.
There are three choices.
&% from part 2; (1)3 from part 1
= ⁵C 3 × ⁷ C 5
= 3!(5−3)!/5! × 5!(7−5)!/7!
= 2/5×4 ×= 2/7×6
=5×2×7×3
=210 ways
(2)4 from part 1 & 4 from part 2
= ⁵C 3 × ⁷ C 5
=4!(5−4)!/5!
×= 4!(7−4)!/7!
=5×= 3×2×1/7×6×5
=5×7×5
=175 ways
(3)5 from part 1 & 3 from part 2
= ⁵C 3 × ⁷ C 5
= 5! 0!/5!
×= 3!(7−3)!/7!
=1×= 3×2/7×6×5
=35 ways
Total number of ways =210+175+35
420 ways
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Brad's mother says she was tested for HCG during her last two doctor visits. On March 21, her
HCG level was 200 mlU/ml (milli-international units per milliliter). Two days later, her HCG
level was 392 mIU/ml.
a. Assuming that the model for HCG levels is of the form y = ab', write an equation that
models the growth of HCG for Brad's mother's pregnancy.
The required function is 200 (1.4)ˣ = 5, where the value of x is calculated to be -11.
The given function is y = a bˣ
x₁ = 0, y₁ = 200
x₂ = 2, y₂ = 392
Let us determine a, b.
a b⁰ = 200
a b² = 392
a = 200
200 b² = 392
b² = 392/200 = 49/25 = 7/5 = 1.4
So, the function is y = 200 (1.4)ˣ
Now, let us determine x for y = 5,
200 (1.4)ˣ = 5
(1.4)ˣ = 0.25
Taking log on both sides,
log (1.4)ˣ = log 0.025
x log 1.4 = log 0.025
x = log 0.025/log 1.4
x ≈ -11
This means the embryo was implanted on March 10th and she visited the doctor 11 days later.
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what number is an integer
An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z or blackboard bold \mathbb {Z}.
amy uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend. if the postage is $1.77, how many of each stamp did amy use?
If Amy uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend worth of $1.77 , then the number of 41 cent stamp used is 3 and the number of 6 cent stamps used is 9 .
Let the number of 41 cents stamps used in postage is = x ;
let the number of 6 cents stamps used in postage is = y ;
the amount 41 cents in dollars is = $0.41 ;
and amount 6 cents in dollars is = $0.06 ;
Amy used 41-cent stamps , 6-cent stamps to pay $1.77 in postage
it is represented in equation form as ⇒ 0.41x + 0.06y = 1.77
Multiplying on both sides by 100 , we get
⇒ 41x + 6y = 177 ;
⇒ y = (177 - 41x)/6 ;
We will test for corresponding values of x and y to satisfies this equation and the number of stamps must be whole numbers.
If x = 1 , then y = 26.66
If x = 2 , then y = 15.83
If x = 3 , then y = 9
If x = 4 , then y = 2.16 .
the only values that shows a whole number is : If x = 3 , then y = 9 .
Therefore , Amy used "3" 41-cents stamps and "9" 6-cent stamps .
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The expression 16t-3t is not equivalent to 3t-16t because the negative sign belongs to the term _____
The expression 16t-3t is not equivalent to 3t-16t because the negative sign belongs to the term 3t
For t = 2, 16t - 3t is equal to 26 and 3t - 16t is equal to -26
We know that an expression is nothing but a mathematical sentence with a minimum of two numbers or variables and at least one algebraic operation.
Also, if two expressions are equivalent expression , then the two expressions must have the same value when we substitute the same values for the variables.
Here we have been given two mathemtical expressions:
16t - 3t and 3t - 16t
For t = 2,
16(2) - 3(2)
= 32 - 6
= 26
and 3(2) - 16(2)
= 6 - 32
= -26
This means, 16t - 3t ≠ 3t - 16t
We can oberve that 16t - 3t = -(-16 + 3t)
= -(3t - 16)
This means, 16t-3t is not equivalent to 3t-16t because the negative sign belongs to the term 3t
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The polling results show the ratio of votes for Candidate A to Candidate B.
Candidate A Candidate B
12 20
18 30
27 45
36 ?
At this rate, if Candidate A received 36 votes, how many votes did Candidate B receive?
36
50
60
72
If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes. (third option)
How many votes did Candidate B receive?The first step is to determine the relationship between the number of votes of Candidate A and B. This can be determined by expressing the number of votes in its simplest form.
12 : 20 in its simplest form is 3 : 5
18 : 30 in its simplest form is 3 : 5
27 : 45 in its simplest form is 3 : 5
Now, determine the factor second factor of 36 if the first factor is 3.
36 / 3 = 12
Now multiply 12 by 5: 12 x 5 = 60
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