Due to the installation of a muffler, the noise level of an engine decreased from 88 to 72 decibels. Find the percent decrease in the intensity of the noise as a result of the installation of the muffler given the following information:


The number of decibels [tex]\beta[/tex] of a sound with an intensity of [tex]I[/tex] watts per square meter is given by [tex]\beta = 10\log\left(\dfrac{I}{I_0}\right)[/tex].


[tex]I_0[/tex] is an intensity of [tex]10^{-12}[/tex] watts per square meter, corresponding roughly to the faintest sound that can be heard by the human ear.

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

Answer: 22

Step-by-step explanation:

25+ [14 - {8+ (13-4)}]​

= 25 + [14 - {8 + 9 }]​

= 25 + [14 - 17]

= 25 - 3

= 22

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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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 ____

Answer:

360

Step-by-step explanation:

0.06x6000=360 also that 6% equal 6/100 wich is 0.06

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!

If the plant is n inches then,

the actual plant = 2n feet.

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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Answer:

5 millimeters

Step-by-step explanation:

15 = 3x

5 = x

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}.

In the diagram which shows right triangular prism UVWXYZ, the volume of UVWXYZ can be expressed in  nearest tenth as 750 cm^3.

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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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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If Candidate A received 36 votes, the number of votes that Candidate B received is 60 votes. (third option)

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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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

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

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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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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The set that represents a Pythagorean Triple is given as follows:

C. 30,40,50

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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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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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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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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Answer:

C=5Q

Step-by-step explanation:

Answer:

Step-by-step explanation:

35368

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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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.

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 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.

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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Answer:

9/10

Step-by-step explanation:

90/100

is 9/10 simplified

Answer:

it 9/10 becuse nvm

Step-by-step explanation:

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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Book 2 with 4 kg weight has the higher gravitational pull and the  pull decreases with increase in distance.

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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