Joe graphed y = -1/2 x + 2 in his graph below.
Joe made a mistake
What is his mistake? How should he fix the mistake?

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.

The 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]

The 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]

Answer: The perimeter of a rectangle is the sum of the lengths of all four sides. If one of the sides is 6(1/2x + 5), then we can find the perimeter by multiplying that by 2.

Perimeter = 2*6(1/2x + 5)

Perimeter = 12(1/2x + 5)

To simplify the expression, we can distribute the 12:

Perimeter = 121/2x + 125

Perimeter = 6x + 60

So the perimeter of 6(1/2x + 5) is 6x + 60.

Step-by-step explanation:

If Desi has a coupon  that entitles him to 35% off the regular price of a sweater , then another expression that represents the price Desi will pay is 0.65x .

the original price of the sweater is = x ;

the percent discount that Desi gets by applying the coupon is = 35% ;

Desi gets 35% discount , it means that Desi only need to pay the remaining 65% of the price .

So , the remaining price of the sweater to be paid by Desi is = 65% of "x" ;

= 0.65x  ...(because 65% = 0.65 ) .

Therefore , the another expression representing the situation is 0.65x .

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Answer:

3:2

Step-by-step explanation:

The statistic is the average diameter of 100 bearings from the lot, which is 2.515 cm. This is outside the specified limits, resulting in the lot being mistakenly rejected.

The statistic in this case is the average diameter of the inspected bearings from the lot. The lot contains a boxcar of ball bearings, and the specified acceptance of the lot is that the average diameter must be 2.503 cm. The inspector happens to inspect 100 bearings from the lot and determines that the average diameter of these bearings is 2.515 cm, which is outside the specified limits. As a result, the lot is mistakenly rejected. The value of the statistic is the average diameter of the inspected bearings from the lot, which is 2.515 cm. This is the value that determined the lot's rejection, as it is outside the specified limits.

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The approximate measure of angle YZX is 39.4°. Option(B) is the correct answer.

we know that

In the right triangle XYZ

[tex]tan(Y Z X)= \frac{opposite side angle YZX}{adjacent side angle YZX}[/tex]

In this problem,

Opposite side angle YZX= XY = 12.4cm

Adjacent side angle YZX= YZ = 15.1cm

substitute the values,

[tex]tan ( Y Z X) = \frac{12.4}{15.1}[/tex]

[tex]Angle ( Y Z X) = arc tan( \frac{12.4}{15.1} )[/tex]

Angle ( Y Z X) = 39.4°

So,  the approximate measure of angle YZX is 39.4°.

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The complete question is:

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?

A .34.8°

B .39.4°

C .50.6°

D. 55.2°

The value for the line segment FG represented by the algebraic expression 2x is equal to 4.

An algebraic equation is a mathematical statement that contains two equated algebraic expressions.

The sum of the line segments FG and GH is equal to FH so;

2x + x + 4 = 10

3x + 4 = 10

3x = 10 - 4 {subtract 4 from both sides}

3x = 6

x = 6/3

x = 2

line segment FG = 2(2) = 4

line segment GH = 2 + 4 = 6

Therefore, the value for the line segment FG represented by the algebraic expression 2x is equal to 4.

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The two values which will make the given equation true are 17 and 4.

By using different processes, simplification refers to reducing the expression to a simpler form. The equation is simplified to its closest value using approximation, which is not perfectly accurate.

Simplification for the given equation:

Consider the given equation and substitute the values 17 and 4 in the blank space.

= 17y∛6y - 14∛48y⁴

= 17y∛6y - 14∛6 × 6y³y

= 17y∛6y - 14 × 2y∛6 × 2³y³y

Further simplifying,

= 17y∛6y - 14 × 2y∛6y

= 17y∛6y - 28∛6y

= - 11∛6y

Therefore, the values for which the 17y∛6y - 14∛48y⁴ = - 11∛6y are 17 and 4.

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The length of one string of lights in feet is closest to 23 feet.

The problem states that students plan to decorate the school's flagpole with strings of lights. One end of each string of lights will be attached to the top of the flagpole, and the other end will be attached to the ground.

The flagpole is 15 feet tall and the distance from the base of the flagpole to the ground is 8 feet. Since the string of lights is attached at the top of the flagpole and at the ground, the length of the string of lights is equal to the height of the flagpole plus the distance from the base of the flagpole to the ground.

Therefore, the length of one string of lights can be calculated by adding the height of the flagpole (15 feet) to the distance from the base of the flagpole to the ground (8 feet), which results in:

15 feet + 8 feet = 23 feet

So the length of one string of lights is 23 feet.

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A short-run economic event like a recession is more likely to have aggregate demand rather than aggregate supply as its main cause.

The theory used in this question is the Keynesian Theory of Income and Expenditure,

It asserts that total spending (C + I + G + X - M) equals total output (Y), where C represents consumption, I represents investment, G represents government spending, X represents exports, and M represents imports.

Step 1: In order to solve for G, we must first recall the equation for calculating Gross Domestic Product (GDP):

GDP = C + I + G + (X - M)

Step 2: We have five of the six variables given in the equation and can solve for G by rearranging the equation to solve for G.

GDP - C - I - (X - M) = G

Step 3: Substitute the given values for each of the variables in the rearranged equation, starting with GDP.

900 - 500 - 300 - (200 - 200) = G

Step 4: To simplify the problem, subtract 500 from each side.

400 - 300 = G

Step 5: 300 should be subtracted from each side of the equation.

100 = G

Therefore, Government spending G = 100.

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Answer:

That is correct. The probability of rolling a 2 and a 5 when rolling two dice is 1 in 36, which is considered likely.

Answer:

not enough information

Step-by-step explanation:

The tire is shaped like a cylinder. The tread of a tire is the lateral surface of a cylinder. We know the diameter of the cylinder, 32 inches, but we are not given the width of the tire which is the height of the cylinder, so we cannot calculate the area.

Answer: not enough information

He used five 40-cent stamps and eight 7-cent stamps.

Let x stand for how many 40-cent stamps he applied.

Let y stand in for the quantity of 7-cent stamps he applied.

41 cents = 40/100 = $0.40

7 cents = 7/100 = $0.07

To cover the $2.56 in postage, he uses 40-cent and 7-cent stamps. That implies

0.4x + 0.07y = 2.56

When you multiply something by 100, you get

40x + 7y = 256

7y = 256 -40x

The accompanying x and y values must both be whole numbers in order to satisfy the equation.

If x = 4,

7y = 256 - 40 × 4 = 96

y = 96/7 = 13.71

If x = 5,

7y = 256 - 40 × 5 = 56

y = 56/7 = 8

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Answer:

A dependent variable represents a quantity whose value depends on how the independent variable is manipulated. y is often the variable used to represent the dependent variable in an equation.

Step-by-step explanation:

Answer: I think its .012

hope this helps

Answer:

0.012

Step-by-step explanation:

Here is the stem and leaf plot:

Stem      Leaf

0            2, 3, 5, 9

1              2, 7, 7,, 8, 8

2

3                 0, 8

A stem-and-leaf plot is a table that is used to display a dataset.  A stem-and-leaf plot divides a number into a stem and a leaf.

The stem is the first number in the digit. In this question, the stem is the tens digit.  The leaf is the last number. In this question, the leaf is the units digit.  For example in the number 18, 1 would be the stem and 8 would be the leaf.

Here is the complete question:

Create a stem and plot diagram using the dataset provided: 3, 18, 18, 5, 2, 17, 30, 9, 38, 17, 12

Key: 30 = 30

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Answer:

{1, 2, 3, 4, 5, 6, 7, 8}

Step-by-step explanation:

In this problem, we use the variable c to represent the independent quantity.  This means that the domain is all possible values for c. Since the store only has 8 cases of water, the domain cannot be any number larger than 8. Since the store only sells complete cases, not partial cases, of water, the domain cannot be a fraction or decimal number. This means that the practical domain, or domain that makes sense for the problem situation, is {1, 2, 3, 4, 5, 6, 7, 8}.

According to the information in the graph, it can be inferred that the percentage of students who have brown eyes among the group that wears glasses is equivalent to 42.9% (option B).

To calculate the percentage of students who have brown eyes in the group that wears glasses we must perform the following mathematical operation.

We must add all the values of the group that wears glasses

According to the previous operation, the result must be approximated to 42.9% and the correct option would be B.

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Answer:

x²y²(x²-2xy)

Step-by-step explanation:

they each include an x²y² so you take out the x²y² from each, and then write what's remaining & then add a bracket.

The value of x would be 7 and perimeter of equilateral triangle would be 75.

What is Equilateral triangle and perimeter of equilateral triangle?

An equilateral triangle is one with the equal length on all three sides. To calculate the perimeter of an equilateral triangle given its area, we must first determine the length of its sides.

An equilateral triangle has three congruent sides, so if AABC is equilateral, we know that AB = BC = AC. We can use this information to write an equation for x, the length of one of the sides.

AB = BC = AC

given equations are,

4x-3 and 2x+11

as we know that, all sides of equilateral triangle are equal then,

4x-3 = 2x+11

2x = 14

x = 7

The perimeter of an equilateral triangle = 3 x side of equilateral triangle

Here, all sides of equilateral triangle are equal then sides = 25

Perimeter of an equilateral triangle = 3 x 25

Perimeter of an equilateral triangle = 75

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By using each of the numbers 0 - 7 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest are,

⇒ 20.3% , 4.56, and 9/1

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Here, We have to use each of the numbers 0 - 7 exactly once.

Hence, The percent, decimal, in fraction below are ordered from least to greatest are,

⇒ 20.3% = 0.203

⇒ 4.56

⇒ 9/1 = 9

Thus, By using each of the numbers 0 - 7 exactly once, so that the percent, decimal, in fraction below are ordered from least to greatest are,

⇒ 20.3% , 4.56, and 9/1

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The possible minutes Ali will run today can be represented by the inequality x ≥ 66.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given that,

Minutes taken to complete one lap = 6 minutes

Also, he will run at least 11 laps today.

This means that Ali will run laps greater than or equal to 11 laps.

Let x be the number of minutes taken by Ali today.

x ≥ 6 × 11

x ≥ 66

Hence Ali runs 11 laps in at least 66 minutes.

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The complete question is as follows :

Ali runs each lap in 6 minutes. He will run at least 11 laps today. What are the possible numbers of minutes he will run today?

According to the given formula, the value of a is:

60

If b=30 then 1/2a+2/3b=50

First, replace the 30 in b.

1/2a+2/3(30)=50

According to the order of operations, we must first multiply 2/3 by 30. yes:

2/3 times 30 is equal to 20.

2/3 times 30/1. 3 is 10 times 30, so 2 times 10 = 20. Now it looks like this:

1/2a+20=50

20 and 50 are similar terms, so I'll put those two together. Move the positive 20 to the other side where the 50 is. 20 has moved to the other side, so it changes sign and becomes negative.

yes:

1/2a=50-20

50-20 = 30

1/2a=30

Multiply each side by 2, because only 2 makes the variable 1a.

1/2a × 2 = 1a

30 times 2 = 60, so:

1a=60, which is also a=60. So a perfect simplification is a= 60

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The standard form of the equation of the line through the point (3,3) with slope -1/2 is y = -1/2x + 9/2.

The standard form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

We are given a point (3,3) and a slope of -1/2, we can use the point-slope form to write the equation of the line as follows -

y - 3 = -1/2(x - 3)

To convert this equation to standard form, we can simplify the equation as follows -

y - 3 = -1/2x + 3/2

y = -1/2x + 3 + 3/2

y = -1/2x + 9/2

Hence, the standard form of the equation of the line through the point (3,3) with slope -1/2 is y = -1/2x + 9/2.

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The time taken to cover the distance from the park to house with an average speed of 22km /h is 42 minutes.

Average speed is the directional speed of an object in motion as measured by a certain unit of time and seen from a particular point of reference. Average speed is a fundamental concept in kinematics, the branch of classical mechanics that investigates how bodies move.

Since average speed is a physical vector quantity, its magnitude and direction must be included in the definition. In the SI, speed is a coherent derived unit whose quantity is measured in metres per second (m/s), where speed is the scalar absolute value (distance) of average speed (metric system). The word "acceleration" describes a change in an object's speed, direction, or both.

we know that

distance = average speed × time

distance = 14×66/60 =15.4 km

now time = distance /average speed

time = 15.4×60/ 22 = 42 minutes

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The measure of the indicated angle is 33 degrees

It is important to note the properties of a triangle

The properties of a triangle are given as;

From the diagram shown, we have;

57° + K + 90° = 180°

Collect like terms, we get;

K = 180° - 147°

Subtract the numbers

K = 33°

Hence, the value is 33°

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Michael wants to place grass on the side of his lap pool, the area of the shaded region that he wants to cover with grass is 204 square yard.

We have to determine the area of the Shaded region that he wants to cover with grass.

By calculating the overall area and taking the area of the lap pool out, the area of the shaded area may be calculated.

We can see that the shape is the trapezium. So;

Area of trapezium = 1/2 × (Sum of parallel sides) × distance between them

Sum of parallel sides = 25 yd + (3 + 12) yd

Sum of parallel sides = 25 yd + 15 yd

Sum of parallel sides = 40 yd

Distance between them = 12 yd

Area of the trapezium = 1/2 × 40 × 12

Area of the trapezium = 40 × 6

Area of the trapezium = 240 square yd

Now finding the area of lap pool.

Area = length × width

Area = 12 × 3

Area = 36 square yd

Now finding the area of shaded region

Area = Area of the trapezium - Area of lap pool

Area = 240 - 36

Area = 204 square yard

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Lila finds out the decimal equivalent of 3 divided by 16 is equal to 0.1875.

Lila knows that 3/16 means "3 divided by 16."

To find the decimal equivalent for 3/16, she would divide 3 by 16 using a calculator or long division. This would give her a decimal answer of 0.1875.

It's important to note that 3/16 is a fraction, which represents a ratio of two numbers, the numerator, and the denominator. The decimal equivalent is simply another way to represent the same value but in decimal form.

Lila understands that to convert fractions to decimals, she can divide the numerator by the denominator. And to convert decimals to fractions, she can write the decimal as a fraction with the denominator as a power of 10.

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