Noise levels at 5 airports were measured in decibels yielding the following data:
152,154,139,124,120
1. Construct the 80% confidence interval for the mean noise level at such locations. Assume the population is approximately normal.
2. Calculate the sample mean for the given sample data. Round your answer to one decimal place.

Answer:Tangent ratio of an angle

Step-by-step explanation:

Tangent ratio of an angle  the ratio of the length of the opposite side of an angle divided by the length of the adjacent side.

Answer:

Step-by-step explanation:

it should be sth like green graph

Answer:

√85

Step-by-step explanation:

a² + b² = c²

6² + b² = 11²

36 + b² = 121

b² = 121 - 36

b² = 85

b = √85

Answer:

Hello! The answer is [tex]b = \sqrt{85}[/tex].

Step-by-step explanation:

To solve this question, we have to use the Pythagorean theorem. We are given one of the legs and the hypotenuse. (The hypotenuse is opposite the right angle).

a^2 and b^2 represent our legs while c^2 represents the hypotenuse.

We have to substitute our values in for a^2 and c^2:

6^2 + b^2 = 11^2

This leaves us with 36 + b^2 = 121

To get b^2 by itself, we have to subtract 36 from both sides:

36 + b^2 = 121

-36             -36

This leaves us with b^2 = 85

To get just b, we have to take the square root:

√b^2 = √85

This leaves us with [tex]b = \sqrt{85}[/tex].

Answer:

w(w-5)

Step-by-step explanation:

Given Width of rectangle = w

Length of rectangle is 5 less than width of rectangle = w - 5

Area of Rectangle = Length x Width = w * w-5 = w(w-5)

Answer:

the second answer option

Step-by-step explanation:

the area of a rectangle is

length × width

or

l × w

l = w - 5

so, when we use the second in the first equation, we get

(w - 5)×w

or

w(w - 5)

Answer:

64:27

Step-by-step explanation:

If the ratio between the old and new radius is described with the ratio: 4:3, then if the first radius was 3, then the new radius is 4.

Also if you multiply 3 by (4/3) it also equals 4

The volume of a sphere is described as:  [tex]\frac{4}{3} \pi r^{3}[/tex]

So let's plug in 3 and 4 and see their ratio.

[tex]\frac{\frac{4}{3}\pi 4^{3} }{ \frac{4}{3}\pi 3^{3} }} = \frac{4^{3} }{3^{3} } = \frac{64}{27}[/tex]

The answer is 64/27 or (4/3)^3

Answer:

by a factor of 64/27   or   64:27

Step-by-step explanation:

Volume of a sphere = 4/3  pi  r^3    

    now increase the radius  by 4/3      ( this is  4:3)

               new volume = 4/3 pi  (4/3 r)^3  

                                     = 64/27  *  4/3 pi r^3

so the original volume is increased by  64/27

Answer:

h = 5t

Step-by-step explanation:

So basically, its a slope problem again. You are trying to find the equation that equals hits. So you can cross off t = 5h and t = h + 5. So now, you need to find the most reasonable answer by calculating the slope.

If you try h = t + 5,

Put in 3 - you get 8

Put in 7 - you get 12

But on the table you get 15, 36 respectively.

If you try h = 5t,

Put in 3 - you get 15

Put in 7 - you get 35

Which is much closer to the numbers in the table, therefore it is the answer.

Step-by-step explanation:

how did you get y, when you don't know how to get x ?

the easiest way to solve this is to base on the fact that the opposite angles must be identical.

so,

2x + 32 = 4x - 12

32 = 2x - 12

44 = 2x

x = 22

and the to be sure

-8y - 14 = -5y + 4

-3y = 18

y = -18/3 = -6

or, the sum of 2 consecutive angles must be 180°.

2x + 32 - 5y + 4 = 180

2x - 5y + 36 = 180

2x - 5y = 144

-8y - 14 + 4x - 12 = 180

-8y + 4x = 206

-4y + 2x = 103

-5y + 2x = 144

- -4y + 2x = 103

------------------------

- y 0 = 41

y = -41

-4×-41 + 2x = 103

164 + 2x = 103

2x = -61

x = -30.5

ha, your teacher either set a trap or made a mistake.

these given angles do not belong to a parallelogram.

there is no solution for x and y with these angle expressions to create a parallelogram.

every condition that has to be true creates a different and inconsistent set of solutions (and implausible ones at that creating single angles larger than 200° and even 300°, or smaller than 0°).

The number of prime divisors of "6n" is 2 numbers 2 and 3

Given

"n"  = 6    

thus 6n  = 6(6) = 36

The positive divisors are   1, 2, 3, 4, 6, 9, 12, 18 and 36

So, the number of prime divisors of "6n" is 2 numbers 2 and 3.

The prime factors of a positive integer are the top numbers that divide that integer exactly. The technique of finding those numbers is known as integer factorization or prime factorization.

The fundamental theorem of mathematics says that every positive integer has a completely unique prime factorization.

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Probability that Martin passed the exam when he attend the class daily is given by 1/3.

Probability is the possibility to occurrence of an event.

In other words, Probability is the ratio of number of favorable cases under an event to total number of cases under that event.

Let P be the event that Martin passed the exam and A be the event that he attend the class daily.

Given that,

40% of students passed tbe exam.

The probability to pass the exam is given by,

[tex]P(P)=40%=\frac{40}{100}=\frac{4}{10}[/tex]

90% students attend the class daily

probability to attend the class daily is given by,

[tex]P(A)=90%=\frac{90}{100}=\frac{9}{10}[/tex]

30% student both passed the exam and attended class

So probability to both passed the exam and attend the class is given by,

[tex]P(P\cap A)=30%=\frac{30}{100}=\frac{3}{10}[/tex]

Now conditional probability that Martin will passed the exam if he attend class daily is given by,

[tex]P(P|A)=\frac{P(P\cap A)}{P(A)}=\frac{\frac{3}{10}}{\frac{9}{10}}=\frac{3}{9}=\frac{1}{3}[/tex]

Hence the required pobability that Martin passed the exam when he attend the class daily is given by 1/3.

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Answer:

r is -11

Step-by-step explanation:

Move the like terms to the same side. 4r-6r is -2r

14 + 8 is 22

22/-2 is -11

Answer:

1/8 of the pizza

Step-by-step explanation:

whole pizza=1

5/8 is gone so 1-5/8=8/8-5/8=3/8

3/8-1/4 = 3/8-2/8=1/8

hope this helps

Answer:

3[tex]\sqrt{10}[/tex] ≈ 9.45

Step-by-step explanation:

calculate the distance d between the points using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 1, 8 ) and (x₂, y₂ ) = (8, 5 )

d = [tex]\sqrt{(8-(-1))^2+(5-8)^2}[/tex]

   = [tex]\sqrt{(8+1)^2+(-3)^2}[/tex]

   = [tex]\sqrt{9^2+9}[/tex]

   = [tex]\sqrt{81+9}[/tex]

   = [tex]\sqrt{90}[/tex]

   = [tex]\sqrt{9(10)}[/tex]

   = [tex]\sqrt{9}[/tex] × [tex]\sqrt{10}[/tex]

   = 3[tex]\sqrt{10}[/tex] ← exact value

   ≈ 9.49 ( to 2 dec. places )

The ordered pair on the inequality y < 2/3x + 2 is D. (1,2)

The inequality is given as:

y < 2/3x + 2

Next, we test the options:

A. (0,3)

3 < 2/3 * 0 + 2

3 < 2 --- false

B. (-3,1)

1 < 2/3 * -3 + 2

1 < 0 --- false

C. (3,5)

5 < 2/3 * 3 + 2

5 < 4 --- false

D. (1,2)

2 < 2/3 * 1 + 2

2 < 2.67 --- true

Hence, the ordered pair on the inequality y < 2/3x + 2 is D. (1,2)

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Answer:

4 m/s

Step-by-step explanation:

Well the constant rate of change can be defined as the slope or rise/run. This can be calculated using any two points. So I'll use (10, 40) and (20, 80). the seconds increased by 10 (run) and the meters increased by 40 (rise) This gives you the equation 40/10 which simplifies to 4. That is the constant rate of change

The statement that accurately describes a cause-and-effect relationship described in this excerpt is C. Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.

A cause-and-effect relationship occurs when:

Thus, the statement that accurately describes a cause-and-effect relationship described in this excerpt is C. Because the French soldiers are tearing down a ruined wall in a fort, they discover the Rosetta Stone.

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The correlation is a strong negative correlation, because as the weights increases the city MPG decreases

To do this, we plot the weights on the x-axis, and the city MPG on the y-axis

See attachment for graph

The correlation is a strong negative correlation, because as the weights increases the city MPG decreases

To do this, we make use of a graphing calculator.

From the graphing calculator, we have the following summary:

The line of best fit equation is

y = bx + a

Where

b = SP/SSX = -857.75/862.94 = -0.99399

a = MY - bMX = 24.25 - (-0.99*28.94) = 53.01354

So, we have:

y = -0.99399x + 53.01354

Approximate

y = -0.99x + 53

Hence, the equation of the line of best fit is y = -0.99x + 53

This means that y = 30

So, we have:

-0.99x + 53 = 30

Subtract 53 from both sides

-0.99x = -23

Divide by -0.99

x = 23.23

Approximate

x =23

Hence, the predicted weight is 23 pounds

This means that x = 1500

So, we have:

y = -0.99 * 1500 + 53

Evaluate

y = -1432

Hence, the city MPG for 1500 pounds is -1432

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W is the width of the quilt, the restrictions are given by the inequality:

7.7ft ≤  W ≤  8.9 ft

Remember that for a rectangle of length L and width W, the area is:

A = L*W

In this case, we know that:

L = 1.2*W

Replacing that we get:

A = 1.2*W²

And we know that the area must be between 72 square feet and 96 square feet, then:

72ft² ≤  1.2W² ≤ 96ft²

Now we can divide all by 1.2:

(72ft²)/1.2 ≤  W² ≤ (96ft²)/1.2

60ft² ≤  W² ≤ 80ft²

If we apply the square root in the 3 sides of the inequality, we get:

√60ft² ≤  √W² ≤ √80ft²

7.7ft ≤  W ≤  8.9 ft

These are the restrictions on the width such that the quilt will meet the required area.

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Answer:

6 sides

Step-by-step explanation:

the interior angle + the exterior angle = 180°

let x be the exterior angle then 2x is the interior angle and

x + 2x = 180

3x = 180 ( divide both sides by 3 )

x = 60

the exterior angle = 60°

the sum of the exterior angles of a polygon = 360°

since the polygon is regular the the exterior angles are congruent, then

number of sides = 360° ÷ 60° = 6

Answer:

I don't understand the formatting of the possible answers.  Below is a solution.

Step-by-step explanation:

906,060 is the same as 9.0606 x 10^5

The given number is equal to [tex]-9.0606 * 10^5[/tex]

Scientific notation is a way to write numbers in an abbreviated way, making it easier to work with these numbers.

The primary reason for converting numbers into scientific notation is to make calculations with unusually large or small numbers less cumbersome. Because zeros are no longer used to set the decimal point, all of the digits in a number in scientific notation are significant.

A widely used floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10

Converting –906,060 into scientific notation, we get

-906060/100000

= - 9.06060*10^5

Thus, The given number is equal to -9.06060*10^5

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Answer:

[tex]x \leq \frac{7 - x}{3}[/tex]

Step-by-step explanation:

This expression is an inequality which is a relation that makes a non-equal comparison between two numbers/expressions

we want x to be alone in one side, y + 3x ≤ 7

Subtract y from both sides,

y + - y + 3x ≤ 7 - y

3x ≤ 7 - y

divided both sides by 3 to get x alone

3x / 3 ≤ 7 - y / 3

x ≤ 7 - y / 3

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The rule is n/(-2)

A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.

Given:

64, -32,16,-8

r= 64/-32

r= -2

again, r= -32/16

r= -2

By above we concluded that the common ratio is is -2.

If n is natural numbers for finding geometric progression the rule which defines it n/(-2).

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Answer:

Keep in mind the rules.

When we multiply terms with same bases we keep one base and add the exponents.

Step-by-step explanation:

Answer:

bro tbh just use like or

Step-by-step explanation:

its not that deep

Answer:

Step-by-step explanation:

The question is asking you to identify the domain for each of the parts of the piecewise-defined function. This means you need to identify the corresponding part on the graph, and determine its horizontal extent.

The first step in solving a problem is to look at the given information. The graph is shown as three (3) non-overlapping horizontal line segments. The open- or filled-circle end points tell you whether that x-value is part of the line segment.

The blanks in the function definition are where the domain descriptions go for the piecewise-defined function. This means you have to match the function description to the left of "if x ∈" with the set of x-values it corresponds to. The "x ∈" notation suggests you want to specify the domain in "interval notation," rather than as an inequality.

The first part of the function definition is ...

  f(x) = -4

This matches the horizontal line segment at the bottom of the graph. The closed dots at its ends mean it is defined for ...

  -6 ≤ x ≤ -2

In interval notation, a square bracket is used when the end point is included in the interval.

  f(x) = -4  if x ∈ [-6, -2]

The second part of the function definition is ...

  f(x) = -3

This matches the horizontal line segment in the middle of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...

  -2 < x ≤ 1

We use a round bracket (parenthesis) when an end point is not included in the interval.

  f(x) = -3  if x ∈ (-2, 1]

The third part of the function definition is ...

  f(x) = 4

This matches the horizontal line segment at the top of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...

  1 < x ≤ 5

In interval notation, this is ...

  f(x) = 4  if x ∈ (1, 5]

The explicit formula that is equivalent to aₙ = -6aₙ₋₁  is; aₙ = 1(-6)ⁿ⁻¹

We are given;

a₁ = 1

aₙ = -6aₙ₋₁

Thus, for second term;

a₂ = -6a₁

a₂ = -6

For the third term;

a₃ =  -6a₂

a₃ = 36

The resulting sequence is 1, -6, 36,......

The sequence is a geometric sequence with;

a = 1

r = -6

The explicit rule will be aₙ = 1(-6)ⁿ⁻¹

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The correct answer is x = 2

(x + 1 < 4) ∩ (x-8>-7)

Make x the subject in each case:

(x<4-1)(x>-7+8)

        (x<3)∩(x>1)

If x<3, then x could be 2, 1, -1, etc.

If x>1, then x could be 2, 3, 4, etc.

Thus (x<3)∩(x>1) = 2

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Answer:

x = 2

Step-by-step explanation:

Hello!

We are looking at the intersection of two sets, or common values found between two sets of data.

We can solve for x on each side and find any common values between.

As you can see, the intersection occurs at the common values. The only value that is common between the two sets is 2.

Therefore, the intersection of these sets is 2.

The height of the new photo must be 945 pixels (option B).

To calculate the height of the photograph, we must first know what proportion the sides of the previous photo have, for this we do the following operation:

According to the above, the height of the photo is equal to 75% of the width. So to find the height of the new photograph we must do the following operation:

So the height of the new photo should be 945 pixels.

Note: This question is incomplete. Here is the missing part:

Question

Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. The original photo was 800 pixels wide by 600 pixels high. The new photo will be 1,260 pixels wide. What will the new height be?

Options

460 pixels

945 pixels

1,680 pixels

1,860 pixels

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Answer:

B

Step-by-step explanation:

7/20 x 1/2 x 1/6

Step-by-step explanation:

118+2×=180

180-118=62

62÷2(×)=31

×=31

Answer:

x + x + 118 = 180

Step-by-step explanation:

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