The planetary boundary layer (PBL) is the lowest layer of the troposphere; its characteristics are influenced by contact with the ground. Wind speed, temperature, and moisture in the PBL all affect weather patterns around the globe. A random sample of days was obtained and the height of the PBL (in meters) above the Great Basin Desert was measured using weather radar. Assume the underlying distribution of PBL heights is normal.
Height(m)
1 673 2 664 3 906 4 956 5 751 6 752 7 654
8 610 9 816 10 667 11 690 12 657 13 920 14 741 15 646 16 682 17 715
18 618 a. Find a 95% confidence interval for the true mean height of the PBL above the Great Basin Desert. b. Is there any evidence to suggest that the true mean height of the PBL above the Great Basin Desert is different from 700 m? There is_____to suggest that the mean height is different from 700 m. The confidence interval_____the value 700 so it is_____as the true mean height of the PBL.

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex] \qquad❖ \: \sf \: \sin {}^{4} ( \alpha) + 2 \sin {}^{2} ( \alpha) \cos {}^{2} ( \alpha) + { \cos {}^{4} ( \alpha) }^{} [/tex]

[tex] \qquad❖ \: \sf \:( \sin {}^{2} ( \alpha) ) {}^{2} + 2( \sin {}^{2} ( \alpha))( \cos {}^{2} ( \alpha)) + {( \cos {}^{2} ( \alpha)) }^{} [/tex]

( use identity a² + 2ab + b² = (a + b)² )

[tex] \qquad❖ \: \sf \:( {\sin {}^{2}( { \alpha}) + \cos {}^{2} ( \alpha)) }^{2} [/tex]

( sin² x + cos ² x = 1 )

[tex] \qquad❖ \: \sf \: {1}^{2} [/tex]

[tex] \qquad❖ \: \sf \: {1}^{} [/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Value of that expression is 1

Answer:

See below

Step-by-step explanation:

Wrong formula  ...and all of your answers are messed up too....

  F = 9/5 C + 32

re-arrange to:  

  C = 5/9 ( F-32)

    C = 5/9 (59-32) = 15 ° C

Answer:

D

Step-by-step explanation:

Area of Part of a Circle = (θ/360)[tex]\pi r^{2}[/tex]

We first find the area of CAB first.

Radius of CAB = AB = 6cm

θ  = 112

Area of CAB = [tex]\frac{112}{360} \pi (6)^{2} \\=\frac{56}{5} \pi cm^{2}[/tex]

Next we will find the area of FAE.

Radius of FAE = AE = 4cm

Area of FAE = [tex]\frac{112}{360} \pi (4)^{2} \\=\frac{224}{45} \pi cm^{2}[/tex]

Lastly,

Area of Shaded Region = Area of CAB - Area of FAE

= [tex]\frac{56}{5} \pi -\frac{224}{45}\pi \\=\frac{56}{9} \pi cm^{2}[/tex]

Therefore the answer is D.

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. The numbers that are located below -3.5 on a vertical number line are (-∞,-3.5).

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

The numbers that are located below -3.5 on a vertical number line are all the numbers that are less than -3.5. The numbers that are located below -3.5 on a vertical number line are (-∞,-3.5).

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The difference between causation and correlation is that, Causation is characterized by cause-and-effect while correlation establishes a probable relationship.

While Causation is characterized by a situation in which an action certainly causes an outcome and hence, is described as a cause-and-effect relationship, Correlation on the other hand only establishes a relationship between the two events and doesn't necessarily ascertain the occurrence of the other event .

An example of two variables which may be correlated is; the height and weight of an individual in which case it is generally perceived that taller people are heavier.

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Answer:

10

Step-by-step explanation:

proportion

35 ÷ 7 = 5

2 x 5 = 10

Answer:

30

Step-by-step explanation:

3mn=3x5x2=30

The height of the cone is 24 cm.

The distance along the curved surface, measured from the edge at the top to a point on the circumference of the circle at the base, is known as the slant height of an object (such as a cone or pyramid). In other words, the slant height, represented either as s or l, is the shortest distance that may be traveled along the surface of the solid.

Slant height(l)=26cm

Radius(r)=10cm

It is known that, [tex]l^{2}=r^{2}+h^{2}[/tex]

Here, h is the height of the cone.

On substituting the values,

[tex]26^{2}= 10^{2}+h^{2}[/tex]

[tex]\\676=100+h^{2}\\[/tex]

[tex]h^{2}=676-100\\[/tex]

[tex]h^{2}=576\\[/tex]

[tex]h=\sqrt{576}\\[/tex]

h=24

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Bobby will have $557 in his account after 4 years.

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account.

Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Simple interest = (principal amount×Rate of interest×time-period)/100

The principal amount deposited was $500.

The rate of interest given by the bank is 2.85%.

The duration of deposit is 4 years.

Simple interest = (500×2.85×4)/100

                         = 57

Simple interest given by the bank after 4 years is $57.

The total sum of money Bobby will have in his bank is $500 + $57 = $557.

Therefore, after 4 years Bobby will have $557 in his account.

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Answer:

d

Step-by-step explanation:

becoz u already answered it lloll

[tex]2x - 15 \leqslant 5 \\ 2x \leqslant 20 \\ x \leqslant 10[/tex]

[tex]\Huge\boxed{x\leq10}[/tex]

To solve for [tex]x[/tex], you need to isolate it on one side of the equation.

Start by adding [tex]15[/tex] to both sides.

[tex]\begin{aligned}2x-15+15&\leq5+15\\2x&\leq20\end{aligned}[/tex]

Now, divide both sides by [tex]2[/tex] for the final answer.

[tex]\begin{aligned}\frac{2x}{2}&\leq\frac{20}{2}\\x&\leq10\end{aligned}[/tex]

Answer:

Jun Wei donated a higher percentage than Lixin

calculate it by multiplying monthly salary by 12 then divide the total donated to total earned for both people... you Will Find 6.25 % for Jun Wei but for Lixin You Will get 5.51%

i hope this helps u :)

thank u

The first three values of g² + 3 are 3, 4, 7. The correct option is the first option 3, 4, 7

From the question, we are to determine the first three possible values of g² + 3

From the given information,

g stands for a whole number

∴ The first three values of g are 0, 1, 2

When g = 0

g² + 3 becomes

0² + 3

= 0 + 3

= 3

When g = 1

g² + 3 becomes

1² + 3

= 1 + 3

= 4

When g = 2

g² + 3 becomes

2² + 3

= 4 + 3

= 7

Hence, the first three values of g² + 3 are 3, 4, 7. The correct option is the first option 3, 4, 7.

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Answer:

[tex]\huge\boxed{\sf \$ \ 38.52}[/tex]

Step-by-step explanation:

Marked price = $36.00

Sales tax = 7%

= 7% of marked price

= 7% of $36 [Key: "of" means "to multiply"]

= 7/100 * 36

= 0.07 * 36

= $2.52

= Marked price + sales tax

= $36 + $2.52

= $38.52

[tex]\rule[225]{225}{2}[/tex]

The total cost of the jacket was the amount of  $38.52. The correct answer is option (d).

To find the total cost of the jacket after adding a 7% sales tax, we need to calculate the tax amount and add it to the original price.

Calculate the tax amount:

Tax amount = 7% of $36.00

Tax amount = 0.07 × $36.00

Tax amount = $2.52

Add the tax amount to the original price:

Total cost = $36.00 + $2.52

Total cost = $38.52

Thus, the total cost of the jacket was the amount of  $38.52.

Hence, the correct answer is option (d).

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The distance Tim drives is 300 kilometers


Average speed= 80 km

Time= 3 hours 45 minutes (15/4 hours)

Distance= Average speed/time

= 80 × 15/4

= 1200/4

= 300 kilometers

Hence the distance Tim drives is 300 kilometres

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The expression that best represents the volume is (b) [tex]V = \pi (13.5)^2 (4)[/tex]

The given parameters are:

Diameter, d = 27

Height, h = 4

Start by calculating the radius using:

r = d/2

This gives

r = 27/2

r = 13.5

The volume is then calculated as:

[tex]V = \pi r^2 h[/tex]

This gives

[tex]V = \pi (13.5)^2 (4)[/tex]

Hence, the expression that best represents the volume is (b) [tex]V = \pi (13.5)^2 (4)[/tex]

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Answer:

for st1: It's Given

For St2: Definition

For St3: Dividing BE as BF and FE or You can write From Figure:

For St4: You can write From st3

for st5: From St 4

For St7 : They are congruent by SSS axiom

Equilateral Triangle: All 3 sides of a Triangle are equal in length

Isosceles Triangle: Two sides of Triangle are equal in length

Scalene: Triangle has different side lengths

So, for example, when you see Q1, you estimate the length of each side and think it is Scalene Triangle because all of its sides are of different length. (You can also use a ruler to find out the side lengths if it can be used for scale)

Q2, you can say that the side lengths AC and BC look similar, so it is an Isosceles Triangle

Q6, when you look at the side lengths, you can tell it is an equilateral Triangle because all the sides are equal in length

You can try the rest and check for yourself. If you still have any doubts, you could ask me. I hope this information helps you.

Answer: D

Step-by-step explanation:

[tex]V=\frac{1}{3}\pi r^{2} h[/tex] is the general formula for the volume of a cone with radius r and height h.

Substituting in s for both r and h, [tex]V=\frac{1}{3}\pi s^{3}[/tex].

Answer:

Step-by-step explanation:

a = 12 mi

b ≈ 14.0 mi

c = 7 mi

m∠A ≈ 59.0 °

m∠B ≈ 91°

m∠C ≈ 30.0 °

The lengths of the triangle are:

a = 12 mi

b ≈ 14.0 mi

c = 7 mi

And the angles of the triangle are :

m∠A ≈ 59.0°

m∠B ≈ 91°

m∠C ≈ 30.0°

What are the angles in a triangle?

Every triangle has interior angles that total 180.

Angles in a triangle are the total (sum) of the angles at each of its three vertices.

Given, in a triangle ∠B is = 91°

length of c = 7 mi

              a = 12 mi

We need to find the missing angles and side length of b.

⇒ b² = a² ₊ c² ₋ 2accosB

⇒ b/sinB = a/sinA = c/sinC

b² = 12² ₊ 7² ₋ 2(12)(7)cos91°

b² = 144 ₊ 49 ₋ 2(84)cos91°

b² = 193 ₋ 168 cos 91°

b² = 195.856

b=√195.856

b = 14.0 mi

⇒14.0/sin91° = 12/sinA

⇒ sinA = 12sin91°/14.0

sin A = 0.857

A = arcsin(0.857)

A = 59.0°

∴ C = 180° ₋ (sum of two angles in a triangle)

C = 180 ₋ (91° ₊ 59°)

C = 180 ₋ 150°

C = 30°

Hence we get the angles in the triangle as m∠A = 59.0°, m∠B = 91° and  m∠C = 30°

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Let us first define what any of these terms mean.

The mean is found by adding all the numbers in the set, and dividing the sum by how many numbers are found in the set.

> Given set {5, 12, 6, 3, 8, 16, 8, 6}, the sum of the numbers is 5 + 12 + 6 + 3 + 8 + 16 + 8 + 6 = 64. 64 ÷ 2 = 32. Thus, the mean is 32.

The median is found by finding the number in the middle of the set, and dividing it by 2. This is easy in odd numbers as there is only one number in the middle that is the same amount of numbers left and right proportionally. However, in even numbers, there are two middles to be proportional. If it as an even number, then add the 2 middles together, and divide by 2.

> Given set {5, 12, 6, 3, 8, 16, 8, 6}, this set has an even number of numbers in the set. Thus, the middles are 3 and 8. 3 + 8 = 11, and 11 ÷ 2 = 5.5. Thus, the median is 5.5.

The mode is the number that most frequently appears in the set. In this case, we have 2 frequent numbers. That is 6 and 8. They both appear 2 times separately. Thus, 6 and 8 are the modes of this set.

The range is the difference (i.e subtraction) between the largest number on the set and the smallest number on the set.

> Given set {5, 12, 6, 3, 8, 16, 8, 6}, the range is 16-3 or 13. Thus, the range is 13.

Now that we have the definitions, we can compute the other set very easily.

> Given set {2, 7, 4, 11, 12, 4, 6}, the mean is 18.

> Given set {2, 7, 4, 11, 12, 4, 6}, the median is 5.5.

> Given set {2, 7, 4, 11, 12, 4, 6}, the mode is 4.

> Given set {2, 7, 4, 11, 12, 4, 6}, the range is 10.

Hope it helped!

The total average credit card debt for  a U.S household will be $9292.

We are given that an expression which gives an approximate value of the total average credit card debt in a U.S. household (in dollars )t years after 1995

We have to find the total average credit card debt will be in the year 2004.

Number of years =2004-1995=9

t=9 years

Substitute the value of t in the given expression

Then , total average credit card debt in a U.S household will be in the year

Debt(t)=418t+5530

Debt(9)=418 * 9+5530= $9292  in 2004

Hence, in the year 2004, the total average credit card debt for  a U.S household will be $9292.

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Answer:

24/5

Step-by-step explanation:

5x : 9

(8 : 3)×3

5x : 9

24 : 9

5x = 24

x = 24/5 = 4/4/5

Hello!

5x : 9 = 8 : 3

5x × 3 = 8 × 9

15x = 72

5x = 24

x = 24/5

x = 4.8

∴ The value of x is 4.8.

Answer:

35= 8x + 3

35 - 3 = 8x

32 = 8x

32/8= 8x/8

x = 4

The fully factorized version of  -x-5 is [tex]-1 \times (x+5)[/tex].

What is Factorization?

Usually, factorization or factoring means writing a number (or another mathematical object) as a product of minor or more uncomplicated objects of the same kind.

Given -x-5 is a linear expression.

For factorizing, first, make the coefficient of x positive. For this take -1 common.

⇒ -x-5 = [tex]-1\times(x+5)[/tex]

Now take the greatest common divisor (gcd) of absolute values of coefficients in x+5.

⇒ gcd(1,5) = 1.

Now take gcd 1 common in the expression.

⇒ [tex]-1\times1\times(x+5)[/tex]

⇒ [tex]-1\times(x+5)[/tex].

∴ The fully factorized version of -x-5 is [tex]-1\times(x+5)[/tex].

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Perpendicular lines are lines that intersect and form right angles

A line is defined as the shortest distance between two points. Its equation is written in slope-intercept form as y = mx + b

Perpendicular lines on the other hand are lines that meet at a point to form a right angle. Hence we can conclude that perpendicular lines are lines that intersect and form right angles

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Step-by-step explanation:

Answer:

1. can't answer, can only approximate

2. when f(x) = 2, x = -1

Step-by-step explanation:

We can't evaluate f(2)  because we don't have f(x), if we did, we would plug in 2 for x.

On the other hand, solve f(x) = 2 asks for what x is equal to when f(x) = 2, f(x) is just the value on the y axis in relationship with x (in short terms, the value on the y axis).

So looking at the graph, we cam see that when x = -1, f(x) = 2.