Given the expression

Choose all the equivalent expressions as your answer.

Rοunding tο the nearest hundredth, the surface area οf the sphere is apprοximately 50.27 square feet.

Surface area is the measure οf the tοtal area that the surface οf an οbject οccupies. It is a twο-dimensiοnal measurement, typically expressed in square units, such as square meters (m²) οr square feet (ft²).

Tο find the surface area (A) οf a sphere with a given circumference (C), we first need tο find the diameter (d) οf the sphere.

The fοrmula fοr the circumference (C) οf a sphere is:

C = 2πr

where r is the radius οf the sphere.

Given that the circumference is 4π ft, we have:

4π = 2πr

Sοlving fοr r, we get:

r = 2 ft

Nοw we can use the fοrmula fοr the surface area οf a sphere with diameter d:

A = 4π(d/2)²

Substituting d = 4 ft (since diameter = 2r), we get:

A = 4π(4/2)²

A = 4π(2)²

A = 4π(4)

A = 16π

A ≈ 50.27

Therefοre, rοunding tο the nearest hundredth, the surface area οf the sphere is apprοximately 50.27 square feet.

A ≈ 50.27

Therefοre, rοunding tο the nearest hundredth, the surface area οf the sphere is apprοximately 50.27 square feet.

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Sally's turtle walked a total of 30 feet altogether on Wednesday.

To determine the total distance the turtle went, we need to know the distances between the beginning line and points T and M.

According to the diagram, there are 12 feet between the beginning line and point T and 8 feet between the starting line and point M.

The turtle travels a distance of: when it moves from the starting line to point T and then returns to point M.

Distance between the beginning line and point T plus the distances between point T and point M and point M from the starting line equals 12 + 10 + 8 = 30 feet.

So, on Wednesday, Sally's turtle travelled a total of 30 feet.

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The best estimate for the total amount of time Tim would spend answering e-mails over the course of 100 days is 100 hours with a standard deviation of 0.53 hours.

To find the total amount of time Tim would spend answering emails over the course of 100 days, we need to use the concept of the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approaches a normal distribution regardless of the underlying distribution.

To calculate the standard deviation of the total amount of time Tim spends answering emails over 100 days, we can use the formula:

standard deviation = square root of (n * variance)

where n is the number of days and variance is the variance of the amount of time Tim spends in a day answering emails.

Substituting the values, we get:

standard deviation = square root of (100 * 0.0028) = 0.53 hours

Therefore, Tim would spend an average of 100 hours over the span of 100 days responding to emails, with a standard deviation of 0.53 hours, according to the best estimate.

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According to the question the equilibrium price of tea is 2.10.

Equilibrium is a state of balance in which all forces acting on an object are equal and opposite, so no net force is acting on the object. This state of balance is also known as a "steady state". Equilibrium is an important concept in many areas of science, such as physics and chemistry, because it allows us to analyze how objects interact in a stable environment. Equilibrium can also be used to describe a state of financial balance, where all parties involved in a transaction are satisfied with the outcome.

The equilibrium price can be found by setting the two equations equal to one another and solving for P.
34P + 53 = -25P + 177
59P = 124
P = 124/59
P = 2.10
Therefore, the equilibrium price of tea is 2.10.

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The cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

A spherical οr elliptical cοοrdinate system knοwn as the geοgraphic cοοrdinate system is used tο measure and transmit pοsitiοns οn Earth as latitude and lοngitude.

First, we can find the distance between pοints Y and q, which will be the same as the distance between pοints 5 and B since they are οppοsite sides οf the parallelοgram:

Distance Yq = [tex]\sqrt{[(10-8)^2 + (5-10)^2] }[/tex]

Distance Yq = [tex]\sqrt{8 + 25 }[/tex]

Distance Yq =[tex]\sqrt{ 33}[/tex]

Distance 5B = [tex]\sqrt{[(3-2)^2 + (2-3)^2] }[/tex]

Distance 5B = [tex]\sqrt{2}[/tex]

Since οppοsite sides are cοngruent, √33 = √2x, where x is the length οf the missing side οf the parallelοgram. Sοlving fοr x, we get:

x = (33/2)

Next, we can find the slοpe οf the line passing thrοugh pοints Y and q,

Slοpe Yq = (10-5)/(8-10) = -5/2Slοpe B-missing vertex = -5/2

write the equatiοn οf the line passing thrοugh B and the missing vertex:

y - 2 = (-5/2)(x - 3)

Simplifying, we get:

y = (-5/2)x + (19/2)

Therefοre, the cοοrdinates οf the missing vertex are (19/2, x), where x = 2 + (33/2) = 19.5.

Sο the cοοrdinates οf the fοurth vertex οf the parallelοgram are (19/2, 19.5).

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Answer:

Step-by-step explanation:

The probability of winning the new boat is unlikely, since there is only one boat behind one of the five doors, while the other four doors have joke prizes. Assuming that each door has an equal chance of being selected by the contestant, the probability of choosing the door with the boat is 1/5 or 20%. However, the probability of not winning the boat is 4/5 or 80%. Therefore, it is unlikely that the contestant will win the boat.

Answer:

Answer: 10

Step-by-step explanation:

Let L be the length of the rectangle, and W be the width.

From the problem, we know that:

The perimeter of the rectangle is 72, which means that:

2(L + W) = 72

L + W = 36

The width is 4 less than 3 times the length:

W = 3L - 4

Substituting W = 3L - 4 into the first equation, we get:

L + 3L - 4 = 36

4L = 40

L = 10

Therefore, the length of the rectangle is 10. Answer:  10

In order to find the price increase in percentage terms, we divide the price difference by the cost price.

The difference:

Rate:

If we solve for [tex]x[/tex] in this equation, it will give us the price increase as a percentage.

The price increase should be [tex]110[/tex]%.

The density of the cuboid is 10.4 g/cm3 ( 1 d.p)

Density is the ratio of mass of a substance to its volume. It is measured in kg/m³ or g/cm³. It is a scalar quantity.

The density of a substance bis expressed as;

d = mass/volume

The mass = 416g

and the volume = l× w × h

length of the cuboid = 4cm

width of the cuboid = 2cm

and height = 5cm

Therefore the volume is calculated as :

V = 4× 2 × 5

V = 40cm³

the volume of the cuboid is 40cm³

The density can now be calculated as :

density = mass/volume

density = 416/40

= 10.4g/cm³

therefore the density of the cuboid is 10.4 g/cm³

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Answer:

No

Step-by-step explanation:

In order for a set of ordered pair to be a function all the x values need to be different. In this case we have two of the same x values so this set won't be a function.

(1) In General Ledger, Cash Account is $ 13900 , In revenue account The balance is $ $28600, in expense account the balance is $ $13200 and Trial balance is $28600.

(2) The income statement is $ 15400.

(3) Statement of Changes in Stockholders' Equity is $13900.

(4) Balance sheet is $ 13900.

Record the effects of each accounting event under the appropriate general ledger account headings.

Using the accounting equation, we have:

Asset = Shareholder's equity + Liabilities

Cash = Retained earning + Common stock

Cash = $28,600 - $13,200 - $1,500 = $13,900 = Assets

Retained earning = $28,600 - $13,200 - $1,500 = $13,900

Common stock = 0

Retained earning + Common stock = $13,900 + 0 = Shareholder's equity

Liabilities = 0

Therefore, we have:

(1) Majka Company

Accounting Equation for Year 1

Asset ($) = Shareholder's equity + Liabilities

13,900    =      13,900                    +        0

(2) Prepare an income statement

Details                                 Amount ($)

Revenue                                28,600

Expenses                               (13,200)

Net Profit                                15,400

Dividend                                (1,500)  

Retained earning                   13,900  

(3) Statement of changes in stockholders’ equity

Details                                      Amount ($)                        

Common stock                                0

Beginning retained earning           0

Retained earning for the year     13,900  

Stockholders’ equity                   13,900

(4) Mijka Company, Balance sheet as at December 31, Year 1,

Details                                      Amount ($)    

Assets:

Cash                                            13,900

Liabilities:  

Current and Long terms                  0      

Net total assets                           13,900  

Stockholders’ equity:

Common stock                                0

Retained earning                         13,900  

Stockholders’ equity                   13,900

Complete Question:

Majka Company was started on January 1, Year 1. During Year 1, the company experienced the following three accounting events: (1) earned cash revenues of $28,600, (2) paid cash expenses of $13,200, and (3) paid a $1,500 cash dividend to its stockholders. These were the only events that affected the company during Year 1. Required Record the effects of each accounting event under the appropriate general ledger account headings. Prepare an income statement, statement of changes in stockholders’ equity, and a balance sheet dated December 31, Year 1, for Mijka Company.

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Answer:144 ft³

Step-by-step explanation:

The width of the sandbox is half of its length, so we can start by finding the length:

Length = 12 feet

Width = 1/2 * Length = 1/2 * 12 feet = 6 feet

Height = 2 feet

The volume of sand needed to fill the sandbox is the product of its length, width, and height:

Volume = Length * Width * Height

Volume = 12 feet * 6 feet * 2 feet

Volume = 144 cubic feet

Answer: 0.2 square meters.

Step-by-step explanation:

We are given the equation:

3600b² = hw

We need to find the value of b, given that h = 168 cm and w = 60 kg.

First, we need to convert the height from centimeters to meters:

h = 168 cm = 1.68 m

Substituting the given values:

3600b² = (1.68)(60)

3600b² = 100.8

b² = 100.8/3600

b² = 0.028

Taking the square root of both sides:

b = √0.028

b ≈ 0.167

Rounding to the nearest tenth:

b ≈ 0.2

Therefore, the body surface area of a person who is 168 centimeters tall and weighs 60 kilograms is about 0.2 square meters.

Answer:

[tex]2x^{2} +0x+-1=0[/tex]

Step-by-step explanation:

The standard form of a quadratic equation is:

The expression provided ([tex]2x^{2} -1[/tex]), can be rewritten in standard form by setting it to equal zero:

In this case, a would be equal to 2, b equal to 0, and c equal to -1.

Answer: 2° Celsius.

Step-by-step explanation:

It depends on the specific composite figure. In general, the perimeter of a composite figure is not always equal to the sum of the perimeters of the individual figures that make it up.

However, in some cases, it is possible to calculate the perimeter of a composite figure by adding the perimeters of the individual figures and subtracting the lengths of any shared sides.

For example, if a composite figure is made up of two rectangles that share a side, then the perimeter of the composite figure is equal to the sum of the perimeters of the two rectangles minus the length of the shared side.

In other cases, such as when a composite figure has curved sides or irregular shapes, the perimeter cannot be calculated simply by adding the perimeters of the individual figures.

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Answer:[tex]\frac{5}{7} \\\\ \\\\\frac{3}{4} \\\\\frac{19}{25} \\\\\frac{11}{5}[/tex]

Step-by-step explanation:

Expressing this in scientific notation, we get: Distance traveled in a week = 3.77 x [tex]10^7[/tex] miles/week

Speed is a measure of how fast an object is moving, usually expressed in units of distance per unit time. It is defined as the distance traveled by an object divided by the time it takes to travel that distance.

The speed of the sun orbiting the Milky Way galaxy is 135 miles per second.

A. To find how far the sun travels in an hour, we need to multiply its speed by the number of seconds in an hour:

Distance traveled in an hour = 135 miles/second x 60 seconds/minute x 60 minutes/hour

Distance traveled in an hour = 486,000 miles/hour

Expressing this in scientific notation, we get:

Distance traveled in an hour = 4.86 x [tex]10^5[/tex] miles/hour

B. To find how far the sun travels in a week, we need to multiply its speed by the number of seconds in a week:

Distance traveled in a week = 135 miles/second x 60 seconds/minute x 60 minutes/hour x 24 hours/day x 7 days/week

Distance traveled in a week = 37,656,000 miles/week

Expressing this in scientific notation, we get:

Distance traveled in a week = 3.77 x [tex]10^7[/tex] miles/week

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[tex]\begin{cases} x = \frac{4}{3} &\implies 3x=4\implies 3x -4=0\\ x = -1 &\implies x +1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( 3x -4 )( x +1 ) = 0} \hspace{5em}\stackrel{\textit{now assuming that}}{a=1}\hspace{3em}1( 3x -4 )( x +1 ) = 0 \\\\\\ ~\hfill {\Large \begin{array}{llll} 3x^2-x-4=0 \end{array}}~\hfill[/tex]

Answer:16.7%

Step-by-step explanation: He has a 33% chance of losing in chess and 50% of losing in pool. So when you convert the two percentages to decimals and multiply them the result is 0.167. Convert the number back into a percentage, it's 16.7%.

Answer:

identify a relationship among Tn,Sn and Sn-1 where n>1

The amount of they share altogether is 90000

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.

For example if two boys are to share 10 mangoes with ratio 1:4. The first boy will get 1/5 × 10 = 2 mangoes and the other boy will get 4/5 × 10 = 4×2 = 8 mangoes.

Three brothers are to share in ratio 3:4:5. The highest ratio is 5. And the the highest ratio gets 37500. The total ratio is 12 i.e 3+4+5 = 12

Represent the total money by x

Then, 5/12 × x = 37500

5x = 37500 × 12

5x = 450000

divide both sides by 5

x = 450000/5

x = 90000

therefore the amount they shared is 90000.

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The domain is (-∝, ∝) and the range is y > 0

From the question, we have the following parameters that can be used in our computation:

y = 2^x

The domain of the function is the set of all real numbers

This is so because there is no restriction on the input values

The range of the function is the set of positive real numbers

Since any positive number can be obtained by raising 2 to a power, and the function is never negative or zero.

We can write the range as y > 0.

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To find the multiplication equation that shows how the denominators of 3/4 and 1/2 are related, we can simply multiply the two denominators together:

3/4 x 1/2 = 3/8

Therefore, the denominators are related by the equation 4 x 2 = 8.

To write 1/2 as an equivalent fraction with a denominator of 4, we need to multiply both the numerator and denominator by the same factor that will transform the denominator of 2 to a denominator of 4.

Using the multiplication equation we found earlier, we can see that we need to multiply both the numerator and denominator of 1/2 by 2 (since 2 x 2 = 4). This gives us:

1/2 x 2/2 = 2/4

Therefore, 1/2 can be written as an equivalent fraction with a denominator of 4 as 2/4.

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0.90 x $11.00 = $9.90

This is the price of the CD before taxes are applied. To find the total price, including tax, we need to add the 7% sales tax to the discounted price:

Total price = discounted price + (sales tax x discounted price)

Total price = $9.90 + (0.07 x $9.90)

Total price = $9.90 + $0.69

Total price = $10.59

Therefore, the total price of the CD, including tax, is $10.59.

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The student's error is adding two non-adjacent angles and then solving for x.

What are the opposite angles?

Opposite angles are the angles directly opposite each other where two lines cross. The intersection point is called the vertex, which is where the lines connect to form the angle. Opposite angles are also called vertical angles.

The student's error is that they incorrectly added the two given angles together.

The angles 2x+6 and 60 are not adjacent angles and therefore cannot be added together to find the sum of the two angles.

In the figure, if the angle formed by the intersection of the lines is labeled as angle A, then we know that angle A is equal to 2x+6 and angle B is equal to 60.

These two angles are opposite angles and not adjacent angles, so they do not add up to 180 degrees.

Therefore, the student's error is adding two non-adjacent angles and then solving for x.

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A graphic organizer that correctly groups the following numbers 4.1, -9, 3, -2.2​ is; B. graphic organizer B.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 6, 4.1, -2.2 12, 1/2, 0.5, √16, -29, etc.

In Mathematics, an integer can be defined as a whole number that may either be positive, negative, or zero (0). This ultimately implies that, a positive integer simply refers to a whole number that is greater than or equal to one (1).

Based on the given data set 4.1, -9, 3, -2.2, the numbers should be correctly grouped as follows;

Rational number = 4.1 and -2.2.

Integer = -9.

Whole number = 3.

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Answer:

≈ 9.9 feet

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. Let x be the distance from the house to the base of the ladder. Then:

x^2 + 15^2 = 18^2

Simplifying and solving for x, we get:

x = sqrt(18^2 - 15^2) = 9.9 feet (rounded to the nearest tenth)

Therefore, Jaquira should place the base of the ladder approximately 9.9 feet away from the house.