Suppose U is a nonempty subset of the vector space V over eld F. Prove that U is a

subspace if and only if cv + w 2 U for any c 2 F and any v;w 2 U

Answer:

[tex]\frac{5}{36}[/tex]

Step-by-step explanation:

Given,

P(A) = [tex]\frac{1}{2}[/tex],

P(B) = [tex]\frac{3}{5}[/tex]

[tex]P(\frac{B}{A})=\frac{1}{6}[/tex]

[tex]\because P(\frac{B}{A})= \frac{P(A\cap B)}{P(A)}[/tex]

[tex]\implies \frac{P(A\cap B)}{P(A)} = \frac{1}{6}[/tex]

[tex]\frac{P(A\cap B)}{\frac{1}{2}}=\frac{1}{6}[/tex]

[tex]2P(A\cap B) = \frac{1}{6}[/tex]

[tex]\implies P(A\cap B) = \frac{1}{12}[/tex]

Now,

[tex]P(\frac{A}{B})=\frac{P(A\cap B) }{P(B)}= \frac{1/12}{3/5}=\frac{5}{36}[/tex]

Answer:

16 g of water.

Step-by-step explanation:

salt : baking soda : water =  20 : 15 : 10

If we have  24 g of baking soda that is 24/15 = 8/5 times of 15.

So by proportion the amount of water would be 10 * 8/5 = 16 grams.

The mass of water in the mixture is 16 gm

When a number is divisible by another number then they can be written in the form of ratio p :q , When two ratios are equal they are said to be in proportion.

It is given that

salt, baking soda, and water in a 20:15:10 ratio by mass are mixed

mixture contains 24 grams of baking soda

Mass of Water = ?

Baking Soda : Water = 15 : 10

Let the mass of water is x

then the ratio is 24 : x

As both these ratios are equal

15 : 10 = 24 : x

15 / 10 = 24 / x

x = 24 * 10 / 15

x = 16 gm

Therefore the mass of water in the mixture is 16 gm.

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Answer:

answered

Step-by-step explanation:

A)lean

B)lean

C)traditional

In Lean manufacturing system works are done reduce inventory levels below what  would be found in a traditional manufacturing system. The company does so by reducing batches into smaller batch sizes rather than large batch sizes. Goods are produced through product  cells rather than departments.

Within-batch wait time is time that product waits in a product cell for the other products in a batch, it is calculated by multiplying the value-added time per unit by number of other products ,one less the total batch size

Answer:

a) There are infinite prime numbers, b) All prime numbers are also abundant numbers

Step-by-step explanation:

To prove a) let's first prove that if n divides both integers A and B then also divides the difference A-B

If n divides A and B, there are integers j, k such that

A = nj and B= nk,

So

A-B= nj - nk = n(j-k)

But j-k is also an integer, which means that n divides also A-B

Now, to prove that there are infinite prime numbers , we will proceed with Reductio ad absurdum.

We will suppose that there are only a finite number of primes and then arrive to a contradiction.

Suppose there are only n prime numbers,

{p1,p2,... pn}

then take P=p1.p2...pn the product of all of them

and consider P+1

If P+1 is prime the proof is complete for P+1 is not in the list.

if P+1 is not prime then by the Fundamental Theorem of Arithmetic there is a prime in the list that must divide P+1, let's say pk

Then pk also divides P+1-P=1 which is a contradiction because no prime divides 1.

b) To prove this, recall that an abundant number is a number for which the sum of its proper divisors is greater than the number itself.

Given that a prime number P is only divided by P and 1, the sum of its divisors is P+1 which is greater than P. So P is abundant

Answer:

72° = 1.25 radians

Step-by-step explanation:

As we know that,

[tex]1 degree = \frac{\pi}{180} radians[/tex]

Thus, [tex]72^{\circ} = 72\times\frac{\pi}{180}radians[/tex]

⇒ [tex]72^{\circ} =\frac{2\pi}{5}radians[/tex]

⇒ 72° = 1.25 radians    {∵ Using π = 22÷ 7 or 3.14}

Both degrees and radians are used to measure the angle. They are units of angle.

The total number of ID cards possible without repeating digits is 10 x 9 x 8 x 7 x 6 = 30,240.

In a college, the number of ID cards possible can be found by calculating the number of possible options for each digit in the 5-digit pin.

Since each digit can be any number from the set {0,1,2,3,4,5,6,7,8,9}, there are 10 options for each digit. Therefore, the total number of ID cards possible is 10 x 10 x 10 x 10 x 10 = 100,000.

Answer: 0.125%

Step-by-step explanation:

Let 1600 corresponds to the 100% value and 2 is a part of the total 100% value 1600.

The formula to find the percent of a part :_

[tex]\%=\dfrac{\text{Part}}{\text{Total}}\times100[/tex]

Substitute Part= 2 and Total = 1600 in the formula, we get :-

[tex]\%=\dfrac{2}{1600}\times100\\\\\Rightarrow\ \%=\dfrac{1}{8}\%=0.125\%[/tex]

Therefore, 2 is 0.125% of 1600.

Hence, the percent of 1600 is 2 = 0.125%

To find what percent of 1600 is 2, divide 2 by 1600 and multiply by 100, resulting in 0.125%. Thus, 2 is 0.125% of 1600.

To determine what percent of 1600 is 2, you can use the formula for percentage:

Percentage = (Part / Whole) × 100

Here, the part is 2 and the whole is 1600. Plug these values into the formula:

Percentage = (2 / 1600) × 100

First, perform the division:

2 / 1600 = 0.00125

Next, multiply by 100 to convert to a percentage:

0.00125 × 100 = 0.125%

Therefore, 2 is 0.125% of 1600.

Answer:

The solution is [tex]x = 1[/tex]

Step-by-step explanation:

We have the following logarithmic properties:

[tex]ln a + ln b = ln ab[/tex]

[tex]ln a - ln b = ln \frac{a}{b}[/tex]

[tex]n ln a = ln a^{n}[/tex]

We have the following logarithmic equation:

[tex]ln(x + 31) - ln (4-3x) - 5 ln 2 = 0[/tex]

Lets simplify, and try to find properties.

[tex]ln(x + 31) - (ln (4-3x) + 5 ln 2) = 0[/tex]

[tex]ln(x + 31) - (ln (4-3x) + ln 2^{5}) = 0[/tex]

[tex]ln(x + 31) - (ln (4-3x) + ln 32) = 0[/tex]

[tex]ln(x + 31) -  ln 32*(4-3x) = 0[/tex]

[tex]ln(x+31) - ln (128 - 96x) = 0[/tex]

[tex]ln \frac{x + 31}{128 - 96x} = 0[/tex]

To eliminate the ln, we apply the exponential to both sides, since e and ln are inverse operations.

[tex]e^{ln \frac{x + 31}{128 - 96x}} = e^{0}[/tex]

[tex]\frac{x + 31}{128 - 96x} = 1[/tex]

[tex]x + 31 = 128 - 96x[/tex]

[tex]97x = 97[/tex]

[tex]x = \frac{97}{97}[/tex]

[tex]x = 1[/tex]

The solution is [tex]x = 1[/tex]

Answer:

The correct option is 4) a ratio variable.

Step-by-step explanation:

Consider the provided information.

Nominal variables are pertaining to names or It merely name differences, it is a qualitative variables.

Ordinal variable: It is a rank-order observations in which order matters but difference between the value doesn't matters. It is a qualitative variables.

Interval variable: It is useful if the difference between two values is meaningful. It is a quantitative variables.

Ratio variable: this variable has all the properties of an interval variable, also it has a clear definition of 0.0. It is a quantitative variables.

Now consider the provided information.

The concentration is in milligrams per liter which is a quantitative variable.

Among the provided options only ratio variable and interval variable is quantitative variable. So option A and B are incorrect.

Since the milligrams per liter can be zero point which is not the characteristic of interval scale. Thus, the option C is incorrect.

The zero point is characteristic of ratio variable. Thus, the concentration of DDT (C14H9Cl5), in milligrams per liter, is ratio variable.

Hence, the correct option is 4) a ratio variable.

Final answer:

The concentration of DDT in milligrams per liter is best described as a ratio variable, as it is measured on a numeric scale that includes a true zero, allowing for meaningful comparisons and arithmetic operations.

Explanation:

The concentration of DDT, which is a chemical compound with the formula C14H9Cl5, in a given volume of solution is a measure that can be categorized using levels of measurement in statistics. In this context, concentration is measured in milligrams per liter (mg/L), which is a unit that indicates the mass of the substance (DDT) in a specific volume of the liquid (water).

Among the four types of variables listed (nominal, ordinal, interval, and ratio), the concentration of DDT in mg/L is best described as a ratio variable. This is because it has a true zero point (0 mg/L indicates the absence of DDT), and the difference between any two concentrations has a meaningful interpretation. Additionally, you can perform a full range of arithmetic operations on ratio variables.

Nominal variables are categorical and do not have a numeric order. Ordinal variables are categorical with a clear order, whereas interval variables have a numeric scale without a true zero. However, for measurements like concentration of DDT, that have a true zero and are continuous, the appropriate level of measurement is the ratio level.

Answer:

See picture attached

Step-by-step explanation:

Answer:

[tex]1=9\cdot 9+20\cdpt (-4)=81-80[/tex]

Step-by-step explanation:

The greatest common divisor between 9 and 20 is 1, so we know the equation [tex] 1=9m+20n[/tex] has a solution. A solution can be found either by inspection, or by applying Euclidean algorithm.

By inspection we just list some multiples of 9:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

and also list some mutiples of 20:

20, 40, 60, 80, 100, 120

And so we see that we can find a multiple of 9 (81) which is 1 away from a multiple of 20 (80). Which is the solution given at the start.

For the Euclidean algorithm, we should divide the greatest of the two numbers, by the smallest one, and keep track of the remainder:

20 = 9 * 2 + 2

Then we divide 9 by the remainder we got, which is 2:

9 =  2 * 4 + 1

we would continue doing this until getting a remainder of 1 (which we just did). Finally we "solve" for 1, from the last equation:

9 - 2*4 = 1

And then we solve for 2 from the first equation, and plug that in into the previous equation:

20 - 9*2 =2

9 - ( 20 - 9*2)*4 = 1

which does give us the same solution: [tex] 9\cdot 9 +20\cdot (-4)=1[/tex]

Answer:

Time take by car to overtake the truck is 7.6 seconds.

Step-by-step explanation:

Given : A car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. The truck has a constant acceleration of 2.10 m/s², and the car has an acceleration of 3.40 m/s². The car overtakes the truck after the truck has moved 60.0 m.

To find : How much time does it take the car to overtake the truck ?

Solution :

According to question,

Taking the origin to be the truck position when it is at rest.

The car overtakes the truck after the truck has moved 60.0 m.

Using the equation to find time,

[tex]x-x_o=v_ot+\frac{1}{2}at^2[/tex]

Where, [tex]x_o=0[/tex] initial distance

[tex]v_o=0[/tex] initial velocity

a= 2.10 m/s² is the acceleration of the truck

x=60 m is the distance truck moved.

Substitute the value in the formula,

[tex]60-0=0(t)+\frac{1}{2}\times 2.10\times t^2[/tex]

[tex]60=1.05\times t^2[/tex]

[tex]t^2=\frac{60}{1.05}[/tex]

[tex]t=\sqrt{\frac{60}{1.05}}[/tex]

[tex]t=7.55[/tex]

Therefore, Time take by car to overtake the truck is 7.6 seconds.

Answer:

 The buffer is the solution which basically oppose pH change upon the expansion of an acidic or fundamental parts. It can kill limited quantities of included corrosive or base, in this way keeping up the pH of the arrangement generally stable and steady.

Acidic buffer is the arrangements are usually produced using weak acidic nature and also by the sodium salt.

Dissolve is the process of break down is to make a solute go into an solution. Dissolving is likewise called disintegration. Regularly, this includes a strong going into a fluid stage, however disintegration can include different changes too.

For instance, when compounds structure, one strong breaks down into another to frame a strong arrangement.

Answer:

(a) The profit function is P(x)=14x-224,000.

(b) The company's profit at x=21000 is 70,000.

Step-by-step explanation:

Cost function is

[tex]C(x)=224,000+32x[/tex]

Revenue function is

[tex]R(x)=46x[/tex]

where, x is number of radios.

(a)

Formula for profit:

Profit = Revenue - Cost

The profit function is

[tex]P(x)=R(x)-C(x)[/tex]

[tex]P(x)=46x-(224,000+32x)[/tex]

[tex]P(x)=46x-224,000-32x[/tex]

[tex]P(x)=14x-224,000[/tex]

The profit function is P(x)=14x-224,000.

(b)

Substitute x=21000 in the above equation to find the company's profit if 21,000 radios are produced and sold.

[tex]P(21000)=14(21000)-224,000[/tex]

[tex]P(21000)=294000-224,000[/tex]

[tex]P(21000)=70,000[/tex]

Therefore the company's profit at x=21000 is 70,000.

The profit function for a company is found by subtracting the cost function from the revenue function. Given the cost and revenue functions, the profit function simplifies to P(x) = 14x - 224,000. If 21,000 radios are sold, the company will take a loss of $56,000.

Profit function in a company can be obtained by subtracting total cost from total revenue, it can be represented as P(x) = R(x) - C(x). Here, R(x) is the revenue function and C(x) is the cost function.

Given, the cost function of the company C(x) is 224,000 + 32x and the revenue function R(x) is 46x. Substituting these values into our profit function we get, P(x) = 46x - (224,000 + 32x), simplifying it leads to P(x) = 46x - 224,000 - 32x, which can be further simplified to P(x) = 14x - 224,000.

For part b of the question, if 21,000 radios are produced and sold, we substitute x=21,000 into the profit function. Hence, P(21000) = 14*21000 - 224,000 = -56,000. This indicates that the company will experience a loss when 21,000 radios are produced and sold.

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Answer:

500 cubic feet is equal to 14158.4 liters.

Step-by-step explanation:

Since, we know that,

1 square feet = 28.3168 liters,

Thus, the number of liters in 500 cubic feet = 500 × number of liters in 1 square feet

[tex]=500\times 28.3168[/tex]

[tex]=14158.4[/tex]

Therefore, 500 cubic feet is equal to 14158.4 liters.

500 cubic feet is 14158.4 liters.

To convert 500 cubic feet to liters, follow these steps:

Using the conversion factor:

1 ft³ = 28.3168 L

So, to convert 500 cubic feet to liters:

500 ft³ × 28.3168 L/ft³ = 14158.4 L

Answer:

$1,369.25

Step-by-step explanation:

Mr. and Mrs. Wong purchased their new house for $350,000.

They made a down payment of 20%

Down payment = 20% of 350000

                        = $70,000

Loan amount, P = $350,000 - $70,000

                         = $280,000

Rate of interest, r = 4.2% or 0.042

Time, t = 30 years

Number of period, n = 12 ( monthly )

Formula: [tex]E=\dfrac{P\cdot \frac{r}{n}}{1-(1+\frac{r}{n})^{-n\cdot t}}[/tex]

Substitute the values into formula

[tex]E=\dfrac{280000\cdot \frac{0.042}{12}}{1-(1+\frac{0.042}{12})^{-12\cdot 30}}[/tex]

E = $1,369.25

Hence, The monthly payment for their mortgage will be $1,369.25

Answer:

P8) [tex]t=7.02 years[/tex]

P4) Today you have to invest $6941.55

P8) Is the same P8 above

Step-by-step explanation:

P8) First of all, we can list the knowns [tex]VP=7425.70[/tex], [tex]I=3250[/tex] and [tex]i=5.3[/tex]%, so we use [tex]VF=VP+I=7425.70+3250=10675.70[/tex] then we use [tex]t=\frac{ln(VF/VP)}{ln(1+i)}=\frac{ln(10675.70/7425.70)}{ln(1+0.053)}  =\frac{0.363}{0.051}=7.02 years[/tex]

P4) First of all, we can list the knowns [tex]VF=9500[/tex], [tex]t=8[/tex] and [tex]i=4[/tex]%, so we use [tex]VP=\frac{VF}{(1+i)^{t} } =\frac{9500}{(1+0.04)^{8} } =6941.55[/tex]

P8) Is the same P8 above

Answer and Explanation:

To prove : The square of any even number is always a multiple of 4.

Proof :

The even numbers is defined as number end with 0,2,4,6,8 or the even number are multiple of 2.

Let the general even number be '2n'.

Squaring the number [tex](2n)^2=2^2\times n^2[/tex]

[tex](2n)^2=4n^2[/tex]

As 4 is the multiple of n².

So, If we square any even number it is always a multiple of 4.

For example,

[tex]2^2=4=4\times 1\\4^2=16=4\times 4\\6^2=36=4\times 9\\8^2=64=4\times 16[/tex]

Hence proved.

Answer:

Mean = 497.5

Median = 379.0

First Quartile = 289

Third Quartile = 771.5

Step-by-step explanation:

Mean is used to measure the central tendency of data which represents the whole data in the best way. It can be found as the ratio of the sum of all the observations to the total number of observations.  

⇒ [tex]Mean=\frac{246+ 299+ 360+ 404+ 379+ 199+ 279+ 749+ 794+ 849+ 914}{11}[/tex]

⇒ Mean = 497.5

Median is the middle observation of given data. It can be found by following steps:

Arranging data in ascending or descending order.

Taking the average of middle two value if the total number of observation is even, and this average is our median.

or, if we odd number of observation then the most middle value is our median.  

Here, number of observation is 11.

So the middle value is (11+1)÷2 = 6th term

⇒ Median = 379

The mode is the observation which has a high number of repetitions (frequency).

Here frequency of all observation is same. So, it is multi- modal data.

First Quartile is the middle value between Minimum value and Median of data after arranging data in ascending order.

First Quartile (Q₁) = 289

The third Quartile is the middle value between Median and Maximum Value of data after arranging data in ascending order.

Third Quartile (Q₃) = 771.5

Answer: The magnitude is: a) continuous numeric.

Step-by-step explanation:

The magnitude is a numeric variable because it represents quantities. These are variables that you can measure or count. A numeric variable can be classified into discrete or continuous. In the present problem, the magnitude is a continuous variable. It can take any number within a scale, and you can find infinite values between two values on the scale. For example, you could measure earthquakes of magnitude 2.3, 2.4, 2.5, 2.6… and so on, following a continuous scale.

On the other hand, if the variable is numeric and discrete, it can only take certain finite values. For example, when you count the number of trees per acre. The number of trees will be always an integer. You can find 1, 2, or 3 trees, but you’ll never count 2.5 trees.

Categorical variables don’t represent quantities. They represent attributes. For example, apple colors: green and red.

Answer:

3865.74 J/s

Step-by-step explanation:

mass of ice, m = 1 ton = 1000 kg

time , t = 24 hours

latent heat of fusion of ice, L  = 334000 J/kg

Heat required to melt, H = m x L

where, m is the mass of ice and L be the latent heat of fusion

So, H = 1000 x 334000 = 334 xx 10^6 J

Rate of heat transfer = heat / time = [tex]\frac{334\times 10^{6}}{86400}[/tex]

Rate of heat transfer = 3865.74 J/s

thus, the rate of heat transfer is 3865.74 J/s.

Answer:

Released oxygen mass: 15.92 kg

Step-by-step explanation:

ideal gas law : P*V=nRT

P:pressure

V:volume

T:temperature

n:number of moles of gas

n [mol] = m [g] /M [u]

m : masa

M: masa molar = 15,999 u (oxygen)

R: ideal gas constant = 8.314472 cm^3 *MPa/K*mol =

grados K = °C + 273.15

P1*V*M/R*T = m1

P2*V*M/R*T = m2

masa released : m1-m2 = (P1-P2) * V*M/R*T

m2-m1 = 200 * 10^-3 MPa * 12 * 10^6 cm^3 * 15.999 u / 8.314472 (cm^3 * MPa/K *mol) * 290. 15 K

m2-m1= 38 397.6 * 10^3 u*mol / 2412.44 = 15916.5 g = 15.9165 kg

The question involves the use of the Ideal Gas Law to calculate the mass of oxygen released from a tank when the pressure drops. The initial and final number of moles of oxygen is calculated using the Ideal Gas Law, then the difference represents the number of moles of oxygen released. Multiplying this by the molar mass of oxygen gives the mass of oxygen released, which is about 255.808 kg.

The Ideal Gas Law states that PV=nRT, where P is pressure in Pascals, V is volume in m3, n is the number of moles, R is the Universal Gas Constant (8.31 J/(mol.K)), and T is temperature in Kelvin. From the question, we know the initial and final pressures (P1=850 kPa, P2=650 kPa ), Volume (V=12 m3), and temperature (T=17°C = 290 K).

First, we need to calculate the initial (n1) and final (n2) number of moles using the equation n = PV/RT. Substituting the given values to the equation, we get n1= (850000*12) /(8.31*290)= 34974.48 mol and n2= (650000*12) /(8.31*290)= 26980.38 mol.

So, the mass of oxygen that has been released is the difference between the initial and final moles. It equals to 7994.1 mol. Since the molar mass of oxygen is approximately 32 g/mol, the mass of oxygen that has been released is 7994.1 mol * 32 g/mol = 255808 g or 255.808 kg. So, the mass of oxygen released from the tank is approximately 255.808 kg.

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Answer:

A ≈ 14.079 square units

Step-by-step explanation:

Area of a triangle is one half the base times the height.

A = ½ bh

A = ½ (10) (2x)

A = 10x

We need to find the value of x.

Starting with the triangle on the left, use Pythagorean theorem to find the length of the base.

(3x)² = (2x)² + a²

9x² = 4x² + a²

a² = 5x²

a = x√5

Repeat for the triangle on the right:

(x + 6)² = (2x)² + b²

x² + 12x + 36 = 4x² + b²

b² = -3x² + 12x + 36

The two bases add up to 10:

a + b = 10

Subtract a from both sides, then square both sides:

b = 10 − a

b² = 100 − 20a + a²

Substitute and simplify:

-3x² + 12x + 36 = 100 − 20(x√5) + 5x²

0 = 64 − (12 + 20√5) x + 8x²

0 = 2x² − (3 + 5√5) x + 16

Solve with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ (3 + 5√5) ± √((-(3 + 5√5))² − 4(2)(16)) ] / 2(2)

x = [ (3 + 5√5) ± √(9 + 30√5 + 125 − 128) ] / 4

x = [ (3 + 5√5) ± √(6 + 30√5) ] / 4

x ≈ 1.4079, 5.6823

If we substitute 5.6823 into our a and b equations, we find that a = 12.706 and b = 7.322, which add up to 20.028, not 10.

So x ≈ 1.4079.

Therefore the area is:

A ≈ 14.079

Answer:

3.1

Step-by-step explanation:

because u have to take away the - sign if it is two negatives :3

Step-by-step explanation:

you draw a line (don't forget to put arrows on the end) then you put the point farthest to the left :(-9.1) and the point farthest to the right (-6.2).

in between these points you add the ponts -9,-8,-7-,6 respectively.

Final answer:

To find out how many milliliters of the solution would contain 0.5 mg of the drug, we can set up a proportion using the given information. The solution would contain 0.125 mL of the drug.

Explanation:

To find out how many milliliters of the solution would contain 0.5 mg of the drug, we need to set up a proportion using the given information. We have 2 g of the drug in one-half liter of solution, so the concentration is 4 g/L. We can convert milligrams to grams by dividing by 1000. By setting up the proportion, we have:

4 g/L = 0.5 mg/x mL

Cross-multiplying, we get:

4 g * x mL = 0.5 mg * 1 L

Converting mg to g and mL to L:

4 * x = 0.5 / 1000

x = (0.5 / 1000) / 4

x = 0.000125 L

Since there are 1000 mL in 1 L, we can convert the answer:

x = 0.000125 L * 1000 mL/L

x = 0.125 mL

Answer: The conclusion cannot be confirmed unless we have the statistic of the men.

Step-by-step explanation: Only looking at the number of women in both times 8 am and 10 am, will not determine if the men prefer of do no prefer earlier classes. We would need the men's statistics as well for both time slots. There may be more men among the 8 am slot e.g 25 women and 30 men. There is incomplete information to come up with a sound conclusion.

Answer:

  see the attachment

Step-by-step explanation:

If the growth is 7 feet in 2 weeks and the rate is constant, then it will be half that in one week, or 3.5 feet per week. At week 3, it will be 3.5 feet more than at week 2. The table below shows this progression.

The point (0, 0) means there was no measurable growth when time was starting to be measured (at week 0).

Answer: [tex]62.8\text{ inches}[/tex]

Step-by-step explanation:

The circumference of a circle is given by :-

[tex]C=2\pi r[/tex], where r is the radius of the circle.

Given : Radius of a circle = 10 inches

Then, the circumference of circle will be :_

[tex]C=2(3.14) (10)\\\\\Rightarrow\ C=62.8\text{ inches}[/tex]

Hence, the circumference of the circle will be [tex]62.8\text{ inches}[/tex]

Answer:

The mass of atmosphere equals [tex]6742.368\times 10^{15}kg[/tex]

Step-by-step explanation:

Since the earth can be assumed to be as sphere ,to calculate the mass of the atmosphere we need to calculate the volume of the atmosphere.

The volume of atmosphere can be found by subtracting the volume of earth from the volume of the sphere formed by envelop of atmosphere around the earth as indicated in the attached figure

Mathematically we have

[tex]V_{atmosphere}=V_{shell}-V_{earth}\\\\V_{atmosphere}=\frac{4\pi (R_{e}+h)^{3}}{3}-\frac{4\pi R_{e}^{3}}{3}\\\\V_{atmosphere}=\frac{4\pi }{3}((6370+11)^{3}-(6370)^{3})\\\\V_{atmosphere}=5618.64\times 10^{6}km^{3}\\\\\\V_{atmosphere}=5618.64\times 10^{15}m^{3}[/tex]\

Now since it is given that 1 cubic meter of atmosphere weighs 1.2 kilogram thus the mass of the whole atmosphere equals

[tex]Mass_{atmosphere}=1.2\times 5618.64\times 10^{15}kg\\\\Mass_{atmosphere}=6742.368\times 10^{15}kg[/tex]

To estimate the mass of the atmosphere, we use the formula Mass = Density × Volume. First, calculate the volume of the atmosphere using the formula for the volume of a cylinder. Then, substitute the given values into the formula and calculate the mass using the formula Mass = Density × Volume.

To estimate the mass of the atmosphere, we can use the formula:

Mass = Density × Volume

First, we need to find the volume of the atmosphere. The height of the atmosphere is given as 11 km, so we can calculate the volume using the formula for the volume of a cylinder:

Volume = π × (radius2) × height

Next, we substitute the given values into the formula:

Volume = π × (6370 km)2 × 11 km

Finally, we calculate the mass using the formula:

Mass = Density × Volume

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