The expression 1125t approximates the distance, in feet, that sound travels in air in t seconds. What does the 1125 represent in the context of this situation? OA. the approximate number of feet that sound travels in air in 1 second OB. the approximate number of feet that sound travels in air in 1125 seconds OC. the approximate number of seconds it takes sound to travel 1 foot in air OD. the approximate number of seconds it takes sound to travel 1125 feet in air​

The population of the town in 2018 will be 5,040.

To predict the population in 2018, we need to use the following formula:

Population in 2018 = Population in 1993 × (1 - rate of decrease)[tex].^n[/tex]

Here, the population in 1993 is 10,500, the rate of decrease is 5.2% or 0.052 (in decimal form), and the number of years from 1993 to 2018 is 25.

Substituting these values, we get:

Population in 2018 = 10,500 × (1 - 0.052)^25

= 10,500 × 0.480

= 5,040

Rounding this answer to the nearest integer, we get a predicted population of 5,040 in 2018.

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Answer:

B. (x - 5)^2 = 21

Step-by-step explanation:

In pigs, the length of pregnancies varies according to a Normal distribution with mean 114 days and standard deviation 5 days, approximately 2.28% of pig pregnancies are longer than 124 days.

We can start by standardizing the value 124 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

So in this case:

z = (124 - 114) / 5 = 2

Using a standard normal distribution table or calculator, we can find that the proportion of values greater than 2 is approximately 0.0228.

Therefore, approximately 2.28% of pig pregnancies are longer than 124 days.

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There are 300 grams in 1500 ml of the 20% solution.

We can use the concept of proportions to solve this problem.

A 20% solution contains 20 grams in 100 ml.

This means that for every 100 ml of solution, there are 20 grams of the solute.

To find out how many grams are in 1500 ml of the solution, we can set up a proportion:

20 grams/100 ml = x grams/1500 ml

where x is the number of grams in 1500 ml.

To solve for x, we can cross-multiply and simplify:

100x = 20 × 1500

100x = 30,000

x = 300 grams

Therefore, there are 300 grams in 1500 ml of the 20% solution.

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There are 30 minutes in [tex]\frac{2}{4}[/tex] of an hour.

To find the no. of minutes in an hour we can multiply the no. of hours by 60. Suppose to find the no. of minutes in an hour we can simply multiply 1 by 60 so we can get 60 minutes in an hour.

Similarly to find the no. of minutes are in [tex]\frac{2}{4}[/tex] of an hour we can multiply the [tex]\frac{2}{4}[/tex] by 60 to get the required minutes.

[tex]\frac{2}{4}[/tex] × 60 = [tex]\frac{1}{2}[/tex] × 60 = [tex]\frac{60}{2}[/tex]  = 30.

So, from the above explanation, we can conclude that there will be 30 minutes in the [tex]\frac{2}{4}[/tex] of an hour.

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This is a word problem, and the cost of one house in rubles is 1200, as the five sisters shared their father's inheritance equally.

If the three oldest sisters each paid 800 rubles, then they collectively paid 2400 rubles (800 rubles x 3 sisters) to the two younger sisters

Each of the the two younger sisters will have a total of 1200 rubles (2400 rubles/2 younger sisters), as they divided the money among themselves.

In conclusion, since the five sisters shared their father's inheritance equally, then 1200 rubles is the cost of one house, which solves the word problem

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Probability that a random sample of 45 oil changes result in a sample mean time less than 10 minutes is 0.0001

Given information:

The mean time is, = 16.2 min.

The standard deviation = 3.4 min.

Let X' is sample mean time :

Now the sample mean time is given by the equation

Z = (X' - μ) / (σ/√n)

Where, μ population mean time

(σ) is Standard deviation

(A) Probability of random sample of 45 oil changes:

p (X' < 10) = 1 - p (Z ≤ 12.33)

Z = (10 - 16.2) / (3.4 √45)

p (X' < 10) = 1 - 0.9999

p (X' < 10) = 0.0001

Hence,

As, the highest critical value of Z is given as 4.40 which has an area of 0.9999.

Thus, Probability that a random sample of 45 oil changes result in a sample mean time less than 10 minutes is 0.0001.

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Complete question is,

The shape of the distribution of the time required to get an oil change at a 15-minute oil-change facility is unknown. However, records indicate that the mean time is 16.2 minutes, and the standard deviation is 3.4 minutes.

(a) What is the probability that a random sample of n = 45 oil changes results in a sample mean time less than 10 ​minutes?

The acceleration of the car at that time was 3 m/s².

We have,

From the kinematic equation to find the acceleration:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Initial velocity u = 15 m/s

Final velocity v = 45 m/s,

Time t = 10 s

We can rearrange the equation to solve for acceleration:

a = (v - u) / t

Substituting the values, we get:

a = (45 m/s - 15 m/s) / 10 s

a = 3 m/s^2

Therefore,

The acceleration of the car at that time was 3 m/s².

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The complete question in English.

A car moving on a straight track increases its speed from 15 m/s to 45 m/s using a po of 10 seconds.

Assuming that the acceleration was uniform, calculate:

acceleration at that time.

A ∩ B is the intersection of sets A and B, which is the set of elements that are in both A and B.

A = {2, 3, 5, 7} and B = {1, 2, 5, 10}, so A ∩ B = {2, 5}.

B ∩ D^c is the intersection of set B and the complement of set D, which is the set of elements in B that are not in D.

B = {1, 2, 5, 10} and D^c = {1, 4, 6, 8, 9, 10}, so B ∩ D^c = {1, 10}.

A^c is the complement of set A, which is the set of elements in U that are not in A.

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 3, 5, 7}, so A^c = {1, 4, 6, 8, 9, 10}.

C ∩ D is the intersection of sets C and D, which is the set of elements that are in both C and D.

C = {1, 2, 3, 6} and D = {3, 5, 7}, so C ∩ D = {3}.

B u D^c is the union of set B and the complement of set D, which is the set of elements that are in B or in the complement of D, or both.

B = {1, 2, 5, 10} and D^c = {1, 4, 6, 8, 9, 10}, so B u D^c = {1, 2, 4, 5, 6, 8, 9, 10}.

Thus, this can be the universal set.

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Answer:

The amount of air needed to fill the basketball is approximately 533.16 cubic inches

Step-by-step explanation:

To find the amount of air needed to fill a basketball, we need to first calculate its volume. We can use the formula for the volume of a sphere, which is V = (4/3)πr^3, where π is approximately 3.14 and r is the radius of the sphere.

Since the diameter of the basketball is given, we need to first find the radius by dividing the diameter by 2:

r = 9.45 in / 2 = 4.725 in

Now we can plug in the value of r into the formula for the volume:

V = (4/3)πr^3 = (4/3)π(4.725 in)^3 = 533.16 in^3

Therefore, the amount of air needed to fill the basketball is approximately 533.16 approx cubic inches.

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The possible sum of Kiran adding 4.7x10 √4 and 1.2 x 10 √5 is 94 + 1.2 x 10 √5

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

Kiran added 4.7x10 √4 and 1.2 x 10 √5

This means that we have

4.7 * 10√4 + 1.2 x 10 √5

Evaluate the square root of 4

So, we have

4.7 * 10 * 2 + 1.2 x 10 √5

When the products are evaluated, we have

94 + 1.2 x 10 √5

Hence, the possible result of the summation is 94 + 1.2 x 10 √5

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Answer:

The mathematical equation for calculating the monthly interest is

I = P * (r / n)

where:

I is the monthly interest

P is the loan amount minus the down payment (i.e., $245,000 - $44,000 = $201,000 in this case)

r is the annual interest rate (i.e., 3.5%)

n is the number of payments per year (i.e., 12 for monthly payments)

then I = $201,000 * (0.035 / 12) = $711.06

The pitch of the roof is equal to 1.14

Since pitch of the roof is the angle between the roof and the horizontal line.

Pitch (slope) = V/H

Where, V represents the rising vertical distance of an object.

H represents the horizontal distance an object runs through.

Substituting the selected points into the formula, we have;

Pitch (slope) = 32/28

Pitch (slope) = 1.14

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Answer:

Yeeeaaa, no.

Hope this helps!

Step-by-step explanation:

( x, y )

Plug the numbers of the ordered pair into the equation: y = 6x

3 = 6 × ( 0 )

3 = 0

Three does not equal zero...

3 [tex]\neq[/tex] 0

Therefore, after 4 weeks, Liz will have $275 in her savings account and Fareed will have $300 in his savings account.

After 1 week

Liz will have saved $75 + $50 = $125, and

Fareed will have saved $100 + $50 = $150.

After 2 weeks,

Liz will have saved a total of $125 + $50 = $175, and

Fareed will have saved a total of $150 + $50 = $200.

After 3 weeks,

Liz will have saved a total of $175 + $50 = $225, and

Fareed will have saved a total of $200 + $50 = $250.

After 4 weeks,

Liz will have saved a total of $225 + $50 = $275, and

Fareed will have saved a total of $250 + $50 = $300.

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Hello! Here are the recursive definitions of the given sequence:

A) The sequence is increasing by 7 for each term, so the recursive definition can be written as:

a1 = 3

an = an-1 + 7

So, the recursive definition of the sequence is: 3, 3+7=10, 10+7=17, 17+7=24, ...

B) The second option given, "anan-1 + 10 a1 = 3" is not a recursive definition of the sequence.

C) The third option given, "San = 10an-1" is also not a recursive definition of the sequence because it uses a different variable 'S' instead of 'a'.

The linear function with the greatest rate of change is f(x) = 2x

The general linear function can be written in the following way.

y = ax + b

a is the slope or rate of change, and b is the y-intercept.

From the given options, the line with the greatest rate of change is the one that grows the fastest, and we can see that the equation for that line is:

y = 2x

So that is the correct option.

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The linear function y = 2x + 5 shows that Sarah charges $5 as fixed amount before she begins selling newspapers.

The table representing amount of money which Sarah charges her customers to sell newspapers.

Let us consider 'x' represents the time per hour charges taken by Sarah from customers.

In the table,

For zero hours charges are $5.

It means Fixed charges taken by Sarah to sell newspaper.

Difference between the rate per hour is,

$7 - $5 = $2

$9 - $7 = $2

It represents for Sarah charges $2 per hour.

let us consider 'y' that represents total amount charges by Sarah.

Required linear function for selling news paper and charging amount is

y = $5 + 2x

⇒ y = 2x  + 5

Therefore, the linear function y = 2x + 5 represents option 1. Sarah charges $5 before she begins selling newspapers.

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Answer:

Step-by-step explanation:

18

18 is a mulitple of both 6 and 18

The value of the integration are:

∫(√(2 + (cos x)²) / sec x - cosec x) dx = 3 ln|cos x - sin x| + √2 + C

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

We have,

∫(√(2 + (cos x)²) / sec x - cosec x) dx:

We can simplify the expression in the integral as follows:

√(2 + (cos x)²)

= √(1 + (cos² x)) + √1

= √(sin² x + cos² x + cos² x) + 1

= √(2cos² x + 1) + 1

So the integral becomes:

∫[(√(2cos² x + 1) + 1) / (1/cos x - 1/sin x)] dx

= ∫[(√(2cos² x + 1) + 1) / ((sin x - cos x)/ (sin x cos x))] dx

= ∫[(√(2cos² x + 1) + 1) / ((sin x cos x - cos² x)/ (sin x cos x))] dx

= ∫[(√(2cos² x + 1) + 1) sin x / (cos x - sin x)] dx

Now we can make the substitution u = cos x - sin x, which gives us

du = (-sin x - cos x) dx, or -du = (sin x + cos x) dx.

Making this substitution and simplifying, we get:

∫[(√(2u² + 2) + 2) / u] du

= ∫[(√2(u² + 1) + √2) / u] du

= √2 ∫[(u² + 1)^(1/2) / u] du + 2 ∫(1/u) du

Using integration by substitution,

let w = u^2 + 1, then dw = 2u du, and we have:

= √2 ∫(1/w) dw + 2 ln|u|

= √2 ln|u| + 2 ln|u| + C

= 3 ln|cos x - sin x| + √2 + C

where C is the constant of integration.

And,

∫arc tan√x dx:

We can make the substitution u = √x, which gives us du = (1/2√x) dx, or 2u du = dx.

Substituting these into the integral, we get:

∫arc tan√x dx = ∫arc tan u x 2u du

Now, using integration by parts with u = arc tan u and dv = 2u du, we get:

∫arc tan u  2u du = u arc tan u - ∫(1 + u²)/(1 + u²)² du

= u arc tan u - ∫1/(1 + u²) du

= u arc tan u - ln|1 + u²| + C

Substituting back u = √x, we get:

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

where C is the constant of integration.

Thus,

The value of the integration are:

∫(√(2 + (cos x)²) / sec x - cosec x) dx = 3 ln|cos x - sin x| + √2 + C

∫arc tan√x dx = √x arc tan √x - ln|1 + x| + C

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Answer:

487.20

Step-by-step explanation:

1. find the area of a rectangle ( length x width)

14ft x 12ft = 168ft²

2. Multiply the number of feet needed to becovered by the price of one foot of paper

168ft x 2.90 = 487.20

The total cost of your eulerization is 111.

We can Eulerize a graph by ensuring  to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.

A good method to do this is by  adding  edges between pairs of vertices that have odd degree until all vertices have even degree.

We have to add all the edges to get the total cost

10+15+20+4+9+3+17+14+19

111

Hence, the total cost of your eulerization is 111.

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By using the substitution method, the value for (x,y) = (-2, 2)

The substitution method for solving a system of algebra equations is a process where by we make a variable (say variable x) the subject of the formula and substitute it into the second equation to solve for the other variable.

In essence, from the given system of equations; let's make x the subject of the formula in the first equation.

5x + 3y = -4

5x = -4 - 3y

Divide both sides by 5;

x = -4/5 - 3y/5

Now, we are going to substitute this value for x into the second equation. The second equation says:

y - 2x = 6

y - 2(-4/5 - (3y/5)) = 6

By solving for y;

y = 2

Now, let's replace the value of y with any of the given equation (2);

y - 2x = 6

2 - 2x = 6

-2x = 6 - 2

-2x = 4

Divide both sides by -2

-2x/-2 = 4/ -2

x = -2

Therefore, we can conclude that by using the substitution method, the value for (x,y) = (-2, 2)

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Answer:

It’s 2.07 pounds/in 3

Step-by-step explanation:

1 kilogram = 2.2 × pounds, so,2.07 × 1 kilogram = 2.07 × 2.2 pounds (rounded), or2.07 kilograms = 4.554 pounds.Step 2: Convert the decimal part in pounds to ouncesAn answer like "4.554 pounds" might not mean much to you because you may want to express the decimal part, which is in pounds, in ounces which is a smaller unit.So, take everything after the decimal point (0.55), then multiply that by 16 to turn it into ounces. This works because one pound equals 16 ounces. Thus,4.55 pounds = 4 + 0.55 pounds = 4 pounds + 0.55 × 16 ounces = 4 pounds + 8.8 ounces. So, 4.55 pounds = 4 pounds and 8 ounces (when rounded). Obviously, this is equivalent to 2.07 kilograms. Step 3: Convert from decimal ounces to a usable fraction of ounceThe previous step gave you the answer in decimal ounces (8.8), but how to express it as a fraction? See below a procedure, which can also be made using a calculator, to convert the decimal ounces to the nearest usable fraction: a) Subtract 8, the number of whole ounces, from 8.8:8.8 - 8 = 0.8. This is the fractional part of the value in ounces.b) Multiply 0.8 times 16 (it could be 2, 4, 8, 16, 32, 64, ... depending on the exactness you want) to get the number of 16th's ounces:0.8 × 16 = 12.8.c) Take the integer part int(12.8) = 13. This is the number of 16th's of a pound and also the numerator of the fraction.Finalmente, 2.07 quilogramas = 4 pounds 8 3/4 ounces.A fração 12/16 não está simplificada, e ainda pode ser reduzida para 3/4 para que possamos expressar como a fração mais simples possível.In short:2.07 kg = 4 pounds 8 3/4 ounces

The expression a + b cannot be added/evaluated because 2.00x and 1.50y are not like terms

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

a + b is equal to what ​

The above statement is an addition expression that adds the values of a and b

However, the terms of the expression are not like terms

i.e. a and b are not like terms

This means that the expression cannot be added/evaluated

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The number of soda bottles the machine can make per minute is 25

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

The linear relation

Where we have the points

(2, 50) (6, 150)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

m = unit rate i.e the required slope

So, we have

2m + c = 50

6m + c = 150

Next, we have

4m = 100

Evaluate

m = 25

So, we have

2 * 25 + c = 50

Evaluate

c  0

So, we have

y = 25x

Hence, the equation of the line in fully simplified slope-intercept form is y = 25x

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The value of airplane's climb angle while this is happening is,

⇒ 35.53 degree

We have to given that;

An airplane is climbing 500 feet for every 700 feet it travels.

Hence, We can formulate;

The value of airplane's climb angle while this is happening is,

⇒ tan x = 500 / 700

⇒ tan x = 0.714

⇒  x = 35.53 degree

Thus, The value of airplane's climb angle while this is happening is,

⇒ 35.53 degree

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