Do the three lines 5x - y = 7, x + 3y = 11, and 2x + 3y = 13 have a common point of intersection? If so, find it. if not, explain why not .

The actual length and width of the swimming pool are 34 meters and 18 meters, respectively, based on a scale of 1 inch to 4 meters.

Based on the given information, we know that the scale of the drawing is 1 inch to 4 meters. This means that every 1 inch on the drawing represents 4 meters in actual length.

The length of the swimming pool on the drawing is given as 8.5 inches. To find the actual length of the swimming pool, we need to multiply the length on the drawing by the scale factor:

Actual length of the swimming pool = 8.5 inches x 4 meters/inch = 34 meters

Similarly, the width of the swimming pool on the drawing is given as 4.5 inches. To find the actual width of the swimming pool, we can use the same formula:

Actual width of the swimming pool = 4.5 inches x 4 meters/inch = 18 meters

Therefore, the actual length of the swimming pool is 34 meters and the actual width is 18 meters.

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The function f(x)= (x+4)(x-2)/(x+4)(x-2) passes through the origin with a constant slope of 1, and has two removable discontinuities at x=-4 and x=2.

The function that passes through the origin with a constant slope of 1 and has removable discontinuities at x=-4 and x=2 is given by:

f(x)= (x+4)(x-2)/(x+4)(x-2). This function can be written in its factored form as f(x)= 1.

The function has a constant slope of 1, which means that for any two points (x_1,y_1) and (x_2,y_2) the slope is given by

(y_2-y_1)/(x_2-x_1)=1.

The function has two removable discontinuities at x= -4 and x= 2. This means that at these points the function is undefined, and the derivative of the function is infinite.

Removable discontinuities can be resolved by factoring out a common factor from the numerator and denominator of the function. In the case of the given function, factoring out (x+4) and (x-2) resolves the discontinuities. The graph of the function is a straight line which passes through the origin. This is because the function is of the form y=mx, where m is the constant slope of 1, which makes the function pass through the origin.

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As before, it follows that A3 is a maximal ideal of R, contradicting the fact that the chain is infinite. Therefore, R satisfies the ACC.

It is given that be an integral domain with a descending chain of ideals. Suppose that there exists an n such that for all i ≥ n, then ai = an. A ring satisfying this condition is said to satisfy the descending chain condition or DCC. Rings satisfying the DCC are called Artinian rings, after Emil Artin.

The statement to be proved is if R satisfies the descending chain condition, it must satisfy the ascending chain condition. Suppose, by contradiction, that R satisfies the DCC but does not satisfy the ACC. Then, there is an infinite ascending chain: A1 ⊂ A2 ⊂ A3 ⊂ A4 ⊂ ···.

Note that if R is an integral domain and if a ∈ R, then (a) is either (0) or is a maximal ideal in R. Hence, (0) is a minimal element in the collection of all proper ideals of R. Suppose A1 is a proper ideal of R that is maximal with respect to not being finitely generated. Since R satisfies the DCC, A1 cannot be infinite. Therefore, A1 is a finite set. Suppose A1 is not principal.

Then there exist two elements a, b ∈ A1 that do not belong to (a) and (b) respectively. This means that (a, b) is a proper ideal of R, properly containing A1, which contradicts the maximality of A1. Thus, A1 is a principal ideal generated by an element a1 ∈ A1.Suppose A2 = (a1, a2, a3, · · · , am) is a proper ideal properly containing A1. If A2 is finitely generated, then A2 ⊃ (a1) ⊃ (0) is a finite descending chain of ideals, which contradicts the DCC.

Thus, A2 is not finitely generated. By the maximality of A1, A2 must be principal, generated by an element a2 ∈ A2. It follows that a2 = c1a1 + c2a2 + · · · + cmam, where ci ∈ R for all i. Hence, (1 − c2)a2 = c1a1 + · · · + cmam, which means that a2 ∈ (a1). Therefore, (a1) = A1 = A2, and it follows that A2 is a maximal ideal of R.

Suppose A3 is a proper ideal properly containing A2. If A3 is finitely generated, then A3 ⊃ A2 ⊃ (0) is a finite ascending chain of ideals, which contradicts the ACC. Thus, A3 is not finitely generated. By the maximality of A2, A3 must be principal, generated by an element a3 ∈ A3.

As before, it follows that A3 is a maximal ideal of R, contradicting the fact that the chain is infinite. Therefore, R satisfies the ACC.

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the height of the triangular pyramid is 13 units.

How to solve?

The formula for the volume of a pyramid is given by V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. In the case of a triangular pyramid, the base is a triangle, so the area of the base is given by A = (1/2)bh, where b is the base length and h is the height of the triangle.

Given that the volume of the triangular pyramid is 273 units³, we have:

V = (1/3)Bh = 273

We know that the base of the triangular pyramid has a base length of 14 units and a height of 9 units, so its area is:

A = (1/2)bh = (1/2)(14)(9) = 63

Substituting this value for B in the equation for the volume, we have:

(1/3)(63)h = 273

Multiplying both sides by 3, we get:

63h = 819

Dividing both sides by 63, we get:

h = 13

Therefore, the height of the triangular pyramid is 13 units.

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Based on the population mean's [tex]95[/tex]% standard error, which is [tex](-10.962 d-0.001)[/tex]

A population can be all the students at a certain school. All of the pupils enrolled at just that institution during the period of data gathering would be included. Data from all of these individuals is gathered based on the issue description.

The major trend discovered from the data sample is the sample mean. The population is used to create the sample data. In statistics, the sampling distribution is denoted by the letter "x." The population mean, on the other hand, is the average of all observations within a certain population or group.

[tex]0.025[/tex] < p value <[tex]0.05[/tex]

for [tex]95[/tex]% CI; and [tex]6[/tex] degrees of freedom, a value of [tex]t= 2.447[/tex]  

therefore confidence interval=sample mean -/+ t*std error    

margin of error [tex]=t*std error=5.4808[/tex]    

lower confidence limit [tex]= -10.9622[/tex]

upper confidence limit [tex]= -0.0006[/tex]

from above [tex]95[/tex]% confidence interval for population mean [tex]=(-10.962[/tex][tex]<[/tex]µd[tex]< -0.001)[/tex]

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The solution to the linear system with repeated eigenvalues can be written in two forms: the exponential form and the Jordan form. In the Jordan form, the solution is written as:  [tex]x(t) = e^(J*t) * v_0[/tex]

In the exponential form, the solution is written as:
[tex]x(t) = e^(lambda*t) * (v + t*w)[/tex]
Where lambda is the repeated eigenvalue, v is the eigenvector, and w is the generalized eigenvector.

In the Jordan form, the solution is written as  :  [tex]x(t) = e^(J*t) * v_0[/tex]
Where J is the Jordan matrix, which is a matrix with the repeated eigenvalue lambda on the diagonal and a 1 on the superdiagonal, and v_0 is the initial condition vector.

Both forms of the solution give the same result, but the exponential form is simpler and easier to compute. The Jordan form is more general and can be used to find the solution for any linear system with repeated eigenvalues.

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To calculate the error interval for x, we must analyse the probable range of values for x before it was rounded to 15.38. Because x was rounded to two decimal places, we know it is between two values.

The biggest number that can be rounded down to 15.38 is 15.375, and the smallest number that can be rounded up to 15.38 is 15.385. As a result, the error range for x is [15.375, 15.385]. The error interval for a rounded integer is the range of possible values for the original number before rounding. The integer x was rounded to 15.38 with two decimal places in this example. To calculate the error interval Consider the highest and lowest feasible numbers for x that might have been rounded to 15.38. We consider the number that ends in.385 for the highest possible value. If x was larger or equal to this value, it was rounded up to 15.39. As a result, the greatest possible value for x is 15.385. Consider the number that ends in.375 for the least feasible value. If x was less than or equal to this value, it was rounded down to 15.37. As a result, the least number that x might have been is 15.375. As a result, the error interval for x is comprised of values ranging from 15.375 to 15.385, inclusive. This might be any number.

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The probability of randomly choosing a red token from the bag is Option C: 4/25.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The total number of trials is 100.

The total number of red tokens chosen is 5 + 5 + 5 + 1 = 16.

The formula for probability is -

Probability = Favourable outcomes / Total number of outcomes

Substitute the values into the equation.

The probability of randomly choosing a red token from the bag is 16/100.

Simplifying the expression -

16/100

= 4/25

Therefore, the value for probability is 4/25.

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The BEST choice for two perpendicular lines is: e) Their slopes are the reciprocal negatives of one another.

Perpendicular lines are those that cross at a correct angle when two separate lines share a plane. Vertical and horizontal lines, or the axes of a coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.

If two lines intersect at the a right angle in Euclidean geometry, they are said to be parallel (90 degrees).

When two lines are parallel, their slopes are the reciprocal of each other's negative values. A slope of the second line would be "-1/m" if the curve of the initial line is "m."

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The angle x has a measure of -55°. It is important to note that this negative angle indicates that the angle is oriented in the opposite direction from the others, but it is still considered a valid angle measure.

The value of angle x when A, B, and C lie on a straight line, angle y = 95°, and angle z = 330°.
To find the value of angle x, we can use the property of angles that states the sum of angles on a straight line is always 180°.
The value of angle w, which is the angle between y and z.
Since angle y = 95° and angle z = 330°, angle w can be calculated by subtracting angle y from angle z:
w = z - y
w = 330° - 95°
w = 235°
As A, B, and C lie on a straight line, the sum of angles x, w, and y should be equal to 180°.
Therefore, we can set up the equation:
x + w + y = 180°
Substitute the values of w and y into the equation.
x + 235° + 95° = 180°
Solve for x.
x = 180° - 235° - 95°
x = -150°
Since the value of x is negative, it indicates that angle x is in the opposite direction of the positive angle measurement. Thus, the value of angle x is 150° in the opposite direction.
In conclusion, angle x is 150° in the opposite direction when A, B, and C lie on a straight line, angle y = 95°, and angle z = 330°.

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 The probability that X lies in the interval [3, 6] is given by:P(3 ≤ X ≤ 6) = ∫3 6f(x)dx.

Suppose we have a continuous random variable that varies from 0 to 15.

To find the probability that the random variable takes on a value in the interval [3,6], we must first calculate the area under the curve within the given interval.

This is accomplished by calculating the integral of the probability density function (PDF) of the random variable, between the two endpoints of the interval. The resulting value is the probability that the random variable takes on a value within the given interval.

To begin, let's consider the probability density function (PDF) of the random variable, f(x), which is the function that describes the likelihood that the random variable will take on any given value within its range. The PDF will be a continuous function that has a positive value for all values of x between 0 and 15, and the area under the PDF will be equal to 1, indicating that the sum of all possible values of the random variable will be 1.

We can then calculate the area under the PDF between the two endpoints of the interval [3,6], which can be represented as the integral of the PDF, f(x), from 3 to 6. This can be written as the following equation: Probability of random variable in interval [3,6] = ∫36f(x)dx.

This integral represents the area under the PDF of the random variable between the two endpoints of the interval, and its value will be the probability that the random variable takes on a value within the given interval.

OR- Given the continuous random variable varies from 0 to 15, and we have to find the probability that the random variable takes on a value in the interval [3,6]. So, let's proceed step by step.What is a continuous random variable?A continuous random variable is a variable that takes on any value within a specified range of values.

In other words, any value within the range of values can occur. Continuous random variables can be measured, such as weight, height, time, and distance. Continuous random variables can't be counted, such as the number of heads in 20 coin flips or the number of cars in a parking lot, and so on.

The probability of a continuous random variable is the area under the probability density function (PDF) that falls in the interval of interest. The probability density function (PDF) must be non-negative and integrate to 1.0 over the whole domain.

Suppose we have a probability density function (PDF) f(x) for a continuous random variable X with support S, and we want to calculate the probability that X lies in the interval [a, b], where a and b are any two numbers in S, and a ≤ b. To compute the probability, we find the area under the PDF between a and b. This is given by the integral of the PDF f(x) over the interval [a, b].

Therefore, the probability that X lies in the interval [a, b] is given by:P(a ≤ X ≤ b) = ∫a bf(x)dx  Suppose we want to calculate the probability that the random variable X takes on a value in the interval [3, 6].

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The inequality is t ≤ 28.

Inequalities serve as the defining characteristic οf the relatiοnship between twο values that are nοt equal. Equal dοes nοt imply inequality. Typically, we use the "nοt equal symbοl (≠)" tο indicate that twο values are nοt equal. But different inequalities are used tο cοmpare the values tο determine whether they are less than οr greater than.

Given that Deshaun runs each lap in 4 minutes. He will run at mοst 7 laps tοday.

Assume that t fοr the number οf minutes he will run tοday.

He will run at mοst 7×4 = 28 minutes.

The symbοl οf at mοst is ≤.

The inequality is t ≤ 28

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Answer:

See below.

Step-by-step explanation:

For this problem, we are asked to solve for CE.

Because Point D is a Centroid, CE is a median.

A Median is a line that connects from 1 vertex of a Triangle, through the Centroid, and then ending on the midpoint of the opposite side.

The distance from the Triangles' Vertex to the Centroid is 2 times the distance from the Centroid to the Midpoint.

Basically;

[tex]ED = \frac{1}{2} CD[/tex]

Let's solve for x first.

[tex]3x+2=\frac{1}{2} (8x-6)[/tex]

Distribute:

[tex]3x+2=4x-3[/tex]

Subtract 4x from both sides:

[tex]-x+2=-3[/tex]

Subtract 2 from both sides:

[tex]-x=-5[/tex]

Divide by -1:

[tex]x=5.[/tex]

CD, and DE are 2 parts of CE. When we add CD, and DE together we will have the value of CE.

[tex]CD+DE=CE.[/tex]

Let's identify CD and DE first since we have the value of x.

[tex]CD=8(5)-6=34.[/tex]

[tex]DE=3(5)+2=17.[/tex]

Add:

[tex]34+17=51 \ (CE)[/tex]

Our final answer is D, CE = 51.

Step-by-step explanation:

The distributive property of multiplication over addition states that for any numbers a, b, and c, a × (b + c) = a × b + a × c.

Looking at Marta's work, we can see that the distributive property was used in line 1, where she distributed the 2 to both terms inside the parentheses:

2(x - 4) + 2x = x + 7

2x - 8 + 2x = x + 7

4x - 8 = x + 7

Therefore, the step in Marta's work that is justified by the distributive property is line 1, where she distributed the 2 to both terms inside the parentheses.

The percent of 25 doctors which is equivalent to 2 as required to be determined is; 8%.

As evident from the task content; the percent of 25 doctors which is equivalent to 2 is to be determined.

On this note, the percentage can be determined using the percent proportion formula as follows where x = the required percentage.

x / 100 = 2 / 25

25x = 200

x = 200 / 25

x = 8.

Hence, the equivalent percentage as required to be determined is; 8%.

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the angle will be Ф = 66.4°

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

the given triangle

cosФ = 10/25

Ф = 66.4°

Hence the angle will be Ф = 66.4°

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Answer:

-2°F

Step-by-step explanation:

Let M and S represent Monday and Sunday's low temperatures respectively. The given information relates M and S with the equation:

[tex]M = 6 + \frac{S}{2}[/tex]

We can rearrange the equation to solve for S.

[tex]S = 2(M-6)[/tex]

We can substitute 5 for M and find that S = -2.

∴The low temperature on Sunday was -2°F.

.

Answer:[tex]180\pi[/tex]

Step-by-step explanation:

[tex]v=\pi rx^{2} h\\v=\pi 6^{2} 5\\\\v=180\pi[/tex]

4. (a) circumference of the figure: 2 * 22/7 * 3 = 18.86 cm

(b)  Area of the figure: 22/7 * 3² = 28.29 cm²

5. (a) circumference of the figure: 22/7 * 35 = 110 ft

(b) Area of the figure: 22/7 * (35/2)² = 962.5 ft²

The area of a circle is given by the formula:

A = πr²

where r is the radius of the circle

The circumference of a circle is given by the formula:

C = 2πr or πd     (Recall: d = 2r)

where r is the radius and d is the diameter of the circle

No. 4

r = 3 cm

(a) C = 2πr

C = 2 * 22/7 * 3 = 18.86 cm

(b) A = πr²

A = 22/7 * 3² = 28.29 cm²

No. 5

d = 35 ft

(a) C = πd

C = 22/7 * 35 = 110 ft

(b) A = πr²

A = 22/7 * (35/2)² = 962.5 ft²

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Option D is true, as the distance from any point to the axis of rotation remains the same after a rotation. Therefore, A'E' is equal to AE.

A polygon is a two-dimensional geometric shape that has three or more straight sides and angles. Polygons are classified according to the number of sides they have, and the most common polygons include triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), heptagons (7 sides), octagons (8 sides), and so on. In a polygon, each straight line segment that connects two vertices is called a side, and each point where two sides intersect is called a vertex. The interior of a polygon is the region bounded by its sides and angles.

Here,

When polygon ABCD rotates 70° counterclockwise about point E to give polygon A'B'C'D', the corresponding sides and angles of the polygons will remain congruent. Therefore, option A is false as BB' and DD' are not corresponding sides.

Option B may or may not be true. If polygon ABCD is a regular polygon, then all the interior angles are equal, and m∠ABC is equal to m∠A'B'C'. However, if the polygon is not regular, then m∠ABC and m∠A'B'C' may have different measures.

Option C may or may not be true, for the same reason as option B. If polygon ABCD is a regular polygon, then all the interior angles are equal, and m∠ABC is equal to m∠A'B'C'. However, if the polygon is not regular, then m∠ABC and m∠A'B'C' may have different measures.

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Looking at the corresponding probability in the distribution will allow you to determine the likelihood of selling a specific quantity of face masks each day.

Here is the probability distribution for the number of face masks sold per day:

X P(X)

10 0.2

12 0.1

14 0.2

15 0.3

20 0.1

25 0.1

To find the probability of selling a certain number of face masks per day, you look at the corresponding probability in the distribution. For example, the probability of selling 15 face masks per day is 0.3.

Note that the probabilities sum to 1, which is a requirement for any probability distribution.

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The probability that the A-rated bond defaults given that the AA-rated bond defaults is approximately 0.74.

What is probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated.

a. To find the probability that at least one of the bonds defaults, we can use the complement rule: the probability that neither bond defaults is (1 - 0.53) * (1 - 0.47) = 0.27, since the events are independent. Therefore, the probability that at least one bond defaults is 1 - 0.27 = 0.73. So the answer is 0.73.

b. The probability that neither bond defaults is (1 - 0.53) * (1 - 0.47) = 0.27, as calculated above.

c. We want to find the conditional probability that the A-rated bond defaults given that the AA-rated bond defaults, which can be expressed as P(A defaults | AA defaults). We can use Bayes' theorem to calculate this probability:

P(A defaults | AA defaults) = P(AA defaults and A defaults) / P(AA defaults)

From the problem statement, we know that P(AA defaults) = 0.53 and P(AA defaults and A defaults) = 0.39. Therefore,

P(A defaults | AA defaults) = 0.39 / 0.53 ≈ 0.74

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Therefore, the system of equations has a unique solution, (0, 5).

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), which are connected by an equals sign (=). The LHS and RHS can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

Here,

The system of equations given is:

y = x + 5

y = 2x + 5

To determine the number of solutions, we can compare the slopes and y-intercepts of the two equations.

The slope of y = x + 5 is 1, and the y-intercept is 5.

The slope of y = 2x + 5 is 2, and the y-intercept is 5.

Since the slopes are not equal, the graphs of the lines are not parallel. Therefore, they will intersect at a single point.

To find the point of intersection, we can set the two equations equal to each other:

x + 5 = 2x + 5

Simplifying, we get:

x = 0

Substituting this value back into one of the original equations, we get:

y = x + 5

= 0 + 5

= 5

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In response to the query, we can state that Salim thereby covered a total fraction distance of about 3.83 miles.

To represent a whole, any number of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio of the numerator to the denominator. They can all be expressed as simple fractions as integers. In the numerator or denominator of a complex fraction is a fraction. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.

Salim therefore walked a total of:

4/3 Plus 5/2 miles

We must identify a common denominator in order to add these fractions:

Six is the least frequent multiple of 3 and 2.

We may therefore rephrase the following fractions with denominators of 6:

4/3 = (4/3) x (2/2) = 8/6

5/2 = (5/2) x (3/3) = 15/6

We can now combine the fractions:

8/6 + 15/6 = 23/6

Salim covered a distance of 23/6 miles in all.

This fraction can be simplified by dividing both the numerator and denominator by their largest common factor, which is 1:

3.83 miles, or 23/6 miles (rounded to two decimal places)

Salim thereby covered a total distance of about 3.83 miles.

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Answer:Which of the following is part of the set of integers?

negative whole numbers

zero

natural numbers

positive whole numbersWhich of the following is part of the set of integers?

negative whole numbers

zero

natural numbers

positive whole numbers

Step-by-step explanation:

A) the probability of winning a positive amount of money is approximately 0.000487.

B) the ticket would have to cost $0.0522 (or approximately $0.05) for this lottery to be fair, in the sense that the expected profit is $0.

(a) To calculate the probability of winning a positive amount of money, we need to add up the probabilities of winning each prize except for the $0 prize:

Probability of winning a positive amount
= Probability of winning $300,000 + Probability of winning $70,000 + Probability of winning $600 + Probability of winning $18 + Probability of winning $5 + Probability of winning $3

Probability of winning a positive amount

= 1/5,518,121 + 1/1,715,449 + 1/9,024 + 1/1,768 + 1/358 + 1/166

Probability of winning a positive amount

≈ 0.000487 (to two decimal places)

Thus, the probability of winning a positive amount of money is approximately 0.000487.

(b) To find the ticket cost that makes the lottery fair, we need to calculate the expected profit, which is the sum of the products of the probability of winning each prize and the amount of money won for that prize. Since there are six possible prizes, the expected profit can be written as:

Expected profit = (1/5,518,121)($300,000) + (1/1,715,449)($70,000) + (1/9,024)($600) + (1/1,768)($18) + (1/358)($5) + (1/166)($3) - Ticket cost

Simplifying the expression above, we get:

Expected profit
= $0.0522 - Ticket cost

For the lottery to be fair, the expected profit should be $0. Therefore, we can set the expected profit equal to $0 and solve for the ticket cost:

$0 = $0.0522 - Ticket cost

Ticket cost = $0.0522

Therefore, the ticket would have to cost $0.0522 (or approximately $0.05) for this lottery to be fair, in the sense that the expected profit is $0.

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Answer:

[tex]4\frac{8}9}[/tex]

Step-by-step explanation:

We can do this mathematically.

[tex]5-\frac{2}{18} = \frac{90}{18} - \frac{2}{18} = \frac{88}{18} = \frac{44}{9} = 4\frac{8}{9} \\[/tex]

We can also work this logically.

We know that [tex]\frac{2}{18}[/tex] is less than 1, so our answer should be (5-1) and a fraction.

Our answer should be 4 plus a fraction less than 1. To find what we need to add to [tex]\frac{2}{18}[/tex] to make 1, we ask ourself how many eighteenths make 1. So if we need to 18 parts and we have 2 already, we add 16 eighteens to make 1. The answer is [tex]4 \frac{16}{18}[/tex], or simplified, [tex]4\frac{8}9}[/tex].

Answer:

Ans: Rs 181.44.

Step-by-step explanation:

The length of the tree house with a base of 7 ft on the model is given as follows:

1/3 ft.

The length of the model is obtained applying the proportions in the context of the problem.

The scale is a ratio that relates the size of a drawing or map to the actual size of the object or area being represented. It indicates how much the drawing or map has been reduced or enlarged in size from the actual object or area.

Hence the scale of 1:21 means that each ft on the drawing represents 21 ft of actual distance, hence the length of the drawing for an actual distance of 7 ft is given as follows:

1/21 x 7 = 1/3 ft.

More can be learned about proportions at https://brainly.com/question/24372153

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Answer:check explanation

Step-by-step explanation:

We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^ t

Where

y represents the population after t years.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 40 × 10^6

r = 2.7% = 2.7/100 = 0.027

a) Therefore, exponential model for the population P after t years is

P = 40 × 10^6(1 + 0.027)^t

P = 40 × 10^6(1.027)^t

b) t = 2020 - 2000 = 20 years

P = 40 × 10^6(1.027)^20

P = 68150471

c) when P = 90 × 10^6

90 × 10^6 = 40 × 10^6(1.027)^t

90 × 10^6/40 × 10^6 = (1.027)^t

2.25 = (1.027)^t

Taking log of both sides to base 10

Log 2.25 = log1.027^t = tlog1.027

0.352 = t × 0.01157

t = 0.352/0.01157 = 30.4 years