The city of St. Louis is creating a welcome sign on a billboard for visitors to see as they enter the city. The following picture needs to be enlarged so that 1/2 inch represents 7 feet on the actual billboard. Will it fit on a billboard that measures 14 feet in height if the height of the figure is 1 in?

⇒I will use the laws of exponents. When you multiply powers of the same base you keep one base and add the exponents.

Below are all the steps in details

[tex]=9^{-8+(-2)} \\=9^{-8-2} \\=9^{-10} \\=\frac{1}{9^{10} } \\=\frac{1}{3486784401}[/tex]

Step 1: Write out the formula for logistic growth model

Step 2: Write out the given values and substitute them into the formula

Hence,

Hence, the number of plants after 5 months is approximately 112

Answer: 156.375

Step-by-step explanation:

Solution

Option D

Hence the correct answer is Option D

∠4 ≅ ∠5 Alternate internal angles

Applying the description we have the table is completed as follows

Statement                                          Reasons

x is parallel to y                                    Given

w is a transversal                                  Given  

angle 4 is congruent to angle 1           Vertical opposite angle

angle 1 is congruent to angle 5            Corresponding angle

angle 4 is congruent to angle 5           Alternate internal angles

The prove ∠4 ≅ ∠5 is done by the Alternate angle theorem

∠4 ≅ ∠ 1 vertical opposite angles

∠ 1 ≅ ∠5  Corresponding angle

then we can say that

∠ 1 ≅ ∠4 ≅ ∠5

hence: ∠4 ≅ ∠5 Alternate internal angles

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Answer:

A ✔ vertical angles

B ✔ corresponding angles theorem

C ✔ transitive property

Step-by-step explanation: i hope this helps :)

The correct  differential equation for [tex]x(e^{y}+1)^{2} e^{-y}dx+ e^{x^{2} }dy =0[/tex]

is [tex](e^{y}+1)^{2}e^{-y}/ -e^{x^{2}}= dy/dx\\[/tex].

to extract the differential equation we need to express it in the form of dy/dx.

[tex]x(e^{y}+1)^{2}e^{-y}dx=-e^{x^{2}}dy\\x(e^{y}+1)^{2}e^{-y} = -e^{x^{2}}dy/dx\\x(e^{y}+1)^{2}e^{-y}/ -e^{x^{2}}= dy/dx\\[/tex]

What are differential equations?

An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a place is determined by the derivatives of the function. Physicists, engineers, biologists, and other professionals primarily use it in these domains.

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The expression that represents the combined function of f(x) and g(x) is h(x) = 2x/(5 - x)

From the question, we have the following parameters:

Function f(x) = 2x

Function g(x) = 2 - x + 3

Evaluate the like terms in the equation of the function g(x)

So, we have

g(x) = 5 - x

From the question, we understand that:

The function h(x) is a combination of the functions f(x) and g(x) by division

This can be represented as

h(x) = f(x)/g(x)

The above also implies that the function h(x) is a composite function

Substitute the known values in the above equation

So, we have the equation of the composite function h(x) to be

h(x) = 2x/(5 - x)

Hence, the equation of the composite function h(x) is h(x) = 2x/(5 - x)

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Given:

The objective is to translate the statement and solve the inequality.

Explanation:

Consider the unknown number as x. The quotient of a number and 7 can be written as,

By subtracting 10 from the quotient, the value is less than -6.

On substituting the equation (2) in (1),

To find x :

On solving the equation (3), the value of x can be calculated as,

Hence, the value of x is less than 28.

The functions are solved below

What is a function?

A function from either a given Set X to a set Y allocates exactly one item of Y to each member of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.

The functions are solved as follows

(a) f(4) = 6x4 = 24

(b) g(2) = 9x2² + 5 = 36 + 5 = 41

(c) f(1) = 6x1 = 6

(d) g(0) = 9x0² + 5 = 0 + 5 = 5

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Lcm of 14. 6,15 is 210 and 15. 8,14 is 840 and 16. 28,8 is 112 and 17. 24,36 is 1224 and 18 25,15 is 450

When a number is represented as the sum of its prime factors, this process is known as prime factorization. In prime numbers, there are just two factors: one and the number itself. 2, 3, 5, 7, 11, 13, and other prime numbers are examples of prime numbers. A number is prime factorized when it is represented as a collection of primes.

i) List all prime factors for each number.

Prime Factorization of 6 is:

2 x 3  =  [tex]2^{1}[/tex] x [tex]3^{1}[/tex]

Prime Factorization of 14 is:

2 x 7  =  [tex]2^{1}[/tex]  x[tex]7^{1}[/tex]

Prime Factorization of 15 is:

3 x 5  = [tex]3^{1}[/tex] x [tex]5^{1}[/tex]

Find the place in the new list where each prime factor appears as a factor the most frequently before adding it there.

The new superset list is

2, 3, 5, 7

To determine the LCM, multiply these elements collectively.

LCM = 2 x 3 x 5 x 7 = 210

In exponential form:

LCM = [tex]2^{1}[/tex] x [tex]3^{1}[/tex] x [tex]5^{1}[/tex] x[tex]7^{1}[/tex] = 210

LCM = 210

Therefore,

LCM(6, 14, 15) = 210

ii)List all prime factors for each number.

Prime Factorization of 8 is:

2 x 2 x 2  =  [tex]2^{3}[/tex]

Prime Factorization of 14 is:

2 x 7  = [tex]2^{1}[/tex] x [tex]7^{1}[/tex]

Prime Factorization of 15 is:

3 x 5  =  [tex]3^{1}[/tex] x[tex]5^{1}[/tex]

Find the place in the new list where each prime factor appears as a factor the most frequently before adding it there.

The new superset list is

2, 2, 2, 3, 5, 7

To determine the LCM, multiply these elements collectively.

LCM = 2 x 2 x 2 x 3 x 5 x 7 = 840

In exponential form:

LCM = [tex]2^{3}[/tex] x[tex]3^{1}[/tex] x [tex]5^{1}[/tex] x [tex]7^{1}[/tex] = 840

LCM = 840

Therefore,

LCM(8, 14, 15) = 840

iii)List all prime factors for each number.

Prime Factorization of 8 is:

2 x 2 x 2  = [tex]2^{3}[/tex]

Prime Factorization of 16 is:

2 x 2 x 2 x 2  =  [tex]2^{4}[/tex]

Prime Factorization of 28 is:

2 x 2 x 7  = [tex]2^{2}[/tex] x [tex]7^{1}[/tex]

Find the place in the new list where each prime factor appears as a factor the most frequently before adding it there.

The new superset list is

2, 2, 2, 2, 7

To determine the LCM, multiply these elements collectively.

LCM = 2 x 2 x 2 x 2 x 7 = 112

In exponential form:

LCM = [tex]2^{4}[/tex] x[tex]7^{1}[/tex]

= 112

LCM = 112

Therefore,

LCM(8, 16, 28) = 112

iv) List all prime factors for each number.

Prime Factorization of 17 shows:

17 is prime  =  171

Prime Factorization of 24 is:

2 x 2 x 2 x 3  =  [tex]2^{3}[/tex] x [tex]3^{1}[/tex]

Prime Factorization of 36 is:

2 x 2 x 3 x 3  =  [tex]2^{2}[/tex] x [tex]3^{2}[/tex]

Find the place in the new list where each prime factor appears as a factor the most frequently before adding it there.

The new superset list is

2, 2, 2, 3, 3, 17

To determine the LCM, multiply these elements collectively.

LCM = 2 x 2 x 2 x 3 x 3 x 17 = 1224

In exponential form:

LCM = [tex]2^{3}[/tex] x [tex]3^{2}[/tex] x [tex]17^{1}[/tex] = 1224

LCM = 1224

Therefore,

LCM(17, 24, 36) = 1224

v)List all prime factors for each number.

Prime Factorization of 15 is:

3 x 5  =  [tex]3^{1}[/tex] x [tex]5^{1}[/tex]

Prime Factorization of 18 is:

2 x 3 x 3  = [tex]2^{1}[/tex] x [tex]3^{2}[/tex]

Prime Factorization of 25 is:

5 x 5  =  [tex]5^{2}[/tex]

Find the place in the new list where each prime factor appears as a factor the most frequently before adding it there.

The new superset list is

2, 3, 3, 5, 5

To determine the LCM, multiply these elements collectively.

LCM = 2 x 3 x 3 x 5 x 5

= 450

In exponential form:

LCM = [tex]2^{1}[/tex] x [tex]3^{2}[/tex] x [tex]5^{2}[/tex]

= 450

LCM = 450

Therefore,

LCM(15, 18, 25) = 450

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The fraction of juice that is orange juice is 40/73

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

Juice containers = 292

Orange juice = 160

The fraction of juice that is orange juice is then calculated as

Fraction = Orange juice/Juice containers

Substitute the known values in the above equation

So, we have the following equation

Fraction = 160/292

Simplify the fraction

Fraction = 40/73

Hence, the fraction is 40/73

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After evaluating the limit we have came to find that the limit of        [tex]\lim_{h\rightarrow 0 }\frac{(4/3 +h)^3-(4/3)^3}{h}[/tex] as h approaches 0 is Undefined

A limit is the value that a function, sequence, or index approaches as an input or as an index approaches a particular value in mathematics. The definitions of continuity, derivatives, and integrals depend on limits, which are essential to calculus and mathematical analysis.

The concept of a limit of a sequence is further generalized to include the concept of a limit of a topological network, in addition to having a connection to the category theory concepts of limit and direct limit.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit

⇒ [tex]\lim_{h\rightarrow 0 }\frac{(4/3 +h)^3-(4/3)^3}{h}[/tex]

Evalúe 0 as h

⇒ [tex]\frac{(4/3 +0)^3-(4/3)^3}{0}[/tex]

⇒ Undefined

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The probability that exactly 11 of them use their smartphones in meetings or classes is 3.89%

Probability is the likelihood of something occurring. This branch of mathematics studies the nature of chance. It is expressed as a number between 0 and 1. Probability has been brought to mathematics in order to foresee the potential of events. Probability can be defined as the degree of likely that something will occur. The probability that the outcomes of a random experiment will be as expected can be calculated using this fundamental theory of probability, which is also applied to the probability distribution. To establish the probability that a particular event will occur, we must first determine the total number of choices.

x = 11

n= 15

P =48%

=0.48

P(x=11)=[tex]15C_{11} (0.48)^{11} (1-0.48)^{4}[/tex]

=1365(0.0003116403)(0.09150625)

=0.0389

=3.89%

The probability that exactly 11 of them use their smartphones in meetings or classes is 3.89%

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The height of the air ballon at 'm' minutes is expressed in the function and the value of h(3)=1600, h(9)=2800,h(11)=3200

We have given a function h in terms of m. Now we have to explain the contextual meaning of each and every expression it contains

1.) h = It is height at which ballon is cruising above from the ground level.

2.) m = It denotes the instance of minute at which we are talking about

3.) h(m) = The height as the function of minute, means the height of the ballon in changing with respect to the minute

4.) 1000 = It is the height at which ballon was cruising earlier and then started ascending

5.)200 = 200 feet the distance covered in a minute while ascending above

6.) 200m = distance ascended for 'm ' minutes

7.) 1000+200m = The total height that balloon covered after ascending for m minutes.

Now,

height at 3 minute = h(3) = 1000+200(3)=1000+600=1600

height at 9 minute = h(9) = 1000+200(9)=1000+1800=2800

height at x minute = h(x) = 1000+200(x)= 3200

1000 + 200x = 3200

200x = 2200

x = 11

Therefore, h(3) = 1600 , h(9)= 2800,h(11)=3200 are the different values of height 'h' at different 'm' minutes.

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The value of [tex]x^{2}[/tex] is 25 when we have (cube of x = 125) [tex]x^{3}[/tex] = 125.

According to the question,

We have the following expression:

[tex]x^{3} = 125[/tex]

Now, we will do the cube roots on both the sides:

[tex]\sqrt[3]{x^{3} } = \sqrt[3]{125}[/tex]

(We can find the cube roots of 125 by finding the Least Common Multiple or LCM.)

So, we will have the following expression:

x = 5

Now, to find the value of [tex]x^{2}[/tex], square on both the sides:

[tex]x^{2} = 5^{2}[/tex]

[tex]x^{2}[/tex] = 25

(More to know: when we square a number we multiply a number two times and when we find cube of a number then we multiply a number three times.)

Hence, the value of [tex]x^{2}[/tex] is 25.

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Answer:

Sine is negative in III and IV quadrants. Now sin 30 1/2. Taking = 30, Sin (180+0) = sin (360-0): =- sin 0. So x = 210 degrees or 330 degrees

Step-by-step explanation:

The length and the width of the sticky note in millimeters are 2.5 × 10⁻⁵ millimeters and 1.25 × 10⁻³ millimeters respectively.

The dimension of Kendra's sticky note using a meter stick are:

The width of the sticky note is 1.25 × 10⁻⁸ meters and the length of the sticky note is 2.5 × 10⁻⁶ meters.

Now we know,

1 meter = 1000 milimeters.

Therefore, the length of the sticky note in millimeters will be:

L = 2.5 × 10⁻⁸ meters

L = 2.5 × 10⁻⁸ × 1000 millimeters

L = 2.5 × 10⁻⁸ × 10³ millimeters

L = 2.5 × 10⁻⁸ ⁺ ³ millimeters

L = 2.5 × 10⁻⁵ millimeters

So, the width of the sticky note is:

W = 1.25 × 10⁻⁶ meters

W = 1.25 × 10⁻⁶ × 10³ millimeters

W = 1.25 × 10⁻³ millimeters

Hence, the dimension in millimeters is: the width and length of the sticky note is 1.25 × 10⁻³ millimeters and 2.5 × 10⁻⁵ millimeters respectively.

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Answer:

I believe it's 160. Hope this helps.

Step-by-step explanation:

170 - 66 = 104

104 / 0.65 = 160

The step function and its graph that represents the relationship between the number x of days and the total cost y of renting the chipper are present in the first option.

Given:

Charge for 1 day = $100

Charge for each additional day = $50

Let's assume

The cost of rent is y.

The number of days is x.

The total cost, y according to the data provided can be calculated by the equation,

y = 100 + 50x

Using y = mx+c, when graphing a step function that represents the relationship between the number of days and the total cost,

The gradient or slope will be always 50 for the graph.

So, when x = 0, y = 100 + 0 = 100

When x = 1, y = 100 + 50 = 150

When x = 2, y = 100 + 50 × 2 = 200

When x = 3, y = 100 + 50 × 3 = 250

Thus the step function is,

f(x) = 100 , if 0 < x ≤ 1

f(x) = 150 , if 1 < x ≤ 2

f(x) = 200 , if 2 < x ≤ 3

f(x) = 250 , if 3 < x ≤ 4

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The possible measures using this scale are 742.5 grams and 300.0 grams.

The link between a measurement on a model and the corresponding measurement on the real item is represented by scale.

Note that a tenth of a gram is 0.1 grams, therefore, the precision of the scale is 0.1 grams.

Note that 370 milligrams are equivalent to 0.370 grams.

Since the measures on the scale increase by 0.1 units, 0.25 and 0.370 are not possible on this scale.

Hence, the possible measures using this scale are 742.5 grams and 300.0 grams.

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Slope

[tex]\frac{-10-(-2)}{1-(-3)}=-2[/tex]

Equation

[tex]y+10=-2(x-1)[/tex]

INFORMATION:

Using the graph of f(x) = x^2, we must describe transformations for the function g(x)=-8x^2

STEP BY STEP EXPLANATION:

First, we need to use the graph of f(x) = x^2 which is

Then, if analyze difference between f(x) and g(x), we can see that g(x) = -1*8*f(x)

So, to graph g(x) we have two transformations:

- Multiply f(x) by -1: When we multiply by -1 we obtain the parabola opening down

- Multiply f(x) by 8: When we multiply by 8 we obtain a more closed parabola

Finally, the final graph would be

ANSWER:

Depth= 45 feet

The force applied perpendicular to the surface of an object per unit area over which that force is distributed is defined as Pressure.

Pressure causes serious problems for people as you travel deeper in water because pressure increases. This is called hydrostatic pressure.  Water doesn’t only push down from above. It pushes from all sides and also from below. The upward force is called buoyancy. It helps you keep afloat in water.

Given Pressure, p of under water is 312,

Given equation is:

P=12+4d/11

312=12+4d/11

312=12*11+4d

312-(12*11)= 4d

312-132= 4d

180=4d

d=180/4

=45 feet

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Answer:

each side would be 9m long

The length of each side of the square garden is 9 meters long.

The perimeter of any 2D figure is the sum of the lengths of all the sides except the circle which has a perimeter or circumference which is 2πr.

We know the area of a square is a product of any two sides of the square and all four sides of a square are of the same length.

Given a square has an area of  81m².

∴ We have to determine such a number which when multiplied by itself results in 81.

Such a unique number is 9.

So, the area of the square can be written as (9×9) m².

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Answer: what

Step-by-step explanation:bye

The number of ways that the landscaper can plant the trees in a row, assuming that the trees are evenly spaced is 630 ways.

According to the data, the golf course architect needs to plant 2 bald cypress trees, 5 white birch trees, and 4 linden trees in a row along a fairway. It should be noted that the number of feasible arrangements will be shown as follows based on the information provided:

Based on the information given, it should be noted that n1 =4, n2 = 5 and n3 = 2.

Therefore, the number of ways that the lineup can be possible will be:

n! / (n − r)!

where n is the number of things to choose from and we choose r of them

This will be illustrated as:

= 10! /4!5!2!

= 630

There are 630 ways.

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Euclidean geometry is the study of flat and solid figures based on the axioms and theorems of the Greek mathematician Euclid (c. 300 BCE). Euclidean geometry is the plane and solid geometry that is usually taught in High schools.

Euclidean features are ideally suited to defining man-made settings (which are usually in 3D) and are reasonably simple for the user to give.

The incorporation of scene restrictions into the model acquisition process decreases the number of unique configurations for calibration and enables model reconstruction using small sets or even single photos despite the presence of multiple occlusions.

Another obvious use for such a technology is augmented reality. After rebuilding, real-world scene models can be merged with other reconstructed or synthetic models. This is particularly beneficial in architectural applications.

Indeed, before an architectural project is approved, its influence on the existing environment is represented using hand-drawn or computer-aided design (CAD) city models.

The process of creating such models is time-consuming and needs more previous knowledge than scene reconstruction from photos.

Furthermore, when necessary, classic architectural resources such as maps and architectural drawings are simple to include in an interactive reconstruction method.

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The value of cos(A - B) in the simplest form​ will be 0.547.

It is defined as the branch of mathematics that is concerned with the size, shape, and orientation of two-dimensional figures.

It is given that,

tan A = 11/60

tan A = p/b

From Pythagoras therorm

h=√(p²+b²)

h=√(11²+60²)

h=61

Sin A = p/h = 11/60

Cos A = b/h = 60/61

If cos B = 5/13

Sin B = 12/13

cos (A - B) = cos A cos B + sin A sin B

cos (A - B) = (60/61)×(5/13)  + (11/60)×(12/13)

cos (A - B) =0.547

Thus, the value of cos(A - B) in the simplest form​ will be 0.547.

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