The population of a town has been growing, following the equation p= 200t+4500
, where t is years after 2010. The number of restaurants in the town has been growing according to the equation R=6t+35
.

Complete an equation for the number of restaurants per capita (per person)

Restaurants per capita:


How many restaurants per capita does this model predict for the year 2016?

8/21 of the lawn still needs to be mowed.

To compare fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.

Miss Lianto's fraction: (2/7) x (3/3) = 6/21

Son's fraction: (1/3) x (7/7) = 7/21

To calculate how much of the lawn still needs to be mowed, we can subtract the combined fractions mowed from the total:

Combined fractions mowed: 6/21 + 7/21 = 13/21

So, Remaining fraction: 1 - 13/21 = 8/21

Therefore, 8/21 of the lawn still needs to be mowed.

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Answer:

a

normal approximation not appropriate in this instance because  

    \(np = 3300 * 0.9998 = 3299.3 > 5\)

and  

     \(nq = 3300 * 0.0002 = 0.66 < 5\)

b

  The probability is  \(P(X = 3300) = 0.52\)

c

 The probability is  \(P(X = 3287) = 0\)

Step-by-step explanation:

From the question we are told that

   The  sample size is  \(n = 3300\)

    The  chance of liking blueberry pie is  \(p = 0.9998\)

    The  chance of not  liking blueberry pie is \(q = 0.0002\)

For normal approximation is possible if  

       \(np > 5\) , \(nq > 5\)

Now let test

      \(np = 3300 * 0.9998 = 3299.3 > 5\)

and  

     \(nq = 3300 * 0.0002 = 0.66 < 5\)  

The  probability that all 3300 people will say they like blueberry pie is mathematically represented as

       \(P(X = 3300) = p^{3300}\)

       \(P(X = 3300) = (0.9998)^{3300}\)

        \(P(X = 3300) = 0.52\)

The probability that 3297 of the people will say that they like blueberry pie is  mathematically represented as

         \(P(X = 3287) = \frac{(np)^{3297! } * e^{-np}}{3297}\)

          \(P(X = 3287) = \frac{0}{\infty}\)

          \(P(X = 3287) = 0\)

By translating (shifting) the graph of f(x) vertically downward by 2 units and right 5 units, the formula for g(x) is equal to g(x) = 2√(x - 5) - 2.

Generally, there are different types of transformation and these include the following:

A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

Since the graph of f(x) is translated (shifted) vertically downward by 2 units and right 5 units, the formula for g(x) would be given by:

Note: f(x) = 2√x

To translate (shift) vertically downward by 2 units, we would subtract 2:

g(x) = 2√x - 2

To shift right by 5 units, we would replace the value of x with (x - 5):

g(x) = 2√(x - 5) - 2

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Answer:

Jordan needs to fly at least 22 times and less than 50 times to attain Gold Status.

Step-by-step explanation:

Let n be the number of flights Jordan needs to attain Gold status

\(\frac{8800}{400}\leq n < \frac{20000}{400} \\22\leq n < 50\)

Answer:

the answer to your questions is 90%

Answer:

The correct answer is coconuts

Step-by-step explanation:

Answer:

the correct answer is 64°

Step-by-step explanation:

Answer:

y=4-4/9x x=9-9/4y

Step-by-step explanation:

jyEahahhhhh

Answer:

Step-by-step explanation:

For the given set, {1x∣∣∣x∈ℤ and 2≤x≤5}, x∈ℤ means that the elements of the set are integers and 2≤x≤5 means the integers are values from 2 to 5.

Note that integers are whole numbers. The integers from 2 to 5 are 2, 3, 4 and. 2 and 5 are included to due the equality sign present in the inequality.

The elements of the set are {2, 3, 4, 5}.

Cardinal number of the set is similar to cardinality of the set. In set theory, cardinality of a set is the total number of element in the set. According to the set above, the total number of element in the set is 4.

Hence the cardinal number of the set is 4

Answer:

\(f(x)=\frac{4^{x} }{2}-1\)

Step-by-step explanation:

\(f(x)=\frac{1}{2}(4)^{x} -1\)

Combine \(\frac{1}{2}\) and \(4^{x}\)

\(f(x)=\frac{4^{x} }{2}-1\)

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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Answer:

It has 2 equal side lengths

Answer:

Are there any choices?..

The correct statement the describes the equation is The lines intersect at (1, 0) and the lines are parallel.

x - y = 1.............equation 1

y - x = 1.............equation 2

Add equations (1) and (2):

(x - y) + (y - x) = 1 + 1

Simplifying

0 = 2

Since 0 = 2, the system is inconsistent, meaning there is no solution. The lines represented by the equations are parallel and will never intersect.

The system of equations has no solution, as the lines represented by the equations are parallel and will never intersect.

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The complete question is- Which statement describes the graph of the system of equations?

[x-y=1

Ly- X= 1

The lines are parallel.

The lines are coinciding.

The lines intersect at(1, 0).

The lines intersect at (-1,0).

Answer:

I believe its  EG and NE but i might be wrong

Step-by-step explanation:

Answer:

1)  695.3 m²

2)  8 ft

3)  172.0 in²

Step-by-step explanation:

To find the area of a regular polygon, we can use the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

Given the polygon is an octagon, n = 8.

Given each side measures 12 m, s = 12.

Substitute the values of n and s into the formula for area and solve for A:

\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)

\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)

\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)

\(\implies A=695.29350...\)

Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.

\(\hrulefill\)

The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.

If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.

To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:

\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)

Therefore:

\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)

\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)

\(\implies 40^{\circ}n=360^{\circ}\)

\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)

\(\implies n=9\)

Therefore, the regular polygon has 9 sides.

To determine the length of each side, divide the given perimeter by the number of sides:

\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)

\(\implies \sf Side \;length=\dfrac{72}{9}\)

\(\implies \sf Side \;length=8\;ft\)

Therefore, the length of each side of the regular polygon is 8 ft.

\(\hrulefill\)

The area of a regular polygon can be calculated using the following formula:

\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)

A regular pentagon has 5 sides, so n = 5.

If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.

Substitute the values of s and n into the formula and solve for A:

\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)

\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)

\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)

\(\implies A=172.047740...\)

Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.

Answer:

1.695.29 m^2

2.8 feet

3. 172.0477 in^2

Step-by-step explanation:

1. The area of a regular octagon can be found using the formula:

\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)

where a is the length of one side of the octagon.

In this case, a = 12 m, so the area is:

\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)

Therefore, the Area of a regular octagon is 695.29 m^2

2.

The formula for the exterior angle of a regular polygon is:

\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)

where n is the number of sides in the polygon.

In this case, the exterior angle is 40°, so we can set up the following equation:

\(\bold{40^o=\frac{ 360^0 }{n}}\)

\(n=\frac{360}{40}=9\)

Therefore, the polygon has n=9 sides.

Perimeter=72ft.

We have

\(\boxed{\bold{Perimeter = n*s}}\)

where n is the number of sides in the polygon and s is the length of one side.

Substituting Value.

72 feet = 9*s

\(\bold{s =\frac{ 72 \:feet }{ 9}}\)

s = 8 feet

Therefore, the length of each side of the polygon is 8 feet.

3.

Solution:

A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)

The area of a regular pentagon can be found using the following formula:

\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)

where s is the length of one side of the Pentagon.

In this case, s = 10 in, so the area is:

\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)

Drawing: Attachment

The fraction of whole pizza has both pepperoni and green peppers exists 1/2.

A number is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction exists less than the denominator.

Given that:

3/4 of the pizza contains pepperoni

2/3 of the pizza with pepperoni contains green pepper ;

The fraction of the whole pizza that contains both pepperoni and green pepper;

The fraction with pepperoni = 3/4

Fraction of whole with green pepper and pepperoni: 2/3 of 3/4

simplifying the above equation, we get

= 2/3 × 3/4

= (2 × 3) / (3 × 4)

= 6/12 = 1/2

Therefore, the fraction of whole pizza has both pepperoni and green peppers exists 1/2.

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Answer:

Step-by-step explanation:

Letter B is the correct answer

Initial population is 200, tripled every hour

200 x 3 = 600

First hour 200

Second hour = 600 + 200 = 800

Third hour 800x3 = 2400 + 800 = 3200

and so on.

Answer:

  86.75

Step-by-step explanation:

Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.

The grade for the course, with fourth test score x, will be ...

  0.20(63.5 +76 +87) +0.40x = 80

  0.40x +45.3 = 80

Solving for x, we get ...

  0.40x = 34.7 . . . . subtract 45.3

  x = 86.75 . . . . . . . divide by 0.4

The minimum score you need on the fourth test is 86.75.

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Answer:

If we are choosing students at random from all students who got a B:

Total number of non-female students who got a B: 19

Total number of students who got a B: 36

Probability: 19/36

If we are choosing students at random from all students:

Total number of non-female students who got a B: 19

Total number of students: 78

Probability: 19/78

Answer:

A number that measures the likelihood that the event will occur.

Step-by-step explanation:

Probability is a measure of the frequency of occurrence of a phenomenon, the value of which can be expressed qualitatively or quantitatively. Probability is quantified as a real number between 0 and 1, although sometimes probability is also expressed as a percentage. The probability is 0 when the event cannot or will never happen, and the probability is 1 when it happens for sure or it always happens. If the probability is between these values, the event is not common and its occurrence is uncertain. The higher the probability value, the more common the event is or the more certain it will occur.

.(a) f'(x) = 2x - 3x² + 1/x ,b) f'(x) = ln(x) - x  c) f'(x) = [(2x + 2y/x) * (x² + 2x)² - 4(x² + 2ylnx) * (x + 1)] / (x² + 2x)⁴ ,d) f'(x) = (1/ (√(1 + 2x))) e) f'(x) = -1/ (2√(x - 1)³)  ,we can get  this answer by simplifying the equation .

what is  simplifying equation ?

Simplifying an equation means to manipulate the equation in order to write it in a simpler or more compact form, while preserving its meaning or solution set. The goal is often to make it easier to analyze or solve the equation.

In the given question,

(a) f(x) = x² - (x³ - ln(x))

f'(x) = 2x - (3x² - 1/x)

f'(x) = 2x - 3x² + 1/x

(b) f(x) = x * ln(x) - x²

f'(x) = ln(x) + x * 1/x - 2x

f'(x) = ln(x) - x

(c) f(x) = (x² + 2ylnx) / ((x² + 2x)²)

f'(x) = [(2x + 2y/x) * (x² + 2x)² - (2 * (x² + 2ylnx) * (2x + 2))] / (x² + 2x)⁴

f'(x) = [(2x + 2y/x) * (x² + 2x)² - 4(x² + 2ylnx) * (x + 1)] / (x² + 2x)⁴

(d) f(x) = √(1 + 2x)

f'(x) = (1/2) * (1 + 2x)⁻⁰⁵ * 2

f'(x) = (1/ (√(1 + 2x)))

(e) f(x) = 1 / (√(x - 1))

f'(x) = -1/2 * (x - 1)⁻⁰⁵ * 1

f'(x) = -1/ (2√(x - 1)³)

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Answer:

Descriptive Statistics is used to   collect, organize and  summarize sample data.

Step-by-step explanation:

Descriptive Statistics is used to   collect, organize and  summarize sample data.

First of all he will collect a sample or maybe samples. A sample is a subset of the data drawn from the population. Here it will be the number of children from different households.

Populations can be described by parameters . These parameters can be inferred on the sample parameters. For example the population mean ,  population variance can be estimated by sample mean and sample mean.

These variables can be further categorized as discrete.

Now he will apply various test to check whether the inferences drawn about the population are true or not.

Answer:

A. x = 58°

B. x = 10m

C. a = 44°

All approximated to nearest whole number.

Step-by-step explanation:

All triangles given are right angled triangles. Therefore, we would apply the trigonometry functions to solve for each missing side and angle.

Recall: SOHCAHTOA

a. Adjacent = 4.8cm,

Hypotenuse = 9cm

Angle to find =x°

Thus, we would apply the following formula:

Cos θ = Adjacent/Hypotenuse

Cos θ = 4.8/9 = 0.5333

θ = Cos-¹(0.5333) = 57.77

x ≈ 58° (to nearest whole number)

b. Opposite side = x

Hypothenuse = 40 m

Included angle = 14°

We would use:

Sine θ = opposite/hypothenuse

Sin (14) = x/40

Multiply both sides by 40

40*sin(14) = x

40*0.2419 = x

x = 9.676 = 10 m (to nearest whole number)

c. Opposite = 87mm

Adjacent = 91mm

θ = a°

We would use:

Tan θ = opposite/adjacent

Tan θ = 87/91

Tan θ = 0.9560

θ = tan-¹(0.9560)

θ = a = 43.71

a ≈ 44° (to nearest whole number)

By increasing the number of wire turns, using a thicker wire, increasing the battery voltage, and using a soft iron core, the student can enhance the electromagnet's strength, allowing it to pick up more paper clips.

To increase the number of paper clips the electromagnet will pick up, the student should take the following actions:

1. Increase the number of wire turns: By wrapping the wire around the iron nail more times, the student will create a stronger magnetic field. This is because each wire turn generates a magnetic field, and when the turns are in close proximity, their fields add up, creating a stronger overall field.

2. Use a thicker wire: A thicker wire will allow more current to flow through it, which will result in a stronger magnetic field. The higher the current, the more powerful the electromagnet becomes.

3. Increase the voltage of the battery: By increasing the voltage of the battery, the student can cause more current to flow through the wire. This will enhance the magnetic field, making the electromagnet more effective at picking up paper clips.

4. Use a soft iron core: Soft iron materials have higher magnetic permeability than other materials, meaning they can easily be magnetized and demagnetized. When the wire is wrapped around a soft iron nail, the resulting electromagnet will have a stronger magnetic field, thus improving its ability to pick up paper clips.

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Answer:

Step-by-step explanation:

4/mx

A soccer player kicks a ball 50ft from a point on the ground. The ball reached a height of 100 ft above the ground. At what angle was the ball kicked?

Answer:

Therefore, the angle ∠CDA is 58°.

Step-by-step explanation:

∠CDA = 58°

In the given figure, let's consider the angle ∠CDA as x.

Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.

In triangle CAD, the sum of angles is 180°. So, we have:

∠CAD + ∠CDA + ∠CAB = 180°

Substituting the known values:

32° + x + 90° = 180°

Combining like terms:

x + 122° = 180°

Subtracting 122° from both sides:

x = 180° - 122°

x = 58°

With a correlation coefficient of 0, A. I can’t be confident at all; this is about as close to a random guess as you can get.

A correlation coefficient measures the strength of the linear relationship between two variables.

Correlation coefficients usually range between -1 to 1, and they show how one variable moves in relation to another.

A positive correlation coefficient indicates that the two variables move uniformly in the same direction, while a negative correlation coefficient shows the opposite.

A zero correlation coefficient shows no linear relationship between the two variables.

Thus, if the correlation coefficient is 0, then Option A is correct.

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Answer:

Probably 5

Step-by-step explanation:

This is an extremely confusing question.  Whoever wrote it most likely had a typo.

The little box in the corner of the triangle means that is 90 degrees. if that is the case, this is a simple question:

Apply pythagorean theorem (a^2 + b^2 = c^2)

In this case:

3^2 + 4^2 = x^2

x^2 = 25

x=5.

HOWEVER: the two given angles are 60 degrees and 50 degrees.

Which does not work. It creates an impossible triangle.

Answer:

The answer is 6!!!

Step-by-step explanation: