2. The population, P, of a village t years after it was founded in 1970, is given by
P(t) = 8000 + 600t.
a) What is the population in 1970?

(Option a) Gonzalez and Bros . Inc has the absolute advantage when it comes to producing phones.

Absolute advantage theory

In his book The Wealth of Nations, the 18th-century economist Adam Smith proposed the concept of absolute advantage to describe how countries could benefit from trade by specializing in producing and exporting the goods that they can make more successfully than other countries.

On the other hand, China, Thailand, and Vietnam create and export low-cost manufactured goods. These three countries benefit greatly from their much lower unit labor costs.

Here, option a Gonzales and Bros. Inc has the absolute advantage when it comes to producing phones.

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Based on the calculations, the value which closest to the mean of the distribution is equal to: B. 18 inches.

A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:

Z = (x - μ)/δ

Where:

If 15 percent of the rainbow trout are longer than 15 inches, then we have:

P(x > 15) = 0.15

From the z-table, the z-value which corresponds to a mean of 0.15 is given by:

z-value = -1.036

Substituting the given parameters into the formula, we have;

Z = (x - μ)/δ

-1.036 = (15 - μ)/2.4

-1.036 × 2.4 = 15 - μ

-2.4864 = 15 - μ

μ = 15 + 2.4864

Mean, μ = 17.4864

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Complete Question:

The distribution of lengths of rainbow trout from a certain river are normally distributed with a standard deviation of 2.4 inches. it 15% of the rainbow trout are longer than 15 inches, which of the following is closest to the mean of the distribution?

A. 26 inches

B. 18 inches

C. 30 inches

D. 33 inches

E. 34 inches

The x-intercept of given equation is x=6 and point is (6,0).

Given the equation is -5x+3y=-30.

Here, we will find the x-intercept of the given equation.

The x-intercept is the point at which a line intersects the x-axis and the y-intersection is the point where a line intersects the y-axis.

We will find the x-intercept by substituting y=0 and applying the inverse operations.

Firstly we will substitute y=0 in equation, we get

-5x+3(0)=-30

Now, we will simplify this, we get

-5x+0=-30

-5x=-30

Further, we will divide both sides with -5, we get

-5x/-5=-30/-5

x=-6

Hence, the x-intercept of the given equation -5x+3y=-30 is x=6.

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Answer:

15 gum

Step-by-step explanation:

55-40 = 15

The equation that can be used to solve for the unknown number that Alex is thinking is 7x + 27 = 111

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the unknown number. The number is multiplied by 7 and the added with 27. The result is equal to 111. Hence:

7x + 27 = 111

The equation that can be used to solve for the unknown number that Alex is thinking is 7x + 27 = 111

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The value indicated of the function indicated on the graph of the function is 2

The graph represents the given parameter

The given graph is a linear function

This is so because the graph is represented by a straight line

A linear function is represented as

f(x) = mx + c

Where the vertex is

m represents the slope

c represents the y-intercept

From the given graph of the equation, we have

f(1) = 2

This means that

When x = 1, the value of f(x) is 2

Hence, the value indicated of the function indicated on the graph of the function is 2

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The instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.

The instantaneous rate of change is simply the change in the derivative value at a specific point.

Given the data in the question;

To determine the instantaneous rate of change of the function, first find the derivative of the function.

f(x) = −4x² − 3x + 1

Applying sum rule, with respect to x

d/dx[ -4x² ] + d/dx[ -3x ] + d/dx[ 1 ]

[ 2 × -4x¹ ] + [ 1 × -3x⁰ ] + d/dx[ 1 ]

[ -8x ] + [ -3 ] + d/dx[ 1 ]

-8x - 3 + d/dx[ 1 ]

Differentiate using constant rule

-8x - 3 + [ 0 ]

-8x - 3

f'(x) = -8x - 3

Next, plug x = -3 into the derivative and simplify.

f'(x) = -8x - 3

f'(-3) = -8(-3) - 3

f'(-3) = 24 - 3

f'(-3) = 21

Therefore, the instantaneous rate of change of the function f(x) = −4x² − 3x + 1 at the point x = -3 is 21.

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Brett will get paid $55.68 for travelling a total of 87 kilometers at an allowance of 54 cents per kilometer.

According to the International System of Units (SI), one kilometer is equal to 1,000 meters in American English. The United States and the United Kingdom are significant outliers, where the statute mile is the unit of measurement used to express distances between geographical locations on land.

One Kilometer is roughly equivalent to 0.621 miles.

Brett delivers produce for the farmer using his truck.

He gets paid a travel allowance of 64 cents per kilometer.

So to calculate his total allowance we multiply the allowance with the distance travelled.

Brett gets paid: $0.64×87=$55.68

Hence Brett gets paid $55.68. So the first option is correct.

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Answer:

[tex]{ \tt{ - 4(2w + 7)}} \\ = { \tt{( - 4 \times 2w) + ( - 4 \times 7)}} \\ = { \tt{ - 8w - 28}}[/tex]

Answer:

x=90, y= 130

Step-by-step explanation:

Answer: Exponential decay

Explanation: The base of the actual exponential function, [tex]0.93^{x}[/tex], is less than 1, which means that the output will become smaller.

The remainder and factor of the given algebraic expression [tex]\frac{5x^{5} -4x^{3} -11x^{2} +12}{x+1}[/tex] is [tex](5x^{4} -5x^{3} +x^{2} -12x+12)(x+1)[/tex] and [tex]0[/tex]

As per the given question, we are supposed to find out the factor and remainder of the given algebraic expression [tex]\frac{5x^{5} -4x^{3} -11x^{2} +12}{x+1}[/tex] using remainder theorem concept.

Before solving this, we need to know the concept of remainder theorem.

According to which "When a polynomial is divided by a linear polynomial, the remainder theorem is used to get the remaining. We are aware that long division of polynomials can be used to find the remainder after dividing one polynomial by another. The remainder can instead be discovered using the remainder theorem."

Hence using the same concept we can conclude that the factors are [tex](5x^{4} -5x^{3} +x^{2} -12x+12)(x+1)[/tex] and remainder is [tex]0[/tex]

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After the solution, we can conclude that (A) the slope of f(x) is higher.

Now that you have a function but can only evaluate it using a table, you can determine the slope using the following formula:

[tex]m=\frac{y^2-y^1}{x^2-x^1}[/tex]

Simply choose two points from the table to enter into the formula; in this example, we'll use points (4, 7) as our points 1 and our second point is (6,9).

This implies:

You just need to enter it into the formula:

Now that we know both slopes, you can see that g(x) has a slope of 1, while f(x) has a slope of 4, indicating that f(x) has a steeper slope than g(x).

Therefore, (A) f(x) has a greater slope.

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The complete question is given below:
Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?

x g(x)

2 5

4 7

6 9

f(x) has a greater slope.

g(x) has a greater slope.

The slopes of f(x) and g(x) are the same.

The slope of g(x) is undefined.

Answer:

After the solution, we can conclude that (A) the slope of f(x) is higher.

Step-by-step explanation:

What is the slope?

A line's steepness can be determined by looking at its slope.

The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

The letter M stands for the slope of a function of the form y=Mx+C, so the slope of the function F(x) =4.

Now that you have a function but can only evaluate it using a table, you can determine the slope using the following formula:

Simply choose two points from the table to enter into the formula; in this example, we'll use points (4, 7) as our points 1 and our second point is (6,9).

This implies:

x¹ = 4y¹ = 7

x² = 6y² = 9

You just need to enter it into the formula:

m = 9-7/6-4

m = 2/2

m = 1

Now that we know both slopes, you can see that g(x) has a slope of 1, while f(x) has a slope of 4, indicating that f(x) has a steeper slope than g(x).

Therefore, (A) f(x) has a greater slope.

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The complete question is given below:

Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?

x g(x)

2 5

4 7

6 9

f(x) has a greater slope.

g(x) has a greater slope.

The slopes of f(x) and g(x) are the same.

The slope of g(x) is undefined.

Answer:

he works 7 dollars an hour so 16 x 7 = 112 that's for a whole week a year would be 356 x 7 = 2,555 that's 1 whole year

Step-by-step explanation:

sorry if i got this wrong

Answer: The first one is 36. The second one is 0. The third one is 1/216 and the last on is 1/1,296.

Step-by-step explanation:

Answer: 1/2  ([tex]\pi[/tex]) sin [tex]\pi[/tex] +  ∫ x cos [tex]\pi ^{2}[/tex] dx + c

               1/2 ([tex]\frac{\pi }{2}[/tex]) sin [tex]\frac{\pi }{2}[/tex] +  ∫ x cos [tex]\frac{\pi }{2} ^{2}[/tex] dx + c

Step-by-step explanation:

We can't just integrate straight away, so we try substitution.

While trying substitution, we observe that we could integrate cos([tex]x^{2}[/tex]) x dx

by substitution.

So, let's split the integrand and use integration by parts.

we can represent θ = x,

so, we can write,

                                = ∫[tex]x^{3} cos x^{2} dx[/tex]

                                = ∫ [tex]x^{2} cos (x^{2} )xdx[/tex]

We notice that we could rewrite this as ∫ u cos(u) 1/2 du, but we don't see how to integrate that, so we'll continue with parts for now.)

                            = ∫ [tex]x^{2} cos (x^{2} )xdx[/tex]

Let    u=[tex]x^{2}[/tex]         and      dv = [tex]cos(x^{2} )xdx[/tex]

Clearly     du= 2x dx,    and

we can integrate  dv by substitution to get.

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

uv - ∫ vdu = 1/2 [tex]x^{2}[/tex] sin([tex]x^{2}[/tex]) - ∫ x sin ([tex]x^{2}[/tex]) dx

Integrate by substitution again to finish.

∫ [tex]x^{3} cos (x^{2}) dx[/tex] = 1/2 [tex]x^{2} sin x^{2}[/tex] + ∫ x cos [tex]x^{2}[/tex] dx + c

Then,

   x = √[tex]\pi[/tex]    and     √[tex]\frac{\pi }{2}[/tex]

 ∫ [tex]x^{3}[/tex] cos [tex]x^{2}[/tex] dx = 1/2 (√[tex]\pi ^{2}[/tex]) sin √[tex]\pi ^{2}[/tex] + ∫ x cos [tex]\pi ^{2}[/tex] dx + c

                        = 1/2 ([tex]\pi[/tex]) sin [tex]\pi[/tex] +  ∫ x cos [tex]\pi ^{2}[/tex] dx + c

∫  [tex]x^{3}[/tex] cos [tex]x^{2}[/tex] dx = 1/2 ([tex]\frac{\pi }{2}[/tex]) sin [tex]\frac{\pi }{2}[/tex] +  ∫ x cos [tex]\frac{\pi }{2} ^{2}[/tex] dx + c            

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38.7 hours would have passed until the trains are 580 miles apart

The given parameters are

Train 1 = 80 mph

Train 2 = 65 mph

The difference in the speeds of the trains is

d = 80mph - 65mph

Evaluate

d = 15mph

The distance moved is

Distance = 15 * t

At 580 miles apart, we have

15 * t = 580

Divide by 15

t = 38.7 hours

Hence, 38.7 hours would have passed until the trains are 580 miles apart

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Answer:

5 1/10

Step-by-step explanation:

let me know if you need an explanation

For the given set of data, the value of mean is 83, median is 87 and standard deviation is 11.03

Standard deviation is a measurement of how evenly distributed a set of numbers is. Since the variance is the average of the squared deviations from the mean, it is the square root of the variance.

The mean score is - Sum of all scores / total number of scores

= 89 + 72 + 96 + 87 + 64 + 93 + 80 / 7

= 83

So the mean of given scores is 83

Median = central term

= 64, 72, 80, 87, 89, 93, 96

Median = 87

Mode of the data is - no mode as there are no recurring terms given

Standard deviation -

variance = (89 - 83)² +(72 - 83)² + (96 - 83)² + (87 - 83)² + (64 - 83)² + (93 - 83)² + (80 - 83)² / 7

= 121.71

standard deviation = √variance

⇒ standard deviation = 11.03

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The library has more volumes in El Paso.

The number sentence that shows the comparison is 1,232,185 < 1,277,003

Hence, El Paso; 1,232,185 < 1,277,003. Option D

This is further explained below.

Generally, A library is a collection of resources, such as books or other forms of media, that are made available for use rather than being kept only for the purpose of the show.

A library is a facility that makes resources available for physical or digital access, and it may exist either as a real place or as a virtual area, or both.

In conclusion, The library has more volumes in El Paso.

The number sentence that shows the comparison is 1,232,185 < 1,277,003

Hence, El Paso; 1,232,185 < 1,277,003.

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It will take Molly and Rob 54/15 hours to mop the warehouse.

For the given question;

Rob takes 6 hours for cleaning the ware house.

Let 'R' be the work done by rob.

Then, work done by Rob in 6 hours is 1/R = 1/6.

Similarly;

Let work by Molly is 'R'.

The, work done by Molly in 1 hour is 1/M = 1/9.

The total work done by both is 1 hour is;

1/R + 1/M = 1/6 + 1/9

Om simplification;

1/R + 1/M = 15/54.

Thus, the total time taken by doing the work is; 54/15 hours.

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The sentence can be written as:

x + 2 = 23

And the solution is x = 21.

Here we have the sentence:

" The sum of 2 and a number is 23."

Let's define x as the number, then we can write the equation:

x + 2 = 23

This is a simple linear equation, to solve this we need to subtract 2 in both sides of the equation, we will get:

x + 2 - 2 = 23 - 2

x = 21

We conclude that the number is 21.

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Step-by-step explanation:

33 1/3 = (3×33 + 1)/3 = 100/3

51 = 100/3 × x

153 = 100x

x = 153/100 = 1.53

1.53 × 33 1/3 = 51

so, "that" number is 1.53.

Answer: 286.474227

Step-by-step explanation:   The answer is correct if doing division, if not then this is wrong. I divided 277.88 with 0.97 and got 286.474227

₋2.3 < ₋8/3 is the correct answer.

Given, we need to compare the terms.

₋8/3 = ₋2.67

therefore, 2.3 is less than 2.667

hence we form it as ₋2.3 < ₋2.67

we form: ₋2.3 < ₋8/3

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Answer: Pilot Error: 15.9%

Human Error: 3.8%

Weather: 19.3%

Mechanical Problems: 41.8%

Sabotage: 19.2%

Step-by-step explanation:

260+62+315+682+313=

322+997+313=

1319+313=1632 total crashes

Pilot error: 260/1632=

0.159=

0.159*1=

0.159*100%=15.9%

Human error: 62/1632=

0.03799=

0.038=

0.038*100%=3.8%

Weather: 315/1632=

0.193=

0.193*100%=19.3%

Mechanical Problems: 682/1632=

0.41789=

0.418=41.8%

Sabotage: 313/1632=

0.191789=

0.192=19.2%