Two groups of people, the Yellow Group and the Orange Group, suddenly find themselves in a world where there are only two 'production opportunities': pumping water and picking berries.

After a little while the Yellow Group has learned that it seems to produce about 2 gallons per hour while pumping water and about 8 berries per hour while picking.

Meanwhile the Orange Group has learned that it seems to produce about 1 gallon per hour while pumping water and about 3 berries per hour while picking.

If there is a division of labor and trade between the Yellow Group and the Orange Group, then it would be possible for each group to consume ______________ than they could if each group consumed what it produced itself.

A. more berries (but not more water)


B. more water (but not more berries)


C. more water and more berries


D. none of the above

In his 1961 speech, Fidel Castro expressed the idea that a revolution is not an easy or smooth process, comparing it to a struggle to the death between the future and the past.

By analyzing Castro's words, we can understand the following key points:

Revolution as a Challenge: Castro suggests that a revolution is not a "bed of roses," meaning it is not a comfortable or peaceful endeavor. Instead, he emphasizes that it is a challenging and arduous path.

Struggle between Future and Past: Castro characterizes revolution as a struggle between the future and the past. This implies that the revolution represents a clash between the aspirations, progress, and desired changes of the future and the existing social, political, and economic structures of the past.

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Answer:

y = 4x + -1/1

-1/1 as a fraction. Down by 1 and right by 1

The equation of line in slope intercept form which is passing through

(1, -1) is  y = 4x -5.

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

The equation of line in slope intercept form is given by y = mx + c.

According to the given question.

We have

The solpe of the line, m = 4

Also, the point through which the line is passing, \((x_{1} , y_{1}) = (1, -1)\)

Since, we know that the equation of line in slope intercept form of the line is given by

y = mx +c

Since, the above line is passing through (1, -1) and the slope is 4.

Therefore,

-1 = 4(1) + c

⇒ -1 = 4 + c

⇒ -1 -4 = c

⇒ c = -5

Substitute the value of m and c in the equation y = mx + c.

⇒ y = mx + c

⇒ y = 4x -5

Therefore, the equation of line in slope intercept form which is passing through (1, -1) is  y = 4x -5.

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The number of minutes that Claudia studied is 9 times the number of minutes Crystal studied.

Answer:

5.25 feet

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

-6.75  is a rational real number

   since it is not a whole number or a counting number

sqrt(175) = 5 sqrt(7) = irrational real number

     since sqrt(7) is irrational

5 pi = irrational real number

      since pi is irrational

30/3 = 10 = natural , whole, integer, rational, real number

since this is a counting number

- sqrt(9) = -3  integer, rational, real number

since this is negative

Answer:

see attached

Step-by-step explanation:

Answer:

$0.50

Step-by-step explanation:

Suppose that a person  bought  six T-bone steaks that cost $15.99 per pound

The weight that is listed on the package is 5.77 pounds.

The scale that weighed the package is accurate to within 1/32 pound

Let assume x is the range of the  weight listed on the package,

Then:

\(|x-5.77| \leq \dfrac{1}{32} \ --- \ (1)\)

Using the method of absolute value inequality;

\(- \dfrac{1}{32} \leq x -5.77 \leq \dfrac{1}{32}\)

\(5.77- \dfrac{1}{32} \leq x \leq \dfrac{1}{32}+ 5.77\)

\(5.77- 0.03125\leq x \leq 0.03125+ 5.77\)

\(5.73875 \leq x \leq 5.80125\)

The amount per kilogram undercharged or overcharged is :

\(=\dfrac{1}{32} \times 15.99\)

= $0.50

Answer:

thousandth

Step-by-step explanation:

Answer:

Thousandths

Step-by-step explanation:

7÷8=0.875

it is thousandths

The size of QRS in the given figure 15 cm.

A fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean theorem, also referred to as Pythagoras' theorem. According to this definition, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

step1

We know

PS=8cm

PQ=12cm

QR=4cm

because we know that both of these parts have to do with right triangles, we know that we can use the Pythagorean theorem.

a²  + b²  = 4²  (add in values)

8²  + 12² +4²   

64 + 144 +16=224

find the square root of 224= 15

Size of QRZ =15 cm

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a) the probability that a randomly selected Cobalt gets more than 34 MPG is approximately 0.7149.

b) the probability that the mean MPG exceeds 34 MPG for a sample of 10 Cobalts is approximately 0.035.

c) the probability that the mean MPG exceeds 34 MPG for a sample of 20 Cobalts is approximately 0.005.

a) To find the probability that a randomly selected Cobalt gets more than 34 MPG, we need to calculate the area under the normal distribution curve to the right of 34 MPG.

Using the z-score formula, we can convert the MPG value to a standard score (z-score) using the formula:

z = (x - μ) / σ,

where x is the given value (34 MPG), μ is the mean (32 MPG), and σ is the standard deviation (3.5 MPG).

Calculating the z-score:

z = (34 - 32) / 3.5 = 0.57

Using a standard normal distribution table or a statistical calculator, we can find the area to the right of the z-score 0.57.

Let's assume the standard normal distribution table gives us a value of 0.2851 for z = 0.57.

Since the total area under the normal curve is 1, the probability of getting more than 34 MPG is:

P(X > 34) = 1 - P(X ≤ 34) = 1 - 0.2851 = 0.7149

Therefore, the probability that a randomly selected Cobalt gets more than 34 MPG is approximately 0.7149.

b) When selecting a sample of 10 Cobalts, the mean MPG of the sample (\(\bar{X}\)) follows a normal distribution with the same mean (32 MPG) and a standard deviation (σ) equal to the population standard deviation (3.5 MPG) divided by the square root of the sample size (√10).

σ( \(\bar{X}\) ) = σ / √n = 3.5 / √10 ≈ 1.107

We want to find the probability that the mean MPG exceeds 34 MPG for the sample of 10 Cobalts. In other words, we need to find P(\(\bar{X}\) > 34).

We can again convert the value of 34 MPG to a z-score:

z = (34 - 32) / 1.107 ≈ 1.805

Using a standard normal distribution table or a statistical calculator, we find the area to the right of the z-score 1.805.

Let's assume the standard normal distribution table gives us a value of 0.035 for z = 1.805.

Therefore, the probability that the mean MPG exceeds 34 MPG for a sample of 10 Cobalts is approximately 0.035.

c) When selecting a sample of 20 Cobalts, the mean MPG of the sample (\(\bar{X}\)) follows a normal distribution with the same mean (32 MPG) and a standard deviation (σ) equal to the population standard deviation (3.5 MPG) divided by the square root of the sample size (√20).

σ( \(\bar{X}\) ) = σ / √n = 3.5 / √20 ≈ 0.78

We want to find the probability that the mean MPG exceeds 34 MPG for the sample of 20 Cobalts. In other words, we need to find P(\(\bar{X}\) > 34).

Similarly, we can convert the value of 34 MPG to a z-score:

z = (34 - 32) / 0.78 ≈ 2.564

Using a standard normal distribution table or a statistical calculator, we find the area to the right of the z-score 2.564.

Assuming the standard normal distribution table gives us a value of 0.005 for z = 2.564.

Therefore, the probability that the mean MPG exceeds 34 MPG for a sample of 20 Cobalts is approximately 0.005.

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The number of people attending affects how much food is prepared for a catered event. The number of people attending is the explanatory variable in this scenario.

One kind of independent variable is an explanatory variable. Both words are frequently used interchangeably. This is the variable that changes as we change it or watch it change. In other words, it is a factor that a researcher has changed in an experiment.

In the given situation, the number of people attending is an explanatory variable and the amount of food prepared is a dependent variable. As the number of people attending increases, the amount of food prepared also increases. This means the effect of one variable alters the effect of another variable. The change of one variable is called an independent variable while the change that occurs because of the independent variable is a dependent variable.

Therefore, the required answer is the number of people attending.

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Answer:

279 feet

Step-by-step explanation:

To find x, we solve using the Trigonometric function of Tangent

tan θ = Opposite/ Adjacent

θ = 64°

Length of the shadow = Adjacent = 136 feet

Height of the building = Opposite = h

Hence,

tan 64 = h/136 feet

Cross Multiply

h = tan 64 × 136 feet

h = 278.84132245 feet

Approximately, h to the nearest foot ≈ 279 feet

Therefore, the height of the building = 279 feet

Answer:

50.24

Step-by-step explanation:

4x4x3.14

(4 because of the radius)

(3.14 because of pi)

Answer:

= a(7b + 1)

Step-by-step explanation:

7ab + a

a(7b + 1).

The expression represents an irrational number are B. √75 and  D. √3-√3 .

Any number that cannot be expressed as the quotient of two integers i.e. p/q.

A. 0.18 = 18/100

⇒ it is expressed as quotient of two integers p/q.

∴ 0.18 is a rational number.

B. \(\sqrt{75}\)

⇒it is not expressed as quotient of two integers p/q.

∴ It is an irrational number.

C. 2/3

⇒it is expressed as quotient of two integers p/q.

∴ 2/3 is a rational number.

D. √3-√3

⇒ √3-√3 is not expressed as quotient of two integers p/q.

∴ B. √75 and  D. √3-√3 are irrational numbers.

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Regarding the exponential function y = 3(2)^x, we have that:

An exponential function is defined as follows:

y = ab^(x/n).

In which the parameters are defined as follows:

The function for this problem is given as follows:

y = 3(2)^x.

Hence the parameters are given as follows:

At x = 3, the numeric value of the function is obtained as follows:

y = 3 x 2^3

y = 3 x 8

y = 24.

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The mass of one worker bee is \,1\cdot{ 10^{-4}}1⋅10 −4 kg, and there are 4\cdot{ 10^4}4⋅10 4 worker bees in the hive.

To find the mass of all the worker bees in the hive together, we need to multiply the mass of one worker bee by the number of worker bees in the hive:

\,1\cdot{ 10^{-4}}1⋅10 −4 kg \times 4\cdot{ 10^4}4⋅10 4 = 4\cdot{ 10^{-4}}4⋅10 −4 kg \times 4\cdot{ 10^4}4⋅10 4

Using the rules of exponents, we can simplify this expression:

4\cdot{ 10^{-4}}4⋅10 −4 kg \times 4\cdot{ 10^4}4⋅10 4 = 4 \times 4 \times 10^{-4}10 4 = 16 \times 10^0 = 16

So, the mass of all the worker bees in the hive together is 16 kg. In scientific notation, this is \,1.6\cdot{ 10^1}1.6⋅10 1 kg.

Therefore, the answer is \boxed{1.6\cdot{ 10^1}}1.6⋅10 1 kg.

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One problem with the arithmetic mean is that it is influenced by outliers. Because with the presence of outliers , the arithmetic mean will be pulled towards the outlier. So, the correct option is A) it is influenced by outliers.

The arithmetic mean is calculated by summing up all the observations in a dataset and dividing by the number of observations. While it is a commonly used measure of central tendency, it has some limitations. One of the main problems with the arithmetic mean is that it can be strongly influenced by outliers.

An outlier is an observation that is very different from the other observations in the dataset. When outliers are present, the arithmetic mean can be pulled towards the outlier and may not be a good representation of the typical value in the dataset.  So, the answer is A) it is influenced by outliers.

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Given the system:

y = 3x + 4

y = 2x - 6

3x + 4 = 2x - 6

3x - 2x = -6 - 4

x = - 10

y = 3(-10) + 4

y = -26

(-10, - 26) one solution

Answer:

Step-by-step explanation:

We can solve this using the pythagorean theorem.

We know that a^2 + b^2 = c^2.

Our c value is the hypotenuse, and it does not matter what a or b is, as we will be solving for one of them.

We can set up our equation as such:

6^2 + b^2 = 20^2

From here, we can solve this algebraically.

\(6^2 + b^2 = 20^2\)

\(36 + b^2 = 400\)

\(b^2 = 364\)

\(b=\sqrt{364}\)

\(b=19.07878403\)

Here, b is our length for y, so y is equal to 19.07878403.

Answer:

\(y=2x-6\)

Step-by-step explanation:

A locus can be defined as a curve or figure formed by all the points satisfying a particular equation of the relation between coordinates.

The condition stated in the question is such that a generic (x,y) point of the curve is equidistant from the points A(2,3) and B(6,1).

The distance d1 from (x,y) to (2,3) is:

\(d_1=\sqrt{(x-2)^2+(y-3)^2}\)

The distance d2 from (x,y) to (6,1) is:

\(d_2=\sqrt{(x-6)^2+(y-1)^2}\)

Since d1=d2:

\(\sqrt{(x-2)^2+(y-3)^2}=\sqrt{(x-6)^2+(y-1)^2}\)

Squaring both sides:

\((x-2)^2+(y-3)^2=(x-6)^2+(y-1)^2\)

Operating:

\(x^2-4x+4+y^2-6y+9=x^2-12x+36+y^2-2y+1\)

Simplifying all the squares:

\(-4x+4x+4-6y+9=-12x+36-2y+1\)

Moving the variables to the left side and the numbers to the right side:

\(-4x+12x-6y+2y=36+1-4-9\)

Simplifying:

\(8x-4y=24\)

Dividing by 4:

\(2x-y=6\)

Or, equivalently:

\(\boxed{y=2x-6}\)

Answer:

5

Step-by-step explanation:

Answer:

This is your answer

Answer:  39.09 km per hour average

Step-by-step explanation:

add total distance and divide by total time

(30+400)/(5.5+5.5)

430/11=39.0909

Given the system of equations:

a) The given system has the equations of lines, so it will be a linear system

b) We will write the equations in slope-intercept from to compare them

From (1): y = -x + 4

From (2): y = x + 4

The slope of the first equation = -1, and the slope of the second equation = 1

so, the given system of consistent independent system

the system has only one solution

c) the system will be consistent

d) the system will be independent

\(\textbf{a)}\\\\3x^2 y^4 \cdot 2x^6 y \\\\=6x^{2+6} \cdot y^{4+1}\\\\=6x^8 y^5\\\\\textbf{b)}\\\\xz^3 \cdot 4x^4 z^5\\\\=4x^{4+1} \cdot z^{3+5}\\\\=4x^5 z^8\\\\\textbf{c)}\\\\4a^3b^2 \cdot 3a^6 b^5 \\\\=12a^{3+6}\cdot b^{2+5}\\\\=12a^9b^7\\\\\textbf{d)}\\\\6s^5t\cdot s^4 t^2\\\\=6s^{5+4} \cdot t^{2+1}\\\\=6s^9t^3\)

Answer:

3x-12 is the simplififed answer

Step-by-step explanation:

the equation is almost already simplified. when you combine -8 and -4, which are like terms, you get 3x-12. because there are no more lie temrs in the equation, it can not be simplififed any further.

Answer:

3x-12

Step-by-step explanation:

3x-8-4                        -8-4=-12

 3x-12

Answer:

2^20

Step-by-step explanation:

2^4x5

= 2^20

Answer:

hi

Step-by-step explanation:

hi

Figure R'S'T'U' is the image of Figure RSTU after a translation of 2 units left and 2 units down, and a reflection across the y-axis.

Examples of transformations are given as follows:

The rule applied for the translation is given as follows:

(x,y) -> (x - 2, y - 2).

Hence:

The rule applied for the reflection is of:

(x, y) -> (-x, y).

Hence the figure was reflected over the y-axis.

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Answer:

Step-by-step explanation:

If you subtract 5 from three times a number, it can be expressed as:

3x - 5,

where "x" represents the number.

Answer:

I'd have to say C

Step-by-step explanation:

The correct option is option B i.e., the total amount George would make if he sells all his cards will be equal to $400 approx.

George estimates that he can make $4.75 per card if he sells baseball cards online. He has total 83 cards.

We have to find out the closest amount George would make if he sells all his cards.

What is the unitary method?

The unitary method is a method in which we find the value of a unit and then the value of the required number of units.

As per the question ;

George estimates that he can make $4.75 per card.

The total no. of cards George have = 83 cards

So ,

The total amount , George would make if he sells all his cards can be calculated by multiplying the total no. of cards to price of each card.

i.e.,

Total amount George will made ;

= 83 × $ 4.75

= $ 394.25

≈ $ 400

Thus , the correct option is option B i.e., the total amount George would make if he sells all his cards will be equal to $400 approx.

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