lets pretend it takes 30 sumerians 10 days to dig a mile long canal. Now they needed to dig 400 miles of canals in 12 weeks, how many people would they need to do the work in time

Just do 20 divided by 4.40

Answer:

1, 500km

Step-by-step explanation:

\( \frac{75}{100} \times 2000 \\ \\ = 1500\)

Answer: 1,500km

Step-by-step explanation:

Answer:

1/78

Decimal form:

0.0 128205...

hope this helps!

Using the Bayes' theorem, we find the probability that the transferred ball was white given that the second ball drawn was white to be 52/89, or approximately 0.5843.

To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given an event B to the conditional probability of event B given event A:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this problem, we want to find the probability that the transferred ball was white (event A) given that the second ball drawn was white (event B). We can calculate this probability as follows:

P(A|B) = P(B|A) * P(A) / P(B)

P(B|A) is the probability of drawing a white ball from urn b given that the transferred ball was white and is now in urn b. Since there are now six white balls and three black balls in urn b, the probability of drawing a white ball is 6/9 = 2/3.

P(A) is the prior probability of the transferred ball being white, which is the number of white balls in urn a divided by the total number of balls in urn a, or 6/13.

P(B) is the prior probability of drawing a white ball from urn b, which can be calculated using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where P(B|not A) is the probability of drawing a white ball from urn b given that the transferred ball was black and P(not A) is the probability that the transferred ball was black, which is 7/13.

To calculate P(B|not A), we need to first calculate the probability of the transferred ball being black and then the probability of drawing a white ball from urn b given that the transferred ball was black.

The probability of the transferred ball being black is 7/13. Once the transferred ball is moved to urn b, there are now five white balls and four black balls in urn b, so the probability of drawing a white ball from urn b given that the transferred ball was black is 5/9.

Therefore, we can calculate P(B) as follows:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= (2/3) * (6/13) + (5/9) * (7/13)

= 89/117

Now we can plug in all the values into Bayes' theorem to find P(A|B):

P(A|B) = P(B|A) * P(A) / P(B)

= (2/3) * (6/13) / (89/117)

= 52/89

Therefore, the probability that the transferred ball was white given that the second ball drawn was white is 52/89, or approximately 0.5843.

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The vertex is (2,14), the axis of symmetry is x = 2, and the x-intercepts are (-1,0) and (5,0).

Given function is \($f(x) = -2x^2 + 8x + 10$\).To find the vertex, axis of symmetry and x-intercepts of the quadratic function \($f(x) = -2x^2 + 8x + 10$\), use a graphing calculator. By using the graphing calculator, we can obtain the following graph.

The quadratic function has its vertex at (2,14) and

the axis of symmetry is the vertical line x = 2.The x-intercepts can be found by setting $y = 0$. Thus, solving the quadratic equation \($f(x) = -2x^2 + 8x + 10 = 0$\) gives the following solutions.\($$-2x^2 + 8x + 10 = 0$$\)Multiply by \($-\frac{1}{2}$\) and

simplify.\($$x^2 - 4x - 5 = 0$$(x-5)(x+1) = 0$$\)

Hence, the x-intercepts are (-1,0) and (5,0).

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Answer:

24 mill

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

$2.15

Step-by-step explanation:

$5 - $2.85 = $2.15

this is the explanation

The cost of dry bag is $2.85 then the change does Alka get back will be $2.15.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the mentioned information in the question,

Cost of dry bag = $2.85

Money given by Alka for the bill = $5.00

Then, the amount she will get back,

($5.00 - $2.85) = $2.15

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Answer:

(-1,3)

Step-by-step explanation:

Thus;

When (-1,3) is placed in the relation 3x + y =0,the answer will be zero.

Let;

x= -1

y= 3

3(-1) + 3 =0

-3 + 3 = 0

(1,-3) ,(-2,6)(2,-6),(-1,3) are ordered pairs represent points on the graph of this equation 3x+y=0.

An equation of the line is defined as the linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line is y = mx + c, where m is the slope and c is the intercept cut by the y.

To calculate the ordered pair by satisfying the equation with each pair of points.

3x+y=0

For (1,-3)

3(1)-3=0   Yes

For (-2,6)

3(-2)+6=0  Yes

For (2,-6)

3(2)-6=0  Yes

For (-1,3)

3(-1)+3=0  Yes

For (6, -1)

3(6)-1=11 No

For (-6,1)

3(-6)+1=-11  No

Hence (1,-3) ,(-2,6)(2,-6),(-1,3) are ordered pairs represent points on the graph of this equation 3x+y=0.

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Answer:

360°

Step-by-step explanation:

The figure is irregular which means it must be completely rotated to have matching sides and vertices. A full rotation is equal to 360°.

The average number of people in the system would be 0.41 customers, where the waiting line would be increasing.

This is a queuing theory problem. Average number of customers in the system:

Arrival rate, λ = 20 students/hour

Service rate, μ = 2 customers/minute = 120 customers/hour

Utilization factor, ρ = λ/μ = 20/120 = 1/6

Average number of customers in the system:

L = λ/(μ-λ)

= 20/(120-20)

= 1/5

= 0.2 customers

Probability that exactly 20 customers will arrive in a 1-hour period:

Number of arrivals, X ~ Poisson(λt) = Poisson(20)

Probability of 20 arrivals, P(X=20):

= = (e^(-20) * 20^20) / 20! = 0.026

The waiting line would increase and the number of people in the system would increase as well. The average number of customers in the system, L = λ/(μ-λ) = 35/(120-35) = 7/17 = 0.41 customers.

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Correct question is:

Union coffee shop at NJIT campus has one barista. Students arrive at the rate of 20 students per hour according to a Poisson distribution. The service time is estimated to be 2 customers per minute (exponentially distributed).

Please calculate the average number of customers in the system. (show your work)

What is the probability that exactly 20 customers will arrive in a 1-hour period? (show your work)

Suppose that a student arrival rate increases to 35 students per hour according a poisson distribution. what dynamics you would observe in the waiting line. how many people would be in the system (both waiting and being served)?

The number of people who waited at least 6 minutes is given as follows:

50 people.

The height of each bin of the histogram represents the number of observations of the data-set in the desired interval.

The desired outcomes for this problem are given as follows:

Hence the number of people who waited at least 6 minutes is given as follows:

20 + 15 + 10 + 5 = 50 people.

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B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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Answer:

area of a circle = πr^2

So to find the area we need to know the radius. This is easy, as the radius is half of the diameter. So let's half it:

34/2 = 17m

And then substitue 17, for r:

= π(17)^2

= 289π

= 907.9202769m^2

You can round this however you like, but the best options are often either 3 significant figures, either 1 or 2 decimal places.

A 95% confidence interval for percent of american adults who believe in aliens:  (0.6578, 0.7822)

In this question we have been given that in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens

We need to find the 95% confidence interval for percent of american adults who believe in aliens.

95% confidence interval = (p ± z√[p(1 - p)/n])

Here, n = 200

p = 72%

p = 0.72

And the z-score for 95% confidence interval is 1.960

The upper limit of interval would be,

(p + z√[p(1 - p)/n])

= 0.72 + 1.960 √[0.72(1 - 0.72)/200]

= 0.72 + 1.960 √[(0.72 * 0.28)/200]

= 0.72 + 1.960 √0.001008

= 0.72 + 0.0622

= 0.7822

The lower limit of interval would be,

(p - z√[p(1 - p)/n])

= 0.72 - 1.960 √[0.72(1 - 0.72)/200]

= 0.72 - 1.960 √[(0.72 * 0.28)/200]

= 0.72 - 1.960 √0.001008

= 0.72 - 0.0622

= 0.6578

Therefore, a 95% confidence interval = (0.6578, 0.7822)

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Answer:

137,257

Step-by-step explanation:

Answer:

137,527

Step-by-step explanation:

Answer:

Quotient=23 and remainder=14

14÷3= 4.6666666...

so 4 cookies for each one... with 2 cookies left

Answer: 180 Inchs

Reason:

75 / 5

180 Inchs = 15 Feet

-DoggyMan5

Answer:

2

Step-by-step explanation:

2

The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).

Given that:

∫3−5f(x)dx=6

∫3−5g(x)dx=3

We need to find: ∫3−5[2f(x) 6g(x)]dx

To solve this problem, we will use the properties of integration:

Property 1:

If c is a constant, then

∫cf(x)dx=c∫f(x)dx

Property 2:

If f(x) and g(x) are two functions, then

∫[f(x) + g(x)]dx = ∫f(x)dx + ∫g(x)dx

Using Property 1, we can rewrite the given equation as:

∫3−5[2f(x) 6g(x)]dx = ∫3−5[12f(x)g(x)]dx

Using Property 2, we can further simplify the equation as:

∫3−5[12f(x)g(x)]dx = ∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx

Now we can substitute the given values:

∫3−5[12f(x)]dx + ∫3−5[12g(x)]dx = 12∫3−5f(x)dx + 12∫3−5g(x)dx

Substituting the given values for the integrals of f(x) and g(x), we get:

12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3)

Simplifying, we get:

12∫3−5f(x)dx + 12∫3−5g(x)dx = 12(6) + 12(3) = 12(9) = 108

Therefore, the answer is

∫3−5[2f(x) 6g(x)]dx = 108

The answer to the given problem is ∫3−5[2f(x) 6g(x)]dx = 108. This can be found by using the properties of integration and substituting the given values for the integrals of f(x) and g(x).

the complete question is :

if ∫3−5f(x)dx=6, and ∫3−5g(x)dx=3 , then ∫3−5[2f(x) 6g(x)]dx will be equal to  ?

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The Gerald ordered and ate more pizza than Sarah .

A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.

Given:

Gerald ordered a small pizza, divided into 8 equal slices and ate 3 of them.

Sarah also ordered a small pizza ,divided into 24 slices, and ate 6 of them.

According to given question we have

Gerald divided into 8 equal slices and ate 3 of them.

=3/8

Sarah divided into 24 slices, and ate 6 of them.

=6/24

=1/4

Multiply with 2 in both numerator and denominator we get,

=1*2/4*2

=2/8

∴3/8>2/8

So, Gerald ate more pizza.

Therefore, the Gerald ordered and ate more pizza than Sarah .

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The coordinates of the midpoint M of segment JK are (-0. 3). The distance between the endpoints of JK is sqrt(104) or approximately 10.198.

To find the coordinates of the midpoint M of segment JK, we can use the midpoint formula, which states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, for segment JK with endpoints J(3, -6) and K(-3, 2), the x-coordinate of the midpoint is (-3+3)/2 = 0 and the y-coordinate of the midpoint is (-6+2)/2 = -2. Therefore, the coordinates of the midpoint M are (0, -2).

To find the distance between the endpoints of JK, we can use the distance formula, which states that the distance between two points with coordinates (x1, y1) and (x2, y2) is given by the square root of [(x2-x1)^2 + (y2-y1)^2]. So for segment JK with endpoints J(3, -6) and K(-3, 2), the distance is sqrt[(-3-3)^2 + (2-(-6))^2] = sqrt[36 + 64] = sqrt(100) = 10. Therefore, the distance between the endpoints of JK is approximately 10.198.

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Answer:

Option (A) and Option (E)

Step-by-step explanation:

Length of a segment between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by,

Length = \(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

Length of the segment between J(-8, 1) and K(-5, 5) will be,

JK = \(\sqrt{(-8+5)^2+(1-5)^2}\)

JK = \(\sqrt{9+16}\)

JK = 5 units

Length of segment between the points P(2, 8) and Q(7, 3) will be,

PQ = \(\sqrt{(2-7)^2+(8-3)^2}\)

PQ = \(\sqrt{25+25}\)

PQ = \(5\sqrt{2}\) units

Length of segment between the points S(-3, -10) and T(3, -2) will be,

ST = \(\sqrt{(-3-3)^2+(-10+2)^2}\)

ST = \(\sqrt{36+64}\)

ST = 10 units

Therefore, Option (A) and Option (E) are the correct options.

We have proven that if the inequality holds true for k, it also holds true for k + 1. By the principle of mathematical induction, the inequality 2^n > n^2 holds true for all n > 4.

To prove the inequality 2^n > n^2 using induction with a basis greater than 4, we will use n=5 as the basis.

Basis: n = 5
2^5 = 32 and 5^2 = 25. Since 32 > 25, the inequality holds true for n = 5.

Now, we need to assume that the inequality holds true for an arbitrary positive integer k > 4, and then prove that it holds true for k + 1.

Assume: 2^k > k^2 for k > 4.

Prove: 2^(k + 1) > (k + 1)^2

Step 1: Multiply both sides of the assumption by 2.
2 * (2^k) > 2 * (k^2)

Step 2: Simplify the left side of the inequality.
2^(k + 1) > 2k^2

Step 3: Show that 2k^2 is greater than (k + 1)^2 for k > 4.
2k^2 > (k + 1)^2
2k^2 > k^2 + 2k + 1

Step 4: Rearrange the inequality to show that it holds true for k > 4.
k^2 - 2k - 1 > 0

Since k > 4, it is clear that k^2 - 2k - 1 > 0, as the left side increases as k increases.

Therefore, we have proven that if the inequality holds true for k, it also holds true for k + 1. By the principle of mathematical induction, the inequality 2^n > n^2 holds true for all n > 4.

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Answer:  b) {-3, 0.5}

Step-by-step explanation:

The new equation is the original equation plus 6.  Move the original graph UP 6 units.  The solutions are where it crosses the x-axis.

\(\text{Original equation:}\quad f(x)=\dfrac{15}{x}-\dfrac{9}{x^2}\\\\\\\text{New equation:}\quad\dfrac{15}{x}+6=\dfrac{9}{x^2}\\\\\\.\qquad \qquad f(x)= \dfrac{15}{x}-\dfrac{9}{x^2}+6\)

+6 means it is a transformation UP 6 units.  

Solutions are where it crosses the x-axis.

The curve now crosses the x-axis at x = -3 and x = 0.5.

The equation of the line that passes through the points (0,-2) and (3,2) is  4x-3y-6 = 0.

A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.

The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.

In the given graph,

The points are (0,-2) and (3,2)

To find the equation of the line,

Find slope by using formula  m = (y₂-y₁)/(x₂-x₁)

m = (2-(-2))/(3-0)

m = 4/3

The equation of line is,

y-y₁ = m (x-x₁)

y-(-2) = 4/3(x-0)

y+2 = 4/3x

3y+6 = 4x

4x-3y-6 = 0

The required equation of line is 4x-3y-6 = 0.

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Answer:

B

Step-by-step explanation:

\(\frac{2}{3}\) + \(\frac{x}{3}\) > 1 ( multiply through by 3 to clear the fractions )

2 + x > 3 ( subtract 2 from both sides )

x > 1

The word problem 4 and one tenth times negative 4 times 5 over 12 have a product of negative 8 and one fifth

Multiplication is one of the basic mathematical operator which is used to solve the given problem. It is the inverse of division. the result of multiplication is called the product

Rewriting the word problem 4 and one tenth times negative 4 times 5 over 12 to figures

4 1/10 * -4 * 5/10

solving the equation

= 4 1/10 * -4 * 5/10

= 41/10 * -4 * 5/10

= -41/5

= -8 1/5

The product of the multiplication is negative 8 and one fifth

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Answer:

27:8

Step-by-step explanation:

189/56 = 27/8