A car can travel 264 miles on 11 gallons of gasoline. How far can it travel on 2
gallons?

Answer:

2/3

Step-by-step explanation:

18/27 simplified is 2/3

The probability that it will take more than four draws until the third shiny penny appears is 2/5. Let A denote the event that it will take more than four draws until the third shiny penny appears.

Let X denote the number of dull pennies that are drawn before the third shiny penny appears.

Then, X follows a negative hypergeometric distribution with parameters N = 7 (total number of pennies), M = 3 (number of shiny pennies), and n = 3 (number of shiny pennies needed to be drawn).

The probability mass function of X is given by:

P(X = k) =\({{k+2} \choose {k}} / {{6} \choose {3}}\)  for k = 0, 1, 2.

Note that k + 3 is the number of draws needed until the third shiny penny appears.

Thus, we have:

P(A) = P(X > 1) = P(X = 2) + P(X = 3)

=\({{4} \choose {2}} / {{6} \choose {3}} + {{5} \choose {3}} / {{6} \choose {3}}\)

= 6/20 + 10/20= 8/20= 2/5

Hence, the probability that it will take more than four draws until the third shiny penny appears is 2/5.

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The probability that it will take more than four draws until the third shiny penny appears is 0.057, or 5.7%.

To find the probability that it will take more than four draws until the third shiny penny appears, we can use the concept of combinations and probability.

First, let's determine the total number of ways to draw 3 shiny pennies and 4 dull pennies in any order. This can be calculated using the formula for combinations:

\(\[C(n, r) = \frac{{n!}}{{r!(n-r)!}}\]\)

In this case, we have a total of 7 pennies (3 shiny and 4 dull), and we want to choose 3 shiny pennies. So, we can calculate C(7, 3) as follows:

\(\[C(7, 3) = \frac{{7!}}{{3!(7-3)!}} = \frac{{7!}}{{3!4!}} = \frac{{7 \cdot 6 \cdot 5}}{{3 \cdot 2 \cdot 1}} = 35\]\)

So, there are 35 different ways to draw 3 shiny pennies from the box.

Now, let's consider the different scenarios in which it will take more than four draws until the third shiny penny appears. We can break this down into three cases:

Case 1: The third shiny penny appears on the 5th draw.
In this case, we have 4 dull pennies and 2 shiny pennies to choose from for the first 4 draws. The third shiny penny must appear on the 5th draw. So, the probability for this case is:

\(P(case 1) = (4/7) \times (3/6) \times (2/5) \times (1/4) \times (2/3) = 0.019\)

Case 2: The third shiny penny appears on the 6th draw.
In this case, we have 4 dull pennies and 2 shiny pennies to choose from for the first 5 draws. The third shiny penny must appear on the 6th draw. So, the probability for this case is:

\(P(case 2) = (4/7) \times (3/6) \times (2/5) \times (1/4) \times (2/3) \times (1/2) = 0.019\)

Case 3: The third shiny penny appears on the 7th draw.
In this case, we have 4 dull pennies and 2 shiny pennies to choose from for the first 6 draws. The third shiny penny must appear on the 7th draw. So, the probability for this case is:
\(P(case 3) = (4/7) \times (3/6) \times (2/5) \times (1/4) \times (2/3) \times (1/2) \times (1/1) = 0.019\)

Finally, to find the probability that it will take more than four draws until the third shiny penny appears, we sum up the probabilities of all three cases:
P(more than four draws until third shiny penny appears) = \(P(case 1) + P(case 2) + P(case 3) = 0.019 + 0.019 + 0.019 = 0.057\)

Therefore, the probability that it will take more than four draws until the third shiny penny appears is 0.057, or 5.7%.

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Answer:

The answer is 7 socks.

Step-by-step explanation:

To ensure one matching pair, you need to pull out 4 socks. If none of the first three match, the fourth one will guarantee a matching pair.

You will then need to pull out 3 more socks, for a total of 7 socks, to ensure two matching pairs.

Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store.

Michael is trying to determine where to open two new store locations. He has population data to determine the amount of revenue he will receive for each location.

He is charged a $1000 fee for opening a new store at a certain location. However, he is unsure whether the population of the city would be large enough to warrant opening a new store at that location.

The first step that Michael needs to take is to analyze the population data that he has.

Based on the population data, he needs to make an informed decision about whether or not to open a new store at that location. This would require him to take into consideration the average income of the population as well as the demographics of the city.

Another important factor that Michael needs to take into consideration is the competition in the area. If there are already several stores in the area, then opening a new store might not be a good idea.

This is because the competition would be too high and he would not be able to generate enough revenue to make up for the cost of opening a new store.

However, if there are no stores in the area, then Michael might consider opening a new store. This would require him to invest a significant amount of money, but he could also generate a significant amount of revenue in return.

Additionally, he needs to take into consideration the cost of opening a new store and whether or not he can generate enough revenue to make up for that cost.

Overall, Michael needs to carefully analyze all the data that he has before making an informed decision about where to open new store locations.

In conclusion, Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store. If the population is large enough and there is no competition in the area, then he should consider opening a new store. However, if there is already a significant amount of competition in the area, then he should avoid opening a new store.

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The probability that P(X1 < X2 < X3) is 1/8.

We can solve this problem using the fact that if X1, X2, X3 are independent exponential random variables with the same rate parameter λ, then the joint density function of the three variables is given by:

f(x1, x2, x3) = λ^3 e^(-λ(x1+x2+x3))

We want to find the probability that X1 < X2 < X3. We can express this event as the intersection of the following three events:

A: X1 < X2

B: X2 < X3

C: X1 < X3

Using the joint density function above, we can compute the probability of each of these events using integration. For example, the probability of A is:

P(X1 < X2) = ∫∫ f(x1, x2, x3) dx1 dx2 dx3

= ∫∫ λ^3 e^(-λ(x1+x2+x3)) dx1 dx2 dx3 (integration over the region where x1 < x2)

= ∫ 0^∞ ∫ x1^∞ λ^3 e^(-λ(x1+x2+x3)) dx2 dx3 dx1

= ∫ 0^∞ λ^2 e^(-2λx1) dx1 (integration by substitution)

= 1/2

Similarly, we can compute the probability of B and C as:

P(X2 < X3) = 1/2

P(X1 < X3) = 1/2

Note that these probabilities are equal because the three exponential random variables are identically distributed.

Now, to compute the probability of the intersection of these events, we can use the multiplication rule:

P(X1 < X2 < X3) = P(A ∩ B ∩ C) = P(A)P(B|A)P(C|A∩B)

Since A, B, and C are independent, we have:

P(B|A) = P(B) = 1/2

P(C|A∩B) = P(C) = 1/2

Therefore:

P(X1 < X2 < X3) = (1/2)(1/2)(1/2) = 1/8

Thus, the probability that X1 < X2 < X3 is 1/8.

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\({\small{\mathcal{\underline{\underline{\purple{ here \: is \: your \: solution...}}}}}} \\ \\ \)

\(\small\mathfrak\green{sin ( \alpha ) =Perpendicular \div hypotenuse \: \: } \\ \\ \small\mathfrak\green{perpendicular =7 \: } \\ \\ \small\mathfrak\green{hypotenuse =25 \: } \\ \\ \small\mathfrak\green{sin( \alpha ) = 7 \div 25}\)

\({\small{\underline{\bf{\red{ Hope \: it \: helps...}}}}}\)

Answer:

B

Step-by-step explanation:

An illiteration is kind of like a rhyme. it's when the first letters of words match.

Answer:

Bbbbbbbbbb

Step-by-step explanation:

The coffee shop owner should use 112.5 pounds of Brazilian coffee and 37.5 pounds of Colombian coffee to make the 150-pound blend.

To solve this problem, we can use a system of equations. Let x be the number of pounds of Brazilian coffee and y be the number of pounds of Colombian coffee. We can set up the following equations:

x + y = 150 (the total amount of coffee is 150 pounds)
10x + 14y = 11(150) (the total cost of the coffee is $11 per pound)

Now we can use the first equation to solve for one of the variables. Let's solve for y:

y = 150 - x

Now we can substitute this into the second equation:

10x + 14(150 - x) = 11(150)

Distribute the 14:

10x + 2100 - 14x = 1650

Combine like terms:

-4x = -450

Divide by -4:

x = 112.5

Now we can substitute this back into the first equation to solve for y:

112.5 + y = 150

y = 37.5

So the coffee shop owner should use 112.5 pounds of Brazilian coffee and 37.5 pounds of Colombian coffee to make the 150-pound blend.

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Answer:

0

Step-by-step explanation:

The slope of a line is also known as the change in the line. it is often referred to as (\(\frac{rise}{run}\)) and can be found using the formula, (\(\frac{y_2-y_1}{x_2-x_1}\)). Substitute in the given points and solve for the slope,

\(\frac{(2)-(2)}{(3)-(-4)}\)

Simplify,

\(\frac{0}{3+4}\\\\\frac{0}{7}\)

The slope of the line is (0).

μ1 <= μ2,

 mean score on campus 1 is higher than on campus 2

There is also a competing theory put forth by the researcher, according to which test results are unrelated and the advanced learning program has minimal bearing on students' academic performance. Because the researcher wants to know if the scores are greater or lower than the state average, this is an illustration of a two-sided hypothesis.

 μ1 <= μ2,

 mean score on campus 1 is higher than on campus 2.

Because the researcher wants to know if the scores are greater or lower       than the state average, this is an illustration of a two-sided hypothesis.

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Answer:

C

Step-by-step explanation:

divide 22.5 by 10

=2.5

so

f=2 1/2c

\( \rm \looparrowright - \frac{1}{4} (8 - 4 + 20x)\)

Subtract the numbers

\( \rm \looparrowright - \frac{1}{4} (4+ 20x)\)

Factor out 4 from the expression

\( \rm \looparrowright - \frac{1}{ \cancel4} \times \cancel4(1 + 5x)\)

\( \rm \looparrowright - (1 + 5x)\)

When there is a - in front of an expression in parentheses, change the sign of each term in the expression to -

\( \rm \looparrowright - 1 - 5x\)

The image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).

What is rotation?

The term "rotation" refers to an object moving in a circle around its center. Different forms can be rotated at an angle around the centre. A rotation is a map in mathematics. The term "rotation group of a unique space" refers to all rotations that revolve around a fixed point and form a group beneath a structure. With respect to three-dimensional shapes, we can turn or rotate the elements about an endless number of fictitious axes.

Here When rotating a point 270 degrees counterclockwise about the origin our point A( x , y) becomes A'(y,-x). Then

=> (x , y) = (-8,0)

Now 270 degrees counter clockwise rotation then,

=> (y,-x) = (0,-(-8))

=> (y,-x)=(0,8)

Hence the image of the point (-8, 0) after a rotation of 270 degrees counterclockwise is (0,8).

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See Explanation

Step-by-step explanation:

1. By interior angle sum Postulate of a triangle.

\( m\angle a+ m\angle y +m\angle z= 180\degree.... (1)\\\\

m\angle a+ m\angle w +m\angle x= 180\degree.... (2)\\\\\)

From equations (1) & (2), we find:

\( m\angle a+ m\angle y +m\angle z= m\angle a+ m\angle w +m\angle x\\\\

m\angle y +m\angle z= m\angle w +m\angle x\\\)

Hence proved

2. In \( \triangle PQS, \: \angle QSR \) is exterior angle.

Therefore, by remote interior angle theorem, we have:

\( m\angle QPS + m\angle PQS= m\angle QSR\\\\

x + m\angle PQS= 2x\\\\

m\angle PQS= 2x-x\\\\

m\angle PQS = x.... (1)\\\\

m\angle QPS = x.... (given).... (2)\\\)

From equations (1) & (2), we find:

\( m\angle PQS = m\angle QPS\\\\

\therefore \angle PQS \cong \angle QPS\\\\

\therefore PS \cong QS\\(sides\: opposite \: to\: congruent \:\angle s) \\\\\)

\( \therefore \triangle PQS \) is an isosceles triangle.

Thus proved.

Let's add the fractions to determine how many miles Rami run:

Therefore Rami run 2 11/24 miles. (In decimal approximation this is 2.4583 miles)

Answer: 16/45

Step-by-step explanation:

\(\displaystyle\\\frac{4}{9}*\frac{4}{5}= \\\\\frac{4*4}{9*5}=\\\\\frac{16}{45}\)

Answer:

Yes

Step-by-step explanation:

It should be a + b/5

According to the desired test, the appropriate null hypothesis is that the mean profit of the industries Computer and Aerospace do not differ.

The test is if the mean profit of the industries Computer and Aerospace differ.

The appropriate null hypothesis considering that the test is false, hence it is that the mean profit of the industries Computer and Aerospace do not differ.

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Let be "t" the total amount of money you will receive.

According to the information given in the exercise, you can sell each share of Michaels Flowers at $7.28. Since you sell 175 of them, you get:

You also know that you can sell each share of Nanotech One at $10.80. Therefore, the amount of money you'll receive for these shares of Nanotech One, can be calculated by multiplying the price of one share by the 445 shares you will sell:

Then, you can set up that:

The answer is: $6,080

Answer :

-7

Step-by-step Explanation :

Step-by-step explanation:

x+3=2x-1

x-2x=-1-3

-x=-4

x=4

The graph of the rational function y = (-3x + 5) / (-5x + 2) can be obtained by analyzing its behavior as x approaches different values.

How to draw a graph?

First, we can find the vertical asymptote(s) of the function by setting the denominator equal to zero and solving for x:

-5x + 2 = 0

x = 2/5

Therefore, the vertical asymptote is x = 2/5.

Next, we can find the horizontal asymptote of the function by looking at the degrees of the numerator and denominator. Since the degree of the numerator (-3x + 5) is less than the degree of the denominator (-5x + 2), the horizontal asymptote is y = 0.

Finally, we can plot some points to get an idea of the shape of the graph. For example, when x = 0, we have:

y = (-3(0) + 5) / (-5(0) + 2) = 5/2

So the point (0, 5/2) is on the graph.

Similarly, when x = 1, we have:

y = (-3(1) + 5) / (-5(1) + 2) = 8/-3

So the point (1, -8/3) is on the graph.

By plotting additional points and using the information about the asymptotes, we can sketch the graph of the rational function as shown below:

Graph of y = (-3x + 5) / (-5x + 2)

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Answer:

X = 2, Y = 0

Step-by-step explanation:

Add the two equations together to cancel out -4y and +4y

leaving you with:

8x = 16

8x = 16

divide both sides of the equation by 8 to get x on its own (8x/8 = x, 16/8 =2)

leaving you with:

x = 2

substitute the value of x back into the equation to calculate y (it can be either equation, top or bottom):

8(2) - 4 y = 16

8 x 2 = 16

leaving you with:

16 - 4y = 16

subtract 16 from both sides to get 4y on its own

leaving you with:

-4y = 0

so y = 0, and x = 2

Answer:

proportional

Step-by-step explanation:

Answer: Yes it is proportional

Step-by-step explanation:

Answer:

50 grams

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

C is going down (negative) and is linear (straight)

Answer:

C

Step-by-step explanation:

I think it's C