2. Recall the 7 bridge problem you studied in this lesson. As you
saw, there was no possible path which uses each bridge once
and only once. This is because there were more than two dots
which had three lines connected to them.
Can you add a single bridge so that there is a path which
uses each bridge once and only once? Give one example
and indicate what points you have to use for your starting
and stopping point.

Mike draws five cards from a standard 52-card deck. The probability that he draws a card from at least three of the four suits is 89.5% (approx),

The number of ways to draw all five cards from a single suit = C(13,5)

There are four ways to accomplish this = C(4,1)

The number of ways to draw five cards from two suits.

We'd like to start by selecting one of four suits = C(4,1)

We want to select three cards from one of these = C(13.3)

Then we'll pick one of the three remaining suits = C(3,1)

We want to choose any two cards from this suit = C(13,2)

And the number of ways to select any five cards is = C(52, 5)

So the likelihood of selecting 5 cards from two suits is =

[C(4,1) × C(13,5)  +  C(4,1) × C(13,3) × C(3,1) × C(13,2)]/C(52,5)

The likelihood of selecting 5 cards from two suits is = 1749/16660

So, the probability of drawing 5 cards from at  least 3 suits = 1 - 1749/16660

The probability of drawing 5 cards from at  least 3 suits = 14911/ 16660

The probability of drawing 5 cards from at  least 3 suits = 89.5% (approx)

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The inequality - 15 > t has the same meaning as t > -15

An inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

The given inequality is - 15 >t

We can rewrite this as  t > -15

The above two inequalities have the same meaning.

Reading from right to left, the first inequality says, "b is greater than or equal to negative 18."

Reading from left to right, the second inequality says, "b is greater than or equal to negative 18."

Therefore the two inequalities have the same meaning.

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Answer:

600

Step-by-step explanation:

She had -350 then ended with 250

First you get -350 to 0... that's by adding 350.

Then getting from 0 to 250, you add 250

Now we add 350 and 250 to get a total of 600

Answer:

x+2=11

Step-by-step explanation:

77/7=11

And x=9

11-2=9

The number can be broken apart from the factor 42 using the place value as 40 + 2 here 4 is in the tens place and 4 is in the one's place.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

The number is 42.

As we know,

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

So, We get;

⇒ 42 = 40 + 2

⇒ 42 = 4 × 10 + 2 × 1

Thus, The number can be broken apart from the factor 42 using the place value as 40 + 2 here 4 is in the tens place and 4 is in the one's place.

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The value of adding x² and y² results to

(-20√7 + 84√3) / 416

In the problem it was given that

1/x = √7 - √3 and

1/y = √7 + √3

hence we can get x and y to be

x = 1/(√7 - √3)

y = 1/(√7 + √3)

rationalization of surd

x

=  1/(√7 - √3) *  (√7 - √3) /(√7 - √3)

= (√7 - √3)/(7 - 42 + 3)

= (√7 - √3)/(-32)

y

=  1/(√7 + √3) *  (√7 + √3) /(√7 + √3)

= (√7 + √3)/(7 + 42 + 3)

= (√7 + √3)/(52)

adding the parameters

x² + y² = (√7 - √3)/(-32) + (√7 + √3)/(52)

= (-52√7 + 52√3 + 32√7 + 32√3) / 416

= (-20√7 + 84√3) / 416

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Answer: a. The area of the rectangular base of the bale of hay is 2 feet * 3 feet = 6 square feet.

The area of the circular base of the bucket is π * (diameter/2)^2, where the diameter is 3 feet, so the area is π * (3/2)^2 = π * (9/4) = 9π/4 square feet.

Since π is approximately equal to 3.14, the area of the circular base is approximately 9 * 3.14 / 4 = 6.935 square feet, which is less than the area of the rectangular base.

So the rectangular base of the bale of hay is larger in area.

b. The volume of the bale of hay is 2 feet * 3 feet * 5 feet = 30 cubic feet.

The volume of the bucket is π * (diameter/2)^2 * height, where the diameter is 3 feet and the height is 5 feet, so the volume is π * (3/2)^2 * 5 = π * (9/4) * 5 = 45π/4 cubic feet.

Since π is approximately equal to 3.14, the volume of the bucket is approximately 45 * 3.14 / 4 = 34.65 cubic feet, which is less than the volume of the bale of hay.

So the bale of hay is larger in volume.

Step-by-step explanation:

The mean rainfall for the highland storms is 15.27 and the mean rainfall for the lowland storms is 12.05mm

The mean is also sometimes called the average

To find the mean, we can add up every number in the data set and divide that sum by the total number of data points within the set.

The sum of the data of Highlands storms:

= 2*2 + 3*4 + 2*6 + 3*8 + 4*10 + 3*12 + 4*14 + 5*16 + 5*18 + 4*20 + 2*22 + 24 + 2*26 + 2*28 + 30 + 32 = 672

the total number of data is 44

Mean = 672/44 = 15.27 mm

The sum of the data of Lowland storms:

= 3*2 + 5*4 + 3*6 + 3*8 + 5*10 + 7*12 + 6*14 + 4*16 +2*18 + 20 + 2*22 + 24 + 2*28 = 530

the total number of data is 44

Mean = 530/44 = 12.05 mm

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Full question:

The dot plots show rainfall totals for several spring storms in highland areas and lowland areas.

What is the mean rainfall for the highland storms?

a) 12.5 mm

b) 14 mm

c) 15.27 mm

d) 24 mm

What is the mean rainfall for the lowland storms?

a) 10.5 mm

b) 12.05 mm

c) 16.05 mm

d) 30 mm

Answer: 15.27 and 12.05

Step-by-step explanation:

An expression for the volume of a rectangular prism with length 7.5 ft, width w ft, and height 4.2 ft is 31.5w ft³.

Therefore the answer is 31.5 ft³.

The volume of a rectangular prism can be found by multiplying its length, width, and height. So, for a rectangular prism with length 7.5 ft, width w ft, and height 4.2 ft, the volume can be expressed as:

V = 7.5 * w * 4.2

V = 31.5 w ft³

So, the expression for the volume of this rectangular prism is 7.5 * w * 4.2, that is 31.5 w cubic feet.

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The linear program has an optimal solution of 28.5 at (A, B) = (2, 5) when the right-hand side for constraint 1 is 10. If the right-hand side is increased to 11, the optimal solution remains 28.5 at the same point.

The dual value for constraint 1 stays the same as long as the right-hand side stays within the range 8.4 to 11. The value of the optimal solution will increase by 0.5 for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is within the range 23 to 27.

a) To find the new optimal solution, we need to graph the feasible region and find the new corner points. After the change, the first constraint becomes 1A + 1B ≤ 11. The other two constraints remain the same. The corner points can be found by substituting the bounds of each variable into the constraints and solving for the other variable. The feasible region can then be graphed, and the maximum of the objective function can be found at one of the corner points.

The new corner points are (0,0), (0,9), (6,0), and (2,5). The feasible region can be graphed as a triangle with these corner points. The maximum of the objective function 3A + 2B occurs at the point (2,5), where the value of the objective function is 28.5.

b) The value of the objective function at the optimal solution is 28.5, at (A, B) = (2, 5).

c) The right-hand side range information for constraint 1 tells us that if the right-hand side is increased from 10 to 11, the dual value will remain the same (since the allowable increase is 2.6 and the right-hand side only increases by 1). The range for constraint 1 is 8.4 to 11. As long as the right-hand side stays within this range, the dual value of 2.6 is applicable.

d) The dual value for constraint 2 is 0.5. Using this dual value and the right-hand side range information, we can conclude that the value of the optimal solution will increase by 0.5 for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is within the range 23 to 27.

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Complete question:

Consider the following linear program.

Max 3A + 2B s.t.

1A + 1B ≤ 10

3A + 1B ≤ 27

1A + 2B ≤ 18

A, B ≥ 0

The value of the optimal solution is 28.5. Suppose that the right-hand side for constraint 1 is increased from 10 to 11.

(a) Use the graphical solution procedure to find the new optimal solution.

What is the value of the objective function at the optimal solution?

(blank) at (A, B) =

Use the solution to part (a) to determine the dual value for constraint 1.

(c) The computer solution for the linear program provides the following right-hand side range information

. Constraint RHS Value Allowable Increase Allowable Decrease

1 10.00000 2.60000 1.00000

2 27.00000 3.00000 13.00000

3 18.00000 Infinite 6.50000

What does the right-hand side range information for constraint 1 tell you about the dual value for constraint 1?

The range for constraint 1 is (blank) to (blank) . As long as the right-hand side stays (within/outside) this range, the dual value of (blank) is applicable.

(d) The dual value for constraint 2 is 0.5. Using this dual value and the right-hand side range information in part (c), what conclusion can be drawn about the effect of changes to the right-hand side of constraint 2?

The value of the optimal solution will increase by (blank) for every unit increase in the right-hand side of constraint 2 as long as the right-hand side is (within/outside) the range (blank) to (blank).

Answer:LxW

Step-by-step explanation:

Length x width

Answer:

I think BC

Step-by-step explanation:

Answer: 2000 times 3000 is 5,000,000. So, 5,000,000 divide by 1000000 is 5 multiplied by 2 is 10 pounds of gold,

Step-by-step explanation:

Answer:

66 inches

Step-by-step explanation:

77→ 14

X→12

In the proportion

a/b=c/d

the product of the means equals the product of the extremes. That is,

ad=bc.

So,

77 * 12 = X * 14

x = (77 X 12) / 14 = 66

The area of rectangle from the given vertices is 90 squared units

The area of a rectangle is the product of its length and width. If a rectangle has length "l" and width "w", its area can be calculated as:

A = l * w

where A is the area and l and w are the length and width of the rectangle, respectively.

The area of a rectangle can be calculated as the product of its length and width. Given the vertices, the length of the rectangle is 14 - 4 = 10 units, and its width is 2 - (-7) = 9 units. Hence, the area of the rectangle is 10 * 9 = 90 square units.

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A number which is 15 more than twice a number is 37 is 11.

Let the number be N.

Let's set up the equation.

A number which is given to us is 15 more than twice a number 37,

2N + 15 = 37

Let's subtract 15 from both sides.

2N = 22

Divide both sides by 2, and you get

N = 11

So, the number which we needed is 11.

It is a type of mathematical notation that consistently expresses the numbers in a set using digits or other symbols. It provides each number with a unique representation and specifies the arithmetic and algebraic structure of the numbers. Additionally, we may use it to carry out mathematical operations like addition, subtraction, multiplication, and division.

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Answer:

see below

Step-by-step explanation:

area of the garden is 4​(6.5x+2.5​).

combined area of the garden and the walkway is 4.5​(8x+4​).

so area of the walkway = 4.5​(8x+4​) -4​(6.5x+2.5​)

=36x+18 -26x-10

=10x+8

Erika has 6.53 kilograms of apples, which is more than the 6 kilograms she needed for the recipe. Therefore, she has enough apples to make the recipe.

To determine if Erika has at least 6 kilograms of apples, we need to add the weight of all three bags of apples. The total weight of the apples is:

2.56 kg + 1.18 kg + 2.79 kg = 6.53 kg

Erika needs a certain amount of apples for a recipe, specifically 6 kilograms. She goes to the store and picks three different bags of apples - a 2.56-kilogram bag of red apples, a 1.18-kilogram bag of green apples, and a 2.79-kilogram bag of yellow apples. To determine if she has enough apples, she needs to add the weight of all three bags. The total weight of the apples comes out to be 6.53 kilograms. This means that Erika has more than the required 6 kilograms of apples and is sufficient to make the recipe. It's important to note that Erika has an excess of apples, which can be helpful in case she needs extra for the recipe or for future use. The combination of different types of apples can also add variety and flavor to the recipe.

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his gives us a coefficient of determination. Of around then see what you get 0.7 and we're going to round to 100.710. Is our explained, variance,

we are looking at the pounds of waste here and the number of people in the home, so we're asked to find the proportion of variance that can be explained. So was this. The variance explained basically refers to the coefficient of determination, r square,

pounds of waste= 0.27 ,1.41, 2.19, 2.83, 2.19, 1.81, 0.85, 3.05

           in home = 2       ,  3    ,  3,       6  ,   4  ,  2,    1,      5.

so we are basically asked to find r squared our r squared equation is

[tex]r^2=\frac{\sum(x_i-x')^2}{N}[/tex]

the mean is 1.8 ,

which is 1.8 multiplied by y minus its mean, which is around 3.3.

we calculate this giving us a sum of products that is = 9.35

We take this sum of x minus a mean 1.8 square, giving us a sum of square of x around 6.3 2 point now. Finally, for a sum with squares of y we're going to do the same

x'-xi=9.35.

his gives us a coefficient of determination. Of around then see what you get 0.7 and we're going to round to 100.710. Is our explained, variance,

The complete question is -

what is the proportioan of variance explained pounds of waste

pounds of waste= 0.27 ,1.41, 2.19, 2.83, 2.19, 1.81, 0.85, 3.05

           in home = 2       ,  3    ,  3,       6  ,   4  ,  2,    1,      5.

a) 0.710 b) 0.842 c)  0.549 d) 1.480

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The least change in temperature is in the eastern region.

What is meant by the temperature of a place?

The physical concept of temperature indicates in the numerical form how hot or cold something is. A thermometer is used to determine temperature. It denotes the direction of the spontaneous movement of heat energy, i.e., from a hotter body (one with a higher temperature) to a colder body (one at a lower temperature).

Thermometers are calibrated according to different temperature scales that used different reference points and thermometric substances as definitions. The Celsius scale, denoted by the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale are the most popular scales (K).

To find the change in temperature we can use the following formula:

Temperature change = Final temperature - Initial temperature

                                    = Maximum temperature - Minimum temperature

Using the above relation, we can find the change in temperature in each region.

North

Temperature change = 10 °F - (-8°F) = 18°F

South

Temperature change = 2 °F - (-3°F) = 5°F

East

Temperature change = 0 °F - (-2°F) = 2°F

West

Temperature change = 3 °F - (-4°F) = 7°F

Hence from the above calculations, it is clear that the least change in temperature is in the eastern region.

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The money the city would earn is $125.000.

One third of the 15000 people who visit take the bus for $5 then

⅓ . 15000=5000

5000 people who got on the bus.

Multiplied by the bus fare

5000x5$=25000$

Then ⅔ of 15000 people means:

⅔x15000= 10000 people obviously do not use the bus.

And there are 2/5 people using private vehicles, so we find the number of people by multiplying 2/5 of the 10,000 people:

2/5 x 10000 = 4000 people.

These 4000 people have to pay for parking their vehicles $25 (assuming that one person per vehicle)

So that

4000x$25=$100000, this is the accumulated parking fee.

From there we can add between $25000+$100000= $125000 , this is how much the city's income is.

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0

The graph is under 0. therefore it can be anything under

Answer: 0

Step-by-step explanation: The graph is shaded below the x-axis, so it includes all values of y that are under (or equal to) 0.

The locus of points is equidistant from X and Y will be x = 3.5. Then the location of point Z is (3.5, -6).

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line in m:n ratio, finding the mid-point of the line, etc.

Consider two dots, X and Y, 7cm apart horizontally.

Let 'X' be at the origin and the 'Y' be at the x-axis. Then the coordinate of X is (0, 0), and the coordinate of Y is (7, 0). Then the locus is given as,

x² + y² = (x - 7)² + y²

x² + y² = x² + y² - 14x + 49

14x = 49

x = 3.5

A third dot Z is 6cm below X. Then the location of point Z is (3.5, -6).

The locus of points is equidistant from X and Y will be x = 3.5. Then the location of point Z is (3.5, -6).

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The point marked on the number line is approximately -1.25.

The tick marks on the number line are spaced at intervals of 1/4, and the point is marked one tick below negative 1. To determine its exact value, we can count the number of tick marks below negative 1 and multiply by the interval size:

1 tick below negative 1: -1 - (1/4) = -1.25

So, the point marked on the number line is approximately -1.25. A vertical number line labeled from bottom to top from negative 2 to positive 2 with tick marks every 1-fourth unit will definitely have the point marked on the number line at approximately -1.25.

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Answer:

933500

Step-by-step explanation:

You move the decimal over 5 spaces to the right

The algebraic expression representing how much more Elena spent is given as follows:

4.20 + p.

Considering the variable p as the price per pound of cherries, the functions modelling each spending are given as follows:

How much more Elena spent is given by the difference of Elena's spending by Taniy's spending, hence the expression is given as follows:

8.85 + 4p - (4.65 + 3p)

8.85 + 4p - 4.65 - 3p

4.20 + p.

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