In a city, the distance between the library and the police station is 3 miles less than twice the distance between the
police station and the fire station. The distance between the library and the police station is 5 miles. How far apart are
the police station and the fire station?
1 mile
3 miles
4 miles
6 miles
Suban

(a) Find the dual of the LP.Primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\) subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n \leq\) \(b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n \leq b_m$ and $x_1, x_2,\)..., x_n\(\geq 0$\)

Let us find the dual of the above primal problem.

Dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq\)\(C_1$...$a_{1n}y_1+a_{2n}y_2+...+a_{mn}y_m \leq C_n$\)

and\($y_1, y_2, ..., y_m \geq 0$\)

(b) Find the standard form of the LP and dual.Standard form of the primal problem isminimize \($b_1y_1+C_1x_1+...+C_nx_n$\)subject to \($a_{11}x_1+a_{12}x_2+...+a_{1n}x_n +s_1 = b_1$...$a_{m1}x_1+a_{m2}x_2+...+a_{mn}x_n +s_m = b_m$\) and\($x_1, x_2, ..., x_n, s_1, s_2, ..., s_m \geq 0$\)

Standard form of the dual problem ismaximize \($b_1y_1+...+b_my_m$\)subject to \($a_{11}y_1+a_{21}y_2+...+a_{m1}y_m \leq 0$...$a_{1n}y\)

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The fraction of ducks remaining on the pond is 2/5.

To determine the fraction of ducks remaining, we need to compare the number of ducks left to the initial number of ducks. Initially, there were 10 ducks on the pond. When 6 ducks flew away, the subtraction of 6 from 10 yields 4 ducks remaining. Therefore, the fraction of ducks left can be expressed as 4/10.

To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which in this case is 2. Dividing 4 by 2 gives us 2, and dividing 10 by 2 gives us 5. Thus, the simplified fraction is 2/5. This means that two-fifths of the original number of ducks are still on the pond.

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Answer: LOGICAL EXPRESSIONS

Step-by-step explanation: An if statement includes a logical expression which is the 'test. ' A logical expression is one that is either true or false. This is also called a Boolean expression.

Answer:

1. x=2 2. x=23

Step-by-step explanation:

1: 7(x+3) = 39-2x

7x+21 = 39-2x

9x=18; x=2

2. 2x-5 = 1/2(3x-13)

2x-5 = 1.5x-13/2

0.5x=11.5; x=23

Answer:

Step-by-step explanation:

Triangles are congruent by SAS postulate.

Answer:

212/100

Step-by-step explanation:

Answer:

2.12 (im so sorry if its wrong)

The value of the initial height of the sunflower before it was planted is 11 units.

A linear equation in two variables is one with two variables and the highest power of a variables is one.

Now, for the stated question;

The height of a sunflower growing in Giulia's garden is shown by the equation:

H = 0.8D +11

The number D represents the number of days since it has planted.

Now, as the initial height of the sunflower is asked before was planted.

Then, the number of days will be zero;

Put D = 0 in the equation;

H = 0.8x0 +11

H = 11

The value of the sunflower's initial height before planting is 11 units.

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Hey there!

PEMDAS simply means (the OVERALL question answer)

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction

Here’s an example

24 - 4^2 + 2 * 4

= 24 - 16 + 2 * 4

= 24 - 16 + 8

= 8 + 8

= 16

Thus, the answer for that equation is: 16

Often people remember PEMDAS by saying. (So, I’d advise you think of it like that way as well!)

• Please
• Excuse
• My
• Dear
• Aunt
• Sally

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

PEMDAS is the order that you solve a problem.

PEMDAS stands for:

Parenthesis

Exponents

Multiplication and Division

Addition and Subtraction

If you have an equation or expression that you need to solve, you solve it in this order. You do the parenthesis first, then you solve the exponents, then you do the multiplication and division from left to right, and last you do addition and subtraction from left to right.

In the equation

2 + 3 * 5,

first you would do 3 * 5 because multiplication is before addition.

2 + 15

Then you would do the addition to get the answer:

17.

Please give brainliest

Answer:

  no

Step-by-step explanation:

You want to know if it would be legal to drive 75 miles in less than an hour in a zone with a speed limit of 65 mi/h.

Speed is the ratio of distance to time. If Mrs. Thomas drove her 75 miles in exactly one hour, her speed would be ...

  rate = distance/time

  = (75 mi)/(1 h) = 75 mi/h

This rate would go up if the time goes down. It exceeds 65 mi/h, so would not be a legal speed.

Mrs. Thomas could not legally drive 75 mi in less than an hour.

Answer:

f =38

Step-by-step explanation:

f-3/4=5/6

f-3×6=5×4

f-18 =20

f =20+18

f =38

Answer:

9/10

Step-by-step explanation:

3 1/3 can be written as 10/3

then we have 3/10/3 we then have 3x3/10 which equals 9/10.

The missing lengths  in the triangles are h = 3/2√2 and b = 4√3

Triangle a and b

From the question, we have the following parameters that can be used in our computation:

A special right triangle

For a right triangle with an angle of 45 degrees

The measure of the leg is

h = Hypotenuse/√2

So, we have

h = 3/√2

Evaluate

h = 3/2√2

For the other triangle, we have

sin(60) = b/6

So, we have

b = 6/sin(60)

Evaluate

b = 4√3

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The mass of aluminum with a volume of 1.50 cm³ is 4.05 grams.

To find the mass of aluminum with a volume of 1.50 cm³, we can use the formula:

Mass = Density x Volume

Given that the density of aluminum is 2.7 g/cm³ and the volume is 1.50 cm³, we can substitute these values into the formula:

Mass = 2.7 g/cm³ x 1.50 cm³

Multiplying these values, we find:

Mass = 4.05 g

Therefore, the mass of aluminum with a volume of 1.50 cm³ is 4.05 grams.

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The 98% confidence interval for the population standard deviation σ, based on a sample of size 19 with a standard deviation of s = 9.4, is (7.15, 16.84).

To construct the confidence interval for the population standard deviation σ, we can use the chi-square distribution. Here are the steps:

Determine the degrees of freedom (df): For estimating the population standard deviation, the degrees of freedom is calculated as df = n - 1, where n is the sample size. In this case, n = 19, so df = 18.

Find the critical values: Since we want a 98% confidence interval, we need to find the critical values that correspond to a significance level of 0.01 on both tails of the chi-square distribution. Using a chi-square distribution table or a statistical software, we find the critical values to be 9.648 and 30.191 for the lower and upper tails, respectively.

Calculate the confidence interval: The confidence interval for σ is given by the formula:

(sqrt((n - 1) * s^2) / sqrt(X^2(df,α/2)), sqrt((n - 1) * s^2) / sqrt(X^2(df,1-α/2)))

where s is the sample standard deviation and X^2(df,α/2) and X^2(df,1-α/2) are the critical values from step 2.

Plugging in the values, we get:

(sqrt((18) * (9.4)^2) / sqrt(30.191), sqrt((18) * (9.4)^2) / sqrt(9.648))

(7.145, 16.838)

Round the confidence interval: Rounding the confidence interval values to at least two decimal places, we have (7.15, 16.84).

Therefore, the 98% confidence interval for the population standard deviation σ, based on the given sample, is (7.15, 16.84).

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Answer:

64 and 81

Step-by-step explanation:

8×8=64 and 9×9=81. 73 falls between these two numbers.

Answer:

x = 3

Step-by-step explanation:

4 ( x - 7 ) = -6x + 12

→ Expand brackets

4x - 28 = -6x + 12

→ Add 6x to both sides

10x - 28 = 12

→ Add 28 to both sides

10x = 30

→ Divide both sides by 10

x = 3

36.74098197 kg in 81 lbs. Likewise, the question how many pounds in 81 kilogram has the answer of 178.57443237 lbs in 81 kg.

81 kg * 2.2046226218 lbs / 1 kg= 178.57443237lbs

The weight of 81 kilograms is equivalent to 178.57443237 pounds (81kg = 178.57443237lbs). It is simple to convert 81 kg to lb. Simply use our calculator above or the method to convert 81 kg to pounds. To convert 81 kg to pounds, multiply the kilogram mass by 2.2046226218. The formula for converting 81 kilograms to pounds is [lb] = 81 * 2.2046226218. Thus, 81 kilos in pounds are 178.57443237 pounds.

One pound is about equivalent to 0.45359237 kilos (kg). The pound to kilogram conversion is accomplished by multiplying the provided pound value by 0.45359237. In addition, one kilogram is about equal to 2.2046226218 pounds.

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The amount of neurotransmitter released from the parasympathetic ganglion is acetylcholine.

The parasympathetic nervous system is part of the autonomic nervous system which helps to regulate involuntary bodily functions such as heart rate, digestion and other processes.

The parasympathetic nervous system is responsible for calming the body and restoring it to its resting state. Parasympathetic ganglia are clusters of neurons that receive and transmit nerve signals from the brain to the organs and muscles.

The amount of neurotransmitter released from these ganglia is acetylcholine, which helps to slow the heart rate and promote relaxation.

The parasympathetic nervous system is part of the autonomic nervous system which helps to regulate involuntary bodily functions such as heart rate, digestion and other processes.

The parasympathetic nervous system is responsible for calming the body and restoring it to its resting state. Parasympathetic ganglia are clusters of neurons that receive and transmit  signals from the brain to the organs and muscles.

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When we round 742396 to four significant digits, then we get the answer of 742400

What we do is circle the first four digits on the left which are the 7,4,2, and 3. That last 3 will bump up to a 4 because we round up to the nearest hundred (due to the next digit being a 9, which is greater than 5).

Put another way, 742396 is closer to 742400 than it is to 742300. The zeros in 742400 are not significant.

---------------------------------------------

When we round 742396 to two significant digits, then we get the answer 740000

This time, we only keep the 7 and the 4 as our two important digits. Everything else becomes a 0 which isn't significant. No rounding happens since the 2 after the 4 isn't larger than five. I.e. the number 742396 is closer to 740000 than it is to 750000

---------------------------------------------

Rounding 0.07284 to three significant digits gets us to the answer 0.0728

We drop the 4 at the end because the 7,2, and 8 take up the three digits we want to keep. The two zeros are not significant.

---------------------------------------------

Rounding 0.07284 to two significant digits gets us the answer 0.073

We keep the 7 and 2 as our two important digits, but bump that 2 up to a 3 because the next digit over is larger than five.

Answer:

Step-by-step explanation: 742396 to four significant digits =7424

742396 to two significant digits =74

0.07284 to three significant digits =0.0728

0.07284 to two significant digits =0.073

Hope it helps!

Here's what I got

B. √5

Ac. 100

2x²+25x+50

a=2 b=√5 c=50

ac=2•50=100

B=√5

ac=100

Answer:

Chloe will refill the bird feeder every 11 weeks.

Step-by-step explanation:

Since Chloe has a bird feeder in her yard, which when it is full of bird seed, it weighs 1234 pounds, and the birds eat 112 pounds of bird seed each week, since she refills the bird feeder when it weighs less than 3 pounds, to determine which equation represents how many weeks, W, it will take until Chloe refills the bird feeder, the following calculation must be performed:

(1234 - 3) / 112 = W

1231/112 = W

10.99 = W

So, Chloe will refill the bird feeder every 11 weeks.

Answer:

v=99

Step-by-step explanation:

This is somewhat like a ratio problem. So, when v is 36, g is 4. We can simplify this. So, if we divided g by 4 we get one, and if we divide v by 4 we get 9. So, we have 1:9 ratio of g to v. If g is 11, then we multiply the 1 by 11 and the 9 by 11 also. Therefore, v is 99

Answer:

If real GDP in a particular year is $80 billion and nominal GDP is $240 billion, the GDP price index for that year is: 300.

Step-by-step explanation:

Among the 2,598,960 possible 5-card poker hands from a standard 52-card deck, there are 259,896 hands that contain at least one ace.

There are a total of 2,598,960 5-card poker hands. Here is how to figure out the total number of possible hands:

Choosing the first card leaves 52 choices. Choosing the second card leaves 51 choices. Choosing the third card leaves 50 choices. Choosing the fourth card leaves 49 choices. Choosing the fifth card leaves 48 choices. Therefore, the total number of 5-card poker hands is:

52 x 51 x 50 x 49 x 48 = 2,598,960

There are 4 aces in the deck. The number of ways to choose 1 ace is 4C1 = 4.

The number of ways to choose 2 aces is 4C2 = 6.

The number of ways to choose 3 aces is 4C3 = 4.

The number of ways to choose 4 aces is 4C4 = 1.

Therefore, the total number of 5-card poker hands that contain at least one ace is:

4C1 x 48C4 + 4C2 x 48C3 + 4C3 x 48C2 + 4C4 x 48C1 = 1,302,540

Conclusion: Among the 2,598,960 possible 5-card poker hands from a standard 52-card deck, there are 259,896 hands that contain at least one ace.

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Answer:

40

Step-by-step explanation:

you can multiply 88 by 5/11 to get 40

Answer:

7

Step-by-step explanation:

a^3 = 2^3 = 8

b^3 = -3^3 = -27

(8 - (-27))/5= (8+27)/5 =35/5=7

Answer:

slope: 150

y-intercept: 250

y= 150x+250

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

:) hope this helps