Find the​ mean, u, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. n=​676; p=0.7

Answers

Answer 1

Answer:

\(\mu=473.2\)

Step-by-step explanation:

Binomial Distribution

The binomial distribution is commonly used to model the number of successes in a sample of size n drawn with replacement from a population of size N.

The mean value of a binomial distribution is given by:

\(\mu=np\)

Where b is the number of trials and p is the success probability for each trial.

We need to find the mean value with parameters n=676 and p=0.7, thus:

\(\mu=676\cdot 0.7\)

\(\boxed{\mu=473.2}\)


Related Questions

Suppose that the demand of a certain item is x=-0.7p+10.
Evaluate the elasticity at 6.

Answers

The item is an inelastic good at a price of 6 because it is negative and have a demand of -0.71.

What is the item's demand if elasticity is at 6?

The formula for elasticity of demand is Elasticity of demand = (% change in quantity demanded) / (% change in price)

The initial quantity demanded at a price of 6 and the quantity demanded at a slightly different price must be know.

Let say Initial quantity demanded is:

x = -0.7(6) + 10

x = 5.8

Assume price changes slightly to 6.01, which gives us a new quantity demanded of x:

= -0.7(6.01) + 10

= 5.793

The % change in quantity demanded will be:

= [(new quantity demanded - initial quantity demanded) / initial quantity demanded] x 100%

= [(5.793 - 5.8) / 5.8] x 100%

= -0.12%

As price has changed from 6 to 6.01, we can calculate the percentage change as follows:

% change in price = [(new price - initial price) / initial price] x 100%

= [(6.01 - 6) / 6] x 100%

= 0.17%

Elasticity of demand = (% change in quantity demanded) / (% change in price)

= (-0.12% / 0.17%)

= -0.71

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Tính tích phân sau bằng cách dùng tọa độ cực I=∫∫ \(\frac{1}{\sqrt{x^{2} +y^{2} } }\)dxdy R là miền nằm trọg góc phần tư thứ nhất thỏa mãn 4\(\leq x^{2} +y^{2} \leq 9\)

Answers

It sounds like R is the region (in polar coordinates)

R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}

Then the integral is

\(\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}\)

rina is climbing a mountain. she has not yet reached base camp write an iequality to show the reaming distance d in feet she must climb to reach the peak

Answers

Answer:

Let b be the distance in feet to base camp and p be the distance in feet to the peak. Then, the remaining distance Rina must climb to reach the peak is:

Rina's distance = p - b

Since Rina has not yet reached base camp, we know that b > 0. Thus, the inequality to show the remaining distance d in feet she must climb to reach the peak is:

p - b > 0

Step-by-step explanation:

A vehicle can travel 132 km with 12 litres of petrol. What is the petrol consumption in km/litre?

Answers

35 litres consumption

Answer:

The amount of kilometers per liter is in terms on fuel consumption, the range in kilometers that a vehicle can travel while consuming one liter of gas

Step-by-step explanation:

help pleaseee geometryyy

help pleaseee geometryyy

Answers

Step-by-step explanation:

angle ABE=angle EBC

2x+20=4x-620+6=4x-2xx=26/2X=13

stay safe healthy and happy.

HELP ME!!!!!

Solve. −n/2 + 3/8 = −6 7/8 Enter your answer as a mixed number in simplest form in the box.

Answers

You subtract the 3/8 to the other side of the equation, and since it’s negative you add it on to the 7/8 and get 10/8. Then you take a whole out and add it to the 6, giving you -7 2/8. To get rid of the 2 under the variable, you multiply it to both sides and cancel out the 2 in the fraction with the variable. You get -14 4/8 on the other side. You then simplify to - 14 1/2. To get rid of the negative on the variable you just divide both sides by -1.

Your answer should be n=14 1/2. Hope this helped.

If f(x) = -x³ + x² + x, find f(-3).

Answers

Answer:

33

Step-by-step explanation:

Substitute f(-3) in the problem and you'll get f(-3) = -x³ + x² + x.

Substitute the given value into the function and evaluate.

Answer:

33.

Step-by-step explanation:

f(x) = -x³ + x² + x.

f(-3) = -(-3)³ + (-3)² + (-3)

= -(-27) + (9) - 3

= 27 + 9 - 3

= 36 - 3

= 33.

Hope this helps!

The width of a rectangle is 4 cm and its perimeter is 26 cm. What is the perimeter of a square has the same area as the rectangle​

Answers

Answer:

length = 9 cm

Step-by-step explanation:

perimeter = p =26 cm

width = w=  4 cm

perimeter of a rectangle= 2*w+2*L

L= length

so we have:

26 = 2*(4) +2*L

26= 8 +2L

26-8 = 2L

18 = 2L

L= 18/2

L =9 cm = length

Mika taught her sister the steps for dividing a decimal by a decimal. Which instructions are correct? 1. Multiply the divisor by a multiple of 10 to create an integer divisor. 2. Multiply the dividend by the same multiple of 10 as step 1. 3. Divide, and apply the rules for dividing signed numbers. 1. Multiply the dividend by a multiple of 10 to create an integer. 2. Multiply the divisor by the same multiple of 10 as step 1. 3. Divide, and apply the rules for dividing signed numbers. 1. Divide the divisor by a multiple of 10 to create an integer divisor. 2. Divide the dividend by the same multiple of 10 as step 1. 3. Divide, and apply the rules for dividing signed numbers. 1. Divide the dividend by a multiple of 10 to create an integer. 2. Divide the divisor by the same multiple of 10 as step 1. 3. Divide, and apply the rules for dividing signed numbers.

Answers

Answer: its A

1. Multiply the divisor by a multiple of 10 to create an integer divisor.

2. Multiply the dividend by the same multiple of 10 as step 1.

3. Divide, and apply the rules for dividing signed numbers.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Two digits are selected with replacement from the digits 1, 2, 3, 4, 5, and 6.
How many possibilities are there for the first digit?

Answers

There are six possibilities for the first digit, as any of the six digits can be selected with replacement.

What is principle of counting?

A fundamental combinatorial rule called the principle of counting, sometimes referred to as the counting principle or multiplication principle, enables us to determine the total number of outcomes in a series of occurrences. According to the principle, there are m n methods to perform both events sequentially if we have m ways to perform one event and n ways to perform another.

Consider that the numbers 1, 2, 3, 4, 5, and 6 are all distinct and equally likely to be chosen in order to understand why. When we choose a digit with replacement, it indicates that, regardless of the digits that were previously chosen, we can choose any of the six digits on the initial draw. Thus, the first digit has six potential values.

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What is the solution to |x − 4| ≥ 7? PLEASE HELP ME I NEED TO GRADUATE

A.
-3 ≤ x ≤ 11
B.
-11 ≤ x ≤ 3
C.
x ≥ 11 or x ≤ -3
D.
x ≥ 3 or x ≤ -11

Answers

Answer:

  C.  x ≥ 11 or x ≤ -3

Step-by-step explanation:

This inequality can be resolved into two:

  -7 ≥ x -4  or  x -4 ≥ 7

Adding 4 to the first one of these gives ...

  -3 ≥ x   ⇔   x ≤ -3

Adding 4 to the second of the inequalities above gives ...

  x ≥ 11

The full solution is then ...

  x ≥ 11 or x ≤ -3 . . . . . matches choice C

______

Additional comment

You can see in the attachment that when the value of the absolute value expression is supposed to be greater than some number, the solution set will have two disjoint parts. That means the answer expression must include "or", eliminating choices A and B.

__

When you are given the inequality in the form ...

  |f(x)| ≤ c . . . . . note "less than ..."

It can be resolved to the compound inequality ...

 -c ≤ f(x) ≤ c

When the inequality symbol points the other way ("greater than ..."), this sort of resolution doesn't really make sense. (You can do it, but you need to recognize the nonsense involved. Your teacher may not appreciate this "work".) In the present case, that would look like ...

  -7 ≥ x -4 ≥ 7

When you add 4 to all parts of this, it becomes ...

  -3 ≥ x ≥ 11

Recognizing the nonsense in this expression, you can rewrite it in two parts the way it should be written:

  -3 ≥ x OR x ≥ 11

What is the solution to |x 4| 7? PLEASE HELP ME I NEED TO GRADUATE A. -3 x 11B. -11 x 3C. x 11 or x -3D.

PLSsssssssssssssssssssssssssssssss need help

Answers

Answer:

yr question is not here!!!!!!!!!!

Where’s your question?

Find the total area of the irregular polygon shown? * m 11 m 36 sqm 84 sq.m 88 sqm​

Find the total area of the irregular polygon shown? * m 11 m 36 sqm 84 sq.m 88 sqm

Answers

Answer:

100

Step-by-step explanation:

Split it into 3 different rectangles, find the area of each, and add them together.

Rectangle 1: length=11   width=4    11×4=44

Rectangle 2: length=11-9=2   width=6    2×6=12

Rectangle 3: length=11   width=4    11×4=44

44+12+44=100

Find the total area of the irregular polygon shown? * m 11 m 36 sqm 84 sq.m 88 sqm

Picture included!!! Please help! Suppose a = 10 and b = 24. Give the value of each of the following. Give answers as integers or rounded to 2 decimal places as appropriate.

Picture included!!! Please help! Suppose a = 10 and b = 24. Give the value of each of the following.

Answers

Answer:

A = 22.62°

B = 67.38°

c = 26

Step-by-step explanation:

\(a^2+b^2=c^2\\10^2+24^2=c^2\\100+576=c^2\\676=c^2\\26=c\)

\(\sin A=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{10}{26}\\\\A=\sin^{-1}(\frac{10}{26})\\\\A\approx22.62^\circ\)<-- You can also use other trig ratios

\(B=180^\circ-(90^\circ+22.62^\circ)=180^\circ-112.62^\circ=67.38^\circ\)

There's no specific order in how to solve for A and B, so there may be more than one way to approach these solutions.

A water trough is 10 m long and has a cross-section in the shape of an isosceles trapezoid that is 40 cm wide at the bottom, 90 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.1 m3/min, how fast (in m/min) is the water level rising when the water is 10 cm deep?

Answers

Answer:

Let's start by finding the volume of water in the trough as a function of its depth.

At a depth of h cm, the cross-sectional area of the water is an isosceles trapezoid with bases of length b1 = 40 + (h/5) cm and b2 = 90 + (h/2) cm, and height 50 cm. The average width of the trapezoid is (b1 + b2)/2 = 65 + (3h/10) cm. Therefore, the volume of water in the trough at this depth is:

V(h) = 10 m x [(65 + (3h/10)) / 100 cm] x h cm

Simplifying this expression, we get:

V(h) = (13/2000) h^2 m^3

Now, we can use the chain rule to find the rate of change of V with respect to time t, given that dV/dt = 0.1 m^3/min:

dV/dt = (dV/dh) x (dh/dt) = (26/2000) h (dh/dt)

At the moment when the water is 10 cm deep, we have:

h = 10 cm

dV/dt = 0.1 m^3/min

Plugging in these values, we get:

0.1 m^3/min = (26/2000) x 10 cm x (dh/dt)

Solving for dh/dt, we get:

dh/dt = 0.1 m^3/min / (26/2000) / 10 cm

dh/dt ≈ 0.192 m/min

Therefore, the water level is rising at a rate of approximately 0.192 m/min when the water is 10 cm deep.

Arrange and Write the Integers in Increasing Order
-13 9 -17 64 -20 -82

Answers

Answer:

-82, -20, -17, -13, 9, 64

Step-by-step explanation:

With positive numbers, larger numbers are greater than smaller numbers.

For example, 64 is greater than 9.

With negative numbers, ignore the negative sign. Then to compare numbers; the smaller numbers are greater.

For example, -20 is greater than -82.

Answer: -82, -20, -17, -13, 9, 64

Answer:

greatest to least: 64, 9, -13, -17, -20, -82

Least to greatest: -82, -20, -17, -13, 9, 64

Was this the way you wanted me to do it?

Step-by-step explanation:

The answer would be “Yes” right? Just double checking :)

The answer would be Yes right? Just double checking :)

Answers

Answer:

yes

Step-by-step explanation:

its correct because opposite sides are parallel

Answer:

yes

Step-by-step explanation:

Solve the system using elimination or substitution. Please help

Solve the system using elimination or substitution. Please help

Answers

The values of the system using elimination method is,

x = 4, y = 3 and z = -1.

Elimination method:

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

Given,

The given system of equations,

-4x + 6y - 2z = 4 -----------------(1)

-2x - 6y - 2z = -24 --------------(2)

x + 6y + z = 21 --------------------(3)

Here we need to solve this one by using elimination or substitution method.

Here we use the elimination method to solve this,

For that, first we have to add the equations (1) and (2),

Then we get,

=> (-4x + 6y - 2z) + (-2x - 6y -2z) = 4 + (-24)

=> -6x - 4z = -20 -------------------(4)

Now we have to add the equation (2) and (3),

Then we get,

=> ( -2x - 6y - 2z) + ( x + 6y + z) = -24 + 21

=> -x -z = -3 -------------------(5)

Now we have to multiply 6 with equation(5),

Then,

=> 6 x (-x - z) = 6 x -3

=> -6x -6z = -18 --------------------(6)

Now subtract equation (6) from equation (4),

Then,

=> (-6x - 6z) - (-6x - 4z) = -18 - (-20)

=> -6x -6z + 6x + 4z = -18 + 20

=> -2z = 2

=> z = -1

Apply the value of z on the equation (5),

=> -x - (-1) = -3

=> -x + 1 = -3

=> -x = -4

=> x = 4

Now apply the value of x and z on the equation (3),

Then we get,

=> 4 + 6y + (-1) = 21

=> 4 - 1 + 6y = 21

=> 3 + 6y = 21

=> 6y = 18

=> y = 3

Therefore, the solutions are x = 4 , y = 3 and z = -1.

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Line A has a slope of −3 . Line B has a slope of 4. Line C has a slope of 2.

Which line is closest to being horizontal?

Line A

Line B

Line C

I don't know.

Answers

Line C is closest to being horizontal.

Given,

Line A has a slope of −3.

Line B has a slope of 4.

Line C has a slope of 2.

To find the which line is closest to being horizontal?

Now, According to the question:

Slope of line A (m1) = -3

Slope of line B (m2) = 4

Slope of line C (m3) = 2

Slope of horizontal line = 0

Closest to being horizontal is given by l m l

For line A = l-3 l = 3

For line B = l4l = 4

For line C = l2l = 2

As 2 is smaller it is closest to horizontal

Hence, Line C is closest to being horizontal.

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how to solve this separable differential equation?​

how to solve this separable differential equation?

Answers

The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

What is a differential equation?

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.

The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).

Now, multiplying both sides by dx we,

\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).

Dividing both sides by \(2^{\sqrt{x}}\) we have,

\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).

\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

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A fence with 2 gates in it surrounds a lion enclosure.

Each gate is 4 m wide.
an image

What is the length of the fence around the enclosure not including the gates?

Answers

The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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a situation for Y=5x+4

Answers

if you need to write one you could Carl charges 5$ an hour for ice skating plus a 4$ skates fee

Four racers are racing on a track.
Raheem covers 26%
of the track, Lila covers 38
of the track, Khalid covers 0.3
of the track, and Juanita covers 0.24
of the track.

List the people in order by the distance on the track each person covers from least to greatest.

Four racers are racing on a track.Raheem covers 26% of the track, Lila covers 38 of the track, Khalid

Answers

The rank of the proportions covered on the track, from least to greatest, are given as follows:

Juanita, Raheem, Khalid, Lila.

How to rank the proportions?

The proportions for each person are given as follows:

Raheem: 26% = 0.26.Lila: 3/8 = 0.375. (fraction to decimal, divide the numerator by the denominator).Khalid: 0.3.Juanita: 0.24.

Considering that 0.24 is the lowest proportion and 0.375 is the highest proportion, the rank is given as follows:

Juanita, Raheem, Khalid, Lila.

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answer the following questions in the picture

answer the following questions in the picture

Answers

a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

How to calculate interest ?

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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answer the following questions in the picture

write 7298 to nearest thousand?​

Answers

Answer:

Rounds down to 7000.

Step-by-step explanation:

What the meaning of statement this?

What the meaning of statement this?

Answers

This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.

The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:

∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))

The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.

The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.

The statement can be interpreted as follows:

"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."

In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.

It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.

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Simplify:
2
(
3
x
)
+
(
x
+
10
)
2(3x)+(x+10)

Answers

Answer:

7x+10

Step-by-step explanation:

2x(3x)+1x(x+10)

6x+1x+10

7x+10

Scott equipment produces high-quality soccer balls if the fixed cost per ball is three dollars when the company produces $15,000 what is the fixed cost per ball went to produce 22,500 boss assume that both volumes are in the same relevant

Answers

The fixed cost per ball went to $4.5 when the company produce 22,500.

what is the fixed cost per ball went to produce?

fixed cost per ball is three dollars when the company produces 15,000

fixed cost per ball went x to produce 22,500

So,

3 : 15000 = x : 22,500

3/15,000 = x/22,0/500

cross product

3 × 22,500 = 15,000 × x

67,500 = 15,000x

divide both sides by 15,000

x = 67,500 /15,000

x = 4.5

Therefore, the fixed cost per ball to produce 22,500 is $4.5

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If a car moves 12 km North,19 km east, and 12 km south, what is its displacement

Answers

Answer:

19 km east

Step-by-step explanation:

By going North 12 then south 12 the two cancel eachother out leaving only the eastern movement

Answer:

19 km, East

Step-by-step explanation:

I hope you get it right

Find the length of side AB. Round to the nearest hundredth inch.

Find the length of side AB. Round to the nearest hundredth inch.

Answers

The value of length of side AB is,

⇒ AB = 5 units

We have to given that;

The figure is shown a trapezoid.

Hence, By using Pythagoras theorem we get;

⇒ AB² = 4² + (5.25 - 2.25)²

⇒ AB² = 16 + 3²

⇒ AB² = 16 + 9

⇒ AB² = 25

⇒ AB = √25

⇒ AB = 5 units

Therefore, The value of length of AB is,

⇒ AB = 5 units

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Find the Volume and Surface Area of the right circular cylinder. 2 inches radius 1 inch talluse 3.14 for pi. Round to the nearest tenth 2. Discuss two real examples of source of measurement noise and the techniques to reduce the noise. (10 marks) what is the oxidation state of p in po4 3 Who was the first Queen of Nepal? Imagine that one of your teachers from your favorite subject wants to teach a new subject for the next few weeks. Your teacher will take suggestions, and then let all students vote on the new subject. What subject would you choose? Write a short essay to support your choice and to persuade the other students to vote for your choice. 200-400 words What is the source for established national objectives and health outcomes that guide health promotion in the united states?. what is the best way to ensure experimental conditions are balanced on all unconsidered charateristics A town in america has 2400 families and 4200 cars. What is the family : cars ratio? Count the least number of additions, multiplications anddivisions required to solve an LPP using the two phase method. Youmay assume the matrix A to have size m x n with m < n and m andn are mor How free was the free labor of the post-war era for black Americans. NATO has imposed economic controls on Russia for its invasion of Ukraine. Identify three of these economic controls and discuss their impacts on business and consumers in Russia. Outline three marketing strategies in response to these economic controls that may be adopted by international firms operating in Russia.(No more than 2 pages). Explain why each of the activities you participated in can be considered moderate or vigorous What is the solution for the system of linear equations shown in the graph?A: three fourths comma negative one fourthB: three halves comma negative one halfC: three halves comma negative three halvesD: negative one fourth comma three fourths The slope of the line that passes through the points (9,11) and (3,6) is what? Read story Theseus in the Minotaur: Explain the theme of this myth using ICE. I - Introduce topicC - Cite evidenceE - Explain what equation is equivalent to the given equation? what are the 5 principles of the constitution Which of the following equations is the translation 2 units left of the graph of y = Ixl?y = |x + 2|y = lx - 2|y = |xl-2 "The time, in hours, during which an electrical generator isoperational is a random variable that follows the exponentialdistribution with a mean of 150 hours.a) What is the probability that a generator of this type will be operational for 40 h? b) What is the probability that a generator of this type will be operational between 60 and 160 h? c) What is the probability that a generator of this type will be operational for more than 200 h d) What is the number of hours that a generator of this type will be operational with exceeds a probability of 0.10" Assume a stock trades at $92, the volatility of the stock is 26%, and the risk-free interest rate is 4.3%. What is the Rho of a $91 strike call option expiring in 142 days if the risk-free interestrate increases by 0.1%?