Which of the following situations involve a continuous random variable? There may be more than one. Do not solve any of them.- The average rainfall in Connecticut during the month of November is 4.53 inches. Assuming November rainfall in Connecticut is normally distributed and there is a 50% chance of less than 3.5 inches of rain, estimate the standard deviation.- An experiment consists of rolling 10 dice and averaging the numbers rolled. What is the probability this average will be greater than 5?- 500 people were surveyed on the number of computers they have in their home. 87 reported having more than 3, 152 reported having 3, 122 reported having 2, 96 reported having 1, 25 reported having 0, and 18 did not report. If three of the surveyed people are selected at random, what is the probability of one of them having no computer at home?- Southwest flight 1533 from Bradley International Airport to Baltimore-Washington International Airport has an average flight time of 1.137 hours with a standard deviation of 5.212 minutes. What is the probability flight 1533 will last between 1.1 and 1.2 hours?

The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.

In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.

The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.

To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.

Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.

As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.

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Answer: ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

-3√2

The correct answers are:

Functions are expressions separated by an equal sign. They have both dependent and independent variables.

* Lets explain how to solve the problem

- The table of the function has two column

# First column labeled x with entries:

 -6 , 7 , 4 , 3 , -5

# Second column labeled f(x) with entries:

  8 , 3 , -5 , -2 , 12

∴ The ordered pairs of the function f(x) are:

 (-6 , 8) , (7 , 3) , (4 , -5) , (3 , -2) , (-5 , 12)

* Lets complete the missing

∵ The value of x in the first row is -6

∵ The value of f(x) in the first row is 8

∴ The function notation in the 1st row is f(-6) = 8

- The ordered pair given in the first row of the table can be

 written using function notation as f(-6) = 8

∵ The ordered pair whose x = 3 is (3 , -2)

∴ The value of f(x) when x = 3 is -2

∴ f(3) = -2

∵ The ordered pair whose f(x) = -5 is (4 , -5)

∴ The value of x when f(x) = -5 is 4

∴ f(x) = -5 when x is 4

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Insured = 72%.

Uninsured = 28%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Here is a table classifying 116 thousand US households (in thousands) in

2013 by tenure and insurance status:

Insurance status      Owns home   Rents home

Insured                              71                13

Uninsured                         27               5

Total house = 71 + 13 + 5 + 27 = 116

Insured = (71 + 13)/116 = 72%.

Uninsured = (5 + 27)/116 = 28%.

Therefore, 72% = insured and 28% = uninsured.

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Note that the limit of the expression as x approaches infinity is 1/2.

start by multiplying both the numerator and denominator by the conjugate  expression

√ (x ² - 9x + 1) + x,

this will eliminates the root in the numerator

lim x->∞ [(√(x ² - 9x + 1) - x)  * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)

Expanding the numerator

lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)

Simplifying further:

lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)

we can see that the 1/x ² term approaches zero, and the expression simplifies to

lim x->∞ [(1 - 0)]  / (√(1 - 0) + 1)

= 1/2

So it is correct to state that the limit of the expression as x approaches infinity is 1/2.

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Answer:

bob goes 28 miles in 2 hours while traveling to the store. how many miles does he drive per hour. the answer is 14 miles per hour

Answer:

x = 15

Step-by-step explanation:

create a proportion:   x + 10 = x + x + 10

                                       5               8

cross-multiply:  8(x + 10) = 5(2x + 10)

                          8x + 80 = 10x + 50

                                  80 = 2x + 50

                                  30 = 2x

                                   15 = x

Answer:

the volume of the square pyramid is 2430 cubic cm

Answer:

1296 cm³

Step-by-step explanation:

V = a² x [√s²- (a/2)²] / 3

a = 18 cm

s = 15 cm

V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3

V = 324 x (√144/3) = 1296 cm³

Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

If the length of the leg of the isosceles triangle is 17 cm and the base is 16 cm then the length of altitude to the base is  15cm .

An Isosceles triangle is defined as a triangle in which any two side are of  equal length .

The Length of the leg is = 17cm ,

the base of the triangle is = 16cm ;

let the length of the altitude to the base be = x cm ,

The altitude to the base of the triangle divides it into two right angle triangle.

So , in one of the right angle triangles, Base = 16/2 = 8 cm

the Hypotenuse of triangle = length of the leg = 17 cm

By Applying Pythagoras theorem,

we get ,

17² = 8² + x²   ,

289 = 64 + x² ,

x² = 289 - 64

x² = 225 ,

taking Square root(√) on both the sides ,

we get , x = 15 .

Therefore , the length of the altitude to the base is = 15 cm .

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To find the altitude of an isoceles triangle with a base length of 16 cm and a leg length of 17 cm, use the Pythagorean Theorem. Calculate 17² + 16² = c², then solve for c² to get c = √545 = 23.3 cm.

The altitude of the triangle can be found using the Pythagorean Theorem.

a² + b² = c²

17² + 16² = c²

289 + 256 = c²

545 = c²

c = 23.3 cm

(or)

17² + 16² = c² => 289 + 256 = c²

=> 545 = c²

=> c = √545 = 23.3 cm

The altitude of an isoceles triangle can be found by using the Pythagorean Theorem. The formula for the theorem is a² + b² = c², where a and b are the two sides and c is the hypotenuse, which is the altitude. In this situation, a is the leg length of 17 cm and b is the base length of 16 cm. Substituting these values into the equation gives 17² + 16² = c². Solving for c² gives c = √545 = 23.3 cm, which is the length of the altitude.

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Answer:

No they are not proportional

Step-by-step explanation:

They arent proportional because if they were on a graph they wouldnt have a straight line ... I'm in wrong lmk

Answer:

no its not proportainal

Step-by-step explanation:

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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Answer:

A

Step-by-step explanation:

If a constant is added to a variable then the graph gets shifted toward left and vice-versa. Then the graphs are shown below.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

The parabola is given below.

f(x) = x²

Then the parabolas with respect to the position of their vertices from left to right will be

1: y = f(x) = x²

2: y = f(x - 4) = (x - 4)²

3: y = f(x + 3) = (x + 3)²

4: y = f(x - 7) = (x - 7)²

5: y = f(x + 2) = (x + 2)²

6: y = f(x - 1/2) = (x - 1/2)²

The graph of the parabola is given below.

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Answer:

Jack = 30

Lacy = 15

Step-by-step explanation:

Let the age of Lacy be " x ".

Jack Is 2 times as old as lacy,

Age of Jack = 2 * Age of Lacy

Therefore,

Age of Jack = 2x.

8 years from now,

the age of Jack = 2x + 8

the age of Lacy = x + 8

8 years from now the sum of their ages will be 61,

2x + 8 + x + 8 = 61

2x + x + 8 + 8 = 61

3x + 16 = 61

3x = 61 - 16

3x = 45

x = 45 / 3

x = 15

The age of Jack

= 2x

= 2 * 15

= 30 years old.

The age of Lacy

= x

= 15 years old.

Hence,

Now,

the age of Jack is 30 years old.

the age of Lacy is 15 years old.

Answer:

2a^4 +12a

\(2 {a}^{4} + 12 { a}^{2} \\ \times \times \)

Answer:

C-D is: \(\mathbf{4b^4 -2a^b^2 -6b^4}\)

Step-by-step explanation:

We are given:

\(C = 7a^4+ + 5a^2b2 - 3b^4\\D=5a^4 + 7a^2b^2 + 3b^4\)

We need to find C-D.

Finding C-D we actually have to subtract D from C

So, finding C-D

\(C-D\\= 7a^4+ + 5a^2b2 - 3b^4-(5a^4 + 7a^2b^2 + 3b^4)\\=7a^4+ + 5a^2b2 - 3b^4-5a^4-7a^2b^2-3b^4\)

Now, combining the like terms.

Like terms are those that have same variables and exponents.

In our case, \(7a^4\: and\: 3b^4, 5a^2b^2\: and\: -7a^b^2, -3b^4\:and\:-3b^4\)

\(=7a^4 - 3b^4+5a^2b^2 -7a^b^2 -3b^4-3b^4\\=4b^4 -2a^b^2 -6b^4\)

So, we get C-D is: \(\mathbf{4b^4 -2a^b^2 -6b^4}\)

Answer: It is just 4

Step-by-step explanation: That means the absolute value of 4 and it is just 4

The equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

Let position vector of point P be:

p = 3 i + j + 2 k

Let position vector of point Q be:

q = i - 2 j - 4 k

So, PQ = Q - P

PQ = n = i - 2 j - 4 k - (3 i + j + 2 k)

n = i - 2 j - 4 k - 3 i - j - 2 k

n = - 2 i - 3 j - 6 k

The Equation of plane passing through point Q and perpendicular to PQ will be:

(r - q).n = 0

r n = q n

q n = (i - 2 j - 4 k) . (- 2 i - 3 j - 6 k)

q n = - 2 + 6 + 24

q n = 28

r n = 28

r (- 2 i - 3 j - 6 k) = 28

r (2 i + 3 j + 6 k) + 28 = 0

Therefore the equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

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Answer:

9

Step-by-step explanation:

f(x) = x•x

f(-3) = -3*-3

f(-3)= 9

Step-by-step explanation:

\( \underline{ \underline{ \text{Given}}} : \)

\( \underline{ \underline{ \text{To \: find}}} : \)

\( \underline{ \underline{ \text{Using \: pythagoras \: theorem}}} : \)

\( \boxed{ \sf{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }}\)

⤑ \( \sf{ Perpendicular = \sqrt{ {(Hypotenuse)}^{2} - {(Base)}^{2} } }\)

⤑ \( \sf{ \sqrt{ {(10)}^{2} - {(8)}^{2} } }\)

⤑ \( \sf{ \sqrt{100 - 64}} \)

⤑ \( \sf{ \sqrt{36}} \)

⤑ \( \boxed{ \sf{6\: units}}\)

\( \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{6 \: units}}}}}}}\)

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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Answer:

36

OR

12

?

Step-by-step explanation:

Area of Triangle:   \(\frac{3*4}{2} = 6\)

Volume:   6*6 = 36

Pyramid part confuses me.

volume of a pyramid:   \(\frac{1}{3}*B*H\) = \(\frac{1}{3}*6*6\) = 12

B = triangle area

H = height

Answer:

I am pretty sure it is when you have a sequence of numbers that you are subtracting or adding from by the same constant over and over

Step-by-step explanation:

an=a1+(n-1)d

d=common difference

an= the nth term in the sequence

a1 first term in the sequence. (Usually you can plug in 1, as the n, and work from there)

The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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