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4) The "random walk theory of stock prices holds that price movements in disjoint time periods are independent of each other. Suppose that we record only whether the price is up or down each year, and that the probability that our portfolio rises in price in any one year is 0.65.



a) What is the probability that the portfolio goes up for 3 consecutive years?



b) What is the probability that the portfolio's value moves in the same direction (either up or down) for 3 consecutive years?



c) What is the probability that the portfolio's value goes up for at least 1 of 3 years?​

The solution set for the pair of inequalities as given in the task content is; (-∞, -4) U (11, ∞).

It follows from the task content that the solution set of the pair of inequalities is to be determined.

Therefore, each inequality can be solved as follows;

-13 > 2x - 5;

-13 + 5 > 2x

-8 > 2x

-4 > x.

Also, the inequality 2x - 5 > 17 can be solved as follows;

2x > 17 + 5

2x > 22

x > 11.

Therefore, the solution set of the inequalities as given in the task content in interval notation is;

(-∞, -4) U (11, ∞).

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Answer:

First option

Step-by-step explanation:

→ Define domain

The set of x values a function can take

→ Identify

2 to negative infinity

Answer:We know that the dilation transformation of a figure either shrink or expand the original figure depending on the scale factor of the dilation.

As here we have scale factor=3>1.

Hence, the dilation  changes the original will expand the original figure.

Hence, each of the coordinate of a figure get multiplied by 3.

Hence, the co

ordinates of the image are given as:

i.e. A(0,0) → A'(0,0)

B(2,3) → B'(6,9)

C(1,-2) → C'(3,-6)

D(-3,-3) → D'(-9,-9)

Step-by-step explanation:

Answer:

212 feet fallen after 7 seconds

Step-by-step explanation:

You visit the Grand Canyon and drop a penny off the edge of the cliff. The distance the penny will fall is 32ft for the first second, 62ft the next second, 92ft the third second, and so on. How far will the penny have traveled after 7 seconds?

if 32 ft for 1 second

if 62 ft for 2 second

if 92 ft for 3 second

We see that the penny from second 1, falls an addition 30 ft/s.

equation: 32 + 30 (t - 1)

when t = 7 seconds:

32 + 30 (7 - 1)

32 + 30 (6)

32 + 180

= 212 feet fallen after 7 seconds

The sentence that describes a benefit of short-term disability insurance is D. It provides 40% to 60% of the policyholder’s income for up to one year.

Short-term disability insurance is meant to cover a portion of a person's wages in the event that they get injured such that they are unable to work and earn a salary in that time.

The short-term disability insurance policies these days generally cover about 40% to 60% of the income that the policyholder would have made in one year and so has less premiums.

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Answer:

domain: [tex](-\infty, \infty)[/tex]

range: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

You can put any real number into [tex]x[/tex] and get any real number out oft the function [tex]f(x)[/tex]

We are going to use these properties :

1. (a^m)^n = a^mn
2. a^m x a^n = a^(m+n)
3. a^m : a^n = a^(m-n)

Using the first property, (3^6)^5 = 3^(6x5) = 3^30

Using the second property :
9 = 3^2
-> 9 x 3^7 = 3^2 x 3^7 = 3^(2+7) = 3^9

Therefore, it is simplified down to 3^30 : 3^9

Finally, we will use the third property :
3^30 : 3^9 = 3^(30-9) = 3^21

Step-by-step explanation:

we have a basic fee of $40 just for renting the car.

and we rent it for 2 days for $30 per day.

so, this costs

40 × 2×30 = 40 + 60 = $100

The quantity of sugar Isabelle would need to make 4 1/5 batches of cookies is 21 cups of sugar

From the question, we are to determine the quantity of sugar that Isabelle would need to make the given number of batches. The number of batches Isabelle wants to make is 4 1/5 batches.

From the given information, Isabelle's lemon cookie recipe calls for 5 cups of sugar. If 1 batch of the lemon cookie calls for 5 cups of sugar

Then, 4 1/5 batches of the lemon cookie will call for 5 × 4 1/5 cups of sugar 5 × 4 1/5

= 5 × 21/5= 21

Hence, Isabelle will need 21 cups of sugar

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Answer:

a) 6 km

b) 66 km

Step-by-step explanation:

a) According to the graph:

To find how much further, subtract the distance cycled those two days:

22 - 16 = 6 km

b) The three days he cycled the most are the three days with the highest lines on the graph, so that would be:

Add them all up to find the total distance cycled:

24 + 22 + 20 = 66 km

The distance covered by the car is 264cm.

Here we have to find the distance covered by the car.

Information provided:

Diameter (d) = 5.6cm

radius(r) = 5.6/2

             = 2.8cm

Rotation = 15 times

Formula to find the circumference of the tire:

Circumference = 2πr

                        = 2 × 22/7 × 2.8

                        = 17.6cm

This is the distance covered by the tire in one rotation.

Distance covered after 15 rotations = 15× 17.6

                                                         = 264 cm

Therefore distance covered is 264 cm.

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24 groups of participants would be needed to partially counterbalance a within-subjects experiment with three treatment conditions.

Given that;

How many groups of participants would be needed to partially counterbalance a within-subjects experiment with three treatment conditions.

Every participant in an experiment is exposed to every treatment or condition in a within-subject design, sometimes referred to as a repeated measures design.

The term "between-subjects design" is comparable to this within-subjects design. People are solely assigned to one treatment in a between-subjects design. As a result, one therapy would be given to one group of volunteers, while a different treatment would be given to another group. After that, the variations between the two groups would be contrasted.

24 groups would be required for a perfectly counterbalanced design for even four treatment conditions. This would obviously be impracticable because a large enough sample size would be required to conduct such an experiment.

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Answer:

  a(n) = 10 -3n

Step-by-step explanation:

You want the explicit formula for the sequence recursively defined by a(1)=7, a(n)=a(n-1) -3.

The recursion relation tells you that each term is 3 less than the one before. That is, the common difference between terms is -3.

A sequence with a common difference is an arithmetic sequence. The formula for the n-th term is ...

  a(n) = a(1) +d(n -1)

where a(1) is the first term and d is the common difference.

The first term is given by the recursive definition as 7. Then the explicit formula is ...

  a(n) = 7 -3(n -1)

This can be simplified to ...

  a(n) = 10 -3n

The maximum area that the material would cover is 640, 000 square yards

A rate of change is a rate that describes how one quantity changes in relation to another quantity. If x is the independent variable and y is the dependent variable, then

rate of change = change in y / change in x

if 3200 yards was used for fencing, then 3200 yards is perimeter

and perimeter of a rectangle = 2( L + B)

so that,

2(L + B) = 3200

L + B = 1600

express L in terms of B

L = 1600 - B

Area(A) = L X B

A = L X B

substitute L = 1600 -B

A = (1600 - B) x B

multiply out

A = 1600B - [tex]B^{2}[/tex]

for maximum area,

[tex]\frac{dA}{dB}[/tex] = 0

But dA / dB = 1600 - 2B

1600 - 2B = 0

2B =1600

B = 1600/2

B = 800 yards

L = 1600 - B

L = 1600 - 800

L = 800 yards

Area = L X B

A = 800 x 800

A = 640,000 square yards

In conclusion, he maximum area is  640,000 square yards and the dimensions are 800 yards by 800 yards

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Answer:

A. [tex]y=-3x+16[/tex]

B. [tex]y=3x+5[/tex]

C. [tex]y=\frac{1}{3}x+1[/tex]

Step-by-step explanation:

A.

[tex]y-10=-3(x-2)[/tex]

[tex]y-10=-3x+6[/tex]

[tex]y=-3x+16[/tex]

B.

[tex]y-2=3(x+1)[/tex]

[tex]y-2=3x+3[/tex]

[tex]y=3x+5[/tex]

C.

[tex]y-2=\frac{1}{3}(x-3)[/tex]

[tex]y-2=\frac{1}{3}x-1[/tex]

[tex]y=\frac{1}{3}x+1[/tex]

The total amount paid in dollars per hour is $19.

Unitary Method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

It is given that the total amount given by the uncle is $133 for the work done by Barn for 7 hours.

We have to find the amount paid per hour.

Total amount given = $133

Number of hour Barn work = 7 hours

Amount paid per hour = 133/ 7

= $ 19

Therefore the amount paid per hour is $19.

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Answer:

7^{2} + x^{2} = 16^{2}

49+x^2=256

x^2=207

x=14.387=14

Answer:

14 units

Step-by-step explanation:

To find the length of the other leg of a right triangle, where one leg is 7 units long and the hypotenuse is 16 units long, use Pythagoras Theorem.

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the legs.  

Let the legs of the right triangle be "a" and "b", and the hypotenuse be "c". Therefore:

[tex]\begin{aligned}a^2+b^2&=c^2\\a^2+7^2&=16^2\\a^2+49&=256\\a^2+49-49&=256-49\\a^2&=207\\\sqrt{a^2}&=\sqrt{207}\\a&=14.3874945...\\a&=14\;\sf(nearest\;whole\;number)\end{aligned}[/tex]

Therefore, the length of the other leg is 14 units (rounded to the nearest whole number).

The series expansion for e z 1 z up to z 5 is obtained by multiplying the Maclaurin series for e z and 1 1 z. For |z| 1, this series converges.

The Maclaurin series for e^z is:

e^z = 1 + z + z^2/2! + z^3/3! + z^4/4! + ...

The Maclaurin series for 1/1-z is:

1/(1-z) = 1 + z + z^2 + z^3 + z^4 + ...

Multiplying these two series together gives:

e^z/(1-z) = (1 + z + z^2/2! + z^3/3! + z^4/4! + ...)(1 + z + z^2 + z^3 + z^4 + ...)

= 1 + (1+z) + (z + z^2/2! + z^2) + (z^2/2! + z^3 + z^3/3!) + (z^3/3! + z^4 + z^4/4!) + ...

= 1 + z + 2z^2 + 3z^3 + 5z^4 + ...

This series converges for |z| < 1

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Answer: 2 + 0.3 +  0.05 + 0.006

Step-by-step explanation: You just have to technically un add the stuff of you understand it that way.

Hope i helped you

Have a great day Darling

Using distributive property, the simplified form of (5x - 7)(4x + 1) is 20x^2- 23x - 7.

In the given question we have to solve the given expression.

The given expression is (5x - 7)(4x + 1).

To simplify the given expression we use the distributive property.

According to property; a(b+c) = ab+bc

Now simplifying the expression;

(5x - 7)(4x + 1)=5x(4x + 1) - 7(4x + 1)

(5x - 7)(4x + 1)=(5x*4x + 5x*1) - (7*4x + 7*1)

(5x - 7)(4x + 1)=(20x^2 + 5x) - (28x + 7)

Simplifying

(5x - 7)(4x + 1)=20x^2+5x -28x - 7

(5x - 7)(4x + 1)=20x^2- 23x - 7

The simplified form of (5x - 7)(4x + 1) is 20x^2- 23x - 7.

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The simplified expression of the radical expression given as 5√7/√35 is 7

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

5√7/√35

The above expression is a fraction and at the same time it is a radical expression

The denominator of the fraction is √35

So, we start by rationalizing the expression by the fraction

This is represented as

5√7/√35 = 5√7/√35 * √35/√35

Evaluate the products of the numerator

So, we have the following representation

5√7/√35 = 5√245/√35 * 1/√35

Evaluate the products of the denominator

So, we have the following representation

5√7/√35 = 5√245/35

Simplify the fraction

This gives

5√7/√35 = √245/7

Simplify the fraction

5√7/√35 = 7√5/7

So, we have

5√7/√35 = 7

Hence, the simplified expression is 7

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The events “blonde hair” and “brown eyes” are not independent.

What are independent events?

The term "independent events" refers to those whose occurrence is not reliant on another event.

When two events A and B are independent then the intersection of the two events is equal to zero. i.e. They do not have any element in common.

But from the given table we can see that the intersection of the events of  "blonde hair" and "brown eyes" exists.

Therefore, the events "blonde hair" and "brown eyes" are not independent.

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Using Combination formula, total 2,24,070 ways to make a math team of 14 selected students in which consist of 8 seniors and 6 juniors.

We have following information,

total number of seniors in math club = 15

total number of juniors in math club = 11

total number of students in math club = 26

A math team of 14 students be choosen from maths club such that it consists 8 seniors and 6 juniors .

Number of ways to choose 8 seniors out of 15 seniors = ¹⁵C₈ = 485

Number of ways to choose 6 juniors out of 11 juniors = ¹¹C₆ = 462

Number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors

= 485 × 462 = 2,24,070

Hence, the number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors is 2,24,070..

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Answer: To find the vertex: use formula x= -b/2a.

plug x into the given equation to find y value.

now you have (h,k)

find a point on the graph and plug in to the vertex form equation to find "a"

Step-by-step explanation:

Answer:

Step-by-step explanation: step 5
they have not proved the ASA postulate i.e. they the are missing a step to proove angle BEF = angle CED (Verticle angles)
so, correct answer is step number 5 and reason 'missing prior step'

Answer:

0, 6 * 0,6 = 0.36

Step-by-step explanation:

Keyword is AND.First AND second matches both. It means you need to use *.

The probability of winning both matches is 0.36 or 36%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

Since the outcome of each match is independent, we can use the multiplication rule of probability to find the probability of winning the next two matches:

P(win both matches) = P(win first match) x P(win second match)

The probability of winning a single match is given as 0.6.

Therefore, the probability of winning the first match is 0.6.

Now, assuming you won the first match, you still have a probability of 0.6 of winning the second match.

Therefore, the probability of winning both matches is:

P(win both matches) = P(win first match) * P(win second match)

= 0.6 x 0.6

= 0.36

Therefore,

The probability of winning both matches is 0.36 or 36%.

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The graph has no vertex

The transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

However, the graph has no maximum or minimum

This means that there is absence of a vertex in the graph

Here, we have:

This transformation can be represented as (x - 4, y - 2)

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