4. What is Probability?
(ii) State the axioms of probability
(iii)Two fair dice are thrown, what is the probability of getting
(a) the sum of 9
(b) two odd numbers
(c) two prime numbers
(d) two factors of 12
4c. What is Statistics?

Answer:

y = -x + 4

Step-by-step explanation:

The slope-intercept form is y = mx + b

4x + 4y = 16

4y = - 4x + 16

y = -x + 4

So, the answer y = -x + 4

The statement "70 decreased by twice chai’s height" as an expression is 70 - 2c

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

70 decreased by twice chai’s height

Represent chai’s height with c

So, we have the following representation

70 decreased by 2c

When the above statement is then represented as an expression, we have the following

Expression: 70 - 2c

Hence, the expression of the statement "70 decreased by twice chai’s height"  is 70 - 2c

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The numeric value of the function f(x) at x = 5 is given as follows:

f(5) = 74.75.

The second derivative of the function f(x) is given as follows:

f''(x) = 2x + 6sin(x).

Integrating the second derivative, the first derivative of the function is given as follows:

f'(x) = x² - 6cos(x) + K.

When x = 0, y' = 2, hence the constant K is given as follows:

2 = -6 + K

K = 8.

Hence:

f'(x) = x² - 6cos(x) + 8.

Integrating the first derivative, the function is given as follows:

f(x) = x³/3 - 6sin(x) + 8x + K.

When x = 0, y = 4, hence the constant K is given as follows:

K = 4.

Then:

f(x) = x³/3 - 6sin(x) + 8x + 4.

The numeric value at x = 5 is given as follows:

f(5) = 5³/5 - 6sin(5) + 8(5) + 4

f(5) = 74.75.

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The time it takes (1/x) + (1/(x + 5)) + (1/(4x + 20))

​

From the question,

Marla takes 5 hours more than Tom: M = T + 5

Bob takes 4 times as long as Marla: B = 4M

work is inversely proportional to the time hence

Tom: 1/T

Marla: 1/M

Bob: 1/B

When we express this,

Marla: 1/(T + 5)

Bob: 1/(4*(T + 5))

We would have to solve for the total work in a given hour

= (1/T) + (1/(T + 5)) + (1/(4*(T + 5))

In one hour, Tom cаn clеan 1/х оf thе building, Mаrlа cаn clеan 1/(x + 5) оf thе building, and Вob cаn clеan 1/(4х + 20) оf thе building.

then 1/T = 1/x

1/(T + 5) = 1/(x + 5)

1/(4*(T + 5)) = 1/(4x + 20)

The expression would be written as:

work in one hour = (1/x) + (1/(x + 5)) + (1/(4x + 20))

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Answer:

C

Step-by-step explanation:

Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.

To find the area of the greatest amount of floor that can be covered with carpet tiles, we need to figure out how many tiles can fit in that area. Since each tile has a side length of 1.5 feet, we can divide the grid into squares with side lengths of 1.5 feet to see how many tiles can fit.

Dividing the grid in this way, we can see that the area of each square is 2.25 square feet (1.5 ft x 1.5 ft). To find the maximum area that can be covered with whole tiles, we need to find the dimensions of the largest rectangle that can be formed using these squares.

In the grid, the longest side that can be formed using whole tiles is 9 squares long (13.5 feet), and the shortest side that can be formed using whole tiles is 7 squares long (10.5 feet). Therefore, the maximum area that can be covered with whole tiles is:

Area = Length x Width = 13.5 ft x 10.5 ft = 141.75 square feet

To find out how many tiles are needed to cover this area, we need to divide the area by the area of each tile:

Number of tiles = Area / Area of each tile = 141.75 sq ft / 2.25 sq ft per tile = 63 tiles

Therefore, Aisha and Jordan need 63 carpet tiles to cover the maximum amount of floor with the whole tiles.

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The values of θ for different conditions were calculated with the help of trigonometric functions.

Given that;

The difference in length of a spring on a pogo stick from its non-compressed length when a teenager is jumping on it after θ seconds can be described by the function,

f (θ) = 2 sin θ + √ 2

Hence, We can simplify as;

A) Function is,

f (θ) = 2 sin θ + √ 2

f (θ) = 2 sin θ + √ 2 = 0

2 sin θ + √ 2 = 0

2 sin θ = -  √ 2

sin θ = - 1/√2

θ = nπ ± π/4

Where, n = 1, 3, 5, 7, ...

So, At θ = nπ ± π/4 pogo stick's spring will be equal to its non compressed length.

2) If the angle was doubled, the function will look like this,

f (θ) = 2 sin 2θ + √ 2

f (θ) = 2 sin 2θ + √ 2 = 0

2 sin 2θ + √ 2 = 0

2 sin 2θ = -  √ 2

sin 2θ = - 1/√2

θ = nπ/2 + π/8

Where, n = 1, 3, 5, 7, ...

n = 1;

θ = π/2 + π/8

θ = 5π/8

n = 2;

θ = π + π//8

θ = 9π/8

Hence, Solutions are, 5π/8, 9π/8, ...

3) g (θ) = 1 - cos²θ + √2

g (θ) = sin²θ + √2

sin²θ + √2 = 2 sinθ + √2

sin²θ - 2 sinθ= 0

sinθ (sinθ - 2) = 0

sinθ = 0

θ = nπ

Where, n = 1, 3, 5, 7, ..

So, θ = nπ , the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.

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Answer:

Step-by-step explanation:

To solve this problem, we can use the multiplication principle of counting, which states that if there are k choices for one task and m choices for a second task, then there are k x m choices for both tasks combined.

In this case, we can apply this principle to each shelf of books, as there are different numbers of books on each shelf. For the first shelf, there are 12 choices, for the second shelf there are 18 choices, for the third shelf there are 25 choices, and for the fourth shelf there are 30 choices.

To choose one book from each shelf, we need to multiply the number of choices for each shelf together, which gives us:

12 x 18 x 25 x 30 = 16,200,000

Therefore, there are 16,200,000 ways to choose three books, one from each shelf, in the library.

The total number of ways of choosing three books , one from each shelf is given by A = 162,000 ways

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

There are 12 ways to choose a book from the first shelf, 18 ways to choose a book from the second shelf, 25 ways to choose a book from the third shelf, and 30 ways to choose a book from the fourth shelf

So , the total number of ways = 12 x 18 x 25 x 30

A = 162,000 ways

Hence , the combination is solved and there are 162,000 ways

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The equation of tangent line related to the parametric equations is equal to y = 3 · x - 22.

In this question we find the case of two parametric equations evaluated at t = - 1, whose tangent line equation must be found. Equation of the tangent line is introduced below:

y = m · x + b

Where:

First, determine the slope of the tangent line:

dx / dt = 1 + 2 · t

dx / dt = 1 - 2

dx / dt = - 1

dy / dt = 2 · t - 1

dy / dt = - 2 - 1

dy / dt = - 3

m = (dy / dt) / (dx / dt)

m = (- 3) / (- 1)

m = 3

Second, evaluate the parametric functions at t = - 1:

x = - 1 + (- 1)² + 8

x = 8

y = (- 1)² - (- 1)

y = 2

Third, determine the intercept of the tangent line:

b = y - m · x

(m = 3, x = 8, y = 2)

b = 2 - 3 · 8

b = 2 - 24

b = - 22

Fourth, write the equation of the tangent line:

y = 3 · x - 22

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The probability of picking L and another A with replacement is: 2/49

Probability of picking A and then another A with replacement is:  1/49

We are given the letter DALLAS.

There are a total of 7 letters. Thus, the probability of picking L is:

2/7

Probability of picking A after that with replacement is: 1/7

Thus, probability of picking L and another A with replacement is:

(2/7) * (1/7) = 2/49

Probability of picking A and then another A with replacement is:

(1/7) * (1/7) = 1/49

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The time it will take for him to have enough money for the project is given as follows:

t = 8.5 years.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The parameters for this problem are given as follows:

P = 4000, r = 0.062, n = 2, A(t) = 6720.

Hence the time needed is obtained as follows:

[tex]4000\left(1 + \frac{0.062}{2}\right)^{2t} = 6720[/tex]

(1.031)^2t = 672/400

(1.031)^2t = 1.68

2tlog(1.031) = log(1.68)

t = log(1.68)/[2 x log(1.031)]

t = 8.5 years.

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Answer:28

Step-by-step explanation:

•C= 2(3.14 x r)

•C= 2(3.14 x4.5)

•C=2(14.13)

•C=28.26

The equation that has an initial value of 10 and has a rate of change of 4 is y= 4x+ 10.

We have,

Initial value= 10

Rate pf change= 4

We know from slope intercept form

y= mx+ b

where is m is slope or rate of change and b is y intercept or initial value.

So, we can take m = 4 and b= 10

Then, the required equation is

y= 4x +10.

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Answer:

Rational

Step-by-step explanation:

Improper fractions are always rational.

The correct answer is,

C. 60(x - 3) = 45x.

This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.

Since,  Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.

Now, To solve this equation, we must use algebra and solve for x.

First, we multiply both sides of the equation by 4/5. This gives us:

48x + 36 = 45x

-36 = 3x

Finally, we divide left side of the equation by 3, giving us the final solution:

x = -12

Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.

that is, 60 (x - 3) = 45x

This equation shows the correct relationship between the two types of wood that the contractor purchased.

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Answer: 2b.[tex]\frac{1}{a^{18} }[/tex]

Answer: graphed and attached

Step-by-step explanation:

to graph a y intercept and slope, first find the y intercept on the graph and place your point. here the y intercept is 3, so (0, 3) because x=0 at a y intercept.

next use slope to find your next point. slope of -2 is the same as -2/1 or down -2 and right +1. so from your y intercept of 3, go down -2 and right 1 and place your point (1, 1). do this again for a 3rd point at (2, -1).

graph is attached.

The single formulas for f and g so that both compositions hold true are f(x) = 3sin(x) and g(x) = π/4(x − 1)

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

f(g(x)) = 3sin (pi/4(x − 1))

g(f(x)) = pi/4(3 sin(x) − 1)

Express pi as π

So, we have

f(g(x)) = 3sin (π/4(x − 1))

g(f(x)) = π/4(3 sin(x) − 1)

In f(g(x)) = 3sin (π/4(x − 1)), replace the expression in bracket with g(x)

So, we have

f(g(x)) = 3sin (g(x))

This means that

f(x) = 3sin(x) and also, it means

g(x) = π/4(x − 1)

Hence, the single formulas that both compositions hold true are f(x) = 3sin(x) and g(x) = π/4(x − 1)

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Answer:

Step-by-step explanation:

You want to compare the future values of two accounts after 10, 20, 50, and 85 years:

The formula for account value with compounding monthly is ...

  A = P(1 +r/12)^(12t) . . . . . . principal P invested at rate r for t years

  A = 4500(1 +0.075/12)^(12·t) . . . . . using given values for P and r

The first line of calculator output shown in the attachment gives the value after 10, 20, 50, and 85 years.

The formula for account value with continuous compounding is ...

  A = P·e^(rt)

  A = 5500·e^(0.0675t) . . . . . using given values for P and r

The second line of calculator output shown in the attachment gives the value after 10, 20, 50, and 85 years.

You will notice this (second) account has higher value up to 20 years, then lower value after that.

The account with the higher interest rate will make more money after the "break-even" period of about 20.6 years.

__

Additional comment

We have rounded the account values to the nearest dollar. For the purpose of value comparison, three significant figures would be sufficient.

The second attachment shows the different account values over the long term. You can see the higher interest rate really makes a difference.

The third attachment shows the shorter-term account values, and the "break-even" time period of about 20.6 years, when the values in both accounts are about $22,063.

Answer:

Step-by-step explanation:

In the right triangle, the value of x is approximately 64°

From the question, we are to set up an equation for x and then solve for the value of x.

To determine the value of x, we will use SOH CAH TOA

sin (angle) = Opposite / Hypotenuse

cos (angle) = Adjacent / Hypotenuse

tan (angle) = Opposite / Adjacent

In the given diagram,

x is the included angle

Adjacent = 12

Opposite = 25

Thus,

We can write that

tan (x) = 25/12

tan (x) = 2.0833

x = tan⁻¹ (2.0833)

x = 64.3586

x ≈ 64° (to the nearest degree)

Hence,

The value of x is approximately 64°

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The value of y when x = 2 is -2.

We are given that;

x = 4

y = -1

Now,

To write an equation relating x and y for inverse variation, you can use the formula123:

xy = k

where k is a constant.

To find the value of k, you can use the given values of x and y:

x = 4

y = -1

xy = k

(4)(-1) = k

k = -4

So, the equation relating x and y is:

xy = -4

To find y when x = 2, you can substitute x = 2 in the equation and solve for y:

xy = -4

(2)y = -4

y = -4/2

y = -2

Therefore, by the given equations the answer will be -2.

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The length QT of the given chords is determined as 14.5.

The length QT is calculated by applying the following formula for intersecting chord theorem.

QS x QT  = OR x TR

Substitute the given values;

10.5QT = 10(OR)

We don't know the length of the radius, so we are going to form another equation.

Since O is the center, angle QRT is a right angle, and we will apply Pythagoras theorem do determine the length QT.

Also, QS = QR

QT² = TR² + QR²

QT² = 10² + 10.5²

QT = √ (10² + 10.5²)

QT = 14.5

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Answer:

(1)

Step-by-step explanation:

11111111111111111111111

The large jar has better value for money than the smaller one.

To see which jar is the best value for the money, we need to take the quotient between the cost of each jar and the size. The smaller that value gets, the best value we have.

For the first jar we have:

q = £4.10/540 = 0.0075

For the second jar we have:

q' = £2.81/360 = 0.0078

Then we can see that the large jar has the best value for money.

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Answer:

0.039 or 0.040

Step-by-step explanation:

this is due to how when u get things like 3.9 and you need to round u just round up bye it to get the closest answer

We can see here that filling up the remaining spaces:

AB ≅ CD: Opposite sides are congruent.

∠ABC and ∠BCD are supplementary: Consecutive angles are supplementary.

An angle is actually known to be a geometric figure that is formed by the joining together of two rays or endpoints which are known as vertex.

The sides or legs of the angle are known to be make up the rays.

Angles are actually known to be measured in degrees, with a full circle containing 360 degrees.

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Miriana rolled the sequence of 3 and then 6 two more times than the theoretical probability would have predicted.

The theoretical probability of rolling a three-on-one number cube is 1/6, and the same is true for rolling a six. Since the two rolls are independent,

The probability of rolling a three and then a six in the sequence is the product of the probabilities: (1/6) x (1/6) = 1/36.

To find the expected number of times this sequence would occur in 180 experiments, we multiply the probability by the number of experiments: (1/36) x 180 = 5.

So, if Miriana had rolled the number of cubes according to the theoretical probability, we would have expected her to roll the sequence of 3 and then 6 five times in 180 experiments.

However, she actually rolled this sequence 7 times, so she rolled it 2 more times than the theoretical probability would have predicted.

Therefore, Miriana rolled the sequence of 3 and then 6 two more times than the theoretical probability would have predicted.

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Answer:

Step-by-step explanation:

1. $4,076.92

2. Assets = Liabilities + Equity

3. They can be used to make online purchases.

4. by using an emergency fund for this unplanned expense

5. a fund with a minimum investment that tracks the value of cash (This question)

6. 1930s

7. Banks because they are highly regulated by the government, so the loan terms will not be predatory.

8. their vacation cabin

9. You should shop around for the best overall deal.

10. If you use a credit card, it is easy to run up huge debts.

11. They are tied directly to your bank account.

12. preventative care

13. $100,000 per person bodily injury, $300,000 per incident for bodily injury, $50,000 for property damage

14. how long the coverage lasts, how much the premium costs, and the cash value

15. 1-year renewable group term life

16. Identity thieves can intercept unencrypted data being sent to Wi-Fi hot spots.

17. Wells Fargo employees were opening unauthorized deposit and credit accounts for its customers.

18. 2 year in state community college degree

19. tuition assistance

20. -a sundae, -movie tickets

Explanation: All of these answers are correct!

Personal Finance Semester Exam

5/11/2023