Lillian has $900 in a savings account that earns 6% interest per year. The interest is not compounded. How much interest will she earn in 3 years?

A. P(A|B) = 0.3; B. P(B|A) = 0.69; C. P(A and B) = 0.207; D. P(A or B) = 0.783.

To solve the problem, we can use the formulas for conditional probability and the probability of independent events:  A. P(A|B) = P(A and B) / P(B). Since A and B are independent events, P(A and B) = P(A) * P(B). Thus, P(A|B) = P(A) * P(B) / P(B) = P(A) = 0.3. B. P(B|A) = P(A and B) / P(A). Using the same reasoning as above, P(B|A) = P(B) = 0.69. C. P(A and B) = P(A) * P(B) = 0.3 * 0.69 = 0.207. D. P(A or B) = P(A) + P(B) - P(A and B). Since A and B are independent, P(A and B) = P(A) * P(B).

Therefore, P(A or B) = P(A) + P(B) - P(A) * P(B) = 0.3 + 0.69 - 0.207 = 0.783. So, the answers are: A. P(A|B) = 0.3; B. P(B|A) = 0.69; C. P(A and B) = 0.207; D. P(A or B) = 0.783.

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If A is a subset of B, it does not necessarily mean that A is a proper subset of B. The union of any set A and its complement is indeed the universal set.

1. False: If A is a subset of B, it does not necessarily mean that A is a proper subset of B. A proper subset is a subset that contains some, but not all, elements of the superset. In other words, if A is a proper subset of B, it means that there exists at least one element in B that is not in A. However, if A is simply a subset of B, it is possible for A and B to have the same elements, making them equal sets.

For example, let's consider two sets:

A = {1, 2}

B = {1, 2, 3}

In this case, A is a subset of B because every element in A (1 and 2) is also in B. However, A is not a proper subset of B since there are no elements in B that are not in A. Therefore, statement 1 is false.

2. True: The union of any set A and its complement is indeed the universal set. The complement of a set A, denoted as A', consists of all elements that are not in A but are in the universal set U. When we take the union of A and its complement, we are effectively combining all elements from A and all elements not in A.

Let's consider a set A and its complement A' within a universal set U. The union of A and A' is denoted as A ∪ A' and can be represented as U. This is because every element in the universal set U is either in A or not in A (in A').

For example, let's consider the following sets:

U = {1, 2, 3, 4, 5}

A = {1, 2}

The complement of A, A', would be {3, 4, 5}. The union of A and A' (A ∪ A') is {1, 2} ∪ {3, 4, 5}, which is equal to U: {1, 2, 3, 4, 5}. Thus, the union of any set A and its complement is indeed the universal set. Therefore, statement 2 is true.

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Yes , the given statement is true , after implying Pythagoras theorem we conclude that the sides can be 5 cm 12 cm 13 cm.

We can use Pythagoras theorem to check whether the sides of a triangle can measure 5 cm 12 cm 13 cm or not .

The sum of square of two smaller sides should be equal to the third side.

13²   = 12² + 5²

13²   = √144 + 25

13²   =√169

13²   = 13

Therefore, we can conclude that the sides of a triangle can be 5 cm 12 cm 13 cm.

Pythagoras theorem states that the sum of smaller sides could be equal to the larger side. AC²   = AB² + BC².

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The probability of John waiting is

0.333.

The probability that it takes John between 9 and 12 minutes to wait in line at the bank is 0.333.

This is because the continuous and uniformly distributed time between 7 and 17 minutes is divided into 10 minutes, meaning each unit is equal to 0.1. Therefore,

the probability of John waiting between 9 and 12 minutes is 3 units of 0.1 which is 0.333.

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The central angle in radians is given by θ = s/r, where s is the arc length and r is the radius of the circle

For given question,

we need to find the radian measure of the central angle of a circle of radius r.

The central angle intercepts an arc of length s.

Let θ be the central angle in radians.

We know that the arc length of circle of radius r is,

s = r × θ

where s is the arc length

r is the radius of the circle

θ is the central angle measured in radians

From above equation,

we have, θ = s ÷ r

Therefore, the central angle in radians is given by θ = s/r, where s is the arc length and r is the radius of the circle

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Answer:

Slope-intercept form is y = 5/6x + 14

Answer:

I’m going to guess and say that it’s 3? Not sure sorry!

Answer:

p= 10000

r= 7

t=20 yrs

I= ?

We know that,

I= P× T × R /100

=10000× 7×20/100

= 14000,,

Answer:

100%

Step-by-step explanation:

If all 27 votes for hunger relief, that would be 100% or all of them.

The amount of radioactive material remaining after 6 days is 7.8 mg

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation.

The amount of time that it takes one half of the atoms present to decay is called “half-life.

The half life is 1 day

2 days = 1/4

3 days = 1/8

4 days = 1/16

5 days = 1/32

6 days = 1/64

Since the question says on the beginning of 7th days , we are going to stop at 6th day

Therefore on the 7th day

500 × 1/64

= 7.8 mg will remain.

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Answer: D 12

Step-by-step explanation:

Answer:

4. 1 units

Step-by-step explanation:

A diameter of a circle is equal to 2 of its radiuses. Just simply divide the diameter by 2.

Answer:

The cosine ratio of angle A is 28/197

Step-by-step explanation:

The cosine of the angle is the adjacent (to the angle) side and the hypotenuse

So, in this case, the side AC and the hypotenuse AB

Hence, cosine ratio of angle A is 28/197

Answer 108 and c

Step-by-step explanation:

for question A the angle is a vertically opposite angle so that means that the answer is 108 degrees for B is C because the angles are vertically opposite .

Answer:

the answer is (1,9)

Step-by-step explanation:

(a) Strings in L: "abb", "aabbb". (b) Strings not in L: "aabb", "bb".

(c) State diagram for a deterministic Turing Machine with 10 states is given below.

(a) Two strings that are in L are:

1. `abb` (Here, i = 0, and w is an empty string).

2. `aabbb` (Here, i = 2, and w = "aa").

(b) Two strings over the same alphabet that are not in L are:

1. `aabb` (Here, the length of w is 2, but there are more than two 'a's before the 'bb').

2. `bb` (Here, the length of w is 0, but there are 'b's before the 'bb', violating the condition).

(c) Here is the state diagram for a deterministic Turing Machine with 10 states that decides L:

```START --> A --> B --> C --> D --> E --> F --> G --> H --> ACCEPT

  a      b      b      a      a      b      b      a      b

  |      |      |      |      |      |      |      |      |

  v      v      v      v      v      v      v      v      v

REJECT  REJECT REJECT  A      E      F      REJECT REJECT REJECT

  |      |      |      |      |      |      |      |      |

  v      v      v      v      v      v      v      v      v

REJECT  REJECT REJECT  REJECT REJECT REJECT  G      H      REJECT

  |      |      |      |      |      |      |      |      |

  v      v      v      v      v      v      v      v      v

REJECT  REJECT REJECT  REJECT REJECT REJECT REJECT REJECT REJECT```

In this state diagram, the machine starts at the START state and reads input symbols 'a' or 'b'. It transitions through states A, B, C, D, E, F, G, and H depending on the input symbols.

If the machine reaches the ACCEPT state, it accepts the input, and if it reaches any of the REJECT states, it rejects the input. The machine accepts inputs of the form `a^i b^bw` where the length of w is i.

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The complete question is:

Let L = {a(^i)bbw|w ∈ {a, b} ∗ and the length of w is i}.

(a) Give two strings that are in L.

(b)Give two strings over the same alphabet that are not in L.

(c)Give the state diagram for a deterministic Turing Machine that decides L. To receive full credit, your Turing Machine shall have no more than 10 states.

Answer:

The list of set of dimensions for fencing the building around a rectangular plot of land is 14.5 meters and 29 meters.

Area of a rectangle

area of rectangle = lw

where

l = length

w = width

Therefore,

perimeter = 2w+ l

58 = 2w + l

l = 58 - 2w

Hence,

area = w(58 - 2w)

380 = 58w - 2w²

-2w² + 58w - 380 = 0

-w² + 29w - 190 = 0

The dimension w can be found as follows;

w = - b / 2a

where

a = -1

b = 29

w = - 29 / 2 ×  -1

w = 14.5 meters

Then,

l = 58  - 2w

l = 58 - 2(14.5)

l = 29 meters

Therefore, the dimensions are 14.5 meters and 29 meters.

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The sum of first 10 terms is 72.

Concept: Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.

Arithmetic Progression Formula

= an - a. nth term of an AP: an = a + (n - 1)d. Sum of n terms of an AP: Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the last term of the arithmetic progression.

Given:

Eighth term is 8.2

Common difference is 0.4

a(8) = 8.2

a + 7d = 8.2

Since d = 0.4

a + 7(0.4) =8.2

a = 5.4

Sum of 10 terms = n/2 (2a+(n-1)d)

= 5(2*5.4 + 9*0.4)

=5(10.8 +3.6)

Sum=72

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Answer:

\(\boxed{\tt y=48}\)

Step-by-step explanation:

\(\tt \cfrac{3}{16}=\cfrac{9}{y}\)

Cross multiply:-

\(\tt 3 \times y=(9)\times (16)\)

\(\tt 3y=144\)

Divide both sides by 3:-

\(\tt \cfrac{3y}{3}=\cfrac{144}{3}\)

Simplify:-

\(\tt y=48\)

_________________

Hope this helps!

Answer:y=48 I hope this is helpful good luck have a good day

Step-by-step explanation:

3/16 = 9/y

Determine the defined range

3/16=9/y y=0 cross out the equal sign y=0

Simplify the equation using cross-multiplication

3y=144

Divide both sides of the equation by 3

y=48

Check if the solution is in the defined range

Answer:

138/80

Step-by-step explanation:

5×5+3/5-3×16+14/16

28/5-62/16

28×16/5×16-62×5/16×5

448/80-310/80

448-310/80

138/80

Answer:

its b

Step-by-step explanation:

got it right on edge

The volume of the metal in the cylinderical pipe given the dimensions of the larger and smaller cylinders is 271.30 mm³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

Volume of a cylinder = nr^2h

Where:

The volume of the metal in the cylinderical pipe = 3.14 x 10 x [(8.4/2)² - 6/2)²] = 271.30 mm³

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Answer:

Slope of BC = 1/2

Step-by-step explanation:

Given collinear points A, B and C

slope of the line AB = 1/2

Answer:

\(sin^{-1}(x) = \frac{55}{73} \\\\cos^{-1}(x) = \frac{48}{73} \\\\tan^{-1}(x) = \frac{48}{55}\)

Step-by-step explanation:

Since you're finding the angle, you use the inverse of sin, cos, and tan.

Answer: the T means "time"

Step-by-step explanation:

distance = rate * time

hope this helps :)

Answer:

9a+5

Step-by-step explanation:

3a+5 and 2a2+4a-2= 6a+3a+5 =9a+5

Answer: y = 5x + 26

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line y = -1/5x + 1 and passes through the point (-5, 1), we need to determine the slope of the perpendicular line. The given line has a slope of -1/5. Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the perpendicular line will be the negative reciprocal of -1/5, which is 5/1 or simply 5. Now, we have the slope (m = 5) and a point (-5, 1) that the perpendicular line passes through.

We can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Substituting the values, we get:

y - 1 = 5(x - (-5))

Simplifying further:

y - 1 = 5(x + 5)

Expanding the brackets:

y - 1 = 5x + 25

Rearranging the equation to the slope-intercept form (y = mx + b):

y = 5x + 26

Therefore, the equation of the perpendicular line that passes through the point (-5, 1) is y = 5x + 26.

Answer:

  f(x) = -2.5x +5

Step-by-step explanation:

You want the linear function f(x) that is represented by the ordered pairs ...

  {(−4, 15), (0, 5), (4, −5), (8, −15)}

The slope of the line can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (5 -15)/(0 -(-4)) = -10/4 = -2.5

The y-intercept of the line is given by the point (0, 5).

The equation of the line in slope-intercept form is ...

  f(x) = mx +b . . . . . . . where m is the slope, and b is the y-intercept

For the values we've identified, the equation of the line is ...

  f(x) = -2.5x +5

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The confidence interval (149.2, 206.4) can be written as ¯x ± me, where ¯x = 177.8 and me = 28.6. The sample mean (¯x) is the midpoint of the confidence interval

To express the confidence interval (149.2, 206.4) in the form of ¯x ± me, we need to calculate the sample mean (¯x) and the margin of error (me).

The sample mean (¯x) is the midpoint of the confidence interval and can be calculated by taking the average of the upper and lower bounds of the interval:

¯x = (149.2 + 206.4) / 2 = 177.8

Next, we calculate the margin of error (me) by finding the half-width of the confidence interval:

me = (206.4 - 149.2) / 2 = 28.6

Therefore, the confidence interval (149.2, 206.4) can be expressed in the form of ¯x ± me as:

¯x ± me = 177.8 ± 28.6

Hence, the confidence interval (149.2, 206.4) can be written as ¯x ± me, where ¯x = 177.8 and me = 28.6.

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