Kamus luined 10 years old. Her mother is four times older than Kim.
How old is Kim's mother?

The correlation between X and Y, captured by the joint pmf Px,y(x,y), allows for this difference in heights and explains the seemingly contradictory result.

The given scenario states that there is a joint probability mass function (pmf) Px,y(x,y) with marginal probabilities Px(u) = Py(u) for all u. However, it also states that the probability of Y being greater than X, P(Y > X), is greater than or equal to 0.9.

This situation seems contradictory at first, as the marginals are equal but the probability of Y being greater than X is significantly high. However, it is important to note that the joint pmf Px,y(x,y) accounts for the correlation between X and Y, not just their marginals.

The correlation between X and Y allows for the possibility that Y may be greater than X with a high probability, even though the marginals are equal. This indicates a dependence between the two random variables.

To illustrate this, let's consider an example where X and Y represent the heights of two groups of individuals. The equal marginals Px(u) = Py(u) imply that the heights in each group have the same distribution. However, the high probability of Y being greater than X (P(Y > X) ≥ 0.9) suggests that, on average, the individuals in one group tend to be taller than those in the other group.

Therefore, the correlation between X and Y, captured by the joint pmf Px,y(x,y), allows for this difference in heights and explains the seemingly contradictory result.

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The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism

The law of syllogism is defined as a type of logical argument using deductive reasoning.

Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:

(1) If a , then b .

(2) If b , then c .

Then we can derive a third true statement:

(3) If a , then c .

Now, applying that law to our question, we see that;

1) If I'm a student, then I go to school.

2) If I go to school, then I learn.

Then we can derive a third true statement:

3)  If I'm a student, then I learn.

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If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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The probability that the person selected is older than 20 years old and watching the drama movie is 0.765.

We have,

The total number of people who watch drama.

= 12 + 20 + 19

= 51

The total number of people who is older than 20 years who watch drama.

= 20 + 19

= 39

Now,

The probability that the person selected is older than 20 years old and watching the drama movie.

= 39/51

= 0.765

Thus,

The probability that the person selected is older than 20 years old and watching the drama movie is 0.765.

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Answer:

3/2 or 1.5

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

y = mx + c

m = the slope

2y = 3x + 4

y = 3x + 4 / 2

y = 1.5x + 2

slope = 1.5

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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The solution of the linear equation 2.8y+6+0.2y=5y-14 is y=10.

Given linear equation 2.8y+6+0.2y=5y-14 and we have to find the solution of the equation.

An equation is relationship between two or more variables which is expressed in equal to form. It is solved in order to find the values of variables. Equation of two variables look like ax+ by=x.

The given linear equation is 2.8y+6+0.2y=5y-14 which can be solved as under:

2.8y+6+0.2y=5y-14

We have to add the coefficients of same variables. Coefficients are the numbers which are present with the variable.

3y+6=5y-14

We have to take same variables at one side.

3y-5y=-14-6

-2y=-20

y=-20/-2

y=10

Hence the solution of the linear equation 2.8y+6+0.2y=5y-14  is y=10.

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To substract two fractions, we have to have common denominators.

For example, if we want to substract 1/3 from 1/2, we have to convert the fractions so they have a common denominator of 6.

The denominators are the ones that give sense to the fraction. In fact, when we substract whole numbers, we can consider we are substracting "fractions of one".

Then, for example, 5 - 4 could have been written as 5/1 -4/1.

If the numbers have different denominators, we can not perform additions or substractions until we express the fractions with the same denominator.

Trying to substract two fractions with different denominators is like substracting two things that are not expressed in the same units and it will yield an incorrect result.

The values of the angles are; x = 12°, m∠PQS = 71°, m∠PQT = 142° and m∠TQR = 41°

The required angles; x, m∠PQS, m∠PQT, and m∠TQR

The given parameters are bisects ∠PQT

m∠SQT = (8·x - 25)°

m∠PQT = (9·x + 34)°

m∠SQR = 112°

We have;

m∠PQT = m∠SQT + m∠PQS (Angle addition postulate)

m∠SQT ≅ m∠PQS (Angles formed by angle bisector are congruent)

m∠SQT = m∠PQS  by Definition of congruency

m∠PQT = 2 × m∠SQT

Therefore;

(9·x + 34)° = 2 × (8·x - 25)° = (16·x - 50)°

Collecting like terms gives:

(34 + 50)° = 16·x - 9·x = 7·x

7·x = 84°

x = 84°/7 = 12°

x = 12°

m∠SQT = (8·x - 25)°

Therefore;

m∠SQT = (8 × 12 - 25)° = 71°

m∠SQT = 71°

m∠PQT = 2 × m∠SQT

∴ m∠PQT = 2 × 71° = 142°

m∠PQT = 142°

m∠PQS = m∠SQT (Angles formed by the same bisector )

∴ m∠PQS = m∠SQT = 71°

m∠PQS = 71°

m∠SQR = m∠SQT + m∠TQR (Angle addition postulate)

m∠SQT = 71°

∴  m∠SQR = 112° = 71° + m∠TQR

m∠TQR = 112° - 71° = 41°

m∠TQR = 41°

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The area of the polygons are;

1. 48 square units

2. 10, 000 square units

3. 432 square units

4. 243√3 square units

5. 100 square units

6. 800 square units

Area of a triangle given radius is expressed as;

Area = radius × semi-perimeter

1. Area = 4 × 4(3)

expand the bracket, we have;

Area = 4 × 12

Area = 48 square units

2. Area = 10 × 10(3)

expand the bracket, we have;

Area = 10 × 1000

Area = 10, 000 square units

3. Area = 12 × 12(3)

Area = 12 × 36

Area = 432 square units

4. Area = 3√3 a²

Substitute the value

Area = 3 √3 × 9²

Area = 3√3 × 81

Area = 243√3 square units

5. Apothem of a square = side length/2

Side length = 10

Area = s²

Area = 10² = 100 square units

6. Area = 4r²

Area = 4(10√2)²

expand the bracket, we have;

Area = 800 square units

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The rational numbers in the given list are 0.29, 0.816¯¯¯, 2.63¯¯¯, and 0.125.

A rational number is any number that can be expressed as a ratio of two integers (where the denominator is not equal to zero).

Looking at the given numbers:
- 0.29 can be expressed as 29/100, so it is rational.
- 0.816¯¯¯ can be expressed as 816/999, so it is rational.
- 2.515115111… and 0.418302… are both irrational since they are non-repeating and non-terminating decimals.
- 2.63¯¯¯ can be expressed as 263/99, so it is rational.
- 0.125 can be expressed as 1/8, so it is rational.

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Answer:

9(4x+3)     :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

the first step in factorising is to look for any common factors.

27

and

36

are both multiples of

3

and

9

.

We use

9

because it is the highest common factor:

Divide

9

out of each term:

27+36x=9(3+4x)

The reverse process would be to use the distributive law to multiply each term in the bracket by

9

.

This will give us the original expression:

9(3+4x)=27+36x

Answer:4

Step-by-step explanation: 3 the “(“ infer multiple so 3x 2 -2 also written as 3(2)-2

Answer:

12 units

Step-by-step explanation:

\( In\: \odot O, \)

The correct option d. the event can take no more than a maximum amount of time, described the  an event has a timebox.

A timebox is a set amount of time during which a work must be completed in agile software development.

Thus, when an event has a timebox, it signifies that the event can only last a certain length of time.

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Answer:

30/64 inches.

Explanation:

The size of the converted metric part = 0.473 in.

Now, we know that:

Therefore:

Thus, we have that:

To the nearest 64th of an inch, the closest size will be 30/64 inches.

Answer:

c 14 marbles

Step-by-step explanation:

Answer:

its c 14

Step-by-step explanation:

Given equation is (x + 2)² + (y + 4)² = 1/16.Since both the squares are same, we can rewrite it as (x - (-2))² + (y - (-4))² = (1/4)².

The given equation represents an ellipse whose center is (-2,-4), length of major axis is 1/2 and length of minor axis is 1/4. Also the standard equation of an ellipse with center (h,k) is given by(x-h)²/a² + (y-k)²/b² = 1

Comparing this with the given equation, we get Center = (-2,-4)

a = 1/4 and b = 1/8

Vertices: The distance between the center and each vertex along the major axis is a. Hence the vertices are (-2, -4 + 1/4) and (-2, -4 - 1/4) or (-2, -3.75) and (-2, -4.25).

Foci: Let c be the distance between the center and each focus. We know that c² = a² - b².

Hence c² = (1/4)² - (1/8)² or c = √15/16. Therefore, the foci are (-2, -4 + √15/16) and (-2, -4 - √15/16). Eccentricity: The eccentricity e of an ellipse is defined as the ratio of the distance between the foci and the length of the major axis. Hence, e = c/a = √15/4. Sketch of the ellipse is shown below.

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Answer:

71.5556 but since you cant have half a pizza its only 71

Step-by-step explanation:

Answer:

Chromebook: 0.25 percent per minute

iPhone: 0.5 percent per minute

1) The phone

2) Faster by 0.25 percent per minute, or 1 percent every four minutes

3) The phone

4) 25 percent more

5) The phone

Therefore \(x/6=12/4\).\(5x=16ft\)The height of the tree will be 16ft.the correct answer is (c).

The study of the correlation between a right-angled triangle's sides and angles is the focus of one of the most significant areas of mathematics in history: trigonometry. Hipparchus, a Greek scholar, introduced this idea. In this article, we will study the fundamentals of trigonometry, including its formulas, tables, ratios, functions, and many solved examples. What are similar triangles If the respective sides of two triangles are proportional and the corresponding angles are congruent, then the triangles are said to be similar. To put it another way, similar triangles have the same shape but may differ in height. In addition, if the matching sides of the triangles are equal in length, the triangles are congruent. In the given figures, these are two similar triangles as the form the same angle with the ground The height of the tree will be 16ft using the property of similar triangles.

by the question.

Let's first find the ratio of Jack's height to his shadow length:

Jack's height / Jack's shadow length = 6 / 4

Simplifying this ratio, we get:

\(Jack's height / 4 = 3 / 2\)

Multiplying both sides by 4, we get:

\(Jack's height = 6\)

Now, let's find the ratio of the tree's height to its shadow length:

Tree's height / Tree's shadow length = x / 12

Since the two triangles are similar, we know that these ratios are equal. So, we can write:

Jack's height / Jack's shadow length = Tree's height / Tree's shadow length

Substituting the known values, we get:

\(6/4=x/12\)

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The number of ways in which three swimmers can advance is 56.

The combination is the selection of items without taking the order of arrangement into consideration.

The formula used in calculating the combination is:

\(\mathbf{C(n,r) = \dfrac{n!}{r!(n-r)!}}\)

\(\mathbf{C(n,r) = \dfrac{8!}{3!(8-3)!}}\)

\(\mathbf{C(n,r) = \dfrac{8\times 7\times 6 \times 5!}{3!(5)!}}\)

\(\mathbf{C(n,r) = 8\times 7}\)

C(n, r) = 56

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The age of Aaron is 16 years old.

We have,

The sum of Tylique and Johanna's ages is 41.

Let the ages are:

Aaron's age: a

Tylique's age: a - 7

Johanna's age: 2a

As, the sum of Tylique and Johanna's ages is 41,

So, (a - 7) + (2a) = 41

Combining like terms, we have:

3a - 7 = 41

3a = 48

Finally, dividing both sides by 3, we find:

a = 16

Therefore, Aaron is 16 years old.

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Answer:

y = 1

x = 3

Step-by-step explanation:

y = 7 - 2x

x - 2y = 1

5x - 14 = 1

y = 7 - 2x

x = 3

y = 7 - 2x

y = 1

Answer:

x = 72

Step-by-step explanation:

36 - x = -36

*subtract 36 from both sides*

-x = -72

*divide by -1*

x = 72

Answer:

0 is the answer of the equation

The area of right triangle QRS will be;

⇒ The area of triangle = 20

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔQRS;

Base = x

Height = 2x

Hypotenuse = 10

Now,

Since, The triangle is a right triangle.

Hence, The triangle QRS satisfy the condition of Pythagoras theorem.

So, We get;

⇒ Hypotenuse² = Base² + Height²

⇒ 10² = x² + (2x)²

⇒ 100 = x² + 4x²

⇒ 100 = 5x²

⇒ x² = 20

⇒ x = √20

So, The Height of triangle = 2√20

And, The Base of the triangle = √20

We know that;

⇒ The area of triangle = 1/2 × Height × Base

⇒ The area of triangle = 1/2 × 2√20 × √20

⇒ The area of triangle = 20

Thus, The area of right triangle QRS = 20

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The risk of owning a home in Randolph County based on the given sample can be calculated as:

Risk of owning a home = Number of residents who own a home / Total number of residents in the sample

Risk of owning a home = 59 / 90

Therefore, the risk of owning a home in Randolph County based on the given sample is approximately 0.656 or 65.6%.

Kathy will have 23 more euros than pounds after withdrawing half of her money in each currency using algebra.

First, let's calculate how much money Kathy will withdraw in pounds and euros. She wants to withdraw half of her $300$ US dollars in each currency, so that would be $150$ US dollars for each.

To find the amount in pounds, we can divide $150$ US dollars by the exchange rate of $1.64$ USD per pound:

Amount in pounds = $\frac{150}{1.64} \approx 91.46$ pounds.

To find the amount in euros, we can divide $150$ US dollars by the exchange rate of $1.32$ USD per euro:

Amount in euros = $\frac{150}{1.32} \approx 113.64$ euros.

Rounding both amounts to the nearest whole number, Kathy will have approximately $91$ pounds and $114$ euros.

To determine how many more euros than pounds she will have, we subtract the amount in pounds from the amount in euros:

$114$ euros - $91$ pounds = $23$ more euros than pounds.

Therefore, Kathy will have 23 more euros than pounds after withdrawing half of her money in each currency.

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Answer:

The slope is 5.

Explanation:

In the slope-intercept form of an equation

m is the slope, and b is the y-intercept of the equation.

Now in our case,

therefore, the slope is 5 and the y-intercept is -3.