41. WRITE a Real-Life Problem to fit the data shown in the GRAPH.
Determine whether the DOMAIN of the function is discrete or continuous. Explain

The length of AB is 12 units. The two smaller triangles formed, namely ABD and BCD, are similar to the original triangle ABC.

In a right triangle ABC, with the altitude BD drawn to the hypotenuse AC, we can use the property of similar triangles to find the length of AB.Let x be the length of AB. Since the triangles ABD and ABC are similar, we can set up a proportion:

AB/AD = AC/AB+BC

Substituting the given values, we have:

x/12 = 27/(x + BC)

Cross-multiplying, we get:

27x = 12(x + BC)

Simplifying further:

27x = 12x + 12BC

Combining like terms:

15x = 12BC

Dividing both sides by 15:

x = (12/15)BC

Since BD is the altitude, we know that BD + DC = AC. Substituting the values:

12 + BC = 27

Simplifying:

BC = 15

Substituting BC = 15 back into the equation for x, we find:

x = (12/15)(15)

x = 12

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Answer:

7m^2+13

Step-by-step explanation:

7m^2 + 10m + 3

Add the numbers ;10+3=13

=7m^2+13

Hope this helped!!!

The cumulative distribution function (CDF) for the given random variable is plotted. To find probabilities, we calculate P[X≤2], P[X=0], P[X<0], and P[2<X≤3] using the CDF formula and integrating the probability density function (PDF) in the corresponding ranges.

a. The CDF is defined as F_X(x) = 0 for x < 0 and F_X(x) = 1 - (1/4)e^(-2x) for x ≥ 0. Plotting the CDF will show a step function that starts at 0 for x < 0 and approaches 1 as x increases.

b. i. P[X≤2] can be calculated by substituting x = 2 into the CDF: P[X≤2] = F_X(2) = 1 - (1/4)e^(-2*2) = 1 - (1/4)e^(-4).

  ii. P[X=0] represents the probability of the random variable taking the value 0. Since the given CDF is continuous, P[X=0] = P[X≤0] - P[X<0] = F_X(0) - lim(x→0-)F_X(x) = 1 - 0 = 1.

  iii. P[X<0] can be calculated by substituting x = 0 into the CDF: P[X<0] = F_X(0) = 0.

  iv. P[2<X≤3] can be obtained by subtracting P[X≤2] from P[X≤3]: P[2<X≤3] = P[X≤3] - P[X≤2] = F_X(3) - F_X(2) = (1 - (1/4)e^(-2*3)) - (1 - (1/4)e^(-2*2)).

These calculations provide the probabilities based on the given CDF for the specified ranges of the random variable X.

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Answer:

5

Step-by-step explanation:

9p-5

9(5)-5

45-5

40

(3+p)5

(3+5)5

(8)5

40

Answer:

6n-1

Step-by-step explanation:

The rule is to add on from previous term to next to find nth terms and the 0 term can be found by doing 5-6 = -1

ANSWER IS 6N-1

HOPE THIS HELPED

Answer:

34

Step-by-step explanation:

Jasmine cell phone company charges $35 a month for phone service

They also charge $0.50 for each text message

Her bill was $52

Therefore the number of text messages sent can be calculated as follows

Let x represent the number of messages sent

35 + 0.5x= 52

0.5x= 52-35

0.5x= 17

x= 17/0.5

= 34

Hence 34 text messages were sent

Answer:

Hope this helps any!

Step-by-step explanation:

What you do is you would add the -4w to w.

Then you would add 6 to -11

5w=-5

w=-1(I think)

x, y, and z are pairwise independent because any two of them are independent. x, y, and z are not mutually independent because their joint distribution does not factor into the product of their marginal distributions.

To show that the random variables x, y, and z are pairwise independent but not mutually independent, we need to examine the definitions of these concepts and demonstrate the properties.

Pairwise Independence:

Two random variables are said to be pairwise independent if any two of them are independent, regardless of the dependence on the third variable.

Mutual Independence:

Three random variables are said to be mutually independent if each pair of them is independent and their joint distribution factors into the product of their marginal distributions.

Now let's analyze x, y, and z based on these definitions.

Pairwise Independence:

To show that x, y, and z are pairwise independent, we need to demonstrate that any two of them are independent, regardless of the dependence on the third variable.

a) x and y:

Since x and y are independent Bernoulli(1/2) random variables, their outcomes do not affect each other. Therefore, x and y are independent.

b) x and z:

We need to consider the joint distribution of x and z. Let's examine all possible combinations:

If x = 0, then regardless of the value of y, z will be 0. Hence, P(x = 0, z = 0) = P(x = 0)P(z = 0) = (1/2)(1) = 1/2.

If x = 1, then z will be 1 only when y = 1. Therefore, P(x = 1, z = 1) = P(x = 1, y = 1) = P(x = 1)P(y = 1) = (1/2)(1/2) = 1/4.

If x = 1, then z will be 0 when y = 0. Therefore, P(x = 1, z = 0) = P(x = 1, y = 0) = P(x = 1)P(y = 0) = (1/2)(1/2) = 1/4.

If x = 0, then regardless of the value of y, z will be 0. Hence, P(x = 0, z = 0) = P(x = 0)P(z = 0) = (1/2)(1) = 1/2.

From the above calculations, we can see that P(x, z) = P(x)P(z) for all possible combinations of x and z. Therefore, x and z are independent.

c) y and z:

Similar to the analysis above, we can calculate the joint probabilities:

If y = 0, then regardless of the value of x, z will be 0. Hence, P(y = 0, z = 0) = P(y = 0)P(z = 0) = (1/2)(1) = 1/2.

If y = 1, then z will be 1 only when x = 1. Therefore, P(y = 1, z = 1) = P(y = 1, x = 1) = P(y = 1)P(x = 1) = (1/2)(1/2) = 1/4.

If y = 1, then z will be 0 when x = 0. Therefore, P(y = 1, z = 0) = P(y = 1, x = 0) = P(y = 1)P(x = 0) = (1/2)(1/2) = 1/4.

If y = 0, then regardless of the value of x, z will be 0. Hence, P(y = 0, z = 0) = P(y = 0)P(z = 0) = (1/2)(1) = 1/2.

From the above calculations, we can see that P(y, z) = P(y)P(z) for all possible combinations of y and z. Therefore, y and z are independent.

We have shown that any two random variables among x, y, and z are independent. Hence, x, y, and z are pairwise independent.

Not Mutually Independent:

To demonstrate that x, y, and z are not mutually independent, we need to show that their joint distribution does not factor into the product of their marginal distributions.

To do this, let's consider the joint distribution of x, y, and z. We can analyze all possible combinations:

If x = 0 and y = 0, then z will be 0. Hence, P(x = 0, y = 0, z = 0) = P(x = 0)P(y = 0)P(z = 0) = (1/2)(1/2)(1) = 1/4.

If x = 1 and y = 1, then z will be 1. Hence, P(x = 1, y = 1, z = 1) = P(x = 1)P(y = 1)P(z = 1) = (1/2)(1/2)(1/2) = 1/8.

However, if we examine the joint probability P(x = 0, y = 0, z = 1), we find that it is not equal to P(x = 0)P(y = 0)P(z = 1). In this case, P(x = 0, y = 0, z = 1) is 0 because z can only be 0 when x and y are both 0. Therefore, P(x = 0, y = 0, z = 1) ≠ P(x = 0)P(y = 0)P(z = 1).

Since the joint distribution does not factor into the product of the marginal distributions for all possible combinations, x, y, and z are not mutually independent.

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Answer:

-4x-32  Can i please get a brainliest because this correct.

Step-by-step explanation:

−4(x+7)−4

Distribute:

=(−4)(x)+(−4)(7)+−4

=−4x+−28+−4

Combine Like Terms:

=−4x+−28+−4

=(−4x)+(−28+−4)

=−4x+−32

Answer:

=−4x−32

Answer:

y = 1/2x + 12

Step-by-step explanation:

The y intercept is 12, and the slope is 1/2

Answer:

(1,10)

Step-by-step explanation:

2-1=1

4+6=10

Answer:

(1, 10).

When you pit on a graph, you are able to easily see that going up 6 and left 1 will put you at (1, 10).

Answer:

The population is increasing

Step-by-step explanation:

You can tell that function is increasing from the equation because the rate of change is \(\frac{5}{4} = 1.25\)

Since this value is greater than \(1\) it indicates that the population is being increased.

plz mark me brainliest. :)

Answer:

y = 10

Step-by-step explanation:

\(\displaystyle \frac{6+9+18}{3}=\frac{12+y}{2}\\ \\\frac{33}{3}=\frac{12+y}{2}\\ \\11=\frac{12+y}{2}\\ \\22=12+y\\\\10=y\)

3

6+9+18

=

2

12+y

3

33

=

2

12+y

11=

2

12+y

22=12+y

10=y

answer: 10=y

Answer:

C. 4(3.30) + 6(1.25)

Step-by-step explanation:

Hope this helps. :)

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

We can begin by finding the circumference of the circle using the formula C=2πr, where r is the radius of the circle. C = 2π(4) = 8π. Radius is defined as length between center and arc of circle.

Since the sector of the circle is three-quarters, its central angle is 3/4 * 360 degrees = 270 degrees.

θ = 270 degrees = 3π/2 radians

L = 4(3π/2) = 6π

Therefore, the lateral surface area of the cone is 6π square inches.

6π = π(4)ℓ

Solving for ℓ, we get:

ℓ = 3

h^2 = ℓ^2 - r^2

h^2 = 3^2 - 4^2

h^2 = 9 - 16

h^2 = -7 (This is not a valid solution since we cannot take the square root of a negative number.)

Therefore, there must be an error in the given problem, as the dimensions provided do not allow for a valid solution.

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Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the required figure is not attached to the question.

From the question, we can deduce that the telescope is a composite figure made from a cone and a cylinder.

To get the volume of the materials used, you have to calculate the volume of the cone and that of the cylinder.

The sum of these volumes, is your answer.

Assume the following dimensions:

Cone

\(r = 5\\\) --- radius

\(h = 7\) --- height

Cylinder

\(r = 5\\\) --- radius

\(h = 20\) --- height

The volume of the cone is:

\(Volume = \frac{1}{3} \pi r^2h\)

\(V_1= \frac{1}{3} \pi *5^2*7\)

\(V_1= \frac{1}{3} \pi *25*7\)

\(V_1= \frac{175}{3} \pi\)

The volume of the cylinder is:

\(Volume = \pi r^2h\)

\(V_2 = \pi * 5^2 * 20\)

\(V_2 = \pi * 25* 20\)

\(V_2 = 500\pi\)

The total is:

\(Volume = V_1 + V_2\)

\(Volume = \frac{175\pi}{3} + 500\pi\)

Take LCM

\(Volume = \frac{175\pi+1500\pi}{3}\)

\(Volume = \frac{1675\pi}{3}\)

Answer: 2.11 yd³ = 1613210.750364 cm³

Step-by-step explanation:

Answer:

Step-by-step explanation:

To convert cubic yards to cubic centimeters, you can use the following conversion factors:1 yard = 91.44 centimeters

1 cubic yard = (91.44 centimeters) x (91.44 centimeters) x (91.44 centimeters) = 7,645,549.23 cubic centimetersTherefore, to convert 2.11 cubic yards to cubic centimeters, you can multiply it by the conversion factor:2.11 cubic yards x 7,645,549.23 cubic centimeters/cubic yard ≈ 16,120,247.02 cubic centimetersSo, 2.11 yards^3 is approximately equal to 16,120,247.02 cubic centimeters.

Using Distributive Property, the two expressions that is equal to 72 are

3(10+14) and 4(5+13).

What are expressions exactly?

In mathematics, expressions are mathematical claims that consist of at least two sentences that contain numbers, variables, or both, and are linked by an operator in between. The operations includes sum, Difference, multiplication, and division. For instance, x + y is an equation in which the words x and y are separated by an addition operator. In mathematics, there are two types of expressions: numerical expressions, which include only numbers, and algebraic expressions, which contain both numbers and variables.

Now,

The expressions using distributive property can be

3(10+14)=3*10+3*14

            =30+42

            =72

4(5+13)=4*5+4*13

            =20+52

           =72

Hence,

            the two expressions that is equal to 72 are 3(10+14) and 4(5+13).

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Answer:

I got 42.5

Step-by-step explanation:

I separated the shapes into 2 trapezoid and a rectangle and add up what I got; 32, 3, 7.5

EXPLANATION:

We are given a circle K with radius KG. Note here that line KJ and line KG are both radii of the circle given.

Also we know that a line tangent to a circle at the point of intersecting with the radius forms a 90-degree angle with the radius.

We can now extract the following triangle from the diagram provided;

We now have a right triangle which we shall solve by use of the Pythagorean theorem;

Where we have c as the longest side (hypotenuse) and then a and b are the two other sides. Substituting into the equation above now gives us;

Subtract 36 from both sides;

Take the square root of both sides;

Rounded to the nearest tenth, the answer is;

ANSWER:

Answer:

Step-by-step explanation:

Let the ten friends represents the 10 letters ABCDEFGHIJ. If they must be divided into three teams with three people in each team and one field judge, the arrangement will become (ABC)(DEF)(GHI)J

This shows that ABC, DEF and GHI are the three teams and J is the chief judge. Since each groups are now a team, we can represent everyone in each teams with the same letter except the judge as shown;

(AAA)(BBB)(CCC)J where J is the judge

Since there are 10 friends in all and there are A, B and C are repeated three times, the arrangement can be done in the following way as shown;

\(\frac{10!}{3!3!3!1!}\)

\(= \frac{10*9*8*7*6*5*4*3!}{3!*6*6*1}\\ = \frac{10*8*7*6*5}{1} \\= 16,800ways\)

This shows that they can do it 16,800 number of ways

The another root for the given polynomial is 3 + 2i.

A complex number is defined as a number containing both real and imaginary part which is written as x + iy. The conjugate of a complex number can be obtained by changing the sign of the imaginary part of the number. the product of a complex number and its conjugate is the square of its magnitude.

One of the complex roots of a polynomial is given as 3 - 2i.

Since, all the coefficients of the polynomial P(x) are real.

The another root should be the complex conjugate of the given root.

Thus, the other root is given as below,

3 + 2i

Hence, the additional root is given as 3 + 2i.

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Therefore, the length of the arc DE is approximately 5.5 units when the central angle is 7π/8 and the radius is 2 units.

In mathematics, an arc is a portion of a curved line, typically a portion of a circle or an ellipse. It is defined as the part of the curve between two points on the curve, and is often measured in terms of its length or angle. The term "arc" is commonly used in geometry and trigonometry to describe the length of the curve of a circle or other curved shape. An arc of a circle is a portion of the circumference of the circle, and it can be measured in terms of its central angle or the length of the curve itself.

Here,

To find the length of the arc DE, we need to use the formula:

Length of arc = (central angle / 2π) x (circumference of the circle)

where the circumference of the circle is given by:

Circumference = 2πr

Here, the central angle is 7π/8 and the radius is 2 units. So we can substitute these values into the formula and get:

Length of arc DE = (7π/8)/(2π) x 2π(2)

Length of arc DE = (7/16) x 4π

Length of arc DE = 7π/4

Using a calculator, we can approximate this to the nearest tenth:

Length of arc DE ≈ 5.5 units (rounded to the nearest tenth)

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Answer:

Step-by-step explanation:

You want to know the value of x and the angle measures in a figure having angles marked (7x +4)° and (6x -6)° forming a linear pair.

The angles of a linear pair are supplementary:

  (7x +4)° +(6x -6)° = 180°

  13x -2 = 180

  x = (180 +2)/13

  x = 14

Then the exterior angle is ...

  (7x +4)° = (7·14 +4)° = 102°

and the interior angle is ...

  (6x -6)° = 6(14 -1)° = 78°

<95141404393>

The measure of x is 14 degree, exterior angle is 102° and interior angle is 78°.

We know, Linear pair refers to a pair of adjacent angles that share a common side and whose non-common sides form a straight line.

So, on a starlight line the sum of angle formed a semicircle is 180 degree or supplementary.

So, 7x+ 4 + 6x- 6= 180 (Linear Pair)

13x - 2 = 180

13x = 182

x= 182/13

x = 14

So, the exterior angle is

=  (7x +4)°

= (7(14) +4)°

= 102°

and the interior angle is

= (6x -6)°

= 6(14 -1)°

= 78°

Thus, the exterior angle is 102° and the interior angle is 78°.

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the partial fraction decomposition of -2x^2 - 14x + 12 / (x - 6) is:

-2x^2 - 14x + 12 / (x - 6) = -144 / (x - 6) - 852

To write the expression -2x^2 - 14x + 12 / (x - 6) in terms of a sum of partial fractions, we need to decompose it into simpler fractions. The general form of a partial fraction decomposition for a rational function is:

R(x) / Q(x) = A / (x - r) + B / (x - s) + ...

where R(x) is the numerator, Q(x) is the denominator, and A, B, etc. are constants.

In this case, the denominator is (x - 6). So, we can write:

-2x^2 - 14x + 12 / (x - 6) = A / (x - 6) + B

To find the values of A and B, we can multiply both sides of the equation by the denominator:

-2x^2 - 14x + 12 = A + B(x - 6)

Now, we can substitute specific values of x to solve for A and B. Let's choose x = 6:

-2(6)^2 - 14(6) + 12 = A + B(6 - 6)

-72 - 84 + 12 = A

Simplifying further:

-144 = A

So, we have found the value of A. Now, let's find the value of B by substituting x = 0:

-2(0)^2 - 14(0) + 12 = A(0 - 6) + B

12 = -6A + B

Substituting the value of A, we get:

12 = -6(-144) + B

12 = 864 + B

Simplifying further:

B = 12 - 864

B = -852

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Answer:

B 9

Step-by-step explanation:

We have 6 green socks, 18 purple socks, and 12 orange socks.

Adding more purple sock means 6 green socks, 18+x purple socks, and 12 orange socks.

We have a  probability of 60% of getting a purple sock.

P( purple) = number of purple socks / total

.60 = (18+x) / (6+18+x+12)

.60 = (18+x) / (36+x)

Multiply each side by 36+x

21.6 +.6x = 18+x

Subtract 18 from each side

3.6x +.6x = x

Subtract .6x from each side

3.6x = .4x

Divide each side by .4

9 =x

Jamal added 9 purple socks

The percentage increase in average commute times between these years = 2.25%

In 2010, the average commute time for wake county workers = 23.9 mins

In 2016, the average commute time for wake county workers = 25 mins.

The increase is = 25- 23.9 = 1.1

The average commute time between the two years,

23.9+25 = 48.9 mins

Therefore, the percentage,

= 1.1/48.9×100

= 110/48.9

= 2.249%

= 2.25% to the nearest two decimal places.

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