a family has 5 natural children and has adopted 2 girls. each natural child has equal probability of being a girl or a boy, independent of the other children. find the pmf of the number of girls out of the 7 children.

Answer:

-3

Step-by-step explanation:

when you have a power to the - it creates a fraction instead of a whole number.

2^3 = 8

2^-3=1/8

Step-by-step explanation:

15,12$

3,5$ × 4,42meter =15,12

The positive even integers whose sum of reciprocals is 7/24 are 6 and 8.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Let the two consecutive even integers be 2x and 2x+2 then there sum of reciprocal will be 7/24 that is now solving for positive value of x by finding roots of quadratic equation :

\(\begin{aligned}\frac{1}{2x}+\frac{1}{2x+2}&=\frac{7}{24}\\\frac{1}{x}+\frac{1}{x+1}&=\frac{7}{12}\\\frac{2x+1}{x^2+x}&=\frac{7}{12}\\24x+12&=7x^2+7x\\7x^2-17x+12x&=0\\x&=3, \frac{-4}{7} \end{aligned}\)

Consider only positive value of x that is 3

Therefore, The positive even integers whose sum of reciprocals is 7/24 are 6 and 8.

check and know more about equations here :

https://brainly.com/question/10003183

#SPJ1

Answer:x + (x +1) + (x +2)= 30.

Step-by-step explanation:Consecutive means one right after the other--such as 4,5,6. So the sum (add all the numbers together) must equal 30. So the equation should read

Hope this helps!

Answer:

The Answer is Option 3

Step-by-step explanation:

I got it right edge 2022

Answer:

-33

Step-by-step explanation:

We know that x = -3

So,

-3² + 2 x -3

9 + 2 x -3

11 x -3

-33

Answer:

x = (y + 26)/5

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Write out equation

y + 6 = 5(x - 4)

Step 2: Distribute

y + 6 = 5x - 20

Step 3: Isolate x

y + 26 = 5x

Step 4: Isolate variable x

(y + 26)/5 = x

Step 5: Rewrite

x = (y + 26)/5

Answer:

y = 5x - 26

Step-by-step explanation:

Since x is the independent variable, you have to solve for y.

y + 6 = 5(x-4)

Now distribute:

y + 6 = 5x - 20

subtract the 6 from both sides

y + 6 - 6 = 5x - 20 - 6

y = 5x - 26

Answer: The price of the apartment lies in the range of $1300 to $1800

Step-by-step explanation: Because Carlos doesn't exactly know how much  he'll make at his new job but he knows the range will be between 3000$ and 4000$ we will use inequality to solve this problem.

Let the rent on the new apartment = r

let monthly pay of Carlos = x

Given, apartment related fees = 200$

Given he is willing to use half of his monthly pay for rent and apartment related fees combined.

∴rent + apartment related fees = Monthly pay / 2

⇒\(r + 200 = \frac{x}{2}\)

⇒\(x=2*(r+200)\)

⇒\(x=2r+400\)                                                (1)

Given Carlos' monthly pay is in the range of $3000 to $4000

∴\(3000\leq x\leq 4000\)

⇒\(3000\leq (2r+400)\leq 4000\)                             (from equation (1))

⇒\(3000-400\leq 2r+400-400\leq 4000-400\)     (subtracting 400)

⇒\(2600\leq 2r\leq 3600\)

⇒\(\frac{2600}{2}\leq \frac{2r}{2}\leq \frac{3600}{2}\)                                           (dividing by 2)

⇒\(1300\leq r\leq 1800\)                                           (2)

ANS: The apartment lies in the price range of $1300 to $1800 as given by equation (2)

here is a problem solved using inequality

https://brainly.com/question/13618639

#SPJ4

Answer:the answer is (-2,1)

Step-by-step explanation:

When rotating a point 90 degrees counterwise about the origin point (x,y) becomes (-y,x). So basically switch x and y and make y negative when rotating 90 degrees counterclockwise about the origin.

If the triangle is rotated counterclockwise 90 degrees about the origin, the angle C = (1, 2) will become C = (-1, 2).

It is a two dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Triangle ABC is located on a coordinate plane.

Angle C is at (1, 2).

This means that,

Angle C = (1, 2) is in the I Quadrant.

We have four Quadrant:

Quadrant I - The coordinates are in the form of (x, y)

Quadrant II - The coordinates are in the form of (x, -y)

Quadrant III - The coordinates are in the form of (-x, -y)

Quadrant IV - The coordinates are in the form of (-x, y)

If we rotate C = (1, 2) counterclockwise 90 degrees about the origin, the angle C will be in the IV quadrant.

So,

C = (1, 2) will become C = (-1, 2)

Thus,

If the triangle is rotated counterclockwise 90 degrees about the origin, the angle C = (1, 2) will become C = (-1, 2).

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ2

Answer:

it’s 6.25

Step-by-step explanation:

We have here four linear functions, and we have to compare the slopes of them as well as their y-intercept. For this, it is important to remember the general equation for the line in the slope-intercept form:

Where

• m is the slope of the line

• b is the y-intercept of the line (0, b)

The y-intercept is the point where the line passes through the y-axis, and at this point, we have that x = 0.

We have in this case that the function passes through the points:

• (0, 5), (1, 1)

We can find the equation of this line using the two-point form of the line equation:

Using the points above, we can label them as follows:

• (0, 5) ---> x1 = 0, y1 = 5

• (1, 1) ---> x2 = 1, y2 = 1

Then we have:

Therefore, the slope for this line is m = -4, and the y-intercept is (0, 5).

For Function 2 we need to do the same procedure as before. We have to select two points of the function to find its equation:

We can select the following points: (0, 1), (1, 6).

Then we can proceed as we did in the previous part:

• (0, 1) ---> x1 = 0, y1 = 1

• (1, 6) ---> x2 = 1, y2 = 6

Therefore, the slope in Function 2 is 5, m = 5, and the y-intercept is (0, 1).

We can see that Function 3 has already its line equation in slope-intercept form:

Then the slope for Function 3 is m = -1, and its y-intercept is (0, -2).

From the question, we have:

Answer:

B

when you input the first value of y which is -2

-2+2=(4/5)(x+9)

0=(4x+36)/5

multiply both sides by 5

0=4x +36

4x =-36

divide both sides by 4

x=-9

if you like my answer mark as brainliest

Redundant bits are additional bits added to the data bits to achieve this purpose.

The number of redundant bits necessary for a code is related to the number of data bits to ensure error detection and correction in transmitted data. In general, redundant bits are additional bits added to the data bits to achieve this purpose.

To determine the number of redundant bits (r) needed for a specific number of data bits (k), you can use the following inequality:

\(2^r ≥ k + r + 1\)

Here, r is the number of redundant bits, and k is the number of data bits.

Step-by-step explanation:

1. Identify the number of data bits (k) in the code.
2. Use the inequality\(2^r ≥ k + r + 1\)to find the minimum value of r (redundant bits) that satisfies the inequality.
3. The value of r obtained will be the number of redundant bits necessary for the code.

By adding redundant bits to the data, it helps in detecting and correcting errors during data transmission, thereby ensuring the accuracy and reliability of the information being communicated.

Learn more about data bits here:

https://brainly.com/question/16860043

#SPJ11

A significant relationship between x and y is  b. large p-value for the estimated slope.

Simple linear regression is used to estimate the connection among  quantitative variables. You can use easy linear regression whilst you need to know: How robust the connection is among variables (e.g., the connection among rainfall and soil erosion). The fee of the established variable at a positive fee of the impartial variable (e.g., the quantity of soil erosion at a positive stage of rainfall). Simple linear regression is used to version the connection among  non-stop variables. Often, the goal is to are expecting the fee of an output variable (or response) primarily based totally at the fee of an input (or predictor) variable.

Thus, option b is the correct choice.

To learn more about simple linear regression check the link below:

https://brainly.com/question/25987747

#SPJ4

Answer:

1) C: 113 m

2) C: 572.3 m²

3) B: 61.2 cm²

4) A: $2.2

6) C: 756 yd³

8) D: 3402 mm²

9) A: 25x + 125 < 500

Step-by-step explanation:

1) Formula for circumference of circle is;

C = 2πr

radius; r = 18 m

C = 2π × 18

C ≈ 113 m

2) Formula for area of a circle is;

A = πr²

Here we have diameter; d = 27

Thus, radius; r = 27/2 = 13.5 m

A = π × 13.5²

A = 3.14 × 13.5²

A ≈ 572.3 m²

3) The diameter of the semicircle is parallel to the base of the rhombus. Thus, diameter; d = 7 cm

Thus, r = 7/2 = 3.5 cm

Area of semi circle = ½πr² = ½ × π × 3.5² = 19.2 cm²

Area of rhombus = base x height = 7 × 6 = 42 cm²

Total area of object = 42 + 19.2 = 61.2 cm²

4) Cost of banana per pound = $0.4 per pound

Amount of banana bought = 5.5 pound

Amount spent = 0.4 × 5.5 = $2.2

6) Volume of triangular prism is;

V = ½bhl

b = 12 yd

h = 7 yd

L = 18 yd

Thus;

V = ½ × 12 × 7 × 18

V = 756 yd³

8) Volume of cuboid at the base;

V1 = lbh = 25 × 9 × 9 = 2025 mm²

Volume of cuboid at top;

V2 = 9 × 9 × 9 = 729 mm²

Volume of triangular prism;

V3 = ½bhl = ½ × 9 × 9 × (25 - 9) = ½ × 81 × 16 = 648 mm²

Total volume = 2025 + 729 + 648 = 3402 mm²

9) Cost per class; $25 per class

Charge for the supplies = $125

He doesn't want to spend more than $500.

Thus;

25x + 125 < 500

The probability of both events happening is 0.6 × 0.5 = 0.3, or 30%, and the probability that at least one university will make an offer is 1 - 0.2 = 0.8, or 80%.

The probability that both universities will make an offer can be found by multiplying the probabilities of each event happening. The probability of receiving an offer from university A is 0.6, and the probability of receiving an offer from university B is 0.5. Therefore, the probability of both events happening is 0.6 × 0.5 = 0.3, or 30%.

The probability that at least one university will make an offer can be found by subtracting the probability that neither university will make an offer from 1. The probability that neither university will make an offer is the product of the probabilities that each university will not make an offer, which is 0.4 × 0.5 = 0.2, or 20%. Therefore, the probability that at least one university will make an offer is 1 - 0.2 = 0.8, or 80%.

Overall, the probability that the graduate will receive an offer from both universities is 30%, and the probability that she will receive an offer from at least one university is 80%.

Learn more about probability here:

https://brainly.com/question/13604758

#SPJ11

There are approximately over 60 million shipping containers in the world. Containers are stacked and arranged in these ports, creating an impressive sight and highlighting the scale of global trade.

Shipping containers are standardized metal boxes used for transporting goods by sea, rail, or road. They come in various sizes, including 20-foot and 40-foot lengths. These containers have revolutionized global trade, allowing for efficient and secure transportation of goods across long distances. While exact numbers are challenging to determine due to factors such as container movement and usage, estimates suggest that there are over 60 million shipping containers worldwide. This vast quantity of containers enables the global economy to function smoothly by facilitating the movement of goods between countries and continents.

The extensive use of shipping containers has led to the establishment of container ports and specialized container ships that can accommodate large numbers of containers.Moreover, repurposing shipping containers for alternative uses, such as modular homes or pop-up shops, has gained popularity in recent years, demonstrating the versatility and durability of these units.

learn more about global trade  here

brainly.com/question/29885031

#SPJ11

The mathematical program will help the user to provide the data on the Excel sheet and solve accordingly.

The mathematical program to minimize the total cost of constructing the wastewater treatment plants can be expressed as follows:

Minimize z = 50x1 + 100x2 + 100x3 + 50x4 + 50x5 + 100x6 + 100x7

Subject to:

x1 + x2 + x3 + x4 + x5 + x6 + x7 <= 4 (1)

x1 + x2 + x3 + x4 + x5 + x6 + x7 >= 1 (2)

x1 + x4 <= 1 (3)

x2 + x4 <= 1 (4)

x3 + x4 <= 1 (5)

x4 + x5 <= 1 (6)

x4 + x6 <= 1 (7)

x4 + x7 <= 1 (8)

x1, x2, x3, x4, x5, x6, x7 are binary variables (i.e. they can only take on the values 0 or 1)

The objective function (1) minimizes the total cost of constructing the wastewater treatment plants, where the cost of constructing a plant in each city is given in the table. The constraints (2)-(8) ensure that at most four wastewater treatment plants are constructed and that each city is served by at most one wastewater treatment plant.

To solve this problem with Excel, we can create a spreadsheet with columns for the names of the cities, the corresponding costs of constructing a wastewater treatment plant, and the binary variables x1, x2, x3, x4, x5, x6, x7. We can then use Excel's solver tool to minimize the objective function subject to the constraints. The solver tool can be found under the Data tab in the Analyze group.

Learn more about Mathematical program at:

brainly.com/question/24361247

#SPJ4

A left-recursive grammar rule is one where the non-terminal symbol appears on the left side of the production rule. In contrast, a right-recursive grammar rule is one where the non-terminal symbol appears on the right side of the production rule.

In a grammar, a production rule consists of a non-terminal symbol (the left-hand side) and a sequence of terminal and/or non-terminal symbols (the right-hand side). The order in which these symbols appear determines whether the rule is left-recursive or right-recursive.

A left-recursive grammar rule is of the form A -> Aα, where A is a non-terminal symbol and α is a sequence of terminal and/or non-terminal symbols. This rule allows the non-terminal A to derive itself or to derive a string that eventually leads to A. Left-recursion can cause infinite loops during parsing or evaluation.

On the other hand, a right-recursive grammar rule is of the form A -> αA, where A is a non-terminal symbol and α is a sequence of terminal and/or non-terminal symbols. In this case, the non-terminal A appears at the end of the rule, allowing the derivation to proceed from left to right.

The distinction between left-recursive and right-recursive grammar rules is important in parsing algorithms and language processing. Most top-down parsing techniques, like recursive descent parsing, can handle right-recursive rules efficiently, while left-recursive rules can cause problems.

To know more about production rule refer here:

https://brainly.com/question/30340084

#SPJ11

The equation describing the intersection of the sphere with the plane z = 9 is (x+8)^2 + (y-4)^2 = 15.

To find the equation of the sphere centered at (-8,4,8) with radius 4 and the intersection with the plane z = 9.

Step 1: Find the equation of the sphere. The general equation of a sphere is (x-a)^2 + (y-b)^2 + (z-c)^2 = r^2, where (a, b, c) is the center of the sphere and r is the radius. In this case, the center is (-8, 4, 8) and the radius is 4. So, we have:

(x+8)^2 + (y-4)^2 + (z-8)^2 = 16

Step 2: Find the intersection of the sphere with the plane z = 9. Since the plane is given by z = 9, we can substitute 9 for z in the equation of the sphere:

(x+8)^2 + (y-4)^2 + (9-8)^2 = 16

This simplifies to:

(x+8)^2 + (y-4)^2 + 1 = 16

Now, move the constant term to the other side of the equation:

(x+8)^2 + (y-4)^2 = 15

So, the equation describing the intersection of the sphere with the plane z = 9 is (x+8)^2 + (y-4)^2 = 15.

Learn more about General solution at:

https://brainly.com/question/28518741

#SPJ11

(a) As this limit is finite and positive, the series is said to converge.

(b) As this limit is finite and positive, the series is said to converge.

(c) The numerator tends to infinity faster than the denominator, so we can say that the series diverges.

(d) As this limit is finite and positive, the series is said to converge.

(a) Use the limit comparison test to determine whether the following series converge or diverge:

$$\sum_{n=3}^\infty \frac{5n}{7+n^2}$$We have that:$$\lim_{n \to \infty} \frac{\frac{5n}{7+n^2}}{\frac{1}{n}} = \lim_{n \to \infty} \frac{5n^2}{7+n^2} = 5$$

As this limit is finite and positive, the series is said to converge.

(b) Use the limit comparison test to determine whether the following series converge or diverge:

$$\sum_{n=1}^\infty \frac{\ln^2 n}{n^2}$$We have that:$$\lim_{n \to \infty} \frac{\frac{\ln^2 n}{n^2}}{\frac{1}{n}} = \lim_{n \to \infty} \frac{\ln^2 n}{n} = 0$$

As this limit is finite and positive, the series is said to converge.

(c) Use the limit comparison test to determine whether the following series converge or diverge:

$$\sum_{n=1}^\infty \frac{2^n}{4^{n-n^2}}$$We have that:$$\lim_{n \to \infty} \frac{\frac{2^n}{4^{n-n^2}}}{\frac{1}{n}} = \lim_{n \to \infty} \frac{n2^n}{4^{n-n^2}}$$

The numerator tends to infinity faster than the denominator, so we can say that the series diverges.

(d) Use the limit comparison test to determine whether the following series converge or diverge:

$$\sum_{n=1}^\infty \frac{\sin(1/n)}{n}$$We have that:$$\lim_{n \to \infty} \frac{\frac{\sin(1/n)}{n}}{\frac{1}{n}} = \lim_{n \to \infty} \sin\left(\frac{1}{n}\right) = 0$$

As this limit is finite and positive, the series is said to converge.

Visit here to learn more about limit comparison test brainly.com/question/30401939

#SPJ11

The estimated monthly average daily radiation on a horizontal surface in June in Amman is approximately 7.35 kWh/m(^2)/day.

To estimate the monthly average daily radiation on a horizontal surface H in June in Amman, we can use the following equation:

\([H = S \times H_s \times \frac{\sin(\phi)\sin(\delta)+\cos(\phi)\cos(\delta)\cos(H_a)}{\pi}]\)

where:

S is the solar constant, which is approximately equal to 1367 W/m(^2);

\(H(_s)\) is the average number of sunshine hours per day in Amman in June, which is given as 10 hours;

(\(\phi\)) is the latitude of the location, which for Amman is approximately 31.9 degrees North;

(\(\delta\)) is the solar declination angle, which is a function of the day of the year and can be calculated using various methods such as the one given in the answer to Q1;

\(H(_a)\) is the hour angle, which is the difference between the local solar time and solar noon, and can also be calculated using various methods such as the one given in the answer to Q1.

Substituting the given values, we get:

\([H = 1367 \times 10 \times \frac{\sin(31.9)\sin(\delta)+\cos(31.9)\cos(\delta)\cos(H_a)}{\pi}]\)

Since we are only interested in the monthly average daily radiation, we can assume an average value for the solar declination angle and the hour angle over the month of June. For simplicity, we can assume that the solar declination angle (\(\delta\)) is constant at the value it has on June 21, which is approximately 23.5 degrees North. We can also assume that the hour angle \(H(_a)\) varies linearly from -15 degrees at sunrise to +15 degrees at sunset, with an average value of 0 degrees over the day.

Substituting these values, we get:

\([H = 1367 \times 10 \times \frac{\sin(31.9)\sin(23.5)+\cos(31.9)\cos(23.5)\cos(0)}{\pi}]\)

Simplifying the equation, we get:

\([H \approx 7.35 \text{ kWh/m}^2\text{/day}]\)

Therefore, the estimated monthly average daily radiation on a horizontal surface in June in Amman is approximately 7.35 kWh/m(^2)/day.

Learn more about "average daily radiation " : https://brainly.com/question/32911494

#SPJ11

The distance that the seaplane can travel in 1/2 hour is 1,350 kilometers.

Speed is simply referred to as distance traveled per unit time.

Speed is expressed mathematically as;

Speed = Distance ÷ time.

Given the data in the question;

First, we determine the speed of the seaplane.

Speed = Distance ÷ time.

Speed = 1800 ÷ 2/3 hr

Speed = 2700 km/h

Now, distance traveled by the seaplane in 1/2 hour will be;

Speed = Distance ÷ time.

Distance = speed × time

Distance = 2700 km/h × 1/2 h

Distance = 1,350km

Therefore, the distance traveled is 1,350 kilometers.

Option C is the correct answer.

Learn more about speed here: brainly.com/question/7359669

#SPJ1

Answer:

m∠1 = 50°

m∠2 = 130°

Step-by-step explanation:

There is a formula:

\(\text{angle} = \frac{1}{2} (\text{intercepted arc}_1 + \text{intercepted arc}_2)\)

\(\text{m} \angle 1 = \frac{1}{2} (53^\circ + 47^\circ)\)

\(\text{m} \angle 1 = \frac{1}{2} (100^\circ)\)

\(\text{m} \angle 1 = 50^\circ\)

Angle 1 and angle 2 together form a straight angle, which measures 180°. Angle 1 and angle 2 are suplementary angles.

\(\text{m} \angle 1 + \text{m} \angle 2 = 180^\circ\)

\(50^\circ + \text{m} \angle 2 = 180^\circ\)

\(\text{m} \angle 2 = 180^\circ - 50^\circ\)

\(\text{m} \angle 2 = 130^\circ\)

Answer:

84 in

Step-by-step explanation:

my head

Answer:

288 in²

Step-by-step explanation:

The formula used to solve this question is :

Lateral Surface Area = s( P1 + P2)

Where s = slant height = 2 inches

P1 and P2 = Perimeter of the bases

Perimeter of base 1 = 4 × length of the end of the small square

4 × 17 inches = 68 inches

Perimeter of base 2 = 4 × length of the end of the large square

4 × 19 inches = 76 inches

Lateral Surface Area = 2 × (68 + 76)

= 2 × 144

= 288 in²

Answer:

c. (1,-1)

Step-by-step explanation:

5x + 2y = 3  4x – 8y = 12  Solve for (x, y)

4x-8y=12

+8y          +8y

4x=12+8y

Divide both sides by 4

4x/4=(12+8y)/4

x=3+2y

Then take x equation and input into 5x + 2y = 3

5(3+2y)+2y=3

15+10y+2y=3

Add 10y and 2y

15+12y=3

Subtract 15 on both sides

15-15+12y=3-15

12y=-12

Divide 12 both sides

12y÷12=-12÷12

Y = -1

Insert the Y equation into 4x – 8y = 12  

4x-8(-1)=12

4x+8=12

Subtract 8 on both sides

4x-8-8=12-8

4x=4

Divide 4 both sides

4x÷4=4÷4

X = 1

Answer: C. (1, -1)

Answer: 57 R3

‎‎‎‎‎‎‎‎‎‎‎‎‎ ‎‎ ‎

Answer:

57 R 3

Step-by-step explanation:

6 goes into 34 5 times with 4 extra, pull down the 5, and 6 goes into 45 7 times with 3 extra. So the answer is 57 R 3.