The problem: take two solutions and plug them into the original equation. To check for extraneous solutions.

The probability that he lost less than 19 pounds is 7 / 9.

According to statement

The weight loss by individual is 12 Pounds

So, by uniform distribution probability

P(c ≤ x ≤ d) = (d - c) / (b - a)

Substitute the values in it then

P(12 ≤ x ≤ 19) = (19 - 12) / (20 - 11)

P(12 ≤ x ≤ 19) = 7 / 9

So, the probability that he lost less than 19 pounds is 7 / 9.

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Both triangles are congruent by either ASA or AAS Congruence Theorem. hence, the right answer is A: Yes, they are congruent by either ASA or AAS.

The ASA Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent included sides.

The AAS Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent non-included sides.

Triangle LMQ is shown in the figure attached below.

Thus, Proving

Triangle MNL ≅ triangle QNL (ASA)

Triangle MNL and triangle QNL have two pairs of congruent angles:

<LNM ≅ LNQ and <MLN and <QLN

Also, they have a common side: side LN (included side).

Therefore, Triangle MNL and triangle QNL are congruent by ASA.

Triangle MNL ≅ triangle QNL ( by AAS)

Triangle MNL and triangle QNL have two pairs of congruent angles:

<LNM ≅ LNQ and <NML and <NQL

Also, they have a common side: side LN (non-included side).

Thus, Triangle MNL and triangle QNL are congruent by ASA.

Hence, the right answer is: A: Yes, they are congruent by either ASA or AAS.

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Answer: option A

Step-by-step explanation:

The probability that 3 separate flights will all take place is 0.531441

let A = event of scheduled flight actually take place

According to the question, P(A)=0.81

Given that 3 separate flights will all take place is an independent event.

Hence, we can use the multiplicative rule which says If the probability that one given flight takes place is 0.81 then the probability of 3 flights taking place is:

P(A∩B∩C) = P(A)*P(B)*P(C)

= 0.81*0.81*0.81

= 0.531441

so, the Probability that 3 separate flights will take place is 0.531441

The formula used for independent events:

P(A∩B∩C) = P(A)*P(B)*P(C)

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56 sets of pictures she can post on her wall

It is given that alyssa's favorite tennis team has 8 players on them. She has taken a picture with every single athlete individually and wants to post some of the pictures on her wall. But she only wants to post 3 pictures on her wall.

For this we hve to use factorials. In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. The factorial of n also equals the product of n with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product.

So it will be - [tex]\frac{8!}{3!(8-3)!}[/tex] as this is the formula for combination

This will be 56.

Thus, 56 sets of pictures she can post on her wall

The list is known as the sampling frame.

To conduct a survey on current social work majors, a researcher gets a list of all students who have declared a social work major from the registrar from which a sample will be drawn.

This list is known as a sampling frame.

The sampling frame is the list from which units are drawn for the sample.

Hence, the list is known as the sampling frame.

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Answer:

A: y=2x+4

B. 34° Celsius

Step-by-step explanation:

A:

Since the temperature goes up at a steady rate of 2 degres per minute, we can assume that 2 is our slope. Since the graph shows us that 4 is the y-intercept, we can substitute both the slope and y-intercept into the equation of a line, or y=mx+b. (m is our slope and b is our y-intercept.)

Doing so gives you:

[tex]y = 2x + 4[/tex]

B.

Using the above formula (y=2x+4), we can substitute x with 15 (since x is the minutes that pass).

Doing so gives you y=30+4, the sum of which is 34.

Therefore, the answer should be 34° Celsius.

The orthographic projection based on the information given is illustrated below.

It should be noted that orthographic projection is a common method that's used for representing three-dimensional objects where each of the object is viewed along parallel lines that are perpendicular to the plane of the drawing.

In this case, it is a form of parallel projection, where all the projection lines are orthogonal to the projection plane which then results in every plane of the scene appearing in affine transformation on the viewing surface.

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Answer:

Step-by-step explanation:

that is my

Answer:

Muhammad ibn Musa al-Khwarizmi

محمد بن موسی خوارزمی

Step-by-step explanation:

no of people=2

time taken=1/60mins

no of people=10

time taken=1/x

2=1/60

10=1/x

x=12mins

Answer:

2.7930 × [tex]10^{4}[/tex]

Step-by-step explanation:

1.9 × 105 × 140 = 27,930

Scientific notation: 2.7930 × [tex]10^{4}[/tex]

Answer:

Step-by-step explanation:

Solution

I'm assuming you want this simplified. If not leave a note.

a(x + 1) - b(x + 1) - x - 1                     remove the brackets

ax + a - bx - b - x - 1                        gather like terms

ax - bx - x + a - b - 1

x(a - b - 1)  + (a - b - 1)                      Use the distributive property to simplify

Answer

(x + 1)(a - b - 1)

The common factor is (a - b - 1). That can be pulled out on either side of the isolated + sign

Based on the game rules of randomly picking a card and multiplying it by the roll from a number cube, the following are true:

There are 6 sides to dice and 4 cards. The sample space is:

Dice             Card            Product        

1                 5                         5

1                 6                         6

1                 7                         7

1                 8                         8

2                 5                         10

2                 6                         12

2                 7                         14

2                 8                         16  

3                 5                         15

3                 6                         18

3                 7                         21

3                 8                         24

4                 5                         20

4                 6                         24

4                 7                         28

4                 8                         32

5                 5                         25

5                 6                         30

5                  7                         35

5                  8                         40

6                 5                         30                        

6                 6                         36

6                 7                         42

6                 8                         48

Frequency table

Product                     Frequency

5                                      1

6                                      1

7                                      1

8                                      1

10                                      1

12                                      1

14                                      1

16                                      1

15                                      1

18                                      1

21                                      1

24                                      2

20                                      1

28                                      1

30                                      2

32                                      1

25                                      1

35                                      1

40                                      1

36                                      1

42                                      1

48                                      1

Total                                24

The frequency table shows that to get 28 or more, a person will have a relative frequency of:

= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1

= 9

Probability is:

= 9 / 24

= 3/8

= 37.5%

The number of products required to win 25% of the time is:

= 25% x 24

= 6

To find the winning number, count down from the highest product 6 times to get 32.

The probability of getting 36 or higher is:

= ∑(Probabability of picking 36 and above numbers)

= 1 / 24 + 1/24 + 1/24 + 1/24

= 1 / 6

The probability of repeating this 4 times is:

= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6

= 1 / 1,296

= 0.0007716

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The correct option is D:

the curves do not intersect, so there is no solution

The area of the rectangle is given by:

f(x) = (x + 7)*(5x - 3)

f(x) = 5x² -3x + 35x - 21

f(x) = 5x² + 32x - 21

For the circle, the area is:

g(x) = 2*pi*(x + 6)^2

g(x) = 2pi*x^2  + 12pi*x + 72pi

The solution is given g(x) = f(x).

By graphing both functions (the green curve is the area of the rectangle, the orange one is the area of the circle). The two curves never do intercept, so the correct option is D.

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Answer:

x > -3     and     x ≤ 1

Step-by-step explanation:

   [First inequality]

Given:

 -2x + 8 < 14

Subtract 8 from both sides:

 -2x < -6

Divide both sides by -2, since it's negative we also flip the sign:

 x > 3

   [Second inequality]

Given:

 -3x - 9 ≥ -12

Add 9 to both sides:

 -3x ≥ -3

 Divide both sides by -3, since it's a negative we also flip the sign:

 x ≤ 1

Answer:

(2,3),(4,3),(-2,-3),(-4,-3)

Step-by-step explanation:

A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).

This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.

The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x = 2, then y = 3, and if x = -2, then x = -3.

A set of ordered pairs is not a function if there are ordered pairs with the same x-values but different y-values.

In the other sets of ordered pairs, one x-value has more than one possible y-value. Let's use the last set as an example:

(5,1),(5,2),(5,3),(5,4)

Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.

Answer:

Step-by-step explanation:

I had this exact question and I figured it out.

the answer is: P(police officer and chooses car)

In order to get this answer I did the P(police officer) X P(choosing car)

It ended up being 36/45 X 15/45. Which is equal to around .2666667.

Now you take the Intersection of police officer and chooses car and you divide it by 45. That value on the chart is 12.

lucky enough, the product of 36/45 and 15/45 is equal to 12/45.

So 0.8 X 0.33 = .26

.26 = .26

Answer:

answer is P(police officer and chooses car)

Step-by-step explanation:

the probability of P(policer officer) and P(choose a car) are independent probabilities ( they are not overlapping probabilities)

Answer:

8.49 units

Step-by-step explanation:

1. The distance formula is: [tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]

2. Let's plug in the numbers: [tex]\sqrt{(-1-5)^{2} +(4--2)^{2} }[/tex]

3. [tex]\sqrt{(-6)^{2} +(6)^{2} }[/tex]

4. [tex]\sqrt{36 + 36}[/tex]

5. [tex]\sqrt{72}[/tex] ≈ 8.485

Answer:

32468.41 yards

Step-by-step explanation:

11,405.59 + 12,048.82 + 9,014 = 32468.41

32468.41 yards

René Descartes provided the first systematic link between Euclidean geometry and algebra.

This branch of mathematics involves the study of object shape, their spatial relationship and that of their surrounding space.

René Descartes is referred to as the father of analytic geometry due to him establishing the relationship between Euclidean geometry and algebra.

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The parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3

This is a way of changing the position of an object on an xy-plane.

Given the parent function expressed as  y = (x + 2^)2

From the resulting image after translation, we can see that the parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3

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Answer: 6

Step-by-step explanation:

The slope of ST is

[tex]\frac{-5-0}{0-(-6)}=-\frac{5}{6}[/tex]

The slope of UV is

[tex]\frac{y-1}{-9-(-3)}=\frac{y-1}{-6}[/tex]
Since parallel segments have the same slope,

[tex]-\frac{5}{6}=-\frac{y-1}{6}\\\\5=y-1\\\\y=6[/tex]

Answer:

[tex]\frac{\sqrt{7} }{4}[/tex]

Step-by-step explanation:

since sin theta = 3/4, opposite length = 3 units and hypotenuse length = 4 units

by pythagoras' theorem, adjacent length = [tex]\sqrt{7}[/tex]

thus cos theta = adjacent/hypotenuse = [tex]\frac{\sqrt{7} }{4}[/tex]

Option b) [tex]x^{2} -x-\sqrt{x} +3[/tex] is not a polynomial

Polynomial equation is equation of dependent variables which is related to the independent variable.

since, the equation ,[tex]x^{2} -x-\sqrt{x} +3[/tex] contains the square root of variable that's why its not a polynomial.

Thus, Option b) [tex]x^{2} -x-\sqrt{x} +3[/tex] is not a polynomial

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Answer:

8. a , c

9. b

10. c

The largest possible volume of the box is 6158.394 cm^3.

Define the dimensions of the box to be L, W, and H.

Square base, L = W

Area: A = L^2 * H

Surface Area (Base + Area of 4 sides):

1600 = L^2 + 4 (L*H) ⇒ H = (1600 - L^2) / (4L)

Area: A = 400L - (1/4)L^3

Maximum (Derivative) A' = 400 - (3/4)L^2

Solving for 0

0 = 400 - (3/4)L^2

L^2 ⇒ (40 * SQRT(3)) / 3 = 23.094 (Maximum)

Solving for dimensions, known L=23.094

L = 23.094 cm

W = 23.094 cm

H ⇒ (1600 - L^2) / (4L) = (20 * SQRT(3) / 3) = 11.547 cm

Volume ⇒ L*W*H = 6158.394 cm^3

To locate the most viable extent, add the greatest viable mistakes to every dimension, then multiply. To find the minimum viable volume, subtract the greatest feasible mistakes from each measurement, then multiply.

Volume is a scalar amount expressing the amount of 3-dimensional area enclosed by a closed surface. For example, the gap that a substance or 3-D shape occupies or consists of.

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Answer:2.5 kg per  meter

Step-by-step explanation:since the rod is uniform i simply divided the weight of the rod(20kg), by the length of the rod(8m). 20kg/8m = 2.5kg/m

Answer:

2c+2b

Step-by-step explanation:

this is because standard form only applies to no. from 10 and above , furthermore, they are unlike terms

The required expression is given by 179.2 - 10.6d.

There were 179.2 gallons of water in the barrel and 10.6 gallons are used each day

Volume, is defined as the ratio of the mass of object to its density.

the volume of water in a rain barrel after "d"days
When there were 179.2 gallons of water in the barrel and 10.6 gallons are used each day.

since the amount of water is getting consumed day by day
therefore, the expression can be given as
  =  179.2 - 10.6d

Thus, the required expression is 179.2 - 10.6d.

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