If m∠QRS = 37° and m∠TQS = 34°, what is m∠TQR?
A. 93°
B. 90°
C. 109°
D. 87°

(A) If Two independent events, A and B, are such that P(A) = 0. 2 P(A U B) = 0. 8, then probability P(B) =  5/8.

The possibility of the result of any random event is referred to as probability. This term refers to determining how likely an event is to occur. What are the chances of getting a head when we toss a coin in the air, for instance? The quantity of outcomes depends on the response to this question. Here, the outcome could be either head or tail. Thus, there is a 50% chance that the result will be a head.

The probability serves as a gauge for the likelihood that an event will occur. It gauges how likely an event is to occur. The probability equation is given by;

P(E) = Number of Favourable Outcomes/Number of total outcomes

We know that

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = P(A) + P(B) - P(A).P(B)

0.8 = 0.2 + P(B) - 0.2.P(B)

0.5 = P(B)  - 0.2.P(B)

0.5 = 0.8.P(B)

P(B) = 0.5/0.8

P(B) = 5/8

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An inequality for this situation "A cruise ship can carry at most 3500 passengers." is x ≤ 3,500.

A graph of the inequality x ≤ 3,500 is shown in the image attached below.

What is an inequality?

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Note: At most simply refers to less than or equal to (≤) in Mathematics.

Since the cruise ship can only carry at most 3500 passengers, an inequality that models this situation is given by;

x ≤ 3,500

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Answer:

\( \sf \: 12m - 3n + 8 \)

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 17m - (5m + 3n - 6) + 2

Let's simplify the expression,

→ 17m - (5m + 3n - 6) + 2

→ 17m - 5m - 3n + 6 + 2

→ (17m - 5m) - (3n) + (6 + 2)

→ (12m) - 3n + (8)

→ 12m - 3n + 8

The answer is 12m - 3n + 8.

The surface area of the regular walls and the roof obtained by finding the  sum of the individual surface area is about 2744.28 square inches

The surface area of a plane is the two dimensional space the plane occupies.

The surface area of the walls and the interior ceiling can be calculated using the formula for finding the area of the rectangular and triangular shapes in the figure as follows;

Area of the rectangular surface = 10 × (24 + 16) + 2 × 28 × 10 + 10 × 16 + 2 × 10 × 18 + 10 × 24 = 1720

Let a and b represent the leg lengths of the wall on the roof, we get;

a·b/2 = (40/2) × 16 = 320

b = 640/a

a² + b² = 40²

Therefore;

a² + (640/a)² = 40²

a = 8·√5

b = 640/(8·√5) = 80·√5/5 = 16·√5

Surface area of the larger roof = 2 × 320 + 28 × 16·√5 + 28 × 8·√5 = 640 + 672·√2 ≈ 1590.35

Let c and d represent the leg lengths of the wall on the smaller roof, we get;

c·d/2 = 120

d = 240/c

c² + d² = 24²

c² + (240/c)² = 24²

c = 4·√3·√(6 + √(11)) and c = 4·√3·√(6 - √(11))

The surface area of smaller roof = 2 × 120 + 18 × (4·√3·√(6 + √(11))) + 18 × (4·√3·√(6 - √(11)) ) ≈ 864.93

The surface area of the figure is therefore; 1720 + 159.35 + 864.93 = 2744.28 square units

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i have attached the solution...

hopefully this will help u

Answer:

3

Step-by-step explanation:

Answer:

5 goals

Step-by-step explanation:

4 goals per game for 15 games means a total of 60 goals in that season. You have 4 goals per game for 14 games meaning you have a total of 56 goals. To overtake the leading team you must score a minimum of 5 goals to become the leading scorer. (Double-check to make sure I am correct)

What is Symmetry ?

In common parlance, the term "symmetry" describes a sense of lovely proportion and balance. A more exact meaning of "symmetry" can be found in mathematics, where it typically refers to an object that is unaffected by certain transformations like translation, reflection, rotation, or scaling.

A definition of symmetry in mathematics states that whether one shape is moved, rotated, or flipped, it exactly resembles the other shape. Just fold the paper, draw one-half of the heart at the fold, then cut it out to discover that the other half exactly matches the first half when you are instructed to cut out a "heart" from a piece of paper. The heart-shaped carving is an illustration of symmetry. Symmetry is defined in mathematics as "a mirror image." Symmetry is the property of an image that remains unchanged after a shape has been rotated or flipped. There are patterns in it. You may have heard the word "symmetry" quite a bit in modern times.

(A)

Any two indices will do i!=j Paul's time and the time of the ith runner are equally distributed and independent, hence according to the Symmetry, p (Ai) = p(Aj)= 1/2. Consider the intersection of Ai and Aj. Thus, Paul is outpaced by both runners I and j. There are 6 possible permutations of their times because they are i.id, with Paul being the slowest. P(Ai intersection Aj) hence equals 1/3.

But now wе have that P(Ai intersection Aj)= 1/3 != 1/4 = P(Ai)P(Aj)

thus, events They are not autonomous, Ai and Aj. However, they are only somewhat independent given Paul's timing. Paul can be removed from the narrative if such is the case. Then, only these two runners are left. Events As a result of their independent and equal distribution of times, Aj and AI are independent.

(B)

Define Ij as the random variable indication that indicates whether or not the jth runner is superior to Paul. via means of symmetry. We know p(Ij = 1)=1/2.

We determine that 

E(N) = E(I1+I2 +.......In) 

= nE(i1) 

=nP(I1-1) 

=n/2

using the linearity of expectation.

(C)

Paul's estimated time of completion is t The probability that each runner will finish ahead of Paul is P (time of rumer I t) = F. (t)

By using part (a), we can determine that other runners' times are independent of Paull's time, and that the number of runners who finish faster than Paul has a binomial distribution with the parameters n and F. To come to the conclusion that N/T= t Binom (n, F(t)) and if we choose T at random, N/T Binom (n, F(T)),

(D)

Let's figure out Var (N)

Var (N)=F(Var (N/T)) + Var(E(N/T))

= E(n F(T) (1- F(T)) + Var(on F(T))

according to Eve's Law.

Here, we can use the uniform distribution's universality to produce

F(T) ~Unif (0, 1) = U

Hence symmetry, which states that U I-U, leads to

Var(N) = nE(U2) + n2 var (U)

=n/3 + n2/12,

where E(U2)=1/3

Var(U)=1/12.

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Answer:

Step-by-step explanation:

Answer:

The inequality   x÷7<-3

The solution      x<-21

Step-by-step explanation:

Solving-  x÷7<-3

                  x<-3x7

                  x<-21

A plane intersects a cylinder perpendicular to its bases this cross section can be described as a rectangle. Therefore, the correct answer is option 1).

The cross section of a plane intersecting a cylinder perpendicular to its bases is a rectangle. This is because when a plane intersects a cylinder perpendicularly (at right angles) the cross-section area has the shape of a rectangle. The base of the rectangle is determined by the diameter of the cylinder and the height is determined by the length of the cylinder.

A parabola, triangle, and circle are not possible when the plane intersects the cylinder perpendicularly since their shapes cannot accurately represent the intersection of two geometric shapes.

Therefore, the correct answer is option 1).

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Answer:  The correct answer is the first number = 10, the second number = 5

Step-by-step explanation:

x = the first number

y = the second number

What we know:

What we need to determine:

Solve using a system of equations:

The first equation (the first number subtracted from four times the second number equals ten):

4y - x = 10

Solve for x:

x = 4y - 10

The second equation (the first number is twice as large as the second):

x = 2y

Substitute the second equation in the first:

2y = 4y - 10

Solve for y:

y = 5

Substitute for y:

x = 2 (5)

x = 10

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f(x) = 9x² + 7x

g(x) = 2 - x

= 5g(x) - f(x)

= 5(2-x) - (9x² + 7x)

= 10 - 5x - 9x² - 7x

= 10 - 12x - 9x²

= 10 - 12x - 9x²= 9x² - 12x + 10.

D is the correct option.

Answer:

D

Step-by-step explanation:

Circumference = pi × diameter

H satisfies all three subspace properties, it is a subspace of R³.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.

Let H be the set of all vectors of the form 4t, where t is any real number. We want to find a vector v in R³ such that H = Span{v}.

Let v = [4,0,0]. Then any scalar multiple of v will be of the form [4t,0,0], which is an element of H. Thus, H is contained in Span{v}.

Conversely, any vector in Span{v} can be written as a scalar multiple of v, which is of the form [4t,0,0] and therefore an element of H. Thus, Span{v} is contained in H.

Therefore, we have H = Span{v}.

This shows that H is a subspace of R³ because Span{v} is a subspace of R³ (since v is in R³) and H = Span{v}. To show that H is a subspace of R³, we need to verify the three subspace properties:

The zero vector of R³ is in H: The zero vector of R³ is [0,0,0], which is of the form [4t,0,0] when t = 0. Therefore, the zero vector is in H.

H is closed under vector addition: Let u and w be vectors in H. Then u = [4t₁,0,0] and w = [4t₂,0,0] for some t₁, t₂ in R. The sum u + w is [4t₁+4t₂,0,0], which is also an element of H. Therefore, H is closed under vector addition.

H is closed under scalar multiplication: Let u be a vector in H and let c be a scalar in R. Then u = [4t,0,0] for some t in R. The scalar multiple cu is [4ct,0,0], which is also an element of H. Therefore, H is closed under scalar multiplication.

Therefore H satisfies all three subspace properties, it is a subspace of R³.

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The statement that is true is "the study is observational and lacks control of too many lurking variables" and "the study should be replicated with other populations."Here are the reasons why:

The study is observational and lacks control of too many lurking variables:

This statement is true since the study was done with people who used turmeric in the meals they consume. There are a lot of things that could affect the difference in mileage walked by the turmeric users compared to those who do not consume it. For instance, the intensity of exercise, lifestyle, and overall diet could have been contributing factors. Thus, there is no guarantee that turmeric is solely responsible for the difference in miles walked.

The study should be replicated with other populations:

This statement is true since the study was carried out with a small sample size and in one geographic location. This means that there is a possibility that the results were just unique to that region. Replicating the study in a different location would help to establish the generalizability of the results and whether or not they are consistent across populations.

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Step-by-step explanation:

10x² - 5x + 10

x = -3

10(-3)² -5(-3) + 10

= (10×9) + 15 + 10

= 90 + 15 + 10

= 115

Answer:

12⁰ = 1

Step-by-step explanation:

Any number raised to the power of 0 equals 1.

e.g.,

1⁰ = 1

2⁰ = 1

3⁰ = 1

The value of 12⁰ just like every other number raised to a power of 0 is; 1

Law of Indices

By mathematical convention; any number raised to a power zero is equal to 1.

This forms a basis for one. of the laws of indices and hence; all mathematical elements, variables or constants when raised to a power of 0; gives 1.

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Answer:

-8, -6, -4, -1, 3

Step-by-step explanation:

Hope it helps! =D

The possible outcomes are Green Large, Green Small, Orange Large, Orange Small, Yellow Large, and Yellow Small. Therefore, option A is the correct answer.

Given that, You're picking out water balloons. There are 3 colors and 2 sizes.

All possible outcomes are

Color           Size

Green         Large

Green         Small

Orange      Large

Orange      Small

Yellow       Large

Yellow       Small

Therefore, option A is the correct answer.

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Complete question:

You're picking out water balloons. There are 3 colors and 2 sizes

If you randomly pick the color and size, which of these tables lists all possible outcomes? (Each row represents one outcome.)

Choose all answers that apply

Table A:

Color Size

Green Large

Green Small

Orange Large

Orange Small

Yellow Large

Yellow Small

Table B:

Color Size

Green Large

Orange Large

Yellow Large

Green Small

Orange Small

Yellow Small

Answer: A and B

Step-by-step explanation: Took the quiz on khan

Answer:

a) 3.39 cm b) 21.29 cm

Step-by-step explanation:

ok so the area of a circle is \(\pi\)r^2.

if the area is 36 cm^2 we can divide it by 3.14, which is pi (\(\pi\)). that gives us 11.46. now we find the approximate square root of this. \(\sqrt{11.46}\)

this is approximately equal to 3.39. the radius is about 3.39cm.

now that we know the radius, we can easily find the circumference. the formula for this is \(\pi\)d. the diameter is just the radius times 2. (3.39)(2)

we plug the numbers into the formula: 3.14(6.78)=21.29 cm =d

Answer:

about 45%

Step-by-step explanation:

it should be right

Answer:

19

Step-by-step explanation:

-8+8=0

0+19=19

Hope it helps.

Answer:

19

Step-by-step explanation:

I just took the quiz

Answer:

Step-by-step explanation:

m = 5

n = 2

c = 7

Answer:

5

2

7

Step-by-step explanation:

In any group of two or more people, there are always two who have the same number of friends within the group.

Suppose we have a group of n people. Each person can have between 0 and n-1 friends within the group. If someone has 0 friends, then everyone else must have at least 1 friend. Similarly, if someone has n-1 friends, then everyone else must have at most n-2 friends.

Therefore, there are only n-1 possible numbers of friends that a person can have within the group. But we have n people, so by the pigeonhole principle, at least two people must have the same number of friends within the group.

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Hence the equation 3(5x - 4) - 8x = 7x -12 has infinite number of solutions.

An equation is a statement of equality between two expressions consisting of variables, numbers and arithmetic operations.

Step-by-step explanation:

The equation 8x = 8(x - 1)+1 can be simplified as

8x=8x-8+1

0=-7( absurd)

This equation does not have any solution.

The equation 2x-5 = 2(x - 5) can be simplified as

2x-5=2x-10

-5=-10(absurd)

This equation does not have any solution.

The equation 22-6x = 2(3x - 11) can be simplified as

22-6x=6x-22

-6x-6x=-22-22

-12x=-44

x=44/12=11/3

This equation has only one solution.

The equation 3(5x - 4) - 8x = 7x -12 can be simplified as

15x-12-8x=7x-12

7x-12=7x-12

0=0, is an identity

This equation has infinite number of solutions.

Hence the equation 3(5x - 4) - 8x = 7x -12 has infinite number of solutions.

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Using the 3D coordinates of the rectangular box, the diagonal of the box is √38 units.

To find the projections of the point (2,3,5) on the xy-, yz-, and xz-planes, we will project the point onto each plane by setting the third coordinate to zero.

1. Projection on the xy-plane:
Set the z-coordinate to zero: (2,3,0). This is the projection of the point onto the xy-plane.

2. Projection on the yz-plane:
Set the x-coordinate to zero: (0,3,5). This is the projection of the point onto the yz-plane.

3. Projection on the xz-plane:
Set the y-coordinate to zero: (2,0,5). This is the projection of the point onto the xz-plane.

Now, let's draw a rectangular box with the origin (0,0,0) and the point (2,3,5) as opposite vertices. The other vertices of the box are the projections on the coordinate planes and the remaining corners.

Vertices of the box:
A(0,0,0) - Origin
B(2,3,5) - Given point
C(2,3,0) - Projection on xy-plane
D(0,3,5) - Projection on yz-plane
E(2,0,5) - Projection on xz-plane
F(0,3,0) - Corner on y-axis
G(2,0,0) - Corner on x-axis
H(0,0,5) - Corner on z-axis

To find the length of the diagonal of the box (AB), use the distance formula for 3D coordinates:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]

Length of diagonal AB = √[(2 - 0)^2 + (3 - 0)^2 + (5 - 0)^2] = √[2^2 + 3^2 + 5^2] = √[4 + 9 + 25] = √38.

So, the length of the diagonal of the box is √38 units.

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Answer:

file?

Step-by-step explanation:

Answer: 30

Step-by-step explanation:

40 + 8x = 280

-40 -40

8x = 240

___ ____

8 8

X = 30

Answer:

Corresponding angles

Step-by-step explanation:

The name of these angels lying in the same position are called corresponding angle.

These angles are equal. When we talk of parallel lines, they are sets of lines that travel in the same direction but never meet. The third line that cuts through the two sets of parallel lines is referred to as the transversal line.

So the positions of these angles on each of the set of the parallel lines are equal in each of the cases and they are equal and are referred to as being corresponding to each other