A bag of marbles has 5 blue marbles, 3 red marbles, and 6 yellow marbles. A marble is drawn from the bag at random . How many possible possible outcomes are there?

° 3
° 5
° 6
° 14
HELP ME ASAP PLZ
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Joey's actual speed is 143.59 mph, and his actual direction is slightly west of northwest.

Given that Joey's aircraft speed: 188 mph

Wind speed: 60 mph

Wind direction: 150 degrees (measured clockwise from due north)

We can consider the wind as a vector, which has both magnitude (speed) and direction.

The wind vector can be represented as follows:

Wind vector = 60 mph at 150 degrees

We convert the wind direction from degrees to a compass bearing.

Since 150 degrees is measured clockwise from due north, the compass bearing is 360 degrees - 150 degrees = 210 degrees.

Joey's aircraft speed vector = 188 mph at 0 degrees (due northwest)

Wind vector = 60 mph at 210 degrees

To find the resulting velocity vector, we add these two vectors together. This can be done using vector addition.

Converting the wind vector into its x and y components:

Wind vector (x component) = 60 mph × cos(210 degrees)

= -48.98 mph (negative because it opposes the aircraft's motion)

Wind vector (y component) = 60 mph×sin(210 degrees)

= -31.18 mph (negative because it opposes the aircraft's motion)

Now, we can add the x and y components of the two vectors to find the resulting velocity vector:

Resulting velocity (x component) = 188 mph + (-48.98 mph) = 139.02 mph

Resulting velocity (y component) = 0 mph + (-31.18 mph) = -31.18 mph

Magnitude (speed) = √((139.02 mph)² + (-31.18 mph)²)

= 143.59 mph

Direction = arctan((-31.18 mph) / 139.02 mph)

= -12.80 degrees

The magnitude of the resulting velocity vector represents Joey's actual speed, which is approximately 143.59 mph.

The direction is given as -12.80 degrees, which indicates the deviation from the original northwest direction.

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The ratio of the floor width to the side wall height that minimizes the total material cost of the tunnel is  (3/2)^(1/3) / (2π)^(2/3), by using lagrange multipliers.

Let the width of the floor be w and the height of the side walls be h. The volume constraint of the tunnel is V = al, where V is the volume of the tunnel. The total cost C of the tunnel is given by:

C = 2whP + 2lhP + πr^2LQ

where P is the price per unit area of the floor, L is the length of the tunnel, Q is the price per unit area of the ceiling, r is the radius of the cylindrical ceiling, and hP is the price per unit area of the side walls.

The Lagrangian is:

L = 2whP + 2lhP + πr^2LQ + λ(al - V)

Taking partial derivatives with respect to w, h, r, and λ, and setting them equal to zero, we get:

2hP + λa = 0

2wP + λa = 0

2πrLQ = λa

al - V = 0

Solving for w/h, we get:

w/h = (2πrLQ - 2hP) / (2hP - 2λa)

Substituting the values for P, Q, a, and L, and simplifying, we get:

w/h = (3/2)^(1/3) / (2π)^(2/3)

Therefore, the ratio of the floor width to the side wall height that will minimize the total material cost of the entire tunnel is (3/2)^(1/3) / (2π)^(2/3).

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Answer:

A

Step-by-step explanation:

ita a bc i know its I did this before

Answer:

speed

Step-by-step explanation:

it's literally stated in the question

Answer:

-2

Step-by-step explanation:

I got it wrong and it told me negative 2 was the correct answer lol

Answer:

6666

Step-by-step explanation:

i removed my answer because it was wrong look at the other peoples answers

Answer: 213/40 or 5.325

Step-by-step explanation:

We can find common denominators for 8 1/5 and 2 7/8.

The Lowest Common Denominator for 8 1/5 and 2 7/8 is 40.

8 1/5 = 41/5 = 328/40.

2 7/8 = 23/8 = 115/40.

Now we can subtract.

328/40 - 115/40 = 213/40.

Therefore, the answer is 213/40 or 5 13/40.

Hyperbolic tan x is verified to equal to  

To verify the identity using the definitions of the hyperbolic functions, we start with the definition of hyperbolic tangent:

tanh x = sinh x / coxh x =  (e^x - e^-x) / (e^x + e^-x)

We can simplify this expression by multiplying the numerator and denominator by e^x:

tanh x = (e^x - e^-x) / (e^x + e^-x) * (e^x / e^x)

tanh x = (e^2x - 1) / (e^2x + 1)

We can see that this expression is equivalent to the given identity

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Answer:

Step-by-step explanation:

k+43=118

k=118-43

k=75

Answer:

Your answer is: k= 75

Step-by-step explanation:

Hope this helped : )

Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)

\(\implies B=88^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)

\(\implies a=13.0876493...\)

\(\implies a=13.1\)

Solve for b:

\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)

\(\implies b=26.9194211...\)

\(\implies b=26.9\)

\(\hrulefill\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies C=180^{\circ}-A-B\)

\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)

\(\implies C=73^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)

\(\implies a=20.8847511...\)

\(\implies a=20.9\)

Solve for b:

\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)

\(\implies b=12.5954671...\)

\(\implies b=12.6\)

Answer: See explanation

Step-by-step explanation:

You didn't specify the equations but let me solve the question.

55% of 80.

The above statement simply means that you need to multiply 55% by 80. This will be:

= 55% of 80

= 55/100 × 80

= 0.55 × 80

= 44

Therefore, 55% of 80 is 44

Based on your question, any other equation that doesn't give 44 as an answer cannot be used to answer the question.

Answer:

7). y = 140

8). x = 9

Step-by-step explanation:

Question (7).

All-right pencil factory will produce the graphite pencils, table formed will represent a linear graph.

Three points on the graph are (12, 42) and (18, 63), (40, y)

Slope of the line passing through these points = \(\frac{y_2-y_1}{x_2-x_1}\)

m = \(\frac{63-42}{18-12}\) = \(\frac{y-42}{40-12}\)

\(\frac{21}{6}\) = \(\frac{y-42}{40-12}\)

3.5 = \(\frac{y-42}{40-12}\)

98 = y - 42

y = 140

Question (8),

If a bicyclist rides at a constant rate, table formed will represent a linear graph.

Slope of a line passing through three points (2, 25), (5, 62.5) and (x, 112.5) given in the table,

m = \(\frac{y_2-y_1}{x_2-x_1}\)

\(\frac{62.5-25}{5-2}=\frac{112.5-62.5}{x-5}\)

\(\frac{37.5}{3}=\frac{50}{x-5}\)

37.5x - 187.5 = 150

37.5x = 337.5

x = 9

Answer:

63°

Step-by-step explanation:

The probability of selecting a student who prefers green is:

5/28

What is frequency?

Frequency refers to the number of times a particular event or value occurs in a given dataset or sample. It is commonly used in statistics and probability to analyze and describe data. In the context of a survey or study, frequency can be used to represent how many times a particular response or answer was given by participants.

According to the question:
The total number of students is:

6 + 9 + 3 + 5 + 5 = 28

The probability of selecting a student who prefers green is:

5/28

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The ratio of a to d can be expressed by multiplying the ratio of a to b, b to c, and c to d. Therefore, a to d = (a to b) x (b to c) x (c to d).

The ratio of a to d can be determined by using the given ratio of a to b, b to c, and c to d. To begin, the ratio of a to b can be expressed as a:b, the ratio of b to c can be expressed as b:c, and the ratio of c to d can be expressed as c:d. Then, the ratio of a to d can be determined by multiplying the ratios of a to b, b to c, and c to d. This can be written as (a:b) x (b:c) x (c:d). Therefore, the ratio of a to d can be expressed as (a:b) x (b:c) x (c:d). For example, if the ratio of a to b is 2:3, the ratio of b to c is 4:5, and the ratio of c to d is 6:7, then the ratio of a to d would be (2:3) x (4:5) x (6:7) or 24:35.

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The probabilities for each case in this problem are given as follows:

a) A and B disjoint -> P(B and not A) = 1/2.

b) A is contained in B -> P(B and not A) = 1/6.

c) P(A and B) = 1/8 ->  P(B and not A) = 3/8.

The probability that we want to obtain in this problem is given as follows:

P(B ∩ Ac).

Which is the probability of B and the complement of A, that is:

P(B and not A).

If A and B are disjoint, it means that their intersection is of 0, hence:

P(B and not A) = P(B) = 1/2.

If A is contained in B, all elements of A are contained in B, hence the proportion of elements that are in B but not A is given as follows:

P(B and not A) = 1/2 - 1/3 = 1/6.

If the probability of the intersection is of 1/8, the proportion of elements that are in B but not A is given as follows:

P(B and not A) = 1/2 - 1/8 = 4/8 - 1/8 = 3/8.

(as 1/8 of them belong to both B and A, hence they do not belong to the complement of A).

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Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

Answer:

OOk

Step-by-step explanation:

The first cellphone service provider to be established in South Africa was Vodacom. Vodacom was launched on April 1, 1994, and it became the country's first cellular network operator.

The company was a joint venture between Telkom, the national telecommunications company of South Africa, and Vodafone, a global telecommunications giant.

Vodacom introduced the GSM network to South Africa, providing mobile voice and data services to customers across the country. Its launch marked a significant milestone in the telecommunications industry in South Africa, as it brought mobile communication to the masses and revolutionized the way people connect and communicate.

Since its inception, Vodacom has played a pivotal role in the development of the telecommunications sector in South Africa. It has continually expanded its network coverage, introduced innovative services, and played an active role in bridging the digital divide in the country.

Today, Vodacom remains one of the leading mobile network operators in South Africa, providing a wide range of mobile services to millions of customers.

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The probable question may be:

Which cellphone service provider was the first to be established in south africa

Hi!

\(y=-5x+95\)

Plug in \(15\) for \(x\)

\(y=-5(15)+95\)

Multiply \(-5\) and \(15\)

\(y=-75+95\)

Add \(-75\) and \(95\)

\(y =15\)

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Betty's percentage is 15%.

The rate of change is the amount it changes for every missing assignment, therefore it would be -5.

Answer:

11

Step-by-step explanation:

√3x+16=7

3x+16=7^2

3x+16=49

3x=49-16

3x=33

X=33/3

X=11

So the answer is 11

Answer:

B:  -0.81

Step-by-step explanation:

Choose the r-value with the largest magnitude.

In this case that r-value is B:  -0.81

This signifies a relatively large negative correlation.

The mark of 38 corresponds to a z score of 3.85.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (x - μ)/σ

Where x is raw score, μ is mean and σ is standard deviation.

Given that μ = 23, σ = 3.9, hence for a score x = 38:

z = (38 - 23) / 3.9 = 3.85

The mark of 38 corresponds to a z score of 3.85.

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The length of e is 29.53 inches.

In the following, the law of sine is presented in detail: In a triangle, the sine of angle A divided by side "a" equals the sine of angle B divided by side "b" equals the sine of angle C divided by side "c".

Given:

f= 33 inches

<F= 140, <D = 5

Now,

<E= 180 - (<F+ <D) = 180 - (140 + 5) = 35

Using Sine law

sin F / f = sin E/ e

sin 140 / 33 = sin 35 / e

0.642/ 33 = 0.573 / e

0.0194 e= 0.573

e= 29.53 inches

Hence, the length of e is 29.53 inches.

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Given the expression of the area is: 24x + 16y

We need to find the area when x = 4 and y = 6

so, substitute with x and y into the given expression as follows:

So, the answer will be 192

Answer:

1400

Step-by-step explanation:

Answer:

1371 or 1401

Step-by-step explanation:

multiply 3 times 457 the round

This question is incomplete, the microstates table is left out which will be uploaded along this answer;

Answer:

a) the required is 65.6%

b) the required time is 4.2666 hrs

Step-by-step explanation:

using the microstates from the table in the diagram;

a)

the percent times the above any of the above microstates occurs is;

% (6 heads and 4 tails, 5 heads and 5 tails, 4 heads and 6 tails)

=   ((210 + 252 + 210)/1024) × 100

= 0.6562 × 100

= 65.6%

Therefore the required is 65.6%

b)

the probability of getting 10 heads and 0 tail or 0 tail head and 10 tails is;

p( 10H, 0T or 0H, 10T = 2/1024

= 1/512

so on average, it will take 512 trails or at a rate of 2 trials/min, 256 mim in hours;

(256 min) ( 1h/60min) = 4.2666 hrs

Therefore the required time is 4.2666 hrs

Solving the quadratic equation, we have:

So the solution for this quadratic equation is x = 0 or x = 4.

Answer: Yes

Step-by-step explanation:

x=2 is a vertical line with an undefined slope, and y=5 is a horizontal line with a slope of 0. Since these lines have slopes that are negative reciprocals, they are perpendicular.